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Published comment, and reply, on Gerlich and Tscheuschner 2009
Topic Started: May 8 2010, 03:45 AM (4,763 Views)
Board owner
Hank Roberts
May 11 2010, 10:45 PM
I'm trying to figure out why they assert--as recently as last month--that Venus's atmosphere is opaque to visible light, saying that means Venus couldn't have a greenhouse effect:
Thanks to Hank's input above, I noticed a few things that looked surprisingly familiar and went to look more closely. Indulge me... some people may find this interesting. The portion Hank quoted from the arxiv linked paper also appears in the reply to our rebuttal, as follows:
GT-2010, Gerlich and Tscheuschner's reply to rebuttal, end section 5.2

Let us return to the claim of Rahmstorf and Schellhuber that the high venusian surface temperatures somewhere between 400 and 500 Celsius degrees are due to an atmospheric CO2 greenhouse effect. Of course, they are not. On the one hand, since the venusian atmosphere is opaque to visible light, the central assumption of the greenhouse hypothesis is not obeyed. On the other hand, if one compares the temperature and pressure profiles of Venus and Earth, one immediately sees, that they are both very similar. An important difference is the atmospheric pressure on the ground, which is approximately two orders higher than on the Earth. At 50 km altitude, the venusian atmospheric pressure corresponds to the normal pressure on the Earth with temperatures at approximately 37 Celsius degrees. However, things are extremely complex (volcanic activities, clouds of sulfuric acid), such that we do not go into details here.

Background: 3 publications and 1 unpublished arxiv upload

Recall! Gerlich and Tscheuschner put up a paper on arxiv in 2007. Two years later, the same paper, with minimal modification and no corrections to flaws which had been pointed out in the interim, appeared in a legitimate science journal as GT-2009, linked in the first post of this thread. It claims to falsify the whole physical basis of the greenhouse effect as conventionally taught in atmospheric physics.

Then, this year, a rebuttal comment was published by six authors (I was one of them) in the same journal. I will refer to it as HCHSSZ-2010, and simultaneously there appeared a reply, which I will refer to as GT-2010.

In the meantime, Gerlich and Tscheuschner had informally produced another paper and uploaded it to arxiv. This is the paper that Hank speaks of above. I will refer to it as GT-2010a. That paper is

This otherwise unpublished arxiv paper has problems of its own. The bulk of it (section 2) is a comparatively trite treatment of some formulae used in atmospheric physics, which (by an abuse of standard terminology) are all called the "Barometric formulas". Barometric means "to do with pressure", or a barometer. Section 3 consists of a single paragraph on results, and there is an appendix called "relevance to current climate debate" which makes no mention or use of the barometric formulae but merely claims that that they have disproved the greenhouse effect with a cite to GT-2009, and a number of glaring errors.

A clever ploy to get your arxiv upload published!

The paper GT-2010a is unpublishable in my opinion, as far as science journals are concerned... or it should be.

However, with the opportunity to make a reply to our rebuttal, the usual difficulties with publications are reversed, and a journal will make every attempt to allow the reply. This gives a way to publish the content of GT-2010a: incorporate it into GT-2010, and it will appear published as part of the reply. The fact that the original paper and our rebuttal all make no mention or use of these barometric formulas might be noticed by a reviewer, but a sympathetic reviewer in a hurry is quite likely to let it pass.

I'll show how it was done with images of the paper as it is modified. For the truly obsessed, you may obtain a copy of GT-2010a from arxiv, and follow along.

Step 1. Shorten the paper by removing the technical mid-section

The pdf of GT-2010a is 13 pages long. Actually 14, but the last page is just a few lines of overflow. There are

  • Three pages for the coversheet, abstract and table of contents.
  • Half a page for the introduction (section 1)
  • Seven pages of maths, walking though barometric and thermodynamic equations (section 2)
  • Just under half a page for a summary conclusion (section 3)
  • A bit over a page for an appendix all about how they falsified the greenhouse effect in another paper -- GT-2009.
  • A page for acknowledgement and references

The first step is to omit the auxilluary material, and the technical setion 2. This leaves section 1, section 3 and the appendix -- about two pages worth. Here is a picture of the original pdf with the extracted sections highlighted in green boxes, and with an inset in the bottom right showing the result, converted to plain ASCII text ready for more editing.
Posted Image

Step 2. Write one new paragraph, remove another, relocate two more.

The next step is to write a brief and glowing point form summary of what was done in in this new paper, to replace the omitted section 2. Also, the summary included in the appendix of GT-2010 is not needed given the next context, and actually looks out of place. Trash it.

The appendix is now reduced to most of the first paragraph, plus two substantial paragraphs at the end. These are still usable. Hm... move the last paragraph of the appendix into the end of section 3, and the next to last paragraph of the appendix up to the start of section 1. Here's how you do it:
Posted Image

Step 3. Final clean up.

That's about it. The references need to be updated for the bibliography of the new paper, and there needs to be a new citation to the original version of GT-2010a on arxiv. The section numbering should be fixed, and then a little bit of rewording and some minor cleanup; possibly indicated by referees, though I cannot tell about that.

The little bit of appendix left works as a start for the conclusion of the whole reply to the rebuttal, so the heading "Appendix..." now becomes "Concluding remarks", and it will be section 6 in its new context. The other two sections become subsections 5.1 and 5.2 of a new section 5 of the reply, called "Barometric Formulas". The first section is no longer an "Introduction", but rather an "Overview".

There are three changes at the level of phrasing. They are:

  • The description of the barometric forumulae is altered. (The original confuses them with the lapse rate calculation, which is not correct.)
  • A phrase is added for a reference to the standard derivation of the barometric formulae.
  • The flow between the two relocated paragraphs from the appendix has been broken, and can be fixed with a bit of rewording.

The three changes are as follows:
"Before and After"
as in GT-2010a originalas in GT-2010 reply to rebuttal
In the following, we derive approximate temperature profiles of an atmosphere, also called adiabatic lapse rates or better barometric formulas.In Refs. 43 and 44 we explicitly derive the approximate pressure profiles, density profiles, and temperature profiles of an atmosphere, also called barometric formulas.
The reader is also referred to the textbook by Riegel and Bridger on “Fundamentals of Atmospheric Dynamics and Thermodynamics”.The reader is also referred to the textbook by Riegel and Bridger on “Fundamentals of Atmospheric Dynamics and Thermodynamics” where the standard derivation of the barometric formulas can be found.
The claim of Rahmstorf and Schellhuber is thatLet return to the claim of Rahmstorf and Schellhuber that

There are a couple of other single word changes. Here is a copy of the paper with some highlighter applied.

  • Yellow indicates a numbering change for references or sections.
  • Blue indicates phrases that are altered.
  • Green indicates text inserted. (fixed in edit: I have also marked in the green the point form paragraph added in step 2, and put a black line marker in the margin for this.)
  • Red indicated text removed.

Posted Image
That's it. There were also a couple of new commas, which I have not worried about.

The new section 6, "Concluding remarks", has already been quoted in full in the second post of this thread. It starts with the single sentence that is extracted from the appendix of GT-2010a; and then has been rounded off by a list of the "mistakes" in our rebuttal comment; but if you look at them they are all more or less of the form "Halpern et al" don't understand something or other, rather than an actual identification of any alleged point of error. Contrast with our conclusion, which identifies substantive points of real error.

What do you think?

The original has not actually been formally published, and the arxiv for GT-2010a is properly cited. They are using their own work in a new context and under the circumstances I don't see any particular problem with that.

What is striking, however, is how completely irrelevant it all is to the original paper GT-2009, and to our rebuttal HCHSSZ-2010, and to the atmospheric greenhouse.

Cheers -- sylas
Attached to this post:
Attachments: step1.gif (93.11 KB)
Attachments: step2.gif (54.93 KB)
Attachments: step3.gif (41.12 KB)
Edited by sylas, May 15 2010, 07:54 AM.
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Well, it's a little marginal, but your analysis shows they left out the main real content of that arXiv paper (section 2) and just reused some of their introductory/concluding text (modified a little at least). The one central claim they highlight in this bit is their completely wrong notion that:

Since the measurable thermodynamic quantities of a voluminous medium, in
particular the specific heat and the thermodynamic transport coefficients, naturally include
the contribution from radiative interactions, we cannot expect that a change of concentration
of a trace gas has any measurable effect.

This claim may hold for an opaque medium, optically thick on short length-scales in the region of thermal radiation, but it certainly does not hold for a nearly-transparent medium like the atmosphere. As Ray Pierrehumbert discusses quite nicely in his book (which I'm rereading my draft copy of again...) the main impact of increasing GHG's in an atmosphere like Earth's with partial infrared transparency is in the wavelength ranges where their optical depth for the whole atmosphere is close to 1 (not too high with full absorption, not too low with almost none). This is very different from what you get by looking at the "bulk thermodynamic transport coefficients". Of course those coefficients don't cover convection either, or phase change heat transport, so those are other issues with G&T's claim.

They do seem to be obsessed with the thermal conductivity issue, by the way!
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This is going to be a very short comment, just to keep the ball rolling.

It might be better if the term 'greenhouse gas' had never been coined. The basic principle of every greenhouse or cloche is that warmed air is trapped and kept from rising as a thermal.

As to the papers under discussion, I think we have a straw man argument:

"a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment"

Firstly, an atmosphere is an integral part of a planetary surface environment.

Secondly, a planetary atmosphere is a heat engine driven by a sun.

The second law of thermodynamics is often stated to demand that heat can only flow from a hot to a cold body. If that is the stance taken by the authors as a founding argument then their conclusions must inevitably be wrong.

The notion that heat can only flow from a hot to a cold body is a basic principle of the caloric theory of heat. Whilst being a very useful fiction in the case of conductive heat transfer it completely fails to describe reality in the case of radiative heat transfer.

Caloric heat flow is unidirectional. Radiative heat transfer is bidirectional.

The temperature of a body is determined by the net radiative transfer.

When two radiating bodies are in proximity there will be a flow of radiated energy from each to the other. If they are of different temperatures then there will be a net flow of energy from the hotter to the colder body.

Unlike caloric theory, the law of net radiative transfer does not completely prohibit the transfer of heat energy from a colder to a hotter body. It prohibits a net positive transfer from cold to hot.

If you consider CO2 and radiative transfer then you must not treat the atmosphere as a single homogenous body. For the purpose of discussion it is a support matrix of Nitrogen with embedded radiating bodies - CO2 molecules.

A CO2 molecule can emit a photon in any direction. In atmosphere, that photon can be directed towards the ground or towards space.

There is no mechanism by which a hot ground surface can force a CO2 molecule to emit a photon towards space.

In the correct model, the planetary surface is a body and each individual CO2 molecule is a body.

By intercepting photons and returning some of them to the surface, CO2 molecules reduce the net radiative transfer between a hot planetary surface as source and empty space as sink.

A CO2 molecule, just like any reflector, can return photons towards their source.

The CO2 effect is less like a greenhouse, more like an assemblage of corner reflector antennas. The more such antennas you hang on your plastic boat, the greater the chance that an echo will be returned to the supertanker that's headed your way.

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Hello fine people interested in the ongoing discussion!

I have followed the discussion at hand now for quite some time and, without taking a stance in this matter, I wanted to comment that G.G. & R.D.T. - notwithstanding any other provisions to the contrary (i.e. by harper et. al.) - are not losing ground here. As "weird" and "unusual" as their claims might sound to professionals (!), to those people interested in the subject but less qualified, as they have non-scientific professions and know their bits and pieces from physics AP in senior high, G.G. and R.D.T. are the ones providing more scientific proof in terms of formulas and diagrams, hence "winning the argument". (vague, I know, but I'm going to elaborate on that later). Again, I'm not judging whether they are right or wrong in applying the formulas to the subject at hand the way they do, it's only that their claims seem more substantial than those of the people making an argument using "vulnerable words" instead of using the respective formulas.
In other words: The people trying to prove G.G. & R.D.T wrong can argue infinitely and repeat a million times over that i.e. "a CO2 molecule, just like any reflector, is capable of returning photons towards their source" - without providing the physical proof in terms of calculations their arguments will seem powerless against G.G. & R.D.T's formula-supported claims.

What I demand is that for the sake of upholding the academic standard, everybody should stick to the universal language of physics, which is of course "a, ,b, c, alpha, beta, gamma, root, +, -, *, /, =, " etc. etc.

Conclusion: Claiming something is easy, proving it on the other hand is so much harder. And so far, for the untrained eye, Gerlich and Tscheuschner have succeeded more in doing the latter.


A short, biased remark: I believe the underlying claim G.G. & R.D.T make is not that global warming in itself or the greenhouse effect as such is non existent, nor are they really trying to chance the situation. From what I can tell about them, I believe their real motivation is to raise the discussion's academic standard. In that, I support them fully as I, too, as well as many people around the globe, have been shocked to learn about the unbearable abuse of the term "scientist" in conjunction with "climate chance" - you all know what I'm talking about. IPCC ... and that's just the tip of the iceberg.
Anyway, what they are explicitly saying is that many people who take a stance in the discussion do in fact not know what they are talking about, especially when using physical terms such as "second law of thermodynamics" since they - allegedly - lack the proper qualification. Well, if all you people who feel offended by that remark, and I sense a truckload of hurt feelings here, really want to prove them wrong about that and not just "chicken-fight", you inevitably HAVE to use the adequate formulas and physical expressions, too.

Please be aware, that every contribution to this discussion can and will be used in the struggle over who is right and who is wrong, when it comes to politicians cutting the funding of research and companies investing less in "going green". Every argument which can be twisted, will be twisted. The only way to elude this is to use "if: a=b & b=c ==> a=c" ...

Thanks for reading this!
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duncan - on the surface your complaint is itself rather superficial. Even in mathematics, it is important that the symbols used have some sort of meaning. In physics and climate science the connection between mathematical symbols and reality, the natural world, is where the real meaning lies - and it is in that logical connection to reality and self-consistency with one another, rather than in their mathematical calculations (of which they don't actually have very many, despite the number of equations) that is in most cases where Gerlich and Tscheuschner have gone wrong. With the second law of thermodynamics, for instance (of which all of us do indeed have considerable experience - I taught an undergraduate section on it one year) the problem is in how G&T apply the law, not in any calculations they do with it.

In fact, the only actual calculations of entropy change (what the second law appear is really about) appear not in the original G&T, nor in their reply to our comment, but in our comment itself. If you download the comment sylas linked to on the original post here - if you have access to the journal - or just download version 2.11 from the Rabett Run Labs link there if you don't - then section 2.1 and 2.2 go into some detail on the entropy change associated with exchange of thermal radiation as happens in the greenhouse effect - and of course it perfectly satisfies the second law requirements.

But all that said, you're right that we haven't gotten into the detailed physical relationships much in this forum yet. If G&T's only desire really was to "raise the discussion's academic standard" (have you actually read their article? Do you really think the name-calling and obtuse mockery, confused argument etc. is a way to "raise standards"?), then by all means the plan here is to meet a high standard for academic discussion of the subject.

Unfortunately G&T themselves were not interested in participating in this discussion, but perhaps if you have a particular section of the original article you felt was compelling, you could indicate it and we can go into some details on that? Sylas already covered the back-radiation (seen observationally) and some of the other issues - see also this commentary that lays out the case quite concisely (though quite similarly to the presentation here) - and the commentary even includes several equations...
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Board owner
Hi duncan,

I am not especially interested in who is or is not "losing ground", because in the long run I am confident that what has real merit will last and what doesn't... won't. What counts as winning or losing ground in public debates seems to be quite a subjective perception, and I do not think Gerlich and Tscheuschner are actually gaining any ground at all.

My own feeling is that the paper by Gerlich and Tscheuschner which appeared in IJMPB in 2009 was quite easily the worst paper I have ever seen get into a real physics journal. We all know that peer review is not perfect and that bad papers can get published from time to time, but this one was really was exceptional. In any case, it has had no impact at all in the world of science until our rebuttal was published, and our rebuttal hardly counts as an impact either. It has been, scientifically speaking, a non-issue.

Wider public reactions are much more diverse. I don't quite know what is the best way to deal with questions from people who think Gerlich and Tscheuschner might be on to something. Usually such claims either make trivial errors in basic physics, or else they describe the paper in terms that do not appear to have any association with what I read in the paper.

The paper GT2009 doesn't provide any scientific or mathematical proof at all of their main claims. What maths is used is generally irrelevant, or taken to have implications which it does not. There are various fairly elementary mathematical formulae with quite unexceptional consequences, but there is certainly no scientific or mathematical proof of their main claim (as I see it) of some kind of second law violation. There is no such violation in any of the work that they have cited as making such errors. Can I persuade the world that GT2009 fails to give any support to their main claims. Probably not. Can I persuade the scientific community? I do not think there is any need.

You say:
In other words: The people trying to prove G.G. & R.D.T wrong can argue infinitely and repeat a million times over that i.e. "a CO2 molecule, just like any reflector, is capable of returning photons towards their source" - without providing the physical proof in terms of calculations their arguments will seem powerless against G.G. & R.D.T's formula-supported claims.

G&T do not have any formula supported view at all of the notion that photons CANNOT go back towards their source. Truly; none of the maths or formulae says any such thing.

Elementary physics says that thermal radiation from a gas goes in all directions. Do you disagree with this? Or what about the direct observation of emissions coming from the atmosphere with spectral qualities clearly showing radiation from water, from carbon dioxide, and from ozone? Doesn't direct observation count for anything here?

I'm somewhat at a loss here. When gases give off thermal radiation, they do so in all directions. It's that simple. Any claim that radiation cannot come back towards the source of radiant energy that is being absorbed by the gas is wrong, and GT2009 don't actually make such a claim. Trust me on this one... do not accuse Gerlich and Tscheuschner of saying that a CO2 molecule is NOT capable of returning photons towards their source! You can't quote them saying this, and so they just say you "misunderstand them". Indeed, in the reply to our rebuttal, the list of "errors" that they attribute to us (listed in post #2) is pretty much a list of things they claim we don't understand or have misread. I think our rebuttal did a much better job of identifying actual errors; but be that as it may, I am content for the rebuttal and reply to be available and compared on their real merits.

A short, biased remark: I believe the underlying claim G.G. & R.D.T make is not that global warming in itself or the greenhouse effect as such is non existent, nor are they really trying to chance the situation. From what I can tell about them, I believe their real motivation is to raise the discussion's academic standard.

I am glad to have you here and commenting duncan, so no offense is intended by this...

But this is one of those times that I wonder whether we can be reading the same paper. This paper has some of the lowest academic standards I have seen. The attacks they make on other much more expert and reputable physicists are not only without any actual scientific merit... they are also scandalous in their wording and frankly the journal owes a number of scientists an apology for letting such unprofessional language past editorial review.

The worst example in the paper is on page 295 of the IJMPB journal, or page 29 of the arxiv manuscript you can obtain freely.
GT2009 page 295

Figure 13 is an obscene picture, since it is physically misleading. The obscenity will not remain in the eye of the beholder, if the latter takes a look at the obscure scaling factors already applied by Bakan and Raschke in an undocumented way in their paper on the so-called natural greenhouse effect. This is scientific misconduct as is the missing citation. Bakan and Raschke borrowed this figure from Ref. 103 where the scaling factors, which are of utmost importance for the whole discussion, are left unspecified. This is scientific misconduct as well.

This is not raising a standard. It is dragging it into the gutter.

On the merit of the claim... they are wrong. This is a simple repeat of the problem of failing to understand normalization, mentioned in post #7. The figure to which they take such exception is the same normalized curves for Planck radiation at different temperatures. It IS in fact cited to a valid source; a basic textbook on atmospheric physics in which the figure appears. The claims of being "misleading" don't stand up to serious examination; the claim of scaling being of "utmost importance" is missing the whole point; but leave that aside. (And if you think I am not explaining the problem clearly enough; look at GT2009 and compare!)

Obscene? Misconduct? The phrasing here is not raising any levels, it is well below professional standards and should never have been accepted in such a form in a professional journal.

The only way to elude this is to use "if: a=b & b=c ==> a=c" ...

Thanks for reading this!

Thanks for writing it. It's good to have someone skeptical of my claims; it leads to helping clarify points of confusion and it also often leads to my finding and fixing my own errors.

I think it would be worth focusing on the matter of whether a molecule of CO2 can emit a photon back towards its source.

I presume here we mean that there is a gas which is absorbing energy from a certain direction; specifically, atmospheric gas absorbing photons coming from below.

I assert the following:

  • A gas which can absorb thermal radiation can also emit thermal radiation.
  • A molecule in a gas can emit a thermal photon in any direction as well as another.
  • Therefore; molecules of CO2 that can absorb thermal radiation from the surface will also emit photons back down towards the surface.

I also assert that this has been known for well over a century (if rephrased as appropriate into the models of radiation used at the time), has never been in any doubt, and the magnitude of thermal radiation coming from the atmosphere back to the surface has been directly measured now for well over 50 years; and with measurements in recent years also allowing spectral characteristics of this backradiation to be seen, and to identify the molecules involved. The major molecules identified as being able to absorb and emit thermal radiation back in the mid nineteenth century were carbon dioxide and water (John Tyndall, who has a picture on the site banner, by the way!) and this is confirmed in the spectral analysis of directly observed atmospheric backradiation.

If you know of any clear mathematical description in G&T which conflicts with this, I would be genuinely interested. That is because it seems to me that the paper DOES sometimes leave people with the impression that there's some problem with a gas radiating back towards a surface that is hotter than the gas itself. I think you are probably not the only person who has taken away that impression, and it would be genuinely useful to see what passage in GT2009 gives that impression to folks. But I can tell you from experience that G&T themselves will not accept that they have made such a claim themselves.

Best wishes -- sylas
Edited by sylas, May 22 2010, 02:39 PM.
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After a fast peer over GT's second "paper", I have some comments. The first one is that most of the results that are correct (which does not imply that all results are correct, only some of them) are already in any of the basic textbooks on atmospheric physics that can be found in any bookstore. I find really surprising that they need 6 pages and 14 equations starting from the Navier-Stokes equations (including ELECTROMAGNETIC FORCES!!!) to arrive to the hydrostatic equilibrium condition $\frac{\partial P}{\partial z}=-\rho g$. This is most surprising, since the starting point of this discussion is "simply" that vertical acceleration is zero. They (incorrectly) state that the hypothesis that wind must be horizontal is needed (their 5th assumption). It is not the case, if the velocity is constant nothing changes. They assert that the usual assertion to arrive to hydrostatic equilibrium is that velocity is identically zero (after their equation 14), which simply is NOT the case, as clearly stated even at wikipedia:

I could be more specific, but I hope the general idea is clear from these comments
Edited by jon_saenz, May 25 2010, 10:09 PM.
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Terry Oldberg

I wish that respondants on the issue of the claims made by the Gerlich and Tscheuschner 2009 paper would do their utmost to avoid the ad hominem fallacy in their responses. By the evidence, this is not happening. There are postings, including at least one by the moderator, on the theme that no legitimate scientific journal should have published the G&T paper. Whether or not a journal should have published the paper is unrelated to the scientific issue. The sole scientific issue is whether G&T are correct or incorrect in their claims. Is the moderator and are any of the participants equipped to address the issue of whether the claims of the G&T paper are correct without use of ad hominem arguments?
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Terry Oldberg
Jul 3 2010, 06:56 AM
I wish that respondants on the issue of the claims made by the Gerlich and Tscheuschner 2009 paper would do their utmost to avoid the ad hominem fallacy in their responses. By the evidence, this is not happening. There are postings, including at least one by the moderator, on the theme that no legitimate scientific journal should have published the G&T paper. Whether or not a journal should have published the paper is unrelated to the scientific issue. The sole scientific issue is whether G&T are correct or incorrect in their claims. Is the moderator and are any of the participants equipped to address the issue of whether the claims of the G&T paper are correct without use of ad hominem arguments?
The moderator was coauthor of the reply.

The claim that back radiation violates the second law of thermodynamics (the premise of G&T's paper) is utterly absurd. They use a literal, parsed definition of the Second Law to make their specious claim. It is not an ad hominem to point out the fact that the journal's reviewers should never have allowed it past the review process with such an absurd claim.

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Terry Oldberg

Thanks for taking the time to reply.

I disagree on the philosophical issue. In philosophy, it is a principle that it is the truth or falsity of a proposition that is at issue and not the identities of the person or persons who are the authors of this proposition. To place the authors at issue is to commit the ad hominem fallacy.

To claim that no legitimate scientific journal should have published the G&T paper is to make G&T the issue rather than to make the claims of G&T the issue. People who adopt the position that it is G&T who are at issue argue circularly that G&T are wrong because they are G&T. I've repeatedly encountered this argument in the blogosphere. For example, on several occasions it has been argued that the claims of G&T should be disregarded because G&T are clowns.

If you, the moderator and owner of this site, were amenable to discussion of whether specified claims are correct or incorrect then I could demonstrate to you that, in the literature of climatology, some authors are guilty of an abuse of the language of thermodynamics in which "heat" is said to flow up a temperature gradient without being pumped and in contravention of the second law of thermodynamics. Among these authors are the authors of the Halpren et al paper.

I understand that you are a co-author of the Halpern et al article. That you as moderator and owner of this forum have erred cannot be a factor in discussion of this issue, under the operative philosophical principle, for the identities of the authors of the putatively erroneous claim cannot be at issue.


Terry Oldberg
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