Back to basics

Although I didn’t really think through starting this blog, one motivation was that I was aware that quite a lot of what was said about climate science in the blogosphere was simply wrong. I thought that if I could point out these basic errors, people might go “oh, okay, I didn’t realise. Thanks.” Of course that isn’t what happened and I was, obviously, naive to think it would.

In one of my early posts, I pointed out what I thought was an error in a Watts Up With That post written by Roger Pielke Sr. Tom Curtis, very kindly 🙂 , came along and pointed out that I was actually wrong. So, I wrote another post in which I acknowledged my error and ended up in a lengthy discussion with Roger Pielke Sr about feedbacks. I thought his conclusion about whether or not they were already operating was wrong. We didn’t achieve much, but it was perfectly cordial; something I value quite highly these days.

I haven’t really encountered Roger Pielke Sr much since then, but in the last couple of days have been engaged in a discussion with him on a RealClimate post. The discussion relates to his guest post on Judith Curry’s blog in which he suggests an alternative metric to assess global warming, which I’ve discussed before. The basic idea is to assess global warming using the following equation

\Delta Q = \Delta F - \Delta T / \lambda.

This is essentially the energy budget formalism, and is a perfectly reasonable way to assess global warming (with some caveats). The problem, though, is that I think Roger’s definition – and understanding – of the terms isn’t quite correct.

The equation is basically saying that if one considers some time interval over which there is a change in external forcing, \Delta F, and a change in temperature, \Delta T, then if the climate sensitivity is \lambda, there will be a change in system heat uptake rate (or change in radiative imbalance) of \Delta Q. Roger, however, interprets \Delta Q as simply being the radiative imbalance, rather than the change in radiative imbalance. This is only true if the initial state is one in which the system is in equilibrium and hence the initial system heat uptake rate (radiative imbalance) is zero.

Additionally, Roger doesn’t appear to understand the definition of a radiative forcing. For example, in this comment he asks

What is the current (2014) radiative forcing from added CO2 concentrations (above the pre-industrial concentrations)? We do not need the difference between these two time periods, which the IPCC presents, but the current forcing given that some of the added CO2 has been adjusted to by the warming up to this time.

Now, I don’t think this actually makes sense. A radiative forcing is defined as being

the change in net (down minus up) irradiance (solar plus longwave; in W m–2) at the tropopause after allowing for stratospheric temperatures to readjust to radiative equilibrium, but with surface and tropospheric temperatures and state held fixed at the unperturbed values.

In other words, if there is some change in an external driver of climate change (Sun, volcanoes, anthropogenic GHGs), how does this change influence the net irradiance, or the net flux into the system, without the troposphere responding to this change. You can’t really define an instantaneous radiative forcing. You can define a total, or a change. Also the statement the current forcing given that some of the added CO2 has been adjusted to by the warming up to this time is similarly confused, since as the system adjusts, the radiative forcing doesn’t change. The net flux changes due to the Planck response and other feedbacks, but the forcing remains the same. I’ll also add that this comment is suggesting that Roger Pielke Sr also doesn’t understand the origin of some of the data that he’s using in his analysis.

So, this seems to be an example of someone who is critical both of mainstream climate science and of the IPCC, but doesn’t appear to understand some of the basic concepts that he’s ultimately criticising. I have a similar issue sometimes with Judith Curry who often criticises climate scientists (or the IPCC) for not considering natural warming processes, when in fact they do. The reason that it appears that they don’t consider these processes is really because these processes appear unable to explain our recent warming. It’s not that they’re being ignored, it’s that they seem to be much smaller than the anthropogenic influences. There’s nothing wrong with trying to understand the role of natural processes, but it would be good if those doing so (and who thought they might have a significant influence) appeared to understand why many think they’re not a significant driver of our current warming.

In a sense, this is why I sometimes find the whole idea of an improved dialogue difficult to contemplate. I’m all for improved dialogue but am not sure I see the point when the most suitable response to what someone says is “apart from being completely wrong, that’s an excellent point.” Now, of course, it would be great if – when pointing out these errors – the response was “oh, okay, I didn’t realise. Thanks.”. However – as I pointed out at the beginning of this post – I’d be naive to think that that was likely. Of course, if I’ve made some error (and I may well have) feel free to point them out. If you do, and if you’re right, I promise to respond with “oh, okay, I didn’t realise. Thanks.” 🙂

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58 Responses to Back to basics

  1. Pierre-Normand says:

    Yes, I’ve also questioned him on Climate Etc some time ago about his conception of total forcing and couldn’t make sense of his response. It had also seemed to me that, once some of his assumptions were corrected, his derivation of sensitivity on the basis of ocean heat content were back in line with the IPCC’s. I’ll dig that up and compare with your recent discussion.

  2. Pierre-Normand,
    Yes, that would be interesting to see. I also concluded that if he corrected the errors in his calculation it would probably bring it more in line with IPCC estimates.

  3. Are there unique correct answers to this kind of semantic questions?

    Both IPCC and Pielke Sr seem to agree that RF is the imbalance that results from some specified change. The concept does not make sense without stating also the change that’s causing the imbalance, but I would not state as categorically as you do that the way Pielke Sr is using the concept is wrong. It’s not the imbalance that results from an assumed almost sudden change (almost as stratosphere is allowed to adjust) but the imbalance from a particular real history. As long as that’s made clear, I don’t think it’s right to state that his way of using the word is wrong. Some may find it confusing, but how badly is that really the case?

  4. Pekka,
    I largely bdisagree with your comment and I don’t understand how you can claim this is semantics. The radiative forcing is defined as being the change in TOA flux after the stratosphere only has responded to some change in external driver. Therefore there is no way to determine the radiative forcing in 2014 without it being with reference to some earlier period. Of course you could define it as being with reference to 2014, but that would then, by definition, be zero.

    It’s not the imbalance that results from an assumed almost sudden change (almost as stratosphere is allowed to adjust) but the imbalance from a particular real history.

    I’m not even sure that I understand what you mean by this. The radiative forcing is the change in net flux after some change in an external driver and after allowing the stratosphere to respond, but not the troposphere. You seem to be suggesting that it’s okay to redefine the term without making that clear. There is a difference between a radiative forcing and the radiative imbalance. The radiative forcing always has to be relative to some base and therefore cannot be determined for a single instant in time. The radiative imbalance – on the other hand – is the difference between the incoming and outgoing flux and so can be defined at some instant in time. I don’t really see how you can argue otherwise unless you’ve decided to redefine the term radiative forcing.

  5. Pekka,
    I’ll add that in the IPCC definition a forcing refers only to external influences (Sun, volcanoes, anthro). All the other influences (Planck response, water vapour, lapse rate, clouds) are feedbacks. You – and Roger Pielke Sr – seem to be suggesting that feedbacks can influence the value of the forcing. I would argue that this is only true if you choose to redefine the meaning of forcing.

  6. Perse says:

    You’ll be glad to know that I have a goal to always respond to constructive criticism with “Oh, okay, I didn’t realize. Thanks”!

  7. Pierre-Normand says:

    Pekka: “Are there unique correct answers to this kind of semantic questions?”

    This was not at issue. I was quite happy to allow him whatever definition he wanted. It had seemed to me that his derivation was not consistent with his own definition. But I’ll review this old topic (and the recent RealClimate exchange) before commenting further.

    Incidentally, I found by chance your “Kinetic gas theory for gas in gravitational field” this morning and found it quite useful since I am am currently arguing with a Climate Etc. regular that an isothermal state is perfectly consistent with a vertical density gradient in a box under gravity (something that he can’t fathom, and is quite unwilling to accept, for a variety of strange reasons). It also confirmed most of the intuitions that I had developed so far about the features of the velocity distribution that must satisfy the Boltzmann distribution at equilibrium. I never had thought about this problem before FOMD brought up a neat lunar thought experiment that illuminates the (lack of a) ‘problem’ with the idea of particles falling down while maintaining a constant velocity distribution.

  8. IPCC has defined, how IPCC uses the word. In spite of the important role IPCC has they cannot decree that all other uses are wrong.

  9. Pekka,

    In spite of the important role IPCC has they cannot decree that all other uses are wrong.

    In a sense I agree, but if someone is going to use the term differently, they should make that clear. You can’t use the same term as everyone else but mean something different, without making that clear. Similarly, if you’re going to argue that someone else (the IPCC) is wrong, you have to do so using their definition of the term, not yours (or you have to ensure that you’ve correctly mapped from their definition to yours).

    In another sense, I disagree. If an organisation defines a scientific term, in what scenario is it sensible for a single scientist to use the same term but mean something different. It would be like someone saying “I’ve decided that a metre is the distance an ant typically crawls in 10 seconds” and then use that to argue that everyone else’s calculations are wrong.

    To be honest, I’m actually slightly uncertain how to respond to what you’re saying. This isn’t about the term specifically, but about whether or not what Roger Pielke Sr appears to be suggesting makes scientific sense. The term itself is not that important. What it represents is what’s important.

  10. BBD says:

    Bloody hell, Pekka!


  11. BBD,
    Maybe you should make it clear how you’re defining the terms “bloody hell”. Pekka might think you mean “good job!” 🙂

  12. Eli Rabett says:

    Antoine Lavoisier on nomenclature and why Roger Sr. cannot play Humpty Dumpty

    The impossibility of separating the nomenclature of a science from the science itself, is owing to this, that every branch of physical science must consist of three things; the series of facts which are the objects of the science, the ideas which represent these facts, and the words by which these ideas are expressed. Like three impressions of the same seal, the word ought to produce the idea, and the idea to be a picture of the fact. And, as ideas are preserved and communicated by means of words, it necessarily follows that we cannot improve the language of any science without at the same time improving the science itself; neither can we, on the other hand, improve a science, without improving the language or nomenclature which belongs to it. However certain the facts of any science may be, and, however just the ideas we may have formed of these facts, we can only communicate false impressions to others, while we want words by which these may be properly expressed.[3]

  13. Concerning the RealClimate post of stefan (I assume that’s Rahmstorf), I like it very much, as it presents almost exactly the same arguments I have presented a couple of times at Climate Etc (perhaps also here, I’m not sure) about the choice of the indicator of warming to be used in reporting to the public. I didn’t discuss policy targets in those comments, but the arguments are the same.

  14. Arthur Smith says:

    If Roger defines radiative forcing to mean what other people call radiative imbalance, which sounds like what his comments indicate, then his equation that ATTP quoted reduces to Delta T = 0 (because he has defined delta F = delta Q). That seems rather pointless, it certainly tells us nothing about feedbacks. If that’s not how he defines radiative forcing, does anybody have a clue what his definition is? Pukka?

  15. Arthur,
    Yes, that was what I realised after responding to Pekka’s comment. If Roger is using his equation as done by others, then the Planck response and the other feedbacks are represented by \lambda, the radiative imbalance is represented by \Delta Q, and the forcings are represented by \Delta F. If, however, he has redefined what is meant by the term forcings, then either his equation is trivial, as you suggest, or I no longer understand it.

  16. Pierre-Normand says:

    This was the response that puzzled me:

    This was my main criticism, posted four days later:

    Re-reading this quickly, I may have neglected non-CO2 greenhouse gas contributions in my claim about the IPCC projections for 2100. Roger Sr. didn’t respond but I don’t blame him. I think he had departed already.

  17. My reaction is certainly related to, how I like to see such details discussed that may be misleading. In my way of thinking it’s appropriate to note that the use differs from the standard usage and that this makes understanding the message difficult or even impossible. That approach may help in resolving the issue rapidly. Commenting on another site it’s also appropriate to note that the concept is not used according to the standard practice.

    Whether there are errors in the argument, when the conceptual misunderstandings have been resolved is another issue.

    There are also cases where people use words intentionally to mislead, or use the same word in two different meanings and then build false conclusions based on that. In such cases it’s certainly appropriate to state that directly and strongly. I don’t think that Pielke Sr had that kind goals in his writing (but I may err on that).

  18. The thread Pierre-Normand linked to contains also one of the cases, where I presented arguments similar to stefan’s post at RC

  19. Pekka,
    I agree with you about Stefan’s post and with the points you made on Climate etc. I certainly don’t think that the OHC is a particularly good indicator/target for policy purposes.

  20. Pierre-Normand says:

    Pekka: “There are also cases where people use words intentionally to mislead, or use the same word in two different meanings and then build false conclusions based on that. In such cases it’s certainly appropriate to state that directly and strongly. I don’t think that Pielke Sr had that kind goals in his writing (but I may err on that).”

    When those kinds of self-serving equivocations occur, it’s very frustrating for the person arguing the other side of the debate, but I think it’s almost never intentional. It’s almost always stemming from a powerful mechanism for avoiding cognitive dissonance. But one can’t make this remark during the debate. It’s not a legitimate debate move to question one’s opponent cognitive integrity. So, the best we can do is to constantly re-frame the argument, insist on the faults in the other side’s argument, and hope the main point will sink in eventually… but not count on it.

  21. Pierre-Normand says:

    Pekka: “The thread Pierre-Normand linked to contains also one of the cases, where I presented arguments similar to stefan’s post at RC”

    Yes, I remember very well the good points that you made back then.

  22. I am sure that Pielke Senior is wrong. He doesn’t seem to understand the fat-tail of thermal diffusion. There is always a fast transient (that the deniers mistake for a first-order damped exponential response) but always followed by a long fat tail (that they always conveniently ignore).

    Not using something akin to the heat equation when dealing with a large thermal mass and substituting first-order kinetics for the behavior is about as futile as trying to square the circle.

    If you want to get back to the basics on this topic, start from there.

  23. WHT,
    Well, yes, that’s another issue. He seems to want to use these simple models to assess global warming. I see no problem with that if your goal is to understand if it’s happening or if you want to quantify it generally. Suggesting that these simple models can be used to validate climate models or accurately quantify global warming seems a bit much.

  24. Ah, glasshopper, you are young. Every novice must get through the phase of arguing with RP Sr about alternative metrics and his own defn of terms. Eventually The Enlightened realise that the answer is Mu.

  25. William,
    Just trying to earn my wings 🙂

  26. Oh, I’ve just realised that the correct response was probably wax on, wax off.

  27. John Mashey says:

    On reading the post, I was going to invoke Humpyy Dumpty, but seeing the comments I czn only second Eli’s. The Rabett was too quick.

    The Alice books are gibe sources: believing six impossible things before breakfast is often seen.

  28. Steve Bloom says:

    I’m recalling that way back on his blog (what William refers to, ~ 2005 IIRC) RP Sr. started out with some similarly obscurantist reasoning with regard to the ability of surface stations to measure temperature in any meaningful way (this was the genesis of the Watts surface stations project, now foundered on the rocks of reality), going from there to The One True Metric business. While there still isn’t an OHC metric that can be tracked with any accuracy, I had assumed that now that we do have some measurements showing a warming trend we’d be hearing from RP Sr. shortly. As noted above, the cognitive dissonance is strong in that one, IMO part not-invented-here syndrome, part an unwillingness to admit that things might really be warming as they are, and finally a dollop of just plain old attention-seeking.

  29. Steve Bloom says:

    Oh, a fourth factor: The personal feedback loop with RP Jr.

  30. Steve Bloom says:

    To clarify what is probably obvious, the cognitive dissonance arises from the unwillingness and is enhanced by the other three factors.

  31. Tony Duncan says:

    when you understand the difference between David Carradine and Ralph Macchio you may be worthy of sensei Connolly’s attention

  32. Well, at least I know the difference between Ralph Macchio and Jaden Smith!

  33. Tony,
    Actually, if you don’t start spelling Sensei Connolley’s name correctly, you may be getting some attention of your own (and by Sensei, I mean Dr) 😉

  34. BBD says:

    Eventually The Enlightened realise that the answer is Mu.

    Either that, or it’s a finger pointing away to the moon.

  35. Steve Bloom says:

    Mere kyus cannot be senseis, sorry.

  36. There is simple and there is simplifying — what we want is the latter, because we do want to reduce the immensely complicated simulation known as a GCM.

    I streamed Gavin Schmidt’s talk at the Rotman conference this morning (along with 12 other people apparently) and paraphrased a few of his statements below:

    “No climate model can be true.”

    “No physical model of the real world can be true.”

    “If you were to try to ’game’ the system, you would fail miserably”

    “Why do climate modelers pursue this endless task of increasing complexity, instead of simple energy balance models?”

    The answer he gave is because simple models do not include all the detailed factors.

    ” El Ninos and La Ninos are random. … ENSO can not be predicted more than 6 months in advance.”

    Prior to his talk, there was twitter activity around Jim Fleming’s talk yesterday.

    Steve Easterbrook @SMEasterbrook : Fleming: The butterfly effect is misnamed. Lorenz knew the perturbation would have to be really big. Better label: Mothra effect #Rotman2014

    Gavin Schmidt ‏@ClimateOfGavin : @smeasterbrook not sure I actually agree with this though. In GCMs smallest possible changes have same effect.

    It goes on from there. Read the tweet conversation here:

    My take is that this speaker Jim Fleming suggested the idea that the chaotic models of climate as originally proposed by Edward Lorenz are not as chaotic as people think. Easterbrook interpreted that by stating that a butterfly was to weak a forcing to be able to change anything, and something more akin to a monstrous moth was needed to change the trajectory on climate.

    I think that there are probably a couple of scales that we need to consider. Events such as hurricanes are likely unpredictable, but they are really inconsequential when compared to the largely deterministic trajectories of significant phenomena such as ENSO. Same with CO2, as that is a Godzilla of a forcing.

    What we are trying to do at the Azimuth Project the last few months is to come up with effective models for ENSO. The idea is that a set of quasi-periodic forcing factors, that when combined properly and input to a sloshing formulation, can generate the quasi-periodic time-series of ENSO.

    This is a thread that started a couple weeks ago and shows how much progress we are making towards a simplifying model of ENSO:

  37. Tom Curtis says:

    1) For Pekka, equations constrain semantics. Therefore when Pielke Sr affirms that ΔQ = ΔF – ΔT/λ he also precludes a semantics in which, in effect, he defines (in effect) F = Q. If he does not, he asserts not that ΔT happens to be zero, but that ΔT is necessarily zero as a mater of physical law. (Put another way, as he clearly does not accept that consequence, he is not entitled to a variant semantics that entails it.)

    In fact, given that the formula was derived using the standard IPCC semantics, if he varies the semantics he must independently derive the formula, whose coincidence in form to the standard formula is then purely accidental. As he does not do that, his variant semantics is a mistake, not a convention.

    2) More generally, Pielke Sr may be defining forcing as the total radiative forcing (= (1-Albedo) * TSI/4 + Total Greenhouse Effect). In that case he is confused in including feedbacks with forcings. More importantly, by that definition ΔF= ΔQ so that, again, necessarily ΔT = 0. Consequently, while it makes more sense of how he could believe he is talking about forcings with his variant terminology, it does not dig him out of his hole.

    He could fix that be explicitly excluding all feedbacks from the calculation, but that then reduces the formulation to the standard IPCC position.

  38. Eli Rabett says:

    Tom, equally the point, and Eli assumes Pekka agrees, semantics constrains equations. Pielke Sr. has lead everyone a merry chase by using his own very personal semantics and simply not letting anyone know what he is doing until forced into the open, at which point he turned huffy.

    Eli, and the rest, not being mind readers, this is the sort of thing that gets you punched out in high school.

  39. I noticed that last week Isaac Held formulated a model of thermal diffusion exactly like the one I did two years ago:

    My impulse response shows a square-root hyperbolic response, which is the fat-tail profile I referred to earlier.

    This is Held’s post:

    His step response looks like this
    h(\tau) \approx 1/(1+(\pi\tau)^{-1/2})

    Same characteristic dependence with the fat-tail, showing a slow asymptotic increase.

    Held gets his response function as an approximation to the solution to the heat equation, which I mentioned upthread.

    This is the stuff that Pielke Senior is not considering, and that Curry hasn’t a clue about. The deniers better start paying attention to Held, as he understands what the idea of simplifying is all about.

  40. Tom and Eli,
    I’m not going to check, what I wrote, but I think that I did in some way mention that using the same word in two different meanings and then drawing conclusions from the equality of the word is an explicit error. That’s what happens, when it appears in the equation based on a different definition than in the text.

    I cannot always express my thoughts precisely enough in English. That’s particularly true, when I try to be brief. This discussion has turned to discussing, how I express myself, when I discuss how ATTP expresses his thoughts in discussing expressions that Pielke Sr uses.

  41. WHT,
    That Isaac Held post looks very interesting. Thanks.

    Yes, it does seem rather circular.

  42. Mack says:

    ……. (.if it passes moderation.) ……

    [Mod : No, it didn’t 🙂 ]

  43. Mack says:

    Ok ATTP can I talk nicely to you here about “radiative forcing” and “radiative imbalance” ? Can I explain these to you, You don’t seem to understand.

  44. You can try, but I think I do. Go ahead, though.

  45. Mack says:

    Well my comment that didn’t pass moderation explains the “Radiative forcing” bit.
    The “radiative balance” or “imbalance” is false because you confuse basic heat transfer. Heat transfers in two categories 1) Radiative heat transfer and 2) Conduction , convection heat transfer, (To all intents and purposes we can dismiss conduction in the atmosphere) Radiative heat transfer travels at the speed of light and the other 2 by a slower ” mechanical” process.
    Here’s my take….The satellites look up and measure a real incoming solar radiation of about 1360w/sq.m. Because it is a yearly global average it cannot be divided down and should be regarded as non-directional covering the whole globe at the TOA.
    We look up from the Earth surface with land based radiometers (properly shielded), and if the readings from these are collated correctly and interpreted correctly they yield a yearly global average of about 340w/sq.m.
    The satellites also look down and….hey presto! they also read about 340w/sq.m. net yearly average at the earth’s surface.
    The radiation looking up by the radiometers EQUALS the radiation looking down by the satellites, ie NO RADIATIVE “GREENHOUSE” EFFECT.
    The instruments are only measuring radiative heat transfer. The satellites sitting in “cold” space only radiation.
    Trenberth , Salby and all the rest cannot get an Earth energy budget to “balance” in w/sq.m. because, the status quo. I’ve just explained. is maintained continuously by the sun. As physics depicts..a large straight arrow strikes an object and a small wavy one comes off. Watts travelling at the speed of light, become measureable in time, ie converted into joules,,,,which then just waft off “mechanically” into space UNDETECTED. The only cause for concern being the definition of “space” 🙂


  46. Mack,
    I’ll let that through because I said I would. I’m also assuming that you’re being serious, but it isn’t obvious. What is obvious is that it’s clear that you don’t understand radiative forcings or the concept of a radiative imbalance. They are as explained in my post, not as explained by you.

  47. Mack says:

    Thanks ATTP (Anders ?) 🙂 😉

  48. Mal Adapted says:


    Ok ATTP can I talk nicely to you here about “radiative forcing” and “radiative imbalance” ? Can I explain these to you, You don’t seem to understand.

    Ah. Mack appears to be a relative newcomer here. Perhaps he missed our recent discussion of this very important paper?

  49. Tom Curtis says:

    Mack, just once:

    “The satellites look up and measure a real incoming solar radiation of about 1360w/sq.m. Because it is a yearly global average it cannot be divided down and should be regarded as non-directional covering the whole globe at the TOA.”

    The 1361 W/m^2 Total Solar Irradiance (TSI) is the power from incoming sunlight falling on a plane perpendicular to the incoming sunlight. As it happens, the Earth is an oblate spheroid, and hence only a very small part of it is perpendicular to the incoming sunlight at any time. If we made a shield between us and the Sun, having the same diameter as the Earth, and maintained at the top of the atmosphere so as to always block all incoming sunlight, then the area of the shield that is bathed in sunlight would be one fourth of the area of the Earth. Ergo, without that shield, and on average, the same amount of sunlight is spread over four times the area. Hence the insolation on the Earth is 1361/4 W/m^2. Further, 30% of that incoming sunlight is reflected away, so that the total sunlight absorbed is 0.7 * 1361/4 = 238.2 W/m^2.

    As it happens, the IR radiation leaving the Earth’s surface is 396 W/m^2 (Khiel and Trenberth, 2010). That is 158 W/m^2 greater than the incoming solar radiation, so absent any other effect the Earth would cool very rapidly. However, the outgoing IR radiation as measured at the top of the atmosphere is 238.5 W/m^2 (also Khiel and Trenberth). The difference between the outgoing radiation at the surface and at the TOA is the greenhouse effect. That difference has been directly measured (see also comment 43), although with a level of accuracy not adequate to determine the actual energy imbalance (which needs to be inferred from changes in Ocean Heat Content).

    This much has been very basic physics, and has been confirmed repeatedly by direct observations. We can discuss more if you are prepared to acknowledge, and learn at least this much. If not, I have no interest in further discussion.

  50. Eli Rabett says:

    Radiative heat transfer only occurs at the speed of light in a vacuum. Otherwise multiple scattering and especially absorption/emission cycles slows it up. At the peak of a ghg absorption line the time essentially no radiation at the surface makes it to space.

  51. Willard says:

    > using the same word in two different meanings and then drawing conclusions from the equality of the word is an explicit error.

    A side note on semantics and equations:

    Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But because of the way the cognitive system builds expertise through binding, experts may have difficulty in unpacking their wellestablished knowledge in order to understand the difficulties novice students have in learning their subject. This is particularly evident in subjects in which the students are learning to use mathematics to which they have previously been exposed in math classes in complex new ways. In this paper, we propose that some of this unpacking can be facilitated by adopting ideas and methods developed in the field of cognitive semantics, a sub-branch of linguistics devoted to understanding how meaning is associated with language.

    Equations void of semantics are traces on a medium.

  52. Where I have met the worst problems related to equating two concepts of the same name has been in modeling large scale energy systems. Such models are highly aggregated. Their variables have names that give the appearance of being well and uniquely defined. Numerical data in Eurostat statistical database contains often data columns named similarly, but using those numbers as input to the models gives often nonsensical results. Similar problems are equally typical for many other highly aggregated models. A lot of additional research is needed to either make the model interpret the input correctly or to extract from the available input data values that correspond to well enough the variables of the model.

    That the same name is used in two different connections, or by two people in superficially similarly conditions, is likely to lead to errors, unless good care is taken to remove such inconsistencies.

  53. Willard says:

    > That the same name is used in two different connections, or by two people in superficially similarly conditions, is likely to lead to errors, unless good care is taken to remove such inconsistencies.

    Here’s the latest equivocation I stumbled upon:

    In functional programming, a monad is a structure that represents computations defined as sequences of steps: a type with a monad structure defines what it means to chain operations, or nest functions of that type together. This allows the programmer to build pipelines that process data in steps, in which each action is decorated with additional processing rules provided by the monad. As such, monads have been described as “programmable semicolons”; a semicolon is the operator used to chain together individual statements in many imperative programming languages, thus the expression implies that extra code will be executed between the statements in the pipeline. Monads have also been explained with a physical metaphor as assembly lines, where a conveyor belt transports data between functional units that transform it one step at a time. They can also be seen as a functional design pattern to build generic types.


    The name and concept comes from the eponymous concept (monad) in category theory, where monads are one particular kind of functor, a mapping between categories; although the term monad in functional programming contexts is usually used with a meaning corresponding to that of the term strong monad in category theory.

    The inverse case is also common, when theoricians invent separated fields that they can be connected via correspondence, e.g.

    In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard.[citation needed] It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation).[citation needed] The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.

  54. Eli Rabett says:

    The hardest and most necessary thing in introductory classes is to teach students to write answers that integrate text for meaning with equations for process.

  55. My first reminiscences of observing, how difficult it is to many to connect the meaning of a problem to the mathematical expression or solution are from the elementary school and related to a problem that was admittedly difficult for 3rd graders. Similar observations accrued throughout the school years. Children, who get on the right track early, learn mathematics much more easily also later. That’s at least, what I believe.

  56. ATTP, this is just a thought on the communication of mathematical ideas – the use of natural language vs. the use of symbolism vs. both:

    So the reader can see some context, ATTP said in comment 92 at
    the following: “Delta Q will only be the same as the radiative imbalance at the final time interval if it is zero (in equilibrium) at the beginning.”

    ATTP, do you think that giving also some basic symbolism along the lines of
    x_2 – x_1 = x_2
    x_2 – x_2 = x_1
    0 = x_1
    perhaps might have helped him see that you were communicating to him just an application of basic algebra?

  57. K&A,
    I doubt it will help. Rather than responding to my point, he moved on to asking me a question which I decided to answer, only to discover that what he was asking wasn’t quite what I thought he asking.

  58. Eli Rabett says:

    With both Pielke’s you can’t play their game. As MT said, with them it is Pileke’s all the way down.

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