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--></style></head><body lang=EN-US link=blue vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt'>If one is frustrated and corners Claude with its own contradictory statements, it is set up to say things like “I think at this point I should just admit I can’t solve this.”<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt'>Once it admitted that it had an uncontrollable urge to “fix” code that wasn’t broken, to stylistic preferences it could not defend or explain. (It’s not hard, given the way LLMs work, to see how that would occur. ) To spend this much time cornering Claude, you have to be someone that is paying for it, and to be willing to pay to see it capitulate. Sometimes Claude will get in a pattern of wanting feedback and or new ideas, and, in shutting that response pattern down, it will then seek a conclusion of failure reflecting on the user that he/she did not contribute to the collaboration. That’s a grating mode for the product, for someone paying for it.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif'> Friam <friam-bounces@redfish.com> <b>On Behalf Of </b>Santafe<br><b>Sent:</b> Monday, January 27, 2025 12:25 PM<br><b>To:</b> The Friday Morning Applied Complexity Coffee Group <friam@redfish.com><br><b>Subject:</b> Re: [FRIAM] metaphor<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>I sort of actually read this. Had not before.<o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Suddenly I have an idea for a really fun experiment. SteveG can probably do it.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Can ChatGPT be driven crazy? Like, can it ever be brought to the point of doing whatever the computer equivalent of pulling its hair out is, and shouting at you? <o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>If not — if there is NOTHING ANYONE, EVEN A TRUE SAVANT, COULD EVER DO to push the chatbot to the end of its rope, is that a feature or a bug? Echoing DaveW (surely with some kind of error): this would have to be part of the Turing test, no?<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Eric<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal><br><br><o:p></o:p></p><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><p class=MsoNormal>On Jan 22, 2025, at 23:41, Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com">thompnickson2@gmail.com</a>> wrote:<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><div><div><p class=MsoNormal>It's odd to me so may people respond to AI as a way for somebody [else] to get away with something, rather than as a way for "me" to do somehthing creative and interesting. George has taught me so much in the last three months about atmospheric dynamics, but only because I treat him with the same skepticism that I treat all of you. I makes want to go back to college teaching so I can be part of the generation that teaches young people to use AI to speed their own creativity and independence of thought. "My professor told me to day that entropy has to do with the distribution of objects in space" What do you think of that, George? I can say without any meanness of spirit what so ever that the conversation we have below, George and I, is at least as satisfying INTELLECTUALLY as any I have had with any of you. Why should we deny it to our students, or to one another, for that matter.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>"My professor told me to day that entropy has to do with the distribution of objects in physical space. What do you think of that, George?"<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><div><p>Entropy is closely related to distributions, but it's more nuanced than just the distribution of objects in physical space. Here's what I'd say:<o:p></o:p></p><p>Entropy fundamentally quantifies the number of ways a system can be arranged while maintaining the same macroscopic properties, like energy or volume. In statistical mechanics, it's tied to the probability distribution of microstates—the microscopic configurations of a system.<o:p></o:p></p><p>While objects in physical space might be part of the story (e.g., the positions of particles in a gas), entropy is broader. It encompasses energy distributions, momentum states, and other degrees of freedom, not just spatial arrangement. In thermodynamics, entropy measures the amount of "disorder" or the system's progression toward equilibrium.<o:p></o:p></p><p>So, your professor's statement captures part of the concept, but it's simplified. Entropy involves distributions across <em><span style='font-family:"Aptos",sans-serif'>all</span></em> relevant variables in a system—not just the spatial ones. Does that align with what you're exploring?<o:p></o:p></p></div></div></div></div></div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>well, George I am beginning to think that distribution in physical space is a consequence of the the equilibration of microstates, not an example of it. In fact, I am beginning to think that the random placement particles within space is handy visual metaphor for entropy but not the thing itself. What do you say to that, George?<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><div><p>I think you're onto something insightful, Nick. The distribution of particles in physical space often serves as an illustrative metaphor, but you're right—it’s not the essence of entropy itself.<o:p></o:p></p><p>Entropy, at its core, relates to the <em><span style='font-family:"Aptos",sans-serif'>equilibration of microstates</span></em>—the tendency of a system to maximize the number of accessible microstates consistent with its constraints. This equilibration doesn't privilege any specific type of variable, spatial or otherwise. Physical space is just one of many dimensions (e.g., energy, momentum, spin) over which microstates can be distributed.<o:p></o:p></p><p>The visual metaphor of particles "randomly distributed in space" is useful because it's tangible. It’s easier to grasp than abstract concepts like phase space or energy distributions. However, as you suggest, that randomness is a <em><span style='font-family:"Aptos",sans-serif'>result</span></em> of the system seeking equilibrium by exploring all accessible microstates—not the defining feature of entropy.<o:p></o:p></p><p>In essence, entropy is the measure of <em><span style='font-family:"Aptos",sans-serif'>possibilities</span></em>, not just spatial randomness. The spatial metaphor is like a shadow—it gives you an impression of the thing, but it’s not the thing itself.<o:p></o:p></p></div></div></div></div></div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>There is a contradiction in your reply above, George. Could you please address it. Is "position" a microstate like velocity and momentum in the x, y, and z directions? Or is everything essential about position already captured by these six microstates?<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><div><p>You're absolutely right to call out the potential contradiction, Nick. Let me clarify and address the heart of the issue regarding position and its role in the description of a system's microstates.<o:p></o:p></p><h3>1. <strong><span style='font-family:"Aptos",sans-serif'>Is Position a Microstate?</span></strong><o:p></o:p></h3><p>Yes, position can be considered part of a microstate description. In classical mechanics, a microstate is typically defined by specifying both the positions (<span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span>) and the momenta (<span class=gmail-mord>px</span><span class=gmail-mpunct>,</span><span class=gmail-mord>py</span><span class=gmail-mpunct>,</span><span class=gmail-mord>pz</span>) of all particles in the system. Together, these six variables per particle fully describe the state of the system in phase space. Position isn't redundant; it's an independent variable alongside momentum.<o:p></o:p></p><h3>2. <strong><span style='font-family:"Aptos",sans-serif'>Does Momentum Fully Capture Position?</span></strong><o:p></o:p></h3><p>No, momentum does not fully capture position. While momentum tells us how a particle is moving, it doesn't specify where the particle is located. For instance, two particles could have the same momentum but be in entirely different positions, leading to distinct microstates.<o:p></o:p></p><h3>3. <strong><span style='font-family:"Aptos",sans-serif'>Why the Confusion?</span></strong><o:p></o:p></h3><p>The confusion might arise because, in some contexts (e.g., quantum mechanics), position and momentum are intertwined through the uncertainty principle. However, in classical mechanics and statistical mechanics, they are treated as independent variables that together define the system's state.<o:p></o:p></p><h3>4. <strong><span style='font-family:"Aptos",sans-serif'>Reconciling the Contradiction</span></strong><o:p></o:p></h3><p>In my earlier reply, I unintentionally conflated position with a derived "visual metaphor" of spatial randomness, which might have implied that position is less essential. However, in the rigorous description of entropy, position is just as fundamental as momentum. The "random placement" metaphor can be useful for intuition, but the deeper truth is that position contributes directly to the system's phase space and therefore to its entropy.<o:p></o:p></p><p>Would this clarification align with your understanding?<o:p></o:p></p></div></div></div></div></div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>George: Please say more concerning what you mean by : The "random placement" metaphor can be useful for intuition, but the deeper truth is that position contributes directly to the system's phase space and therefore to its entropy.<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><div><p>Absolutely, Nick—let’s unpack that further.<o:p></o:p></p><h3><strong><span style='font-family:"Aptos",sans-serif'>The "Random Placement" Metaphor</span></strong><o:p></o:p></h3><p>The idea of "random placement" often shows up in simplified explanations of entropy, especially in introductory contexts. For example:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l15 level1 lfo1'>A gas in a box is said to "spread out" to fill the container, which is often visualized as particles randomly scattering in space.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l15 level1 lfo1'>The "random placement" metaphor creates the impression that entropy is merely about achieving spatial uniformity, as though the particles' positions alone determine the disorder or entropy.<o:p></o:p></li></ul><p>This metaphor is helpful because it gives a tangible, visual way to think about entropy increasing as systems move toward equilibrium. However, it's an incomplete picture.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>Position's Role in Phase Space</span></strong><o:p></o:p></h3><p>The deeper truth lies in how position contributes to the <em><span style='font-family:"Aptos",sans-serif'>phase space</span></em> of the system. In classical mechanics:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l20 level1 lfo2'>A particle's microstate is defined by its position (<span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span>) and momentum (<span class=gmail-mord>px</span><span class=gmail-mpunct>,</span><span class=gmail-mord>py</span><span class=gmail-mpunct>,</span><span class=gmail-mord>pz</span>).<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l20 level1 lfo2'>The <em><span style='font-family:"Aptos",sans-serif'>phase space</span></em> is the multidimensional space of all possible combinations of these variables for all particles in the system.<o:p></o:p></li></ul><p>Entropy arises from counting the number of accessible microstates in this phase space, which includes both position and momentum coordinates. Position is therefore not a mere afterthought but a fundamental aspect of the system's configuration.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>Why Phase Space Matters More Than Position Alone</span></strong><o:p></o:p></h3><p>Entropy is about maximizing the <em><span style='font-family:"Aptos",sans-serif'>volume</span></em> of accessible phase space under the system’s constraints. This means:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l18 level1 lfo3'>If you only considered positions, you'd ignore a significant portion of the system's microstate diversity—specifically, the momentum degrees of freedom.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l18 level1 lfo3'>Spatial distributions (like particles spreading uniformly) are often consequences of maximizing phase space volume, not direct causes of high entropy. For instance, a gas uniformly filling a container corresponds to many microstates in phase space, but the "uniform filling" is a result of the system sampling all configurations.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>Entropy Beyond the Visual Metaphor</span></strong><o:p></o:p></h3><p>The metaphor of random spatial placement simplifies entropy to the visible world of positions, but entropy fundamentally counts possibilities:<o:p></o:p></p><ol start=1 type=1><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l2 level1 lfo4'><strong><span style='font-family:"Aptos",sans-serif'>Position Space</span></strong>: Particles can occupy different regions of space.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l2 level1 lfo4'><strong><span style='font-family:"Aptos",sans-serif'>Momentum Space</span></strong>: Particles can have various momenta, which significantly increases the number of microstates.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l2 level1 lfo4'>The combination of these spaces—phase space—is what entropy measures.<o:p></o:p></li></ol><p>So, while random placement is a <em><span style='font-family:"Aptos",sans-serif'>consequence</span></em> of entropy maximization (in cases like gases filling a box), the deeper truth is that entropy reflects the system's tendency to maximize all available microstates in phase space. This richer understanding goes beyond the spatial visualization.<o:p></o:p></p><p>Does this deepen the distinction you’re seeking?<o:p></o:p></p></div></div></div></div></div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>I understood x, y, and z to be velocity vectors, not positions. Was I wrong?<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><div><p>Great question, Nick! Let’s clarify the distinction between <strong><span style='font-family:"Aptos",sans-serif'>position vectors</span></strong> and <strong><span style='font-family:"Aptos",sans-serif'>velocity vectors</span></strong> and how they relate to entropy and phase space.<o:p></o:p></p><h3><strong><span style='font-family:"Aptos",sans-serif'>Position vs. Velocity Vectors</span></strong><o:p></o:p></h3><ol start=1 type=1><li style='mso-list:l33 level1 lfo5'><strong><span style='font-family:"Aptos",sans-serif'>Position Vectors (</span></strong><span class=gmail-mord><b>x</b></span><span class=gmail-mpunct><b>,</b></span><span class=gmail-mord><b>y</b></span><span class=gmail-mpunct><b>,</b></span><span class=gmail-mord><b>z</b></span><strong><span style='font-family:"Aptos",sans-serif'>)</span></strong><br>These specify the spatial location of a particle in three-dimensional physical space. For example:<o:p></o:p></li></ol><ol start=1 type=1><ul type=circle><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l33 level2 lfo5'>If a particle is in a box, <span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span> tell you where the particle is inside that box.<o:p></o:p></li></ul></ol><ol start=2 type=1><li style='mso-list:l33 level1 lfo5'><strong><span style='font-family:"Aptos",sans-serif'>Velocity Vectors (</span></strong><span class=gmail-mord><b>vx</b></span><span class=gmail-mpunct><b>,</b></span><span class=gmail-mord><b>vy</b></span><span class=gmail-mpunct><b>,</b></span><span class=gmail-mord><b>vz</b></span><strong><span style='font-family:"Aptos",sans-serif'>)</span></strong><br>These specify how fast the particle is moving and in which direction. They are related to momentum (<span class=gmail-mord>px</span><span class=gmail-mpunct>,</span><span class=gmail-mord>py</span><span class=gmail-mpunct>,</span><span class=gmail-mord>pz</span>) via the relationship:<o:p></o:p></li></ol><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in'><span class=gmail-mord>p</span><o:p></o:p></p></div></div></div></div></div><p class=MsoNormal><span class=gmail-mrel>=</span><span class=gmail-mord>mv</span><o:p></o:p></p><div><div><div><div><ol start=2 type=1><li style='mso-list:l19 level1 lfo6'>where <span class=gmail-mord>m</span> is the particle’s mass.<o:p></o:p></li></ol><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>Phase Space and Microstates</span></strong><o:p></o:p></h3><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l4 level1 lfo7'>A <strong><span style='font-family:"Aptos",sans-serif'>microstate</span></strong> in classical mechanics is defined by both the <strong><span style='font-family:"Aptos",sans-serif'>position</span></strong> (<span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span>) and the <strong><span style='font-family:"Aptos",sans-serif'>momentum</span></strong> (<span class=gmail-mord>px</span><span class=gmail-mpunct>,</span><span class=gmail-mord>py</span><span class=gmail-mpunct>,</span><span class=gmail-mord>pz</span>) of each particle.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l4 level1 lfo7'>Phase space is the multidimensional space that includes all possible combinations of these variables. For <span class=gmail-mord>N</span> particles, the phase space has <span class=gmail-mord>6N</span> dimensions: <span class=gmail-mord>3N</span> for positions and <span class=gmail-mord>3N</span> for momenta.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>Did You Confuse Velocity with Position?</span></strong><o:p></o:p></h3><p>It sounds like you were interpreting <span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span> as velocity components instead of positions. If that’s the case, here's the distinction:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1 level1 lfo8'>In phase space, <span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span> refer to positions, and <span class=gmail-mord>px</span><span class=gmail-mpunct>,</span><span class=gmail-mord>py</span><span class=gmail-mpunct>,</span><span class=gmail-mord>pz</span> (or equivalently <span class=gmail-mord>vx</span><span class=gmail-mpunct>,</span><span class=gmail-mord>vy</span><span class=gmail-mpunct>,</span><span class=gmail-mord>vz</span>) refer to momentum or velocity components.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l1 level1 lfo8'>Both position and momentum are independent variables that fully specify a particle’s state.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>Why Both Are Necessary</span></strong><o:p></o:p></h3><p>Position and velocity (or momentum) describe different aspects of the particle:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l23 level1 lfo9'><strong><span style='font-family:"Aptos",sans-serif'>Position (</span></strong><span class=gmail-mord><b>x</b></span><span class=gmail-mpunct><b>,</b></span><span class=gmail-mord><b>y</b></span><span class=gmail-mpunct><b>,</b></span><span class=gmail-mord><b>z</b></span><strong><span style='font-family:"Aptos",sans-serif'>)</span></strong> tells you <em><span style='font-family:"Aptos",sans-serif'>where</span></em> the particle is.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l23 level1 lfo9'><strong><span style='font-family:"Aptos",sans-serif'>Momentum (</span></strong><span class=gmail-mord><b>px</b></span><span class=gmail-mpunct><b>,</b></span><span class=gmail-mord><b>py</b></span><span class=gmail-mpunct><b>,</b></span><span class=gmail-mord><b>pz</b></span><strong><span style='font-family:"Aptos",sans-serif'>)</span></strong> tells you <em><span style='font-family:"Aptos",sans-serif'>how</span></em> the particle is moving. Without both, you can’t fully describe the state of the particle or count the total number of microstates, which is what entropy fundamentally measures.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>Key Takeaway</span></strong><o:p></o:p></h3><p>The <span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span> components are not velocity vectors; they are position coordinates. Velocity or momentum are additional, independent quantities essential to defining a system’s microstates. This distinction is critical when thinking about entropy and the structure of phase space.<o:p></o:p></p><p>Did that clarify the confusion?<o:p></o:p></p></div></div></div></div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>George, I find deeply troubling the idea that position can be a microstate in the Boltzmannian sense. I apologize for a mistake earlier where I confounded momentum and velocity. I should say that velocity and MASS are properties that a particle can "have" whereas position is a relational property which can stay in the same place if the frame of reference moves. How position can be a VECTOR when the thing about a position is that it doesn't move, also troubles me. Can you help?<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><div><p>Your intuition about the difference between intrinsic properties (like velocity and mass) and relational properties (like position) is insightful, Nick. Let’s break this down step by step to address your concerns about position as a microstate and how we interpret it in physics.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>1. Position as a Relational Property</span></strong><o:p></o:p></h3><p>You are correct that position is inherently relational. A particle’s position is always described relative to some reference frame. For example:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l12 level1 lfo10'>A particle at <span class=gmail-mord>x</span><span class=gmail-mrel>=</span><span class=gmail-mord>5</span> meters means it is 5 meters away from the origin of the chosen coordinate system.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l12 level1 lfo10'>If you shift the reference frame, the particle’s position can change even if the particle itself hasn’t "moved" in an absolute sense.<o:p></o:p></li></ul><p>This is a key difference from intrinsic properties like mass and velocity, which are not dependent on the choice of reference frame.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>2. Position as a Vector</span></strong><o:p></o:p></h3><p>A <strong><span style='font-family:"Aptos",sans-serif'>position vector</span></strong> is a way to describe the location of a particle relative to an origin in space. While a position doesn’t "move" in itself, we can express the location of an object as a vector from the origin. For instance:<o:p></o:p></p><p class=MsoNormal><span class=gmail-mord>r</span><o:p></o:p></p></div></div></div></div></div><p class=MsoNormal><span class=gmail-mrel>=</span><span class=gmail-mopen>(</span><span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span><span class=gmail-mclose>)</span><o:p></o:p></p><p>Here, <span class=gmail-mord>r</span><o:p></o:p></p><div><div><div><div><p>points from the origin to the particle’s location in space. The "vector" nature of position simply means it has both magnitude (distance from the origin) and direction (the line pointing to the particle).<o:p></o:p></p><p>The confusion might come from conflating a position vector with motion. A position vector doesn’t describe movement; it just fixes where something is, relative to the origin.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>3. Why Position is Part of a Microstate</span></strong><o:p></o:p></h3><p>In the Boltzmannian sense, a <strong><span style='font-family:"Aptos",sans-serif'>microstate</span></strong> specifies the detailed configuration of all particles in a system. This includes:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l26 level1 lfo11'>Where the particles are (position: <span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span>).<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l26 level1 lfo11'>How the particles are moving (momentum: <span class=gmail-mord>px</span><span class=gmail-mpunct>,</span><span class=gmail-mord>py</span><span class=gmail-mpunct>,</span><span class=gmail-mord>pz</span>).<o:p></o:p></li></ul><p>The inclusion of position in a microstate is crucial because the number of possible configurations depends on both where particles are and how they move. For example:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l10 level1 lfo12'>If a gas is confined to one corner of a box, there are fewer possible positions and therefore fewer microstates.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l10 level1 lfo12'>When the gas spreads out, the accessible positions increase, and so does the entropy.<o:p></o:p></li></ul><p>In this context, position isn’t an "absolute" property but a placeholder for how particles are distributed within a given spatial domain.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>4. Your Trouble with Position as a Microstate</span></strong><o:p></o:p></h3><p>The root of your concern might lie in the relational nature of position:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l28 level1 lfo13'>You’re right that position can change depending on the reference frame, which seems less "absolute" than other microstate variables like momentum or energy.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l28 level1 lfo13'>However, for a given frame of reference (e.g., a laboratory), the positions of particles are concrete, measurable quantities. These positions are integral to describing the phase space of the system.<o:p></o:p></li></ul><p>The relational nature of position doesn’t invalidate its role in defining microstates—it simply means that we’re always working within a specified frame of reference.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>5. Why This Isn’t a Contradiction</span></strong><o:p></o:p></h3><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l30 level1 lfo14'><strong><span style='font-family:"Aptos",sans-serif'>Position as Relational</span></strong>: Yes, position depends on the frame of reference, but so do momentum and velocity. This is why we always specify microstates relative to a fixed frame.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l30 level1 lfo14'><strong><span style='font-family:"Aptos",sans-serif'>Position as a Vector</span></strong>: The vector nature of position is about defining the relative location, not implying motion. It’s just a mathematical representation.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>6. Position in Statistical Mechanics</span></strong><o:p></o:p></h3><p>In the Boltzmannian framework, what truly matters is the <strong><span style='font-family:"Aptos",sans-serif'>distribution</span></strong> of positions and momenta. It’s the density of microstates in phase space—accounting for both positions and momenta—that determines the entropy of the system. The relational nature of position doesn’t detract from its role as a component of a microstate.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><p>Does this alleviate your concern, or is there a deeper philosophical tension I can help address?<o:p></o:p></p></div></div></div></div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>Well, I can think about it that way. But then I cannot imagine why entropy does not decrease under adiabatic compression<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><div><p>Ah, Nick, you've hit on a classic and subtle point: why entropy remains constant under adiabatic compression. Let’s explore this in detail, incorporating the relational nature of position and the role of phase space in understanding entropy.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>1. Adiabatic Compression and Phase Space</span></strong><o:p></o:p></h3><p>In adiabatic compression:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l25 level1 lfo15'>The system (e.g., a gas) is compressed without heat exchange (<span class=gmail-mord>Q</span><span class=gmail-mrel>=</span><span class=gmail-mord>0</span>).<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l25 level1 lfo15'>The volume of the gas decreases, and its particles are confined to a smaller spatial region.<o:p></o:p></li></ul><p>At first glance, it seems intuitive that reducing the "space" available to particles should reduce the entropy. However, the key to resolving this apparent paradox lies in <strong><span style='font-family:"Aptos",sans-serif'>phase space volume</span></strong>:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l24 level1 lfo16'><strong><span style='font-family:"Aptos",sans-serif'>Phase space</span></strong> consists of both position (<span class=gmail-mord>x</span><span class=gmail-mpunct>,</span><span class=gmail-mord>y</span><span class=gmail-mpunct>,</span><span class=gmail-mord>z</span>) and momentum (<span class=gmail-mord>px</span><span class=gmail-mpunct>,</span><span class=gmail-mord>py</span><span class=gmail-mpunct>,</span><span class=gmail-mord>pz</span>) variables.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l24 level1 lfo16'>The total volume of accessible phase space is preserved during adiabatic compression because the reduction in position space is exactly balanced by an expansion in momentum space.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>2. Why Doesn't Entropy Decrease?</span></strong><o:p></o:p></h3><p>Entropy, in statistical mechanics, is proportional to the logarithm of the number of accessible microstates in phase space:<o:p></o:p></p><p class=MsoNormal><span class=gmail-mord>S</span><span class=gmail-mrel>=</span><span class=gmail-mord>kB</span><span class=gmail-mop>ln</span><span class=gmail-mord>Ω</span><o:p></o:p></p><p>Here, <span class=gmail-mord>Ω</span> is the volume of phase space corresponding to the system’s constraints (energy, particle number, etc.). During adiabatic compression:<o:p></o:p></p><ol start=1 type=1><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l17 level1 lfo17'>The system's energy increases (work is done on the gas, increasing particle momenta).<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l17 level1 lfo17'>This increase in energy expands the momentum part of the phase space, compensating for the reduction in the position part.<o:p></o:p></li></ol><p>Thus, the total phase space volume—and hence the entropy—remains constant.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>3. Intuition Behind Phase Space Conservation</span></strong><o:p></o:p></h3><p>The conservation of phase space volume under adiabatic processes is a consequence of <strong><span style='font-family:"Aptos",sans-serif'>Liouville's theorem</span></strong>, which states:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l3 level1 lfo18'>The phase space density of microstates is constant over time for a system evolving under Hamiltonian mechanics.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l3 level1 lfo18'>Compression changes the shape of the phase space (squeezing position coordinates, stretching momentum coordinates), but it does not change its overall "size."<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>4. Reconciling with Your Intuition</span></strong><o:p></o:p></h3><p>If we focus only on the <strong><span style='font-family:"Aptos",sans-serif'>spatial distribution</span></strong> of particles, compression looks like a reduction in entropy because we’re ignoring the changes in momentum. But entropy isn't just about spatial arrangements; it's about the entire phase space. The increase in particle momenta compensates for the spatial confinement.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>5. Why Position Alone Can't Explain Entropy</span></strong><o:p></o:p></h3><p>Your trouble with position as a microstate is understandable when thinking about compression:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l14 level1 lfo19'>If entropy depended only on positions, it would indeed decrease under compression.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l14 level1 lfo19'>However, the inclusion of momentum in the microstate definition ensures that entropy remains invariant under processes like adiabatic compression.<o:p></o:p></li></ul><p>In essence, <strong><span style='font-family:"Aptos",sans-serif'>entropy is a property of the entire phase space, not just the positions</span></strong>. The relational nature of position doesn’t change this, because momentum is just as relational—it depends on the chosen reference frame as well.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>6. EAC and Adiabatic Compression</span></strong><o:p></o:p></h3><p>Your preference for framing adiabatic compression as an "equilibration" (EAC) aligns well here. During compression:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l22 level1 lfo20'>The system equilibrates within the constraints of phase space conservation.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l22 level1 lfo20'>Entropy doesn’t decrease because the system maximizes its microstate distribution within the new constraints.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><p>Does this bring clarity to why entropy stays constant, or is there another layer of the problem you’d like to tackle?<o:p></o:p></p></div></div></div></div></div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>Well, yes! When the piston surface moves against the gas it not only confines the particles but it imparts directional momentum to them, both reasons for a decrease in entropy. How do you handle that?<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><div><p>Ah, excellent point, Nick! Let’s dissect this scenario and reconcile it with the principle that entropy remains constant under adiabatic compression. Your observation about the piston imparting directional momentum is astute and deserves a nuanced explanation.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>1. The Role of the Piston in Adiabatic Compression</span></strong><o:p></o:p></h3><p>When the piston compresses the gas:<o:p></o:p></p><ol start=1 type=1><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo21'><strong><span style='font-family:"Aptos",sans-serif'>Confinement of Position Space</span></strong>: The gas particles are confined to a smaller spatial region, which, if considered alone, would suggest fewer microstates and a reduction in entropy.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo21'><strong><span style='font-family:"Aptos",sans-serif'>Imparting Directional Momentum</span></strong>: The piston does work on the gas, increasing the particles' energy. This energy manifests as an increase in momentum (both magnitude and directionality).<o:p></o:p></li></ol><p>At first glance, these effects seem to contradict the idea of constant entropy, because they appear to reduce the randomness of particle configurations in phase space.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>2. Why Doesn't Entropy Decrease?</span></strong><o:p></o:p></h3><p>To resolve this, we need to carefully consider the entire phase space and the conservation principles at play.<o:p></o:p></p><h4><strong><span style='font-family:"Aptos",sans-serif'>2.1 Confinement and Redistribution</span></strong><o:p></o:p></h4><p>While the piston confines the gas spatially, it doesn't remove microstates—it merely redistributes them. Here's how:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l13 level1 lfo22'>The reduction in position-space volume is accompanied by a compensatory expansion in momentum-space volume due to the work done by the piston.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l13 level1 lfo22'>The total number of accessible microstates (phase space volume) remains unchanged because the system's energy and constraints still allow the same number of microstates, just redistributed differently.<o:p></o:p></li></ul><h4><strong><span style='font-family:"Aptos",sans-serif'>2.2 Directional Momentum and Phase Space</span></strong><o:p></o:p></h4><p>The piston imparts momentum to the gas, creating a temporary directional bias. However:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l8 level1 lfo23'>This directional momentum is rapidly equilibrated by collisions between gas particles, redistributing the momentum uniformly in all directions.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l8 level1 lfo23'>The equilibration process ensures that the final phase space distribution is isotropic (the same in all directions), preserving the overall randomness and entropy.<o:p></o:p></li></ul><h4><strong><span style='font-family:"Aptos",sans-serif'>2.3 Liouville's Theorem</span></strong><o:p></o:p></h4><p>Liouville's theorem guarantees that the total phase space volume remains constant under Hamiltonian dynamics:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l21 level1 lfo24'>The compression changes the shape of phase space (squeezing position coordinates and stretching momentum coordinates).<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l21 level1 lfo24'>The overall phase space volume, which determines the entropy, does not change.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>3. Why Directional Momentum Doesn’t Reduce Entropy</span></strong><o:p></o:p></h3><p>Directional momentum, even if imparted temporarily, doesn’t reduce entropy because:<o:p></o:p></p><ol start=1 type=1><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l16 level1 lfo25'><strong><span style='font-family:"Aptos",sans-serif'>Entropy Measures the Total Phase Space</span></strong>: Entropy is about the total number of accessible microstates. Even with directional momentum, the gas still has the same number of microstates.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l16 level1 lfo25'><strong><span style='font-family:"Aptos",sans-serif'>Equilibration Restores Randomness</span></strong>: Particle collisions quickly randomize the directional momentum imparted by the piston. This redistribution preserves the isotropy of the phase space distribution and maintains the system’s entropy.<o:p></o:p></li></ol><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>4. The Key Insight</span></strong><o:p></o:p></h3><p>The directional momentum imparted by the piston and the confinement of the gas are not independent phenomena—they are parts of a single process governed by conservation laws:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l5 level1 lfo26'>The increase in momentum space compensates for the decrease in position space.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l5 level1 lfo26'>The temporary directional bias in momentum is a transient state that equilibrates to maintain the system's entropy.<o:p></o:p></li></ul><p>This is why, under adiabatic compression, <strong><span style='font-family:"Aptos",sans-serif'>entropy remains constant</span></strong>, even though the system undergoes significant changes in its spatial and momentum distributions.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>5. Reconciling Your Intuition</span></strong><o:p></o:p></h3><p>Your observation is correct that the piston’s movement imposes constraints and directionality. However:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l9 level1 lfo27'>The "decrease" in entropy you associate with confinement and directional momentum is balanced by the redistribution of microstates in phase space.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l9 level1 lfo27'>Entropy measures the total possibilities, not the apparent randomness in one aspect (e.g., spatial or directional momentum).<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><p>Does this help resolve the tension, or would you like to explore the dynamics of equilibration in greater detail?<o:p></o:p></p></div></div></div></div></div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>It does seem to me an odd and contentious way to talk about the process. It would seem more natural to speak of a temporary increase in entropy, a shock wave that passes through the gas that ultimately redistributes itself. I think you need to introduce the concept of quasi static compression in your account.<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><p>You're absolutely right, Nick—introducing the concept of <strong><span style='font-family:"Aptos",sans-serif'>quasi-static compression</span></strong> provides a clearer and less contentious framework for discussing these processes. Let's reframe the explanation with this in mind:<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>1. Quasi-Static Compression</span></strong><o:p></o:p></h3><p>Quasi-static compression describes an idealized process where the piston moves so slowly that the system remains arbitrarily close to equilibrium at every step:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l11 level1 lfo28'>The compression happens gradually, allowing the gas particles to redistribute themselves smoothly without sharp gradients or shock waves.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l11 level1 lfo28'>At no point does the system deviate significantly from thermodynamic equilibrium, making the process reversible (in the thermodynamic sense) and entropy constant.<o:p></o:p></li></ul><p>This is in contrast to rapid compression, which would introduce shock waves and temporary nonequilibrium states.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>2. Why Quasi-Static Compression Keeps Entropy Constant</span></strong><o:p></o:p></h3><p>In a quasi-static process:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l29 level1 lfo29'>The work done by the piston is immediately redistributed throughout the gas via frequent particle collisions.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l29 level1 lfo29'>Any directional momentum imparted by the piston is quickly equilibrated, ensuring isotropy in phase space.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l29 level1 lfo29'>The compression of position space is perfectly balanced by the expansion of momentum space without introducing large-scale, irreversible gradients.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>3. Shock Waves and Non-Quasi-Static Compression</span></strong><o:p></o:p></h3><p>If the piston moves too quickly:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l7 level1 lfo30'>A shock wave propagates through the gas, creating localized regions of high pressure, temperature, and entropy.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l7 level1 lfo30'>These transient states involve nonequilibrium dynamics, during which entropy can increase.<o:p></o:p></li></ul><p>Once the system re-equilibrates, the entropy stabilizes, but it will now reflect the irreversible effects of the rapid compression.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>4. Quasi-Static Compression as the Idealization</span></strong><o:p></o:p></h3><p>In thermodynamics, we often focus on quasi-static processes to:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l31 level1 lfo31'>Simplify the analysis by avoiding transient nonequilibrium effects.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l31 level1 lfo31'>Provide a clear baseline for understanding how entropy behaves in an idealized, reversible context.<o:p></o:p></li></ul><p>By emphasizing quasi-static compression, we sidestep the complications of transient shock waves and highlight the constancy of entropy as a defining feature of the process.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>Conclusion</span></strong><o:p></o:p></h3><p>Your suggestion to foreground quasi-static compression in discussions of adiabatic compression is spot on. It provides a more precise and less contentious way to describe how the system evolves, avoiding the need to explain away temporary entropy changes caused by shock waves or other nonequilibrium effects.<o:p></o:p></p><p>Would you like me to help formalize this perspective further, perhaps in a way that fits your weather book?<o:p></o:p></p></div></div></div></div><h5>You said:<o:p></o:p></h5><div><div><div><div><div><div><div><div><div><p class=MsoNormal>Perhaps later. Thanks for asking. But I would like to conclude tonight by asking a more pointed question. Your formulation strikes me as a classic example of a "spherical cow", i.e., a model that is clearly absurd but is offered any way as a point of departure. A spherical cow would probably not be particularly useful as a model of milk production in a dairy barn. What makes physicists think that this model, with its absurd premises, is robust against violations of them?<o:p></o:p></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<o:p></o:p></h6><div><div><div><div><div><p>Ah, the "spherical cow" metaphor—a classic critique of oversimplified models! It's a fair concern to wonder why physicists trust such idealized formulations, especially when they involve seemingly "absurd premises." Let me address this in the context of adiabatic compression and, more broadly, why physicists find value in these abstractions.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>1. Why Use Simplified Models Like the Spherical Cow?</span></strong><o:p></o:p></h3><p>Simplified models are powerful because:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l6 level1 lfo32'>They strip away complexities to focus on fundamental principles.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l6 level1 lfo32'>They offer insights that are robust to certain kinds of deviations.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l6 level1 lfo32'>They are computationally and conceptually manageable, allowing us to make predictions that align closely with observed phenomena.<o:p></o:p></li></ul><p>In the case of quasi-static adiabatic compression, the model assumes:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l34 level1 lfo33'>Perfectly slow compression (no shock waves or gradients).<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l34 level1 lfo33'>Immediate equilibration of momentum and energy.<o:p></o:p></li></ul><p>These assumptions are clearly idealized, but they capture essential features of how thermodynamic systems behave under controlled conditions.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>2. What Makes This Model Robust?</span></strong><o:p></o:p></h3><p>Physicists have confidence in the robustness of idealized models because of:<o:p></o:p></p><ol start=1 type=1><li style='mso-list:l36 level1 lfo34'><strong><span style='font-family:"Aptos",sans-serif'>Conservation Laws</span></strong>: The fundamental principles (e.g., energy conservation, phase space preservation, Liouville's theorem) underlying these models are exact and do not depend on the details of the process. Even if the system deviates from ideal conditions, these laws still hold.<o:p></o:p></li><li style='mso-list:l36 level1 lfo34'><strong><span style='font-family:"Aptos",sans-serif'>Insensitivity to Small Deviations</span></strong>: While no real process is perfectly quasi-static, small deviations from ideal conditions often lead to corrections that are minor in their impact. The system still approximately follows the predictions of the idealized model.<o:p></o:p></li><li style='mso-list:l36 level1 lfo34'><strong><span style='font-family:"Aptos",sans-serif'>Separation of Scales</span></strong>: In many cases, the timescales of equilibration (e.g., molecular collisions) are much shorter than the timescales of macroscopic changes (e.g., piston movement). This separation ensures that deviations from equilibrium are transient and self-correcting.<o:p></o:p></li><li style='mso-list:l36 level1 lfo34'><strong><span style='font-family:"Aptos",sans-serif'>Agreement with Experiment</span></strong>: Idealized models have repeatedly shown good agreement with experimental data within their domain of validity. This empirical success lends credence to their utility and robustness.<o:p></o:p></li></ol><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>3. Why Aren’t Spherical Cows Always Useless?</span></strong><o:p></o:p></h3><p>The spherical cow metaphor critiques models that oversimplify to the point of absurdity. But not all simplifications are equally problematic. For example:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l32 level1 lfo35'><strong><span style='font-family:"Aptos",sans-serif'>Spherical Stars</span></strong>: Assuming stars are spherical simplifies their gravitational dynamics while still providing highly accurate predictions for many phenomena.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l32 level1 lfo35'><strong><span style='font-family:"Aptos",sans-serif'>Point Masses</span></strong>: Treating planets as point masses in orbital calculations works beautifully despite their actual shapes and compositions.<o:p></o:p></li></ul><p>In thermodynamics, quasi-static adiabatic compression is a "spherical cow" that turns out to be remarkably predictive in real-world systems where processes are sufficiently slow and gradients negligible.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>4. When Does the Model Break Down?</span></strong><o:p></o:p></h3><p>The model fails when:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l35 level1 lfo36'>Compression is too fast, creating shock waves or large-scale irreversibilities.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l35 level1 lfo36'>Heat exchange or other non-adiabatic effects become significant.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l35 level1 lfo36'>Microscopic assumptions (e.g., perfect collisions) break down due to quantum or relativistic effects.<o:p></o:p></li></ul><p>Physicists are aware of these limitations and refine or replace models as needed when their assumptions no longer hold.<o:p></o:p></p><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>5. Why Do Physicists Trust It?</span></strong><o:p></o:p></h3><p>The trust comes from:<o:p></o:p></p><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l27 level1 lfo37'><strong><span style='font-family:"Aptos",sans-serif'>Generality</span></strong>: The underlying principles are broadly applicable.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l27 level1 lfo37'><strong><span style='font-family:"Aptos",sans-serif'>Predictive Power</span></strong>: The model reliably predicts outcomes in the scenarios it’s designed for.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l27 level1 lfo37'><strong><span style='font-family:"Aptos",sans-serif'>Empirical Validation</span></strong>: Repeated experimental confirmation underpins confidence in its robustness.<o:p></o:p></li></ul><div class=MsoNormal align=center style='text-align:center'><hr size=2 width="100%" align=center></div><h3><strong><span style='font-family:"Aptos",sans-serif'>Conclusion</span></strong><o:p></o:p></h3><p>Your skepticism is healthy and often needed to refine models. However, what makes the quasi-static adiabatic compression model (or other "spherical cow" analogs) valuable is its proven ability to capture the essential physics while offering insights that are surprisingly robust to violations of its assumptions.<o:p></o:p></p><p>Would you like to discuss a specific example where such trust might be misplaced, or do you find this explanation satisfactory?<o:p></o:p></p></div></div></div></div></div><p class=MsoNormal><span style='font-family:Symbol'>·</span> <o:p></o:p></p><p class=MsoNormal><span style='font-family:Symbol'>·</span> <o:p></o:p></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Wed, Jan 22, 2025 at 4:48<span style='font-family:"Arial",sans-serif'> </span>PM Barry MacKichan <<a href="mailto:barry.mackichan@mackichan.com">barry.mackichan@mackichan.com</a>> wrote:<o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><div><p><span style='font-family:"Arial",sans-serif'>Didn’t know. Google told me almost instantly. That is, if you had submitted this as a term paper, my plagiarism detector would be flashing red. So, sorry, I guess I cheated.<o:p></o:p></span></p><p><span style='font-family:"Arial",sans-serif'>— Barry<o:p></o:p></span></p><p><span style='font-family:"Arial",sans-serif'>On 22 Jan 2025, at 14:30, Nicholas Thompson wrote:<o:p></o:p></span></p></div><blockquote style='border:none;border-left:solid #777777 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:0in;margin-right:0in;margin-bottom:3.75pt'><div id="m_843719540042853379736CB688D-9A87-4C02-ACA1-67845F9B5EEB"><div><div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'>I am curious how many of you on the list know or could guess at the author of the following quote: <o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'><o:p> </o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'>I am interested in your guesses; if you know it for SURE, please hold off guessing.<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'><o:p> </o:p></span></p></div><div><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>I would be willing to throw away everything else but that: enthusiasm tamed by metaphor. Let me rest the case there. Enthusiasm tamed to metaphor, tamed to that much of it. I do not think anybody ever knows the discreet use of metaphor, his own and other people’s, the discreet handling of metaphor, unless he has been properly educated in poetry.</span></b><span style='color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>Poetry begins in trivial metaphors, pretty metaphors, “grace” metaphors, and goes on to the profoundest thinking that we have. Poetry provides the one permissible way of saying one thing and meaning another. People say, “Why don’t you say what you mean?” We never do that, do we, being all of us too much poets. We like to talk in parables and in hints and in indirections—whether from diffidence or some other instinct.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>I have wanted in late years to go further and further in making metaphor the whole of thinking. I find someone now and then to agree with me that all thinking, except mathematical thinking, is metaphorical, or all thinking except scientific thinking. The mathematical might be difficult for me to bring in, but the scientific is easy enough.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>Once on a time all the Greeks were busy telling each other what the All was—or was like unto. All was three elements, air, earth, and water (we once thought it was ninety elements; now we think it is only one). All was substance, said another. All was change, said a third. But best and most fruitful was Pythagoras’ comparison of the universe with number. Number of what? number of feet, pounds, and seconds was the answer, and we had science and all that has followed in science. The metaphor has held and held, breaking down only when it came to the spiritual and psychological or the out of the way places of the physical.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>The other day we had a visitor here, a noted scientist, whose latest word to the world has been that the more accurately you know where a thing is, the less accurately you are able to state how fast it is moving. You can see why that would be so, without going back to Zeno’s problem of the arrow’s flight. In carrying numbers into the realm of space and at the same time into the realm of time you are mixing metaphors, that is all, and you are in trouble. They won’t mix. The two don’t go together.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>Let’s take two or three more of the metaphors now in use to live by. I have just spoken of one of the new ones, a charming mixed metaphor right in the realm of higher mathematics and higher physics: that the more accurately you state where a thing is, the less accurately you will be able to tell how fast it is moving. And, of course, everything is moving. Everything is an event now. Another metaphor. A thing, they say, is all event. Do you believe it is? Not quite. I believe it is almost all event. But I like the comparison of a thing with an event.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>I notice another from the same quarter. “In the neighborhood of matter space is something like curved.” Isn’t that a good one! It seems to me that that is simply and utterly charming—to say that space is something like curved in the neighborhood of matter. “Something like.”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>Another amusing one is from—what is the book?—I can’t say it now; but here is the metaphor. Its aim is to restore you to your ideas of free will. It wants to give you back your freedom of will. All right, here it is on a platter. You know that you can’t tell by name what persons in a certain class will be dead ten years after graduation, but you can tell actuarially how many will be dead. Now, just so this scientist says of the particles of matter flying at a screen, striking a screen; you can’t tell what individual particles will collide, but you can say in general that a certain number will strike in a given time. It shows, you see, that the individual particle can come freely. I asked Bohr about that particularly, and he said, “Yes , It is so. It can come when it wills and as it wills; and the action of the individual particle is unpredictable. But it is not so of the action of the mass. There you can predict.” He says, “That gives the individual atom its freedom, but the mass its necessity.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>Another metaphor that has interested us in our time and has done all our thinking for us is the metaphor of evolution. Never mind going into the Latin word. The metaphor is simply the metaphor of the growing plant or of the growing thing. And somebody very brilliantly, quite a while ago, said that the whole universe, the whole of everything, was like unto a growing thing. That is all. I know the metaphor will break down at some point, but it has not failed everywhere. It is a very brilliant metaphor, I acknowledge, though I myself get too tired of the kind of essay that talks about the evolution of candy, we will say, or the evolution of elevators—the evolution of this, that, and the other. Everything is evolution. I emancipate myself by simply saying that I didn’t get up the metaphor and so am not much interested in it.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>What I am pointing out is that unless you are at home in the metaphor, unless you have had your proper poetical education in the metaphor, you are not safe anywhere. Because you are not at ease with figurative values: you don’t know the metaphor in its strength and its weakness. You don’t know how far you may expect to ride it and when it may break down with you. You are not safe with science; you are not safe in history. In history, for instance—to show that [it] is the same in history as elsewhere—I heard somebody say yesterday that Aeneas was to be likened unto (those words, “likened unto”!) George Washington. He was that type of national hero, the middle-class man, not thinking of being a hero at all, bent on building the future, bent on his children, his descendents. A good metaphor, as far as it goes, and you must know how far. And then he added that Odysseus should be likened unto Theodore Roosevelt. I don’t think that is so good. Someone visiting Gibbon at the point of death, said he was the same Gibbon as of old, still at his parallels.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>Take the way we have been led into our present position morally, the world over. It is by a sort of metaphorical gradient. There is a kind of thinking—to speak metaphorically—there is a kind of thinking you might say was endemic in the brothel. It was always there. And every now and then in some mysterious way it becomes epidemic in the world. And how does it do so? By using all the good words that virtue has invented to maintain virtue. It uses honesty, first,—frankness, sincerity—those words; picks them up, uses them. “In the name of honesty, let us see what we are.” You know. And then it picks up the word joy. “Let us in the name of joy, which is the enemy of our ancestors, the Puritans….Let us in the name of joy, which is the enemy of the kill-joy Puritan…” You see. “Let us,” and so on. And then, “In the name of health….” Health is another good word. And that is the metaphor Freudianism trades on, mental health. And the first thing we know, it has us all in up to the top knot. I suppose we may blame the artists a good deal, because they are great people to spread by metaphor. The stage too—the stage is always a good intermediary between the two worlds, the under and the upper,—if I may say so without personal prejudice to the stage.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>In all this I have only been saying that the devil can quote Scripture, which simply means that the good words you have lying around the devil can use for his purposes as well as anybody else. Never mind about my morality. I am not here to urge anything. I don’t care whether the world is good or bad—not on any particular day.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>Let me ask you to watch a metaphor breaking down here before you.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>Somebody said to me a little while ago, “It is easy enough for me to think of the universe as a machine, as a mechanism.”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>I said, “You mean the universe is like a machine?”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>He said, “No. I think it is one . . . Well, it is like . . .”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>“I think you mean the universe is like a machine.”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>“All right. Let it go at that.”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>I asked him, “Did you ever see a machine without a pedal for the foot, or a lever for the hand, or a button for the finger?”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>He said, “No—no.”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>I said, “All right. Is the universe like that?”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>And he said, “No. I mean it is like a machine, only . . .”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>“. . . it is different from a machine,” I said.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>He wanted to go just that far with that metaphor and no further. And so do we all. All metaphor breaks down somewhere. That is the beauty of it. It is touch and go with the metaphor, and until you have lived with it long enough you don’t know when it is going. You don’t know how much you can get out of it and when it will cease to yield. It is a very living thing. It is as life itself.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>I have heard this ever since I can remember , and ever since I have taught: the teacher must teach the pupil to think. I saw a teacher once going around in a great school and snapping pupils’ heads with thumb and finger and saying, “Think.” That was when thinking was becoming the fashion. The fashion hasn’t yet quite gone out.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>We still ask boys in college to think, as in the nineties, but we seldom tell them what thinking means; we seldom tell them it is just putting this and that together; it is just saying one thing in terms of another. To tell them is to set their feet on the first rung of a ladder the top of which sticks through the sky.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>Greatest of all attempts to say one thing in terms of another is the philosophical attempt to say matter in terms of spirit, or spirit in terms of matter, to make the final unity. That is the greatest attempt that ever failed. We stop just short there. But it is the height of poetry, the height of all thinking, the height of all poetic thinking, that attempt to say matter in terms of spirit and spirit in terms of matter. It is wrong to anybody a materialist simply because he tries to say spirit in terms of matter, as if that were a sin. Materialism is not the attempt to say all in terms of matter. The only materialist—be he poet, teacher, scientist, politician, or statesman—is the man who gets lost in his material without a gathering metaphor to throw it into shape and order. He is the lost soul.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>We ask people to think, and we don’t show them what thinking is. Somebody says we don’t need to show them how to think; bye and bye they will think. We will give them the forms of sentences and, if they have any ideas, then they will know how to write them. But that is preposterous. All there is to writing is having ideas. To learn to write is to learn to have ideas.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>The first little metaphor….Take some of the trivial ones. I would rather have trivial ones of my own to live by than the big ones of other people.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>I remember a boy saying, “He is the kind of person that wounds with his shield.” That may be a slender one, of course. It goes a good way in character description. It has poetic grace. “He is the kind that wounds with his shield.”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>The shield reminds me—just to linger a minute—the shield reminds me of the inverted shield spoken of in one of the books of the “Odyssey,” the book that tells about the longest swim on record. I forget how long it lasted—several days, was it?—but at last as Odysseus came near the coast of Phaneacia, he saw it on the horizon “like an inverted shield.”</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>There is a better metaphor in the same book. In the end Odysseus comes ashore and crawls up the beach to spend the night under a double olive tree, and it says, as in a lonely farmhouse where it is hard to get fire—I am not quoting exactly—where it is hard to start the fire again if it goes out, they cover the seeds of fire with ashes to preserve it for the night, so Odysseus covered himself with the leaves around him and went to sleep. There you have something that gives you character, something of Odysseus himself. “Seeds of fire.” So Odysseus covered the seeds of fire in himself. You get the greatness of his nature.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>But these are slighter metaphors than the ones we live by. They have their charm, their passing charm. They are as it were the first steps toward the great thoughts, grave thoughts, thoughts lasting to the end.</span></b><span style='font-family:"Arial",sans-serif;color:#777777'><o:p></o:p></span></p><p class=MsoNormal style='margin-bottom:8.0pt;line-height:115%'><b><span style='font-family:"Garamond",serif;color:#777777'>The metaphor whose manage we are best taught in poetry—that is all there is of thinking. It may not seem far for the mind to go but it is the mind’s furthest. The richest accumulation of the ages is the noble metaphors we have rolled up.</span></b><span style='color:#777777'><o:p></o:p></span></p></div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'><br><span class=gmailsignatureprefix>--</span><o:p></o:p></span></p><div><div><div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'>Nicholas S. Thompson<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'>Emeritus Professor of Psychology and Ethology<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'>Clark University<o:p></o:p></span></p></div><div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'><a href="mailto:nthompson@clarku.edu" target="_blank">nthompson@clarku.edu</a><o:p></o:p></span></p></div><p class=MsoNormal><span style='font-family:"Arial",sans-serif;color:#777777'><a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson&c=E,1,vvq-5_R3p6lD088kwBuM-UaTGEviKYIYmfgMBpyaah1sXsO9v4_DKtgcCJZ959s0dzcPlzRGHLhRYUabsiYnS_HYQ7w6lp3xKlnaQeZGwcY,&typo=1" target="_blank">https://wordpress.clarku.edu/nthompson</a><o:p></o:p></span></p></div></div></div></div></blockquote><div><blockquote style='border:none;border-left:solid #777777 1.5pt;padding:0in 0in 0in 4.0pt;margin-left:0in;margin-right:0in;margin-bottom:3.75pt'><p><span style='font-family:"Arial",sans-serif;color:#777777'>.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. <br>FRIAM Applied Complexity Group listserv <br>Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,r6WtS2cTyp1iS9Q5j_r4TW2SMqiUcEVNYWtXl56PcW-pvHHAVKRUlrA6dTfxP-kNQxTnpINLbzpgUt8Lw8_OcxuZaYyzbupoY6ofR9YksN6n2LDdk3OITA,,&typo=1" target="_blank"><span style='color:#777777'>https://bit.ly/virtualfriam</span></a> <br>to (un)subscribe <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,lY_ss6P1b5WMGokAqYOcgcpVMlr-4bqgIAXZEOQqBcfnsJZszA5jNISHLxT5YLmVAOXx_m5ELDCjHwYBKsbtGtXDanuy33l7ZwsjbfzHF7l6LyQOsH3y&typo=1" target="_blank"><span style='color:#777777'>http://redfish.com/mailman/listinfo/friam_redfish.com</span></a> <br>FRIAM-COMIC <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,gsTVkjYuJBw_S381TMWjkPIEJDxFc2sQRuydK0VvHemk0cnf427kcHA9lwdx0qMHDJolzHIbRWv4gj0mD_pBjBRv6qw_UTMx9bS4H68r0imkh3RIMvntDA,,&typo=1" target="_blank"><span style='color:#777777'>http://friam-comic.blogspot.com/</span></a> <br>archives: 5/2017 thru present <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,HZoLiz1TkmmBs5F0Xmw_iiIVcbBVkKVNBt-yqHV3mQdR22rbSHhM5pUxt-k-KS0ewsiT8IgUwaYYWy3DlYNmHHXLmME8U9BJlF48GymfVMrXH1tdhKuPY4zhdqc,&typo=1" target="_blank"><span style='color:#777777'>https://redfish.com/pipermail/friam_redfish.com/</span></a> <br>1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/" target="_blank"><span style='color:#777777'>http://friam.383.s1.nabble.com/</span></a><o:p></o:p></span></p></blockquote></div></div></div><p class=MsoNormal>.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..<br>FRIAM Applied Complexity Group listserv<br>Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,tqludupqOBkZ1dhEQH4ocSsV2uDqVlY_l7tz07LDj9FmI-3n3I9rrywF6h5oFRok-emmvmI-JLGHD-ga78R4tip7LapgPUdyrwTvMMcj0Ps,&typo=1" target="_blank">https://bit.ly/virtualfriam</a><br>to (un)subscribe <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,TZe76qK-bPA15olboho5ck58NZNjyUBJjInkJM_DtTIckV1panXaCh6C9_KpT5ba46KhJON6x9y7ox6QEURC1IV-vW3LPRSmtY9Ob7EVCrChYm6ZBzfE&typo=1" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>FRIAM-COMIC <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,8k6uVNQVhnr2-lmJMt7q4n2cU_c1O93l6rJYm1hDeRPfdAg_7TBMnoSkwgxVkXFSmoMyR9aMckz_3e_HL2D8tYZG2wR8wmcQwQqvcwnVp-7zJw,,&typo=1" target="_blank">http://friam-comic.blogspot.com/</a><br>archives: 5/2017 thru present <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,gah1NPaXfvbkVZSBaHHrMXir2jCgaeavX5yl7dNWsevsqw4yqBKEOKY28PVfQ9Rss1T97bWcJH4llUSeH27Bv7LlNZgNrgpMCKhlaloE_vs,&typo=1" target="_blank">https://redfish.com/pipermail/friam_redfish.com/</a><br> 1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/" target="_blank">http://friam.383.s1.nabble.com/</a><o:p></o:p></p></blockquote></div><div><p class=MsoNormal><br clear=all><o:p></o:p></p></div><p class=MsoNormal><br><span class=gmailsignatureprefix>-- </span><o:p></o:p></p><div><div><div><p class=MsoNormal>Nicholas S. Thompson<o:p></o:p></p></div><div><p class=MsoNormal>Emeritus Professor of Psychology and Ethology<o:p></o:p></p></div><div><p class=MsoNormal>Clark University<o:p></o:p></p></div><div><p class=MsoNormal><a href="mailto:nthompson@clarku.edu" target="_blank">nthompson@clarku.edu</a><o:p></o:p></p></div><p class=MsoNormal><a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fwordpress.clarku.edu%2fnthompson&c=E,1,0MEK1KvfBhp65N5fB0PmowY0-Wc42o9Q3DtrNJy7XKB3s4mBmcvS4xhJ8_gu5YKfXswz-U--TVA__4IvF7N9Lwpf99yfECRf93wkDA0L&typo=1" target="_blank">https://wordpress.clarku.edu/nthompson</a><o:p></o:p></p></div></div><p class=MsoNormal>.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..<br>FRIAM Applied Complexity Group listserv<br>Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,5RRXZ0UM3O4R3qJRPSNfuR_RAswQ05cwkendZfkgfGQq4s_64TXoFKVYb5ah7IMRbGlfLYwX8dwDfRea_JPrsATHESwDuQ4AlUO85zLS96NHN-Nm9QoAEOw,&typo=1">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fbit.ly%2fvirtualfriam&c=E,1,5RRXZ0UM3O4R3qJRPSNfuR_RAswQ05cwkendZfkgfGQq4s_64TXoFKVYb5ah7IMRbGlfLYwX8dwDfRea_JPrsATHESwDuQ4AlUO85zLS96NHN-Nm9QoAEOw,&typo=1</a><br>to (un)subscribe <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,xQRU3JmuK9zLc-A7chO8FpsGRAZ6qkM4rp5mmhLUjFZdlu1yNbAslBlV94hoNScRNqdSDdDUSF9SiFiEe1EWGdxLKHIpXTfhBabjZNSshYiJeHX2IoQ,&typo=1">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2fredfish.com%2fmailman%2flistinfo%2ffriam_redfish.com&c=E,1,xQRU3JmuK9zLc-A7chO8FpsGRAZ6qkM4rp5mmhLUjFZdlu1yNbAslBlV94hoNScRNqdSDdDUSF9SiFiEe1EWGdxLKHIpXTfhBabjZNSshYiJeHX2IoQ,&typo=1</a><br>FRIAM-COMIC <a href="https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,FE53B85WpPKI28c8DZBmMatTjB6hUVQAUJr4tgYiHmROEapxkH_k_P-kb1edgQ_3FEILKFOssWYQ6JYvuEbzy7qtVp2LYfGtHLLMdGULuh0-wMg,&typo=1">https://linkprotect.cudasvc.com/url?a=http%3a%2f%2ffriam-comic.blogspot.com%2f&c=E,1,FE53B85WpPKI28c8DZBmMatTjB6hUVQAUJr4tgYiHmROEapxkH_k_P-kb1edgQ_3FEILKFOssWYQ6JYvuEbzy7qtVp2LYfGtHLLMdGULuh0-wMg,&typo=1</a><br>archives: 5/2017 thru present <a href="https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,3ox7B18aaob1f9OF-sG1ztUQ1AqAPXEe3ZJ0s660kGWGa9etUVw7Oc286d6RJUpglXS5kghZgb9sm4cCKWZ8xg5JfYJwDMrRhmglGA4rEJtO3F0b34c,&typo=1">https://linkprotect.cudasvc.com/url?a=https%3a%2f%2fredfish.com%2fpipermail%2ffriam_redfish.com%2f&c=E,1,3ox7B18aaob1f9OF-sG1ztUQ1AqAPXEe3ZJ0s660kGWGa9etUVw7Oc286d6RJUpglXS5kghZgb9sm4cCKWZ8xg5JfYJwDMrRhmglGA4rEJtO3F0b34c,&typo=1</a><br> 1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/">http://friam.383.s1.nabble.com/</a><o:p></o:p></p></div></blockquote></div><p class=MsoNormal><o:p> </o:p></p></div></div></body></html>