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

Wed Mar 30 14:59:51 EDT 2022

Roger writes:

< 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.>

It seems weird to think there could be isolated, Platonic, truly distinct native types in the universe and that there would NOT be functions which could be discovered to that could convert amongst them.
Getting over the caution bar seems to involve finding transformations on types and instances of types that are being precise enough to compute with, while also relating to observable physical things.   And it seems weird to say tools are good with the proviso that one needs to know the right way to use a tool and its limitations BUT that the expertise cannot itself be made precise enough to automate.
What is it one believes about the universe if one is an essentialist or a foundationalist?    Why call it a universe and not just a bunch of independent problems to address?  Why talk about parallax or posit that any isolated experience anything but its own unique universe?

From: Friam <friam-bounces at redfish.com> On Behalf Of Roger Critchlow
Sent: Wednesday, March 30, 2022 11:24 AM
To: The Friday Morning Applied Complexity Coffee Group <friam at redfish.com>
Subject: Re: [FRIAM] To repeat is rational, but to wander is transcendent

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/ 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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