<html><head><meta http-equiv="content-type" content="text/html; charset=utf-8"></head><body style="overflow-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;">Yeah; <div><br></div><div>I remember the first thermodynamics class I had.  I hated it.  It all seemed like total voodoo (apologies, Dave, I don’t mean the good kind; this is a colloquialism), and I was convinced I would never even be able to get through it; totally give up understanding it.</div><div><br></div><div>Then there was a statistical mechanics class that helped somewhat, and with a lot of slogging (like a form of hazing), I could get through calculations and sometimes get the right answer.  Still, there didn’t seem to be much I would have called (then) or would call (now) “understanding”.  </div><div><br></div><div>At some point, by very roundabout concerns, involving stuff that overbuilds the math very heavily compared to what one needs in equilibrium thermo, and getting even more lost in that overhead, I finally got to the point of realizing that the main ideas were never actually a problem.  Then I got really mad at the way this subject is taught.  It never needed to be hard, not for stupid undergrad me, nor for still-stupid but determined and head-bashing graduate me, or for the (still not any smarter, but I had time at SFI) ten years of going in circles with things I could have understood much earlier with a bit more careful presentation.</div><div><br></div><div>And the stuff the language bots are handing back is the only thing it can be; a regurgitation of the canons of the textbooks.  So absolutely, it sounds no better than listening to mystics, who mainly seem to want to tell you they have the greatest thing in the world but they aren’t going to tell you what it is (and _you’ll_ never understand; thats for sure!). </div><div><br></div><div>My own belief is that the way around this is not to retrace the first empirical way we hit these surprises, but rather to inherit the 100 years of related thought that has gone on since then, and take advantage of the much simpler routes (because they are conceptually orderly) made available at various points in that other work.   We have to have the anchoring in empirics, of course.  But that anchoring is not what ties down the concept structure that makes the subject sensible.  The difference between good and bad presentation of the empirics is that at least the good kind has a comprehensible unpacking.</div><div><br></div><div>Of course, I am not a pedagog.  And what I want from it (not getting lost) is very different from what most educators are serving (getting very, very fast at turning the crank so you can do your engineering job, which now is also most of what gets done in physics.)  So the things I like would probably be completely ineffective for what the customers of the business of education really want.  Happily, I am not in charge of anything, so the world can continue as it was.</div><div><br></div><div>But a lot of it comes down to forcing people to slow down and _say what they are doing_: the kind of thing everybody finds tedious and nobody has any patience for.</div><div><br></div><div>0.  Is this experiencing nature, or is it setting out terms and rules in formalism?  (formalism)  Deciding when the formalism has a good binding to nature is like it generally is in science.</div><div>1. What kind of systems are you modeling?  Those in which the way you set up the system fixes all of its degrees of freedom (remember, in our formalism!), or one in which some of the degrees of freedom are not fixed?  The former is Newtonian clockworks, the latter is thermo.</div><div>2. What kinds of question will you be asking?  THIS ONE IS THE KEY THAT EVERYBODY INADEQUATELY EMPHASIZES: I will be asking question that must be answered from _distributions_.  Why is that so?  Why are the phenomena you are studying such that when you formalize them, the questions you will ask are all answered from distributions?  (and we can say, etc.)  The key point that, when an equilibrium thermo person says “state”, that is a tag referring to some kind of distribution, focuses the attention where it needs to be, on how many kinds of distributions there are, and what determines them.  </div><div>3. How do the kinds of distributions that will answer your questions relate to the way you set up the system?  Answering this with some care gets at the difference between steady and unsteady distributions, those that require many boundary-condition variables to prepare and those that require fewer, and so forth.</div><div>4. What is an entropy functional anyway?  as a function on distributions that just represents them by some number?  What properties do you want an entropy function to have, and how does that tie the form you need to the characteristics of the distribution that will answer the questions you want?  This gets at Nick’s question whether there is one entropy concept or many, which is different from whether there is one entropy functional form or many.  Here it really is better to use what the information-theory people have found clean good ways to say, and to avoid intimidation, one need not even use fancy technical words.  It’s just about how one stipulates particularity out of a field of variation, and how to attach measures to how particular something is among its alternatives.  </div><div>5. Finally we can get to questions about whether the distributions that answer our questions are steady or dynamical, whether (even if they are steady) the samples from them that answer our questions (mathematically, called correlation functions) would look the same if played backward in time, or would change in some way, and so forth.  That gets at what one means by, among the vastness of possible distributions, the ones that the tag “state” in the equilibrium-thermo jargon point at.  This is what I mean by pinning the bastards down and saying “When you use this term “state”, you all seem to mean the same thing by it, but I have no idea what the HELL any of you mean, because you haven’t told me.  So [please] tell me.”  THIS POINT IS AGAIN ONE OF THE CRUCIAL ONES: it gets around the oddness that there can be entropy functions of most any distribution, but almost-none of those are the-entropy-that-is-a-state-function, which Frank forwarded to Nick, or which I have referred to.  And the reason they aren’t, is that the distributions on which they are computed aren’t those special “states” of equilibrium thermo.  </div><div>6. There is a little clean-up that one should do, which is to point out that getting to distributions that really are steady and mirror-symmetric if we reverse the direction of play in time will often whittle us down to a small number of boundary-condition properties that we can arrange, and these then account for the origin of pressure and temperature (or what you like).  </div><div><br></div><div>There’s more, but it proceeds more or less like this; very plumber-like, or like tax forms: what line goes to what next line?  All that goes on to unpack in choices about how to use the equations, and get us away from the goddamned focus on energy, from which none of this makes particular sense, to a focus on probability, where suddenly it all becomes pretty straightforward.  But most people don’t feel like listening to this, so I won’t do it here. </div><div><br></div><div>So that’s the pre-processing that would fall before the here-memorize-this “starting point” that the chatbots are mostly handing Nick (or any of us).  Rather than do that work properly (which, you see, is not so very hard; 6 bullet points), they will tell yarns until the cows come home, which ultimately never contain the thing one actually needs to know, which is what choices went into making some claim.   The yarns are fine, for getting visual and other metaphors, but they aren’t a substitute.</div><div><br></div><div>Anyway.  Only my opinions.  Probably most people will find the above approach appalling.  But I have had a surprising number of younger people tell me that, for the first time, they didn’t feel lost and intimidated by it, but realized they could navigate comfortably from these starting points.  Often these are people I didn’t meet before they told me that, but some of them I have had longer teaching relations with.  So at least for somebody it is helpful.</div><div><br></div><div>Eric</div><div><br></div><div><br></div><div><div><br><blockquote type="cite"><div>On Jun 18, 2025, at 12:38, steve smith <sasmyth@swcp.com> wrote:</div><br class="Apple-interchange-newline"><div>

  
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
  
  <div><p>my guess is that Nick (like many of us) is just trying to get a
      handle on some Thermodynamic concepts intuitively, by making up
      his own simple examples and building on them?   A little
      world-building/exploration by some measure?<br>
    </p><p>Entropy is perhaps the most arcane (but not occult) of
      thermodynamic concepts and in the top handful in all of physics?  
      Pressure, Temperature, and Volume are roughly directly
      apprehensible with the likes of Energy, Work, Ergodicity,
      Equilibrium, Reversibility taking a little more thought, and
      Entropy, Enthalpy, and the wycked mother of them all the Partition
      Function (Z) really difficult to think about in their own terms.</p><p>Entropy blends <span data-start="179" data-end="210">macroscopic
        state functions</span> with <span data-start="216" data-end="253">microscopic statistical behaviors</span>.  It
      resists <span data-start="268" data-end="298">single-intuition
        anchoring</span>: it's about disorder, information,
      irreversibility, energy quality, and more.</p><p>Over decades, starting with a BS in Physics, I have been through
      the combinatorics of iso baric/choric/thermal (PVT)systems and all
      of their combinations, designed to implement the suite of common
      cycles (rankine, stirling, otto, diesel, etc) at different times
      and while that helped to carve out an intuition for the other 
      more abstract quantities (like Entropy).  I don't know I've ever
      been lead directly to those, instead having to absorb (much of?)
      the full suite of examples to begin to appreciate the arcane
      (albeit not quite occult) quantities?</p><p>Ruth and Bruce would have a few canned examples to work through
      which is sometimes a good way to get there, but sometimes there is
      nothing more satisfying than making up your own narratives and
      exploring their implications, providing your world-building is
      consistent and coherent.  George is a very patient copilot in such
      adventures, if not always the perfect navigator?</p><p>I'm probably just stirring (increasing the entropy of this
      thread)?<br>
    </p><p><br>
    </p>
    <br><p><br>
    </p>
    <div class="moz-cite-prefix">On 6/17/25 2:47 PM, Frank Wimberly
      wrote:<br>
    </div>
    <blockquote type="cite" cite="mid:CAA5dAfov6aHvfmyE7mT3FrUt_QqbbnePyKD5REzEXjrRhJ0ybQ@mail.gmail.com">
      <meta http-equiv="content-type" content="text/html; charset=UTF-8"><p dir="ltr">I supplied another prompt to Géminis which i thought
        would yield an illuminating response:</p><p dir="ltr">What is isentropic expansion?</p><p dir="ltr">Isentropic expansion is a thermodynamic process where
        a substance (usually a gas) expands without any change in its
        entropy. This is an idealized process, meaning it assumes two
        key conditions:<br>
        * Adiabatic: No heat is transferred into or out of the system.<br>
        * Reversible: There are no irreversible losses due to factors
        like friction, turbulence, or unrestrained expansion.<br>
        Because entropy is a measure of disorder or randomness in a
        system, a constant entropy implies that the process is as
        efficient as possible, with no energy "lost" or converted into
        less useful forms.<br>
        Key characteristics of isentropic expansion:<br>
        * Constant entropy (\Delta S = 0): This is the defining
        characteristic.<br>
        * No heat transfer (\text{Q} = 0): Since the process is
        adiabatic.<br>
        * Decrease in temperature: As the substance expands and does
        work, its internal energy decreases, leading to a drop in
        temperature. This is in contrast to an isothermal expansion
        where heat would be added to maintain constant temperature.<br>
        * Decrease in pressure: As the volume increases and temperature
        drops, the pressure of the substance also decreases.<br>
        Why is it important?<br>
        Isentropic expansion is a crucial concept in thermodynamics and
        engineering for several reasons:<br>
        * Idealized model: It serves as a theoretical benchmark against
        which real-world processes can be compared. No real process is
        perfectly isentropic, but understanding this ideal helps
        engineers evaluate how efficiently actual systems operate.<br>
        * Efficiency calculations: The concept of isentropic efficiency
        is used to measure how closely an actual expansion process (like
        in a turbine) approaches the ideal isentropic case. This helps
        in designing more efficient engines and power systems.<br>
        * Design and analysis: It's fundamental to the design and
        analysis of various engineering systems, including:<br>
           * Turbines: In gas and steam turbines, hot, high-pressure
        fluids expand to produce work. Isentropic expansion helps
        determine the maximum work output.<br>
           * Nozzles: In applications like rocket propulsion and jet
        engines, nozzles are designed to accelerate fluids to high
        velocities through isentropic expansion.<br>
           * Internal combustion engines: The expansion (power) stroke
        in these engines is often approximated as an isentropic process
        for analysis.<br>
           * Refrigeration cycles: Isentropic expansion plays a role in
        these cycles as well.<br>
        In essence, isentropic expansion represents the most efficient
        possible expansion of a fluid, and while it's an idealization,
        it provides a powerful tool for understanding, analyzing, and
        optimizing energy conversion systems.<br>
      </p>
      <div data-smartmail="gmail_signature">---<br>
        Frank C. Wimberly<br>
        140 Calle Ojo Feliz, <br>
        Santa Fe, NM 87505<br>
        <br>
        505 670-9918<br>
        Santa Fe, NM</div>
      <br>
      <div class="gmail_quote gmail_quote_container">
        <div dir="ltr" class="gmail_attr">On Tue, Jun 17, 2025, 2:44 PM
          Santafe <<a href="mailto:desmith@santafe.edu" moz-do-not-send="true" class="moz-txt-link-freetext">desmith@santafe.edu</a>>
          wrote:<br>
        </div>
        <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
          <div style="line-break:after-white-space">Hi Nick, 
            <div><br>
            </div>
            <div>Yes; I can report how things appear to me.  Feel free
              to growl that they are not correct.  I will stay away from
              making claims about what things, or you, “are”.  I have no
              access to that.</div>
            <div><br>
            </div>
            <div>What I see is you sort-of-demanding that the terms that
              happen to interest you will be the terms in which natural
              phenomena admit an understanding.  So you give more and
              more elaborate descriptions of experiments and ask about
              outcomes, but you leave out 2/3 of the specification that
              an actual outcome would depend on, as somebody pointed out
              in this latest case about the tapping.  This is why
              Marcus’s advocacy of putting things into an algorithm is
              so central.  If a machine generates an algorithm, it might
              do so by simply making guesses about all the things you
              didn’t actually tell it, but at least, for the algorithm
              to exist, we will have an explicit record of what its
              assumptions were. </div>
            <div><br>
            </div>
            <div>Your comments about category errors upped the ante on
              that; I see them as a premise that the terms you choose
              going in, and the rules of argument you learned in
              parochial school, will grant you access through thinking
              to how nature really is.  That’s why I called you a
              metaphysician before (and at which you growled).</div>
            <div><br>
            </div>
            <div>What I saw was people repeatedly telling you that, when
              the part of humanity that works in this area uses “the
              entropy” referring to equilibrium, they have the property
              of “being constructed to mean a state function” entailed
              in that term, and then you continued to make
              assertion-statements that entropy is not a function
              determinable by whatever one means by “a state”.  One
              response to such a situation might be to ask “Hmm; I
              wonder what-all they mean when they say `a state’; they
              might not be telling me enough for me to follow them.”
               Or, one could conclude that they are making category
              errors, and that your rules of argument from parochial
              school tell you what those errors are.  Choosing to do the
              latter, to me, is as close as one can get in real life, to
              the pupil for whom the master pours tea, and continues to
              pour after the cup is full.  The student asks why do you
              keep pouring when the cup is full?  etc.  The standard
              story.</div>
            <div><br>
            </div>
            <div>It’s interesting: I would be the last one to criticize
              anybody for trying to understand something in other terms
              that occur to him, than those that a field conventionally
              uses.  I very much like that mode of working, and it is
              mostly what I do — not through any greatness of soul; just
              because I can’t follow other people, so I grab on where I
              can from my own proclivities.  Mostly I end up in a mess
              that way, too.  So the difference is all in what you do
              when you hit a snag, and the people around you seem to be
              able to coordinate with each other enough to be getting
              something done.  It’s evidence, to at least be reflected
              upon. </div>
            <div><br>
            </div>
            <div>Your statement "I’ve gone back to feeling that  I don’t
              even know enough to ask a question.” struck me as a
              glimmering of the recognition that we don’t get to dictate
              to nature the terms in which phenomena become
              understandable.  Those terms are something we have to
              figure out along the way, along with the rules of argument
              that apply to them.  Glen has written in many posts (a
              burst of them a year or two ago) about the role of
              embedded practice in this “coming to terms”.  Of course,
              we can always dictate.  (We used to say “It’s a free
              country”; though that seems more awkward now.)  But
              wherever that dictation gets you, it won’t be
              understanding.</div>
            <div><br>
            </div>
            <div>Anyway.  DaveW can tell you that I don’t understand
              anything about Zen or about any contemplative tradition.
               (And if he can’t tell you that, I can find others who
              will.  It is a *secret* in the closed hand!)  But I hear
              these things that come out of the various literatures, and
              they often seem to me like delightful distillations of how
              people are; just the kind of things you would expect
              cultures to keep and to transmit over millennia, through
              innumerable hands, because they bring the world into
              better focus.</div>
            <div><br>
            </div>
            <div>Eric</div>
            <div><br>
            </div>
            <div><br>
            </div>
            <div>
              <div><br>
                <blockquote type="cite">
                  <div>On Jun 18, 2025, at 1:01, Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" target="_blank" rel="noreferrer" moz-do-not-send="true" class="moz-txt-link-freetext">thompnickson2@gmail.com</a>>
                    wrote:</div>
                  <br>
                  <div>
                    <div style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt"> I
                      did not understand, and wanted to understand, your
                      zen comment. <span> </span><span style="font-size:16px">I am reluctant to ask you
                        to punch the tar baby again .   You are, of
                        course, under no obligation to cure my madness
                        or buffer my aging.  But given the coincidence
                        between that comment and DaveW's, who often
                        presses Zen on me, I thought you might be
                        pointing at something there I should pay close
                        attention to.</span></div>
                    <div style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt"><br>
                    </div>
                    <div style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt">It
                      will be ok.  You was born and bred in a briar
                      patch.  </div>
                    <div style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt"><br>
                    </div>
                    <div style="font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif;font-size:12pt">Nick </div>
                    <hr style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;display:inline-block;width:698.734375px"><span style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;float:none;display:inline!important"></span>
                    <div id="m_7979061136628741176divRplyFwdMsg" dir="ltr" style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none"><font style="font-size:11pt" face="Calibri, sans-serif"><b>From:</b><span> </span>Friam
                        <<a href="mailto:friam-bounces@redfish.com" target="_blank" rel="noreferrer" moz-do-not-send="true" class="moz-txt-link-freetext">friam-bounces@redfish.com</a>>
                        on behalf of Santafe <<a href="mailto:desmith@santafe.edu" target="_blank" rel="noreferrer" moz-do-not-send="true" class="moz-txt-link-freetext">desmith@santafe.edu</a>><br>
                        <b>Sent:</b><span> </span>Monday, June 16, 2025
                        11:30 PM<br>
                        <b>To:</b><span> </span>The Friday Morning
                        Applied Complexity Coffee Group <<a href="mailto:friam@redfish.com" target="_blank" rel="noreferrer" moz-do-not-send="true" class="moz-txt-link-freetext">friam@redfish.com</a>><br>
                        <b>Subject:</b><span> </span>Re: [FRIAM] Entropy
                        RE-redux</font>
                      <div> </div>
                    </div>
                    <div style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;line-break:after-white-space">Zen
                      moment Nick: <br id="m_7979061136628741176x_lineBreakAtBeginningOfMessage">
                      <div><br>
                        <blockquote type="cite">
                          <div>On Jun 17, 2025, at 12:00, Nicholas
                            Thompson <<a href="mailto:thompnickson2@gmail.com" target="_blank" rel="noreferrer" moz-do-not-send="true" class="moz-txt-link-freetext">thompnickson2@gmail.com</a>>
                            wrote:</div>
                          <br>
                          <div>
                            <div dir="auto"> I’ve gone back to feeling
                              that  I don’t even know enough to ask a
                              question.</div>
                          </div>
                        </blockquote>
                        <div><br>
                        </div>
                        <div>Just there for an instant, the teacup
                          dipped below full.  btw.: this sentence is a
                          wonderful encapsulation of the difference
                          between the metaphysician and the scientist. 
                          Welcome back.</div>
                        <div><br>
                        </div>
                        <div>Frank’s language below is good.  It’s work
                          to understand it, of course, but the crucial
                          starting point is that it admits an
                          understanding because there is a consistent
                          thing being asserted.</div>
                        <div><br>
                        </div>
                        <div>Eric</div>
                        <div><br>
                        </div>
                        <blockquote type="cite">
                          <div>
                            <div dir="auto">
                              <div>
                                <div dir="ltr">
                                  <div dir="auto">
                                    <div>You've probably done this.
                                      Nick.</div>
                                    <div dir="auto"><br>
                                    </div>
                                    <div dir="auto">
                                      <div dir="auto">Yes, entropy (S)
                                        is a state variable in
                                        thermodynamics.</div>
                                      <div dir="auto">Here's what that
                                        means:</div>
                                      <div dir="auto"> * Definition of a
                                        State Variable: A state variable
                                        (or state function) is a
                                        property of a thermodynamic
                                        system that depends only on the
                                        current state of the system, not
                                        on the path or process taken to
                                        reach that state. If a system is
                                        in a particular equilibrium
                                        state, its state variables will
                                        have specific, unique values.</div>
                                      <div dir="auto"> * Why Entropy is
                                        a State Variable:</div>
                                      <div dir="auto">   * Path
                                        Independence: The change in
                                        entropy between two states is
                                        the same regardless of the
                                        reversible or irreversible path
                                        taken to go from the initial
                                        state to the final state.</div>
                                      <div dir="auto">   * Unique Value
                                        for a Given State: For any given
                                        equilibrium state of a system
                                        (defined by other state
                                        variables like temperature,
                                        pressure, and volume), there is
                                        a unique value of entropy.</div>
                                      <div dir="auto">   * Mathematical
                                        Property: Mathematically, a
                                        quantity is a state variable if
                                        its differential is an exact
                                        differential, meaning that its
                                        integral over a closed path is
                                        zero. This is true for entropy.</div>
                                      <div dir="auto"> * Contrast with
                                        Path Variables: In contrast,
                                        quantities like heat (Q) and
                                        work (W) are not state
                                        variables. The amount of heat
                                        transferred or work done depends
                                        entirely on the specific path
                                        followed during a process.</div>
                                      <div dir="auto">In summary,
                                        entropy is a fundamental
                                        property that characterizes the
                                        state of a thermodynamic system
                                        and is independent of its
                                        history.</div>
                                      <div dir="auto"><br>
                                      </div>
                                    </div>
                                    <div><br>
                                    </div>
                                    <div data-smartmail="gmail_signature">---<br>
                                      Frank C. Wimberly<br>
                                      <a href="https://www.google.com/maps/search/140+Calle+Ojo+Feliz,+Santa+Fe,+NM+87505?entry=gmail&source=g" moz-do-not-send="true">140 Calle
                                        Ojo Feliz,</a><span> </span><br>
                                      <a href="https://www.google.com/maps/search/140+Calle+Ojo+Feliz,+Santa+Fe,+NM+87505?entry=gmail&source=g" moz-do-not-send="true">Santa Fe,
                                        NM 87505</a><br>
                                      <br>
                                      505 670-9918<br>
                                      Santa Fe, NM</div>
                                  </div>
                                  <br>
                                  <div>
                                    <div dir="ltr">On Sun, Jun 15, 2025,
                                      9:27 AM Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" target="_blank" rel="noreferrer" moz-do-not-send="true" class="moz-txt-link-freetext">thompnickson2@gmail.com</a>>
                                      wrote:<br>
                                    </div>
                                    <blockquote style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex">
                                      <div dir="ltr">
                                        <div dir="ltr">
                                          <div>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?</div>
                                          <span>--<span> </span></span><br>
                                          <div dir="ltr">
                                            <div dir="ltr">
                                              <div>Nicholas S. Thompson</div>
                                              <div>Emeritus Professor of
                                                Psychology and Ethology</div>
                                              <div>Clark University</div>
                                              <div><a href="mailto:nthompson@clarku.edu" rel="noreferrer noreferrer" target="_blank" moz-do-not-send="true" class="moz-txt-link-freetext">nthompson@clarku.edu</a></div>
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                                          </div>
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                    <span style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;text-decoration:none;float:none;display:inline!important"> 1/2003
                      thru 6/2021  </span><a href="http://friam.383.s1.nabble.com/" style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant-caps:normal;font-weight:400;letter-spacing:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px" target="_blank" rel="noreferrer" moz-do-not-send="true" class="moz-txt-link-freetext">http://friam.383.s1.nabble.com/</a></div>
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FRIAM Applied Complexity Group listserv
Fridays 9a-12p Friday St. Johns Cafe   /   Thursdays 9a-12p Zoom <a class="moz-txt-link-freetext" href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,scI3Zb9I46TVjw3QcGcuCxQlUZ89QAHgPVXy-WLsPJVoGeu_RZId802vY15aK_XKys_dFDcsETnY_mNpnnPvmbjD-dS1y-zwM5xwO8YXrpIq&typo=1">https://bit.ly/virtualfriam</a>
to (un)subscribe <a class="moz-txt-link-freetext" href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,UKrMRpldBuRW0or6rODl9peXzhW4h7BNcndiY_pWoBJrD1jcoNlYA-sTyE8DrodhmhsrMg9AINEyr482BNo3wpmObV2l4LMCOA7l2QhvBfq1MqBLgqxB&typo=1">http://redfish.com/mailman/listinfo/friam_redfish.com</a>
FRIAM-COMIC <a class="moz-txt-link-freetext" href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,APLBZHasUmyTXdQBbK400g3OcArYUiQHeLIYehkmXfnHGMoFHuevwtgA3wCx1vhDTD1j-4OkxpaVnslqiq0_JFc9U2h3uEN2UhSRdT2CsH2z3_1Wa3Cbn4A,&typo=1">http://friam-comic.blogspot.com/</a>
archives:  5/2017 thru present <a class="moz-txt-link-freetext" href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,8lI_F3hDpcCPpIR-iXQAS-BPaHcGjloFODJr53zO18ZuIvuBhDhvGzTLaQVyhqDn19eRKkoCWzf8VIPNY9g92RlLBNoxE5MetgTMKO1hj0Sd3g,,&typo=1">https://redfish.com/pipermail/friam_redfish.com/</a>
  1/2003 thru 6/2021  <a class="moz-txt-link-freetext" href="http://friam.383.s1.nabble.com/">http://friam.383.s1.nabble.com/</a>
</pre>
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<span id="cid:C3C3A051-9B3A-4745-8AA8-5821167CE068"><OpenPGP_0xD5BAF94F88AFFA63.asc></span>.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..<br>FRIAM Applied Complexity Group listserv<br>Fridays 9a-12p Friday St. Johns Cafe   /   Thursdays 9a-12p Zoom https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,eOR6lXHbkz9FDp_F5EhvtBdVA011L8K9ntJGytID_gg0tuW1mbXJJIh1Ao_DveQtQClCQf5VHo_KZ-aJZqhB43Z8l02-HMRur-tQnD7uRjdvnCQhnaU,&typo=1<br>to (un)subscribe https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,3R-CpTO75xCb8a586XMCGfZNO4N1YAqWott72o-esdXhNom1IZwQciEW4YoNVNtUa-GzzfnrBSQMGYflcmc70H3uUPWL9v86gfaaWBreVKH_iaI5E9r1qER0gj-C&typo=1<br>FRIAM-COMIC https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,iP5UtG9cXGZb9iFbdK7S9-wjB-lxbUCrHrAJVtf8z4uHkrqHO2zXuOiFjR7LQD9MgGajU2fDwW1MHM4C9zspD9Xd6RL9W6GGCEBVt4icMjO1fW4FEsk,&typo=1<br>archives:  5/2017 thru present https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,2-ZbJ6GSm8x03lzF6kWDloQOmS-ED-aQOkQE2Jqjsxdm33er5ijqoQTRCTHLzTqrrCEa1WfYUnK49Bs6T8bg40GTs-qw08LIBLBeh6480UGC6GSfvlxXbfnc8g,,&typo=1<br>  1/2003 thru 6/2021  http://friam.383.s1.nabble.com/<br></div></blockquote></div><br></div></body></html>