Are We Chasing Imaginary Numbers?

Guest Essay by Kip Hansen

 i_gsl

 Spoiler Alert: This essay is not about the mathematical entity the imaginary number. I do think that an essay here about imaginary numbers of that sort would be interesting, but this isn’t going to be it. This essay, while not about the usual fare seen here – AGW; CAGW; Catastrophic Climate Change; Global Cooling; various oxides of carbon; the pH, level, or surface temperature of oceans; or the antics or ethics (or lack of ethics) of various international scientists and politicians — will hopefully be interesting to the majority of readers. It will ask more questions than it answers.

Last Saturday, 3 October 2015, WUWT’s indefatigable Willis Eschenbach published a guest essay regarding an NPR radio report by Ira Flatow that labelled “some recent pictures of flooding in Miami, Florida, as evidence that climate change is real and is already affecting Florida.” In response to a comment I made to that essay, Willis asked this very interesting question:

“…as you say, we can measure sea level with a “high degree of accuracy” … so are we measuring an imaginary thing? And if we average those highly accurate measurements, why would we not get a global average sea level? What am I missing here?”

In science, asking the Right Question is often, maybe always, more important than having the Right Answer. Let’s look at Willis’s questions and see what we can find out about the world and the world of science.

What are the questions here?

  1. Can we measure sea level with “a high degree of accuracy”?
  2. Are we measuring an imaginary thing (when we do so)?
  3. If we average those highly accurate measurements, why would we not get a global average sea level?
  4. What am I [we] missing here?

It is my idea here to ask a more generalized question — what are we measuring in Climate Science and are we measuring an imaginary thing when we do so? — but we can use “sea level” as the thought experiment example.

Let me address the first question first: Is it really possible to measure something like sea level (or surface air temperature 2 meters above the ground or sea surface temperature) with “a high degree of accuracy”?

When I stated in my original comment that we had been measuring sea level with a high degree of accuracy for years, I meant that we knew what sea level could be expected at various places at future times and had an idea what a more generalized “global sea level” might be and what changes had been seen over longer time periods like the last century or so. But for our thought experiment in this essay, let’s define “high degree of accuracy” as the commonly mentioned “annual anomaly” in the scientific literature. For “global average sea level” this is in single digit millimeters, usually 1.7/1.8 up to 3.4 mm per year, somewhere in that range. (For those thinking along on other paths, that might be tenths and hundredths of a degree Centigrade for global average surface air temperature and sea surface temperature, and even smaller, thousandths of a degree C for ocean water temperatures leading to a calculation of ocean heat content.)

Before we get very far, let’s ask “Why do we [they] want to measure global sea level?” The major reason seems to be, in our politicized world of global warming politics, that many want to measure global sea level to show that it is rising (which it has been for quite some time, at least the last 20,000 years) and that this continuing rise is 1) dangerous and 2) due to recent surface temperature rise over the last century, thus 3) due to Global Warming.   The theme is to use sea level rise as a proof of increased thermal expansion of the water in the oceans and increased addition of water from melting land ice deposits, both asserted to be the result of Global Warming caused by increased atmospheric concentrations of greenhouse gases, primarily CO2, since the 1880s . We’ll see later in this essay that this is part of a larger modern scientific movement to produce “single numbers” to represent dynamic systems (some of which are properly known to be nonlinear dynamical systems).

Can we measure sea level to that (+/- 3 to 4 mm) degree of accuracy? Well, for sea level, even at a single precise location, the answer is “No, we can not.” Now, I am not trying to be provocative here, it is a simple matter of fact. If the sea would be so kind as to stand still, even for just a few moments, we could get in a very accurate measurement at a single spot, or even a lot of spots.   Alas, the sea is never still, it is always moving up and/or down: tides, currents, wind chop, waves, wakes of passing vessels, rising and falling air pressure and, in most important locations, all of those at once. Thus, we cannot physically do it; the sea does not stand still long enough for us to make this measurement to that degree of accuracy. This gets only worse when we add in the information that both the dry land itself and the bottoms of the oceans, almost everywhere, are also in vertical motion and busy changing the volume of the ocean basins.

Many will protest: “Look here, Mr. Hansen. You can’t say that. There are scads of very scientific tables, charts, and journal articles very carefully telling us that now only can we make that measurement, we have been doing so for much of human history and [drum roll, please] since 1992 with [gasp!] satellites!”

It is my point here that what we are doing, where the doing is done, is not measurement, but derivation. Many measurements are taken, in many and diverse locations, at many and diverse times. In some cases, there are nearly continuous time series of measurements for particular locations. From these numerous individual measurements, for example, the tide station reports from the Battery in New York City, an interesting (but not to be detailed here) formula is applied to derive a figure, a single number, that represents the average difference between the sea surface and a geodetic bench mark (set in the bedrock of Manhattan Island years ago) over some period of time. We will skip the nearly infinite details as to whether the derived number represents a simple average between highs and lows, or is an average against time.

Let me point out that the NOAA CO-OPS system of tide stations has a very important and pragmatic purpose. Ships and boats need to know the depth of the water they will find in a particular spot – at a dock on the Hudson River or over the sand bar across the inlet – and at a particular time. Thus, tide tables are very important to sea going commerce and recreational boaters. It answers important questions such as: “Can I get there without hitting those nasty rocks (or going aground on that sticky mud) on the bottom? Can I stay here without being set down by the tide on those rocks or mud?” This system was never designed to measure “sea level rise” nevertheless it is used to compute changes in relative sea level trends in ports of American interest. Here are two Wiki articles on sea level: here and here. In the second article, this image is shown:

gslr

Notice please the difference between the trend calculated from tide gauges (orange line with grey error range) and the blue satellite measurements. Tide Gauge data (which measures Relative Sea Level at each tide gauge) accelerates while satellite data, which measures absolute sea level, keeps to its century long trend.

But what of those marvelous satellites? The official NOAA claim is: ”A series of satellite missions that started with TOPEX/Poseidon (T/P) in 1992 and continued with Jason-1 (2001–2013) and Jason-2 (2008–present) estimate global mean sea level every 10 days with an uncertainty of 3–4 mm.”    Results can be seen on graphical form at NOAA’s Laboratory for Satellite Altimetry web site. It is interesting to see the difference in visual impact that results from the use of alternate coloring schemes and to observe the lumpiness of the oceans.

slr_colors

I know many of the readers here are familiar with the sea – Willis and I have each spent a hefty fraction of our lives living on the sea, and an ever greater fraction living at the edge of the seas. Three to four millimeters is between 0.12 and 0.16 of an inch – about the thickness of two American pennies stacked atop one another. Or, for our cousins in the United Kingdom, about as thick as a one pound coin. It is a rare and beautiful and awe inspiring sight to see the ocean smooth as glass to the horizon, or even just across the bay or harbor. In my one-third of a lifetime of living on the sea (totaling > 20 years), I have only occasionally seen the sea so smooth – the slightest breezes bring up wind ripples and chop that far exceeds 3-4 mm, and can build quickly to feet and meters. If a body of water is open to the ocean, undulating ocean swells march from one horizon to the other, swells also measured in multiple feet or meters, and not necessarily traveling in the same direction as the wind chop. This all adds up to a great deal of vertical motion of the sea’s surface – at times exhilarating and at times downright frightening.

Now if NOAA wants to claim that their satellites in their perfect orbits can somehow transmogrify the undulating, rising and falling, uneven surface of the Earth’s ocean to a resolution of +/- 3 to 4 mm, then very well. Who am I to say they can’t, even if I can’t imagine how they might even theoretically do so. Nonetheless, for our purpose here, let us make this distinction: they do not measure “global mean sea level every 10 days” – they don’t even claim to, their claim is that they estimate it. In every real pragmatic sense, they somehow derive a single number from a fabulously massive amount of data – data which in and of themselves are not direct measurements, but inferences of measurements made from other kinds of data.

Let’s quit fooling around. While it would be possible to measure sea level in individual locations, it is difficult and even when done it is not a true measurement, but a derivation from accumulated data and dependent on mathematical and statistical methods and definitions. If you ever find a particular section of sea at “sea level”, it will be totally momentary and accidental.

Sea Level, even “Sea Level at the Battery in New York”, is not properly represented by a single number, above and below some geodetic bench mark. What we call sea level is a derived, calculated number – an average of averages of an array of measurement time series. In this sense, as the calculated mid-point of a range over time, it is, in a practical sense, an imaginary number having no existence in the day-to-day life of the Port of New York.

There is, however, a pragmatic “sea level at the Battery in New York” – which itself is a predictable range above and below some depth of water at a certain point (a point referred to as Local Mean Sea Level) which, when modified by information of expected, predicted tides, can be extrapolated to other points in the harbor, which is useful for mariners despite its less-than-real aspect. It can be used in its gross form (fractions of feet or meters) to determine the depth of water over the bottom at a place and time important to a ship’s captain and crew. Here is the prediction of water levels, relative to MLLW, made for October 9th thru October 11th.

Tides_the_Battery

The bottom line is that sea level, anywhere and at any time, is not a direct measurement. Never. It is a calculated, derived number that represents a precisely defined, but actually quite complicated, idea.

In order to define global sea level, one must participate in an exercise of imagination along the lines of: Imagine that the planet has stopped spinning; that moon has never existed; that the planet is a perfect sphere (or perfectly regular ovoid or flattened sphere); that there is no wind; that the atmosphere is evenly distributed and air pressure is the same at all points; that the temperatures of the seas are all exactly even, everywhere, to all depths; that there are no currents;, that there are no ice caps; that the rivers have stopped flowing into the sea and that gravity is magically equal at all points on the Earth’s surface (it is not, btw): under those conditions, we could then say that global sea level would be precisely “there”, within 3 or 4 mm. My friends, this is what makes Global Average Sea Level, in this special sense, an imaginary number.

So, we have answered Question 2: Are we measuring an imaginary thing (when we do so)?  Yes, we are “measuring”, in a sense, an imaginary thing when we say we are measuring sea level. The resulting calculated, derived number is a creature of our imaginations, an imaginary number.

Question 3 almost answers itself. “If we average those highly accurate measurements, why would we not get a global average sea level?” One can carry out a dizzying number of statistical and mathematical steps and arrive at some number – the more division steps involved the more precise looking the number will be. One can average any set of numbers. In this case, will one arrive at a number that is the “global average sea level”? Let’s look at Question 4 first and come back to this.

Question 4 is “What am we [originally “I”] missing here?”

This is a question of logic, and kind of follows on from an earlier essay I published here in February regarding Uncertainty Ranges.   When one averages a series of numbers that are in reality themselves ranges, then the result must also be a range. In our case today, when averaging a series (or in this case, a computer-full) of imaginary numbers then the result must be another imaginary number, in the same sense as the numbers in the original data set.   You can not average away original measurement error, you can not average away the fact that data given are themselves really ranges rather than single numbers, you can not average away the fact that original numbers themselves are, in the sense discussed here today, imaginary.

Before we too far afield here, let’s try to be clear on what the distinction is between a real number and what I have been calling here an imaginary number. This discussion takes place in the context of the measurement of characteristics of the physical world. For the result of a measurement to be a real number, the thing being measured must itself be measurable and the numerical result representing that measurement must represent something that exists in some meaningful and useful sense. However, the result of a measurement of a thing that itself is not physically measurable, but which can only be derived mathematically based on a definition that itself is an object of our imaginations (not something actually found in the real world), then that result should itself be considered, in this special sense, imaginary as well, despite its seeming precision.

There are innumerable averages of things that can be derived and calculated. Despite that, many of those averages are themselves imaginary, and their meaning and usefulness must always be thoughtfully considered. Such imaginary numbers may have some interesting meaning and some pragmatic usefulness but great care must be taken with their application, because, after all, they are imaginary and do not exist in reality.

Thus the average height of American citizens can be useful in determining the sizes of beds sold to Americans, at least indicating a range to be considered, it would be foolish to declare it the proper height of doorways for all new construction, even with an inch to spare tacked on, or to make exaggerated, scary, claims about public health threats based on the tiniest changes in such a number over some narrowly-selected time period.

Worse yet, and I hope there will be some comments in support of at least this idea, simple averages of averages of averages (all of which start with averaged, imaginary, derived numbers rather than actual measurements) are abominable absurdities. [ref: Simpson’s Paradox, etc.]

Here’s a ridiculous example: If we calculated the average altitude of the land in the state of South Carolina, first averaging the altitude of each county, then averaging the altitude of multi-county regions, and finally averaging regional altitudes, the result would be a number like (a totally pulled-out-of-the-air guess) 125 feet above sea level and when trended from the highest point in the Blue Ridge Mountains to the sea the state could be said to have a slope of XX feet per mile. It makes no difference in this sense if we weight the averages, krig the missing points, homogenize or smooth or smear. This procedure calculates and/or derives an imaginary number in the special sense of our working definition here. Thus, with our magic new imaginary number, it might be claimed that while some areas of South Carolina could be flooded by extreme high tides simultaneous with two feet of rain, on average the people there would not be prone to disaster as even the few expected flooded areas would quickly drain into the Atlantic.  Applying such a totally mathematically correct yet imaginary number to the real world can result it wildly inappropriate conclusions. It was this type of logic powered by imaginary numbers that led a New York Times science journalist to erroneously claim that the global sea level rise caused by global warming (a real rise but an imaginary number) caused increased damages to New York City during Hurricane Sandy — the same error Ira Flatow made in the NPR segment about flooding in Miami, where the flooding referred to occurs at a spot that is below the long-term Mean High Tide, and was so when the street was constructed.

Now, coming back to Question 3:  “If we average those highly accurate measurements, why would we not get a global average sea level?” If we average the very large data set of imaginary numbers for a specific moment in time, we will arrive at a new, even more imaginary, single number that could be called, if everyone were willing to allow it, “global average sea level”.   Would it be pragmatically, practically, meaningful and useful? Maybe, but in a very limited sense…and we would have to be very careful as to what meaning we assigned to it.

Why? See my essay last year about Hurricane Sandy and damages to NY City. The purported sea level rise for the 50 year period 1960 – 2010 “caused by global warming driven sea level rise” should have been 4 inches (roughly half of the 8 inches over the last century). In actuality, only when we use the lowest estimate of subsidence for the Battery couple with the highest estimate of local relative sea level change do we see any positive contribution of absolute, global sea level change to the relative sea level at the Battery, the 0.59 inches in the upper right-hand corner:

Battery_RSL

What’s up here? The acknowledged century-long estimated global sea level rise did not show up at the Battery, not even over the most recent 50 year period. This should not surprise us – attempts to apply a single-number, “global sea level rise”, is ill-thought out – trying to apply an imaginary number to a specific real situation.

Today’s discussion is one way of looking at the current trend in Science in which attempts are made to reduce very complicated dynamic systems to a single number which can then be graphed against time, usually in attempts to do one or more of the following:

  1. to cast blame for the increasing or decreasing number on a substance or action or group, usually incorrectly
  2. using two such graphs of single numbers to correlate some single number with some other single number to sell a desired story, usually to cast blame or give credit, usually incorrectly
  3. to bring attention to [read this as: to cause public concern or worry about] some rising or falling single number in hopes of generating gain [in research funds, fame, public sympathy, public or political support], usually unwarranted

These single numbers, meant to somehow illuminate some feature of the real world, are often, maybe almost always, not real numbers representing real things, but imaginary numbers representing concepts that exist, on a pragmatic practical level, only in our imaginations, which may lack meaningfulness and usefulness, or both. In this special sense, we can rightly refer to them as imaginary numbers. And because they are almost never acknowledged as imaginary numbers which require special care in application, each of the three uses above is followed by “usually incorrectly” or “usually unwarranted”.

 

Now, even if you don’t agree with me, it should be interesting to discuss in comments some of the ongoing efforts to [mis-] use this special breed of derived number, the imaginary number, to sway public opinion in differing scientific fields around the world. I’d really like to hear your views and benefit from your experience.

# # # # #

Author’s Comment Policy: This essay is not really about global sea level, but I doubt we’ll be able to discuss it without also touching on the issues surrounding the issue of global mean sea level. I do know something about it and will try to answer questions.

I’d rather discuss the concept of “Are we chasing imaginary numbers?”

It’s just an idea…let’s talk about it.

# # # # #

 

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478 thoughts on “Are We Chasing Imaginary Numbers?

  1. Many numbers in scientific endeavors are imaginary numbers, constructs of statistical methods and excessive significant figures. Thousands of measurements w/ 1 meter resolution can be averaged, the result carried out to several decimal points, and the illusion of an 0.001 difference will appear.

    In engineering the CAD program can describe the part with 0.0001 precision. The tool maker measures to 0.01 precision and the hacksaw or cutting torch gets within +/- 0.5.

    Like that only the other direction.

    Any number/data over 3 significant figures exceeds the resolution of typical instruments to actually measure.

      • Then go back and grind out the fillet welds so that it fits together with the other part designed to 0.001 precision in CAD.

      • Well we are constantly told that the Egyptians carved the stones for the great pyramid with such precision that they fitted together without any visible cracks. I see people putting their fists in some of those invisible cracks; well maybe that’s in the Mayan pyramids. In any case, they exaggerate the degree of fit.

        The Stonehenge builders must have been total dopes, as they couldn’t even get the rocks into a decent geometrical shape, let alone fit together. Maybe that’s why they left huge gaps in the wall.

        g

    • Improperly redefining “imaginary number”
      Kip Hansen
      You do a severe disservice to the general population by redefining “imaginary number” in an indefinite way that confuses the general reader.

      “Imaginary number” has a precise definition in mathematics and physics:

      An imaginary number is a quantity of the form ix, where x is a real number and iis the positive square root of -1. The term “imaginary” probably originated from the fact that there is no real number z that satisfies the equation z2 = -1. But imaginary numbers are no less “real” than real numbers. The quantity i is called the unit imaginary number. In engineering, it is denoted j, and is known as the j operator.

      Moderator – please flag such confusing articles and require then to restate the issue in accurate terms.

      [Reply: Sorry, that’s not our job. But you can submit your own article if you like. ~mod.]

      • He very clearly stated in the introduction that he was not talking about the square root of -1. He very clearly stated what he was discussing. If it confused you, you might want to take a reading course or take more care in reading.

      • I found the argument difficult [not impossible] to follow because the term ‘imaginary number’ is already claimed territory,so to speak. In my mind I had to substitute the word to avoid thinking of, well, imaginary numbers! I’m not sure what would be a better alternative though. Derived has the same issue although to a smaller degree. But the core argument is something I heartily endorse. From medical stories to almost any economic discussion, the urge to reduce some phenomenon to a single number is everywhere, and almost always misleading.

      • The creative mind works in mysterious ways. I had no such cognitive dissonance on reading this, even though I am familiar with the term in the strict mathematical context.
        Perhaps more coffee?
        Or maybe less coffee?
        Just a thought.

      • Reply to David L. Hagen ==> I tried to warn readers in the Spoiler Alert: section, right up front, in the very first sentence, that I wasn’t going to talk about your particular beloved definition of “imaginary number”.

        I’m afraid that mathematics and physics do not own the English language and do not get to cry cry cry when someone else uses the same word for a different use. This happens to statisticians too, who would prefer to own certain words and prevent others from using them despite the fact that they are rather common English language words, with many other uses.

        I do know that it can be hard for people who have been indoctrinated through university education in narrow fields to read essays in which a piece of their fields nomenclature is used in a different sense, even when carefully defined and alerted. I am sorry for your discomfort — but your objection is hubristic.

      • In reality kip it’s your idea so you get to name the term. However….doesn’t make a lot of sense to use a term that has has a standard definition.

      • I used the term “Fantasy Number” in this exact context a few weeks ago, in a comment, to much hate and confusion despite making very clear my meaning. You do not have the right to reinterpret the meaning and intent of an author to suite your preconceptions, especial when the author is clear in this regard. It is disgusting and leads you trapped by your language.

      • I’ve used complex numbers for several decades and had no problem in following what Kip meant by imaginary number. Hist term “derived number” might be a bit more rigorous, but it doesn’t have the same impact as “imaginary number”. I might go so far as to say that using “imaginary” for SQRT(-1) is misleading, though it does have a long tradition.

        In short, what Kip is saying is that a lot of numbers do not mean what most people think they mean.

      • David L. Hagen,

        “You do a severe disservice to the general population by redefining “imaginary number” in an indefinite way that confuses the general reader.”

        It seems to me (nobody special) that you are demonstrating by your comment/attitude, the very thing Mr. Hansen is trying (I feel quite successfully) to bring to the general population/general reader’s grasp of what is really going on “behind the scenes” as it were, in a wide array of scientific investigations and discussions.

        The very idea of a general population/general reader is itself, it seems to me, really and “imaginary” thing (within your mind in this case), which is not particularly useful or justifiably evoked as if a real thing, in criticizing another person’s attempt to convey his thoughts on such matters as the author here attempts to do.

        I, for instance, am only vaguely aware of what imaginary numbers are in a technical/mathematical sense, and I don’t feel any need whatsoever to have more than that level of knowledge about what to me are irrelevant details.

        However, the sort of imaginary numbers the author here introduces, seem to my mind quite familiar, and easily understood as relevant in a very “concrete” way, to the sorts of pronouncements and manipulations I see going on all the time in the “mass media” show and tell hyperspace, and I think the general population/reader would be well served to see his analysis of what is going on in that space, in this regard.

        And I ask; Who are you to attempt to limit this man’s communication to me? . . who am I feel, surely not your imagined general reader, as is no one real person on earth. You can write your own essays if you wish, in service to your own concept of the general population/reader, and I promise not to criticize you for “missing the mark” in the case of myself. I don’t expect anyone to actually hit such a mark with all of the actual general public simultaneously, and favor each of us attempting without undo hesitation, to convey what we feel led to convey at any given moment of time.

      • Anyone whom has a problem relating because of the strict term of imaginary numbers is probably not married.

      • I agree that the use of ‘imaginary’ in this author-defined context is misleading to the casual reader. Obviously it is possible with a little effort to turn away from the mathematical meaning of ‘imaginary number’ and focus on this different usage. However, I suggest that the adjective ‘factitious’ would convey Kip Hansen’s idea more accurately: a ‘factitious number’ is one that is constructed, contrived, but not one that is ‘imaginary’ in either the mathematical or literary sense (where ‘fictitious’, meaning made up from whole cloth, would be more appropriate).

        The numbers used to represent ‘global temperature’ would appear to be good examples of factitious numbers.

        /Mr Lynn

      • Term ‘imaginary numbers’ used in the above context, justifiable or not, appear to affront many engineers (including myself) sensitivity.
        May I propose a more appropriate term ‘fata-morgana’ numbers.
        Definition: fata-morgana is an illusion based on distortion of an object to such an extent that the actual object is no further recognizable.

      • Well I know about imaginary numbers in mathematics, which is where we invented them; but then If they are imaginary, and aren’t real, they couldn’t be a part of physics, which is all about the real universe.

        And yes, I do think that Author Kip, adequately issued a disclaimer distinguishing his category of imaginary (real) numbers from the mathematically (real) imaginary numbers.

        If anyone was confused by the distinction, I don’t read that in any of the posts here.

        g

      • Reply to vukcevic ==> Interesting word, but can’t say that “fata-morgana numbers” is a term that exactly rolls gracefully off the tongue…. (chuckle).

        I have seen this type of mirage at sea many times — one instance drove me quite mad for a few minutes, making it appear that an entire city sat on the sea coast directly in front of me where no sea coast could be!

      • I suppose if Kip had wanted to use some word different from ” imaginary “, he could have perhaps used “fictional” or “fictitious” or even Frenchified it and said “faux” numbers.

        But most people seemed to have got the distinction.

        There are far worse situations of confusion between words in everyday colloquial usage, and those same words which may have a precisely defined scientific or mathematical definition.

        Heat, and light are two very common examples; also the word “bright” or “brightness”, which we use colloquially as an antonym of dim, or dimness (no not the stupid kind of dimness).

        In Physics, “brightness” is a very loose usage, where we intended to mean “radiance” or “luminance”, which are strictly defined terms, related to EM radiation, and its psychophysical manifestation as “light”. But particle beam types (accelerator nuts) also talk about the “brightness” of particle or ion beam sources. Well we used that term back in the “valve” days for cathode or filament brightness; that’s “vacuum tubes” for you middle aged folks, and for the millennials; just forget it and keep on tittering, or taking selfies !

      • Reply to Kip Hansen
        ‘Fata-morgana numbers’ , I should have put /sarc in, hence let’s file that one under your definition of ‘ Simpson paradox’.

      • To my mind, such as it is, those who find the “borrowing” of the phrase ‘imaginary number’ for this essay to be worrisome have little to be concerned about,. because those who really know what the phrase means in mathematics are not going to be confused much (beyond the title phase of this essay), and those who don’t are unlikely to be more confused about that math meaning than they already are.

        And unless those in the latter state of confusion happen to be climate siantists or UN bureaucrats working on ‘Common Core’, I see little chance of this (to my mind) rather pedestrian lingo lifting leading to much in the way of real world consequences.

        But, I do think something like “imaginary norms” or “imaginary knowns” or some such thing, might be a bit more informative/unconfusing to the climate confused, if a phrase based on ‘imaginary’ (which I feel is most “truthful” in this realm of thought) is eventually to make it’s way into the popular vernacular. Imaginary numbers is likely to be conflated by such folk with data manipulation or more mundane forms of statistician hokum, and not be considered/grasped in the specific way the author intends here.

      • Hagen

        Frankly, the concept of somebody saying they understand the formal mathematical meaning of “imaginary number” (i.e.: square root -1) and claiming to have difficulty/discomfort understanding what Kip Hansen has written due to re-use of the word ‘imaginary’ is simply difficult to accept at face value.

      • Kip Hansen said :
        “I’m afraid that mathematics and physics do not own the English language and do not get to cry cry cry when someone else uses the same word for a different use. This happens to statisticians too, who would prefer to own certain words and prevent others from using them despite the fact that they are rather common English language words, with many other uses.”

        I couldn’t agree more! It happens in other fields too. I get sick and tired of “special” groups trying to usurp what were once common English language terms and concepts for their own definitions and purposes.

      • I found the overloading of the term “imaginary” livable, but annoying. I use Fictional Number in that use…

        And while folks can and do regularly define and redefine jargon for their own special needs, avoiding collisions with prior art and confusion ought to be a goal.

        Overall, I find the article useful and raises an important point, especially for averages of intensive / intrinsic properties that give fictional results…

    • Well hold on there. There are plenty of numbers that can be routinely measured to better than 3 significant digits.

      I myself have made experimental measurements that are accurate to at least six, and maybe seven digits. The wavelength of the ” Red Cadmium Line ” that was once one of the wavelength standards, is 6438.4696 Angstrom units. I’ve remembered that number from my early College (University ) days. In New Zealand, a ” College ” is a high school; not a University. I believe the Red cadmium line was one of the ones that Michelson measured the Standard metre bar with, using his Michelson Interferometer. Today one could use a Fabry Perot Etalon instead of he Michelson set up.

      I used a 1 cm long FP etalon to measure a whole bunch of red orange yellow lines n the spectrum of Neon.

      One cm is 10,000 microns, so it is 15,000 wavelengths of red radiation, or 30,000 half wavelengths, which gives 30,000 fringes in the multiple beam interference pattern of a FP interferometer.
      You use a simple refractive prism spectrometer, to separate the spectral lines into a normal looking atomic line spectrum, and then the etalon converts each of those bright lines, into a set of concentric ring segments, but because of the 30,000 order, you only see the outside rings, as short arcs. The Michelson interferometer is just a two beam interferometer, so the fringes are sinusoidal in profile, and it is somewhat difficult to estimate a fraction of a fringe. But with the multiple beam FP, you get very narrow sharp rings that aren’t even remotely sinusoidal, and it is quite easy to resolve 1% of a fringe.

      So even my cheap toy FP etalon could resolve one part in 3 million. You have to measure the length of the etalon quartz spacer with a micrometer, which you can easily do to 25 microns, and maybe 10 microns with a good micrometer, (or better tools today), so that gets you to within 30 fringes of the correct optical length. Then you use a very clever trick (Michael Mann is not the only one who knows tricks), by simultaneously observing a number of lines at the same time; about five is enough but the more the merrier.

      Each different wavelength, will give you a different fractional order, resolved from the Fabry Perot rings, which you add on to the mechanically measured integer order, and you make a table for say +/- 10-15 orders about the best estimate number.
      Only one of those guesses will replicate the correct set of fractional orders, for the five or more lines you measure.

      If you correctly allow for the refractive index of air, including how it varies with wavelength and relative humidity, then you can turn a cheap toy FP etalon into a precision measurement tool.

      Some atomic frequency standards are good to 15 digits I think.

      Well (c) is an exact number with no uncertainty. Everything else links to that.

      BUT ! as to measuring sea level; I have seen the sea as flat as a sheet of glass, as far as the eye could see, down on a tarpon flat n the Florida Keys, west of Key West.
      But under ordinary circumstances, all kinds of things are going to cause sea level change, and the bigger the change, the less often you will encounter such a change.
      I really wonder whether the real time analog sea level observed at some location actually has a 1/f noise behavior, so that the observed level over long periods of time, can drift around aimlessly, BUT with no actual apparent driving cause (it is noise after all).

      The behavior of 1/f noise is such that each octave of frequency contains exactly the same energy as any other octave. So even though the amplitude of the noise would seem to increase without limit, because of the ever lowering frequency, those high peaks don’t come along that often, so the energy is not infinite.

      It would ot surprise me at all to find out that sea level at some location, has a 1/f noise spectrum, in which case, you are actually observing quite imaginary numbers.

      Actually, the imagination is in what you choose to believe the numbers you re seeing actually mean; it could be, that they don’t mean anything. Statistical results don’t actually mean anything; it’s just numerical origami. But we choose to believe it is somehow real.

      g

      • George,

        It’s always a pleasure reading your engineer’s take on things. I prefer engineers over scientists (a vague designation) because engineers put things in perspective re: the real world.

      • In the MKS system, 6 decimal places (micron and milligram) are easily measured.
        Imperial (colonial) measures used on the other side of the pond are relics of history; NASA need updating their instrumentation.

      • vukcevic, the next time you pay an insurance bill, keep in mind that it is “numerical origami” that actuaries use determine the amount you pay.

      • Mr Jones
        They are indeed, and oversized origami to boot, paid thousands (possibly tens of thousands) of pounds in years gone by, health, mortgages, houses, cars, travels and what else. Fortunately I had never had to claim on any.

      • vukcevic,

        “They are indeed, and oversized origami to boot, paid thousands (possibly tens of thousands) of pounds in years gone by …”

        Oh my goodness, tens of thousands of pounds of what?

        (And my feet, in boots, are a foot long, on real ruler ; )

      • Hi Mr Knight, nice to hear from you.
        I have nothing against insurance salesmen, but to store all the pennies I paid ( granted, totally voluntarily) ‘the giant’s Seven-league boots’ would just about do.

      • Yo, vukcevic . . . Apparently, but wouldn’t money be a good alternative? It’s the freakin’ 21st century for peats sake.

      • Perhaps the author should have used the term “homogenized” instead of “imaginary” in his text.
        We all know that some sort of adjustment is made to all data before it is published.
        I doubt that anyone knows with certainty exactly WHAT is done.

  2. Interesting post. I started wondering about this kind of thing years ago when I was watching gymnastics in the Olympic Games. Each athletic routine was given a score out of ten from half a dozen judges and scores regularly varied by two points at least. In the end they were averaged and summed for team points. Russia won gold on about 287.6 points and USA got silver on 286.2 points. Or some such scores. I felt it was all rather ridiculous but I never had the training to work out the correct error bars. Ideas?

    • Maybe my grey matter is starting to decrease, but one thing that I remember (and can probably look up, is that when multiplying numbers of different accuracies,the accuracy of the answer is that of the least accurate multiplicand.

      Eg 50.25 x 2.0 = 100.5

      • Yes. So the first thing we need to work out is what the individual error bars are on the scores and given that different judges could give the same performance scores which differed by up to 25% of the total available score of 10 I really did not see much credibility when the medals were decided by a difference of maybe 1% in the team totals.

      • No, you are mistaken. In multiplication you add the both the percentage errors. In addition or subtraction you add the actual errors.
        For example if you measure the speed of a vehicle by the time is passes two marks you have say 0.5s uncertainty at each end. The time interval has 1.0s uncertainly. You then add the %age uncert. in the time and the distance measurements to get the %age uncert. in the speed.

        For large sets of data this is all further complicated by the statistical nature of the uncertainties . If two errors are statistically independent then you’d take the ‘vector sum’ of the errors, not the arithmetic sum.

      • I, too, have been suspicious about the scores given in, say, figure-skating events. Who is to say how much the scores are influenced by the country of origin of the judges? Are the judges perfectly objective, or will (e.g.) the Latvian judge, unconsciously or intentionally, sway his vote according to whether or not the Latvian representative is skating? With margins of tiny fractions of a point determining the placement of the skaters, it would not take much for that Latvian judge (or, of course, any of the others) to influence the outcome; and yet, the scores are presented as being an accurate presentation of precisely how well the skaters performed. BAL DER DASH ! I won’t discuss how scoring could be influenced by the actual degree of expertise of the judges, their “pet peeves,” the state of their digestion, how pretty they think the girls are, and the like. Accuracy to hundredths of a point? Sure . . .

      • And what about a figure skater from Jamaica who has no one from his/her country on the panel of judges?

      • Mike, if you have a product of several variables, each with a statistical error band, I believe the more likely overall error of the product is the RMS sum of the individual errors.

        It is after all a statistical combination.

        Simply summing the error bars for each variable would give you a worst case overall error, not the most likely error bound.

        g

        But I cold be rong !

    • When watching gymnastics at the elite level I’ve found that it’s better to think of all the scoring as starting with a minimum of 9 and a maximum of 10, and the real base for a well executed routine is about 9.6. Then the variance and difference in the scores will make a lot more sense. The team scores become more like 28 to 27, and the 3 to 4% difference makes sense given the capabilities of these elite athletes.

    • Back in the 70’s and 80’s my friends and I used to play a game called “Can you guess the country?”
      The rules were simple. Knowing the country the gymnast was from, knowing the scores of each judge and given a list of the countries that the judges were from, can you identify which judge gave which score.
      The sad thing was, how trivially easy it was to get a perfect score at this game.
      I remember one competition in which an aging Russian champion was competing injured. During the floor performance he completely left out two required moves, a mandatory 1 point deduction for each exclusion. The Eastern block countries still gave him near perfect scores.

      The Olympic committee finally grew tired of such blatant partisanship on the part of the judges, so they did what international socialists always do. They stopped identifying the judges by the countries they were from.

    • The interesting point here is that the scores in any “judged” event are physically meaningless. They are the result of an opinion survey of the judges. In order to assign a “winner” and a “loser” they are mangled mathematically(the point of this article) so the contestants can get an answer. Occasionally one skater will do a couple of standout figures that the judges can really see and they will get noticeably higher scores. But that leave the muddle for 2-10th still in place. The contestants and the crowd do not like the result “Irena took first place, 2-10th place are tied between …….

      Figure skating has a compulsory program, which usually isn’t televised, where the precision of the skaters in a predetermined set of figures was judged. Good skaters can perform astonishingly well. Occasionally one could do something like make two circles three meters across with a variation in the track the width of a skate blade. Skaters who made the cut went into the free skate part of the competition, which everybody watches, and was scored primarily artistic terms- performance/execution, choreography/composition, and interpretation, doing the skater’s choice of figures set to music.

      • The compulsory portion of figure skating was phased out of the Olympics in 1990. It was boring, and the officials were tired of explaining how someone who performed brilliantly in ice dance or pairs could lose a gold medal because of poor performance in compulsories. Over the years there has been a lot of controversy in figure skating (and particularly ice dance), because it seems so obvious that the results are pre-determined.

  3. Reblogged this on The Arts Mechanical and commented:
    Like Willis and Mr. Hansen I’ve spent a good part of my life near tidewater. Mr. Hansen is absolutely right that there is no possible way you could measure sea level to the accuracy that the climate team claims. The error potential in the instruments used in larger than the potential measured value, to say nothing of the fact, that as fluid, seawater is very difficult to measure. For that matter it’s impossible to get measurements to within +/- 2mm in a tank measuring flow. So how are we to expect such accuracy from a measurement taken from a seaside.

    • Having read this and understood a little I get the idea that measuring global average sea level is on a par with herding cats.
      As I say of many things “It’s all aunts and uncles” meaning it’s relative.

      James Bull

      • I think there is far more than that to this article. This phrase–“These single numbers, meant to somehow illuminate some feature of the real world” struck me in particular because so much of the focus in K-12 education globally, now and for the past twenty years or so, has been to get students to internalize the desired mental images of how the world supposedly works. The point is NOT to have accurate perceptions, but conceptual models that create both a belief and a motivation to act for transformational change.

        The sea level rise is just such a graphic image and tied to a real world example that most people can relate to from personal experience. A key feature of what the systems theorists and cyberneticians call constructionism. Most people have been to a beach or the coast or a harbor. They can visualize these dire effects even if they are not actually likely to occur.

        Remember a political or sociological theory that is real in its effects on behavior is real. It need not be factually true to serve its purpose of social change. With these classroom projects while the brain is still quite malleable, http://www.middleweb.com/25495/climate-ed-projects-to-engage-tweens/ , few adults of the next generation will have the factual knowledge of science to know the narratives are false anymore or the numbers imaginary.

      • If you count the visible cats in your herd, and you get the right number; you are an expert cat herder !

        g

    • Deep ocean bottom pressure recorders aren’t affected by the ups and downs of the ocean surface, and are capable of 1 mm resolution. Useful for picking up tsunamis, where the mid-ocean rise is very small.

    • Agreed you may not be able to polish a turd, but they never stop trying. And if they sneak past Paris and get some BS resolution passed etc, it will cost many trillions of dollars by 2030 and it will deliver SFA on the investment.

      • I ran into something like this as a hardbitten old wargamer. A longtime opponent was trying to determine who was “luckiest” in any particular game. He attempted this by averaging all the die rolls in the game. That one set off the old alarm bells. Because some die rolls are more important than others.

        If you win the important die rolls, it generally doesn’t matter damnall whether the average of all your rolls is above or below average. But determining which die rolls are more important, and by how much, can be, to put it mildly, murky.

        Also the timing. If you get a good attritional result early in the game, that means the opponent is deprived of force for the entire game, and that affects the odds all down the line, whereas an attritional result towards the end may hardly affect the overall results at all. On a narrow or wide front, the affect of attrition can vary wildly, both strategically and operationally. It can create a decisive weakness in your line (if indeed lines are the schwerepunkt), or it can create but a trivial effect on your reserves — or anything in between.

        Not to say whether the victory conditions involve casualties, strategic objectives, or both (or even neither).

        At the same time, a die roll at the end of a game, aimed at a precise strategic result can be decisive, while early “bad luck” can sometimes be compensated for by subsequent adjustment of strategy. Think “Prevent Defense” vs. “Hail-Mary Pass”.

    • Of course not. But you can spray it with lacquer and dust it with glitter, then listen to the crowds go, “Ooh, shiny!”

      • Gary

        Real life examples

        Send off present for one not popular – a well iced (frosted in US I think) one as a cake. Also seen done over a foam chair seat.

        South African retirement example. Well dried, lacquered, on plaque with inscription

        “Sometimes you spoke it, sometimes you wrote it, but mostly you were in it, so take it and go”

      • I remember buying a plastic dog pile at a gag-gift shop – got in trouble at school for putting it on the teacher’s desk chair!

      • “got in trouble at school for putting it on the teacher’s desk ”

        That is how you know it worked!

      • Speaking of dog piles, the city of San Jose CA commissioned a sculptor, to craft a bronze sculpture of the coiled up Aztec Serpent god Quetzalcoatl, for either $35,000, or $350,000.

        Instead the ” artist ” made a brown painted fiber glass sculpture, which looked exactly like a big pile of dog crap, instead of the intended serpent god for St James’ Park in San Jose.

        When this was reported to the suckered public on a talk radio show from their San Jose studio (KGO) they immediately got a listener call in who pointed out that if you
        spell ” Park God ” backwards, you get ” Dog Krap ”

        Very appropriate. I think that pile of fiberglass dog crap is still there in the Park.

        g

  4. Thanks, Kip for a fine essay. After having surveyed the northern oceans: the North, Norwegian, and Barents Seas for over 30 years for the offshore hydrocarbon industry, I can testify the difficulty in estimating the correct MSL (mean sea level) for particular locations on the shelf. On one occasion, the operating company wanted to know the correct figure with engineering accuracy, e.g., to 1 mm plus or minus…Ok, we said, give us x million kroner, and a couple of years of observations and we’ll do it. Indeed, it was done by placing an underwater tide gauge on the seafloor inside a carefully surveyed cage, at 340 m water depth. However, to cut a long story short, we never managed to estmate the local MSL to more than plus minus 50 mm. Yes, I said 50 mm plus minus ( 5 cm !).

    • On one occasion, the operating company wanted to know the correct figure with engineering accuracy, e.g., to 1 mm plus or minus…

      I’ve seen lots of young engineers do stupid stuff but the example you cite still leaves me gobsmacked!

      The example that comes first to my mind is the guy who specified a two inch diameter pulley for a one inch diameter steel cable (the correct pulley was about four feet diameter for that particular application).

      One of the things that separates engineers from scientists is that engineers get correction from all quarters. In my example above, the foreman in the boat yard had a quiet word* with the chief engineer. Scientists tend not to have anyone to drag them back to reality.

      *I could hear all the gory details from way down the hall.

      • As a shooting buddy put it.
        Precision is hitting the same spot every time.
        Accuracy is hitting the right spot.

      • @PiperPaul
        Great illustration.

        In estimation theory (lack of) “precision” corresponds with “variance”. And (lack of) “accuracy” corresponds with “bias”.

        In many problems variance and bias are trade-offs. For example, sampling a larger area of ocean can improve overall estimation accuracy at the expense of making the “bullseye” area much larger.

  5. Interesting article, Kip. Averages of averages may or may not have value, in my opinion.

    For example: If you took the average monthly/daily global sea level readings calculated for the last fifty years, maybe the resulting number means little, but it seems to me that it is the trend that reveals information when viewed over the length of the series. Where am I going wrong?

    • I get the impression that the author is not saying that there is no value, so much as he is saying that the output could be considered as low resolution data, or perhaps medium resolution data.

      • Author fell in love with the term “imaginary number” and built his article around it. Repeating this term many times does not amount to any scientific argument. Inadvertently author conveys that he does not really know what he wants to convey.

      • I agree, Peter. A better phrase would be “contrived number”. Had the author used “contrived”, his point would still be valid and it would convey the truth that the numbers that are used are “made-up” – in the sense that they do not represent anything tangible. The use of the word “imaginary” just annoys the mathematically minded and confuses everyone else.

    • Bob, this assumption that there is a “trend” and that it can be ASSUMED to mean something seems ingrained modern western pop science culture. I suspect that this largely comes from reporting of economic statistics in mainstream media.

      Nightly bulletins report stuff like GDP, “cost of living index” and inevitably “trends” over x amount of time.

      It is somewhere implicitly ( but never openly stated ) that there is a linear “trend” to be extracted and more importantly another implied assumption that this can be expected to continue unless policy does something to change it.

      In science, before fitting a mathematical model to the data, you must start out by saying why you think the model is suitable. There is nothing special about about a linear trend that means is is suitable to any and all data and even less that it is valid as a basis for extrapolation ( projecting future change ).

      In auto-correlated random data ( another mathematical, statistical model ) where the next value is a random deviation from the previous one, the best guess ( projection ) of the next value is that is will be the same as the last. There is little chance it will be the same but it’s the best estimation. Since the deviations from point to point are by definition random ( gaussian or normally distributed or “white noise” ) the mean change will be zero, so that’s your best guess.

      The “trend” is the mean rate of change and this is where the fallacy creeps in via the unstated assumptions that are swept under the carpet.

      If one takes the “trend” to be an indicator of future change one is assuming that data sample is sufficiently long that all random changes have averaged out that the calculated trend represents some ‘anomalous’ deviation and that the cause of this deviation is a linear change in whatever is being measured.

      However, this kind of “random walk” time series , derived by integrating white noise of random changes has extended trends in both directions on ALL time-scales. So there is absolutely no guarantee that your sample period is not just one of those and there is no a priori reason to think it is caused by something else that can be expected to continue.

      The climatologic application of this is to global mean temperatures. Here we “know” that GHG cause warming and ASSUME that all other natural change is totally random ( a part from the volcano fiddle factor ).

      The problem is that the cumulated random changes ALWAYS produce some slope because white noise contains equal amounts of all frequencies, even very, very long ones, so you are never in a situation where you not have the risk of a random walk. We all know the result of the “trend” depends on where you start and where you end.

      It is actually a totally useless statistic for projection in this context.

  6. The author seems to be implying that “imaginary numbers” like global sea level as derived from satellite data are inherently flawed and need to be treated very carefully. There is one important consideration with such an approach – the time span over which the data is collected.

    The author claims that there are far too many variables to be ever able to get a grip on local sea level, let alone global sea level. In the short term that is correct. Over longer time periods the satellite will start to see patterns emerge which do correlate quite well with the average sea level, in my opinion. From tide gauge data I believe the minimum time frame for accurate measurement is 30 years minimum of continuous data?

    Also, regular tide gauges fitted with GPS chipsets do provide very accurate data on actual tide (sea) levels against which other data can be correlated etc. They have not yet been installed long enough to provide the necessary data for calibration i.e. less than 30 years, but I do believe there is hope.

    At the end of the day all measurement contains uncertainty. That is not any kind of problem with modern science, it is the problem that modern science should strive to overcome (and often does). The true problem with modern science is the failure to report that uncertainty alongside the presentation of the data. It is the corresponding implied certainty of single numbers denoting moving averages that science gets itself into trouble with all the time.

    This is partly the fault of the media and partly the fault of the scientists. Politicians are not helpful either…

    I am leaving aside examples of where scientists deliberately misrepresent the uncertainty contained in their data (for a variety of reasons, not all sinister) as that is a whole different animal to this discussion about imaginary numbers as presented by the author.

  7. Finally someone makes some sense. This is a well written article exposing how uncertainty in measurements and even what is measurable is exploited by people with political agendas. More to the point, it is very true that the numbers “measured” are all imaginary at the level of “precision” they are presented. So called climate science carries all the characteristics of pathological science:

    “Symptoms of Pathological Science:

    1. The maximum effect that is observed is produced by a causative agent of barely detectable intensity, and the magnitude of the effect is substantially independent of the intensity of the cause.
    2. The effect is of a magnitude that remains close to the limit of detectability; or, many measurements are necessary because of the very low statistical significance of the results.
    3. Claims of great accuracy.
    4. Fantastic theories contrary to experience.
    5. Criticisms are met by ad hoc excuses thought up on the spur of the moment.
    6. Ratio of supporters to critics rises up to somewhere near 50% and then falls gradually to oblivio
    n.”

    https://www.cs.princeton.edu/~ken/Langmuir/langB.htm#Characteristic%20Symptoms

    • Thanks for linking that long forgotten article. I read it long ago and it is a classic. It should be mandatory reading for any serious science student.

      rgb

      • What’s interesting is that Langmuir spent a good portion of his working life at GE, where his work was judged in part on how many new/better products resulted from his efforts as opposed to how many citations for a paper. I’ve seen a fair amount of his writings in the General Electric Review, the articles are usually clear and interesting.

        Would have been interesting seeing a discussion between Langmuir and Feynman.

  8. Interesting post, and entirely apropos of the MultiModel Ensemble Mean used extensively by the IPCC. This is an average of averages of GCM results produced by (usually) perturbed parameter (Monte Carlo) runs of a chaotic climate model starting from some narrowly distributed set of initial conditions and with common e.g. RCP-X or “historical” drivers.

    There is some small justification for doing PPE runs from a single model, because this directly investigates the tendency of the model to fill a phase volume with the future trajectories. It is not at all clear that the PPE mean and standard deviation have any extrinsic meaning in a statistical sense — each run is very much a truly imaginary vector timeseries as the model does not contain the same physics that the planet uses to evolve in time in countless ways, and is integrated at an absurdly high resolution, is known to be a chaotic dynamical map (it is where chaos was first discovered), etc. But at least it is clear what it is for that one model! It is an honest statistical sampling of the range of chaotic trajectories resulting from the dynamical iterated map of that one model from a sampling from an “ensemble” of possible initial states and/or parameters. The average and distribution tell us something about that particular model, even if it is utterly irrelevant to anything else and unfit for any useful purpose.

    What do we get when we take (say) 36 of these models, when the models themselves are not independent, nor are the initializing data, or are the parameters, and where the overlap is not systematic or even fully known, run them different numbers of times in multiple PPE computations to obtain PPE average results (with no particular rhyme or reason dictating how many times any given model is run other than the means/resources available to run them and the whim of the modelers) and then average the averages into the MME mean? We don’t even get something that is characteristic in any useful way of the distribution of mean model results of the different non-independent models! What, exactly does the envelope of these differently weighted PPE means mean?

    It is as if the IPCC and CMIP5 modelers think that by some sort of statistical alchemy they can squeeze blood from a stone, transform a moth-eaten sow’s ear into a shiny silk purse, nay, this is still too kind. It is as if they think that if they just process an image, a computer simulation of a rotten sow’s ear cleverly enough, it will eventually turn into a real silk purse.

    One, I doubt not, filled with money.

    I think they are right.

    rgb

    P.S. — I saved the Simpson’s Paradox article, as I was not familiar with this at least by this name. At first I thought it might have something to do with Homer and was looking forward to some humor, but it looks most unfunny…

    • Furthermore, can we say that if a single run of a model matches the actual climate reasonably well, that the model may be a good one even if the average of its runs do not? If so, how many permutations of parameters and initial conditions will produce ‘good’ models? Contrary to ‘all models are wrong’, almost all models are right.

      • All models have a punchers chance of creating a simulation which resembles observation. However, unless all variables are identical in both cases all that can be said it’s that a strong resemblance exists. Two loaves of bread may look similar, despite vastly different ingredients, methods etc. When the vast majority of models demonstrate a striking resemblance to observation, and the ingredients and variables are represented in equal measures, can it be said that models have skill.

    • Dr. Brown,
      Best critique yet, and done with an economy of words!
      If you do not mind, I would like to share this, via my FB page, with my friends and acquaintances, along with the lead post by Kip Hansen.

      Thank you to you both for your thoughts here.

    • BTW, Homer did apparently create quite the paradox when he correctly inferred the mass of the Higg’s Boson to a pretty close margin, and did so before the eggheads spent $13,000,000,000 doing it
      Oh…and provided a proof for Fermat’s Last Theorem at the same time:

      • It was his donut work, at bottom, which was most fascinating though. He seems to have arrived at the actual shape of the Universe, and a potential fusion reactor configuration.

    • I’ve just finish reading few notes on the Simpson Paradox.
      Next note explains correlation-causation relationship.
      Example quoted:

      “There is a high statistical correlation between ice cream and drowning”
      That reminds me of number of correlations I found, but they are readily dismissed by the experts.
      But wait a moment.
      Sometimes there is a variable hiding in the background.
      In this case the day of the year is hiding in the data.
      More ice cream is sold on hot summer days than snowy winter ones.
      More people swim in the summer, and hence more drown in the summer than in the winter.
      Beware of Lurking Variables !”

      In my case ( see this link a lurking variable is elusive and difficult to detect.

      A small but important note, it goes on to say:

      “When we find that two numerical data sets are strongly correlated, we should always ask: “Could there be something else that is causing this relationship?”

    • Reply to rgbatduke ==> For Simpson’s Paradox, we might try something like “A profound truth accidentally spoken by a total idiot.”

  9. Correct me if I have misunderstood but I have often wondered about the issue in the finite probability that if all the molecules in my desk oscillated ( “jumped”) in the same direction then my desk, of course, would jump. Unless of course the use of probability in ordering the conduct of the universe is just such an “imaginary number” and the real universe would NEVER let the desk make its finitely possible leap even over an infinite period of time.

    • in Physics they are all models which allow us to visualise and work with invisible concepts. When we use the models and apply them to things we think we can measure the two results match reasonable enough.

    • Molecules within a solid only oscillate relative to their neighboring molecules. Because each molecule’s movement is constrained by those neighbors by electrostatic forces, each molecule is forced to move in the opposite direction of its momentarily nearest neighbor. It is impossible for all the molecules within your desk to oscillate together.

      However, even if they somehow did, you could not detect it because molecules and their oscillations are so small.

      SR

  10. I would add a couple more questions to the four you started with

    Are the numbers reliable (i.e. consistent over time) – so even if the numbers are imaginary the trend in the number has relevance
    Are the numbers useful – in the scientific sense, not the political one

    • Are the numbers reliable and accurate? (i.e. consistent over time)…this has always been the fly in the ointment for me. Concerning AGW: Older temperatures earlier in the 1900,s and before were measured with older instruments. Which thermometers were used to collect data? Were they accurate? Standardized? Were those taking the measurements trained? How was the information recorded? Were the barometric pressure, wind velocity, humidity measured as well as the temperature? These may have an impact upon the accuracy of the specific temperature measurement. With what were these variables measured? What was the accuracy of these instruments? Was the location of the temperature recording standardized? How was the location measured for older temperature samplings? GPS was not used, it did not exist for older recordings. Sextant? Maps? Accuracy, reproducibility, reliability, relevance all matter. Currently this AGW data is being used as a tool to advance political motives, not to actually solve a “real” problem, but a problem of “Imaginary numbers.”

      • If a station hasn’t moved, the GPS co-ordinates for the current station would serve as a usable proxy for the position of the station in the past. For stations that have moved, we sometimes have photos or maps of the earlier station from which a reasonable guess can be made of the older stations location.
        For the rest, or worse, for those that were moved without documenting the move, your just out of luck.

  11. Just how many Angels can dance on the head of a pin…that’s what I want to know.
    And could someone please tell me the temperature of the Pacific Ocean?

  12. Very good article. Thank you.
    Anyone who has ever stood up in a rowboat on a river, lake, or sea knows that any point on the boat. (prow, stern, highest point, etc.) does not follow a simple up and down regular motion. Each point seems to roll generally up and down in some kind of complex path and each cycle appears to be different. That’s for a single point. Now imagine being able to see all points on the boat at the same time. Furthermore, as you stand and move your body to maintain a standing position, you influence the movement of the boat. Magnify the complexities you see in a small boat, to the great distances as the oceans surround the earth.
    So what is the average elevation of any point on the boat? How long would you have to measure the elevation of that point to have the average elevation of that point have meaning? Would the wind, tides, movement of things and people on the boat make each measurement at a point unique? Now ask the same question for every point on the boat, and every point on the world’s oceans surface (whatever that means).
    If your imagination is good and you are a land lubber, maybe you should reach for the seasickness medicines.
    It doesn’t take much imagination to ask the above questions. But who can answer them?

    • Rowboats are small enough that they are fairly inflexible over their length. Now a dinghy or Kodiak would be a completely different problem.
      Large ships are long enough that the principle of inflexibility has to be abandoned. Dealing with the bending and flexing that large vessels experience in the course of normal seas (much less major storms) is what keeps ship builders awake at nights.

      • Reply to MarkW ==> Being aboard a 40 400 [corrected-kh] foot or so steel vessel in a Force 10 storm out in the open ocean and hearing the hull and deck plates bend, flex, and groan kept me awake on several occasions. In those conditions, I preferred to be at the helm or at least on the bridge.

      • Probably Kip has heard it all before but I read a practical (albeit humorous) description of the Beaufort scale it was on the order of. No wind, too little wind, too much wind, much to much wind, wind wind wind woo whee will it ever stop …..

      • “Being aboard a 40 foot or so steel vessel in a Force 10 storm out in the open ocean and hearing the hull and deck plates bend, flex, and groan keep me awake on several occasions. In those conditions, I preferred to be at the helm home or at least on the standing on a bridge.”

        FIFY

      • Glad to see the correction for boat length. I’m in awe of the pilot who can keep a boat upright in wave heights seriously exceeding the length of the boat. Regardless I prefer to be my the living room in those conditions. Probably everyone has heard an 800 ft container ship El Faro (33 people) lost to Hurricane Juaquin (sp?) Apparently dead in the water in a category 4. Doesn’t seem to leave any good options.

      • Here is where (for my own purposes) would like to see money spent on hurricane model improvement over the fantasy climate models. To credit the hurricane models, they did get the overall path correct. I’m sure the Bahamas and the El Faro would liked to have had better timing and intensity(yes the hardest) predictions. One of the other axioms is never sail into weather you haven’t accidently sailed into before. My opinion is the Captain (maybe unknowingly) sailed into the error bars of the model prediction.

  13. Given the bridge clearance on the Intracoastal Waterway is 65 foot (at Mean Low Water) and that there are bridges along the ICW from New York to Miami, and that some of those bridges had been built some time ago, a simple test of whether sea level is in fact rising would be the number of boats with a bridge clearance of 65 foot are now unable to pass under the bridges. According to the climate scientists then in about another 10 years no boat with an approx. 65 foot clearance previously passing under the bridges will then be able to do so?

    • You are right that such structures can cause a lot of problems in shipping.

      A ship may be able to pass under when fully laden but not after it has discharged, even when it has been fully ballasted (since the available ballast may be less than that required), and flooding holds (to increase ballast) can cause dangers of their own due to free surface effect, Many ferries have been lost due to small amounts of water ingress since the free surface effect of that water can be catastrophic.

      I suspect that if one could examine historic records of ship movements some insight could be obtained, but whether those historic records exist is a different matter.

      • Squat and rise occur at the same time (back of boat down front up) with a net imaginary number up or down depending on speed and hull shape. LOL more imaginary numbers that produce a not very useful number.

      • Obviously a dinghy can plane, and therefor lift, so too hydrofoils, but as Geoff suggest ships squat with speed, but in a navigational channel with a known hazard the ship will presumably be proceeding quite slowly.

        That said, apparently squat has been used to get under a bridge: ” The second largest cruise ship in the world, Oasis of the Seas, used this effect as a contributing factor to pass under the Great Belt bridge, Denmark, 1 November 2009, on her voyage from the shipyard in Turku, Finland to Florida, USA.[5] Without the presence of the squat effect, the ship wouldn’t have been able to clear the bridge safely – the margin would have been very slight. However, travelling at 20 knots (37 km/h) in the shallow channel, Oasis experienced a 30 cm squat, allowing sufficient room to clear the bridge safely.”

        Obviously there would have to be a lot of consultation with the port authorities, in which consultant naval architects and the shipyard would also no doubt play a significant role, and I suspect that a trial run (short of the bridge) would have been performed to verify theoretical calculations, before the port authority would give the required ‘clearance’ (to use a pun).

        See generally : https://en.wikipedia.org/wiki/Squat_effect describing the effect.

    • Reply to bananabender56 ==> I have passed under those bridges many time[s], in both directions. The actual controlling factor is the Clearance Gauge mounted at water level under the bridge. It looks like this:

      It works because the board is set my by measuring down from the bottom of the bridge steel and setting the board at the right vertical level. Thus, regardless of the water level or tides, it always shows the correct distance from the top of the water to the bottom of the bridge. [typo corrections – kh]

      • Your example shows how much clearance is available on any given hour of any given day, and that of course is very useful (this simplifies the position where clearance is given in general with respect to chart datum and then assessed by reference to tidal information), but this deals with only half the problem since the air draught of a vessel is dependent upon the sea draught being drawn at any one instant in time, and herein lies the problem (which is part of the subject of your article).

        It is often difficult to measure the sea draught of a vessel accurately because of factors that you have mentioned but also parallax error, and again averages are often used when taking fore, middle and aft measurements (assessments/guestimates depending on sea state), on both port and starboard, and the bridge of a vessel is frequently not located where sea draught measurements are taken, and a ship may sag or hog either over time or because of the manner in which it is laden.

        This really impacts upon what is a safe tolerance

  14. It is certainly true that many have overstated the meaning of their measurements. rgb’s description of the CIMP ensemble averages is most apropos.
    I would like to make the point that we take care not to overstate the problem. At base, we can still measure things, and those measurements are real and can be useful. Also, we do not want to get carried away and reject measurements of derived quantities as imaginary, just because they are derived quantities. The CIMP ensemble averages are surely imaginary, in the context of this essay. The mass of a platinum cylinder most surely is not, even though mass is a derived quantity. (We say we measure mass as a more fundamental quantity than weight, but in reality, we usually determine the weight in a gravitational field.)
    {Please, no semantic warfare on the point}.

    • TonyL:

      You say

      I would like to make the point that we take care not to overstate the problem. At base, we can still measure things, and those measurements are real and can be useful.

      That presents three semantic assertions (although you say you don’t want a semantic argument).

      What statement of fact is “to overstate the problem”?
      What do you mean by “useful”?
      What do you mean by “measurements”?

      If the fact is stated then anyone can assess if the fact presents a problem. And if the fact does present a problem then it merely indicates the problem so it does not “overstate the problem”.

      An obtained datum may be “useful” as an indication of a physical reality, or as a propaganda tool, or as etc.. Some uses are only desired by the users.

      All climate data are estimates and NOT measurements. A measurement is a comparison to a standard. In times past the calibration standard was a variable (e.g. the calibration for a ‘yard’ was the length of the arm owned by the person doing a measurement). More recently approved calibration standards have been adopted. All climate data are estimates and NOT measurements because there is no possibility of a calibration standard for any of them. Furthermore, there is no agreed definition for most climate data so, for example, the estimates of global temperature alter almost every month because the used definitions are changed almost every month.

      These semantic issues are what the entire ‘climate change’ issue is about.

      Richard

      • I have seen arguments to the effect that there is no such thing as a temperature measurement, because what you are really measuring is the expansion of a liquid, and using that as a proxy. I find such arguments to be making a distinction without a difference at best, and disingenuous at worst. If left to themselves, sometimes people making that argument go on and claim that there is no such thing as temperature, because it cannot be measured.
        *sigh*
        For myself, I like the laboratory definition of measurement, which is to quantify a physical parameter.
        Consider a weather balloon: I would consider the instrument package to be taking measurements. The balloon was at a specific place, at a specific time, and recorded specific information. Once the data goes into some big pot of climate data, it probably gets used to estimate the properties of some volume of atmosphere. I would say that the balloon made measurements of the air and sampled the atmosphere.
        In short, one can overstate the case that we measure everything, just as one can overstate the case that we measure nothing, and therefore everything is an estimate of some imaginary quantity.

      • TonyL:

        Yes, as you say, a measurement is “to quantify a physical parameter”.
        But you are ignoring the fact that a physical parameter cannot be quantified without comparison to a reference standard. The quantification is a statement of how much more or less than the reference the measured item is.

        Your illustrations each make comparison to a reference standard or reference standards.

        Global climate data have no possibility of a reference standard and, therefore, they are NOT measured. And if you think this is unimportant then please explain why you think this is unimportant.

        Richard

      • TonyL

        I too find it very irritating when on an article say dealing with proxy reconstructions (or some such similar thing) someone suggests that temperature measurements are just proxies (since they are based upon expansion of liquid in glass, or some algorithm interpreting changes in resistance, current flows, voltage drops whatever) and then seeks to liken temperature measurements to the proxy under discussion. Or when the article is dealing with say computer models, someone starts arguing that temperature measurements are just models and then seeks to argue that models are useful. I shall not name these individuals, we all know who they are.

        I consider these arguments spurious when the manner in which temperature measurements are made is well known, understood, and rigorously tested and calibrated against known and accepted standards. Personally, I consider it makes the person raising the issue appear foolish, but it still irritates me.

        I am also not keen on a debate regarding semantics, but I consider that point being made by Richard is rather different. We do not have a figure for the average temperature of the globe, and there is therefore no reference. It would be all but impossible to ascertain the global average temperature, and as far as the temperature anomaly data is concerned, the anomaly is being ascertained against a reference which is not stable but constantly altering, eg., over time stations are added to the data set, stations drop out, some stations get polluted by UHI, some more than others, there is equipment changes and the like. We are never comparing oranges with oranges, so we do not know how things have in practice changed over time.

        I consider the temperature anomaly to be a meaningless entity, with no scientific usefulness.

        A couple of weeks back, I suggested that if someone wants to put out a data set as to global temperatures (temperature anomalies) as from 1880 to date, then that data plot should consist only of data being returned from the stations that were reporting data in 1880 and no others. Such for example, if there were 400 stations reporting data in 1880, and since then some 150 of these have fallen by the wayside such that there are only 250 stations which have continuous data going back to 1880 those 250 stations and only those station should be used. This will mean that the same spatial distribution will be consistent throughout the record. Of course sensible error bounds would have to be set out to take account of measurement errors, urbanisation, equipment changes and the like.

        If one wants to present data from say 1930 to date, one would identify the stations reporting data in 1930 and use only those stations which are still returning data today and which have a continuous data record stretching back the entire 85 years.

        One of the many issues with the thermometer data set is that the stations in that reconstruction are continually altering and disturbing spatial coverage and weighting. Back in 1880 there may have been a few hundred, it has peaked at about 6,500 and today it is down to less than 3000 stations. Whatever this data stream is returning, it is not anything meaningful because it is not a like for like comparison with any defined and accepted standard reference.

    • Reply to TonyL ==> I quite agree with “we take care not to overstate the problem. At base, we can still measure things, and those measurements are real and can be useful. Also, we do not want to get carried away and reject measurements of derived quantities as imaginary, just because they are derived quantities.”

      The point is more nuanced that “derived = imaginary” as I think you already understand.

      The importance of the central theme here is that one recognize when when one [corrected – kh] is creating or referring to, what I am calling here, an imaginary number so that the appropriate care can be taking in the use and application of the number to the larger, real world. And to recognize when the necessary care has not been taken with application or assigned inappropriate meaning or use.

  15. Very interesting – but does it really matter whether the numbers are imaginary or not? As long as they are useful. The Dutch noticed some numbers a few hundred years ago, didn’t fuss about the quality of their imagination; but realised that the figures were going one way – so simply built higher dams. And, in hindsight, we agree that was a wise decision.

    • Reply to Andy ==> What the Dutch noticed wasn’t numbers….but actual water levels, both inside and outside of their dike system. Perfectly valid, who can argue with reality?

      With the sea level question, for instance, it is actually experienced Relative Sea Level — where the top of the sea water meets the shore in this particular location — that is important. The imaginary quantity “rise in global average sea level” does not impact New York harbor at the Battery, as I have already mentioned. So, NYers don’t give a hoot about that imaginary number, it doesn’t hasn’t affected them in the slightest, as far as local relative Sea Level is concerned.

      • This comment is what you should have used as your post. Prior to that, I had no idea what your were driving at.

        I agree with TonyL and AndyE. Derived, “imaginary” numbers can have value. It’s just that people tend not to agree about when they do.

  16. What would be the reference datum for all these imaginary numerical distance estimates? The geodetic centre or Centre of Gravity of the Earth? No, I would say they are just as imaginary as the examples already given. Surely it is the mass or volume of water in the ocean basins that we seek to measure or define. Sea level is just another proxy chosen by the church of climatology to misdirect its followers into folliowing blindly.

  17. In every real pragmatic sense, they somehow derive a single number from a fabulously massive amount of data – data which in and of themselves are not direct measurements, but inferences of measurements made from other kinds of data.

    This is how digital audio works these days. When presented with a 16 or 24 bit digital representation of a voltage your stereo doesn’t convert that number directly to a voltage, that’s too expensive and inaccurate. Instead it converts it to a long fabulous massive stream of 1s and 0s (i.e. +/- 50% resolution), which the hardware then averages down to a nice high resolution voltage. That final voltage isn’t imaginary, it’s the beautiful sound of cymbals, snare drums, oboes, etc coming out of your speakers. The reverse operation works the same way in the recording studio, which is more analogous to what you are talking about. A long fabulous massive stream of 1s and 0s from a voltage comparator (note how poor that resolution is for each individual measurement!) is averaged down to a 16 to 24 bit number, 10s thousands or hundreds of thousands of times per second.

    A more simple way to put it is yes, nobody will notice 100mm of “imaginary average” rise during Hurricane Sandy, but if you wait several hundred years you will get several meters, and you will definitely notice that during a hurricane. Or you can start allowing deeper draft boats in your harbor several hundred years from now. This is analogous to your stereo – you can’t year the 40kHz signal, but you certainly can hear a 1Khz signal.

    I think you misunderstand the problem here. The problem is not averaging to get more accuracy – the resolution increases by 1/sqrt(n)*, that is a very well know statistical property.

    A real problem is that assumption is not entirely accurate if you have autocorrelated data (such as the height of various points in South Carolina, temperature, etc), or your data isn’t normally distributed. You didn’t address this real problem.

    Another real problem you hint at in the article above is that of extrapolation – extrapolating out to the future very small changes in your “imaginary” average is a problem because that imaginary average has error bars, and you have to multiply those as well, and like in investing the past doesn’t always indicate the future…

    In the end the article above does a disservice to our cause because it’s emotionally charged and mathematically unsound. Anyone with a good background in signal processing or statistics understands that averaging increases resolution of measurements, and the result isn’t imaginary, it’s used in all sorts of systems all over the place, such as your stereo. Or the fact that we know that average sea levels during the Ice Ages were far lower than today, or that the average ice extent was far larger than today. Those are very real things, not imaginary.

    Peter

    * I note for completeness that audio equipment doesn’t use strict averaging, it uses a feedback method that results in better than 1/sqrt(n) increase in resolution. I’m trying to simplify the terminology here…

    • I think the analogy breaks down at the point where you think of the two complete systems. Digital playback was developed to playback digitalised music. On the other hand “why was a global average sea level was created?” is an interesting question to ask and it really is essential to ask and answer before evaluating the utility of any attempt.

      Unlike decoding a digitalised audio signal we have a system that we know little about producing any signals we measure. It is quite possible that averaging actually destroys information for any particular application, rather increase it.

      • Yes, as I understand the problem: the signal to be processed (Peter Sable’s example is music) has an understood meaning. What I think Kip is asking is whether Mean Sea Level has a similarly coherent meaning. This is a separate issue from Peter’s excellent point about averaging.

      • What I think Kip is asking is whether Mean Sea Level has a similarly coherent meaning.

        Leaving aside the problem that Kip attempted to answer this question in a mathematically incoherent manner, it’s a good question.

        Taleb has addressed some of these problems in The Black Swan and other writings. If you have a skewed distribution with a lot of outliers then the mean is… mostly meaningless. (also the std deviation for that matter). In our case the mean sea level change of 100mm is irrelevant in the face of 3000mm of storm surge. However a mean sea level change of 3000mm IS relevant in the face of a 3000mm storm surge.

        The CAGW-ists are projecting thousands of milliimeter changes off of very small 10s of mm changes. (same with temperature/C02 relationship as well). That’s probably wrong. It’s good to point that out, but the argument needs to be mathematically coherent, not, well, imaginary.

        If Kip had argued that very small changes in mean are meaningless given the other wide variations, and that projecting off of those small changes in mean is fraught with statistical peril, that would have been a good argument. But that’s not what he did. What did instead was basically condemn all attempts to simplify large amounts of data down to simple understandable numbers.

        Peter

    • The whole claim that the oceans are rising at an accelerating rate is based on the numbers that you casually dismiss as being not that accurate.
      We do know that over the last 20K years, the oceans have been rising, because we can see the results.
      Whether this rise continues at the historic rate, has increased, or decreased is impossible to say using only a few years of the kind of data we have now.
      I agree, in 100 years, we will have enough accumulated data to make a more definitive statement.
      So until then, chill out.

      • Whether this rise continues at the historic rate, has increased, or decreased is impossible to say using only a few years of the kind of data we have now.

        I agree.

    • Reply to Peter ==> Your analogy is faulty — as it does not deal with measurement but with encoding. I have been a professional cryptographer and the process of encoding sound frequencies as digital information and then decoding it again as analog sound is not similar at all to the process involved in converting satellite data to distances to sea levels of an undulating, never still surface to averagings of the “seven seas” over 2/3rds of the surface of the Earth and then claiming an accuracy of 3 to 4 mm.

      ” Anyone with a good background in signal processing or statistics understands that averaging increases resolution of measurements, and the result isn’t imaginary”. I am afraid you are making the statistician’s error” when you say “averaging increases resolution of measurements”. That is only true if you are averaging more than one measurement of the same thing at the same place at the same time. Averaging different measurements of different things at different places at different times produces only more apparent precision.

      We know this : “Or the fact that we know that average sea levels during the Ice Ages were far lower than today, or that the average ice extent was far larger than today. Those are very real things, not imaginary.” not from averages of averages of averages but by physical evidence that shows that sea levels were far lower in lots of places in the past. Don’t confuse real knowledge from the production of what I am calling here, in this essay, and only in the sense I have fairly clearly (I hope) defined, imaginary.

      • That is only true if you are averaging more than one measurement of the same thing at the same place at the same time.

        That’s not true of delta sigma converters I was referring to.. Each sample of 0 and 1 is done at a different time. It’s just done so close together it doesn’t matter after decimation rate of say 100,000. Same thing with hourly tide measurements… after 30 years it doesn’t matter that there was a little change every hour. There is a mean change you can look at that is meaningful (at least for relative sea level there is). Same thing if you want to talk spatially instead of time. That math for this is graduate level math, but it’s well known in several fields of engineering (alas, not by climate scientists however, Mann’s hockey stick was partly due to complete ignorance of signal processing theory and practice).

        the process involved in converting satellite data to distances to sea levels of an undulating, never still surface to averagings of the “seven seas” over 2/3rds of the surface of the Earth and then claiming an accuracy of 3 to 4 mm.

        I have not looked at the process involved for the satellite measurement of sea level. You may be entirely correct that that satellite measurement of sea level is bad metrology. I don’t believe traditional tidal measurements by buoys and such is bad metrology though, it’s pretty straightforward stuff.

        My problem with this article is you munge a bunch of stuff together that is correct, incorrect, and don’t address when averaging is actually correct. It makes for a bad rhetoric style and bad teaching style, because it’s too easy for those opposing your arguments to refute them.

        I’d love a clear written article into the problems of satellite measurement of sea level, by itself.

        If I’m going to condemn Mann for bad signal processing technique, I’m going to condemn our side probably even more so. Such is the nature of engineers.

        Peter

      • Got up this morning and was about to respond to Dave Canmore in similar terms when I noticed this comment further down making the points I was going to make.

        In thinking about global sea level it is possible that we are hypothesizing that sea level at any point in space and time is a (say) linear function of a time independent locational anomaly (that sums to zero across the globe) and a common global time dependent variable (GSL(t)) plus noise of some kind.

        This is how GSL tends to get used – we estimate it from history, do a projection, then use the inverse function to calculate a projection of SL at a specific point of interest.

        It is better to explore the accuracy and utility of this kind of underlying model as an assumption in these kinds of uses, and the extent to which it is statistical well behaved.

        If you do I think you quickly get to the point where you realise this simple linear model is inadequate to the task and simple statistics not much use. This is doubly so since most users are interested in the risks in projected sea level rise, and risk is uncertainty and uncertainty means the second and third moments of the projected distribution are as important as the first.

      • My comment was in response to Kip, Peter posted while I was typing.

        To Peter I’d just add to my comment above and note that you need to get the model you are fitting sorted (whether over time or over space) before you can assert how things will behave with more information.

      • To Peter I’d just add to my comment above and note that you need to get the model you are fitting sorted (whether over time or over space) before you can assert how things will behave with more information.

        Absolutely agree. I’ve played with autocorrelated-in-space monte carlo simulations. There appears to be some constant multiple related to how the 1/f noise rolls of that you have to multiple by 1/sqrt(n) to see the increased resolution (for global temperature the constant appears to be 2.5x).

        There’s also this intriguing article that says for some spectral shapes of noise, it’s not just a constant multiplier – there is no convergence in some cases – you DON’T get improvement with sample size. Darnit, I can’t find the reference. It was in relation to a metrology standard (I think the platinum bar metre standard). Hope I can find it again.

        Here’s some other references on this topic though:

        https://statistics.stanford.edu/sites/default/files/EFS%20NSF%20476.pdf
        http://wwwf.imperial.ac.uk/~ejm/M3S8/Problems/beran92.pdf
        http://journals.ametsoc.org/doi/pdf/10.1175/JCLI4291.1

        The article above doesn’t do any of this analysis, it just casts a wide emotional net on any attempt to summarize a big data set down to a few numbers, which is mostly my gripe with it.

        Peter

  18. Just to make it even more complex, seawater densities vary and lower density water floats on denser water raising local sealevels but without affecting the level at the coast (just like ice in your g&t!).

    • Just to make it even more complex, seawater densities vary and lower density water floats on denser water raising local sealevels

      Is there a plausible mechanism for the locations moving with a period on the order of 30 years? If not, then it won’t significantly affect a trend calculation.

  19. The averages over a region, country or globe has realistically no meaning or use. Basically because the meteorological parameters are highly local and region specific. When put them in a box, it neither reflect the individual locations or regions. For example the Atlantic Ocean temperature natural variability present an opposite pattern. When I look at natural variability in precipitation, I fit to station data then try to understand the homogeneous zone for which this natural cycle of the single station applies. This is exactly what I did for northeast Brazil. This way we can identify homogeneous zones to relate agricultural aspects or agroclimate, etc.

    All these global pronouncements are really not of any use to local or regional level planning as announced by UN, US President, Pope Francis, etc. and finally the Parid draft. This only help them to collect 100 billion dolars and share them.

    Dr. S. Jeevananda Reddy

    • Dr. S. Jeevananda Reddy October 10, 2015 at 1:01 am

      The averages over a region, country or globe has realistically no meaning or use. Basically because the meteorological parameters are highly local and region specific. When put them in a box, it neither reflect the individual locations or regions. […]

      Thank you, Dr. Reddy. I was going to make a similar point except I would have used three times as many words and they would have been garbled beyond understanding. I’d only add this useful reminder of the Koppen Classification System.
      http://meteorologyclimate.com/koppenclassification.htm

      • I keep on making this point since it seems to be constantly overlooked, namely that climate is regional. On the timescale that we are talking about there is no such thing as global climate (on a global scale the climate is that of an interglacial, in the longer time scale it will almost certainly become glacial).

        Further, climate is the combination of a number of variable parameters each one of which is never in stasis and each is continually varying between bounds. Temperature is but one of the multivariate components.

        Since climate is dynamic, and the component parts are never in stasis but instead constantly varying, the change of any one parameter (at any rate not beyond the bounds of natural variation) is not climate change, and change in and of itself is not even evidence of climate change. That is simply what climate is and what climate does.

        Climate and its natural bounds in relation to any given region has to be viewed over a substantial period of time probably over a multi- centennial time frame, and one of the fundamental errors is seeking to evaluate climate over a 30 year time span.

    • The averages over a region, country or globe has realistically no meaning or use.

      So the fact that the average global sea level was so low that ~15k years ago that allowed humans to navigate the land bridge between Asia and North America has no meaning? Or that the ice had retreated on average far enough for this to happen?

      Or are you arguing against gravity that it’s possible that only the arctic ocean was low enough to allow such a passage? Yes, this is absurd, but so is a blanket statement about global averages having no meaning.

      A more accurate statement would be “at changes smaller than some number there is no realistic meaning in changes in global averages”. The debate is then – what is that level? I hope we can all agree that 30 meters change in the average would have meaning, right? We can also probably agree 1mm is meaningless. Somewhere in between is the statistically meaningful change point.

      Peter

  20. There are other factors to consider when measuring sea level as well – like land subsidence, but we all know that here….I don’t know how that would work into the numbers, but I think a global average of sea level would probably be as meaningless as a global average temperature – it won’t flood anything any more than a global average temp would melt anything. Neither are “real” – they’re statistics. :)

  21. Interesting.
    Trouble is there are five “averages”,- Arithmetic mean, geometric mean , harmonic mean, median and mode. Take your pick to show which alarmist claim is apt at the time.

    • johnmarshall:

      Actually there are an infinite number of different averages.
      For example, there are an infinite number of possible weightings that can be applied when obtaining a weighted average.

      This matters because the providers of average global temperature data sets change the definitions of ‘average’ that they use almost every month with this resulting effect.

      Richard

      • And this means that there is no assessment against a fixed and accepted reference point. The reference against which the so called anomaly is being calculated is itself constantly changing.

      • Mr. Verney
        At least on that point I am in a complete agreement with you. I spend lot of time ‘messing’ with the CET and always show it with full Centigrade scale, and not as an anomaly, similarly with N. Atlantic SST. When data is de-trended than it fluctuates around zero, but that is an abstract concept of the ‘real’ data.
        Even graphs with proper temperature scale as this one from NOAA should avoid the ‘colour by numbers’ tendency. I have no idea why global temperatures below 57.6F are considered cold, and those above warm, or even more ridiculous that temperatures below CO2 concentration of 330ppm are cold and those above are warm.
        Perhaps someone can explain.

    • Even when selecting the best “average” the final point may be totally wrong. Consider a circus knife thrower. We know from observation that his beautiful assistant rarely receives as much as a scratch, but by averaging all throws he needs a new assistant for every performance. The use of statistical techniques that are not valid (which I am starting to feel is most of the time) gives a totally false impression.

    • The trouble is the law of large numbers. Everything has to be perfect but people ignore this. If using the median instead of the mean gives you a different result, then millions of measurements to the nearest inch (altimetry) will not make an inch increase in a decade meaningful.

      With regards to people’s heights, would you take drastic action if by sampling 1% of the population to the nearest cm that you found heights were increasing 0.1mm/year for the past century? And then you find that an algorithm was used to decide that some were wearing high heels many years later, and the adjustments correlate better with consumption of milk (which is causing this) than is the actual increase in height.

  22. This gets only worse when we add in the information that both the dry land itself and the bottoms of the oceans, almost everywhere, are also in vertical motion and busy changing the volume of the ocean basins.

    It gets worse when you add water extraction from underground that ends up in the oceans. What about water held back by dams?…………Decelerated. See links for water abstraction and dams.
    http://dx.doi.org/10.1029/2010GL044571
    —–
    http://onlinelibrary.wiley.com/doi/10.1029/2012GL051230/pdf
    http://dx.doi.org/10.1029/2012GL051230

    Bottom lines:
    • Sea level has been rising since the end of the last glaciation.
    • In the last few thousand years it has been flattening.

    • Jimbo @Oct 10 at 2:14 am The graph of sea level rise gives me pause. It seems the intent is to draw the viewer to the insert of the graph showing the sharp rise over the most recent period. However, there doesn’t seem to be any real change in the curve when you look at the longer time scale. Is there was a graph to show the last 6 or so thousand years at the same resolution as the insert? It might be quite telling. Is the sharp rise really something new or is it more par for the course as it were?

  23. Kip Hansen:

    Thankyou for your important essay.

    As I explained in my above reply to TonyL the subject of your essay is what the entire ‘climate change’ issue is about.

    Examples are the impossibility of measuring global values for sea levels and temperatures.

    As the late John Daly succinctly stated in is excellent article on sea level that I have linked

    an observed quantity ± a modeled quantity = a modeled quantity

    Richard

    PS
    I, too, have some experience of the ocean having lived on a boat for the first five years of this century.

  24. Interesting discussion, but defining “imaginary numbers” this way in a scientific discussion adds nothing whatsoever to understanding.

    I am skeptical about global climate alarmism but that does not make me accept the idea that real physical phenomena are imaginary. Rather I am skeptical because I believe the level of uncertainty in the science is still to high for me to accept that human activities are sufficient to overcome the internal and external climate variability that results from natural processes.

    Global sea level is a conceptual artifact because the geoid itself is irregular. Local sea level changes for many reasons and may differ from global variations because of plate movements both vertical and and lateral. Americans may not be aware that post-glacial rebound is still affecting local sea level in the northern Atlantic states.

    Estimating the average increase / decrease in sea level compared to some historical mean value is more or less how global sea level change is calculated. Afterwards you need to adjust for a lot of things: water lost by inland water bodies (Aral Sea and the Ogallala Aquifer), water impounded by dams, and water lost/gained by growing and shrinking glaciers. The residual ought to be the rise in sea level resulting mostly from expansion by warming of the water. There may be an increase or decrease as a result of ice formation on land.

    Finally, you estimate of the increase in ocean heat content based on the expansion of water in the oceans and compare this with other estimates of ocean warming.

    Best of luck when you claim precision after so many adjustments based on models that use multiple parameters. I am not convinced that global sea level is a useful metric for anything.

    But imaginary?

    If the result is imaginary then the increase in average height of Americans between 1776 and 2015 would be imaginary. Mixing white paint and red paint would give imaginary pink.

    But there is nothing imaginary about either of these examples, though it may be difficult to quantify the resultant physical states with any degree of precision.

    Was the post-glacial rise in sea level of 120 meters (400 feet) or so also imaginary? Some of the rise was from melting ice. But some was from expansion of water as the oceans warmed, the same phenomenon that scientists try to estimate today.

    The term “imaginary” is pejorative when applied to real phenomena. It implies that the phenomena do not exist.

    Instead, it reveals a fundamental misunderstanding of geophysical processes..

    The scientific term we want is “uncertain” not “imaginary”. That is why we use error bars when we calculate values for physical quantities. I give an example below including hints on how to read a scientific paper.

    When there is uncertainty, there is often “empty precision”. We often see too many significant digits indicating that the author has not taken into account the effect of the arithmetical operations. But in the extract quoted the author points out that the energy balance estimate at the top of the atmosphere is problematical because it is a small number derived from the difference in two relatively big numbers (energy in minus energy out). Spot on.

    In the following extract we learn that the authors estimated the average increase in ocean heat content (OHC) as 0.6 +/-0.4 watts per square meter, which means as high as 1.0 or as low as 0.2 Wm-2 (watts per square meter). They also stated that the uncertainty in the satellite measurements of net energy imbalance at the top of the atmosphere (TOA) is more than 10 times bigger than the estimated increase in OHC.

    (One order of magnitude = 10 times. “Watt” is a measure of power. Watt-hour would be a measure of energy flow.)

    Unfortunately many authors (and the IPCC) are not as forthcoming about uncertainties as the authors of the paper I cite here.

    “The net energy balance is the sum of individual fluxes [at the top of the atmosphere]. The current uncertainty in this net surface energy balance is large, and amounts to approximately 17 Wm–2. This uncertainty is an order of magnitude larger than the changes to the net surface fluxes associated with increasing greenhouse gases in the atmosphere (Fig. 2b). The uncertainty is also approximately an order of magnitude larger than the current estimates of the net surface energy imbalance of 0.6 ±0.4 Wm–2 inferred from the rise in OHC.” [Words in square brackets added.]

    Source: An update on Earth’s energy balance in light of the latest global observations. Stephens and others. Nature Geoscience, 2012

    When I read papers such as this one and others by the same authors and their colleagues, I conclude that the scientific community still does not have much of grip on what is happening to the global climate.

    The null hypothesis seems to me still to be viable: observed temperate variations may have been caused mostly by processes that are internal to the climate system, such as redistribution of ocean heat content by oceanic oscillations. Man’s impact may be almost entirely due to land-use changes during the last 300 years.

    • +1
      Very good comment, and cuts to the heart of the issue.

      Yes, there is a lot of uncertainty in the calculated rate of MSL increase, and yes, that varies by location. Yes, the sea level has been rising since the last ice age. But none of that means that substantial rises might not take place IF warming were as great as the GCMs project. The current average rate of rise (near 3mm per year against an isostatically stable shoreline) is not at all alarming and would not be worth worrying about very much. But like all projections in climate science, large future increases (multi-meter increases within 100 years!) are based entiredly on projected temperature increases from GCMs, along with violent arm waves, hysteria, and crys of “it’s worse than we thought”. The model projected temperature increases are treated by climate scientists as if they were real, when those model based projections are indeed ‘imaginary’, and almost certainly wrong. Seems to me the real argument is not with measurement based sea level estimates, but with wild-eyed projections of future warming…. which are already clearly divergent from reality. Measurement based sea mean sea level estimates are not the problem at all.

      • Reply to Frederick Colbourne ==> I am not sure if you are misunderstanding intentionally for rhetorical purposes or if you just plain misunderstand.

        It is the single NUMBER that is imaginary, not the physical thing, and the number is only imaginary in the narrow sense of the central theme of this essay.

        Paint colors are physical properties and can be easily measured with agreed upon metrics — there are many color standards to choose from — and a slew of standardized instruments to perform the measurement. Heights of American citizens over time can be recovered from historical records which contain the actual physical measurements of real people, thus average heights at one time period can be compared with average heights at another time period without resorting to creating what I have called here an imaginary number.

      • Sorry Kip, but I think you are spending a lot of time and effort advancing an argument which is irrelevant. The real questions are: How much future warming will there be? How will that warming change sea level via thermal expansion and melting of land supported ice? There is nothing imaginary about estimated mean sea level from tide gauges and satellite altimetry; there is some uncertainty, yes, especially in the short term (less than a few decades). But unless you believe warming water does not cause thermal expansion, or that adding to the total quantity of water in the oceans does not raise the average level, then the suggestion the resulting increase in level is ‘imaginary’ seems to me silly.

      • Reply to Steve Fitzpatrick ==> You are possibly making the mistake that so many commenters here and on other sites that discuss climate related topics make — the mistake is thinking that everything, every fact, every number, every essay, every word must be considered and responded to only in the context of The Climate Wars.

        This essay is not about the Climate Wars — this essay is about something else.

        By the way — in my own synopsis (in the Author’s Comment Policy section) I state (quite clearly I thought): “This essay is not really about global sea level, but I doubt we’ll be able to discuss it without also touching on the issues surrounding the issue of global mean sea level.”

        You see, you are playing the wrong game here.

      • Kip,
        Fine. But your essay is not about sea level, then it seems to me irrelevant. Sea level matters; this essay doesn’t.

    • Physical properties are real.
      The numbers that we use to measure those physical properties can at times be mostly imaginary.

    • Frederick:
      “The scientific term we want is ‘uncertain’ not ‘imaginary’.”

      I totally agree. In my view all measurements are really estimates. However some estimates have much greater uncertainty than others. I tend to think of measurements as those estimates that have a high degree of certainty. Mean global temperature and global mean sea level are very abstract ideas with complicated derivations that thus imply great uncertainty in my view. In regards to mean sea level, what really matters most for most human activities is the mean sea level in coastal areas and not in the middle of the ocean. Thus for looking at impacts on human endeavors, our best mean sea level estimates derived from coastal measurements are more appropriate than satellite derived estimates covering the entire surface of all the oceans.

      • Reply to oz4caster ==> It is not just that they are “uncertain”…. it is that these types of numbers do not actually represent something that can be found in the physical universe or that can be actually measured — they are rather derived from massive amounts of data, averages of averages of averages, reduced to a single number of great precision and then treated as if they were simple measurements — which they are not — of some actual physical property of the world — which they are not. I have been careful to confine the use of the term imaginary number to this one sense for the purpose of this discussion.

        Of course, imaginary numbers are also hugely uncertain — in some cases, the existence of the property alleged to have been measured itself is uncertain.

      • Kip, thanks for the reply. I understand what you are saying, but I don’t think using the word “imaginary” is the best choice of words because it is likely to cause more confusion than not. I would call “mean sea level” a theoretical concept. And yes, in a sense, it is an imaginary number. But most people think of “imaginary” as fiction which is not really appropriate in this case. Hence the potential for causing confusion that is not necessary.

        That said, the mean global temperature anomalies based on massively adjusted GHCN measurements are beginning to look more and more like fiction invented to push an agenda.

      • Reply to oz4caster ==> Mean Sea Level, at a particular place, is a very useful datum. I tired to make this clear.

        It is the in-a-sense imaginary “global mean sea level” that is the issue — how it is derived, the accuracy claimed for it, and how this marvelous “single number” for a vast dynamic system is being applied.

        I have no apologies for my use of the words imaginary number. Others may prefer something else, it is the concept that is important. (As an author, one has to pick something — this is just an essay afterall, I’m not defining a new scientific field of study.)

      • The use of constructs derived from large and complex data sets is common (think of a whole range of indices used in economics).

        These are not problematic per se, or per the fact they are constructs rather than more direct measurements.

        The issue is whether they are useful or not, and in particular whether they are fit-for-purpose.

        As I’ve noted above this can only be decided by looking at why the construct was created and how well it performs.

  25. When I was young I was taught to be in awe of Academia. It was a state of higher being, or a place of wonderment, or a coddling home for life. So when I went out into the oil fields and the oceans at 17 to earn a crust instead of entering this higher plane of existence I was slightly jealous of the perceived benefits and kudos, the letters after the name, the titles etc.
    I did not realize back then the sacrifices that academics had to make. What a terrible operation it must be to have your common sense surgically removed. The agony caused by the insertion of the socialist morally superior conscience implant. The genetic engineering of the conformity gene, no doubt extracted from a sheep and implanted in the spine in tandem with the yellow streak. Then the modification of the voice box and trachea to enable one to talk absolute rubbish about global climate and not actually choke on it.
    I truly realize now the sacrifices that I would have had to make to reach that pinnacle of humanity, the Phd climate scientist and how lucky I was to be allowed to go and get chucked about on a rig boat in the North sea. That really does give you a good grip on reality.
    Believe me, when I say that the CAGW meme is utter claptrap it comes from a much firmer grip on reality than 97% of the population of Academia can ever grasp.

    • Ivor,

      Well said. Well written. Sounds as if you got a fairly good grip on intelligence outside of the “must be paid for” letters before and after your name.

  26. I have to say this is a muddled essay, and I didn’t really like it. For reasons I am struggling to express.,

    Firstly it is vaguely anti-science and anti-mathematics. Like much of the AGW outpourings it pretends to belittle a science it doesn’t really understand with appeals to ‘common sense’ (instead of ‘97% of scientists’ etc).

    Secondly, the author appears to suffer from an extreme case of Rational Materialism. He thinks there are ‘facts’ and there are ‘models’ and never the twain shall meet.

    The only remedy will be to complete my essay ‘models all the way down’ and present it for publication, but in essence it makes the case that it is more rational (if less materialistic) to regard the world as we can know it as almost entirely constructed of models.

    As an amateur philosopher of amazing persistence, if not perspicacity, I am deeply worried by anyone who claims to have discovered the One Truth, since I can honestly say that the only One Truth I have ever found is the proposition that the One Truth may well exist, but it will forever be unknowable.

    This is of course a very post modern position on knowledge, and has been taken by the third rate brains that infest the Liberal Left to mean that since the ‘Truth is a Social Construct’ any old crap will do and as long as people believe it, it is the Truth. Welcome to the IPCC.

    However, as Orwell might easily have remarked, ‘some Truths are more Truthful than others’ and we need to understand, to counteract this post modern mishmash of ‘equivalent ideas’ with a healthy dose of Reality. Reality is what makes some Truths more truthful than others. Reality may be unknowable, but it hasn’t ceased to exist, we posit.

    Now if you have followed these rambling to this point, wondering what on earth the point is, it is this.

    All knowledge and facts depend on a previous (a priori) metaphysic. Reality, we presume, is there somewhere, but what we experience it as, is constrained by our ability to render it into stuff that we can both talk about and think about, and finally do sums about and make theories about, and so we construct a story in space-time comprising Matter/Energy, Causality and Physical Laws. Etc.

    My beef with the rational materialists who call this construct reality, is that it is not, its just the best model we have come up with so far.

    My beef with the post-modern Trotsky-ite anti-scientists, is that they conclude that just because it’s a human construction, it has no more validity than any other human construction, implying in fact that Reality does not exist, only the models. And whatever we believe can become the truth. Which is essentially Magick of course.

    Yep. The Left believes in Magick.

    Now of course belief is a free choice. :)

    You can believe all manner of arrant nonsense, and if somehow it doesn’t kill you before you produce offspring, it can persist. Adherence to sanity is not a Darwinian prerequisite, and indeed if you dont have to be mad to live here, it certainly helps…There is no intelligent life on earth because frankly, its not that useful a quality..

    In a post modern post industrial world where no one is actually working on creating wealth or maintaining the infrastructure at all – just a bunch of machines and a few instantly dismissable geeks – As with Rome, we have the elite, the slaves to do the actual work, and the plebeians provided with bread and circuses only. What matters in such a society is the ability to entertain, to dissemble and to construct the sorts of narratives that get you into positions of political power.

    Welcome to the 21st century.

    Where the truth, relative to context as I have outlined, is no longer needed by anyone, since no one – apart from the few geeks aforementioned, needs to actually deal with Reality at all. The rest live in a post modern (sub)urban bubble that reads like a Jane Austen Novel. Work is not an issue, only social ideas, morality and the interplay of human relationships.

    The world of Convenient Lies.

    However this is a geek site, and therefore we have to apply the geek context. It is relatively true to say oceans exist, because we may sail upon them: it is relatively true to say that the concept of sea level has some meaning because the Rockies are not submerged, whereas the Marianas trench is. Ergo sea level may be presumed to lie somewhere between the two, and therefore it has some kind of bounded value and the best technique we have to assessing what that value is in a time and spatial invariant way, is by taking the average of a time and spatial series and averaging them. And if different sets of such measurements taken over different time periods show a rising trend with time (whatever time actually is, of course) then, within the context of rational materialistic interpretation of reality into the ‘physical world as we all know it’, we can make statements like ‘global sea level is rising 3mm a year’ and that has some meaning. And relative to the models and methodologies used to derive it, it is relatively true, and even has some kind of correlation with observer effects in Reality. Whatever and wherever that may be.

    So I cannot stand by and let this post pass. No, just because the context, the way the measurements are done, and the way they are adjusted may shed uncertainty upon the value of sea level rise, it does not invalidate the concept of sea level rise.

    That game is the anti scientists game. It belongs in the touchy feely realm of post modern ideological egalitarianism (“all ideas are equal, and are only opinions, until 97% of people believe them, when they become facts”).

    In short if you are going to regard the world as a rational materialist does, that that touch feely stuff is in fact Reality and has an independent existence that is quite unconcerned about whether people believe in it or not,…then measuring it cannot be an ideological mistake, and just because its hard to measure, doesn’t mean it doesn’t have size.. We cannot say ‘sea level has no meaning’ when we can go to the beach and watch the tides come in and go out and realise that that is in fact what sea level is, and does. And if year upon year it seems to come in a bit further every year, then we can surely say the sea level is rising… and if other people elsewhere in the world report similar, then we can give meaning to the phrase ‘global sea levels are rising’. And indeed try and put some ‘value’ on that rise, and rate of rise.

    Whether our values are accurate, and whether the rises are alarming or not, and whether or not there is a casual linkage to man made emissions, is another matter. But we are not disputing that, here. We are disputing the innate validity of measurement itself…

    …And that way lies ruin and the complete disintegration of any semblance of lip service to Reality beyond human conception of it.

    You have to decide, punk, whether the world exists independently of our attempts to conceive of it and our experience of it, or whether its all just a ‘social construct’.

    And if it does exist, and has – or at least we can say that the best way to conceive of it it – is that it has the qualities of size, shape, quality, persistence in time, causality and the like, then measuring it may be fraught with inaccuracies and uncertainties, but it is not per se an invalid thing to do just because we cant achieve 100% accuracy or certainty…

    • Leo Smith:

      You say

      I have to say this is a muddled essay, and I didn’t really like it. For reasons I am struggling to express.,

      I have to say yours is a muddled comment, and I didn’t really like it. For reasons that are easy to express; for example, your comment concludes saying

      You have to decide, punk, whether the world exists independently of our attempts to conceive of it and our experience of it, or whether its all just a ‘social construct’.

      And if it does exist, and has – or at least we can say that the best way to conceive of it it – is that it has the qualities of size, shape, quality, persistence in time, causality and the like, then measuring it may be fraught with inaccuracies and uncertainties, but it is not per se an invalid thing to do just because we cant achieve 100% accuracy or certainty…

      You have to understand that:

      (a) when there is no agreed definition of a physical parameter
      and

      (b) there is no possibility of a calibration reference for the parameter
      then

      (c) there is no possibility of measuring the parameter.

      Anything done to quantify the undefined and calibration-free datum provides – at best – a meaningless estimate with accuracy, precision and reliability that cannot be known.

      Richard

      • I agree that the comment was almost a rambling as the article but it did see more coherent. At least I got to the end of Leo’s comment with skipping. At least a little philosophy is in order.

        There is a certain reality is tidal gauge measurements since they relate to when things get wet. The main concern with sea level is whether is above where we live. We don’t really give a damn about isostatic glacial rebound and inverse barometers. whichever way they “correct” the data. What we need to know water is.

        At least there is some ground truth in a tide gauge.

        Satellite altimetry is another game entirely. There are so many models, assumptions and adjustable parameters involved in ‘retrieval’ of the mean water level in a 2m swell by looking at the reflection from the bottom of the waves that you can make the result just about anything you believe to be reasonable according to your preconceived expectations.

        There have been such wholesale “corrections” to various satellite data in order to align them and then all the earlier data is hidden away from view so no one sees the real uncertainty of those who declare themselves to certain of their latest results That I have little faith in any of it.

        Rather like the shifting history of temperature time series, all these records are being manipulated to give a ‘homogeneous’ story to the public and policy makers.

      • Dahlquist:

        And your comment states what you are. Hopefully I will not have the unpleasant task of removing you from the instep of my shoe.

        Richard

      • I consider the issue here to be:

        “…we can make statements like ‘global sea level is rising 3mm a year’ and that has some meaning. And RELATIVE TO THE MODELS AND METHODOLOGIES USED TO DERIVE IT, it is relatively true, and even has some kind of correlation with observer effects in Reality. Whatever and wherever that may be.” (my emphasis).

        The problem in Climate Science is the Models and Methodologies used. They do not provide us with some identified absolute and unchanging standard reference, against which measurement can be assessed.

        Often the measurements (or derivation therefrom) are meaningless, or nearly meaningless, or not useful because they are not being made against a proper defined standard reference, and therefore are not telling us some of real substance.

      • Yeah, I think that pretty much sums up what I was trying to say. Sometimes you realise that someone’s worldview is simply in doublethink mode, trying to have cake and eat it.

        Usually its AGW protagomists, with their use of science in the same sentence as they deny it.

  27. I find the measurements/estimates of sea level interesting. Not the exact numbers, but the ups and downs. I think it is two benchmarks on global temperature change, and that is ocean heat content and sea level. These two follow each other close. So I think that the sea level estimates is not that wrong. As a tool to understand climate change i would have much more trust in sea level change than what comes out of climate models. So if we use a rise of sea level of 3.2mm pr century for the lasst ten years, that is perhaps the imaginary number we need to reflect on what is happening. What matters is to nderstand climate dynamics, and what measurements or estimates that can help us with that. It is all about energies in and out of the oceans, and in and out to space. I think that sea level proxies are very important in relation to climate history, and also difficult to estimate. Should we give this up?

    • And it should be 29 cm sea level rise between 1750 and 2014, with a rate of rise that shows that much of temperature rise cannot be man made since preindustrial time. This would be much more uncertain without Amsterdam tide gauge measurements and other historical data. Don`t throw out the baby with the bath-water.

    • Let me see if I have this right. You admit that the actual numbers are hard to gather, so you believe that well meaning scientists should instead just estimate what the numbers should be.
      And that since these estimates confirm the biases of the people making the estimates we should then use these estimates to confirm the estimates that other scientists in other areas are making and that these re-enforcing estimates can prove that global warming is a problem that we need to do something about?

    • Reply to nobody ==> Yes, the ups and downs are interesting…I’m not sure what you are asking though….Should we give [what?] up?

  28. Frederick Colbourne:

    You say

    Interesting discussion, but defining “imaginary numbers” this way in a scientific discussion adds nothing whatsoever to understanding.

    I am skeptical about global climate alarmism but that does not make me accept the idea that real physical phenomena are imaginary.

    I don’t know of anyone who is claiming “real physical phenomena are imaginary”.

    The discussion concerns the “numbers” that are claimed to indicate the magnitude(s) of real physical parameters. Those ‘numbers’ are highly uncertain estimates but are falsely asserted to be measurements with known accuracy.

    For example, much information (crop changes, glacier retreats, etc.) suggests that global temperature has risen over the last century, but the claims that this has been measured as being a rise of 0.8°C are not true. Calling that value of 0.8°C an “imaginary number” helps understanding that it is NOT a measured value.

    Perhaps you would prefer ‘imagined number’ to avoid confusion with the mathematical term ‘imaginary number’?

    Richard

  29. Dear Kip Hansen and Anthony,

    It’s getting closer to the Parisites’ Sing-along-abama-Festival when all persons attending will use OPM (other people’s money) and direct that money to their own bank accounts AND …we know that the entire charade is based upon carbon-dioxide !

    Q. Are We Chasing Imaginary Numbers?

    A. No; “We” are not but yes, “they” are.

    Your essay Kip Hansen is absolutely spot on !
    Many thanks indeed.

    Many people have gone to the trouble of debunking common myths and here are just a few of them (and I haven’t even included the splendid words of dear Alan Caruba from 21st. April 2015).

    11th. September 2015 – WUWT article. THE PAGES2K GOAT-ROPE
    QUOTE
    “But that’s just what they claim that they’ve done. They’re claiming that it’s simple, all they have to do take those crazy results from those six oceans, standardize them, take a weighted average based on the area of the ocean in question, and presto, they come up with the global ocean temperature history for the last 2,000 years …I say that’s dumb as a bag of ball bearings.”
    END PARA..
    (The Pages2K Goat-Rope Willis Eschenbach / September 11, 2015 Guest Post by Willis Eschenbach).

    23rd. April 2015 – cFact article. FINANCING CLIMATE CRISIS, INC..
    QUOTE
    “The Obama Administration is using climate change to “fundamentally transform” America. It plans to make the climate crisis industry so enormous that no one will be able to dismantle it, even as computer models and disaster claims totally lose credibility — and even if Republicans control Congress and the White House after 2016.”
    END PARA..
    – cFact article by Paul Driessen (senior policy advisor for CFACT).
    – See more at: http://www.cfact.org/2015/04/23/financing-climate-crisis-inc/#sthash.zzMPhxII.dpuf

    29th. August 2015 – Propaganda Guard article.
    “GLOBAL TEMPERATURE IS A MEANINGLESS STATISTIC.
    – Propaganda Guard article by Micheal Winston and “blogged” by Robin Rey R. Shaw
    http://ift.tt/1O0Mbc0

    … the bottom line is …

    It’s all a complete and utter NONSENSE and is based upon the MYTH that carbon-dioxide is bad. It’s the biggest con, hoax, money-re-routing scam the world has ever seen, or rather, has NOT been ABLE TO SEE.

    I fervently hope that all WUWT readers will be given the opportunity and facility to contribute their money to help pay for the myth-busting film when it comes out.
    We should then all be privileged and also have the honor to “put our money where our mouths are”.

    Regards,
    WL

    • Dear “Moderator”,

      Why did my reply (above) need to go through your approval ?

      WL

      [Reply: WordPress often (but not always) puts comments into moderation hold if they have more than one link. Other times, WordPress does it for no apparent reason. ~mod.]

  30. The actual definition of sea level is not simple.
    This video shows some of the problems involved.



    So before you try and decide whether sea level has changed by 1 mm, it would be a good idea to define precisely what you are measuring.

  31. We used to wonder ,as kids, in the 50’s why when we caught the ferry from Liverpool to New Brighton why the landing stage was about 30 foot higher when we returned; we did not know about AGW then!

  32. @KipHansen
    “It is my point here that what we are doing, where the doing is done, is not measurement, but derivation. Many measurements are taken, in many and diverse locations, at many and diverse times. In some cases, there are nearly continuous time series of measurements for particular locations. From these numerous individual measurements, for example, the tide station reports from the Battery in New York City, an interesting (but not to be detailed here) formula is applied to derive a figure, a single number, that represents the average difference between the sea surface and a geodetic bench mark (set in the bedrock of Manhattan Island years ago) over some period of time.”

    All measurements are derivations. No measurement is perfect, i.e. without error. (“All models are wrong. But some are useful.” -George Box)

    When you “measure” the length of an object with a meter stick, you are really collecting, and interpolating, data from a “model” consisting of equally spaced (more or less) calibration points on the stick. You derive the measurement by comparing the span of the object over the stick and deciding which calibration points are “closest” to the extent of the object perceived by your eyeball.

    So, measuring is “simple” for most of us, but it is a computation (“interpolation”), performed by our brains, subject to errors of perception and interpretation, and totally dependent on the accuracy of the inscribed markings on the meter stick.

    Yes, the average value of a collection of measurements could be viewed as “imaginary”, in the sense that it may not match the actual measured value of any item in the collection. For example, you may determine that the “average” family in a population study has 2.5 children. But you will not find a family in your collection with that exact “measurement”. Nonetheless the average-family-size statistic is extremely important and useful for scientific understanding of population growth and distribution.

    So the “average value” of a collection parameter is very real, very useful and indispensable in the practice of science and engineering. Because it allows us to estimate the error of measurement, from which we can decide how confident we should be about interpreting the measured parameter. Confidence tends to increase as the estimated mean square error decreases.

    So if the satellite “derived” MSL estimates of MSL have sufficiently low MSE, then should accept them as “real” estimates of the actual level of the sea, because the evolution of those estimated values over time and space, within acceptable error, will give us better understanding of the underlying physical processes which affect sea level.

    It would be foolish to dismiss them as “imaginary”.

    • Reply to johanus ==> If you read the essay one more time, you will find that I never suggest dismissing these types of single-numbers, imaginary numbers, I call them.

      I say that they must be very thoughtfully used, that their use has to be considered carefully, because of their nature.

      You mustn’t just protest out of some protectiveness of your knowledge base — I am not saying that applied mathematics is useless, you know. Some measurements must be derived from data. I am talking about some rather specific cases and specific applications that results, in the sense intended here in this essay, that create a type of number that falls in my created class of “Imaginary number”.

      Surely, if you reread the paragraphs that detail the defintion, you can think of some examples and share them with us.

      • Of course I agree that we should always be thoughtful and careful in our considerations, but I think you are falling into a philosophical trap when you insist that properties of entities should be directly measured and not derived:

        For the result of a measurement to be a real number, the thing being measured must itself be measurable and the numerical result representing that measurement must represent something that exists in some meaningful and useful sense. However, the result of a measurement of a thing that itself is not physically measurable, but which can only be derived mathematically based on a definition that itself is an object of our imaginations (not something actually found in the real world), then that result should itself be considered, in this special sense, imaginary as well, despite its seeming precision.

        I have already mentioned that all measurements depend on derivations from a model. But there is another “philosphical” problem here too, in that by avoiding “derived” properties that are not directly observable, you will fall into the same trap as the Logical Positivists of the late 19th century, who refused to accept the existence of any entity that could not be directly sensed and measured. Thus the notable physicist Ernst Mach opposed Boltzmann’s theory of statistical mechanics in thermodynamics, because it depended on the existence of “atoms”, which could not be directly sensed or verified. Mach’s authority above Boltzmann impeded the acceptance of this theory until Mach’s retirement.

        So, yes, it seems that the “global MSL” derived from satellites is not a directly observable entity. But as long as it can be depended on to explain or predict ocean phenomenology in a useful way, then it should be admitted into discussions and experimentation in that research community. Further research may falsify its claims. Or newer research may reinforce it with a more detailed explanation.

        This happened many times in physics, e.g. when Wolfgang Pauli introduced a purely empirical wave function to predict the behavior of half-spin particles. He couldn’t explain the need for deriving the “complicated” 2×2 matrices in the function, except that it just worked. Later, Dirac’s relativistic wave equation provided the theoretical justification for the use of these complex matrix components:
        https://en.wikipedia.org/wiki/Dirac_equation#Comparison_with_the_Pauli_theory

        Another example are the “market indices” used to predict or explain stock market prices. One could quibble about the composition or derivation of such indices. But the ultimate validation depends only on its success in following market trends. You would say the DJI is “imaginary” because it contains averages of averages, but it certainly has been successful:

  33. I will start a new block here:
    Especially @ richardscourtney :
    Richard is speaking directly to the issues of climate science, and make some good points about the lack of reference standards. In every field of measurement, we take reference standards very seriously. When it came time to map out the continent, there were no references, no standards. The solution was geodetic survey markers. Thousands upon thousands upon thousands of them. There is no such system for sea level or for global surface temperature. So without a fixed reference, your data sets can drift all over the place.
    On the other side, if no physical standard is apparent, an empirical one can be made. You define it, you agree on it, and you keep anyone from messing with it. This is the case with the geodetic survey.
    For climate science, we are not even close. The Climate Reference Network in the US is purported to eventually provide such a reference, eventually. Time will tell.
    What has been left out, but I think is an integral part of data integrity, is the topic of honest brokers. If we are talking about data quality, and there are those in the field who are not operating in good faith, we are going to have a real hard time.

  34. Notice please the difference between the trend calculated from tide gauges (orange line with grey error range) and the blue satellite measurements. Tide Gauge data (which measures Relative Sea Level at each tide gauge) accelerates while satellite data, which measures absolute sea level, keeps to its century long trend.

    That is Church and White’s alarmist acceleration from tide gauges , Jevrejeva 2014 reports NO acceleration during 20th c.

    • Was that an effort designed to raise the credibility of satellite sea level measurements (which indeed are models all the way down)?

  35. Some time in the 18 hundreds my mind does not remember exactly, the British Admiralty did a world wide programme that was as big as the programme to land man on the moon.
    A scientific endeavour to measure the world in all aspects, temperature, pressure, accurate mapping and the marking of low tide dry rocks.

    For some odd reason these rocks with their low tide marks on the rocks with the date Lat and Long marked are still there high and dry at low tide. Many are up the East coast of OZ. There are hundreds of these rocks around the world, the Admiralty records will pinpoint every one. Just saying.


  36. from the Wikipedia page linked in the article.

    No acceleration from tide gauges in 20th c.

    The other graph shown in the article is Church and White , N.Z. alarmists.

    Jevrejeva 2014 similarly shows no accel since the trough in around 1880.

  37. “There are hundreds of these rocks around the world, the Admiralty records will pinpoint every one. Just saying.”

    I’m aware of one such rock. Interesting indeed.

    Can you provide a reference for any of the “hundreds” you claim exist, or is that just figment of bar-room wisdom ?

  38. Satellites don’t measure the level of the sea. Satellites measure the distance from the satellite to the surface of the ocean or land. As time passes the satellite’s velocity gradually decreases as does the diameter of the orbit.
    So what is actually changing? Is the sea level rising or is the orbit shrinking?
    I suppose the satellite calibrates itself by checking its distance to some assumed steady surface, say Death Valley.
    Low earth orbit is no less than 160 km, i.e. 160,000,000 mm. Measuring that distance to +/- 0.x mm seems a bit too good to be true.

    • The biggest problem is the radar reflection they get back is from the bottom of the wave swell. Even if you can measure that reasonably well, you need to know the depth of the swell to get the mean. They do with by statistical analysis of how noisy the signal is. Yet another of the these tunable ‘parameters’ .

      You tweak the parameter until the answer ‘looks’ right.

      No one is measuring the swell , it’s all guessing games and the usually incredible claims of accuracy.

      • Of course if the roughness depends upon some weather factor like wind speed or direction or turbulence you model may drift a bit if climatic conditions change over a few years and you may misinterpret the depth of the swell by couple of feet. But since you’re only claiming 0.1mm accuracy on each retrieval , that’s fine ;)

  39. Many are up the East coast of OZ. There are hundreds of these rocks around the world, the Admiralty records will pinpoint every one. Just saying.

    Bar-room ‘science’ or fact?

    I’m aware of one such rock. Interesting indeed. An ancient penal colony in Tassie, IIRC. Can you “pinpoint” any of the alleged admiralty records to back up your claim of hundreds? Just asking …

    • Was on the island of St. Lucia a ways back. One of the museums has a display dedicated to the Admiralty mapping project. As the room was located, one could look out to the harbor and compare to an original Admiralty chart posted beside the window. It was interesting to see how much of the island had eroded in 120 years. (Like all islands in the West Indies chain, it is mostly volcanic ash and till, and very susceptible to erosion). IIRC, the mapping accuracy was +/- 6 feet over the whole island, and +/- 0.5 ft. in the harbors and points important to navigation. Most, if not all of the islands got this treatment. (I do not know about the French possessions, there may have been “tensions”.) The British Admiralty Mapping Expedition (ca. 1860 – 1880) was truly epic in scope and worldwide in scale. The resulting maps are works of art and were the most accurate ever produced at that time. Many are still in use today, and many more form the basis of modern navigation charts. On St. Lucia, the marker rocks are well known. In England, the records of the Admiralty Expedition are carefully preserved as the national treasure that they are.

  40. Are we not measuring coastal lands sinking, rather than ocean levels rising? In Northern Sweden land is still rising out of the sea at up to 9mm/year. The Mid Atlantic ridge is rising. All the water displaced has to go somewhere.

    • Don’t worry, it’s all accounted for . You just need to know the viscosity of rock a few moraines from Canada and you can model how much deeper the oceans are getting.

      You make guess at the viscosity of rock and tweak it until you get the desired result.

    • Verticle land movement is now being measured by GPS stations. There are over 300 of these stations now around the world with the majority of the these stations also being co-located with a Tide Gauge station.

      GPS stations provide noisy data but after about 3 years of operation, a clear trend of the land motion, up or down and then north south east west can be determined. One can probably assume this vertical land motion has been in place for centuries if not thousands of years.

      GPS more-or-less confirms that average land location is moving up by 0.3 mms/year (this is still the rebound recovery from the last ice age) but there is wide variation in the stations ranging from land sinking at -8.0 mm/year to the land rising at 12.5 mm/year (half an inch per year).

      One can also check to see what the co-located Tide Gauge station is also measuring after it has been corrected for the local vertical land movement measured by the GPS station.

      SONEL is the main organization which is maintaining a database of these measurements. The latest data available from 1984 to 2013 (they only provide 30 year tide periods), is that after correction, Tide Guages are measuring 2.34 mms/year of sea level rise.

      Download page here. You need to select a time period, file format and then coverage area to download.

      http://www.sonel.org/-Sea-level-trends-.html?lang=en

      • I’ve also seen that it is very useful to have a gravimeter as well as a GPS receiver. The GPS gives the elevation to a geoid (an “imaginary” surface derived from physical measurements) and the gravimeter makes a correction to what GPS thinks is the geoid.

    • Very difficult to account for the complex dynamics. Land rising would result in sea level drop. Lay in bath tub and bring your knees up, water level drops. Even if GPS stations are measuring vertical movement, it would be extremely difficult to model the volume above sea level. The crust also has a lot of water in it (water table). Sinking crust could result in cavities being below sea level which then slowly fill in (lowering sea level). Rising crust could result in cavities being above sea level (raising sea level). This is in addition to all the other dynamics (temperature, volcanism, multiple sources of tides, rotation, solar, weather etc.).

      Lake Erie, perhaps because of it’s orientation and shape has a sloshing effect, where a low frequency wave moves from Detroit to Buffalo and back continuously.

      Unless these other dynamics are accounted with accuracy, I think the abstract concept “mean sea level” is meaningless from an AGW point of view.

  41. I find this is a remarkably disingenuous essay.

    Firstly, it begs the entire question at the outset by labelling some numbers as imaginary, even bolding each instance of the use in a very McLuhanesque way. The implication is that such values do not reflect anything real and have no value and that those who engage with them are fools.

    Secondly, it goes on to indulge the overarching ignorance of statistical and scientific methods found in the commenters here (and, I’ll point out to be fair, pretty much everywhere on the internet but particularly acutely on sites related to climate) to try to drum up some pitchforks and torches to attack the ivory tower just outside of town.

    Those ‘imaginary’ numbers in this essay are what a statistician would call the ‘true value’ of a set of observations. The fundamental concept behind that is that there are a lot of natural phenomena we can never measure accurately, but there is some semi-Platonic ‘true’ value of that measurement we can say with a defined degree of confidence lies within a certain range. That does not make them fake, or useless, or worthy of being loaded with emotion-laden words like ‘imaginary.’ That does make it mandatory that the value not be expressed singularly (ie. it must have a value and a confidence interval to be valid).

    It has always irked me that many post-hoc sciences (climate science, economics, nutrition science, and so on) express their values as accurate, precise, single-valued numbers as if that held any meaning other than rhetorical. I agree with the intent of this essay that without the proper consideration of the accuracy of such numbers, they’re useless as scientific data. I’m just disappointed by the prevalent use of rhetoric rather than logic to sway the reader, and the thesis itself that all observed data are imaginary, therefore fake, therefore useless.

    • I think that the term imaginary does not equate to fake or useless, except in the context of trying to use these numbers to describe some very precise mechanism. If the numbers are being used to describe sea level rise, with an extremely small margin or error, then they are imaginary. If the same numbers are being used to approximately describe sea level rise, with a corresponding large margin of error, then they are real.

      It is similar to temperature measurements, that were carefully recorded by hand, and sometimes kept track of at a local airfield. If those measurements are used for the original purpose, which was for local farmers and ranchers to use in comparing a current year to the last few years, then those are real measurements. If those same measurements are used, with some assigned impossibly small error bar, to make a political point about some sort of global temperature, then they are imaginary.

    • bregmata

      Thanks for bringing some reason to this debate…

      What we miss in many “single value” numbers is the error range around these numbers.

      In the case of tide gauges it is extremely huge and you need decades to statistically distinguish any “signal” from the noise caused by waves and tides, but that doesn’t mean that the figures are meaningless. The satellite(s) may be better, but I like to see the error bars in all cases…

      The fact that the satellites don’t show any acceleration in the averaged sea level trend, despite climate model expectations, in my opinion is already a good sign that the satellite people have no intent to “adjust” their data in the right direction…

    • @bregmata
      “Those ‘imaginary’ numbers in this essay are what a statistician would call the ‘true value’ of a set of observations. “

      No, not “true value”. The so-called “imaginary” numbers Hansen is referring to are the “derivations” of satellite and other sensor observations, attempgin to produce a single estimate of a collection of wildly varying values.

      “True value”, as defined by statisticians, is the hypothetical, error-free (i.e. “imaginary”) value measured by an “oracle”, who can measure “actual” values perfectly, with absolutely no error.

      But the values actually returned by sensors are not error-free, so cannot be called “true values”. Rather, they can be called “estimates” or “expected values” (sum of probability-weighted observations).

      If derived correctly, the expected value provides the best estimate of the true error, in the least square error sense, and tends to reduce uncorrelated measurement errors. In other words, averaged values, far from being useless, tend to provide more accurate estimates of the “true value” than any single measurement would, provided that the expected value of the error (“noise”) approaches zero.

    • >> I’m just disappointed by the prevalent use of rhetoric rather than logic to sway the reader, and the thesis itself that all observed data are imaginary, therefore fake, therefore useless.

      If true, then this is an example of an anti-science mentality. I hope that wasn’t the intent.

    • Bregmata: The way I read this essay was not that, for example the observed heights of people are imaginary observations but rather an “average height” person is an imaginary person. No detective would happen upon a murder scene and suggest that the 6 foot 8 suspect couldn’t reach the gun on the high shelf because the average American is only 5 foot 11. In this example the “average height” is not relevant to the issue perhaps in the same way that an irregular surface ocean with dynamic properties also has an average that is meaningless to anyone in any particular spot. The particular spatially located observations are valuable because they in fact do represent what you call “some semi-Platonic ‘true’ value of that measurement.” I don’t think Kip is calling that imaginary. Instead he is questioning whether combining multiple locations together has any real meaning. If it does not have any real meaning, then the use of the word imaginary is more than appropriate.

      I think that is the question that Kip is raising. Unless I am reading his intent wrong.

      • Reply to Bregmata and Dave in Canmore ==> Thank you Dave. You are right of course,

        Bregmata doesn’t seem to have read the entire essay or perhaps is simply misunderstanding. I went to some lengths to limit the sense of what I call imaginary numbers, to define and redefine them, and to carefully state that it is the use or mis-use of them that is the issue.

        As for statisticians, Dr. Brown at Duke [commenter rgbatduke here at WUWT] who is often my nemesis, coming to the defense of all things statistical, when I stray into talking about the misuse of numbers and statistics — seems to have understood my point and not found much here objectionable.

        That said, you can’t please everyone.

  42. Isn’t the heart of the matter this?

    If you are consistent in measuring “Whatever It Is That You Are Measuring” then over time you can discern whether or not “Whatever It Is That You Are Measuring” has changed. But it still does not follow that “Whatever It Is That You Are Measuring” is what you think it is.

    • “… over time you can discern whether or not “Whatever It Is That You Are Measuring” has changed.”

      Good point. And that explains why critical weather/climate parameters such as “mean sea level” (and “mean temperature”) are almost always expressed in the literature as “anomalies”, i.e. the change from some “baseline” value.

      So no one cares that the actual sea-level, right now, at Lat-Lon (y,x) is exactly 1,234,567.8 mm. But we are all very interested in how much it has changed over time.

      • Unfortunately, the baseline is not an absolute reference since it does not remain constant.

        So although the baseline may be said to be the 30 year average, what goes into that baseline changes not simply with respect to time but also with respect to composition. It therefore does not provide a reference against which things can be measured in a meaningful and significant manner.

      • @richard verney
        “So although the baseline may be said to be the 30 year average, what goes into that baseline changes not simply with respect to time but also with respect to composition.

        My understanding of weather/climate “baselines” is that they include the long-term, slowly changing components of the “signal” (temperature, sea-level etc), which are supposed to be viewed as the “expected value” of the signal at any point in time, up to and including “seasonal” variations. Then the remaining short-term components are supposed be interpreted as “anomalies” from the baseline of expected values.

        In practice it looks like a frequency decomposition, where a low-pass filter, in effect, generates the baseline, and a high-pass filter, in effect, generates the anomalies.

        So using that decomposition scheme, it would be impossible to detect a “low-frequency” anomaly, i.e. spanning several years, if such an anomaly truly exists. Nor would high-frequency signal “spikes” or “notches” be included as part of the baseline, even if they occurred on a regular and predictable basis.

        Is that what you meant by “with respect to composition”?

      • johanus unfortunately in a non-linear world one has to care about discontinuities. So anomalies break down. I’m always amused that GCMs model (hindcast) a globe at significantly different absolute temperatures (and this is concealed by using anomalies). One has to ask what happens to ice melt and vapour forming processes on these differing planets.

      • @HAS
        > … concealed by using anomalies

        Yes, it has also occurred to me that “cooling trend” anomalies could be hidden merely by moving the downtrend to the baseline, thus making the “anomalies” look like a flat or even rising series of values.

        So looking at anomalies alone, without reference to an annotated baseline for comparison, could be very misleading.

      • johanus, it’s more fundamental than that. We have GCMs that model the base period temp 1961–1990 across a range from 12.6C to 15.4C absolute (HadCRUT4 14C). See Fig 9.8 a AR5 WG1.

        The physical processes on those model worlds are said to accurately reflect the physical processes on our world. But how can that be?

      • The chart in Fig 9.8 shows an absolute mean surface air temperature of about 14C, which is consistent with the baseline for 1961-1990 in the zone between 60°S and 60°N, so not really a “global” mean:

        Jones, P.D., M. New, D.E. Parker, S. Martin, and I.G. Rigor. 1999. “Surface air temperature and its changes over the past 150 years.”, Reviews of Geophysics 37:173-199.

        Note NH (mean 14.6C) is warmer than SH (mean 13.6C), so biases global mean (14.0C) towards a Jul-Aug maximum.

  43. Mr Hansen
    Thanks for the interesting and easily to follow essay.
    Global sea level as is the case with global temperatures is an imaginary and abstract concept.
    Looking at N.Y. Battery tides, is ok for N.Y city but hardly relevant to (take special case) Stockholm.
    However, there is one more serious problem regarding anything to do with tides, and that is interference between the two clocks running at different frequencies.

    resulting in the well known 60ish year and millennial cycles. Further more, it is hard to determine if this is what the nature is doing by itself or it is simply product of numerology.

  44. Presumably, if the sea level is rising we should be able to detect a commensurate increase in the length of day. Is that happening? And can we separate the sea level component from all the other causes of changes in the earth’s rotation speed?

    • Since land-based ice fields are at higher elevations than sea-level, it does seem like the earth’s rotation should increase – but here again, even if this happened all at once, what tiny fraction of a second are we looking at? Can anyone contribute a rough calculation?

    • Leap seconds are added to compensate for a slowing of Earth’s rotation:

      1972 – 1980: 9 seconds added
      1981 – 1990: 7 seconds added
      1991 – 2000: 6 seconds added
      2001 – 2010: 2 seconds added
      2011 – 2015: 2 seconds added

      The rate of change of Earth’s rotation slowdown has been slowing over the last four decades.
      Does it indicate that sea level rise has slowed?
      Does it indicate that land-based glacier melting has increased (moving high-altitude ice to sea level)?
      Does it indicate that land-based glacier melting has decreased (moving less water from high latitudes to low latitudes)?
      Hmmm…

  45. Chasing meaningless, imaginary numbers is how you get grant money. As long as you convince the grantor that these numbers are real and have meaning with an emphasis on disaster.

  46. When it comes to making measurements, claiming and doing are two entirely different things.
    You can claim any level of accuracy that you want when publishing the results of your measurements.
    The tough part is actually proving that your measurements are that accurate and that your method of compensating for the millions of measurements that you didn’t make are that accurate.

  47. Perhaps we are trying to measure sea level at the wrong side of the ocean. Rather than trying to measure the level at the top of the ocean, where there all sorts of interferences, it would seem to make more sense to measure sea level from the bottom of the ocean. I’m probably making this way too simplistic. But it seems that a pressure measurement device, perhaps located in a few hundred feet of depth (staying on the Continental Shelf), could give a smoother data measurement for that particular location, than any measurement attempted at the surface. Nothing is going to be perfect, of course.

  48. >> transmogrify

    Love the reference!

    >> Imaginary

    From an EE & SwEng POV, I think “Abstract” would be a more appropriate term. Imaginary implies fictional, while “Abstract” implies conceptual and no instance of and dependent on strict definition.

    Excellent article.

    • Statisticians should develop a massage metric which simply counts the number of arithmetic operations applied to these imaginary/fictional/abstract/etc. numbers. That would give us a feel for the amount of massaging that takes place – until the AGW climatologists figure out ways to obfuscate that as well.

  49. Can we find common ground among scientists to launch a”reproducability project” like the one in Behavioural Science.

    We have a great beginning in Climate Audit. Is this a valid approach.

  50. When in college in 1973 I took a course on Statics and Dynamics. Showed up to the class with my trusty slide rule and the required text book. One of the first things the professor said in his introduction was that “The department has decided that the use of the digital calculator is acceptable for all courses in the engineering department.” (not a direct quote) Immediately bought one. However, by the third week I noticed that my calculations did not agree with the answers in the book. I was spending hours recalculating the problems. Learned quickly that every one that did not agree with the book came out perfect on the slide rule.
    I also have had the same problem as someone above said in trying to calibrate the instrument measuring the level of a material in a tank. The new digital displays indicates a level with 2 and 3 digits after the decimal point on a tank containing 100,000 gallons. Meaningless, GARBAGE. everything after the decimal point is in parts per million. 1 part in a million accuracy from off the shelf commercial grade equipment – B/S – not possible. Even the manufacturer only claims 1% accuracy meaning the measured value is 100,???.? Now read the Accuracy statement on an instrument. Everyone I have ever specked out states = 1% of FULL RANGE, between 20% and 80% of full range (or something like that.) Calculate the accuracy required to measure the top of the ocean from a satellite from space and indicate it in mm, cm, or even meters.

  51. Kip, it’s apparent that the root of your problem is your inability to understand a fundamental idea in math (limits) used as a basis for Calculus. Lets take your example of South Carolina and simplify it. Imagine you build a sandbox in your back yard for your children to play in. Say it measures six feet on a side, and the side boards enclosing it are eight inches high. You fill it with sand and your children play in it. Now one of your children is very inquisitive and asks you how much sand did you put in the sand box? You look at the sandbox and see that the surface of the sand is not smooth, but has many hills and valleys, footprints and maybe a constructed sand castle.
    ..
    Of course you could smooth out the surface then measure it’s depth, and get the answer to the question. Is that measurement you get after smoothing an “imaginary number?”
    ..
    Now, try to make that same measurement without smoothing out all of the sand in the box. You could lay out a grid, and take a depth measurement in the center of each grid square,. then average out the measurements to find out how much sand is in the box. Is that “average” now an imaginary number?
    ..
    But….hold on……we all know that the smaller the grid squares, the more “accurate” our measure is right?
    ..
    so you shrink the grid size, and increase the number of grid squares, and aren’t you getting a more accurate “imaginary number?”

    In math, they define the limit of a function with the delta-epsilon argument. Roughly speaking, for any given accuracy you wish, you can specify a grid size that will provide the accuracy.

    Now, your complaint about “imaginary” numbers is specifically due to the fact that no matter how small the grid is, you’ll never get an exact measure. The logic of math says that as the grid size shrinks, the measure approaches the limit

    SO…..yes, the “imaginary” number you get is the volume of sand in the sandbox. There is a real value to that volume, but alas, no matter how precise your ruler, the measure is “imaginary.” No matter how small your grid size, again, it never is small enough.

    But, as you well know, derivatives and integrals are widely used, and you are free to call their results “imaginary” if you choose, but I would think you could find a better term.

    • PS Kip, when you post “Well, for sea level, even at a single precise location, the answer is “No, we can not.” you obviously think that you cannot measure the “area under a curve”

      If you plot the time series of measurements, you get a squiggly line representing your measurements. If you divide the area under that curve, by the length of time, you get the AVERAGE.

      Need more accuracy for the measurement? Increase the length of the interval. You get more accuracy with the same instrument.

      • Reply to Steve Jones ==> You are being far to mathy and far too under-pragmatic — thus I fear you have missed the entire point.

      • I haven’t missed the point. The mere fact you consider my response “too mathy” means a lot. It means you don’t have a very good grounding in simple mathematics. I did try to keep the level of it toned down so that you could comprehend it. Pragmatically, the ideas of averages, std deviations, distributions and probability abound in the sciences. Rejecting these ideas when it comes to observations of our environment seems to be your problem .

      • Reply to Steve Jones ==> We appear to be speaking different languages. This essay is about a philosophical concept – dealing with the tendency of modern science to attempt to reduce huge complex dynamic systems into a single number that can be graphed against time — an idea I name here, just for use in this essay, an imaginary number.

        You seem only able to speak mathematics.

        It is unseemly to witness a grown-man, an educated man, standing in a public place, red-faced, stamping his feet, shouting “I’m right, I know I’m right, and if you weren’t so stupid, you’d know it too!”.

        No one here. least of all me, has suggested “Rejecting……the ideas of averages, std deviations, distributions and probability.”

        Try reading the essay again, as if your major had been in the humanities.

      • The evidence of significant changes in sea level are everywhere to be found. We know it changes over geologic time. I suggest you consult a geologist for a rendition of the evidence, and dispense with your armature attempt at the “philosophy” of scientific measurement. The men and women out there in the field, doing the grunt work of taking these measurements and publishing the results are doing a heck of a lot more for the advancement of science, than a person like you that sits at a keyboard and produces pointless negative comments on the results of their work.

      • Reply to Steve Jones ==> It is now apparent that you did not actually read the essay … too bad, it’s interesting.

    • I would suggest your analogy doesn’t represent the problem here. In your example, there exists a discrete value for the amount of sand in the sandbox. That volume has a meaning regardless of how it is arranged. Your example shows how to calculate it. More relevant to the discussion would be to ask what is the height of sand in the sandbox. The answer is more complicated now and any discrete value bears little resemblance to the actual sandbox in question.

      • It is a perfect analogy especially with regard to the “average” height above sea level for South Carolina. It would analogous to finding out what the volume of South Carolina is that sits above sea level.

  52. Kip Hansen,

    Thanks for a very well written thought provoking essay. You really put the entire CAGW nonsense in perspective. Those nitpicking your use of the term “imaginary number” are missing the bigger points.

  53. Nano-resolution (parts per billion) ocean depth sea level measurement
    Janice the Elder and Kim Hansen
    Sea level is already being measured from the bottom of the ocean using highly accurate pressure sensors.
    See Nano-Resolution (parts-per-billion) Oceanic and Atmospheric Pressure Sensors
    The Digiquartz sensors have a resolution of 0.001 mm (1 micrometer).
    Digiquartz Nano-Resolution Update April 29, 2011

    The 1400-meter depth sensor has a full scale of 2000 psia. The deployed depth is near 900 meters, or 1300 psia. The recorded data is in units of psia. The static pressure scales as P = ρ g h (density, gravity, height). Normally, the preferred metric pressure unit is Pascal (full scale of the sensor is 14 MPa and the pressure at the deployed location is 9 MPa). The sensor self-noise is expected to be near -180 dB or 0.009 Pa (in the time-domain near 1 Hz). Since the NOAA group was until now primarily interested in tsunami waves, their preferred unit is mm of water. The conversion is 1 mm ≈10 Pa.

    Some major issues need to be addressed:
    Uncertainty Analysis including Type A and Type B uncertainties
    e.g., Resolution, Accuracy, Spatial averaging and Temporal averaging
    While resolution is ppb, accuracy is of the order of 3E-5 (0.003%)

    Uncertainty Analysis
    Please study uncertainty analysis using the BMIP GUM, and NIST TN1297, especially about Type B errors. The GUM Intro states:

    4.6 Knowledge about an input quantity Xi is inferred from repeated indication values (Type A evaluation of uncertainty) [JCGM 100:2008 (GUM) 4.2, JCGM 200:2008 (VIM) 2.28], or scientific judgement or other information concerning the possible values of the quantity (Type B evaluation of uncertainty) [JCGM 100:2008 (GUM) 4.3, JCGM 200:2008 (VIM) 2.29].

    Similarly see NIST Evaluating uncertainty components: Type B

    • I also question how they are compensating for the weight of the atmosphere above the column of water this instrument is measuring?
      How do the compensate for the change/variation in temperature and the effect that has on density throughout the height of the column of water?
      How do the compensate for the change/variation in salinity and the effect that has on density throughout the height of the column of water?
      How do they compensate for the change in density due to the compression due to the weight of the water and atmosphere above each mm of water all the way down to the bottom?
      How do they compensate for known/unknown currents upwelling/down-welling on the column of water?

      Having made the calculations to determine the calibration curve for the level instruments on a boiling water pressure steam generator operating at about 600# pressure and about half water half steam with both water and steam flow, the problem they face is a little more complicated than they think. Then they need to consider that they are trying to get precession out to the 8th, 9th, 10th place in a system measuring over 10,000 pounds. ain’t going to work, but it will give them more “imaginary” numbers that “trend,” assuming they make all of the obvious compensations.

      • Pressure Uncertainty Analyses
        I agree that those are some of the issues that need to be addressed in the applications in addition to the uncertainties arising from pressure gauge lab tested accuracy. The uncertainty in calibration by the NIST is a fundamental limit between the official “accuracy” of 1E4 and the reproducibility of 1E9. See NIST Metrology School – Pressure calibration presentation.
        Yet also look at the amazing stability and resolution of the Digiquartz pressure sensors at the ppb level.

        long-term stability test of three Digiquartz barometers. Measurements on these instruments indicate that the median drift rate of the units tested is – 0.007 hPa (-0.0002 inHg or 7 parts-per-million) per year over the nineteen-year test period

      • PS annual drift of 7ppm is NOT parts ber billion – maybe the nano-resolution thing is a bit OTT.

      • Billy Nope. I delight in precision metrology and provide a good example of resolution vs accuracy. I’m a research engineer. So I “dream” of how to improve the accuracy to provide quantitative data to ground/ constrain/ validate climate models. When the digiquartz sensor achieve ppb resolution but pressure calibration is limited to 10 ppm, that’s 4 orders of magnitude difference – suggesting at least one to two orders of magnitude room for improvement!

      • Billy – Distinguish resolution vs accuracy. Resolution of ppb is different from “accuracy” or total uncertainty – which includes the drift of 7 ppm/yr, temperature variations, calibration etc. You can graduate “a fisherman’s ruler” in 100s of an inch, but if it is only 6″ long you have massive Type B error.

  54. Thanks for this amusing and informative essay.

    I would rather call the numbers “bogus” as opposed to imaginary (imagined? pseudo-number? ….).

    The idea of averaging seems tio rather widely abused. Yes, I agree according to the Central Limit theroem averaging points taken deom any distribution will reuslt in a normally distributed mean with a variance that decreases with the number of averages.

    However, thw problem is that many variables in Climate are not normally distributed and may be mutimodal. Furthermore, the CLT requires that the points are uncorrelated. Thus the mean may be highly misleading and must be qualified by the distribution and the correlation.

    In other wor words the mean may not mean what you think it means! (Sorry ghastly pun).

    This applies strongly to the mean of model outputs as rgb@duke has so often pointed out.

  55. Mean sea level is defined by a surface of constant gravitational potential, whose value is a very real number in the sense that the gravitational potential anywhere on that surface will result in the exact same acceleration on any mass whose center of mass lies on that plane. The geometric figure defined by that potential is known (though it is being refined continuously), and is called the “reference geoid.” It is described by a spherical harmonic expansion having hundreds of coefficients, which allows one to calculate the x,y,x coordinates of a point on the local geoid in earth centered coordinates.

    Any sea level measurement anywhere in the world at any given time will likely not correspond to the local geoid radius. The oceans are never in equilibrium. But more to the point, the reference geoid itself is constantly changing as more and more accurate measurements become available. I find it difficult to believe that we can resolve a change of 3 to 4 millimeters out of a number whose “mean value” (the earth’s mean radius) is 6,371,000,000 millimeters – particularly when the geoid itself has changed by as much as 30,000 millimeters in the past 50 years (by dint of better measurements).

    Here’s a good article on the subject by a guy at ERSI, the world’s leading geodetic information center.

    http://www.esri.com/news/arcuser/0703/geoid1of3.html

    • MfK,

      As I see these matters (admittedly somewhat dimly), what you bring to the discussion here is perhaps the most illustrative of all the things brought to explain why speaking of “sea level” as if a global surface that can be directly related to the actual volume or mass of all the water in the seas, is misleading.

      If the whole globe itself is in flux, so to speak, everything in this arena of equating minute changes in amalgamated estimates of “local” sea levels, to real world changes in how much total actual water is in the seas, becomes blatantly questionable, to my mind. I waited to see what the “experts” around here would say about your comment . . but decided to thank you regardless.

  56. Some people need to get a grip! It isn’t enough that Mr. Hansen explains carefully what he means by using the term imaginary – I for one simply substituted invented in my mind for imaginary. There are people who a looking for some reason to complain, rather than try to understand. Hansen’s discussion is dead on point.

    We have a large number of physical entities which are derived from a theoretical exposition. Enthalpy being one of them, mean sea level being another. They are invented entities, we don’t measure them directly, we infer them from the calculations we make on the direct measurements of other entities. Many of them involve sets of time averaged samples – take a look with speckle interferometry at the end of a heated metal rod to see the effective length of the rod change dynamically. Any measurement is a time average of the length, not the “true length.”

    I’ve read a exposition on the physics of the world that said that uncertainty wasn’t just a feature of the quantum world, rather it propagates throughout our world in our measurement estimates. Different behaviors at different levels, but that is part of the fractal nature of the universe. You can’t know anything exactly, but you can know it well enough to do something with it – kind of the mantra of good engineering.

    Ultimately, we can reduce everything to time, mass, and distance. Ultimately we are basing those other entities on derived values from those three. You can measure time using oscillations, crudely with a pendulum, or more precisely using oscillations of selected atom groups, way more precise, but still with known uncertainty. The same is true of mass, and distance. Mr. Hansen is obviously very aware of the foregoing statements as is rgb.

    • “Ultimately, we can reduce everything to time, mass, and distance”

      Technically time and distance are equivalent, as Einstein has theorized. If you also look at the bending of space-time as “mass”, you can derive mass from both time and distance.

  57. @ Kip Hansen

    Great essay, thanks for publishing it.

    Abstract or imaginary numbers, … especially averages and percentages, …. have no real value other than as “reference” data or information and should never be touted or claimed as being factual proof or evidence of anything …. except maybe for a specific event that occurred at a specific past time or place.

    And I would like to add, it is long past time that someone said it and you did a fine job at doing it.

    And in doing so, me thinks you have thrown a big bucket of ice-cold water on many of the “claims of scientific fact” being touted by WUWT authors/commenters/posters.

    Cheers

  58. I remember being told by a wise math professor that God gave us the rainbow and the Central Limit Theorem. I have found over the years that the distribution of averages being Normally Distributed to be a quite useful Imaginary Number for application in the engineering field especially for noisey data. That being said, the usefulness of the technique is in the taking of the averages to get the benefit of the Normal Distribution.

    • Reply to Ric Diola ==> Yes, that old Normal Distribution — a statistical animal – the assumption of which has led many a number man astray.

      For sea levels, see the lumpy map from NOAA in the essay — in six alternate color schemes.

    • The major problem with the Gaussian distribution is that there are a lot of processes out there that are not Gaussian. From the New York Stock Exchange, to fat molecules suspended in a liquid, what might look to be Gaussian, turns out to be some long tailed distribution, which is Gaussian only when circumstances are just right. The rest of the time it isn’t. Yes, that’s just another way of saying that a whole lot of the world is really fractal.
      Really, the usefulness of the Normal Distribution is that it’s easily differentiated. You get a lot of analytical “solutions” to problems using it. It’s the outliers that kill you, Black Swan events in the markets, floods in many areas, all are problems that arise when we believe too much in Normal Distributions.

      • Good point there. People believe in normal distribution when there is only an approximate normal distribution. People forget they use an approximation.

        Point-like car on frictionless, spherical road, again.

      • And if we are worrying about sea level rise because of effect on erosion risk it is exactly the likelihood of extreme events that create those risks, and the distribution of extreme events ain’t nice and normal.

  59. In reading this thread I kept thinking that if the gov’t took about 0.0097% of the grant money it shovels into ‘studying climate change’, and spent it on, say, 1,000 new tide gauges in appropriate locations around the planet, the question of SL change would be answered within reasonably tight error bars.

    I suppose that’s wishful thinking; government and .edu scientists do not want an accurate SL measurement, because then what would they do? They’d have to think up a whole new set of “but what if…” grant proposals.

    They’re already regretting launching the satellite measuring CO2 concentrations. Better for them if we don’t have good SL answers. Speculation = more grant $$.

    • Reply to dbstealey ==> What a thousand more tide gauges would only answer the question: How much is the Relative Sea Level changing at those thousand new points? Averaging those points, even added into the data base of existing tide gauges, might not inform us about changes in Absolute Global Average Sea Level. Relative sea level is the level of the top of the water where it meets the land. As one can see by looking at the data in the New York Battery tide gauge example, it may have little to do with what is being called Global Sea Level or Global Sea Level rise because, as one commenter said somewhere recently, “The ocean is not a bathtub.” In my essay on Hurricane Sandy, I showed that Global Sea Level change never arrived at the Battery, even after 50 years.

      • Kip Hansen:

        dbstealey commented on the use of climate data by politicians and your answer says

        How much is the Relative Sea Level changing at those thousand new points? Averaging those points, even added into the data base of existing tide gauges, might not inform us about changes in Absolute Global Average Sea Level. Relative sea level is the level of the top of the water where it meets the land. As one can see by looking at the data in the New York Battery tide gauge example, it may have little to do with what is being called Global Sea Level or Global Sea Level rise because, as one commenter said somewhere recently, “The ocean is not a bathtub.”

        True, “The ocean is not a bathtub” but the illustration you need which concurs with dbstealey’s point is not “the New York Battery tide gauge” but is sea level rise near London.

        Politicians repeatedly assert that the need to close the London Barrage is becoming more frequent because of global sea level rise from global warming. In fact, the apparent rapid rate of sea level rise near London is almost entirely caused by isostatic rebound.

        The ‘London example’ shows you are both right.

        Richard

    • Kip,

      I was making a suggestion that would correct for land rising, subsidence, and general isostatic changes. Satellite SL measurements have been criticised because they produce different results than tide gauges.

      Global sea level changes are difficult to measure accurately. Wouldn’t a sufficient number of tide gauges produce a good number? If not, then what’s the best way to accurately measure global SL rise?

      [BTW, thanks for the Battery Park link. Interesting conclusion re: AGW.]

      • Reply to dbstealy ==> Personally, I’m not sure that measuring “global” sea level rise is even a worthwhile effort.

        What matters to people is where the sea hits the land — how high or low is the water? Ask the Dutch, they understand this. This datum is called Relative Sea Level.

        There is some utility in knowing, in a general way, how fast the seas are currently rising — we know they are and have been. The practical difference between 1.8 and 3.2 mm a year approaches zero, even though it is nearly double. In the end it means 8 to 16 inches, or something like that, over a century. No one expects this difference to have any practical effect. What really matters is LOCAL Relative Sea Level and its change. Some places need to get busy with adaptation. Some couldn’t care less.

        Ports in Maine, with 20 foot daily tides, are not worried about +/- 12 inches.

      • Kip,

        I think you’re missing the most important point: ∆SL is not a scientific question. It is a political question.

        The alarmist crowd argues that SL is rising, and that the rise is accelerating. There is no good evidence to support that narrative, but that doesn’t mean it can be ignored. It needs to be rebutted.

        The only good way to do that is to establish a reliable measure of the global SL trend.

        Naturally, alarmists do not want that. It would be very likely to show that there is no problem, and that the SL argument is just another false alarm. They do not want reliable, testable, empirical measurements of things like sea level trends, Arctic ice trends, etc., because such measurements would probably falsify their ‘dangerous man-made global warming’ conjecture.

        We all know that if climate alarmists believed that a verifiable measurement of the SL trend would show that SL rise is accelerating, the money to obtain those measurements would be found, stat.

        For that reason we must produce reliable, testable measurements showing where the SL is going (the trend), and how fast. If there is a better way to do that than establishing a network of a sufficient number of tide gauges to give a reliable answer, please post it.

        I don’t care how they do it; like skeptics everywhere I just want reliable data. If there is a problem we’ll deal with it. But if, as I suspect, there has been no acceleration in SL rise (and as your link shows, possibly even a deceleration due to AGW), then the only way to demonstrate that is with verifiable, testable measurements.

        What is the best way to measure global ∆SL, and the global SL trend?

      • Reply to dbstealy ==> I guess I am missing your point. My point is that the (what I call an) imaginary number, global mean sea level or its delta, is not a useful or meaningful thing, except as a political cudgel.

        It need not be debunked because when it wakes up in the morning, the sea is rising, has been rising, and as far as the science is concerned can be expected to continue to rise for the foreseeable future. Satellite ‘measurements’, whether or not they are measuring an imaginary thing or number, seem to confirm this long term, very stable trend.

        It is only local relative Sea Level that needs addressing if it is a problem.

        The city of New York found this out with Hurricane Sandy — 13 feet of storm surge floods their tunnels and infrastructure. Time to raise the intakes, and be able to sandbag the tunnel entrances in an emergency.

        One can engage in the Climate Wars if one is so inclined — me, not so much.

      • dbstealey – October 10, 2015 at 3:17 pm

        For that reason we must produce reliable, testable measurements showing where the SL is going (the trend), and how fast.

        HA, the “Tilting at windmills” is not a logical action because the “climate alarmists” do not care one “twit” about reliable, testable measurements, …. scientific facts and evidence …… nor logical reasoning and intelligent deductions.

        The “climate alarmists” have an agenda they are committed to and no amount of reliable, testable “rain, sleet or snow” will deter them from completing their mission.

        The Public Schools are producing “climate alarmists” faster n’ quicker than you can ever hope to re-educate them.

  60. I used to be disturbed by the concept of ‘i’ (or the square root of -1) until I realized that all numbers are imaginary and that ‘i’ is as valid as 1.
    e to the power (i x π) + 1 = 0, remains the most beautiful equation ever discovered.

  61. I consider that this article makes a number of good points (for which it should be welcomed), but I also consider that for practical purposes, it may be overstating the case. Like others, although Kip has in my opinion done an excellent job in defining what he means by imaginary and thus what he is seeking to convey, I do not consider that imaginary is the best word to be used. This is perhaps a subjective point, but to me the word imaginary comes with baggage of its own which I find difficult to displace.

    I also consider that kip would have been better to use the global temperature anomaly as the subject of the illustration of his article rather than sea level, since I consider that to be a far stronger illustration of the problems behind the issue that Kip is raising with respect to imaginary numbers.

    I consider that as far as se level is concerned (and the post is not about sea level), we are deluding ourselves if we consider that we can measure sea level rise on an annual basis. The problems with measurement are such that one cannot measure a change over a period as short as a year. The signal is lost within the noise. I have pointed out for years that the satellite measurements are fraught with difficulties and I would imagine that we are only now beginning to be able to determine whether there has been any change since launch in global sea levels.

    However, I consider that it is possible to make a measurement (with appropriate error bounds and these could be quite large) over a multi- decadal period. We can detect a change over say a 30 year period. We can be confident when we say that sea level has risen the past century that it has actually risen, and with acceptable error bounds, we could put a figure by how much it has risen the past century.

    But of course, like so many matters, sea level is regional and is relative to the topography against which it is being judged, especially because of isostatic and plate tectonic issues. The impact of sea level rise is also a regional matter.

  62. So many numbers are essentially arbitrary . Basically they are always about the marketing. The question becomes what is the number that will be credible to make people believe we have a problem ; not too high to be clearly rubbish and not to low to be not scary. Whether that be 97 % of scientists or 50 cm rise or 400 parts per million of CO2 or 2 degree rise or 10 years of pause till AGW is falsified. If the response to the number is not alarmist enough or too alarmist then adjust the number or if the actually number is clearly false change the number. The AGW theory survives by starting with answers and trying to manipulate data to reach that conclusion.
    I always marvel when I read about 99% fat free or 99 % of consumers etc? when selling a product? What happened to the other 1%. The use of numbers is about the propagander no more and no less. For any person to assume that these figures has no error margins is naive. Unfortunately our media class is very naive and they export their nativity onto their readers/ viewers. Numbers are critical in any argument and discrediting them is the most important action that skeptics have to take.

  63. Kip Hansen says:

    One can engage in the Climate Wars if one is so inclined — me, not so much.

    It needs to be rebutted, Kip: Qui tacet consentire videtur. ‘Silence implies consent.’ The alarmist cult says that the rise in sea level is accelerating. We cannot leave that narrative unchallenged.

    As David S points out:

    The AGW theory survives by starting with answers and trying to manipulate data to reach that conclusion.

    They are doing the same thing regarding the claim that the rise in sea level is accelerating. The best way to counter that would be to produce a verifiable measure of the global SL trend. This is the third time I’ve asked: what is the best way to measure that? You didn’t like my suggestion of more tide gauges, so what is a better way to measure the true SL trend?

    Next, richard verney says:

    …we are deluding ourselves if we consider that we can measure sea level rise on an annual basis… However, I consider that it is possible to make a measurement (with appropriate error bounds and these could be quite large) over a multi-decadal period. We can detect a change over say a 30 year period…

    All good points. Another thing to consider: if the putative rise in SL was accelerating as claimed, there would be plenty of empirical evidence showing that accelerating rise. But there isn’t. Some measurements show a long term deceleration:

    OTOH, there is plenty of real world evidence that makes alarmist claims very questionable. One such instance is this mean sea level (MSL) mark carved into rock in 1841:

    Today’s MSL is the same. OK, some may argue that uplifting has caused the MSL mark to remain the same. But by exactly the amount of uplifting required to show no change in MSL? For 174 years? Occam’s Razor comes into play here.

    Other readers have commented that two century old Royal Navy charts from various locations around the globe show no change in MSL; a one fathom (6 feet) depth is still one fathom today.

    Those are much longer than your proposed 30-year period, in which we should be able to detect any ∆MSL — but the counter argument by the climate alarmist side lacks such empirical evidence.

    The central question as always is: which side is right?

      • That’s what I try to do every day, Kip, using facts, evidence, and logical arguments. I don’t have to try and convince you, and it’s impossible to convince the climate alarmist crowd of anything. We’re fighting for the undecided middle ground.

        I don’t understand why you seem to have a problem with that. This is a political fight. If it was based on facts and evidence we would have won the debate long ago.

      • Reply to dbstealy ==> Don’t get me wrong, I appreciate what you and so many others do. It’s just that that’s not what I see as my part in the overall scheme of things.

        My real avocation is religious and humanitarian work. On the side, I do minor wanna-be journalism on the topics of health issues, science communications, science journalism (most of my work here), personal and scientific ethics and the use and misuse of science in the media.

    • dbstealey – October 10, 2015 at 4:19 pm

      ‘Silence implies consent.’ The alarmist cult says that the rise in sea level is accelerating. We cannot leave that narrative unchallenged.

      Why not leave it unchallenged? You will only be “spinning-your-wheels” and getting nowhere if you challenge the alarmist cult’s claim that CAGW is causing an accelerating rise in sea levels ……. simply because you are challeging the measured/calculated/estimated “results” of an action ….. rather than challenging the root “cause” of said action (CAGW).

      Challenging abstract or imaginary “numbers” is a waste of time.

      And in reference to your concern about “leaving a narrative unchallenged”, …… there is a far, far more important “narrative” that you should be challenging rather than the above SL thingy.

      • Samuel Cogar says:

        … the “climate alarmists” do not care one “twit” about reliable, testable measurements, …. scientific facts and evidence …… nor logical reasoning and intelligent deductions.

        Agree completely. But we’re not trying to convince them of anything. That just isn’t possible, given their eco-religion.

        We are fighting for the undecideds — the middle ground. The public needs to see skeptics’ point of view, otherwise all they will be aware of is the alarmists’ climate scare.

        BTW, I challenge what you call the “root cause” of alarmism every day, and more than most. I do it on many different sites. We do what we can, and educating the undecided public is working. A few years ago there was still a lot of concern in the general media over ‘dangerous man-made global warming’. Public comments under those articles expressed the fear that there might still be a problem.

        But no more. Now, about 70% – 80% of public comments openly ridicule the CAGW fanatics. People are laughing at them, and ridicule is a potent weapon.

        Personally, I think educating the undecided public is very important; I certainly don’t view it as ‘spinning my wheels’ to educate people. We each fight the alarmist crowd in our own way. My way is working.

      • dbstealey says:

        Personally, I think educating the undecided public is very important; I certainly don’t view it as ‘spinning my wheels’ to educate people. We each fight the alarmist crowd in our own way. My way is working.

        I think educating the misnurtured/miseducated public is very, very important and it has been my non-paid mission to do so for the past 50 or so years. I was educated to be a Professional educator of the Natural Sciences and have conducted myself in a Professional manner all those years henceforth.

        Uh, .. uh, ..uh, … my “spinning wheels” comment was in reference to educating your per se eco-religious “climate alarmists”. Like I’ve always said, …. “Religion will rot your mind if you become obsessed or engrossed with it.

        And I agree, the public needs to see/hear/read the denialist’s refutations of the “junk science” claims being touted by the avid proponents of AGW or CAGW. I am NOT a skeptic or doubter of their silly arsed clams, ….but an avidly vocal denier of said claims ….. simply because said claims are not based in/on actual, factual science, physical evidence or intelligently deduced logical reasoning.

        And that is the primary reason I post my learned knowledge and/or “denials” on public forums or blogs. I have always figured there could be as much as “1,000 to 1 ratio” of …. public viewers verses forum posters ……. and it is those “public viewers” that need to read the “factual science” side of the discussion so that they can better make an informed decision on what to believe.

        Claims of fact” that are totally or partially dependent on ….. associations, correlations, insinuations, guesstimations, percentagations, consensus of opinions, etc., …. should be considered “tripe n’ piffle” commentary that is in dire need of physical evidence and/or mathematical/experimental proof.

        And ps, the science associated with the “drying” and/or “refrigeration” for the preservation of edible food items ….. negates …….. the CAGW claim that the Northern Hemisphere wintertime microbial decomposition of dead biomass is directly responsible for the bi-yearly 6-8 ppm cycling of atmospheric CO2. ….. Source references: Bacteriology 101 & Botany 101

  64. Thanks Kip for a very interesting post.

    Just for fun on the thought of averaging and imaginary numbers. If we were to average the rain over South Carolina last week with that of the regions on California experiencing drought then we could relieve the CA drought and ease SC flooding at the same time (at least on paper).

    If I did such a trick I would imagine some folks in CA would imagine that I was imagining some imaginary mathematical slight of hand. Could you imagine that?

    ;-)

  65. I must point out that as an engineer I have a skeptical view of the accuracy of most of the data presented by “climate scientists”. On the other hand I am quite familiar with large tank level measurement techniques.
    Stilling wells have been used in crude oil and fuel storage tanks for decades (maybe longer) because there is a lot of $$$ at stake to achieve accuracy and the level varies in the tank during fluctuations during filling/emptying and wind induced flexure. Today more accurate devices have replaced or supplemented the old level gauges. A stilling well is a pipe with slots at the bottom to allow liquid in/out while dampening the “waves” in the tank
    I suspect the tank stilling well technology that is/was used was adopted from tide gauges for tank level gauges. I can’t comment on the accuracy for tide gauges but someone has tried to compensate for normal wave action back in 1830. Of course a stilling well does not compensate for soil subsidence.

    “Until the early 19th Century, sea-level measurements were made using tide poles or staffs. These still form part of modern-day tide gauge instrumentation, but have not been used as a primary source of sea-level information since the introduction of self-recording tide gauges. The earliest form of self-recording tide gauges were mechanical float and stilling well gauges, which were introduced in the UK during the 1830s. They were the primary means of sea-level measurement for over 150 years and continue to operate at some UK locations today. However, they are generally auxiliary systems to newer pressure gauges.”

    One final question. I recall that the recorded sea level rise has been increased to account for subsidence under the sea which in my mind exaggerates the real sea level impact on surrounding land. How can that make sense?

    • Catcracking,

      I think most engineers ( at least in the mechanical/physical fields) have a view of the physical reality that it ‘is what it is’, not one of ‘it is what they want it to be’.

      Those in the engineering fields are most likely to be the most skeptical of observers in the global warming debate (if you could call the great CAGW scam a debate). Makes you kind of wonder if we will face RICO charges and Executive Orders to stand down and comply with the 97% narrative.

      ;-)

    • Reply to Catcracking ==> “…recorded sea level rise has been increased to account for subsidence under the sea which in my mind exaggerates the real sea level impact on surrounding land. How can that make sense?”

      This is a science-wide problem, which i describe as trying to produce a single-number to represent vast dynamic systems (usually to ridiculously claimed precision). Local Relative Sea Levels (which are physically measured to some degree of accuracy, say 1/2 inch) can not be used to estimate Global Average Sea Level. It is inappropriate. To to do [corrected – kh] so is like buying a new larger shoe size for your child based on the average growth rates of other children (especially give, with sea level, that some other kids feet are shrinking and some growing).

  66. “imaginary numbers” was an unfortunate misnomer in mathematics. In reality, “imaginary numbers” come up all the time in “REAL” physics problems. When they do, the solution includes an oscillation 0 a sine or cosine function. Since imaginary numbers are actually real, Kip Hansen should have used a new term, such as “fantasy numbers”.

    • Alan,

      I didn’t have any problem with “imaginary numbers” but “fantasy numbers” would have been a most excellent choice.

      But then you would have to subject that term for review to find out if someone has dibs on it. ;-)

  67. On the subject of REAL numbers and real lives:

    One’s predictive track record is an objective measure of one’s technical competence, and based on its negative predictive track record, the IPCC has NO credibility.

    Since its first report (FAR, 1990) the IPCC has predicted catastrophic global warming due to increased atmospheric CO2. However, global temperatures in the Lower Troposphere (LT) have NOT warmed in more than 18 years despite significant increases in CO2, according to the most accurate temperature data measured by satellites. The Surface Temperature (ST) data claims some warming, but it is increasingly obvious that the ST data is inaccurate, due to its increasingly large divergence from the satellite data.

    Despite claims of more extreme weather due to global warming, the incidence and severity of extreme weather has not increased. The climate has been remarkably stable despite substantial increases in atmospheric CO2.

    Over-hyped fears of global warming are utterly wrong. In fact, cold weather kills. Throughout history and in modern times, many more people succumb to cold exposure than to hot weather, as evidenced in a wide range of cold and warm climates. Evidence is provided from a study of 74 million deaths in thirteen cold and warm countries including Thailand and Brazil, and studies of the United Kingdom, Europe, the USA, Australia and Canada.

    Contrary to popular belief, Earth is colder-than-optimum for human survival. A warmer world, such as was experienced during the Roman Warm Period and the Medieval Warm Period, is expected to lower winter deaths and a colder world like the Little Ice Age will increase winter mortality, absent adaptive measures. These conclusions have been known for many decades, based on national Excess Winter Mortality statistics.

    Excess Winter Mortality in the USA typically totals about 100,000 per year – that is, 100,000 Excess Winter Deaths every year during the cold months of December through March. Excess Winter Deaths range from about 5000 to 10,000 in Canada and up to 50,000 per year in the United Kingdom.

    Despite our colder climate, Canada typically has slightly lower Excess Winter Mortality Rates than the USA and much lower than the UK. This is attributed to our better adaptation to cold weather, including better home insulation and home heating systems, and much lower energy costs than the UK, as a result of low-cost natural gas due to shale fracking and our lower implementation of inefficient and costly green energy schemes.

    Global warming alarmists seeks to reduce the use of fossil fuels and increase the use of green energy. In Europe, where green energy schemes have been widely implemented, the result is higher energy costs that are unaffordable for the elderly and the poor, and increased winter deaths. European politicians are retreating from highly-subsidized green energy schemes and returning to fossil fuels.

    The problem with green energy schemes is they are not green and they produce little useful energy, primarily because they are too intermittent and require almost 100% fossil-fueled (or other) backup.

    The lessons are clear: When misinformed politicians fool with energy systems, the costs are enormous – globally, trillions of dollars of scarce resources have been squandered, economies have been severely damaged, and innocent people have needlessly suffered and died.

    Yours truly, Allan MacRae

    The UN’s IPCC Has No Credibility on Global Warming 6Sept2015
    https://friendsofsciencecalgary.files.wordpress.com/2015/09/the-uns-ipcc-has-no-credibility-on-global-warming-6sept2015-final.pdf

    Cold Weather Kills MacRae D’Aleo 4Sept2015
    https://friendsofsciencecalgary.files.wordpress.com/2015/09/cold-weather-kills-macrae-daleo-4sept2015-final.pd

  68. Years ago when discussing global temp the official stance seemed to be the number was only good to show us longer term trends. Year to year trends meant little. After it became so political though we seem to pretend this product is accurate to tiny fractions of a degree rather then only longer term trends.

  69. Kip, thanks for an interesting article. I had not expected such a detailed response to my question.

    However, like many readers, I was put off by your redefinition of “imaginary numbers”, so much so that I didn’t read far into it at all when it was posted. You defended this, saying:

    Kip Hansen October 10, 2015 at 11:37 am Edit

    Reply to David L. Hagen ==> I tried to warn readers in the Spoiler Alert: section, right up front, in the very first sentence, that I wasn’t going to talk about your particular beloved definition of “imaginary number”.

    I’m afraid that mathematics and physics do not own the English language and do not get to cry cry cry when someone else uses the same word for a different use. This happens to statisticians too, who would prefer to own certain words and prevent others from using them despite the fact that they are rather common English language words, with many other uses.

    I do know that it can be hard for people who have been indoctrinated through university education in narrow fields to read essays in which a piece of their fields nomenclature is used in a different sense, even when carefully defined and alerted. I am sorry for your discomfort — but your objection is hubristic.

    Now, suppose I wrote an article, and in the very first sentence I warned you that whenever I said “angry men”, I actually meant “nice women”. So then I started off saying something like “Angry men are the most dangerous kind of men. When you see angry men, you should get nervous” …

    I assume you can see the difficulties with that.

    And then suppose that when somebody busted me for that redefinition, I pointed out that they don’t own the English language, and that if they object to my use of the term “angry men” to mean “nice women”, that is just “hubristic” …

    I’m sure you can see the problem. Yes, you are free to redefine “freedom” to mean “slavery” … but would that be conducive to or an impediment to communication?

    And calling those like myself who think it would be an impediment to communication “hubristic”?

    Well, your first paragraph was where I stopped reading. I jumped to the comments at that point, and stopped after your first comment. You are free to redefine anything. You are not free to diss people when they say that it’s not helping communication when you do that.

    Finally, you may not realize it, but you’ve shot yourself in the foot by making it impossible to quote sections of your work. What would anyone who is mathematically literate make of this quote, for example?

    There are innumerable averages of things that can be derived and calculated. Despite that, many of those averages are themselves imaginary, and their meaning and usefulness must always be thoughtfully considered. Such imaginary numbers may have some interesting meaning and some pragmatic usefulness but great care must be taken with their application, because, after all, they are imaginary and do not exist in reality.

    Now that I’ve read your work, I have more substantial objections, but I wanted to get that out of the way first.

    My best to you,

    w.

    • Reply to Willis ==> Truthfully, the choice of the word “imaginary” was yours. There is no “redefinition” here, as many readers have already pointed out…simply using English words in a different usage, outside of the narrow higher mathematical nomenclature, and clearly stating so. There are a limited number of words in the English language, and different fields of knowledge are not allowed to “dibs” them and forbid their use outside their own field. A good example is the word “species“, which has several definitions in different nomenclatures: biology, monetary, ecclesiastical, logic, and then an everyday usage. In reality, even within the field of biology, the definition is in serious dispute.

      Further, I have used the word quite correctly to refer to things, certain types of proffered numbers, as “imaginary numbers” using the common use of “imaginary” here: “1. a : existing only in imagination : lacking factual reality, b : formed or characterized imaginatively or arbitrarily” with some rather clearly stated caveats.

      “What would anyone who is mathematically literate make of this quote, for example?” Personally, I would suggest thinking about it in context of the essay — but that’s just me…others may prefer to do something else.

      • Kip Hansen October 11, 2015 at 11:16 am Edit

        Reply to Willis ==> Truthfully, the choice of the word “imaginary” was yours.

        Truthfully, YOU wrote the post, not me, so don’t try to blame me for your choices.

        There is no “redefinition” here, as many readers have already pointed out…simply using English words in a different usage, outside of the narrow higher mathematical nomenclature, and clearly stating so.

        You have said that averages (a mathematical term) are imaginary numbers (another mathematical term). That’s called “redefinition”.

        “What would anyone who is mathematically literate make of this quote, for example?” Personally, I would suggest thinking about it in context of the essay — but that’s just me…others may prefer to do something else.

        Sorry, but the nature of a quote is that it is offered OUTSIDE of the context of the essay …

        w.

      • Reply to Willis ==> Respectfully, you need to re-read the essay more carefully before commenting further. Only one other person (apparently a High Priest of Mathematics) misunderstood my point so thoroughly.

        Taking quotes out of context is not a virtue — it is what makes conversations impossible.

        I’d love to hear from you again when you can restate the overall point of the essay in your own words, using 100 words or less. If you are even close, then we can discuss the finer points.

        Are you back from your extended trip?

      • Kip Hansen October 11, 2015 at 3:21 pm

        Reply to Willis ==> Respectfully, you need to re-read the essay more carefully before commenting further. Only one other person (apparently a High Priest of Mathematics) misunderstood my point so thoroughly.

        OK, so tell me what I misunderstood. I find no change in my understanding having re-read your post.

        Taking quotes out of context is not a virtue — it is what makes conversations impossible.

        Unless you quote an entire document, all quotes are removed somewhat from the context. To make sense out of the lines I quoted, I’d also have to quote your entire introduction. Pass.

        I’d love to hear from you again when you can restate the overall point of the essay in your own words, using 100 words or less. If you are even close, then we can discuss the finer points.

        Sorry, pal. I’ve made a number of specific points about your claims below, here. How about you climb down off of your high horse and summarize my points in 100 words or less?

        Or more to the point, forget about the summary—how about you just show where I’m wrong in my other comments?

        Are you back from your extended trip?

        Indeed I am. I was going to write up the rest, but it never came to pass. I had much more interesting scientific work to do.

        All the best,

        w.

      • Last Reply to Willis ==> From the git-go you have misunderstood even the area of science the essay is about. Quoting you : “I am saying that in an essay ABOUT MATHEMATICS…”

        The essay is not about mathematics, which others have already pointed out to you. It is also not about the mathematicians “imaginary unit or numbers”, not about “AGW; CAGW; Catastrophic Climate Change; Global Cooling; various oxides of carbon; the pH, level, or surface temperature of oceans; or the antics or ethics (or lack of ethics) of various international scientists and politicians”, stated clearly “This essay is not really about global sea level, but I doubt we’ll be able to discuss it without also touching on the issues surrounding the issue of global mean sea level.” It certainly is not about simple averages of numbers.

        I offer a good summary of what it IS about in the Post Script.

    • Reply to vukcevic ==> Probably right, that. Hard to please everyone with word choices — after all, look at what Mathematicians did when they chose “imaginary number” and “imaginary unit” as the nomenclature for “An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i 2 = −1. “

  70. Thanks Kip great post.
    I appreciate your effort to define your terms.
    Perhaps it also is a lesson in reading comprehension.
    The persons claiming confusion and protesting that mathematics owns the term “Imaginary numbers”™ do provide examples of how the whole meme of Climatology has prospered in its impersonation of science, while refusing to define its terms, for far too long already.
    Funny how what we are sure is so, tends to mislead our understanding of other peoples points of view.

    • john robertson October 11, 2015 at 12:01 pm

      The persons claiming confusion and protesting that mathematics owns the term “Imaginary numbers”™ do provide examples of how the whole meme of Climatology has prospered in its impersonation of science, while refusing to define its terms, for far too long already.

      I am not saying that mathematics owns the term “imaginary numbers”.

      I am saying that in an essay ABOUT MATHEMATICS, using the term “imaginary numbers” to mean something other than the normal mathematical meaning causes problems … as is proven by the number of people who turned away from the article or were unhappy with it for that very reason.

      My aim is to write for comprehension, not for problems and dissension. Everyone here who is discussing the mis-use of the term is NOT discussing the essence of the article. Perhaps that’s OK with you and Kip.

      Had I written the article, I’d be bummed to see people discussing my word choice rather than my ideas … but hey, that’s just me.

      w.

      • Thankyou Willis, I think you reinforce my observation
        “An essay ABOUT MATHEMATICS..”
        Sorry to add to the confusion ,but I was lead to believe that Kip Hansen was discussing measurement of certain parameters of the real world and then what we claim to infer from these interpretations(measurements).
        The 4 questions of Paragraph two or block quotation 2 is not the subject of this post?

      • Willis

        “Had I written the article, I’d be bummed to see people discussing my word choice rather than my ideas … but hey, that’s just me.”

        They do sometimes, because you often use the expression “warming” when you really mean “slows down the rate of cooling”.

        When discussing physics, different processes are at work when something is “warming” than when the “rate of cooling is being slowed down”. It is unhelpful and confusing to use the expression “warming” and although this has been pointed out to you for many years, you often still use the expression out of its true and recognised scientific meaning and context. Just saying, perhaps you should reflect on that before too harshly criticizing Kip; stones and glass house etc. .

        I am one of the people who noted that “imaginary” was an unfortunate use of words, but I did recognise that Kip had defined what he meant when using that expression. I suspect that it made good by line, which is a game frequently employed in the newspaper business to grab people’s attention and draw them in; it is an attention seeker, snazzy word and hence difficult to put down, and I suspect that explains why Kip decided to run with it. It was simply too irresistible to use a more appropriate expression for the principle that he was seeking to convey.

        But the issue is the correctness and relevance of the point(s) being set out in this article and does it have real significance, or only passing significance. Whilst semantics are important debates should not really centre on that (which you often mention when someone picks you up for using the word “warming” out of its proper scientific meaning).

        Like everyone else (well almost everyone), I enjoy reading your opinions and views, so welcome seeing your views on the substance of the point9s0 being made by Kip.

      • richard verney October 11, 2015 at 5:35 pm Edit

        Willis

        “Had I written the article, I’d be bummed to see people discussing my word choice rather than my ideas … but hey, that’s just me.”

        They do sometimes, because you often use the expression “warming” when you really mean “slows down the rate of cooling”.

        Naw, I gave that up years ago. People like you obviously think that if you put on a jacket, it doesn’t warm you up, and if you add an extra blanket at night, it doesn’t make you sleep warmer. OK, fine, got it.

        So I stopped using it, although to me that’s just semantic silliness.

        Anyhow, I doubt that you can find any recent example of me saying that.

        Now, note that I made that change and stopped using that term just so folks would NOT discuss my word choices, but would instead discuss the ideas … exactly the course of action that I recommended for Kip, and that I have been repeatedly rubbished for recommending.

        It’s not a question of whether I can understand it. I can. Most anyone who knows what an imaginary number is can still understand Kips claims.

        But it doesn’t advance communication to assign a clearly defined mathematical name to something completely different, as is proven by the amount of electrons we’ve already wasted on the subject.

        Which was my point.

        Regards,

        w.

  71. Kip, here are my further objections to your work.

    First, you’ve re-defined “imaginary number”, but it is not clear what you’ve redefined it to mean. For example, you say:

    Sea Level, even “Sea Level at the Battery in New York”, is not properly represented by a single number, above and below some geodetic bench mark. What we call sea level is a derived, calculated number – an average of averages of an array of measurement time series. In this sense, as the calculated mid-point of a range over time, it is, in a practical sense, an imaginary number having no existence in the day-to-day life of the Port of New York.

    I’m sorry, but I don’t understand this distinction. Is every average an “imaginary number” in your world? It appears that you have defined an average as an “imaginary number” … but why?

    And if an average is an “imaginary number”, then what about a trend? What about the error of an average? What about the first Principal Component? Are those “imaginary” as well?

    In your world, it appears (but is far from clear) that everything but a measurement is “imaginary” … so that’s my first objection—no clear “bright-line” definition that would allow me to tell whether the result of calculation X is real or “imaginary”.

    My second objection is that if averages in your world are “imaginary” … so what? Me, I call an average a “mathematical construct”, but that doesn’t make it wrong or useless as you seem to assume. We use averages in lots of ways every day. Businesses use monthly and yearly averages of their operations to make business decisions, and they don’t seem bothered by the claim that such averages are “imaginary”. The Social Security folks use the average of my best 35 years of earnings to determine my benefits, and they don’t seem to notice that the average is “imaginary”.

    So that’s my second objection—I don’t understand what the problem is with averages on your planet?

    My final objection is that often, the absolute value of the average is not meaningful … but the CHANGE in the average can be very meaningful. For example, nobody cares about the absolute average sea level height in New York. It’s generally not discussed in the slightest. We’re only interested in the the rate of change of the sea level—is it accelerating, slowing down, or staying the same.

    And again, what difference does it make if the sea level in New York is “imaginary” or not? If it starts rising faster and faster, are you going to say “No problem, folks, it’s just an imaginary number, nothing to see here, move along”?

    Me, I refer to such things as averages and the like as “mathematical constructs”. But this doesn’t mean that they are second-class mathematical citizens. To me this just means that averages do not exist in the real world, but are calculated values. Yes, there is no such thing as an “average temperature” or “average rainfall” … but California is in a drought, and the average annual rainfall is pathetic compared to its normal value.

    Unless you think that’s just a coincidence, you’d have to admit that the changes in averages have meaning and value.

    Best regards,

    w.

    • Willis says:

      …what about a trend? …the CHANGE in the average can be very meaningful. …We’re only interested in the the rate of change of the sea level—is it accelerating, slowing down, or staying the same.

      That’t’s the critical observation. The trend is the most important metric, IMHO.

      The alarming argument, made over and over, is that the SL rise is accelerating. They have to say that, because if the trend is not changing from the LIA (or worse for their side, if it’s starting to decline), then Occam’s Razor indicates that it’s natural.

      That’s why I think we need a reliable, accurate method to measure the trend in sea levels. I know it’s not easy, and it probably can’t be measured accurately until we have several years (or decades) of measurements. But the claim has been made, and the only way to answer it is with verifiable measurements.

      Finally, it seems that if the global SL was rising at an accelerating rate, there would be plenty of empirical evidence. But there’s not. In fact, a MSL marker carved into rock 174 years ago shows no change, and there are many other observations showing that the ‘acceleration’ scare is flat wrong.

      • I only partially accept that the rate of change is the important factor.

        Let us assume that there is no rate of change but sea level rise at a uniform rate of 3 inches a year. We would have to adapt to that rising sea level in any event. This is so whether or not there is an increase in the rate of change.

        Further, the rate of change does not necessarily confirm AGW. First, we do not know precisely how the change is made up; glacial melt, expansion of sea water, extracting water from below the water table and dumping it in the sea etc. Second, just because the rate of change increases, it does not mean that that is the consequences of manmade activity. It may merely be the result of natural processes (a rebound from the LIA, or even from the depths of the deepest lows of the current ice age), or it may be that the oceans are warming due to natural processes (less cloudiness, changes in solar insolation etc).

        That said, I do accept that the absence in the increase of rate of change weakens the argument that sea level rise in of anthropogenic origins.

      • Richard V,

        I agree with everything you wrote. It could well be all natural (meaning no human influence).

        But the argument we’ve heard for many years is that AGW causes SL rise to accelerate. My point is that I don’t see any empirical evidence to confirm that. I don’t even see much real world evidence for a 3 mm rise.

    • Reply to Willis ==> (repeating what I said to your last comment)

      Respectfully, you need to re-read the essay more carefully before commenting further. Only one other person (apparently a High Priest of Mathematics) misunderstood my point so thoroughly.

      Taking quotes out of context is not a virtue — it is what makes conversations impossible.

      I’d love to hear from you again when you can restate the overall point of the essay in your own words, using 100 words or less. If you are even close, then we can discuss the finer points.

      Are you back from your extended trip?

      • Kip, to be fair, everyone takes quotes out of context. It’s how people converse; always referring to an entire article would be incredibly clumsy.

        Willis has taught me one valuable technique: quote someone’s words. So now I start my replies by writing (for example), “Willis says…”, and then I paste in his words, verbatim.

        That’s a really good way to avoid misunderstanding. IMHO, of course.

      • Reply to Willis and dbstealy re “Taking things out of context” ==> Looks like I’ll have to do a little teaching here:

        “Out of context” and “taking out of context” is an idiom that has its own definition, I’ll give several from online dictionaries:

        “to use only part of something that someone said, so that the original meaning is changed”

        “without the surrounding words or circumstances and so not fully understandable” as in “comments that aides have long insisted were taken out of context”

        “To report (something) without taking into account the context in which it occurred.”

        and

        Fallacy of quoting out of context

        “The practice of quoting out of context (sometimes referred to as “contextomy” and quote mining), is an informal fallacy and a type of false attribution in which a passage is removed from its surrounding matter in such a way as to distort its intended meaning.[1] Contextomies are stereotypically intentional, but may also occur accidentally if someone misinterprets the meaning and omits something essential to clarifying it, thinking it non-essential.”

        It is not a virtue, it is not a common practice (except in yellow-journalism). It is improper and creates a logical fallacy. Quotes taken from a larger piece of writing or speaking must be considered in light of the larger piece of writing and the general thrust or intent of it.

        Honest.

      • Kip,

        So what happens when someone wants to comment on something you wrote? They’re not allowed to quote what you said?

        I’m not talking about distorting someone’s meaning. That is the fallacy, not simply responding to some particular comment.

      • John Knight,

        The quote was:

        …I start my replies by writing (for example), “Willis says…”, and then I paste in his words, verbatim.

        I was giving a hypothetical example of how I post a verbatim comment that I would like to reply to.

        I’m not sure what you meant by your comment. Did you inadvertently post it too soon? Or maybe I’m just slow to understand it…

      • dbstealey,

        I was just tying to demonstrate that just about anything can be misleading if taken out of context, and duplicating the exact words written by another is no exception.

      • John Knight,

        OK, thanks for explaining.

        That means the character of the person posting is very important. I’m sure Willis would never try to distort someone’s meaning by deliberately taking a quote out of context, and neither would I. Or you, or Kip. Most folks wouldn’t do that, because you can’t get away with it.

        But I’m afraid that some would. After a few comments, we can decide if that’s what they’re doing, and disregard them. On the internet, it’s easy to see if someone is distorting a comment or quote. They don’t get very far.

        But it’s not a logical fallacy to simply quote something that someone has written, and reply to it. If we couldn’t do that, conversations would become very weird and stilted; readers would have to try and understand what, exactly, anyone was replying to.

      • dbstealey,

        Thanks for your thoughtful reply. I agree that quoting out of context is often fallacious on purpose when done, but there is the potential for someone to accidentally engage in such fallacy, particularly when the person quoted has indicated early on that they are not using terms in their customary manner. In this essay, Mr. Hansen opens himself up to much apparently valid criticism, if that initial proviso is not born in mind throughout . . and slips back into expectations based on the customary use.

      • dbstealey:

        I think you know that I usually support your arguments and comments, but in this case I am writing to disagree with you.

        You say

        Kip, to be fair, everyone takes quotes out of context. It’s how people converse; always referring to an entire article would be incredibly clumsy.

        Willis has taught me one valuable technique: quote someone’s words. So now I start my replies by writing (for example), “Willis says…”, and then I paste in his words, verbatim.

        That’s a really good way to avoid misunderstanding. IMHO, of course.

        Sorry, but no. Most quotations are NOT ‘out of context’. As Kip Hansen says

        “Out of context” and “taking out of context” is an idiom that has its own definition, I’ll give several from online dictionaries:

        “to use only part of something that someone said, so that the original meaning is changed”
        {snip}

        An out of context quotation – either deliberately or inadvertently – misleads as to the message of the quoted article.

        And you also say

        That means the character of the person posting is very important. I’m sure Willis would never try to distort someone’s meaning by deliberately taking a quote out of context, and neither would I. Or you, or Kip. Most folks wouldn’t do that, because you can’t get away with it.

        But I’m afraid that some would. After a few comments, we can decide if that’s what they’re doing, and disregard them. On the internet, it’s easy to see if someone is distorting a comment or quote. They don’t get very far.

        Again, no. That is an example of the Appeal to Authority logical fallacy. The nature of a person presenting an argument does not – of itself – indicate the validity of the argument.

        A person making or refuting a claim that a quotation is ‘out of context’ needs to explain why they think that. And ‘because X said it’ is not a valid explanation.

        Taking your example as illustration, your opinion of Willis is not relevant to whether Willis has or has not quoted Kip out of context. You say your experience leads to you think Willis would not do that (at least, not deliberately). So what? My experience is that he has often done that to me and has refused to withdraw when his blatant error is pointed out (e.g. here). Neither your experience nor mine is relevant to whether Willis has or has not quoted Kip out of context. It is for Willis and Kip to explain their different understandings so others (including you and me) can assess whether or not Willis quoted Kip out of context.

        Richard

      • JohnKnight and Richard Courtney,

        Good points. I don’t want to argue about this because I save my arguments for the alarmist commenters.

        I don’t disagree with anything, but I ask your opinion: do you think it is always wrong to quote a sentence or two out of an article like this, and reply to it?

      • dbstealey:

        You ask me (and JohnKnight)

        I don’t disagree with anything, but I ask your opinion: do you think it is always wrong to quote a sentence or two out of an article like this, and reply to it?

        No it is not “always wrong” and I fail to understand why you consider I might think it is. I agreed with Kip’s explanation of ‘out of context’, and I quoted it, then I wrote

        Most quotations are NOT ‘out of context’.

        I stand by that.

        Richard

      • Richard,

        In that case, I think we are in agreement. As I wrote above:

        “I’m not talking about distorting someone’s meaning. That is the fallacy, not simply responding to some particular comment.”

      • dbstealey

        “…do you think it is always wrong to quote a sentence or two out of an article like this, and reply to it?”

        Certainly not, but because of the provisional meaning the author is giving to the key phrase “imaginary numbers”, it is necessary to avoid presenting portions of the essay outside that provisional context he generated, to avoid quoting his words out of context.

        The alternative to we readers/commenters being careful about that, would be for the author to include many repetitions/echoes of his initial distancing statement throughout the essay, such that it would be difficult to select a few sentences that did not make it clear he was not using the key phrase in it’s traditional math sense.

        This sort of provisional space generation is very common in literature, and it would be quoting Mr.. Twain (for instance) out of context, if one quoted something he wrote as Huck Finn speaking, as though it was Mr. Twain writing his own thoughts outside the provisional context of a novel.

        Mr. Hansen is doing something roughly akin to that, as I read it, in an attempt to convey a subtle truth about numbers that are often presented as though very definite and precise (imaginary), but are actually somewhat indefinite and vague when their origins are considered carefully (reality).

        It’s an attempt at “counter-spin” to my eyes (not speaking in the classical mathematical or biological senses here ; )

    • Willis,

      Just average the rainfall over CA with that of SC and problem solved. No drought and no flooding.

      ;-)

      • Or if you live in a two roomed apartment, and one room is minus 100 degC and the other room is plus 140 degC, who would claim that you have a the perfect living conditions at an equitable 20degC.

        Averages can often distort matters since you lose important information when averaging.

        And what do the changes in averages tell you?

      • richard verney October 11, 2015 at 5:58 pm

        Or if you live in a two roomed apartment, and one room is minus 100 degC and the other room is plus 140 degC, who would claim that you have a the perfect living conditions at an equitable 20degC.

        Averages can often distort matters since you lose important information when averaging.

        Thanks, richard. Indeed they can. For example, the average human has one breast and one testicle.

        Does that mean that we should eschew using averages?

        No, it means that we should eschew using averages wrongly.

        And what do the changes in averages tell you?

        The changes in which averages? The changes in the average of my 35 most productive years tells me how much my Social Security benefits will be, and whether it’s worth working another year or taking retirement now.

        So, you tell me the average you’re talking about, and I’ll tell you what changes in that average might mean … which may, of course, be nothing.

        However, even the changes in apparently meaningless averages can tell us things. For example, what if after a while the average human has three-quarters of a testicle and one-quarter of a breast … what would that tell you?

        Best regards,

        w.

    • Reply to vukcevic ==> Ah…if you review my total output here at WUWT, you’ll see that I sometimes like to stir the pot a bit, shake things up and poke the complacent with a stick to see what happens.

    • (Well, you better hope Apple doesn’t get wind of this, or you may be in for some serious trouble ; )

    • (Hmm . . i numbers. Judging by the reaction to imaginary numbers, you might have been summarily i shot, if you used i numbers instead ; )

  72. Dang: I was going to comment about the HUGE UTILITY of imaginary numbers. With which we wouldn’t have PHASORS, for power systems analysis. Here’s a webpage and some pictures of “imaginary power” generators. http://www.tepcoegypt.com/Products-MV%20Reactive%20Power%20Compensation%20Banks.html

    The key point here is THIS IMAGINARY NUMBER actually creates something USEFUL! And quantifiable. Unlike the “climate scientist’s” imaginary numbers which are…just that, made up and imaginary.

    • Reply to Max Hugoson ==> Alas, as I say in the first paragraph “This essay is not about the mathematical entity the imaginary number. I do think that an essay here about imaginary numbers of that sort would be interesting, but this isn’t going to be it.”

      Maybe you’ll submit an essay here on that….it would be interesting.

      • To understand how the graph I’ve shown above (it refers to magnetic fields and the AMO) is generated, go to the last animation in the link. There are two pointers in the graph yellow and orange. Assume that yellow is the solar magnetic cycle, and orange the earth core magnetic field. Further assume that the two pointers are rotating at different speed, ie. the phase marked as B is continuously changing, then by using slightly modified formula shown above the animation (exponents are changed to i*omega*t1) and (i*omega*t2) , and hey presto, the wave form is generated that so closely (wiggle) matches the AMO.

    • For those new to the ‘phasor’ terminology there is an easy to follow article Phasor Diagrams

      Climate science shouldn’t shy away from this versatile tool. Static magnetic fields can be represented by ‘vectors’, but if they are harmonic (or idealised as such) oscillations then the ‘phasor’ is the next step. Two magnetic fields of such type are solar magnetic field and a component of the Earth’s field measured at surface, but assumed to be generated by thermal convection at the boundary of the earth’s mantle and the outer liquid core.
      When the sum of two phasors is presented in Decartesian instead of the phasors’ polar system coordinates, result has an uncanny resemblance (correlation if you wish) with the N. Atlantic SST oscillation better known as the AMO

      • p.s.
        It is hard to comprehend the power of imagination of Nikola Tesla, the inventor of alternative poly-phase electrical power systems (generator, transformers, motors etc) visualising all the physical processes involved, just with a few paper sketches, usually penned down after the whole idea was mentally worked out.

      • For beginners who got familiar with phasor diagrams in the previous link, this page is useful next step, with some nice animations.
        http://resonanceswavesandfields.blogspot.co.uk/2007/08/complex-phasors.html#complex-rotor-animation
        You will see references to the real and imaginary axis. In this case ‘imaginary’ doesn’t mean some is trying to fool the reader, it is a mathematical term to get over fact that there are positive and negative numbers (depending on your point of reference.

      • Here it is again:
        To understand how the graph I’ve shown above (it refers to magnetic fields and the AMO) is generated, go to the last animation in the link. There are two pointers in the graph yellow and orange. Assume that yellow is the solar magnetic cycle, and orange the earth core magnetic field. Further assume that the two pointers are rotating at different speed, ie. the phase marked as B is continuously changing, then by using slightly modified formula shown above the animation (exponents are changed to i*omega*t1) and (i*omega*t2) , and hey presto, the wave form is generated that so closely (wiggle) matches the AMO.

      • vukcevic,

        Thanks for these comments on real imaginary numbers ; )

        I “think” I get what’s going on in this realm, but it’s hard for me to tell exactly what is the imaginary aspect(s) of what I’m trying to decipher/grasp. Would I be crudely correct to say something like; In “real” number-land, negative and positive values are not mirror images of each other, but in “imaginary” number-land, they can be?.

    • Max says:

      …THIS IMAGINARY NUMBER actually creates something USEFUL!

      There are lots of mathematical discoveries that at the time appear to have nothing whatever to do with reality. They are considered oddities, which was the original perception of imaginary numbers when they were first discovered and proven.

      But interestingly, just about every such mathematical discovery has real world applications. It seems mathematics really is the language of the universe. We may not understand a lot of what it is saying at first, but eventually it becomes clear. Even despite Godel…

  73. Post Script:

    My thanks to those who have taken time to read this essay — a cautionary tale. I hope that you have taken away from it at least the idea that maybe some of the numbers proffered to us by some practitioners of science of what-they-claim-to-be-measurements may have to be very carefully examined as to how we use them to interpret properties of the real world.

    In particular, I have attempted to illustrate a special type of number which is the result of attempts to reduce vastly huge planet-wide dynamic systems to a single number (usually of great precision as with Global Sea Level) which in this essay I have referred to as an “imaginary number”. The continuous attempts we see in scientific literature and the main stream press to use these types of single-numbers, my imaginary numbers, and minute changes in these single-numbers over short time periods, to make broad claims about the world around us, represent a scientifically questionable practice and are often the basis of propagandistic advocacy for and against targeted social and political ideas.

    It is my view that we need to be much more cautious in our acceptance of such numbers and the applications suggested to us by their producers …. because of their underlying nature.

    This problem is not confined to Climate Science, of course. We see worse examples in the health sciences, mostly in epidemiology, which I write about elsewhere.

    And finally, had Willis E. asked “so are we measuring an illusory thing?”, you would have read an answering essay about “illusory numbers” instead of imaginary ones and some mathematicians would have had an easier time of it absent a perceived trespass on their closely held, deeply beloved, nomenclature.

    I do hope that some brave soul will write an essay here about the “imaginary unit” of the mathematicians and its applications in science. Feel free to blame me for bringing up the subject.

    • Mr. Hansen
      Thank you for looking into and clarifying one of the important and controversial data issues. Despite the minor matter of the i numbers, your essay is appreciated judging by numerous comments. Thanks for the relaxed and polite way of dealing with the ‘nothing better to do’ detractors i myself included.

      • I agree.
        It is important to expose the controversial accuracy issues of the “claimed” data.
        Thank you.

    • Kip, I would still appreciate your answers to the issues I raised above. You’ve been more than happy to discuss my take on the “imaginary number” question in great detail, but unless I missed it, you haven’t said one word about the three specific and substantive issues that I raised in that comment … and now you are trying to declare that the discussion is over by adding a “Post Script” and walking away.

      Well, perhaps it is over … but if so, you have not done your part. I asked specific questions which to date you have not been willing to answer.

      w.

  74. Kip Hansen October 12, 2015 at 7:30 am

    And finally, had Willis E. asked “so are we measuring an illusory thing?”, you would have read an answering essay about “illusory numbers” instead of imaginary ones and some mathematicians would have had an easier time of it absent a perceived trespass on their closely held, deeply beloved, nomenclature.

    One final comment about this part of your Post Script. Please stop blaming me for your word choice. I said “are we measuring an imaginary thing“. I said nothing about imaginary numbers, that’s all you, and your attempt to blame me for it is a joke. Man up and own your own choice of words, they’re not my words and have nothing to do with me.

    w.

      • Dang, that’s depressing. You didn’t strike me as a man who would turn and run rather than answer a few scientific questions.

        Well, live and learn. I guess we’ll never find out what your bright-line definition of an “imaginary number” is that will let us determine what you were talking about, or what you have against averages or trends.

        Before, I said that I’d asked questions that you were unwilling to answer. Now I see that in fact, I asked questions that you have categorically refused to answer.

        Ah, well. I expect that kind of tactic from Phil Jones, not from skeptics. Like I said …

        … depressing.

        w.

      • Willis ==> I suppose it is depressing for you to discover that you don’t get to control every conversation, and that others, including myself, do not owe you answers. Bullying and blackmail-by-name calling make it even less likely that people will respond to you. You are often your own worst enemy.

      • Kip Hansen October 12, 2015 at 2:42 pm

        Willis ==> I suppose it is depressing for you to discover that you don’t get to control every conversation, and that others, including myself, do not owe you answers. Bullying and blackmail-by-name calling make it even less likely that people will respond to you. You are often your own worst enemy.

        Your idea, that I think I can control a conversation involving a herd of unruly netizens, is so far from reality that it’s not even wrong. NOBODY can control the conversation here at WUWT, that’s what makes it so interesting.

        In any case, I said quite clearly what was depressing, and it had nothing to do with control. Let me quote it, since you didn’t do so and as a result you were just addressing your own straw man:

        Dang, that’s depressing. You didn’t strike me as a man who would turn and run rather than answer a few scientific questions.

        It was your moral cowardice that I found depressing, not anything about “control”. You had me fooled. I thought you were a man with some starch … foolish me.

        In any case, I’m glad you’ve clarified the question of responsibility. According to you, it was my fault that you called what you were talking about “imaginary numbers”. And now it’s my fault that you refuse to answer my questions.

        Is there anything that you take responsibility for, or is every bad thing in this discussion my fault?

        Anyhow, I got it. You only answer scientific questions from people that you like and approve of. Or as Phil Jones famously said to Warwick Hughes, “Why should I give my data to you, when you’ll only try to find fault with it?”

        Phil didn’t understand that that is exactly WHY he should have given his data to Warwick Hughes, because that’s how science works. It’s an adversarial game, and you are foolishly doing just what Phil did, refusing to act like a scientist because you don’t like the people who happen to be asking the questions. I don’t care in the slightest if you like me. It’s not a popularity contest, it is a discussion of scientific ideas. If you are a scientist, you’ll answer questions about your own work from anyone, PARTICULARLY those that you dislike.

        Heck, my advice has always been, give your best ideas to your worst enemies, because if they can’t find anything wrong with them you’re likely home free.

        Anyway, is that your final excuse for running away from the tough questions, blaming it on me because I’m such a big krool meany and I didn’t talk nice to you?

        Or are you willing to put your personal feelings aside, act like a scientist, stop blaming me, and answer my questions?

        Your choice … but don’t even think of blaming this choice on me. You’ve tried that twice already. Doesn’t work.

        w.

      • So I take it you won’t be answering my scientific questions now, because you don’t like my style? Well, fair enough. I can be cantankerous.

        But remind me again … what was your excuse for avoiding my questions back when I asked them, back when I was still a good guy, before you decided I was krool and heartless?

        Why didn’t you answer my scientific questions back then? Click the link and read them. I was calm and polite in the asking. We could easily have avoided all of this. All I’ve done since then is ask you, again and again, to answer my questions.

        You’ve decided that me asking you to answer simple scientific questions about your own claims, and then asking you again when you didn’t answer, and then again, and at the end, me calling you out on it when you finally flat-out refused to answer those questions, is somehow bad and wrong …

        Let me suggest that you might want to re-examine your choices if you ever wish to gain any traction on this or any other skeptical website. That kind of evasion of scientific questions is the specialty of the climate alarmists, so you could probably make it fly over at say RealClimate or OpenMind.

        But it doesn’t serve you well in scientific circles. Regardless of your reasons, even if your reasons are fully justified in your mind, even if the guy asking the questions is a total jerkwagon, you look simultaneously evasive, arrogant, and unsure of yourself when you refuse to answer scientific questions about your own claims. No bueno.

        Best of luck, Kip. You seem like a decent man, and your refusal to answer simple scientific questions is a total mystery to me.

        Regardless, and in all seriousness, I do wish you well and I sincerely hope you don’t get caught again in this kind of trap of your own making,

        w.

  75. Kip: (AKA “Pokey” ) (grin)
    Another interesting essay and lively debate!
    I’ve had no trouble distinguishing between the concept of imaginary numbers as you are using it, and the formal mathematical construct. But then, I tend to annoy both idiots and savants about equally.

  76. For the record:

    Here are the “scientific questions” [his emphasis] which Willis has been demanding that I answer: (since most of them are not really questions, per se, I include everything followed by a question mark):

    I’m sorry, but I don’t understand this distinction. Is every average an “imaginary number” in your world? It appears that you have defined an average as an “imaginary number” … but why?

    And if an average is an “imaginary number”, then what about a trend? What about the error of an average? What about the first Principal Component? Are those “imaginary” as well?

    My second objection is that if averages in your world are “imaginary” … so what?

    So that’s my second objection—I don’t understand what the problem is with averages on your planet?

    And again, what difference does it make if the sea level in New York is “imaginary” or not? If it starts rising faster and faster, are you going to say “No problem, folks, it’s just an imaginary number, nothing to see here, move along”?

    The quality of the “questions” speak for themselves.

    As the rest of you already know, the essay is not about simple “averages”, these issues are fully covered in the original essay, discussed and clarified at length.

    • Seriously? Your response is to ridicule what you call the “quality” my questions?

      So you are now refusing to answer my questions because in your world they are “low-quality”?

      Really?

      Man, the last response I expected from my most recent comment was a new excuse for not answering them.

      And that the excuse would be that I’m not going to answer the questions because I don’t like them?

      It’s just a variation of the Phil Jones evasion, “Why should I give my data to you, when you’ll only try to find fault with it?”

      Of course you don’t like my questions! Nobody likes to answer questions. We all think that we’ve explained things perfectly, and that if people would just open their eyes all would be obvious.

      But that’s not the case. People have scientific questions, that’s the reality.

      And I don’t get to go “Oh, Kip’s question is not up to my quality standards, no need to answer that one”. If I tried that BS on the folks who ask me questions of every level of quality, I’d get roasted for it, and rightly so. What do you think this is, one of those fake political interviews where the Russian President gets to approve of all the questions in advance?

      THE NATURE OF SCIENCE IS THAT YOU DON’T GET TO JUST ANSWER THE QUESTIONS YOU LIKE!

      w.

      • Willis ==> Saying “The quality of the “questions” speak for themselves.” is ridicule?

        I’m sure you must feel your questions are exemplars of scientific enquiry.

        I’m also sure other readers, if there are still any following this thread (which I doubt), will make their own evaluations of the scientific value or validity of your questions in their context here in the comments to my essay.

        I just wanted others who may read your long series of comments here to know exactly what “scientific questions” you had asked and have been insisting that I answer.

      • Kip Hansen October 13, 2015 at 10:41 am

        … I’m sure you must feel your questions are exemplars of scientific enquiry.

        I’m also sure other readers, if there are still any following this thread (which I doubt), will make their own evaluations of the scientific value or validity of your questions in their context here in the comments to my essay.

        Kip, you still seem to think that you get to decide which scientific questions to answer. However, when someone does that, it’s no longer science.

        I just wanted others who may read your long series of comments here to know exactly what “scientific questions” you had asked and have been insisting that I answer.

        Nonsense. I’d cited my entire comment containing the questions just above.

        You, after giving us a very pompous lecture on what “out of context” means, merely selected from my nuanced and clearly posed comment, every sentence ending in a question … dude, that is the most out-of-context procedure I can imagine. Re-read your own definition above of out-of-context … then look at how you’ve mangled my words.

        In any case, my point remains. You’ve given us a host of reasons for e.g. not giving us a bright-line definition of what an “imaginary number” is. I’ve gone through your post, and I can’t find any such definition. And without such a definition, I can’t answer the following kinds of questions, e.g.

        Are all averages, no matter of what, “imaginary numbers”?

        Or are just some special kinds of averages “imaginary numbers”?

        Are trends “imaginary numbers”?

        Does it matter if the variable being measured is intensive or extensive?

        The average of 3 and 5 is 4. Does that make 4 an “imaginary number”?

        The ocean height in point A is 3, and at point B it is 5. Is the average ocean height of 4 an “imaginary number”?

        My income is 3 and my gorgeous ex-fiancee’s income is 4. Is our average income of 4 an “imaginary number”?

        I continue to be mystified by your refusal to respond to a simple request to clearly define your own freakin’ term. You’ve redefined a common math term, “imaginary number”, to have some other meaning … but then you refuse to give a bright-line definition of or even discuss the new meaning.

        I have constantly been offering you a chance to act like a scientist and, you know, discuss your own claims and define your own terms. I continue to be mystified that you don’t just take me up on my offer, instead choosing to dig your hole even deeper.

        Kip, it doesn’t matter that you don’t like my questions or you don’t like me. If you refuse to answer scientific questions about your ideas, you’re not a scientist, you’re no better than Phil Jones, and you’ll never get traction on any scientific site.

        With my best wishes,

        w.

      • Willis ==> Maybe if you re-read the concluding summary:

        Today’s discussion is one way of looking at the current trend in Science in which attempts are made to reduce very complicated dynamic systems to a single number which can then be graphed against time, usually in attempts to do one or more of the following:

        1. to cast blame for the increasing or decreasing number on a substance or action or group, usually incorrectly
        2. using two such graphs of single numbers to correlate some single number with some other single number to sell a desired story, usually to cast blame or give credit, usually incorrectly
        3. to bring attention to [read this as: to cause public concern or worry about] some rising or falling single number in hopes of generating gain [in research funds, fame, public sympathy, public or political support], usually unwarranted

        These single numbers, meant to somehow illuminate some feature of the real world, are often, maybe almost always, not real numbers representing real things, but imaginary numbers representing concepts that exist, on a pragmatic practical level, only in our imaginations, which may lack meaningfulness and usefulness, or both. In this special sense, we can rightly refer to them as imaginary numbers. And because they are almost never acknowledged as imaginary numbers which require special care in application, each of the three uses above is followed by “usually incorrectly” or “usually unwarranted”.

        Now, even if you don’t agree with me, it should be interesting to discuss in comments some of the ongoing efforts to [mis-] use this special breed of derived number, the imaginary number, to sway public opinion in differing scientific fields around the world. I’d really like to hear your views and benefit from your experience.

        and in reponse to you way above:

        The essay is not about mathematics, which others have already pointed out to you. It is also not about the mathematicians “imaginary unit or numbers”, not about “AGW; CAGW; Catastrophic Climate Change; Global Cooling; various oxides of carbon; the pH, level, or surface temperature of oceans; or the antics or ethics (or lack of ethics) of various international scientists and politicians”, stated clearly “This essay is not really about global sea level, but I doubt we’ll be able to discuss it without also touching on the issues surrounding the issue of global mean sea level.” It certainly is not about simple averages of numbers.

        and

        As the rest of you already know, the essay is not about simple “averages”, these issues are fully covered in the original essay, discussed and clarified at length.

        and

        Sea Level, even “Sea Level at the Battery in New York”, is not properly represented by a single number, above and below some geodetic bench mark. What we call sea level is a derived, calculated number – an average of averages of an array of measurement time series. In this sense, as the calculated mid-point of a range over time, it is, in a practical sense, an imaginary number having no existence in the day-to-day life of the Port of New York.

        There is, however, a pragmatic “sea level at the Battery in New York” – which itself is a predictable range above and below some depth of water at a certain point (a point referred to as Local Mean Sea Level) which, when modified by information of expected, predicted tides, can be extrapolated to other points in the harbor, which is useful for mariners despite its less-than-real aspect. It can be used in its gross form (fractions of feet or meters) to determine the depth of water over the bottom at a place and time important to a ship’s captain and crew. Here is the prediction of water levels, relative to MLLW, made for October 9th thru October 11th.

        Please note that you are the ONLY reader that seems to have mistaken this essay to be about simple averages of everyday things.

        You have worn out my patience, sir. Time for a little straight-talk:

        Your attempts to bully others — in this case myself — into answering your mis-characterized “scientific questions”, which are based entirely on your own misunderstandings and, because of that fact, are the qualitative-equivalent of attack comments typically left by malicious clueless teenage-trolls, is typical of your behavior in the comment sections here at WUWT. Simply put, I do not like bullies and I do not feed trolls.

        My apologies for being so blunt — maybe I should have just come out and said this at the beginning of your near-endless stream of nonsense.

        [edited five minutes later to add an omitted emphasis to the first section — kh]

    • Hi John
      sorry about link not working.
      Lets try again with this abbreviated version
      On the x axis we have ‘real’ numbers with 0 (zero) in the middle , negative numbers to the left, positive numbers to the right.
      Square of any number from either side of zero is to be found to the right hand side of zero, i.e. in the positive section, and consequently since none of them fall to the left of zero, i.e. in the negative section, we can not calculate sq. root of negative numbers.
      This is a limitation of the one dimensional axis, implying that numbers in everyday use are simple and one-dimensional.
      Since negative numbers also must have square roots we have to overcome this ‘minor’ difficulty. Let’s assume that numbers are more ‘complex’ than just one-dimensional, i.e. that they have second dimension, which we are not aware of up to now, so for a brief moment have to imagine it, thus so called ‘imaginary’ numbers.
      It is much better and less misleading to just think of this new ‘complex’ idea as ‘complex’ numbers, encompassing both dimensions.
      To represent this new two dimensional entity we need a two dimensional plane, where the old y axis is replaced with new i axis, which also has a positive and negative section. In this new system sq. roots of ‘real’ negative numbers now fall in the positive section of i axis.
      In a two dimensional complex number, value of the first dimension is projected on the x axis and value of the second dimension projected on the i axis.
      To make distinction between first and second dimension, we add an ito the value in the second dimension.
      Hence a complex number is written as z = x+yi, if y=1 we just write i.
      Fact is that all numbers are complex, but if the value in the second dimension is zero, i.e. y=0, then number is simple and called ‘real’ number, and if value in the first dimension is zero i.e. x=0, we have so called an ‘imaginary’ number
      It would be far more appropriate for terms ‘imaginary’ and ‘real’ to be dropped all together, and just think of all numbers as the ‘complex’.
      Note that to understand complex numbers we do not need to start with notion that i = sq. root (-1)
      In complex numbers whereby value in either dimension is not equal to zero, are found all over complex plane. Using polar coordinates, instead Cartesian to describe complex plane it is a much neater and mathematically more efficient way of applying complex number calculations, I would compare it to changing from the Roman to Arabic numerals annotation. By doing so we automatically encounter periodic functions (sin & cos) in which case complex numbers become an essential tool for studying harmonic oscillations as found in mechanical, electrical & electronic engineering, radio communications, electro-acoustics etc.
      Anyone familiar with vectors should have no difficulty in comprehending the notion of two dimensional numbers.

      The above including number of graphics, was roughly content of an essay I had to write in the last term of my grammar school, subsequently I went to University, and had no problems (as encountered by many students) with the understanding applications using complex numbers

      • Thank you much, vukcevic, your patience is admirable.

        It seems to me my impression was correct, though my question was perhaps a bit clumsy. I do see this “disregard” for the often apparent reality of “real numbers” as wise and quite useful, now. I always suspected as much, but it’s good to have a better idea of how this manifestation of freedom of the mind has born good fruit.

      • John, tnx.
        It just emphases futility of the squabble further up the thread. English language has disadvantage since expressions as imaginary, differential, integral etc, are used in informal conversations as well as strictly precise mathematical formulations. In other minor languages, like mine own, colloquial terms are very different while those used in science are identical to the above ‘internationalised’ terms.

        To paraphrase ‘most of maths is fiction, people who think that things that happen in fiction are not real, they are wrong.’

  77. Mod, I apologize … but I’m entering this test reply to see if my “chemistry set and bullets” preprocessor is packaging the right codes to become the beauteous neo-HTML that this site accepts as input. Pardon me, please.

    • bullet 1 with bold stuff
    • bullet 2 with italics text
    • bullet 3 with underlined points

    CO + H₂O + heat → CH₄OH + stuff.
    H₂SO₄ + 2 Fe → Fe₂SO₄
    ²³⁸U is fertile; ²³⁵U is fissile. A fact that could ‘blow you away’. LOL
    And this¹ is a footnote²

    — end of test —
    GoatGuy
    _______
    ¹ first footnote
    ² second footnote.

    [Reply: Please use the ‘Test’ page for this. Thanks. ~mod.]

  78. Kip Hansen October 14, 2015 at 7:14 am
    Willis ==> Maybe if you re-read the concluding summary:

    Today’s discussion is one way of looking at the current trend in Science in which attempts are made to reduce very complicated dynamic systems to a single number which can then be graphed against time, usually in attempts to do one or more of the following:

    1. to cast blame for the increasing or decreasing number on a substance or action or group, usually incorrectly
    2. using two such graphs of single numbers to correlate some single number with some other single number to sell a desired story, usually to cast blame or give credit, usually incorrectly
    3. to bring attention to [read this as: to cause public concern or worry about] some rising or falling single number in hopes of generating gain [in research funds, fame, public sympathy, public or political support], usually unwarranted

    These single numbers, meant to somehow illuminate some feature of the real world, are often, maybe almost always, not real numbers representing real things, but imaginary numbers representing concepts that exist, on a pragmatic practical level, only in our imaginations, which may lack meaningfulness and usefulness, or both. In this special sense, we can rightly refer to them as imaginary numbers.

    Thanks for the response, Kip. I’ve read that several times. Unfortunately, it doesn’t allow me to distinguish between real numbers and “imaginary” numbers.

    Under the first part of your definition, if I understand it, if someone calculates an average (or some other “single number”) representing some factor of a complex system (say the average depth of the ocean), that does NOT necessarily make it an imaginary number.

    However, under the first part of your definition, if they use that single number to cast blame, or if they compare that single number to some other single number, or if they use that number to generate funds or public sympathy, then it IS necessarily an “imaginary number”.

    Unfortunately, that definition is completely contradicted by the final quoted paragraph of your summary. It says that “imaginary numbers” are not “real numbers representing real things”. Instead, “imaginary numbers” are numbers that represent “concepts that exist, on a pragmatic practical level, only in our imaginations”.

    Now, in my understanding, the following numbers are NOT “real numbers representing real things”, but numbers that represent concepts that exist only in our mathematical imaginations:

    • averages
    • medians
    • variances
    • standard deviations
    • skewness
    • kurtosis
    • first differences
    • principal components
    etc.

    So by the definition in your final paragraph quoted above, all of those are “imaginary numbers” no matter what they are averages or variances of. They exist only in our mathematical imaginations—you can’t directly measure say variance in the real world.

    So I fear that I still don’t have enough information from your definition to tell if a number is a real number or an “imaginary number”. For example, which of these are real numbers and which are imaginary numbers?

    1. The average expenditures of my wife and myself.

    2. The standard deviation of the rainfall amounts in Sheboygan, Wisconsin.

    3. The average shirt size of the American male.

    4. The median lifespan of people in Buenos Aires.

    5. The average of one day’s worth of minute-by-minute measurements of the sea level measured in a stilling well in Galveston, Texas.

    6. The average per-capita energy use graphed against average per-capita GDP (PPP values), categorized by country.

    7. The average of the highest 35 years of your earnings, which is used to calculate your Social Security benefits.

    8. The median human dietary requirement for Vitamin D.

    According to the your definition, these are all, every one of them, not “real numbers representing real things”, but “imaginary numbers” that represent “concepts that exist, on a pragmatic practical level, only in our imaginations”.

    But are all of them “imaginary numbers” in your world, or are some of them real numbers, and why?

    Finally … so what if they exist only in our imagination? Why does this make them second-class numerizens, “imaginary numbers” in your terms? All of those are numbers which are actually used in practical, beneficial ways in the world. It is valuable to know how much Vitamin D people need. It is useful for the city planners in Sheboygan to know how much rainfall there has been in the past.

    So I’m still very unclear about just what it is that distinguishes an “imaginary number” from a real number, and I don’t understand why you think it makes a difference.

    My best to you, and thanks for pointing out the paragraphs you think define an “imaginary number”.

    w.

      • Kip Hansen October 14, 2015 at 12:17 pm

        I still don’t feed trolls … go beg attention elsewhere.

        Oooh, you’ve invented a brand new excuse to avoid answering scientific questions.

        Well, folks, there you see it. He refuses to give us a clear “bright-line” definition of what he is talking about. He refuses to discuss my scientific questions about his vague definition. And now we get yet another excuse for his not answering questions. This time I’m a “troll”. A peculiar kind of “troll”, one who is doing nothing but asking clearly stated scientific questions …

        As to “begging attention”, what bizarre fantasy is that? My work attracts about a million page views per year … I have much, much more attention on me and my work and my claimed failings than most men would ever desire. I don’t need more.

        Kip, I ask you questions because you’ve advanced a vague theory that somehow some numbers are good and some numbers are bad. It’s an interesting theory, but you haven’t told us how to tell the difference.

        Me, I’m just trying to figure out which numbers are which on your planet. What’s mystifying to me is, why don’t you just answer the questions? Seems like if you truly believe in your theory, you’d want to explain it to everyone’s satisfaction.

        I gotta confess, though … near as I can remember, that’s the first time ever that anyone has seriously called me a troll. Makes me think you’re not entirely clear on the meaning of the word. I’m asking real scientific questions for a real reason—you have not given us a clear definition of the central idea of your claims, your concept of the “imaginary number”.

        Best regards,

        w.

      • Mr. Eschenbach,

        It’s kinda hard for me to imagine what the problem is for you, in understanding what I and it seems to me dozens of other people understood Mr. Hansen was trying to convey about the “rubberyness” of some numbers presented on the mass media as hard and precise.

        If you hear the talking heads on the news saying; “Good news on the economy, employment rose a quarter of a percent again last month, beating expectations for the twelfth month in a row now.” . . Are you convinced anything particularly good has really happened . in reality-land? Don’t you treat such “numbers” as sort of illusory and highly suspect in terms of reflecting a significant truth beyond the speaker having those words in front of them to read?

        I don’t see any reason to have a problem with the general idea Mr. Hansen seems to me to be presenting . . it seems almost self evident to me.

        This may come as a shock to you. but I don’t trust Siants, the big lumbering institutionalized quasi Entity, any further than I trust the TV talking heads. That Moron decided CO2 in a pollutant, I’m not bowing to that Idiot. He’s not my Idol.

      • Mp. Hanson . . illusory? . chasing illusory numbers? My inner poet cried out in it’s tiny little voice; *Yeah, it’s the correct term, AND it fills the metaphor perfectly* . . What would you suggest I tell the little imp? ; )

      • Reply to JohnKnight ==> Thank you — I can not really believe that W.E. has so thoroughly failed to understand what you and the (probably) a couple of hundred other readers here managed to comprehend, most at first reading — albeit a few only after a little discussion in the Comments. He is a normally bright guy.

        His dogged insistence that I answer his questions, each based on his own mis- or non-understanding of the topic, and the labeling them as “scientific questions”, has me utterly baffled. When combined with his bullying commenting style it does make for comments that are the qualitative-equivalent of those nasty attack comments normally left by malicious clueless teenage-trolls (although W.E. does have a better vocabulary than most of that ilk). Given this, I have finally decided to quit responding to him, in effect, applying the same policy I do with other trolling : Don’t Feed the Trolls.

        Overall, his behavior in the comment sections here at WUWT, which often follows the pattern he has exhibited here with this essay, has always been a subject of some interest to me in a sociological study sort of way. Can’t say I’ve come to any conclusions yet though.

        I do agree that “illusory” might be a better choice if I were to write about this idea again — but as I’m sure you’ve already realized, the word originally comes from responding to a question from Mr. E and I stuck with it in this tangential, answering essay — I tried to head off the expected objections — stepping on a few nomenclaturists toes — in the first sentence with almost zero success!

        I have an upcoming essay about “The Single-Number Fallacy” (logical fallacy) following on to this general idea — don’t worry — I shall not call the Single-Numbers “imaginary numbers” (once burned…)

      • Reply to vukcevic ==> You are probably right….but part of the Fallacy of the Single-Number is that these sorts of numbers are almost always proffered in a form that implies “great precision”…..which is a hefty percentage of what is wrong with them. For example, this from NOAA for August 2015:

        The combined average temperature over global land and ocean surfaces for August 2015 was 0.88°C (1.58°F) above the 20th century average of 15.6°C (60.1°F) and the highest August in the 136-year record. This value surpassed the previous record set in 2014 by 0.09°C (0.16°F).

        Here the “precision” is claimed at 1/100ths of a degree C.

        Now I understand why you are cautioning me, but I need to address this issue somehow, and would appreciate your advice.

        I have seen references make this differentiation of defintion:

        “Accuracy is the proximity of measurement results to the true value; precision, the repeatability, or reproducibility of the measurement”.

        Is this what you are talking about?

        How would you suggest I speak about this aspect of my posited Single-Numbers? Perhaps I should refer to them as being “proffered with claims of great accuracy” ?

        Appreciate you willingness to help….

      • JohnKnight October 15, 2015 at 1:13 am

        Mr. Eschenbach,

        It’s kinda hard for me to imagine what the problem is for you, in understanding what I and it seems to me dozens of other people understood Mr. Hansen was trying to convey about the “rubberyness” of some numbers presented on the mass media as hard and precise.

        Thanks, John. I understood that part very well The problem lies in your phrase, “some numbers” … my question, the question that Kip has repeatedly refused to answer, was and still is, which numbers? Because if we can’t tell the good numbers from the bad, what use is his theory?

        And his examples don’t help. For example, as to precision, he says:

        Can we measure sea level to that (+/- 3 to 4 mm) degree of accuracy? Well, for sea level, even at a single precise location, the answer is “No, we can not.” Now, I am not trying to be provocative here, it is a simple matter of fact. If the sea would be so kind as to stand still, even for just a few moments, we could get in a very accurate measurement at a single spot, or even a lot of spots. Alas, the sea is never still, it is always moving up and/or down: tides, currents, wind chop, waves, wakes of passing vessels, rising and falling air pressure and, in most important locations, all of those at once. Thus, we cannot physically do it; the sea does not stand still long enough for us to make this measurement to that degree of accuracy.

        This simply reveals his lack of knowledge of his subject. The SEAFRAME sea level measuring systems measure sea level routinely to that accuracy, by using a combination of an acoustic measuring system and a “stilling well”. This is a simple vertical tube placed in the ocean, with a tiny hole drilled in it.

        As you can imagine, the level inside the stilling tube rises and falls with the tides … but not with the waves of passing vessels and the like.

        If you hear the talking heads on the news saying; “Good news on the economy, employment rose a quarter of a percent again last month, beating expectations for the twelfth month in a row now.” . . Are you convinced anything particularly good has really happened . in reality-land? Don’t you treat such “numbers” as sort of illusory and highly suspect in terms of reflecting a significant truth beyond the speaker having those words in front of them to read?

        Do I treat them as illusory? It depends on the particular numbers and the particular claim. Again I point you to the problem—merely saying that some numbers can’t be trusted doesn’t help us unless we have some method to distinguish between the real numbers and the “imaginary numbers” … and Kip has refused to answer questions about how he is making that distinction.

        I don’t see any reason to have a problem with the general idea Mr. Hansen seems to me to be presenting . . it seems almost self evident to me.

        I don’t either, as a general principle … but as always, the devil is in the details. Merely saying some numbers can’t be trusted doesn’t help us in the slightest, unless we know which ones.

        This may come as a shock to you. but I don’t trust Siants, the big lumbering institutionalized quasi Entity, any further than I trust the TV talking heads. That Moron decided CO2 in a pollutant, I’m not bowing to that Idiot. He’s not my Idol.

        While I appreciate the example, this may come as a shock to you, but I have no clue who either Siants or “that Moron” are …

        All the best,

        w.

      • Kip here is an example that illustrates the “accuracy” issue you raise.
        ..
        Suppose you had a measuring stick with marks at the 1-foot, the 2-foot, 3-foot, 4-foot, 5-foot, 6-foot, and 7-foot lengths.

        Now using this stick, you measure 10,000 adult American males, recording each measurement to the nearest foot.

        If you take the average of your measurement results, you’ll find that it comes very close to 5.8333 feet. (which is 5 foot, 10 inches)

        In fact if you used 20,000 observations, your results would be even closer to 69.7 inches.

        The standard error is inversely proportional to the square root of the number of observations. So your 1-foot measuring stick will get closer to the population average with a higher number of observations.
        ..

      • Reply to vukcevic ==> Yes, I get the “single precision number” angle — I’d be stepping into another cow-pie of nomenclaturists objections. I will avoid combining the words “single” and “precision” (along with “imaginary”).

        Thank you.

      • Mr. Eschenbach,

        “Thanks, John. I understood that part very well. The problem lies in your phrase, “some numbers” … my question, the question that Kip has repeatedly refused to answer, was and still is, which numbers?”

        You’re welcome . . And if I were someone who didn’t yet understand what you do about the “example” I conjured, how would you answer if they asked you what you are asking Mr. Hansen? …which numbers, etc?

        Is not the question itself asking about something rather “illusory” and difficult to pin down with any single “equation”?

      • JohnKnight October 15, 2015 at 3:15 pm Edit

        Mr. Eschenbach,

        “Thanks, John. I understood that part very well. The problem lies in your phrase, “some numbers” … my question, the question that Kip has repeatedly refused to answer, was and still is, which numbers?”

        You’re welcome . . And if I were someone who didn’t yet understand what you do about the “example” I conjured, how would you answer if they asked you what you are asking Mr. Hansen? …which numbers, etc?

        Is not the question itself asking about something rather “illusory” and difficult to pin down with any single “equation”?

        John, Kip refused to just give us a clear definition of what is and isn’t an “imaginary number”. He’s given us a number of excuses for his actions, but none of them included the excuse that the answer was too “difficult to pin down” … so please, don’t give him ideas for new evasions.

        However, following your general thought, since he had refused to give us a general definition, I decided to see if we could put some bounds on it by asking him about specific examples. These examples would not be either “illusory” or “difficult to pin down”, to use your words. I asked:

        For example, which of these are real numbers and which are imaginary numbers?

        1. The average expenditures of my wife and myself.

        2. The standard deviation of the rainfall amounts in Sheboygan, Wisconsin.

        3. The average shirt size of the American male.

        4. The median lifespan of people in Buenos Aires.

        5. The average of one day’s worth of minute-by-minute measurements of the sea level measured in a stilling well in Galveston, Texas.

        6. The average per-capita energy use graphed against average per-capita GDP (PPP values), categorized by country.

        7. The average of the highest 35 years of your earnings, which is used to calculate your Social Security benefits.

        8. The median human dietary requirement for Vitamin D.

        According to the your definition, these are all, every one of them, not “real numbers representing real things”, but “imaginary numbers” that represent “concepts that exist, on a pragmatic practical level, only in our imaginations”.

        But are all of them “imaginary numbers” in your world, or are some of them real numbers, and why?

        Since he also refused to answer those questions, I fear that your objection that the concept is vague or hard to define lacks merit.

        w.

      • Mr. Eschenbach,

        “John, Kip refused to just give us a clear definition of what is and isn’t an “imaginary number”. ”

        Sure, and I didn’t give you one either, but you understood me just fine it seems. And it seems to me Mr. Hansen is trying to sort of brainstorm here, with us, on how to best approach what he sees as a difficult to define problem, certainly in terms of CAWG propaganda weaponry, so to speak.

        Why not give it a try, and see if you can’t come up with something more definitive, using that newscast example you seem to understand in terms of the numbers being illusory and suspect insofar as reflecting realistically on much of anything, despite sounding hard and precise etc?

        As we start hearing monthly updates on the current temperature of the earth, in hundredths of a degree updates, what shall we say? How shall we respond in a way that helps more people know that’s just an imaginary thermometer in mommy Earth’s mouth ; ) or anything truly like that?

      • JohnKnight October 15, 2015 at 11:51 pm Edit

        Mr. Eschenbach,

        “John, Kip refused to just give us a clear definition of what is and isn’t an “imaginary number”. ”

        Sure, and I didn’t give you one either, but you understood me just fine it seems.

        Sorry, I have no idea what you’re referring to here.

        And it seems to me Mr. Hansen is trying to sort of brainstorm here, with us, on how to best approach what he sees as a difficult to define problem, certainly in terms of CAWG propaganda weaponry, so to speak.

        DEAR HEAVENS, WHY DO YOU THINK I PUT FORWARD THOSE EIGHT QUESTIONS???

        Mr. Hansen is REFUSING to brainstorm. I’ve asked those questions to try to brainstorm about the issue, to try to narrow down what he’s talking about. Unfortunately, he will not even say which of those are real numbers and which are “imaginary numbers”.

        Why not give it a try, and see if you can’t come up with something more definitive, using that newscast example you seem to understand in terms of the numbers being illusory and suspect insofar as reflecting realistically on much of anything, despite sounding hard and precise etc?

        You truly don’t seem to understand what’s happening. I am and I have been attempting to get to something more definitive. Unfortunately, Mr. Hansen flatly refuses to engage with me in any shape or form. He won’t define what he’s talking about. He won’t say whether my examples are real numbers or imaginary numbers. He just says he doesn’t like the questions … sorry, that cuts no ice with me.

        Now, if you think you understand what Mr. Hansen’s “imaginary number” is, I’m happy to discuss it with you … so how about you answer the questions, and we can start from there. Here they are again:

        For example, which of these are real numbers and which are imaginary numbers?

        1. The average expenditures of my wife and myself.

        2. The standard deviation of the rainfall amounts in Sheboygan, Wisconsin.

        3. The average shirt size of the American male.

        4. The median lifespan of people in Buenos Aires.

        5. The average of one day’s worth of minute-by-minute measurements of the sea level measured in a stilling well in Galveston, Texas.

        6. The average per-capita energy use graphed against average per-capita GDP (PPP values), categorized by country.

        7. The average of the highest 35 years of your earnings, which is used to calculate your Social Security benefits.

        8. The median human dietary requirement for Vitamin D.

        According to the your definition, these are all, every one of them, not “real numbers representing real things”, but “imaginary numbers” that represent “concepts that exist, on a pragmatic practical level, only in our imaginations”.

        But are all of them “imaginary numbers” in your world, or are some of them real numbers, and why?

        Not a hard question. Give me your answers and your reasons, and you can do what Kip refuses to do, what did you call it … ah, yes, to brainstorm here, with us, on how to best approach what he sees as a difficult to define problem

        Finally, you say:

        As we start hearing monthly updates on the current temperature of the earth, in hundredths of a degree updates, what shall we say? How shall we respond in a way that helps more people know that’s just an imaginary thermometer in mommy Earth’s mouth ; ) or anything truly like that?

        Mmmm … given the response to this post, I doubt talking about an “imaginary thermometer” will get you much traction anywhere. To me, claiming that some measurement is “imaginary” is a horrible claim. The problem with the current global temperature records include but are not limited to:

        • it is an average of an intensive property, which
        • makes the uncertainty of the results larger than folks think, plus
        • the temperature records have a high Hurst Exponent, which
        • makes the uncertainty of the results larger than folks think, plus
        • the records are short, spotty, irregular, and
        • the number of records changes over time, and
        • they contain confounding factors (UHI, land use changes, instrument changes, location changes) which
        • have either been removed or not, and the removal may be accurate or not, which
        • makes the uncertainty of the results larger than folks think

        Now, any or all of those are perfectly valid messages to help people understand the meaning and importance of the thermometer records.

        But telling folks “Don’t worry, it’s just an imaginary thermometer”? Man, I’d never try that on on. Saying it’s an “imaginary thermometer” has no real meaning. It doesn’t point to the real problems. It doesn’t further understanding.

        And more to the point, it’s NOT an imaginary thermometer. It’s a real thermometer, just one with real and large problems.

        My best to all,

        w.

      • Mr. Eschenbach ,

        “You truly don’t seem to understand what’s happening. I am and I have been attempting to get to something more definitive.’

        Go for then, batter up, sport.

        “DEAR HEAVENS, WHY DO YOU THINK I PUT FORWARD THOSE EIGHT QUESTIONS???”

        To sabotage rational dialog, I think you’re “cointelpo”.

      • JohnKnight October 16, 2015 at 2:04 am

        Mr. Eschenbach ,

        “You truly don’t seem to understand what’s happening. I am and I have been attempting to get to something more definitive.’

        Go for then, batter up, sport.

        Thanks, John, but you have the metaphor backwards. I am pitching the questions, and I’ve invited Kip to bat. Since he refused, I invited you to bat … is this your form of a refusal?

        “DEAR HEAVENS, WHY DO YOU THINK I PUT FORWARD THOSE EIGHT QUESTIONS???”

        To sabotage rational dialog, I think you’re “cointelpo”.

        Asking rational questions and trying to get a definition of mathematical terms is “sabotaging rational dialog”????

        On what planet is that true?

        w.

      • Reply to JohnKnight ==> I tried to warn you. The minute you give him any attention at all, even negative attention, he just laps it up and then goes on and on and on…more-of-the-same…bully and name-call … demanding answers to his inane self-proclaimed, mis-characterized, pseudo-“scientific-questions”.

        He’ll never stop until you quit feeding him attention.

      • Kip Hansen October 16, 2015 at 9:30 am

        Reply to JohnKnight ==> I tried to warn you. The minute you give him any attention at all, even negative attention, he just laps it up and then goes on and on and on…more-of-the-same…bully and name-call … demanding answers to his inane self-proclaimed, mis-characterized, pseudo-“scientific-questions”.

        He’ll never stop until you quit feeding him attention.

        Thanks, Kip, I’m glad to see that you are now coming up with a new excuse for not answering simple questions about your own claims. Now it’s because I’m a “bully” … ooooh, is poor little Kip getting bullied?

        Kip, to “bully” someone you have to be able to threaten them. The classic example is from school, “Give me your lunch money or I’ll beat you up”.

        Bullying is less than effective if the threat is “Give me your lunch money or I’ll … I’ll … I’ll do nothing to you.”

        So if you are feeling bullied, perhaps you could let us know just what you think the threat is? Because as far as I know, I have absolutely no way to threaten you, and more than that, I have no desire to threaten you.

        In other words, claiming oh poor me, now I’m the victim of krool bullying by the eeevil Willis is just one more in your endless list of excuses.

        As to me going on and on, there’s a very simple way to stop me—ANSWER THE QUESTIONS ABOUT YOUR OWN CLAIMS, so that we can understand what it is you are talking about.

        But noooo, you’d rather whine about being “bullied” than answer simple questions about your work.

        Pathetic.

        w.

      • Mr. Hansen,

        Sorry I ruined your comment thread ; )

        I heard ya, I was just doing a bit of “research” of my own.

        I say he’s an imaginary troll ; )

      • Reply to JohnKnight ==> Weird, huh?

        You can email me at my first name at the domain i4 decimal net if you want to share your research findings.

        Cheers.

      • Yeah, very weird . . too weird for me to swallow. Like I said earlier; I highly suspect flack is inevitable over this target

  79. Hi John
    re chasing illusory: I vaguely remember reading somewhere:
    ‘Don’t believe everything you think. Thoughts are just inclusions of the mind’

    • Thanks for the suggestion, vukcevic . . I thought I heard; *Garbage in, garbage in . .* and lilting laughter . .

  80. Excuse the lateness of this reply. I initially thought that I would merely hint at this in my comment above but decided to elaborate.

    The mean is the expectation of the distribution ie the temperature anomaly if there were no local factors creating a divergence from the climate mandated temperature. This equals the mode and the median for a normal distribution so irrelevant which you choose.

    Do you really want the mean when the distribution is more skewed? If you think that the temperature is proportional to the amount of energy in the atmosphere around the station, then yes but air that’s falling warms without more energy input and cooling as it rises up a mountain. The minimum temperature is also highly dependent on the dew point so what is the justification to use the mean? The min and maximum are highly dependent on when cloud cover arrives over the station.

    More importantly is the missing data. I’ve noticed that in the Aus records that the data that’s missing the most is mostly the very hot days. Such missing data can make a large difference to the annual mean but little to the median.

    Why this fascination with the mean as an indicator when it physically has little meaning and will be affected more by dodgy numbers? Surely the median is a better indicator of what the climate does.

    Median filtering in image process is used for speckle noise rather than blurred noise and surely that is the bigger problem in using minimum and maximum station temperatures (dew point, cloud cover, wind shifts).

    • Reply to Robert B. ==> In support of your view:

      Marcia Glaze Wyatt, in the text that accompanied her PowerPoint presentation “Uncertainty in Climate Science” these provocative statements:

      {There is] “No such thing as “average temperature”!”

      “How does one choose a sampling of temperatures whose average will really tell us anything about the heat content of the climate system? Earth systems transport heat from where there is more to where there is less; thus, heat is constantly being re-distributed laterally and vertically in Earth’s on-going planetary mission to rid itself of excess energy. How can local temperatures of a very limited area capture the heat energy of the planet in any meaningful way? Temperature really says less than might be assumed. So it becomes obvious that choice of location of where a temperature is measured influences any “average” taken.”

      “Average temperature is the average of average motion of molecules in select locations…In short, average temperature is nothing more than a statistic. It holds no physical meaning!!!”

      This follows the general idea behind my essay here — “average temperature” in the sense Marcia is using is an example of my “imaginary numbers” — a single-number proffered to us as the essence of a huge and vast complex dynamic physical system, an essence that does not exist in the pragmatic real world.

      Thank you for stopping back and elaborating your earlier comment.

    • The CET is one of the more accurately calculated regional temperatures with the UHI corrections.
      Here you can see daily maximum, minimum and 20 year averages all compared to the insolation.

      From the graphs I could make number of i/relevant observations, but there is no need to do so since most are self-evident.

  81. Kip, thanks for posting Marcia Wyatt’s comment.

    How does one choose a sampling of temperatures whose average will really tell us anything about the heat content of the climate system? Earth systems transport heat from where there is more to where there is less; thus, heat is constantly being re-distributed laterally and vertically in Earth’s on-going planetary mission to rid itself of excess energy. How can local temperatures of a very limited area capture the heat energy of the planet in any meaningful way? Temperature really says less than might be assumed. So it becomes obvious that choice of location of where a temperature is measured influences any “average” taken.

    This illustrates a problem with averages of intensive variables like temperature. To remind folks, an “extensive” variable of a given substance like a litre of water is something like mass, where if you double the amount (extent) of the substance, you get twice the mass. But temperature is an intensive variable. if you double the amount of water, you don’t get twice the temperature.

    Now, if you have a block of some unknown substance, you can get an accurate measure of the mass with one measurement. But you can’t do the same with temperature, because it might be hot at one end and cold at the other, and frozen in the middle where you can’t measure it.

    This causes problems … but not insuperable problems. What the measurement of intensive quantities involves is:

    • It means that you need more than one measurement to give you an answer.
    • It means that the uncertainty of your result is greater than if you were measuring an extensive variable.
    • It means that the more measurements you take, in both time and space, the more accurate your answer is.

    However, it doesn’t mean that the answer is “imaginary” or useless. Statisticians long ago recognized the problem you and Marcia are referring to, and people have developed statistical tools to get value out of those types of measurements.

    FOR EXAMPLE: In mining exploration, you are looking for an “ore body”, an area where there is a concentration of the desired item. Now, the average density of the ore in the ore body is an intensive quantity. As both you and Marcia point out, measuring an intensive quantity is difficult, and in addition, the location of the measurements influences the answer.

    SO … in response, did people:

    a) Throw up their hands and say it’s an “imaginary number”, or,

    b) Develop methods for getting the best estimate of the true value for the intensive variable given the limited information available?

    The answer, of course, is b). Statisticians developed things like kriging, and Kalman filters, and first-difference analysis, and optimum interpolation, to deal with exactly the problems that you and Marcia seem to think are insuperable.

    In fact, although Marcia seems unaware of it. the value of the surface air temperature at any time is pretty tightly constrained by the amount of ground stations that are currently in place. The problem is not the number of stations, although more stations would help. But the main problem is that we can’t really trust the individual station time series because of undocumented moves, instrumentation changes, and the like.

    These problems are somewhat obviated by the use of satellite measurements of the temperature. Of course it brings up its own problems, but the coverage is much better and the trends are not affected by UHI, station moves, or thermometer changes.

    Now, here is the important point. All that any of these techniques can do is VARY THE UNCERTAINTY of the calculated result. In general, they can’t change an intensive variable into an extensive variable.

    So suppose I want to measure the temperature of my swimming pool. I toss in one floating thermometer and tie the string to the ladder. I record the temperature every three hours for ten days and take an average. The average is 20°C. Is this an imaginary number?

    Absolutely not, no way. It’s just a number with a large amount of uncertainty. We don’t know the temperature of the other end of the pool, or the bottom of the pool. Maybe the other end is always in shade. And the bottom is not warmed as much as the surface by the sun, but then the surface loses more heat through radiation and evaporation than the bottom, that kind of thing. So maybe the temperature is really 20° ± 5°C.

    But I’m not satisfied by that, so I get 8 thermistors and I put them at the four corners of the top and the four corners of the bottom of the pool. In this case, I record the eight temperatures every minute and average them and I get 23.3° ± 0.5°C … is that an imaginary number?

    Again, absolutely not. Again, it’s just a number with an associated uncertainty. In this case, as you’d expect, since we have more measurements in both time and space, the answer that we get is more certain. But that’s just the nature of intensive measurements—all we can ever get are estimates with associated (and usually largish) uncertainties.

    So let me suggest that if you want to distinguish between real numbers and what might be called “illusory numbers”, here is a bright-line definition— illusory numbers are those without an associated uncertainty. They give the illusion that they are scientific, when in fact they are not.

    A corollary, of course, relates to the importance of accurate estimates of total uncertainty. This is an entire branch of statistics, one that in climate science is often given short shrift, or wrongly calculated, or ignored entirely … but that’s another post entirely. My experience in general is that in climate science, someone who overestimates the uncertainty of their results is a rara avis indeed …

    w.

    • Mr. Eschenbach.

      I give you credit for trying to actually give a definition, and I hope you won’t react too negatively, but it seems to me you’re not yet quite getting the problem Mr. Hansen is attempting to find a way to deal with.

      The problem, as I see it, is not about one such “illusory” number as you defined it there, but dozens, crammed together with “illusory” number glue, to arrive at a sort of “hyper-illusory” single number, presented as though the reading on a giant thermometer.

      Sort of like what Mr. Mann did when he used different data sets to construct his infamous hockey stick graph, on steroids, so to speak. A whole slew of “Illusory” numbers as you defined them, blended together in “illusory” ways, and presented as though a single measurement.

      Just my take . . .

    • An intensive property is independent of the size of the sample and the same in any part of it.

      Willis, you’re imagining that the mean of max and min thermometer readings of atmospheric readings are intensive properties like density (quotient of two extensive properties – mass/volume) or concentration (eg. amount of solute/volume of solution). Your pool example is more like the mining example where carefully analysing many samples will give you a good estimate of total thermal energy divided by the heat capacity but thats a liquid, and a small quantity.

      Strange considering what you wrote about SST being limited by evaporative cooling that’s exponential with temperature that you can’t appreciate that its not the same as concentration.

      • Robert B October 18, 2015 at 5:14 pm

        An intensive property is independent of the size of the sample and the same in any part of it.

        Thanks, Robert, but that’s only half true. An intensive property is independent of the size of the sample, but it is NOT the same in any part of it.

        w.

      • The average of concentration is not an intensive property unless the sample is homogeneous. I know that we tend to call the total amount of one component divided the total amount of all components in the system an average concentration but its not the average of the densities of the samples except where the whole sample is analysed evenly, in which case you might as well add up the amounts and then divide.

      • Sorry the above was written in a rush (and so is this). Σmi/Vi /n ≠Σmtotal/Σvtotal. Think about what you need to do to get that average to be meaningful and can you do it with SST and/or min/max measurements 2m above the ground. You need to consider more than how much thermal energy in the mass of air is represented by the measurement and if the uncertainty for the 1km3 around the station is most likely ±1°C, whats the point?

        (fingers crossed that the html come out OK).

  82. JohnKnight October 17, 2015 at 9:24 pm

    Mr. Eschenbach.

    I give you credit for trying to actually give a definition, and I hope you won’t react too negatively, but it seems to me you’re not yet quite getting the problem Mr. Hansen is attempting to find a way to deal with.

    The problem, as I see it, is not about one such “illusory” number as you defined it there, but dozens, crammed together with “illusory” number glue, to arrive at a sort of “hyper-illusory” single number, presented as though the reading on a giant thermometer.

    Thanks, John. If you could give an example of such a “hyper-illusory” single number, that would be useful.

    All the best,

    w.

    • Mr. Eschenbach,

      Not with certainty . . I’m trying to give you my impressions, as a layman, observing the discussion. Are there any numbers at all that you would consider beyond plausible, like monthly global temps in hundredths of a degree?

      • JohnKnight October 18, 2015 at 3:43 am Edit

        Mr. Eschenbach,

        Not with certainty . . I’m trying to give you my impressions, as a layman, observing the discussion.

        Thanks, John, but without examples it’s very hard to respond to your claim that there are “hyper-illusory” single numbers.

        Are there any numbers at all that you would consider beyond plausible, like monthly global temps in hundredths of a degree?

        The problem is not the number of decimals in the answer. It’s the lack of accurate estimates of uncertainty in the answer that makes it illusory and problematic. Climate science in general has forgotten that science without error bars is not science at all …

        All the best,

        w.

      • Willis,

        Well, isn’t the entire IPCC ~CAWG is settled science~ claim, an assertion about such a hyper-illusory number; 100% chance it will happen (if we don’t cough up trillions of bucks ; ) with lots of error bars involved along the way to reaching that certainty conclusion? The error bars don’t seem to have played much of a limiting/reality check roll in coming up with that (to my mind) hyper-illusory number.

        Isn’t that 100 a good example to your mind, of what I tried to “define”,?

      • JohnKnight October 18, 2015 at 2:10 pm

        Willis,

        Well, isn’t the entire IPCC ~CAWG is settled science~ claim, an assertion about such a hyper-illusory number

        John, how would I know? The idea of a “hyper-illusory number” is your own, so I don’t have a clue what the definition might be. That’s why I asked for examples …

        w.

      • Willis,

        ” The idea of a “hyper-illusory number” is your own, so I don’t have a clue what the definition might be.”

        ?? . . I wrote what my idea is, such as it is;

        +Sort of like what Mr. Mann did when he used different data sets to construct his infamous hockey stick graph, on steroids, so to speak. A whole slew of “Illusory” numbers as you defined them, blended together in “illusory” ways, and presented as though a single measurement.+

        “That’s why I asked for examples …”

        I gave you three examples that capture the idea, I feel;

        Employment numbers

        Current global temperature

        The certainty of catastrophic anthropogenic global warming

        I’m really not sure what you want . . I mean, I’m just trying to give you my impression, not a testable scientific hypothesis.

      • JohnKnight October 18, 2015 at 11:43 pm

        “That’s why I asked for examples …”

        I gave you three examples that capture the idea, I feel;

        Employment numbers

        Current global temperature

        The certainty of catastrophic anthropogenic global warming

        John, as you may note I was asking for examples of your “hyper-illusory single number”. The examples you list above were all given by you as examples of Kip’s “imaginary numbers”.

        I’m really not sure what you want . . I mean, I’m just trying to give you my impression, not a testable scientific hypothesis.

        I give up, John. If you want to wave your hands and offer your “impressions”, there’s no meat there for me to respond to.

        Having said my piece, I suspect I’ll just leave you to discuss these matters with Kip unless you do offer something with substance.

        All the best,

        w.

      • Willis,

        “John, as you may note I was asking for examples of your “hyper-illusory single number”. The examples you list above were all given by you as examples of Kip’s “imaginary numbers”.”

        The notion that you don’t realize I used your definition of illusory number to generate a different way to say imaginary number, is not believable to me.

        If you’d like a meatier way for me to say that, just ask.

  83. “Are there any numbers at all that you would consider beyond plausible, like monthly global temps in hundredths of a degree?”
    Hi John
    I think that the global temps are hopelessly inaccurate, but we can assume that intra-decadal trends may just about resemble to reality. I say that, because there is another global variable (geomagnetic poles–dipole) having similar trends, but it leads the GT by about a decade

    Do I have an explanation? Not for a time being, that I would be able to fully justify.

    • Yo, Vuk (hopefully not a derisive term in Euronese ; )

      That is interesting, and I find the “electric universe” (as I’ve heard it called) explanation(s) more and more plausible as I learn more about this conceptual framework . . all these cycles pulsing and swirling everywhere . . one wonders why such things wouldn’t effect our climate(s).

      (assuming we have climate . . some apparently deny it ; )

    • Dr. Svalgaard from Stanford university, made an attempt to invalidate it, but inadvertently confirmed the hypothesis

      Svalgaard – yellow and brown lines, directly superimposed by Svalgaard on the existing
      Vukcevic graph – blue, green and red lines.
      To be fair correlation fails before 1850, but then, we do not have much of reliable instrumental data of magnetic intensity before 1850, Gauss invented magnetometer in mid 1830’s, and was not in wide use until decade or two later. There is no need to comment on accuracy of global temps before 1850,

      p.s jo – pronounced ‘yo’ means ‘good’ in Hungarian

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