Guest Essay by Kip Hansen – 30 July 2022
One cannot average temperatures.
Let’s start with this simple statement – this statement is true but comes with some common-sense caveats.
Important Note: The purpose of this essay is not to refute the basic underlying concepts of “global warming” or “climate change”. Those concepts and their supporting data are an entirely different topic. This essay is about a scientific point: One cannot average temperature. This fact may affect your understanding of some of the supporting points of Climate Science.
Let’s say you run a web site for corporations interested in having conventions in Topeka, Kansas in August and you’d like to inform attendees what kind of weather, in terms of temperature, they should expect, so that they can pack clothes suitable for the trip. A chart like this is perfectly appropriate. It shows the average of historical high and low temps for each day of the month and appropriately shows this as a range and not just a number. It provides a common-sense answer to the corporate question: “What’s the weather like in August in Topeka?” Answer: Hot days and pleasant warm nights. So, speeches and presentations inside the air-conditioned auditorium during the day and in the evening, the Tiki Bar Luau around the hotel pool is definitely on!
In this case, they have not really attempted to “average temperatures” — they just averaged the numbers about temperatures to find an expected range of historic highs and lows – they don’t think this is a real temperature that could be measured – they acknowledge that it is a rather vague but useful range of expectable daily highs and lows.
This acceptable and reasonable approach is far different than taking the high temperature of San Diego, Los Angeles, Mohave and Palm Springs, adding them up, dividing by four, and pronouncing that you have produced the temperature average of the SW California Desert. You may have an absolutely correct — precise to many decimal places — mathematical mean of the numbers used, but you will not have produced anything like a numerical temperature or a physically meaningful result. Whatever numerical mean you have found will not represent the physical reality of “temperature” anywhere, no less the region of interest.
“But, but, but, but” ….. no buts!
One cannot average temperature
Why not? Temperature is just another number, isn’t it?
Temperature is not just another number – temperature is the number of – the count or measurement of — one of the various units of temperature.
temperature, measure of hotness or coldness expressed in terms of any of several arbitrary scales and indicating the direction in which heat energy will spontaneously flow—i.e., from a hotter body (one at a higher temperature) to a colder body (one at a lower temperature). Temperature is not the equivalent of the energy of a thermodynamic system. [ source ]
So, we can say that objects with temperatures with higher numbers, regardless of which scale one is using (°F, °C, K), are “more hot” and objects with temperatures with lower numbers (using the same scale) are “less hot” or “more cold”….and we can that expect that heat energy will flow from the “hotter” to the “colder”.
Multiplying temperatures as numbers can be done, but gives nonsensical results partially because temperatures are in arbitrary units of different sizes but most importantly because the temperatures do not represent the heat energy of the object measured but rather relative “hotness” and “coldness”. “Twice as hot” in Fahrenheit, say twice as hot as 32°F (freezing temperature of water) is 64°F – obviously warmer/hotter but only nonsensically “twice as hot”. In Celsius degrees, we’d have to say 1°C (we can’t double zero) and we’d have 2°C or 35.6°F (far different than 64°F above). Yes, that is because the unit sizes themselves are different. However, if we wanted to know how much “heat” we are talking about, neither degrees Fahrenheit or degrees Celsius would tell us….temperature is not a measure of heat content or of heat energy.
A cubic meter of air at normalized sea level air pressure (about 1,013.25 millibars) and 60% humidity at a measured temperature of 70°F contains far less heat energy than a cubic meter of sea water at the same temperature and altitude. A one cubic meter block of stainless steel at 70°F contains even more heat energy. The relative hotness or coldness of a body of matter can be expressed as its temperature, but the amount of heat energy in that body of matter is not expressed by giving its temperature.
How is heat expressed – quantified – in science?: the units of heat energy are calories, joules and BTUs. [ source ] We see that none of the units of heat are units of temperature (°F, °C, K). (Note: If thermodynamics were easy, I wouldn’t have had to write this essay.)
Temperature is a property of matter – and temperature is specifically an Intensive Property.
Extensive properties can be added together – Volume: Adding 1 cubic meter of topsoil to one new cubic meter of topsoil equals two cubic meters of topsoil and fills twice the volume the raised-bed garden in your yard. Length: Adding one mile of roadway to one mile of existing roadway gives two miles of roadway.
But for Intensive Properties, this does not work. Hardness is an Intensive Property. One cannot add the numerical Mohs scale hardness of apatite, which has a value of 5, to the numerical Mohs scale hardness of diamond, which has a value of 10, and get any meaningful answer at all – certainly not 15 and likewise, not “5 plus 10 divided by 2 equals 7.5”.
Color is an Intensive Property. Color has two measures, wavelength/frequency and intensity. Most of us can easily discern the color of matter – our eyes tell our brains the generalized wavelength of the light reflecting off or emanating from an object which we translate to a color name. Scientifically, the wavelength (or mixed wavelengths) of the reflected or emanated light can be measured as frequencies (in terahertz — terahertz, 1012 Hz ) and wavelengths (in nanometers). Colors cannot be added as numbers. In colored light, adding the three primary colors evenly results in “white” light. In pigments, adding the three primary colors results in “black”, and other combinations, such as magenta and yellow, in surprising results.
Similarly, temperature, an Intensive Property, cannot be added.
“Intensive variables, by contrast, are independent of system size and represent a quality of the system: temperature, pressure, chemical potential, etc. In this case, combining two systems will not yield an overall intensive quantity equal to the sum of its components. For example, two identical subsystems do not have a total temperature or pressure twice those of its components. A sum over intensive variables carries no physical meaning. Dividing meaningless totals by the number of components cannot reverse this outcome. In special circumstances averaging might approximate the equilibrium temperature after mixing, but this is irrelevant to the analysis of an out-of-equilibrium case like the Earth’s climate.” [ source: Does a Global Temperature Exist? By Christopher Essex, Ross McKitrick and Bjarne Andresen ( .pdf ) ]
That is a wonderful, but dense, explanation. Let’s look at the salient points individually:
1. Temperature, an intensive property, is independent of system size and represents a quality of the system.
2. Combining two systems (such as the temperatures of two different cubic meters of atmosphere surrounding two Stevenson Screens or two MMTS units) will not yield an overall intensive quantity equal to the sum of its components.
3. A sum over intensive variables carries no physical meaning – adding the numerical values of two intensive variables, such as temperature, has no physical meaning, it is nonsensical.
4. Dividing meaningless totals by the number of components – in other words, averaging or finding the mean — cannot reverse this outcome, the average or mean is still meaningless.
5. Surface Air Temperatures (2-meters above the surface) are all spot temperature measurements inside of mass of air that is not at equilibrium regarding temperature, pressure, humidity, or heat content with its surroundings at all scales.
We can see that even at very small scales, the few meters surrounding the MMTS sensor at the Glenns Ferry weather station in Idaho, the air temperature system is far from being at equilibrium — air over a hot transformer, frozen bare grasses, snow patches and brush, each absorbing heat energy from the sun and with differing heat content. All these smaller sub-systems are actively out-flowing heat or absorbing heat energy from the unequal systems around them. In a practical sense, if one was standing next to the sensor, you would know it was “cold” there, the air at the sensor being well below freezing – but in a pinch, you might be able to cuddle up to the transformer and feel warmer sharing its heat. It is not, however, scientifically possible to “average” the air temperatures even inside of the two-meters-on-a-side cube of air around the sensor.
One cannot average temperature.
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Author’s Comment:
I am under no illusion that this essay will be widely accepted by all that read here. It is, however, scientifically and physically correct and might shatter a lot of firmly held beliefs.
I will be writing a follow-up, Part 3, covering the excuses used in CliSci for pretending that they can validly average temperatures – including the lame excuses: “We don’t average temperatures, we average anomalies”; “We don’t just find means, we find weighted means”; “We don’t average, we krig”; “We don’t make data up, we ‘use numbers from the nearest available stations, as long as they are within 1,200 kilometers’ [750 miles].” (Note: This is the approximate distance from Philadelphia to Chicago or London to Marseille, which as we all know, do not share common climates, no less air temperatures); and many more. In all cases, temperatures are inappropriately averaged resulting in meaningless numbers.
One can, however, average and work with heat content which is an extensive property of matter. It is the heat content of the “coupled non-linear chaotic system” which is Earth’s climate that Climate Science is concerned with when they insist that increasing atmospheric CO2 concentrations are trapping more heat in the Earth system. But CliSci does not measure heat content of the system but instead insists on substituting the meaningless numbers various groups label as Global Average Surface Temperature.
Please feel free to state your opinions in the comments – I will not be arguing the point – it is just too basic and true to bother arguing about. I will try to clarify if you ask specific questions. If speaking to me, start your comment with something like “Kip, I wonder….”
Thanks for reading.
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How should I trust someone who states that one m³ of stainless steel (which one by the way) at 70°F contains more heat energy than one m³ of sea water?
What numbers did Kip Hansen take to calculate this? Or was it just a gut feeling?
Epilogue:
Well, this has been an interesting project — still requiring a Part 3 which I promise to deliver.
The majority of comments have come from 4 or five readers — who represent to opposing views. One set is what I call “Numbers People” — those who insist that “Numbers are Numbers” and can all be treated the same. The other set are science and engineering people, who realize that “Number Ain’t Just Numbers” and that they represent physical things and properties and must be treated only in manners that can deal with specific physical properties.
Thank you all for reading.
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You just gave me chills about when I tried to point out 12 years ago that Global Average Temperature had to be based on dozens of subjective choices.
I guess you count me on the “numbers are numbers” side. Yet I’m pointing out that one of the problems with the Essex paper is it tries to treat the Celsius scale as if it was just numbers, and doesn’t seem to understand why that gives them meaningless results.
As far as I’m concerned, I and “Numbers People” have given plenty of reasons why the argument that you cannot average any intensive values, is wrong, and none of them have involved arguing that numbers are just numbers.
Let me assure you that there are many, many physicists and chemists that will go along with temperatures being intensive and that you can not average them to get a meaningful temperature. You must deal with enthalpy if you wish to thermodynamically average a condition.
Temperatures are intensive. I’ve never argued there weren’t.
All I’m saying is that the logic that intensive values can never be averaged to get a meaningful result is wrong. The logic that the sum is meaningless and so the average must also be meaningless is not correct, and that there are plenty of counterexamples, e.g. density and velocity that prove that it is possible to average some intensive values and get a meaningful result.
There may be reasons why it’s different for temperature, but don’t claim that it’s because temperature is an intensive property.
“All I’m saying is that the logic that intensive values can never be averaged to get a meaningful result is wrong.”
Can you refute the general proof offered in the Essex paper on Page 6? If you can’t then you are doing nothing but offering a non sequitur.
“The logic that the sum is meaningless and so the average must also be meaningless is not correct, and that there are plenty of counterexamples, e.g. density and velocity that prove that it is possible to average some intensive values and get a meaningful result.”
Where have you shown that you can average densities? All you’ve ever done is average mass and volume and then show you can calculate the average density from the average of those extensive properties.
In order to calculate average velocity you must have total distance travelled and total time spent – so you are deriving an intensive property from extensive properties, distance and time. You are *NOT* averaging an intensive property.
Think of it this way. You monitor the velocity of your vehicle continuously. You find that going from point a to point b the velocity forms a sine curve, start off slow, reach a velocity peak, and then coast to a stop. Integrate that velocity curve and what do you get? ∫sin(t) dt
sin(t) is in meters/sec and it is multiplied by dx in seconds so you wind up with the area under the curve in meters – i.e. distance travelled, an extensive property. If you then want to know the average velocity, an intensive property, you divide the total distance by the total time in seconds and get an average velocity. You haven’t averaged the intensive property of velocity, you’ve averaged the extensive properties of distance and time and then used that average to calculate an intensive property. How does that prove that you can average an intensive property?
“As far as I’m concerned, I and “Numbers People” have given plenty of reasons why the argument that you cannot average any intensive values, is wrong, and none of them have involved arguing that numbers are just numbers.”
You haven’t provide ANY reasons at all. You have offered that you can calculate an intensive property from an average of extensive properties. And you have offered that you can too calculate an average of temperature numbers – See?
You haven’t showed *any* reasons as to why an average of intensive properties means anything in the real world. You’ve not refuted the general proof in the Essex paper on Page 6 in any way, shape, or form. All you’ve offered is that “numbers is numbers” is both your premise and conclusion. Circular logic at its finest.
“You haven’t provide ANY reasons at all. You have offered that you can calculate an intensive property from an average of extensive properties”
Your second sentence answers your first.
Clearly I have given a reason, you just dismiss it.
“You haven’t showed *any* reasons as to why an average of intensive properties means anything in the real world.”
I have, but you keep ignoring it. E.g. does an average density mean anything in the real world? Think about ships and the Archimedes’ principle before answering.
“You’ve not refuted the general proof in the Essex paper on Page 6 in any way, shape, or form.”
Do have to refute every piece of nonsense in the paper before you exercise some critical thinking? I find it difficult to refute that part because the whole premise appears flawed and at best badly defined.
It basically says that if an average can represent the temperature of a system it leads to a contradiction, but never defines what they mean by “the temperature”.
The argument is if you have two isolated boxes A and B and an average derived from the two, then if the temperature in box A changes, so does “the temperature” even though B hasn’t changed. That apparently is their contradiction. But I’ve no idea why they assume that changing an average has to change each part. I can only assume that they think “the temperature” must mean a homogeneous temperature, but that’s obviously falsified by the fact they start with two different temperatures.
They go on to make the same claims about global temperature, except there they actually use an average global anomaly. But they still insist that if all parts don’t change at the same rate it’s not possible for it to be the global temperature.
“All you’ve offered is that “numbers is numbers” is both your premise and conclusion.”
I’ve not said that once. As always you seem to be arguing with your own imagination.
No that’s a false dichotomy. You are labelling all those who disagree with your “thesis” as those who do not consider the real-world applications of maths and statistics. You say “those who insist that “Numbers are Numbers” and can all be treated the same” but I (and others) never said that (show me that statement or words to that effect in any of the posts of mine). Of course what the measurements are about is crucial. If you knew anything about statistical theory you would know that it is the methods that can be the same across different applications. I often used statistical methods developed in medicine to model mortality in even-age tree plantations because a proportional hazards model is the same in each case. The issue is that statistics that are measures of central tendency of a particular response variable using a sampling procedure are still valid even if a sum of that response variable over the sample does not have a real-world application (e.g. my sum of fish lengths which you said was interpretable as an Extensive variable while in fact the sum has no real-world application contradicting your definition of Extensive, go figure!). You throw the “baby-out-with-the-bathwater” and the implication you make is that a huge swathe of empirical research has been a wasted effort based on your “thesis”. Sorry but its your “thesis” that is a waste of effort. Your hubris is quite extraordinary and your attempts to smear those that disagree with you with false labels is disingenuous.
“I often used statistical methods developed in medicine to model mortality in even-age tree plantations because a proportional hazards model is the same in each case.”
How do you classify mortality as either intensive or extensive? Death has no physical attributes to classify.
I think this is worth repeating here since Kip looks keen to have the last word and summarise the discussion to his advantage:
I cannot seem to get through to some of you the fact that Kip’s theory is general since it only specifies Intensive versus Extensive variables and the statistical operation of calculating a sample average. Therefore this theory assumes it applies for every and all statistical distributions of Intensive and of Extensive variables. To disprove this general theory in an incontrovertible and mathematically precise way I only need to specify one distribution for which it is false for some notional Intensive variable to disprove Kip’s general theory that sample means of Intensive variables have no practical (real-world) value i.e. interpretation. I chose one distribution, the normal or Gaussian distribution where it is straightforward to disprove this general theory in a simple and mathematically precise way. That’s how mathematical proofs work. I DO NOT need to show that one particular Intensive variable (i.e. temperature) has a normal distribution. So I falsified the theory for the case of a Gaussian distribution so its up to Kip to mathematically prove it is valid for all non-Gaussian distributions or some defined subset of these distributions. You cannot just propose a general statistical theory without mathematically proving it including any necessary restrictions on its generality. Good luck with that Kip because you are neither a mathematician or mathematical statistician or any sort of bona fide statistician/scientist.
Still running away from my point…
what point is that? Have you got any intelligent criticisms to offer about the above technical statement? I suppose not otherwise you would have made them in your reply.
Gigantic unstructured word salad—does this count?
NO it does not count. Its just your way of distracting from the fact that I have produced a valid counter example using a rigorous mathematical approach. “Rigorous mathematical” does not remotely apply to Kip’s essay and those who have tried to justify it. BTW still waiting to see your qualifications to judge statistical theory. Your postings demonstrate already that there is not much to expect in that department.
You’ve got a highly inflated hat size.
And you didn’t read the Essex paper, this is glaringly obvious.
Having no intelligent, well-reasoned response to a technical post by lazily labelling it a “gigantic unstructured word salad” shows you have nothing worthwhile to contribute. Its a tactic of desperation and over-used to deflect in WUWT posts. Silence would even be better at least then you wouldnt out yourself as a shill for the article you are desperate to defend.
So I was right, you didn’t read the paper, and instead just whined a lot.
Read this paper. [PDF] Thermodynamical definition of mean temperature | Semantic Scholar
You seem to have a chip on your shoulder about statistical analysis. That is not the purpose of KH’s paper. The issue is that intensive can not be added to obtain a sum for computing an average. The averaging beginning with daily Tmax/Tmin is not proper. You can not add the two together and get a proper value for HEAT in the system.
Can you add the numbers and take an average, sure, but not only is it meaningless from a thermodynamic sense, it makes no sense physically. You can’t even measure the temperature of latent heat in water vapor to include in the measurements. That is why enthalpy is needed.
There are certainly arguments to be made about the statistical analysis methods being used on the numbers but that is not the point here. If you want to argue about that, tell us why none of the statistical descriptors of distributions is available for purview for any of the GAT distributions. No one, and I mean no one has ever volunteered to provide these even after numerous requests. Tell us why the mean values are the only statistical descriptor available.
You’ve pretty much nailed it, Kip.
The Essex paper gives a mathematical, generalized, high level proof of why intensive properties can’t be averaged. Not a single numbers person has refuted that proof in any way. Their arguments boil down to the following:
In essence it’s all just saying that numbers are always just numbers and you can treat them in any manner you wish. It’s just math.
I just wish some of the “numbers” people would attempt to refute the general proof provided early in the paper.
Kip,
Let me point you to another paper about temperature and means.
[PDF] Thermodynamical definition of mean temperature | Semantic Scholar
Jim ==> Thanks for the link — it is in support of the ideas that “mean temperature”, as is being used in CliSCi today, is a physically improper metric.
In fact, it says that it’s crucial. Yes, materials have different specific heats and crystallization energies, but they don’t detract from the utility of mean temperature evaluations.
“The notion of mean temperature is crucial for a number of fields including climate science.”
It says:
“The notion of mean temperature is crucial for a number of fields including climate science. However, so far its correct thermodynamical foundation is lacking or even believed to be impossible.” (bolding mine, tg)
Why do you not provide the full context of what is being said? You are a cherry-picker just like bellman and bdgwx!
It was a general statistical theory you proposed that you applied to Intensive variables in general and not just temperature. So it was not a thermodynamic theory so I state again it was a statistical theory and you have to play by the rules of mathematical statistics and give a mathematical proof of your theory of statistics.
Again, for at least the second time, look at Page 6 in the Essex paper. The mathematical proof is right there in print!
Keeping things in perspective, Kip’s general theory of statistics of Intensive variables cannot do any harm to the practice of empirically-supported science or any field of empirical research, for that matter, because it will have vanishingly small, like effectively zero, influence on professionals since WUWT Essays are not citable in the peer-reviewed literature and it would never make it through review by theoretical or applied statisticians. So I will not lose any sleep over the issue. It does however lower the credibility of the WUWT web site. I wont be bothered to read instalment 3.
I’m certain Kip is absolutely devastated by this news.
Yes I am sure he is. One less to hold him to a account for lack of intellectual rigor in WUWT’s amateur (stats theory) hour. Going to save my intellectual capital for paid consultancy work and publishing in peer-review journals.
I am going to walk back my contention that this is Kip’s theory. I apologise for that false attribution. This discussion has got a bit heated. I didnt appreciate the statement I never made being attributed to me as one of the “numbers are numbers” lot and therefore apparently not in the company of the “science and engineering people”. My counter-example still stands and I have no apologies for that.
That’s my mea culpa. Any comment from Kip on my above gripe?
Steven ==> I do no such thing. I report about an interesting and valid science question. I am waiting for you to respond to the paper being referenced in an adult way.
I accept and concede this point and withdraw the comment that its your theory. Evenso, my counter-example for the contention that averages of Intensive variables have no real-world application or comonsense interpretation still stands. It is not really a theory since no proof is given by Essex et al. of the second sentence as far as it infers a sample average in their contention on page 5; “A sum over intensive variables carries no physical meaning. Dividing meaningless totals by the number of components cannot reverse this outcome“. The discussion about temperature as an Intensive variable does not address the above general contention. I could find no proof of the above contention in their paper. If there was my counter-example would not be correct BUT it is in fact correct so that would explain their lack of a proof. Some contentions are harder to prove than to disprove using the counter example method. The issue they raise of different statistics for estimation of central tendency [their Eqn(9)] of simple average, harmonic mean etc, (I could add the geometric mean) does not invalidate these as alternative estimates of the population mean (central tendency) and all have a real-world interpretation whether for Intensive or Extensive variables. Which estimate is minimum mean square error depends on the underlying distribution.
You need to recognize that there are multiple problems here. One, the traditional arithmetic mean requires adding values in a sum.
If the values consist of intensive measurements you can not add them directly since they are not quantities per se, they are QUALITIES.
KH used a chart to show this. One of the intensive items is “color”. Does a mean of red, blue, green, turquoise, black have a value? Is it meaningful? Now if you use the frequencies/wavelengths of those colors in a mean is it meaningful? Is frequency/wavelength intensive or extensive? If you average the frequencies of the three primary colors, do you the wavelength of “white”? Better yet, if you cut a block of red material in half, do you get two blocks with the value of “red/2”? Can I add “red+red+red” and get a value of red3?
How about melting point? Can I average the melting points of aluminum, gold, titanium, and sulfur and have a value that is meaningful? Would it be the melting point of a mixture of equal portions of each? I hope not, because separating ethanol from the other products of fermentation would be very, very difficult!
If you know thermodynamics, you’ll know that temperature does not define the amount of heat in a substance. It is a measure of the kinetic energy within a substance. But it can not measure latent heat, which is very important due to the liquid water and water vapor in the climate. It can not tell you how much energy (heat) is required to raise the temperature of a substance, say a parcel of air, one degree.
For this reason, temperature can not tell you how much energy is contained in a certain mass. Ultimately, energy is what is important to monitor. Many of us on WUWT have maintained that for some time. The papers referenced on the thread only verify that. How much energy is contained in the surface and atmosphere is what we should be studying. This varies throughout the globe with a dependence on many things. Clouds, composition, winds, waves, etc. The only way account for all these is to have a proper base of energy content variations.
If you want to discuss the statistical methods currently being used, get the authors to start a thread about how the statistics are calculated starting with Tmax and Tmin. I would love to get some experts to even commit to whether an annual averages of stations is a sample or a population. I would like to know how they deal with variance that appears when you average winter and summer temperatures from two different hemispheres. But, that is a totally different discussion. First, a decision should be made as to what a well-posed problem contains.
Notice that he ignored all the physics in the paper (esp. the nonequilibrium discussion) and went straight to “no, it is possible to add up the number and divide by N”. He then ignored the whole discussion on how the “anomalies” are calculated.
Jim, ordinal scales are extremely common in many fields of research eg psychology, agricultural research. The colours you mention could be treated as an ordinal scale and in a study using a sample of visual observers that is all you could record. The researcher could assign an integer to each colour knowing the order of frequency ranges those colours represent. A basic approach is to average the ordinal scores given as integers but the statistically sophisticated approach is to fit an ordinal regression model that respects the order but does not attribute a metric score to the simple integer scores. The above statistical model assumes an underlying probability density function where the ordinal classes are defined by, sometimes unknown and therefore estimated, ordered cut-point parameters. For the colour example these cut-points are known from physics and could be input as known values to the fit of the ordinal regression model. That underlying distribution has an expected value (i.e. mean), which may vary systematically with continuous covariate or factor values, and has a useful interpretation in terms of estimates of difference (factors) or trends (covariates) in the mean. If the contention is that it does not because it is ordinal and thus Intensive (?) is promoted then you have just cancelled most of psychometrics and a lot of other worthwhile research. Also in the colours example we know that the cut-points and thus the mean have a useful physical interpretation as EM frequencies. So we have to careful that a focus on the physical sciences does not lead to contentions that push their restrictions onto all fields of research and data-types in a sort of all-conquering way. Again even for physical sciences the contention about Intensive variables in the discussion has yet to be proven and my counter-example says that in its general form it cannot be proven because it is disproved.
“That underlying distribution has an expected value (i.e. mean), which may vary systematically with continuous covariate or factor values, and has a useful interpretation in terms of estimates of difference (factors) or trends (covariates) in the mean. “
Let’s look at what you are doing. One is basically trying to determine how often a color appears, the other (the subject at hand in this thread) is how do you *add* colors to get a sum. In the first you *can* assign a number to a color and determine an average number. You cannot assign a number to each member of a set of colors, sum the numbers, and determine what color the average value will represent.
If you have three colors, red/green/blue, and you assign each the number 1, add them up to 3, average them to get a value of 1, exactly what does that represent? They each have a number of 1!
If you give them different numbers, say 1/2/3, then the total is 6 and the average is 2. Does that mean that green is somehow the average of red, green, and blue? What if you have 3 reds, 10 greens, and 5 blues. The average is 6. What does that average represent? It tells you nothing about how often each color appears nor does it tell you what color the average represents. There is no color with the number of 6.
What you are doing is trying to justify treating temperatures as just numbers rather than physical measurements. Kip was basically right. Treating intensive properties as just numbers on the number line really tells you nothing about the physical world. If you have five bars of gold and 100 balloons full of air in a box, averaging their densities tells you nothing meaningful. There is nothing in that box that will have that “average” density. In fact, averaging their masses won’t tell you anything either since nothing in the box will have that average mass. All the average mass does is represent a number you can multiply by the total number of elements to get the total mass back, i.e. cancel “n” out of the average. Mental masturbation at its finest. But you *can’t* multiply the average density by the number of elements and get the total density. There is no such thing as a “total density” unless you just assume that density is just another number on the number line.
“One of the intensive items is “color”.”
Not a good example. Colours can be additive, you can add and average them to get different colours and intensities. It’s how TVs and Monitors work.
In other cases, e.g printing, they are subtractive, but you can still combine them to get average colours.
No they can not be added mathematically.
(Red + Red + Red) / 3 = what?
You are talking about what you see, not the mathematical addition of physical qualities.
Again, if I have a red object and cut it in half what changes?
Length –> YES
Width –> YES
Height –> YES
Mass –> YES
Color –> NO
Temperature –> NO
Make up (elements) –> NO
Both color and temperature what something is made of are intensive qualities. They can not be added (multiplied) or subtracted (divided). They remain constant. Alchemists didn’t know this and spent years trying to change the makeup of substances.
Its really simple to show that this whole generalisation of a dichotomy of Intensive and Extensive variables and the interpretation of the sum over a sample (or any collection of discrete units of each general type) is completely inconsistent and thus not general. Yes it works for mass or volume but not for Length or Height. I have a sample of humans and I measure their height and since you say Height is Extensive and the sum of values makes sense then tell me what does the sum of the size-N sample of those Heights mean in the real world? One gigantic person or the N-individuals laying head to toe so that one could run a tape measure for the total length to validate it equals the sum of the individual heights (might be a slight difference due to compression of the spine and your favourite subject of measurement error). So total Height is really not sensible and useful in that context when considered in isolation. I pointed out this inconsistency about so-called “Extensive” variables to do with a sample of fish lengths and no one has addressed that inconsistency.
What is N for a time-series air temperature measurement?
Relevance to the above example where the sum of a so-called Extensive variable makes no real-world sense? You are a master of non sequiturs. Is that your main qualification?
It is of primary relevance to the subject of the meaninglessness of global air temperature averages, which have nothing to do with “sampling” any population regardless of distribution.
Slippery! You edited this after I replied.
And you still don’t grasp the importance of a time-series measurement.
It does depend on what you mean by colour. This is more about our perception of colour.
“(Red + Red + Red) / 3 = what?”
Red, obviously. A more interesting question is what is Red + Red + Red.
“Again, if I have a red object and cut it in half what changes?”
Nothing, that’s why it’s an intensive property. Now what happens, if you shine two red lights on a white wall, and then turn one of them off?
“They remain constant.”
In what sense? My laptop screen keeps changing colour, and it keeps getting hotter.
You’re insane.
You didn’t answer anything! If you can’t add colors and get a meaningful answer, why do you think you can temperatures and get a meaningful answer?
That’s just bad logic.
First, my point is that there are ways of adding colours that give meaningful results. But as I said, I don’t think “colour” is a good example, because it’s a complicated subject.
Second, I don;t think you can add temperatures and get a meaningful result. The question isn’t about adding it’s about averaging.
Third, you can’t argue from one case to another. Even if you can’t add colours doesn’t mean you can’t add any other intensive property. There are different types of intensive property and they don’t all behave the same way.
And you accuse others of circularity—please to explain the magic that occurs when dividing a meaningless sum of disparate air temperatures by a constant transmogrifies it into something with meaning.
He won’t explain it. It’s an article of religious faith.
Anything to keep the trends alive.
Yes, that’s right it’s against my religious belief. Either that or I can’t be bothered to explain something obvious to someone who never listens, shows no ability to lear, and will just throw up another witty one liner about me whining.
Honestly, if you can’t figure out why the average of your 100 thermometers is a more meaningful than their sum, I doubt anything I say will make a difference.
Color is a *perfect* example.
If you can add temps then how do you get an average?
What other intensive properties can you add and get a meaningful result. We know that color, density, and temperatures are out. Give us some other examples.
“If you can[not] add temps then how do you get an average?”
I keep trying to explain, but it offends your religious believe.
You can sample temperature, or you can multiply it by an extensive property.
“What other intensive properties can you add and get a meaningful result.”
If you mean average rather than add, you can get meaningful results from averaging density and velocity.
“We know that color, density, and temperatures are out.”
No idea why you think there cannot be an average density. I assume you’ve never worked in ship building, and claiming you cannot average temperatures is just begging the question.
And you need to study more logic. You don’t prove you cannot average any intensive property just by pointing to examples of intensive properties you cannot average.
And as I say, colour is an awful example as it can mean many different things, and in many contexts can be added and averaged.
“No idea why you think there cannot be an average density. I assume you’ve never worked in ship building, and claiming you cannot average temperatures is just begging the question.”
I’ve already answered this. If you have sponge and a lead weight in a bucket, what does the average density tell you? You *still* have to know the masses of each in order to judge anything about their impact! There is nothing in that bucket that exists that has the average density. Even if you have a weight of gold and one of lead in the bucket what does the average density tell you? It doesn’t tell you what the bucket will weigh on a scale.
Btw, the buoyancy of a ship is found by Fs = Vs + D + Fg. D is the density of the fluid the object is immersed in and Vs is the volume of the object. The density of the ship is irrelevant. It’s the volume of liquid the ship displaces that is of importance. Fg is the force exerted by gravity which is dependent on the mass, not the density, of an object.
“I’ve already answered this”
No. That’s just your back to front logic of arguing that if you can show a situation where the average is not useful, than the average can never be useful.
“Btw, the buoyancy of a ship is found by Fs = Vs + D + Fg.”
Very good. Now try to use that formula to determine if an object with a given average density will sink or float.
Climate Science is the modern-day equivalent of alchemy…
“The discussion about temperature as an Intensive variable does not address the above general contention. “
” I could find no proof of the above contention in their paper”
He gives a proof on Page 6. You have yet to refute that proof. The fact that you apparently didn’t understand it or bother to read it is not refutation.
You’ve been spamming this page 6 example for last few days. Could you explain what you think it actually proves?
I gave my thoughts on it here:
https://wattsupwiththat.com/2022/08/09/numbers-tricky-tricky-numbers-part-2/#comment-3576815
and you haven’t responded to it.
Let’s start from the beginning and try to make it simple.
From Page 5.
1) “Let us propose that an average over temperatures from both systems is required to be a temperature. This proposition produces a contradiction.”
2) “The state, and the temperature, of system a, say, is completely determined by the variables {Xia} and does not change in response to a change only in {Xib}.”
3) “Thus, while each temperature is a function of the extensive variables in its own system only, the average must depend explicitly on both sets of extensive variables, {Xia} and {Xkb}.”
4) “That is it must depend on both states and it can change as a result of a change in either one. Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b.”
The conclusion of this is that the average temperature must also be an intensive value, but, the average can change based on the temperature of either system. Therefore, the average temperature is not based on the extensive values of either system.
In other words, it is not reality based and can not be an actual temperature in the system. It does not describe the conditions that created it.
For example, if I tell you the temperature is Tavg, can you tell me the mass, the specific heat, and the heat that was added to that to get that temperature. If you can’t, and believe me you can’t, then you can not consider it a real temperature.
The problem only gets worse as you add additional temperatures that are a function of their local extensive variables. As you add more and more to the average, you do not have a real system because the conditions that caused the actual temperatures is subsumed and disappear.
Remember temperature is a quality, more precisely, it is a measure of kinetic energy in a substance. Temperature is not calculated, it is measured. Heat on the other hand is a calculated value of the amount of energy transferred. The general formula is Q = m * c * ΔT. Please note the ΔT. Just knowing temperature does not tell you how much energy had to be transferred to a substance to reach the final temperature. You also need to know the starting temperature. Consequently you know nothing about the heat involved when you attempt to derive a global average temperature.
Page 6 proof is a basic mathematical proof of using anomalies. It is basically the problem and generates a similar conundrum, how much energy was used where?
“Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b.”
Which is the problem, in that I don’t see any problem. Why does the average temperature have to be a temperature for either a or b?
“The conclusion of this is that the average temperature must also be an intensive value, but, the average can change based on the temperature of either system.”
Yes the average temperature is an intensive value, yes it depends on both systems. Where’s the problem?
“Therefore, the average temperature is not based on the extensive values of either system.”
I’d say it was based on both systems.
“In other words, it is not reality based and can not be an actual temperature in the system.”
It’s based on the reality of the two systems. And it doesn’t have to be an actual temperature in the system.
“For example, if I tell you the temperature is Tavg, can you tell me the mass, the specific heat, and the heat that was added to that to get that temperature.”
No. But if I tell you the temperature of a or b you cannot tell me all those things.
“Remember temperature is a quality….”
I still can’t find any explanation as to what this means, or why you think it’s important. Every reference I’ve found says it’s a physical quantity.
“… more precisely, it is a measure of kinetic energy in a substance.”
I assume mean average kinetic energy, otherwise it would be extensive.
And if it is defined as average kinetic energy it’s difficult for me to understand why there cannot be an average temperature in this two box system.
Go take a stat mech class…
Because temperatures are intensive. You can’t add them, they don’t change. Yet that is what an average does, it “creates” a new number that is not a temperature.
You are saying temperatures don’t change? I’m sure that’s not what you mean.
“Yet that is what an average does, it “creates” a new number that is not a temperature.”
I don’t care if you call it an actual temperature of an average temperature, it still has meaning.
I’m sure that in some abstract technical sense it’s impossible to assign an actual temperature to any system not in equilibrium, but that has very little to do with the real world question of is the system getting hotter or not. If the theory can’t tell you that, then I don’t think it’s of much use.
Page 6 does not give a proof of the contention (given on page 5) “A sum over intensive variables carries no physical meaning. Dividing meaningless totals by the number of components cannot reverse this outcome” . It is simply restated with respect to temperature on page 26 as “Since temperature is an intensive variable, the total temperature is meaningless in terms of the system being measured, and hence any one simple average has no necessary meaning.” Restating a contention is not a proof. Show me a proof of this specific contention that is based on the property “Intensive” and not a specific variable. I cannot see one. Remember “this specific contention”… dont stray from “the straight and narrow”.
Do you see the circular reasoning in Essex et al? Contention1: “Dividing meaningless totals by the number of components cannot reverse this outcome” (page 5). Contention2:”Since temperature is an intensive variable…any one simple average has no necessary meaning” (page 26). Contention1 gives Contention2 gives Contention1. So Contention1 = Contention2. So no proof of their contention at all, just a “sleight of hand”. Despite all the complex arguments about temperature they still have to revert back to their circular argument “Since temperature is an intensive variable…”. Like I said if they had given a proof my counter example would be wrong which it is not and no one has proven any flaw in the logic of that counter example. Ignorant comments of “sorry no maths to see here (paraphrase)” on par with “that’s just a gigantic word salad” are just inane.
Stop whining.
I see no problem. It doesn’t appear to be circular, just two different assertions.
If a sum is made of intensive variables, then the result has no physical meaning.
If a sum with no physical meaning is divided by N, then the result has no physical meaning.
One assertion (or contention) since we could collapse it without loss of information:..
“since the sum of an intensive variables has no physical meaning then dividing by N also has no physical meaning”
Cut and paste the text from Essex et al that proves this assertion for Intensive variables in general or even part (b) of your two-part assertion if you want to maintain its two assertions not one. It is an assertion about Intensive variables in general and the proof needs to address that. Start with temperature if you like and use an inductive proof but it needs to be more than just temperature because in mathematics one example does not prove a general theory BUT one counter-example can disprove a general theory.
Xa/i is general, it’s not just temperature. If Xa/i is not determinstic for Xb/k then it can’t be deterministic for any other X.
For some reason you just can’t seem to accept this.
For temperature I don’t need a “mathematical” proof. You may be a dood mathematician but you also need to study some physical science as do most climatate scientists.
Here is an easy page to read from wiki that explains thermodynamic temperature. I am attaching a small portion that discusses particle motion and how it relates to temperature.
As you can see, temperature is a property of particle motion and how energetic it is. In other words translational kinetic energy.
The following is from the same wiki page:
https://en.m.wikipedia.org/wiki/Thermodynamic_temperature
“”Though the kinetic energy borne exclusively in the three translational degrees of freedom comprise the thermodynamic temperature of a substance, molecules, as can be seen in Fig. 3, can have other degrees of freedom, all of which fall under three categories: bond length, bond angle, and rotational. All three additional categories are not necessarily available to all molecules, and even for molecules that can experience all three, some can be “frozen out” below a certain temperature. Nonetheless, all those degrees of freedom that are available to the molecules under a particular set of conditions contribute to the specific heat capacity of a substance; which is to say, they increase the amount of heat (kinetic energy) required to raise a given amount of the substance by one kelvin or one degree Celsius.
The relationship of kinetic energy, mass, and velocity is given by the formula Ek = 1/2mv^2. [10]
Accordingly, particles with one unit of mass moving at one unit of velocity have precisely the same kinetic energy, and precisely the same temperature, as those with four times the mass but half the velocity.””
Please note the part about specific heat capacity, it is important.
As you can see the kinetic translational movement of particles is what is measured as “temperature”. If you have a block of a distance, a block of iron or a parcel of air, the particle movement within it generate temperature.
If you cut the block in one-half, the particles in each block continue to move with same energy and voila, each smaller block retains the same temperature.
That is why temperature is a QUALITY (intensive) of a substance. It is like color. If a leaf reflects green light, you can cut in half and each half continues to reflect green light.
Translational kinetic energy is what makes an object read a temperature. Energy that is stored in vibrational or rotational movement of a molecule is NOT sensible, you can’t measure it with an external device, therefore it is not sensible, it is LATENT. Water has a high specific heat capacity and lots of the heat it absorbs is LATENT heat.
The sun provides the predominate amount of energy we are discussing. If you want to allocate heat energy properly, you must account for the heat you can not measure by temperature, e.g., LATENT heat. This makes temperature the wrong measurement to use in determining the heat at a location.
Water vapor can vary from location to location, so can cloud cover, and surface composition. This changes the heat measured by a thermometer when compared to another location. In other words, the conditions vary.
The ultimate question is can you compare temperatures that have varying allocations of heat energy to obtain an average.
BTW I like the term “contention” better than “assertion” because “contention” gives a sense of a “contentious assertion”. It is certainly contentious based on the comments here. More importantly, the implication of this contention is to cancel all empirical research that uses Intensive variables and Extensive variables, for that matter, whose sum has no real-world meaning. Cannot say I have seen a mass exodus of empirical scientists and applied statisticians for other vocations because of Essex et al 2007. No tsunami of hand-wringing that “we have had it all wrong all this time!”.
Poor steven, people failed to worship before his statistical greatness and brilliance.
At least I can show some humility when needed. This statement by Kip to start the discussion was more like a Papal Bull from the Vatican than an invitation to a scientific discussion.
“Please feel free to state your opinions in the comments – I will not be arguing the point – it is just too basic and true to bother arguing about. I will try to clarify if you ask specific questions.”
My counter-example is simple maths no need for worship.
When do you start?
refute this:
——————————————————–
Setting mixing aside, consider two disjoint isolated equilibrium systems, a and b, with functions of state Ua = f_a(Xa/1 ; Xa/2 ; … ; Xa/n) and Ub = f_bXb/1 ; Xb/2 ; … ; Xb/n) respectively, where Ua and Ub are the respective internal energies. Xa/j and Xb/j represent the corresponding extensive variables in systems a and b, respectively. Obviously, given fa, the extensive variables for system a completely define the thermodynamic state of system a. Similarly for system b. The partial derivatives, δUa= δXa/j and δUb= δXb/j , are the jth intensive variables for the respective systems. The temperature of each system is, of course, the particular partial derivative with respect to the system’s entropy,
T = δU/δS: Together, the intensive variables form the tangent spaces of the respective functions of state. As such, they are local properties of the state space and are thus independent of the scale of the system. Does a Global Temperature Exist? Let us propose that an average over temperatures from both systems is required to be a temperature. This proposition produces a contradiction. The state, and the temperature, of system a, say, is completely determined by the variables {Xa/i) g and does not change in response to a change only in {X b/i}. But any average is a function of both temperatures. Thus, while each temperature is a function of the extensive variables in its own system only, the average must depend explicitly on both sets of extensive variables, {Xa/i} and {Xb/k}. That is it must depend on both states and it can change as a result of a change in either one. Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b. Consequently, the average is not a temperature anywhere in the system, which contradicts the proposition that the average is a temperature. While it is thus simple, obvious, and unavoidable that there is no one physically defined temperature for the combined system, the example illustrates the contradiction that arises in requiring an average over a local equilibrium temperature field to be itself a temperature of anything.
————————————————————–
He won’t—he’s had at least six opportunities to refute it and has run away each time.
I don’t expect an answer. He *is* a numbers-are-numbers guy. He thinks you can average anything and get something meaningful. There are several of those people on wuwt!
Absolutely, adding columns and dividing by N is pretty much all they have. No one does any detailed distribution analysis that he tossed out. It might reveal the fraudulent data mannipulation!
Even if it were very complicated maths, or the most elegant and sophisticated maths ever developed, worship is unjustified. Question: how come maths so elegantly and often so simply describes the real world as evidenced in the physical sciences? Just asking…
The Global Average Temperature was the main point of the Essex paper, and you ignored this completely.
This includes ignoring all the physics presented plus the discussion of the myriad of functions used to extract anomalies.
And there was exactly zero math in your alleged “counter example”.
“And there was exactly zero math in your alleged “counter example””.
The formula for calculating the expected value of the normal distribution is so well known by anyone with math stats training/experience that it needs no reminder of the mathematical formula but just to let you know it involves integration. Proving the population median equals the population mean for a normal distribution is even easier. The sample mean and median are consistent estimators so they both converge to the expected value as sample size increases. The variance for the sample median is less well known and is given by Wilks, S.S., 1948. Order statistics. Bull. Am. Math. Soc. 54, 6–50.
NONE of this applies to time-series measurements of air temperatures!
And again you run away from the real-world physics issues.
Yeah, yer an expert on everything, sure.
I don’t think you understand what an intensive property is nor do you understand what temperature is. An intensive property remains consistent with a change in the amount of material in an object. A red block cut in one-half results in two red blocks. The property red doesn’t change! A block at 100 degrees cut in half results in two blocks both at 100 degrees!
Now can you add two intensive properties? The answer is no. I tried to explain this to Bellman. Can I take the two 100 degree blocks above, molecular bond them and up with a block at 200 degrees (100 + 100)? How about the two red blocks? Do I end up with a doubly red block (red + red)?
The paper gives you the math for temperature, T = δU / δS. Can I say
T1 + T2 = T if,
U1 ≠ U2 or,
S1 ≠ S2.
This is the question that must be answered before proceeding to statistical analysis.
You may want to study up on thermodynamics before you go on.
“Even if it were very complicated maths, or the most elegant and sophisticated maths ever developed, worship is unjustified. Question: how come maths so elegantly and often so simply describes the real world as evidenced in the physical sciences? Just asking…”
No worship. Just an understanding of the math in the Essex paper. Where is your refutation of the math on Page 6 of the paper? *THAT* math elegantly and simply describes the real world and refutes your assertion that you can average intensive properties and get an answer that describes the real world.
As best I can tell the only thing Essex et al. are saying on pg. 6 is that for two bodies A and B not in equilibrium:
[Ta + Tb] / 2 != Ta_i for all i.
and
[Ta + Tb] / 2 != Tb_i for all i.
In other words, the average temperature of the two body system A&B does not equal Ta_i or Tb_i for all points i.
That is a rather obvious fact that is self evident. It does not require two full pages of text to communicate that idea.
Are you saying that the only way to convince you that [Ta + Tb] / 2 is meaningful and useful is to disprove the above statement?
You do understand that temperature is a composite of other conditions, right? The paper tells you that,
T = δU / δS.
If T1 = δU1 / δS1 and T2 = δU2 / δS2, can you say,
Tavg = { (δU1/δS1) + (δU2/δS2) } / 2 ?
Temperature is made up of heat content and entropy. When you add temperature numbers directly are you adding numbers that are similar?
You need to answer this question in your own mind. At a given temperature, does a parcel of dry air have the same amount of heat energy as a similar parcel of moist air?
Then you need to answer the question, does temperature accurately reflect the amount of heat energy a parcel of air absorbs from the sun? If it doesn’t, are you losing or gaining heat energy when averaging?
If [Ta + Tb] / 2 != Ta_i for all i and [Ta + Tb] / 2 != Tb_i for all i is true then how can an average temp exist?
Essex: “Let us propose that an average over temperatures from both systems is required to be a temperature. This proposition produces a contradiction. The state, and the temperature, of system a, say, is completely determined by the variables Xa/i and does not change in response to a change only in Xb/i. But any average is a function of both temperatures. Thus, while each temperature is a function of the extensive variables in its own system only, the average must depend explicitly on both sets of extensive variables, Xa/i and Xb/k. That is it must depend on both states and it can change as a result of a change in either one. Then the average cannot be a temperature for system a, because system a is mathematically and thermodynamically independent of system b by assumption. Similarly, it cannot be a temperature for system b. Consequently, the average is not a temperature anywhere in the system, which contradicts the proposition that the average is a temperature.”
Think about it for a minute: Expand this to the average being Xc/h.
If Xa/i and Xb/k are independent and fully defined then they are functions only of the extensive variables in their own systems. Xa/i does not change when Xb/i changes. This also applies to Xa/i and Xc/h and Xb/k and Xc/h. Thus Xa/i and Xb/k don’t generate Xc/h meaning there is no average temperature determined by the two separate, independent systems.
Heat doesn’t exert a force field like gravity or EM radiation, there is no “temperature acting at a distance”. Thus there is no way to assume that Xa/i and Xb/k can cause a defined average temperature to exist somewhere in the space between them. Thus that “average” temperature is meaningless insofar as reality is concerned.
As Kip has already pointed out, if you are a “numbers is numbers” guy then you can do anything you want with the numbers. That simply doesn’t mean they are useful or meaningful in the real world we live in.
“If [Ta + Tb] / 2 != Ta_i for all i and[Ta + Tb] / 2 != Tb_i for all i is true then how can an average temp exist? ”
That’s not what’s being said. You are implying there are multiple different temperatures in both a and b, which would imply Ta and Tb are both averages, thus refuting the claim that an average temperature cannot be the temperature.
But as I said in response to bdgwx, if the claim is that an average temperature cannot exist if it doesn’t equal a single temperature in the system, why not just state that as the argument? That statement is easily proven – if Ta != Tb, then the average of Ta and Tb cannot be the same as Ta or Tb, so the average isn’t “the temperature” QED.
But if you are saying the average temperature only has to be present somewhere in the system to be real, then that isn’t a problem when looking at global temperatures as any average, even the silly ones they use in later sections, has to be present somewhere on the planet, because of the mean value theorem.
This also means the first argument involving two isolated systems is invalid as it assumes discontinuous temperature distributions.
So Pt. Barrow Alaska and Capetown South African are not discontinuous?
HAHAHAHAHAHAHAHAH
Keep digging, this is amusing.
He truly believes that the extensive values that determine temperature at one place can act a distance and *CAUSE* what the temperature somewhere else might be!
It’s no wonder the CAGW crowd has so many followers.
Spooky action-at-a-distance!
“He truly believes that the extensive values that determine temperature at one place can act a distance and *CAUSE* what the temperature somewhere else might be!”
Really? What makes you think that?
What are the variables that determine temperature? Look at the equation the text gives you for “T”. Are they all the same everywhere in space and time?
My question was why do you think that “He truly believes that the extensive values that determine temperature at one place can act a distance and *CAUSE* what the temperature somewhere else might be!”
How else would the temperature at one place be a cause of the temperature at another place? If the temperature here doesn’t determine the temperature at another place then there is no “acting at a distance”. If there is no “acting at a distance” then an average temperature is meaningless.
The temperature at a single point is determined by a multiplicity of things, i.e. Xa/i. Those things include humidity, clouds, elevation, latitude, longitude, terrain, geography, etc. The geography at one point doesn’t determine the geography at another place or anyplace in between. The terrain at one place doesn’t determine the terrain at another place or anyplace in between. The elevation at one place doesn’t determine the elevation at another place or anyplace in between. The humidity at one place doesn’t determine the humidity at another place or anyplace in between. Clouds at one place doesn’t determine clouds at another place or anyplace in between.
I.e. NO ACTING AT A DISTANCE FOR TEMPERATURE. If there is no acting at a distance then averaging temps at two places doesn’t define the temperature at another place.
Enthalpy, on the other hand, forms a gradient field all of its own, just like pressures on a weather map or elevations on a topographic map, both of which are extensive properties. You could look at an enthalpy gradient map and know that you are looking at something that takes into account all the factors heat is involved with. You can’t do the same thing with temperature, temperature is not a good proxy for enthalpy. The same temperature could exist in Phoenix and Miami but the heat contents (i.e. enthalpy) would be vastly different.
Anyone that tries to tell you that temperature is a good proxy for heat content is either ignorant or a liar.
“How else would the temperature at one place be a cause of the temperature at another place?”
It doesn’t. The average is determined by the average of temperatures, which in turn are caused by the multitude of things that cause the temperature at individual points. Changing one temperature changes the average, but does not have to change all other temperatures.
Consider the average of personal wealth. Person A has 10000 currency units, person B has 30000. Each persons wealth is the result of multiple factors, inheritance, earnings, gambling etc.
Their average wealth is 20000, and that 20000 is indirectly derived from all these factors for both A and B.
Now suppose A comes into some money and their wealth increases to 20000. That’s due to the factors that determine A’s wealth. The average increases to 25000, but that does not mean that anything has happened to the factors that determine B’s wealth. Nor does it mean the wealth is acting at a distance.
No. The temperatures between the two places are continuous.
Little wonder you are so confused.
Is humidity the same everywhere? Are clouds the same everywhere? Is the sun’s insolation the same everywhere?
It also explains why there is no statistical description other than a mean. If a temperature exists somewhere, anywhere on the earth, how can it possibly be the mean. Location does enter in here. Another thing that gets lost in the shuffle and why everywhere is warming.
Of course that’s what is being said. Temperatures don’t act at a distance. If they don’t then they don’t determine the temperature at an intermediate point. And that is what some of us have been saying forever! It’s why the temperature on the north side of the Kansas River never matches the temperature on the south side! Different humidities, different pressures, different winds, different weather fronts, different cloud cover, etc! You would be hard pressed to average the two temperatures and find the average anywhere in between. Each local temperature is determined by its own set of extensive values.
“You are implying there are multiple different temperatures in both a and b,”
Here we go again! Xa/i is a set of extensive values at a specific location – it’s *NOT* a set of temperatures. You *really* didn’t bother reading for comprehension did you?
” if the claim is that an average temperature cannot exist if it doesn’t equal a single temperature in the system, why not just state that as the argument?”
Wow! What do you think everyone has been trying to tell you?
Why do you think we’ve been beating you up over the fact that the average of a 6′ board and an 8′ board doesn’t exist in the real world, or at least in that portion of the real world where those two boards exist?
“That statement is easily proven – if Ta != Tb, then the average of Ta and Tb cannot be the same as Ta or Tb, so the average isn’t “the temperature” QED.”
NO! It means that Ta and Tb can’t determine the temperature at a third point! Just as the average of a 6′ board and an 8′ board can’t magically create a 7′ board!
“But if you are saying the average temperature only has to be present somewhere in the system to be real, then that isn’t a problem when looking at global temperatures as any average, even the silly ones they use in later sections, has to be present somewhere on the planet, because of the mean value theorem.”
You JUST CAN’T FIGURE IT OUT, CAN YOU?
A temperature in the system is defined by its own set of extensive values, not by the extensive values somewhere else. No acting at a distance. Temperature is not subject to the mean value theorem!
“This also means the first argument involving two isolated systems is invalid as it assumes discontinuous temperature distributions.”
YOU STILL DON’T GET IT! Two isolated systems do *NOT* determine the temperature at a third system! They are not connected and they don’t act at a distance! Since they are not connected there is no discontinuity to consider!
If I just walk across the street and measure the temperature in my neighbors yard over bermuda grass and take mine over sand will they be the same? Are they causually connected? If they aren’t the same is there a discontinuity somewhere? Those two temps are related to the extensive values at each location. The extensive values at one are *NOT* the cause of the extensive values at the other! So how can there be an average calculated from them?
“That simply doesn’t mean they are useful or meaningful in the real world we live in.”
The argument in the paper is that they are not a real temperature, not that they are not useful. As always when you talk about usefulness of averages you show a very limited imagination.
So unreal is useful.
Yes, you are insane.
I’ll echo that.
“limited imagination’! So we are going to spend trillions of dollars, destroy how many birds, destroy how many economies based on someone’s imagination? That certainly sounds like a green liberal.
The average is *NOT* a real temperature!
Just as the average of a 2kg mass and a 4kg mass is *NOT* 3kg. There isn’t a 3kg mass anywhere in the system!
The average is useless for anything except mathematical masturbation!
So now you are saying the average of extensive properties are meaningless?
Are you going to give up the magical properties of the 1/N operator anytime soon?
One other point
None of this argument on page 6 has anything to do with temperature being intensive. The same logic would apply to an average of an extensive property.
Take two different metal bars, with masses Ma and Mb. Does the average of these masses equal to either Ma or Mb? Does that mean it isn’t a real mass? Does that mean all averages of masses are non-existent, or that they have no use? .
Put two bars of the same substance and size in your hands. Can you see a third bar that has the average mass? No. It is an unreal physical number. Does it have use? Surely. You can put any number of bars of different substances on a scale and get the sum of their masses (after dealing with gravity). You can find a standard deviation and a distribution and do all kinds of statistical analysis.
Now do temperatures add? Do they subtract? They actually move toward equilibrium. What does temperature tell you about the bars? Do you know their specific heat capacities just from temperature?
Now let’s get down to the nubbin.
Could certain bars of different substances have different amounts of heat contained within them, yet have the same temperature?
If that is true, how do you calculate total heat from all the bars as a whole just from an average temperature?
Ask yourself, are we after the heat being trapped in the atmosphere or the temperature or does that not matter. Can the temperature increase but the amount of heat be less? Think about water vapor that has latent heat that is unmeasurable.
“Could certain bars of different substances have different amounts of heat contained within them, yet have the same temperature?”
What do you mean by heat?
As I’ve said before my knowledge of thermodynamics is limited, but I’m not sure if you can talk about heat contained within a bar. I thought heat was to do with the movement of energy.
If the question is could they have different Enthalpy yet have the same temperature the answer is definitely yes.
“If that is true, how do you calculate total heat from all the bars as a whole just from an average temperature?”
You can’t.
“Ask yourself, are we after the heat being trapped in the atmosphere or the temperature or does that not matter.”
It depends. If you are interested in calculating total energy budgets, and modelling the greenhouse effect and what not, I assume the former. If I just want to know how hot it is, the later.
I suspect there isn’t really that much difference as the specific heat capacity of the atmosphere at the surface doesn’t change that much and so on a global scale temperature rise is roughly proportionate to total energy, at least at the surface.
“Can the temperature increase but the amount of heat be less?”
“Can the temperature increase but the amount of heat be less?”
I’ve no idea. Someone will have to do the calculations, but either way it means the climate is changing, and shows that knowing if there is a change in global average temperatures is useful.
“I suspect there isn’t really that much difference as the specific heat capacity of the atmosphere at the surface doesn’t change that much”
Is that why they call the same temperature in Phoenix a “dry” heat and in Miami a “wet” heat? Is that why cold air can’t hold as much moisture as warm air?
” on a global scale temperature rise is roughly proportionate to total energy, at least at the surface.”
Specific heat is:
Cp’ = 1005 + 1884*ω
where ω is the absolute humidity
And you think absolute humidity is the same everywhere on earth?
You’ve never once used the steam tables, have you?
You know why these discussions keep going on forever? Because the goalposts keep moving. This whole article is meant to be about whether the intensive nature of temperature means you cannot get an average. But now were on to whether humidity will have much of an effect on the global average temperature.
“You’ve never once used the steam tables, have you?”
Nope. As I keep saying I know little of thermodynamics, that’s why I was asking if someone could do the calculations.
“Is that why they call the same temperature in Phoenix a “dry” heat and in Miami a “wet” heat?”
I maybe wrong, but I thought the difference in feeling from wet and dry heat was due to are ability to lose heat through sweating, not because of the specific heat content of the air.
“Specific heat is:
Cp’ = 1005 + 1884*ω
where ω is the absolute humidity”
Yes, thanks, I looked into this just now.
At 40°C and 100% relative humidity the absolute humidity is around 0.05. So the difference in specific heat capacity between absolutely dry air and very hot and humid would be about 10%. So even if the entire planet went from on extreme to the other it would only require an extra 10% energy to get the same temperature rise.
So given moist the planet is going to have much smaller changes in humidity, I think you’ve confirmed my suspicions that changes to humidity will have a minimal effect on global temperatures.
A blazing strawman; first line of the ABSTRACT:
Who is moving goalposts? This would be YOU.
The words of a dyed-in-the-wool religionist.
Your cherished global average temperature is meaningless so all you can do is hope and pray this is true.
It isn’t.
NO!!!!
You can add extensive properties and average them. HAVE YOU READ NOTHING IN ESSEX AT ALL? That doesn’t make them useful either!
You have to join Ma and Mb into one system! Like put them in a bucket! If they are separate systems, e.g. one of 2kg in one bucket and 4kg in a second bucket then why do you think the average of 3kg would exist anywhere in between them? There’s no third bucket!
Put them in the same bucket and they will have a mass of 6kg. Why would you think they would have an average mass of 3kg?
You can certainty calculate an average mass, divide it by 2, and get 3kg. So what? If you want to know what the mass in the bucket is you need to multiply 3kg by 2 to get the total! Math masturbation! Nothing useful is transmitted by the average!
Not only that but the average has lost the data that one has 2kg in mass and the other 4kg in mass! Just like when you average daily temps, weekly temps, monthly temps, and annual temps. You lose all the data of what is happening where! Without that knowledge how do you make informed judgements about what is happening. You can’t tell from the average if max temps are going up or min temps are!
“HAVE YOU READ NOTHING IN ESSEX AT ALL?”
Yes and disagreed with it. Just as many did when it came out 15 years ago.
“You have to join Ma and Mb into one system!”
Why?
“Like put them in a bucket! If they are separate systems, e.g. one of 2kg in one bucket and 4kg in a second bucket then why do you think the average of 3kg would exist anywhere in between them? There’s no third bucket!”
For once and for all, I do not think taking an average magically conjurers up a new bucket. I just think the average can be useful.
“Put them in the same bucket and they will have a mass of 6kg. Why would you think they would have an average mass of 3kg?”
Because that’s what an average is. I agree that for an extensive property the average is probably going to be less useful than a sum. For intensive properties the average is all that is useful.
“You can certainty calculate an average mass, divide it by 2, and get 3kg. So what?”
I’ve no idea. It’s your example. What are these masses you’ve put in the bucket. If they are gold bars it might be useful to know what their average is. If they are buckets of water, than the average loses all meaning when you mix them.
“If you want to know what the mass in the bucket is you need to multiply 3kg by 2 to get the total!”
So you have found a use for the average.
“Not only that but the average has lost the data that one has 2kg in mass and the other 4kg in mass!”
Unless you wrote it down somewhere.
“Just like when you average daily temps, weekly temps, monthly temps, and annual temps. You lose all the data of what is happening where!”
In the same way as you lose all that data if you add them up. Remind me about why CDD’s are useful.
“You can’t tell from the average if max temps are going up or min temps are!”
But you can’t tell if any type of temperature is going up or down if the Essex paper is correct, so why worry about the difference between max and min?
Appeal to masses, bzzzt.
That’s how I read it.
The main complication is they want to claim the average temperature is the temperature. This in turn is based on the claim made in the introduction that some claim the global average temperature is the temperature of the globe. They don’t give any context for this, but just seem to assume that “the temperature” can only mean a single temperature that is the same for the entire globe.
If that is their argument it could have been made in a single sentence, hence my feeling that this is deliberately obfuscated to make it seem more meaningful than it is.
More insanity.
My apologies, they do say it’s required to be “a temperature” not “the temperature”.
Intellectual rigor?
Where is yours? Where have you disproved the mathematical proof offered in the Essex paper on Page 6?
Saying it is wrong just isn’t sufficient. Saying it is wrong is *NOT* intellectual rigor.
Heal thyself, physician!
Science journalists are supposed to be objective about the for and against arguments in science controversies ““But, but, but, but” ….. no buts!
One cannot average temperature”. That’s not objective reporting. This article is no different in that regard from MSM science journalist that are simply influencers for the climate alarmist scientists.
The statement sure got you going.
The global average temperature(s) was and remains a meaningless number.