I’ve been looking at the Nikolov and Zeller paper again. Among other things, they claim to be able to calculate the surface temperature Ts of eight different planets and moons from knowing nothing more than the solar irradiation So and the surface pressure Ps for each heavenly body. Dr. Zeller refers to this as their MIRACLE equation. He says:
Why aren’t you all trying to disprove our MIRACLE equation rather than banging your heads against walls trying to prove or disprove who knows what and exclaiming you have problems with this or that? The question is how can we possibly have done it – there is no question that our equations work – if you haven’t verified that it works, why haven’t you? […] Why aren’t you thinking: “hmmmm, N&Z have given us an equation that lo-and-behold when we plug in the measured pressures and calculate Tgb as they suggest, gives us a calculated Ts that also matches measured values! You can’t disprove the equation? So maybe we are cooking the data books somehow, but how?
This is supposed to be evidence that their theory is correct, and people keep telling me ‘but they’ve got real evidence, they can make predictions of planetary temperatures, check it out”. Plus it’s hard to ignore an invitation like Dr. Zellers, so I checked it out.
Figure 1. These are not the equations you are looking for.
They first postulate something called the “Near-surface Atmospheric Thermal Enhancement” or “ATE” effect that makes the earth warmer than it would be without an atmosphere.
The “ATE effect” is measured by something called Nte(Ps), which is defined and estimated in their paper as follows.
where Nte(Ps) is a measure of the “Near-surface Atmospheric Thermal Enhancement” effect.
Nte(Ps) is defined as the actual average surface air temperature of the planet Ts divided by the theoretical “graybody” temperature of the planet Tgb calculated from the total solar insolation So of the planet. Nte(Ps) is estimated using a fitted function of the surface pressure of the planet Ps.
Let me simplify things a bit. Symbolically, the right part of equation (7) can be written as
Nte(Ps) = e^(t1 * Ps ^ t2 + t3 * Ps ^ t4) (7Sym)
where “e” is the base of natural logs and Ps is the surface pressure on the planet or moon. There are four tunable parameters (t1 through t4) that are “fitted” or tuned to the data. In other words, those values are repeatedly adjusted and tuned until the desired fit is obtained. This fitting can be easily done in Excel using the “Solve…” menu item. As you’d expect with four parameters and only eight datapoints, the fit is quite good, and their estimate is quite close to the actual value of Nte(Ps).
Amusingly, the result of equation (7) is then used in another fitted (tuned) equation, number (8). This is:
where So is total solar irradiation.
This is their piece de resistance, their MIRACLE equation, wherein they are saying the surface temperature of eight different planets and moons can be calculated from just two variables— Pr, the surface pressure, and So, the total Solar irradiation. This is what amazes the folks in the crowd so much that they write and tell me there is “evidence” that N&Z are right.
Obviously, there is another tuned parameter in equation (8), so we can rewrite this one symbolically as:
Ts = t5 * (Solar + adjustment ) ^ 1/4 * Nte(Ps). (8Sym)
Let me pause a minute and point something out about equation (8). The total solar irradiation Solar ranges from over 9,000 W/m2 for Mercury down to 1.51 W/m2 for Triton. Look at equation 8. How will adding the adjustment = 0.0001325 to any of those values before taking the fourth root make the slightest bit of difference in the result? That’s just bizarre, that is. They say they put it in so that the formula will be accurate when there is no solar, so it will give the background radiation of 3 Kelvins. Who cares? Truly, it changes Ts by a maximum of a thousandth of a degree for Triton. So for the moment let me remove it, as it makes no practical difference and it’s just confusing things.
Back to the tale. Removing the adjustment and substituting equation 7 into equation 8 we get:
Ts = t5 * Solar^0.25 * e^(t1 * Ps ^ t2 + t3 * Ps ^ t4) (eqn 9)
This is amazing. These guys are seriously claiming that with only eight datapoints and no less than five tunable parameters , they can calculate the surface temperature of the eight planets knowing only their surface pressure and solar irradiation. And with that many knobs to turn, I am sure they can do that. I did it on my own spreadsheet using their figures. I get about the same values for t1 through t5. But that proves nothing at all.
I mean … I can only stand in awe at the sheer effrontery of that claim. They are using only eight datapoints and five tunable parameters with a specially-designed ad-hoc equation with no physical basis. And they don’t think that’s odd in the slightest.
I will return to this question of the number of parameters in a bit, because even though it’s gobsmacking what they’ve done there, it’s not the best part of the story. Here’s the sting in the tale. We can also substitute equation (7) into equation (8) in a slightly different way, using the middle term in equation 7. This yields:
Ts = t5 * Solar^0.25 * Ts / Tgb (eqn 10)
This means that if we start out by knowing the surface temperature Ts on the right side of the equation, we can then calculate Ts on the left side … shocking, I know, who would have guessed. Let’s check the rest of the math in equation (10) to see why that works out.
Upon inspection it can be seen that the first part of the right side of equation (10),
t5 * Solar^0.25
is an alternate form of the familiar Stefan-Boltzmann equation relating temperature and radiation. The S-B equation can be written as
T = (Solar / c1) ^ 0.25.
where T is temperature and c1 is a constant equal to the S-B constant times the emissivity. We can rewrite this as
T = 1/(c1^0.25) * Solar^0.25
Setting another constant c2 equal to 1 / (c1^0.25) gives me the Stefan-Boltzmann equation as:
T = c2 * Solar^0.25
But this is exactly the form of the first part of the right side of equation 10. More to the point, it is an approximation of the graybody temperature of the planet Tgb.
We can check this by observing that if emissivity is .9 then constant c1 is 5.103E-8, and c2 is therefore about 66. However, that value will be reduced by the rotation of the planet. Per the N&Z formula in their latest post, that gives a value of about 27.
Their fitted value is 25, not far from the actual value. So curiously, what it turns out they’ve done is to estimate the Stefan-Boltzmann constant by a bizarre curve fitting method. And they did a decent job of that. Actually, pretty impressive considering the number of steps and parameters involved.
But since t5 * Solar^0.25 is an estimation of the graybody temperature of the planet Tgb, that means that Equation 10 reduces from
Ts = t5 * Solar^0.25 * Ts / Tgb (eqn 10)
to
Ts = Tgb * Ts / Tgb.
and finally to
Ts = Ts
TA-DA!
CONCLUSION
Let me recap the underlying effect of what they have done. They are looking at eight planets and moons.
1. They have used an equation
e^(t1 * Ps ^ t2 + t3 * Ps ^ t4)
with four free parameters to yield an estimate of Ts/Tgb based on surface pressure. As one would expect given the fact that there are half as many free parameters as there are data points, and that they are given free choice to pick any form for their equation without limit, this presents no problem at all, and can be done with virtually any dataset.
2. They have used an equation
t5 * Solar^0.25
with one free parameter in order to put together an estimate of Tgb based on total planetary insolation. Since Tgb does depend inter alia on planetary insolation, again this presents no problem.
3. They have multiplied the two estimates together. Since the result is an estimate of Tgb times an estimate of Ts/Tgb, of course this has the effect of cancelling out Tgb.
4. They note that what remains is Ts, and they declare a MIRACLE.
Look, guys … predicting Ts when you start out with Ts? Not all that hard, and with five free parameters and a choice of any equation no matter how non-physically based, that is no MIRACLE of any kind, just another case of rampant curve fitting …
Finally, there is a famous story in science about this kind of pseudo-scientific use of parameters and equations, told by Freeman Dyson:
We began by calculating meson–proton scattering, using a theory of the strong forces known as pseudoscalar meson theory. By the spring of 1953, after heroic efforts, we had plotted theoretical graphs of meson–proton scattering. We joyfully observed that our calculated numbers agreed pretty well with Fermi’s measured numbers. So I made an appointment to meet with Fermi and show him our results. Proudly, I rode the Greyhound bus from Ithaca to Chicago with a package of our theoretical graphs to show to Fermi.
When I arrived in Fermi’s office, I handed the graphs to Fermi, but he hardly glanced at them. He invited me to sit down, and asked me in a friendly way about the health of my wife and our newborn baby son, now fifty years old. Then he delivered his verdict in a quiet, even voice. “There are two ways of doing calculations in theoretical physics”, he said. “One way, and this is the way I prefer, is to have a clear physical picture of the process that you are calculating. The other way is to have a precise and self-consistent mathematical formalism. You have neither.
I was slightly stunned, but ventured to ask him why he did not consider the pseudoscalar meson theory to be a selfconsistent mathematical formalism. He replied, “Quantum electrodynamics is a good theory because the forces are weak, and when the formalism is ambiguous we have a clear physical picture to guide us. With the pseudoscalar meson theory there is no physical picture, and the forces are so strong that nothing converges. To reach your calculated results, you had to introduce arbitrary cut-off procedures that are not based either on solid physics or on solid mathematics.”
In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?”
I thought for a moment about our cut-off procedures and said, “Four.”
He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.” With that, the conversation was over. I thanked Fermi for his time and trouble, and sadly took the next bus back to Ithaca to tell the bad news to the students.
The Nikolov and Zeller equation contains five parameters and only eight data points. I rest my case that it is not a MIRACLE that they can make the elephant wiggle his trunk, but an expected and trivial result of their faulty procedures.
My regards to everyone,
w.
PS—There is, of course, a technical term for what they have done, as there are no new mistakes under the sun. It is called “overfitting”. As Wikipedia says, “Overfitting generally occurs when a model is excessively complex, such as having too many parameters relative to the number of observations.” Five parameters is far, far too many relative to eight observations, that is a guaranteed overfit.
PPS—One problem with N&Z’s MIRACLE equation is that they have not statistically tested it in any way.
One way to see if their fit is even remotely valid is to leave out some of the datapoints and fit it again. Of course with only eight datapoints to start with, this is problematic … but in any case if the fitted parameters come out radically different when you do that, this casts a lot of doubt on your fit. I encourage N&Z to do this and report back on their results. I’d do it, but they don’t believe me, so what’s the point?
Aother way to check their fit is to divide the dataset in half, do the fit on one half, and then check the results on the other half. This is because fitted equations like they are using are known to perform very poorly “out of sample”, that is to say on data not used to fit the parameters. Given only eight data points and four parameters for equation 7, of course this is again problematic, since if you divide the set in half you end up with as many parameters as data points … you’d think that might be a clue that the procedure is sketchy but what do I know, I was born yesterday. In any case I encourage N&Z to perform that test as well. My results from that test say that their fit is meaningless, but perhaps their test results will be different.
[UPDATE] One of the commenters below said:
Willis – go ahead – fit an elephant. Please!
Seriously N&Z are only demonstrating in algebra what has been observed in experiments, that heating a gas in a sealed container increases both pressure and temperature.
OK, here’s my shot at emulating the surface temperature using nothing but the data in the N&Z chart of planetary body properties:
Figure 1. Willis’s emulation of the surface temperature of the planetary bodies.
My equation contains one more variable and two less parameters than the N&Z equation. Remember their equation was:
Ts = 25.3966 * Solar^0.25 * e^(0.233001 * Pressure ^ 0.0651203 + 0.0015393 * Pressure ^ 0.385232)
My equation, on the other hand, is:
Ts = 0.8 * Tgb + 6.9 * Density + 0.2 * Gravity)
Note that I am absolutely not making any claim that temperature is determined by density and gravity. I am merely showing that fitting a few points with a few variables and a few parameters is not all that difficult. It also shows that one can get the answer without using surface pressure at all. Finally, it shows that neither my emulation nor N&Z’s emulation of the planetary temperatures are worth a bucket of warm spit …
[UPDATE 2] I figured that since I was doing miracles with the N&Z miracle equation, I shouldn’t stop there. I should see if I could beat them at their own game, and make a simpler miracle. Once again, their equation:
Ts = 25.3966 * Solar^0.25 * e^(0.233001 * Pressure ^ 0.0651203 + 0.0015393 * Pressure ^ 0.385232)
My simplified version of their equation looks like this:
Ts = 25.394 * Solar^0.25 * e^(0.092 * Pressure ^ 0.17)
Curiously, my simplified version actually has a slightly lower RMS error than the N&Z version, so I did indeed beat them at their own game. My equation is not only simpler, it is more accurate. They’re free to use my simplified miracle equation, no royalties necessary. Here are the fits:
Figure 2. A simpler version of the N&Z equation 8
Again, I make no claim that this improves things. The mere fact that I can do it with two less tuned parameters (three instead of five) than N&Z used does not suddenly mean that it is not overfitted.
Both the simplified and the complex version of the N&Z equations are nothing but curve fitting. This is proven by the fact that we already have three simple and very different equations that hindcast the planetary temperatures. That’s the beauty of a fitted equation, if you are clever you can fit a lot using only a little … but THAT DOESN’T MEAN THAT PRESSURE DETERMINES TEMPERATURE.
For example, I can do the same thing without using pressure at all, but using density instead. Here’s that equation:
Ts = 25.491 * Solar^0.25 * e^(0.603 * Density ^ 0.201)
And here’s the results:
Figure 3. An emulation of the planetary temperatures, using density instead of pressure.
Does this now mean that the planetary temperature is really controlled by density? Of course not, this whole thing is an exercise in curve fitting.
w.
Tilo Reber says:
January 25, 2012 at 4:59 pm
Oh, please. They have used a single variable twice, with different parameters, as the exponent in their equation. I have never, ever seen that in the physical description of any system. I will guarantee you that they will never, ever attempt to justify it as being physical, because it isn’t.
But sure, Tilo, if you want to wait for further handwaving from N&Z, be my guest.
w.
PS—Since there is no way at present to determine by your method if it is a “meaningful fit”, due to the lack of other planets to compare it to … and no hope of new planets … you could be waiting a while.
John Day says:
January 25, 2012 at 5:20 pm
The real question is, where do you get off answering a question for Ned? You don’t know what’s in his mind. You don’t know whether he’s made a typographical error or not. You don’t know what his claims are about. You don’t know what lunar mass he is speaking of. I doubt greatly you even understand what I said about flows and amounts of energy. You can’t speak for him, don’t bother trying.
If I want to know about the music, I ask the organ grinder, not the monkey.
w.
Martin Mason:
You are right. I believe the reason we have so much bickering is because some the leading figures here apparently think that this is an EGO contest instead of being interested to solve an issue. The lesser one knows the bigger seems to be the Ego, that’s a steep relationship with high correlation coefficient! But maybe that’s what some people are paid to do here … 🙂
Richard M says:
January 25, 2012 at 5:35 pm
Cool. Let us know when you decide to commit to a position. Will there be balloons? Is it gonna be BYOP (bring your own position)?
w.
Willis: “PS—Since there is no way at present to determine by your method if it is a “meaningful fit”, due to the lack of other planets to compare it to … and no hope of new planets … you could be waiting a while.”
Yes, I’m aware of that, so for now I’ll have to do with a good physical explanation. I’ll decide if it’s handwaving after I’ve heard it. I suspect that you will call it handwaving regardless of what it is since you are now deeply committed to N&Z being in error.
martin mason says:
January 25, 2012 at 7:56 pm
Right, we should paper over any disagreements and hide any differences in the name of “the cause” … after all, that worked so well for the other side …
Unfortunate, martin, this is how sausage gets made.If you don’t want to see it, read one or more of the many, many other threads at WUWT. There’s lots of non-gravity stuff going on.
w.
Isn’t the fact that temperature is an intensive variable important in all of these analyses? I’m really just asking. It is not my intent to increase the temperature of this discussion (begging the reader’s forgiveness).
Ned: I don’t think that anyone here is paid. And I think than each and every one of us has a substantial ego. I’ve been reading quite a bit of neurological research lately, and you would be amazed at the level of self delusion that we, as humans, are capable of. It’s just jaw dropping. Intelligence and academic credentials don’t make anyone immune. It only makes them more able to invent more plausible explanations for the inconsistencies that they are denying. I’m susceptible, you’re susceptible, and so are Joel and Willis. But to each of us, and in good faith, it looks like only the others are susceptible. There’s really nothing that any of us can do about it. We have to continue to debate the ideas and hope that reality will eventually prevail.
@Willis
> The real question is, where do you get off answering a question for Ned?
Happens all the time on these WUWT pages.
> You don’t know what’s in his mind. You don’t know whether he’s made a
> typographical error or not. You don’t know what his claims are about.
> You don’t know what lunar mass he is speaking of.
Yes, I know what he’s talking about: the amount of extra solar radiation it would take to bring the temperature of the _Earth_ up from airless, gray-body levels to atmospheric GHE levels, with the Moon as the reference gray-body.
I was more concerned about what was in _your_ mind
> I doubt greatly you
> even understand what I said about flows and amounts of energy.
The point I was making was _you_ don’t need to know the _amount_ of energy only the power per unit area.
What I’m really concerned about is that you claim that you don’t understand the N&Z theory, yet you don’t seem willing to try to understand it, instead getting all defensive and snarky about it.
I think you (and Joel) have written this off as BS and N&Z as idiots, or worse. Then why are you even bothering to discuss it with them?
I’m here because I want to learn more about it, right or wrong. Either way there is a lot to be learned.
😐
Joel: “I am not perfect…but unlike some others I admit when I may have been mistaken.”
Okay, let’s move on. Why do you consider Konrad Hartmann’s experiment “ill conceived and carried out”.
http://tallbloke.wordpress.com/2012/01/22/konrad-hartmann-experiment-to-determine-the-effect-of-pressure-on-temperature-in-earths-atmosphere/
Some years ago I worked with Artificial Neural Networks (ANN) that we intended to use to recognize certain types of targets. We began our research with a “training set” of hand printed characters and “rewarded” the connection weights in the neural pathways when the ANN guessed correctly and “penalized” them when the guess was wrong. Our “training set” was run repeatedly until the weights became tuned and the ANN got correct results for all the members of that “training set”.
As John Day wrote, that is only the preliminary step. The next step was to input a “test set” that the ANN had never seen before, and determine if the ANN could interpret those correctly. Of course the real test of such a system is to input real world samples, such as hand-printed addresses and determine if those results are correct.
In other words, we did not celebrate any kind of MIRACLE when the ANN developed the skill to recognize the “training set”. Any neural network with a certain number of nodes can learn to do that.
N&Z have worked years to come up with their MIRACLE equation (and Willis spent minutes to tune up three more). All four equations do a good job on the “training set”. The next step is to get a “test set” of pressure and temperature data for several dozen additional planets that N&Z (and Willis) have never seen before, and see how well their respective equations do.
Of course, it may take some years or decades to obtain suitable data, but I will not accept that N&Z (or Willis) have made any real scientific contribution until their equations work for a “test set” -OR- until N&Z provide some physical explanation, or a laboratory test, for their pressure “enhancement” theory. Perhaps N&Z part 2 will help along those lines.
Zipf could do more than wave his hands! He could show that Zipf’s Law applied to new sets of data that he had never seen before, and he could invite others to look for examples both pro and con. So, either provide a derivation based on accepted principles of physics -OR- show that your equation works for data you have never seen before. That is how a Law gets tested. That is how science is done. Right now I give no more scientific credence to your theory and equation than I (or Willis) give to Willis’s three equations.
-Ira
Ned Nikolov says:
January 25, 2012 at 8:23 pm
Paid to do? Are you under the impression we are paid here for our labors? Not true.
In any case, Ned, I’m quite interested in your answer to the questions about your statement about the moon and the 14,800 W/m2.
I was curious because the number seems way out, no matter how I interpret the question. You had said:
14,800 W m-2 corresponds via S-B to 442°C. If this were 133 kelvin warmer than the moon, that would make the moon 309°C … so that made no sense.
In any case, your clarification would be appreciated.
Finally, do you have any comments on the overfitting question? There’s a good discussion of it here. From that cite, regarding the ratio between the number of parameters and the amount of data:
Since you have five parameters, that would mean you need at least fifty data points. Me, that still seems small, and the other reference in that citation gives larger minimum numbers. But let’s say it should be fifty data points for 5 parameters.
You have eight …
Many thanks,
w.
John Day says:
January 25, 2012 at 8:53 pm
Great. Then I’m sure you can explain his statement.
14,800 W m-2 corresponds via S-B to a blackbody temperature of 442°C. For a blackbody, T = (Q / SB) ^ 1/4, where Q is radiation and SB is the Stefan-Boltzmann constant, 5.67e-8.
T = (14800 W m-2 / 5.67e-8)^1/4 ≈ 715K ≈ 442°C
If this were 133 kelvin warmer than the moon, that would make the moon 309°C.
Since that obviously is not true … just what does Dr. Nikolov mean by his statement?
Your move. Please show your work.
w.
Tilo Reber says:
….. and you would be amazed at the level of self delusion that we, as humans, are capable of….
Tilo, I gotta tell you this is my 1st blog experience. Prior to this I was a solid “We are ONE, I AM’r” now based on WUWT hard facts data I’m back to the good ‘ole duality paradigm.
Tilo Reber says:
January 25, 2012 at 8:31 pm
Naw, I’m deeply committed to the scientific method, including the Laws of Thermodynamics. I’ve offered up a proof that no mechanism (not just Jelbrings or N&Zs, but no mechanism) can bring the planets temperature above theoretical S-B temperature if the atmosphere is transparent and GHG-free.
I am deeply committed to that proof, because I’ve posted it and nobody poked any holes in it. I understand that N&Z claim that their mechanism can raise the temperature above the S-B temperature regardless of atmospheric composition. If so, I think their claims violate conservation of energy. If no, then fine.
So I’m not deeply committed to N&Z being wrong. If they make that claim, they’re wrong.
w.
Dr Zeller, you say above
“Tilo, I gotta tell you this is my 1st blog experience. Prior to this I was a solid ‘We are ONE, I AM’r’ now based on WUWT hard facts data I’m back to the good ‘ole duality paradigm.”
Such an outcome would be a shame. You have everything to gain by this engagement. Think of it as analogous to the Republican Primaries. They are all on the same side, but nonetheless relentlessly probe each other for weakness. The point is that when it comes to the real thing, all the potential lines of attack will have already been well and truly canvassed. If you are right, your place in history is assured. If you are right, but publish without having expressed your case with sufficient clarity to meet all possible objections, then the doomers will tear you apart. If you are wrong, you will have been spared the embarrassment of having your error immortalized in the literature. It’s win-win-win. I’m reminded of a documentary I saw about Wiles’ proof of Fermat’s last theorem. His peers exposed many weaknesses in the early stages. Wiles just kept at it until everyone agreed the proof was solid. Please do not let the wild-west nature of blog debates discourage you.
@Willis
> Since that obviously is not true … just what does Dr. Nikolov mean by his statement?
That was his point, he was trying to show, via reductio ad absurdum, that GHG’s can’t be the cause of GHE.
@Ira Glickstein
> Of course, it may take some years or decades to obtain suitable data,
> but I will not accept that N&Z (or Willis) have made any real scientific
> contribution until their equations work for a “test set” -OR- until N&Z
> provide some physical explanation, or a laboratory test, for their
> pressure “enhancement” theory.
Agreed. I think we’re quibbling over the word used (“miracle”) to describe this preliminary “good fit”. As you know, research typically starts with some “promising results”, which are discovered in “good fits” like, but are also, typically, at the “solving a toy problem” stage.
Many years of further research and testing are required, as you point out, to validate the theory.
And of course, empirical laws are often useful, even when we don’t know why they work. Another good example, in addition to Zipf’s Law, is the S-B Law, which was originally called ‘Stefan’s Law’ based on his empirical fitting of Tyndale’s data. Boltzmann later showed how the law could be derived from his laws statistical mechanics.
kzeller said @ur momisugly January 25, 2012 at 9:46 pm
What on earth is this supposed to mean? It looks like English! Will it help me understand if I imbibe some hallucinogenic drugs and chant: “Wow! Reality! What a concept!”?
WWhat on earth is this supposed to mean?
Willis Eschenbach says:
January 25, 2012 at 10:32 pm
So I’m not deeply committed to N&Z being wrong. If they make that claim, they’re wrong.
Willis, I think it’s pretty obvious that you are angry. Hey, Ned has essentially denigrated you a couple of times. Your reaction is normal. Maybe you can’t see it but others can. I suspect you’re trying as hard as you can to not let it affect you, but you are human after all (and a cowboy at heart).
OTOH, you have been basically calling their baby ugly. I suspect that’s why you got the reaction from Ned that you got.
Nick Stokes says:
January 25, 2012 at 7:49 pm
[Richard M says: January 25, 2012 at 5:45 pm
“Nowhere have I stated anything about what Miskolczi theorized. My only reference was to the empirical data he discovered.”]
Miskolczi produced no empirical data at all. He looked up a database of measured profiles of air temperature and pressure from balloon ascents. Absolutely no measurement of optical depth, or anything involving IR. That all came from his theory.
And, if you read what I actually wrote you’ll see the word “discovered” and not the word “produced”. Nick, this is one reason why you have such low credibility at WUWT. You tried to change the meaning of what I said and then produced absolutely no evidence to back up your claim. If his computations based on the empirical data were wrong, then demonstrate it. Otherwise, you’re once again acting like a troll.
A comet is as much a heavenly body as a planet. I wonder if they can test ther theory on a comet. I remember Halley, quite some data should be available on that one from Esa’s Giotto probe. In 2014 the rosetta spacecraft will even land on comet Comet 67P/Churyumov-Gerasimenko.
@Willis
> So I’m not deeply committed to N&Z being wrong.
> If they make that claim, they’re wrong.
Just to set the record straight (and then try to resume a productive scientific discussion) :
It seems you and Joel have both played around with the N&Z ideas a bit and attempted to understand them. But Joel obviously now thinks N&Z is quackery:
> There is no scientific theory; it is just a bunch of caballed
> together nonsense that appeals to people who can’t
> distinguish between real science and stuff that sounds
> sort of science-y.
But he also said …
> Willis and I in fact apparently understand Nikolov and Zeller’s
> work better than anybody else (including them).
which suggested [there I go again] that he thinks that you think like he thinks.
But your statement above clears the air for me. Good for you. So let’s continue this discussion about N&Z’s theory, which is real science (even if it turns out be mostly wrong).
That is how scientific theories (and sausages) are made. Ain’t always pleasant.
😐
Tilo Reber says:
January 25, 2012 at 9:05 pm
For one, PETG isn’t perfectly rigid. If you put it under pressure the bottle will expand. Since the painted surface isn’t flat, it can’t all be perpendicular to the incoming sunlight. But a pressurized bottle would have an increased diameter so it would absorb more solar energy and get hotter. And that’s just one thing off the top of my head.
Interesting that shortly after my most recent posting here about N & Z’s omission of heat capacity both Ned and his colleague have posted here but they won’t touch that issue with a ten foot pole!
Yes, Ned, see Phil. above. WUWT?
Maybe what is needed is a chair swap.
For one thread, Willis should argue why this theorem is correct and Ned should argue why his theorem is false. Perhaps points of understanding will be transferred. This dog’s breakfast is rapidly producing entrenched positions, where there should not be any, considering it is just appearing, in this forum. Ned – it was a little naive of you to think that your hypothesis would be overwhelmingly accepted, just because it is “anti GHE CAGW”. Validation can be more difficult here, than many so called, peer reviews of academia. GK