[FRIAM] Entropy RE-redux

Mon Jun 16 12:38:53 EDT 2025

>
> Pieter,

Thanks for taking the time to answer my question.  I need the exercise.
I am going to try and annotate your comment.

On Sun, Jun 15, 2025 at 2:34 PM Pieter Steenekamp <
pieters at randcontrols.co.za> wrote:

> Nick,
>
> Let me first directly answer your specific question, and then I’ll share a
> few thoughts to help place it in the broader context of entropy and how to
> develop a solid understanding of it.
>
> First, your question:
> There are two parts to consider: the transient behavior and the steady
> state.
>
> Transient: The divider can move in either direction depending on the taps.
> For example, if you initially tapped larger on the right, the piston will
> move left due to the pressure difference.
>

AGREED.

>
> Steady state: Over time, the piston will settle in the center. The
> movements to the left and right will cancel each other out, resulting in no
> net movement.
>
> The reason is simple: at steady state, the pressures on both sides are
> equal.
>
> AGREED
>

> And why are the pressures equal? Because if you have two cylinders with
> the same volume, same number of air molecules, and same temperature, then
> the ideal gas law tells us the pressures must be the same. This has nothing
> to do with entropy.
>
> Now, regarding entropy and your example:
> A few key points to keep in mind:
>
> a) Entropy differs across domains.
> While entropy generally relates to disorder or uncertainty, its precise
> meaning varies. In thermodynamics, information theory, statistics, machine
> learning, and biology, the definitions and implications are different. So,
> context matters.
>

i BELIEVE THAT IN SCIENCE, THIS SORT OF RESOLUTION IS A KIND OF COP OUT.
EITHER WE HAVE ONCE CONCEPT OR TWO OR THREE OR FOUR.  MATHEMATICAL
SPECIFICATION IS FINE BUT IT LEAVES ASIDE THE QUESTION OF WHAT CONCEPTS ARE
AT WORK HERE.  ONE CAN ARGUE, AS ERICS OR FRANK OR ALEX MIGHT, THAT THE
MATHEMATICAL DEFINITIONS ARE THE CONCEPT BUT i THINK THAT DEFIES THE COMMON
UNDERSTANDING OF MATHEMATICS THAT IT RELATES TO OUR EXPERIENCE ON INSOFAR
AS IT IS RELATED TO OUR EXPERIENCE BY EXPLICIT NON-MATHEMATICAL
STATEMENTS.   "Let X = ....."

>
> b) In thermodynamics:
>
> Total energy in a closed system stays constant.
>
> But the amount of useful energy (for example that can be converted to
> mechanical work) does not stay constant.
>
> One of the key motivations behind developing the concept of entropy was to
> answer this:
> In a closed system with constant total energy, how much of it is available
> to do useful work?
>
> Take the classic example from a steam engine:
> If you burn coal to produce steam that drives a turbine, how can you
> design the system to maximize mechanical output from a given amount of coal?
>
> The answer, using entropy, is:
> The higher the temperature of the steam drum (within practical limits),
> the more mechanical energy you can extract.
>
> c) Back to your example:
> While interesting, I don’t think it’s a great one to build a deep
> understanding of entropy. Here's why:
>
> For a given volume of air, at a given temperature, with a fixed amount of
> air, the pressure is fully determined by the ideal gas law:
> PV = nRT
>
> It doesn’t matter how you got there — THIS IS THE WHOLE BALLGAME, RIGHT
> HERE, i THINK.  whether you moved the piston, opened taps, or changed the
> temperature over time. Once the system settles at a given state, entropy
> doesn’t factor into calculating the pressure. That’s why this setup might
> not help much if your goal is to really grasp what entropy is all about.
>

HERE IS A THE PARADOX AS I NOW UNDERSTAND IT.  IS ENTROPY A STATE
VARIABLE/  WELL, YES AND NO.  IT IS NOT IN THE SENSE THAT YOU CANNOT
CALCULATE IT FROM INSTANTANEOUS STATE VARIABLES, IN PERHAPS THE WAY THAT
YOU CANNOT CALCULATE ACCELERATION FROM AN INSTANTANEOUS MEASUREMENT OF
LOCATION AND VELOCITY.  ACCELERATION AT INSTANT IS A CATEGORY ERROR, A
MATHEMATICAL FICTION.  BUT, STRANGE TO DISCOVER, THAT ALL PROGRESS IN
MATHEMATICS, BEGINNING WITH THE MATHEMATICAL LINE, PERHAPS, IS THE RESULT
OF THE EXPLOITATION OF SUCH FICTIONS.   fOR THE MOMENT LETS CALL THEM
NEWLIEBZIAN CATEGORY ERRORS.  iF MY CURRENT INTUITION IS CORRECT AND
ENTROPY IS NEWLIEBZIAN CATEGORY ERROR, THEN IT FOLLOWS THAT THE REASON i AM
CONFUSED BY IT IS BECAUSE PEOPLE KEEP ATTRIBUTING IT TO INSTANTS AND PLACES
WHEN IT KNOWN THROUGH THE COMPARISON OF DYNAMICS AND ARRAYS.  BEWARE
BECAUSE THIS IS A VERY FAMILIAR CONFUSION TO ME, BETWEEN MOTIVES, WHICH ARE
THOUGHT OF INTERIOR INSTANTS, WHEN THEY ARE ACTUALLY KNOWN THROUGH THE
COMPARISON OF DYNAMICS AND ARRAYS OF BEHAVIOR.   THE WHOLE PURPOSE OF OUR
NERVOUS SYSTEM (THE STUFF IN SIDE)  IS TO MAKE COMPUTATIONS BASED ON THE
DYNAMICS AND ARRAYS OF BEHAVIOR AND APPLY THEM TO THE NEXT APPLICABLE
INSTANT.  PHILOSOPHERS CAN SAY ALL THE WANT ABOUT THE FALLIBILITY OF
INDUCTION, BUT IT IS ALL WE GOT.

>
> On Sun, 15 Jun 2025 at 19:25, Marcus Daniels <marcus at snoutfarm.com> wrote:
>
>> Can you make this more fun and ask George or your favorite virtual
>> correspondent for a Python or Mathematica implementation?  Then we’d have
>> something definite to debug.
>>
>>
>>
>> *From:* Friam <friam-bounces at redfish.com> *On Behalf Of *Nicholas
>> Thompson
>> *Sent:* Sunday, June 15, 2025 8:27 AM
>> *To:* The Friday Morning Applied Complexity Coffee Group <
>> friam at redfish.com>
>> *Subject:* [FRIAM] Entropy RE-redux
>>
>>  BBC that t I’m
>>
>> Same setup as before. Cylinder with two plungers and a peggable slider at
>> dead center.  Lets fill our compartments with bbs of the same volume. Unpeg
>> the divider.  Now lets tap on the two opposite plungers with a series of
>> blows of the same average magnitude but different but different positive
>> skew in the distribution of magnitudes. Will the divider move?
>>
>> --
>>
>> Nicholas S. Thompson
>>
>> Emeritus Professor of Psychology and Ethology
>>
>> Clark University
>>
>> nthompson at clarku.edu
>>
>> https://wordpress.clarku.edu/nthompson
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-- 
Nicholas S. Thompson

Emeritus Professor of Psychology and Ethology
Clark University
nthompson at clarku.edu
https://wordpress.clarku.edu/nthompson
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