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 <[email protected]
<mailto:[email protected]>> 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.
--
Mɥǝu ǝlǝdɥɐuʇs ɟᴉƃɥʇ' ʇɥǝ ƃɹɐss snɟɟǝɹs˙
.-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - .
FRIAM Applied Complexity Group listserv
Zoom Fridays 9:30a-12p Mtn UTC-6 bit.ly/virtualfriam
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/
