[FRIAM] To repeat is rational, but to wander is transcendent

[glen]

Very nice! Believe it or not, I did flip through to see if I could find where you covered it. I didn't look at the boxes though. I've scanned that box here: https://slate.host/_/view/5d83c6f0-536c-4cf7-b77f-acc893abdcbe

Thanks.

On 3/30/22 13:34, David Eric Smith wrote:
> Roger’s sources at the end here are great, and they are ones I hadn’t read.
> 
> In principle, Legendre duality (the exchange between function arguments and derivatives with respect them) is a main theme in all the thermodynamics textbooks.  I am so far out of date that I have no idea what I seeing used to teach these days, but when I was an undergrad, it was old war horses like Kitten and Kroemer, which are quite serviceable, though slow as one becomes older and more impatient:
> https://www.amazon.co.jp/Thermal-Physics-Charles-Kittel/dp/0716710889 <https://www.amazon.co.jp/Thermal-Physics-Charles-Kittel/dp/0716710889>
> 
> I say “in pcinriple” because there is one thing in the standard teaching that I think is a less-than-ideal choice, and it is repeated nearly universally.  That choice is to introduce thermodynamic potentials as outgrowths of the Newtonian potential energy, and then work with everything in energy units.  So usually the gradients are not explicitly shown to be of the entropy with respect to its arguments, but rather “of the internal energy”, with respect to other variables that aren’t actually its arguments, since (from the perspective that emphasizes states and ensembles)  it isn’t a function but rather just a boundary condition.  That approach introduces entropy as aa kind of secret sauce that gets added to conservation relations, for incomprehensible reasons, makes the rules for when to set the outcome of an irreversible transformation to the same values as the outcome of a reversible transformation obscure and confusing, and in general gives the whole field the aura of some 
> kind of black art.
> 
> So — and sorry to do this — as the only remedy I knew at the time, I tried to write things in a less tangled order in the book with Harold:
> https://www.amazon.co.jp/Origin-Nature-Life-Earth-Emergence/dp/1107121884 <https://www.amazon.co.jp/Origin-Nature-Life-Earth-Emergence/dp/1107121884>
> The only version available to me right now is an old electronic proof copy, but I am sure the sections are right and the pagination may even be correct.
> 
> The general section where I try to start at some kind of a sensible beginning and work in a linear order is Sec.7.3, maybe on p.436.  It’s all large-deviations framing and some examples for several pages, but interacting systems and the origin of intensive variables is introduced in Sec.7.3.2, p.439.  The general relation, introduced in its own name, without digressions and examples, is Eq.(7.6) on p.441.
> 
> Again, speaking of too long for the old and impatient…
> 
> But, to try to get to the point of introducing all the standard content, in a way that (for me, at least) is more sensible and scannable, I try to put all this into a self-contained pane in Box 7.1 starting on p.443, and only running a couple of pages.  That box is written to be free-standing, and includes everything I made reference to in my earlier post here.  The prepending text would only be needed if one wanted to know what various letter of the alphabet (S, U, V, N) actually _stand for_ in operational terms.  If one takes the letters as given and familiar, and just wants to see the relations, the box is sufficient.
> 
> 
> To use the energy framework to make contact with the measurable phenomenology of thermodynamics, starting from a premise that mechanics (or, more specifically, thermometry and calorimetry, hearkening back to brewer Joule) will be more widely known, isn’t necessarily bad, and one could do it very compactly as Fermi does:
> https://www.amazon.co.jp/Thermodynamics-Dover-Books-Physics-Enrico/dp/048660361X <https://www.amazon.co.jp/Thermodynamics-Dover-Books-Physics-Enrico/dp/048660361X>
> I view Kittel and Kroemer as fulfilling a similar role, and it deserved to become a gold-standard text, for its very good design in that role.
> 
> After one has realized, however, that the old conversation about energy was not the semantics for these questions, and that the conversation has shifted to one about stability, you would think it must then seem natural to stop clinging to antiquity, and just reformulate the presentation in its natural language.  Why physics teaching is so slow to do this, I do not understand.  They say they do, when they shift away from “thermodynamics as a phenomenological discipline” to “statistical mechanics as the basis for thermodynamics”, as in the usual shift from undergrad to early grad texts like Huang:
> https://www.amazon.co.jp/Statistical-Mechanics-2E-Kerson-Huang/dp/0471815187 <https://www.amazon.co.jp/Statistical-Mechanics-2E-Kerson-Huang/dp/0471815187>
> Yet they retain the energy framework and the energy-denominated intensive state variables, so the obscurity remains.  As if it were believed that students would never actually become capable of shifting frames of mind and simply seeing phenomena in new terms.  I fear this is a case of professors projecting their own inflexibility onto their students, who could do much better if given appropriate supports.
> 
> Eric
> 
> 
> 
> 
>> On Mar 31, 2022, at 3:24 AM, Roger Critchlow <rec at elf.org <mailto:rec at elf.org>> wrote:
>>
>> I think the trap of essentialism is that there exist contexts where it works, and works magnificently, but in most contexts it's nothing but pet rattlesnakes, often being waved around with no caution at all.  And I suppose the back side of the trap is that we have an innate essentialist heuristic which we use for organizing essentially everything we encounter in the world.  So in certain contexts -- mechanics, chemistry, thermodynamics, electronics, computation -- we have refined our naive essentialism into categories and operations which essentially solve or are in the process of solving the context.  And in other contexts, we have lots of enthusiastic application of naive essentialist theories, lots of ritualistic imitations of the procedures employed in the contexts which are succeeding, and lots of proposals of ways that the unresolved contexts might be reduced to instances of the solved.
>>
>> EricS's dimensional analysis in a nutshell, which is an essential description of a successful essential analysis of a context, leaves a lot of problems for the reader to work out if taken as a recipe for action.   How do you identify the units of aggregation?   What are the rules for forming larger aggregates from smaller and vice versa?  What is entropy, anyway, and what is the correct entropy (*dynamic potential) in this context?
>>
>> Thermodynamic state functions as derivatives with respect to entropy are all over JW Gibb's On the Equilibrium of Heterogeneous Substances.  It is the point.  PW Bridgman's Dimensional Analysis essentially summarizes all of physics up to 1922 as a problem of combining and factoring units of measurement, one of my favorite library discoveries as an undergraduate.  Both available in the internet archive.
>>
>> -- rec --
>>
>>
>> On Wed, Mar 30, 2022 at 12:12 PM Marcus Daniels <marcus at snoutfarm.com <mailto:marcus at snoutfarm.com>> wrote:
>>
>>     Here is a situation I frequently experience with software development where I try to adopt some code, even my own.  I stare at the code and..
>>
>>     1) It becomes clear how to assemble it into to what I want
>>
>>     2) I become confused or frustrated.   As a ritual, I remove it from my sight and open a blank editor window to start over.  Sometimes I must walk away from the screen to think, until I want to type.
>>
>>     I think the reason I dwell in #2 space is because I believe in #1.   That is, when I have just the right combinator library things just snap into place.   I seem to spend a lot of time trying to convince myself of why it can't work, and whether it is a bad fit or something that needs to be fixed in the platform.  What is important, in this value system, is that platforms are good, not that this or that problem gets solved.   I think it is basically the Computer Science value system in contrast to the Computational Science value system.
>>
>>     To [re]abstract and [re]concretize can be expensive and those who don't do it have a productivity advantage, as well as the benefit of having particulars to work from.   I don’t think it is a case of confusing the sign for the object.   It is a question of what kind of problem one wants to solve.
>>
>>     In contrast, I have met several very good computational people that hate abstraction and indirection.  They want code to be greppable even if it that means it is baroque and good for nothing else.
>>
>>     -----Original Message-----
>>     From: Friam <friam-bounces at redfish.com <mailto:friam-bounces at redfish.com>> On Behalf Of glen
>>     Sent: Wednesday, March 30, 2022 8:40 AM
>>     To: friam at redfish.com <mailto:friam at redfish.com>
>>     Subject: Re: [FRIAM] To repeat is rational, but to wander is transcendent
>>
>>     Of all the words being bandied about (quality, property, composition, domain, continuity, intensity, general, special, iteration, etc.) EricC's "contextless" stands out and reflects EricS' initial target of dimension analysis. The conversation seems to be about essentialism. Maybe that's a nice reflection that we're sticking to the OG topic "analytic idealism". But maybe it's Yet-Another example of our pareidolia to see patterns in noise and then to *reify* those patterns. [Re]Abstracting and [re]concretizing heuristics across contexts may well be what separates us from other life forms. But attributions of the "unreasonable effectiveness" of any body of heuristics is the most dangerous form of reification. The superhero ability to [re]abstract and [re]concretize your pet heuristics convinces you they are "properties" or "qualities" of the world, rather than of your anatomy and physiology. Arguing with myself, perhaps Dave's accusation is right. Maybe this is an example
>>     of swapping the sign for the object, or reworded prioritizing for the description over the referent, confusing the structure of the observer with the structure of the observed.
>>
>>     Those of us with less ability tend to attribute (whatever haphazard heuristics they've landed on) to the world *early*. Those of us with more ability continue the hunt for Truth, delaying attribution to the world until we get too old to play that infinite game any more.
>>
>>     I think Possible Worlds helps, here, too: https://plato.stanford.edu/entries/possible-worlds/ <https://plato.stanford.edu/entries/possible-worlds/> Patterns are simply (non-degenerate) quantifiers over possible worlds.
>>
>>     Regardless, I'd like to ask whether the formulation of intensive properties as derivatives of entropy w.r.t. extensive properties is formalized somewhere? If so, I'd be grateful for pointers. I'm used to the idea that the intensives divide out the extensives. But I haven't seen them formulated as higher order derivations from entropy.
>>
>>     Thanks.
>>     -glen
>>
>>     On 3/29/22 14:37, David Eric Smith wrote:
>>     > [snip]
>>     > 1. One first has to have a notion of a macrostate; all these terms
>>     > only come into existence with respect to it. (They are predicates of
>>     > what are called “state variables” — the intensive ones and the
>>     > extensive ones — and that is what the “state” refers to.)
>>     >
>>     > 2. One needs some criterion for what is likely, or stable, which in general terms is an entropy (extending considerably beyond the Gibbs equilibrium entropy, but still to be constructed from specific principles), and on the macrostates _only_, the entropy function (which may be defined on many other states besides macroststates as well) becomes a _state function_.
>>     >
>>     > 3. Then (actually, all along since the beginning of the construction)
>>     > one needs to talk about what kind of aggregation operator we can apply
>>     > to systems, and quantities that do accumulate under aggregation become
>>     > the arguments of the state-function entropy, and the extensive state
>>     > variables.  (I say “accumulate” in favor of the more restrictive word
>>     > “add”, because what we really require is that they are what are termed
>>     > “scale factors” in large-deviation language, and we can admit a
>>     > somewhat wider class of kinds of accumulation than just addition,
>>     > though addition is the extremely common one.)
>>     >
>>     > 4. Once one has that, the derivatives of the entropy with respect to the extensive variables are the intensive state variables.  It is precisely the duality — that one is the derivative of a function with respect to the other, which is the argument of that function — that makes it not bizarre that both exist and that they are different.  But as EricC rightly says, if one just uses phenomenological descriptions, why any of this should exist, and why it should arrange itself into such dual systems, much less dual systems with always the same pair-wise relations, seems incomprehensible.  For some of the analogistic applications, there may not be any notions of state, or of a function doing what the entropy does, or of aggregation, or an associated accumulation operation, or gradients, or any of it.  Some of the phenomenology may seems to kinda-sorta go through, but whether one wants to pin oneself down to narrow terms, is less clear.
>>     >
>>     > [snip]
>>     >
>>     >> On Mar 30, 2022, at 5:04 AM, Eric Charles <eric.phillip.charles at gmail.com <mailto:eric.phillip.charles at gmail.com> <mailto:eric.phillip.charles at gmail.com <mailto:eric.phillip.charles at gmail.com>>> wrote:
>>     >>
>>     >> That is a bizarre distinction, that can only be maintained within some sort of odd, contextless discussion. If you tell me the number of atoms of a particular substance that you have smushed within a given space, we can, with reasonable accuracy, tell you the density, and hence the "state of matter". When we change the quantity of matter within that space, we can also calculate the expected change in temperature.
>>     >>

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