Are We Chasing Imaginary Numbers?

Guest Essay by Kip Hansen


 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:


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.


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.


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:


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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October 9, 2015 10:06 pm

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.

Andrew N
Reply to  Nicholas Schroeder
October 9, 2015 11:23 pm

In other words – measure it with a micrometer, mark it with chalk and cut it with an axe.

Reply to  Andrew N
October 10, 2015 5:24 am

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.

Reply to  Andrew N
October 10, 2015 9:19 am

… only to find out after the wear and tear of a few uses, you have to make another one.

George E. Smith
Reply to  Andrew N
October 11, 2015 11:11 am

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.

Reply to  Andrew N
October 11, 2015 12:03 pm

Mr. Smith, you may got that wrong.
Stonehenge purpose was hijacked by academic historians. My wife comes from a town just few miles further south, so I should know. Here is an image the possible reconstruction ideas , and here is an image of the ritual kept alive in collective memory some six millennia later. Take a note of inner and outer circles.

David L. Hagen
Reply to  Nicholas Schroeder
October 10, 2015 7:07 am

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.]

Reply to  David L. Hagen
October 10, 2015 9:22 am

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.

Reply to  David L. Hagen
October 10, 2015 9:38 am

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.

Reply to  David L. Hagen
October 10, 2015 10:21 am

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
October 10, 2015 4:38 pm

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.

Reply to  David L. Hagen
October 10, 2015 4:43 pm

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.

NW sage
Reply to  David L. Hagen
October 10, 2015 4:56 pm

Perhaps “number with imagination’ would be a better fit? Not as neat to write about though.

Reply to  David L. Hagen
October 10, 2015 5:54 pm

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.

Reply to  David L. Hagen
October 10, 2015 6:50 pm

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.

Pierre DM
Reply to  David L. Hagen
October 10, 2015 9:07 pm

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

Reply to  David L. Hagen
October 11, 2015 6:31 am

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

more soylent green!
Reply to  David L. Hagen
October 11, 2015 9:51 am

‘Imaginary measurement?’ Perhaps ‘imaginary data’ instead?

Reply to  David L. Hagen
October 11, 2015 10:21 am

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.

George E. Smith
Reply to  David L. Hagen
October 11, 2015 11:20 am

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.

George E. Smith
Reply to  David L. Hagen
October 11, 2015 11:40 am

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  David L. Hagen
October 11, 2015 12:47 pm

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’.

Reply to  David L. Hagen
October 11, 2015 4:05 pm

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.

Chip Javert
Reply to  David L. Hagen
October 11, 2015 4:28 pm

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.

Reply to  David L. Hagen
October 12, 2015 9:53 pm

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.

Reply to  David L. Hagen
October 16, 2015 1:55 am

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…

George E. Smith
Reply to  Nicholas Schroeder
October 10, 2015 11:04 am

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.

Reply to  George E. Smith
October 10, 2015 11:15 am

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.

Reply to  George E. Smith
October 10, 2015 11:16 am

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.

Reply to  George E. Smith
October 10, 2015 11:22 am

Great quotes from big G-eorge :
Numbers you re seeing are mean; they don’t mean anything.
Statistical results are just numerical origami.

Steve Jones
Reply to  George E. Smith
October 10, 2015 11:25 am

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.

Reply to  George E. Smith
October 10, 2015 11:32 am

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.

Reply to  George E. Smith
October 10, 2015 8:25 pm

“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 ; )

Reply to  George E. Smith
October 11, 2015 1:33 am

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.

Reply to  George E. Smith
October 11, 2015 1:40 am

JohnKnight: “……. pounds of what?”
would this do?

Reply to  George E. Smith
October 11, 2015 6:37 pm

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

Reply to  George E. Smith
October 13, 2015 8:26 pm

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.

Lew Skannen
October 9, 2015 10:07 pm

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?

Reply to  Lew Skannen
October 9, 2015 10:55 pm

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

Lew Skannen
Reply to  Rascal
October 10, 2015 12:35 am

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.

Reply to  Rascal
October 10, 2015 2:10 am

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.

John M. Ware
Reply to  Rascal
October 10, 2015 2:54 am

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 . . .

Reply to  Rascal
October 10, 2015 9:24 am

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

George E. Smith
Reply to  Rascal
October 10, 2015 4:22 pm

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.
But I cold be rong !

Mark from the Midwest
Reply to  Lew Skannen
October 10, 2015 5:29 am

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.

Reply to  Mark from the Midwest
October 10, 2015 11:38 am

You are obviously a man who has never seen Eurovision song contest.

Evan Jones
Reply to  Lew Skannen
October 10, 2015 6:31 am

As SNL put it back in 1984, 9.7, 8.9, 9.1, 9.1 . . . “and a 5.4 from the East German judge”.

Reply to  Lew Skannen
October 10, 2015 6:38 am

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.

Reply to  Lew Skannen
October 10, 2015 6:54 am

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.

Monna Manhas
Reply to  PhilC
October 10, 2015 7:25 am

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.

Reply to  Lew Skannen
October 10, 2015 10:29 am
George E. Smith
Reply to  Menicholas
October 10, 2015 4:25 pm

They don’t do figures in figure skating, any more. The spectators all got bored.

Reply to  Menicholas
October 10, 2015 11:30 pm

What a massagenistic post, Menicholas.

Gary Hladik
Reply to  Menicholas
October 11, 2015 11:49 am

JohnKnight, this is a thread about “massaging” data, isn’t it? 🙂

Chip Javert
Reply to  Lew Skannen
October 11, 2015 4:35 pm

Error Bars?
Years ago in the Olympics it had more to do with the judges being corrupt.

October 9, 2015 10:30 pm

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.

James Bull
Reply to  jccarlton
October 10, 2015 1:25 am

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

Reply to  James Bull
October 10, 2015 2:01 am

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, , few adults of the next generation will have the factual knowledge of science to know the narratives are false anymore or the numbers imaginary.

Reply to  James Bull
October 10, 2015 6:57 am

The answer is 42. We just don’t know the question.

George E. Smith
Reply to  James Bull
October 10, 2015 4:26 pm

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

Reply to  James Bull
October 11, 2015 6:00 am

Brilliant and well said Robin!

Mike McMillan
Reply to  jccarlton
October 10, 2015 8:43 am

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.

Reply to  Mike McMillan
October 10, 2015 8:52 am

Do you have any specs on one. I’ve worked in instrumentation, had lectures on how pressure transducers work and I just cannot believe that level of precision on any instrument that I’ve ever seen. That’s would be better than .001% in an instrument measuring at several thousand PSI.

Billy Liar
Reply to  Mike McMillan
October 10, 2015 12:45 pm

See this page:
0.015%, 0.003% corrected

October 9, 2015 10:31 pm

The bottom line is: “You can’t polish a Turd”.

Reply to  peyelut
October 9, 2015 10:46 pm

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.

Reply to  Neville
October 10, 2015 4:30 am

Polished or not, we cannot put the poop back into the puppy neither.

Evan Jones
Reply to  Neville
October 10, 2015 6:53 am

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”.

Reply to  Neville
October 10, 2015 11:04 am

Sounds like you, like me, were likely no fun to play a game of Risk with.
I never lost.

Reply to  peyelut
October 10, 2015 12:22 am

you can actually and sell them e-bay. Look up “coprolite”.

Reply to  peyelut
October 10, 2015 12:41 am

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

Another Ian
Reply to  gary turner
October 10, 2015 1:22 am

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”

Reply to  gary turner
October 10, 2015 10:19 am

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!

Reply to  gary turner
October 10, 2015 1:10 pm

“got in trouble at school for putting it on the teacher’s desk ”
That is how you know it worked!

George E. Smith
Reply to  gary turner
October 10, 2015 4:53 pm

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.

Martin Hovland
October 9, 2015 10:39 pm

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 !).

Reply to  Martin Hovland
October 10, 2015 3:59 am

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.

Reply to  commieBob
October 10, 2015 6:43 am

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

Reply to  commieBob
October 10, 2015 8:09 am

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.

Reply to  Martin Hovland
October 10, 2015 4:51 am

Very telling

David L. Hagen
Reply to  Martin Hovland
October 10, 2015 8:19 am

What quality gauges were you using? Resolution? Accuracy? See nano resolution quartz barometers capable of micron level resolution. The issue is absolute accuracy.

M. Hovland
Reply to  David L. Hagen
October 10, 2015 9:15 am
David L. Hagen
Reply to  M. Hovland
October 10, 2015 12:23 pm


Resolution: 0.0001% FSO
Accuracy: ±0.02% FSO

Compare nono-resolution Digiquartz
For uncertainty analysis in use see e.g., Depth Accuracy in Seabed Mapping with Underwater Vehicles”, BJØRN JALVING. In this dynamic mapping application, the uncertainty was about 130 mm.

A complete DTM depth error budget has been identified. Modeling and quantification of the individual error sources reveals that a DTM depth accuracy of 0.13 m (1σ) can be achieved for 300 m UUV depth, 50 m altitude and 30° MBE beam angle (see Fig 2)

October 9, 2015 10:42 pm

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?

Reply to  Bob
October 9, 2015 11:33 pm

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.

Reply to  goldminor
October 10, 2015 7:18 am

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.

Interested Observer
Reply to  goldminor
October 10, 2015 8:54 am

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.

Reply to  Bob
October 10, 2015 2:01 am

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.

October 9, 2015 10:45 pm

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.

October 9, 2015 10:54 pm

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

Reply to  Amatør1
October 9, 2015 11:06 pm

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.

Reply to  rgbatduke
October 10, 2015 9:18 pm

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.

October 9, 2015 11:04 pm

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.
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…

Reply to  rgbatduke
October 10, 2015 7:48 am

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.

Reply to  bobbyvalentine466921
October 10, 2015 1:13 pm

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.

Reply to  rgbatduke
October 10, 2015 8:52 am

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.

Reply to  rgbatduke
October 10, 2015 10:45 am

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:

Reply to  Menicholas
October 10, 2015 10:47 am

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.

Reply to  rgbatduke
October 10, 2015 12:34 pm

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  vukcevic
October 10, 2015 12:38 pm

Here is the lost link

Reply to  Kip Hansen
October 11, 2015 6:45 am

…. he said after reading the comment just above….

October 9, 2015 11:06 pm

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.

Stephen Richards
Reply to  fossilsage
October 10, 2015 1:51 am

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.

Steve Reddish
Reply to  fossilsage
October 10, 2015 8:29 pm

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.

Reply to  Steve Reddish
October 11, 2015 3:13 pm

Steve you are missing the point

October 9, 2015 11:16 pm

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

Reply to  AndyL
October 10, 2015 5:57 am

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.”

Reply to  BillB
October 10, 2015 6:49 am

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.

charles nelson
October 9, 2015 11:17 pm

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?

Steve Case
Reply to  charles nelson
October 9, 2015 11:47 pm

How many climate scientists can dance on the head of …..? Why 97% of course.

Reply to  charles nelson
October 9, 2015 11:47 pm

Right now it is still very red looking…

Reply to  charles nelson
October 9, 2015 11:58 pm

…could someone please tell me the temperature of the Pacific Ocean?

Hot, hot hot! Crazy hot, and getting hotter!
Run for your life!!

Reply to  dbstealey
October 10, 2015 8:36 am

That’s because it’s sucking up all of the heat from the pause…

Reply to  charles nelson
October 10, 2015 9:07 am

“Luke warm …”
(jump in) “Damn, its cold. I thought you said it was warm.”
“… loook warm to me …”

Reply to  charles nelson
October 10, 2015 5:28 pm


Leonard Lane
October 9, 2015 11:45 pm

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?

Reply to  Leonard Lane
October 10, 2015 6:53 am

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
October 10, 2015 10:23 am

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 …..

Reply to  MarkW
October 10, 2015 11:09 am

“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.”

Reply to  MarkW
October 11, 2015 8:09 am

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.

Reply to  MarkW
October 11, 2015 10:06 am

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.

October 9, 2015 11:46 pm

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?

richard verney
Reply to  bananabender56
October 10, 2015 2:06 am

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.

Reply to  richard verney
October 10, 2015 4:03 am

Vessel speed is a factor too. Vessels tend to squat as speed increases.

Reply to  richard verney
October 10, 2015 6:55 am

Do you know the physics of that? I would have expected them to ride up as they go faster.

David Riser
Reply to  richard verney
October 10, 2015 7:26 am

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.

richard verney
Reply to  richard verney
October 10, 2015 12:06 pm

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 : describing the effect.

richard verney
Reply to  Kip Hansen
October 10, 2015 12:36 pm

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

October 9, 2015 11:51 pm

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}.

Reply to  TonyL
October 10, 2015 2:03 am

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.

Reply to  richardscourtney
October 10, 2015 2:45 am

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.
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.

Reply to  richardscourtney
October 10, 2015 3:19 am

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 verney
Reply to  richardscourtney
October 10, 2015 1:16 pm

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.

October 10, 2015 12:12 am

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  AndyE
October 10, 2015 2:06 am

Yes, it does matter. Please see my reply to TonyL.

Joe Born
Reply to  Kip Hansen
October 10, 2015 10:28 am

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.

October 10, 2015 12:18 am

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.

Peter Sable
October 10, 2015 12:21 am

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.
* 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…

Reply to  Peter Sable
October 10, 2015 1:19 am

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.

Dave in Canmore
Reply to  HAS
October 10, 2015 8:31 am

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.

Peter Sable
Reply to  HAS
October 10, 2015 1:11 pm

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.

Reply to  Peter Sable
October 10, 2015 7:09 am

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.

Peter Sable
Reply to  MarkW
October 10, 2015 7:15 pm

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.

Peter Sable
Reply to  Kip Hansen
October 10, 2015 1:27 pm

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.

Reply to  Kip Hansen
October 10, 2015 1:38 pm

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.

Reply to  Kip Hansen
October 10, 2015 1:44 pm

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.

Peter Sable
Reply to  Kip Hansen
October 10, 2015 7:05 pm

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:
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.

Tim Crome
October 10, 2015 12:57 am

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!).

Peter Sable
Reply to  Tim Crome
October 10, 2015 7:06 pm

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.

Dr. S. Jeevananda Reddy
October 10, 2015 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. 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

Reply to  Dr. S. Jeevananda Reddy
October 10, 2015 7:45 am

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.

richard verney
Reply to  H.R.
October 10, 2015 1:50 pm

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.

Peter Sable
Reply to  Dr. S. Jeevananda Reddy
October 10, 2015 7:14 pm

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.

October 10, 2015 1:10 am

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. 🙂

Reply to  4TimesAYear
October 10, 2015 7:10 am

The article mentioned movements of dry land and sea beds.

Reply to  MarkW
October 12, 2015 9:13 pm

My eyes must have jumped that segment. Glad they caught it 🙂

October 10, 2015 2:06 am

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.

Reply to  johnmarshall
October 10, 2015 2:30 am

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 verney
Reply to  richardscourtney
October 10, 2015 1:54 pm

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.

Reply to  richardscourtney
October 10, 2015 2:25 pm

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.

Richard of NZ
Reply to  johnmarshall
October 10, 2015 3:28 pm

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.

Robert B
Reply to  johnmarshall
October 11, 2015 1:46 am

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.

October 10, 2015 2:14 am

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

Ron Braud
Reply to  Jimbo
October 10, 2015 4:27 am

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?

Reply to  Ron Braud
October 10, 2015 7:01 am

Ron Braud, the point of the graph is the flattening. It’s to put things into perspective AND inform warmists who aren’t aware that sea level has generally been rising for thousands of years. I can’t recall the number of times I have read: “but sea levels are rising!”comment imagecomment image

Reply to  Ron Braud
October 10, 2015 7:05 am

GOOGLE phrase search
“but sea levels are rising”
“but sea level is rising”
“sea level is rising”

As you can see – nothing new.

Reply to  Ron Braud
October 10, 2015 8:46 am

The time to be worried is if sea levels start dropping as fast as they were rising between 7 and 8 thousand years ago.

October 10, 2015 2:23 am

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

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

October 10, 2015 2:26 am

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.

Reply to  Frederick Colbourne
October 10, 2015 3:08 am

Frederick Colbourne:
For some reason my reply to your comment has appeared here.

Reply to  Frederick Colbourne
October 10, 2015 5:41 am

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.

Steve Fitzpatrick
Reply to  stevefitzpatrick
October 10, 2015 11:12 am

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  stevefitzpatrick
October 10, 2015 2:11 pm

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

Reply to  Frederick Colbourne
October 10, 2015 7:13 am

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

Reply to  Frederick Colbourne
October 10, 2015 8:56 am

“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
October 10, 2015 11:22 am

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
October 10, 2015 4:19 pm

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.

Ivor Ward
October 10, 2015 2:43 am

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.

Reply to  Ivor Ward
October 10, 2015 1:27 pm

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.

Leo Smith
October 10, 2015 2:43 am

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…

Reply to  Leo Smith
October 10, 2015 3:04 am

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

Reply to  richardscourtney
October 10, 2015 3:54 am

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.

Reply to  richardscourtney
October 10, 2015 1:38 pm

You are an ignorant, pest and an Ahole.

Reply to  richardscourtney
October 10, 2015 2:36 pm

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 verney
Reply to  richardscourtney
October 10, 2015 2:37 pm

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.

Leo Smith
Reply to  Kip Hansen
October 10, 2015 1:37 pm

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.

October 10, 2015 2:46 am

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?

Reply to  nobodyknows
October 10, 2015 2:53 am

It should be 3,3mm pr decade.

Reply to  nobodyknows
October 10, 2015 3:01 am

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.

Reply to  nobodyknows
October 10, 2015 7:25 am

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?

October 10, 2015 2:46 am

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’?

Warren Latham
October 10, 2015 3:29 am

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
“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.”
(The Pages2K Goat-Rope Willis Eschenbach / September 11, 2015 Guest Post by Willis Eschenbach).
23rd. April 2015 – cFact article. FINANCING CLIMATE CRISIS, INC..
“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.”
– cFact article by Paul Driessen (senior policy advisor for CFACT).
– See more at:
29th. August 2015 – Propaganda Guard article.
– Propaganda Guard article by Micheal Winston and “blogged” by Robin Rey R. Shaw
… 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”.

Warren Latham
Reply to  Warren Latham
October 10, 2015 11:17 am

Dear “Moderator”,
Why did my reply (above) need to go through your approval ?
[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.]

Walt D.
October 10, 2015 3:33 am

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.

John law
October 10, 2015 3:36 am

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!

October 10, 2015 3:45 am

“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  Kip Hansen
October 10, 2015 1:46 pm

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:
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:

October 10, 2015 4:11 am

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.

October 10, 2015 4:41 am

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.

Billy Liar
Reply to  Mike
October 10, 2015 2:21 pm

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

wayne Job
October 10, 2015 4:43 am

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.

Reply to  wayne Job
October 10, 2015 5:28 am

Wayne, do you have proper ref. for any of that? I think there’s ONE such rock.

Reply to  Mike
October 10, 2015 5:30 am
October 10, 2015 4:52 am

comment image
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.

October 10, 2015 5:02 am

“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 ?

October 10, 2015 5:05 am

From one of the WP links provided by Kip:
No acceleration in 20th c.

October 10, 2015 5:06 am

Imaginary numbers are all fun and games until someone loses an i.

Reply to  stevek
October 10, 2015 10:48 am

Clever! ヅ 

October 10, 2015 5:08 am

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.