> On Aug 2, 2025, at 4:43, Nicholas Thompson <[email protected]> wrote: > > In the meantime, I would like to explore a thought which Eric S offered me > several weeks ago which has continued to echo in my head like wolf howls in a > box canyon. It was something like, "entropy does not appear in the monotonic > idea gas equation because it is the landscape that determines the shape of > that equation" Please forgive the misattribution, EricS.
That’s actually about a perfect characterization, Nick. The language in it can be taken as metaphor, but when one understands “landscape” as a language-tag for a variety of formal constructions, it will also support that reading as a description of structure within the formal system. > I have been struggling to come up with a metametaphor by which to understand > this aphorism and it be something like gravity does not appear in > calculations of travel time from here to chicago. I am tempted to say > something like, "Instead of heat flowing down a temperature slope as Carnot > would have it, we have energy flowing down an entropy slope." I am giving > you all a chance to pre-box my ears for saying it. It’s not terrible. To the extent that (internal) energy, as an additive quantity distributed among several variables that characterize a system, can change its distribution among them something like an incompressible fluid, one can push it all through. The invoking of gravitation in travel time is a bit funny, because depending on whether you are speaking from an understanding of general relativity or absent any reference to it, the meaning the analogy is meant to carry could be quite different. In the general relativity-aware version, the relevant “travel time” is the Proper Time of a traveler (which in experience we refer to as the traveler’s elapsed aging, and which can then subsequently be related to various time-measures for others who are not going along the same ride), and in that case, general relativity is indeed, exactly, the characterization of the spacetime that determines what that travel-proper-time will be. And again, permitting the term “landscape” to be used to tag a broad range of formal constructions (in this case, just as a synonym for “geometry”, albeit spacetime geometry), the language could support a formal reading. In that reading, gravity _absolutely does_ appear in calculations of travel time, and indeed it is the _entire_ input to those calculations. However, gravity as Newton’s force does not appear, because in the geometric description Newton’s force is a language-tag that no longer has anything actual to refer to. If you meant the gravity analogy in a general relativity-unaware sense — something like an intent that gravitation, while present, simply is an irrelevant factor to the travel time, as in Newton’s picture in a Cartesian space-x-time it would be — then I think it makes a claim of irrelevance that isn’t the most helpful direction to go in understanding equations of state. Your formulation “entropy does not appear in the monotonic ideal gas equation” is, in a way, the assertion I wanted to rebut. You might _think_ it doesn’t appear in the equation, if you _think_ its appearance depends on whether somebody has written a letter S in the equation, and if you _think_ you already know what pressure and temperature mean (better said, what they “are” as concepts). What the physicist would consider correct, and try to get you to “see” for yourself as correct, is that your _thinking_ you already _knew_ what pressure and temperature mean was a kind of category error. What you had was an experiential familiarity with phenomena and the way they get bound to usage patterns for terms (warm, temperature, pressure, etc.) But that familiarity with conventions doesn’t have the kind of structure that would be required for any sort of analysis, beyond a very limited re-invocation of fragments of the common usage. There is very little if anything new that one could conclude from it. The physicist would then try to built up a trackable explanation that a meaning for the terms “pressure” and “temperature”, from which one can do analysis and get to new conclusions, can indeed be built, and that it is built entirely from various slope-directions of the entropy. So, coming back to common experience and what one would like to be allowed to say: If, in a park, I lay out a blanket but find I can’t sleep because all the places I can find to lay are on the side of a hill and I keep rolling down the hill, would you want to say that I make no reference to “the hill”, because I only refer to “the slope of the hill at each place I try to lay down”? I think even in the common language we would think that a strange set of permissions, kind of like Dirac’s (apocryphal?) belief that the correct answer to some philosopher’s question about sheep was “the sheep is white on this side”. All best, Eric .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. FRIAM Applied Complexity Group listserv Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom https://bit.ly/virtualfriam to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ archives: 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
