[FRIAM] Entropy Redux

[Nicholas Thompson]

Dear LongSuffering Colleagues

I know the joy of watching an 87 year old bald man bash his head against a
brick wall isn't for everybody, so I treasure you who find it in your heart
to respond, even if you are exasperated.

I have arrived at a place, I think pointed to by the castigations of EricS
and Alex.  My whole approach doesn't make sense!   You remember I am trying
to create two boxes, equal in every respect, but one created adiabatically
and the other created diabatically.  Box A has reached its current state
through compression, Box B by heating.  I am beginning to think that this
is procedurally, if not logically, impossible, that entropy is a vector
through a point and my search  for entropy in instantaneous values of the
gas equation is a category error.

So I tried this thought out on George. Edited down to one page, that
correspondence appears below and as an attachment.  .

NICK TO GEORGE

*Ok, so in my monist psychology I assert that motives are the integrals (or
derivatives, I have never been sure) of behavior. To say I am motivated in
an instant is a category error, benign only so long as I recognize that the
empirical basis for our instantaneous attribution is the shape of the curve
of behavior over time.*



GEORGE TO NICK

*🧠 Claim (Paraphrased):*

To say "I am motivated" at a given instant is a shorthand—a projection
backward or forward from a trajectory of behavior.

In your *monist psychology*, motives are not hidden essences, not inner
engines.
They are *summaries of behavioral curves*:

   - Perhaps *integrals*, when motives are inferred from accumulated actions
   - Perhaps *derivatives*, when motives are inferred from sudden changes
   in behavior

But in either case:

*“Motivation” is not an instantaneous property—it is a curve-fitting
hypothesis over time.*
------------------------------

*🧭 Why this matters:*

This reframes motive as:

   - Not a *thing* in the head
   - Not a *cause* per se
   - But a *description of continuity* or curvature in behavior space

This is a kind of *teleological realism* without metaphysical baggage.
You’re not positing ghosts or mental levers. You’re saying:

“We read intentions the way we read acceleration—from position over time.”
------------------------------

*🧬 Parallel to entropy?*

You could say:

   - Entropy is not something you *have* in a moment.
   - It’s something you can *measure* from the path a system is disposed to
   take—or the configuration space it tends to spread into.
   - It becomes *visible* only in the *shape of change*—not the snapshot.

So both *motivation* and *entropy* are:

   - Not intrinsic point-properties
   - But *interpretive functions over time and configuration*
   - *Curve-based attributions* grounded in empirical regularities

------------------------------

*📐 And the category error?*

To say "I am motivated *now*" is like saying "this point *has* curvature."
Strictly speaking, no point does.
But give me a neighborhood—give me a path—and I can calculate a derivative
or an integral and give the illusion of an inner quality.

It’s a *useful illusion*, but one we must not mistake for substance.
------------------------------

NICK TO GEORGE

*Is there such a move to be made around entropy. Could I vary the gas
equation variables in box B in such a way that they would point to equality
with box A without actually getting there, and thus reveal entropy?*

-
Nick
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