<!DOCTYPE html><html><head><title></title><style type="text/css">p.MsoNormal,p.MsoNoSpacing{margin:0}</style></head><body><div style="font-family:Arial;">If submitted as the student's own work — definitely.<br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;">My college prof friends, because Dean's are so afraid of holding students accountable, have modified syllabi to note that a student may use an LLM, but must append a minimum one-page argument for why the LLM should be believed, disbelieved, or answer interpreted, based on what was learned in class. They can't use the LLM for this, because it was not in class.<br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;">davew<br></div><div style="font-family:Arial;"><br></div><div style="font-family:Arial;"><br></div><div>On Sun, Jan 26, 2025, at 4:03 PM, Eric Charles wrote:<br></div><blockquote type="cite" id="qt" style=""><div dir="ltr"><div>Nick was a college professor much longer than I was... as were several others on this list... <br></div><div><br></div><div>Nick (and those others), what is your confidence that the interaction, if submitted as a paper, would or would not violate the plagiarism standards you would have held a student to? <br></div><div><br></div><div><div dir="ltr" class="qt-gmail_signature"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div><span style="color:rgb(34, 34, 34);">Best,<br>Eric<br></span></div><div><br></div></div><div dir="ltr"><a href="mailto:echarles@american.edu" target="_blank"></a><br></div></div></div></div></div></div><div><br></div></div><div><br></div><div class="qt-gmail_quote qt-gmail_quote_container"><div dir="ltr" class="qt-gmail_attr">On Thu, Jan 23, 2025 at 1:05 AM Marcus Daniels <<a href="mailto:marcus@snoutfarm.com">marcus@snoutfarm.com</a>> wrote:<br></div><blockquote class="qt-gmail_quote" style="margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204, 204, 204);padding-left:1ex;"><div lang="EN-US" style="overflow-wrap:break-word;"><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">In the sense that any synthesis of a read text is also plagiarism. Is copying a skill plagiarism? Doesn’t that make education ridiculous?<u></u><u></u></span><br></p><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><u></u> <u></u></span><br></p><div style="border-right-width:medium;border-right-style:none;border-right-color:currentcolor;border-bottom-width:medium;border-bottom-style:none;border-bottom-color:currentcolor;border-left-width:medium;border-left-style:none;border-left-color:currentcolor;border-top-width:1pt;border-top-style:solid;border-top-color:rgb(181, 196, 223);padding-top:3pt;padding-right:0in;padding-bottom:0in;padding-left:0in;"><p class="qt-MsoNormal" style="margin-bottom:12pt;"><b><span style="color:black;"><span class="size" style="font-size:12pt;">From: </span></span></b><span style="color:black;"><span class="size" style="font-size:12pt;">Friam <<a href="mailto:friam-bounces@redfish.com" target="_blank">friam-bounces@redfish.com</a>> on behalf of Eric Charles <<a href="mailto:eric.phillip.charles@gmail.com" target="_blank">eric.phillip.charles@gmail.com</a>><br><b>Date: </b>Wednesday, January 22, 2025 at 8:54 PM<br><b>To: </b>The Friday Morning Applied Complexity Coffee Group <<a href="mailto:friam@redfish.com" target="_blank">friam@redfish.com</a>>, Jon Zingale <<a href="mailto:jonzingale@gmail.com" target="_blank">jonzingale@gmail.com</a>>, Alex Rasmus <<a href="mailto:alex.m.rasmus@gmail.com" target="_blank">alex.m.rasmus@gmail.com</a>>, Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" target="_blank">thompnickson2@gmail.com</a>><br><b>Subject: </b>Re: [FRIAM] metaphor<u></u><u></u></span></span></p></div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">I definitely did not read the whole thing... but it seemed pretty coherent... and I am glad you are having fun with the plagiarism bots. <u></u><u></u></span><br></p></div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><u></u> <u></u></span><br></p></div><div><div><div><div><div><div><p class="qt-MsoNormal"><span style="color:rgb(34, 34, 34);"><span class="size" style="font-size:11pt;">Best,<br>Eric<br><br>-----------</span></span><span class="size" style="font-size:11pt;"><u></u><u></u></span></p><div><div><p class="qt-MsoNormal"><span style="color:rgb(34, 34, 34);"><span class="size" style="font-size:11pt;">Eric P. Charles, Ph.D.<br>Head, Data Analytics and Delivery<br>Human Capital Data Modernization and Management (HCDMM)<u></u><u></u></span></span></p></div><div><p class="qt-MsoNormal"><span style="color:rgb(34, 34, 34);"><span class="size" style="font-size:11pt;">Office of Personnel Management (OPM)<u></u><u></u></span></span><br></p></div><div><p class="qt-MsoNormal"><span style="color:rgb(34, 34, 34);"><span class="size" style="font-size:11pt;">American University - Adjunct Instructor<u></u><u></u></span></span><br></p></div></div></div></div></div></div></div></div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><u></u> <u></u></span><br></p></div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><u></u> <u></u></span><br></p><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">On Wed, Jan 22, 2025 at 11:42 PM Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" target="_blank">thompnickson2@gmail.com</a>> wrote:<u></u><u></u></span><br></p></div><blockquote style="border-top-width:medium;border-top-style:none;border-top-color:currentcolor;border-right-width:medium;border-right-style:none;border-right-color:currentcolor;border-bottom-width:medium;border-bottom-style:none;border-bottom-color:currentcolor;border-left-width:1pt;border-left-style:solid;border-left-color:rgb(204, 204, 204);padding-top:0in;padding-right:0in;padding-bottom:0in;padding-left:6pt;margin-left:4.8pt;margin-right:0in;"><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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.<u></u><u></u></span><br></p></div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><u></u> <u></u></span><br></p></div><div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">"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?"<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></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:<u></u><u></u><br></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.<u></u><u></u><br></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.<u></u><u></u><br></p><p>So, your professor's statement captures part of the concept, but it's simplified. Entropy involves distributions across <i><span class="font" style="font-family:Calibri, sans-serif;">all</span></i> relevant variables in a system—not just the spatial ones. Does that align with what you're exploring?<u></u><u></u><br></p></div></div></div></div></div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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?<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></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.<u></u><u></u><br></p><p>Entropy, at its core, relates to the <i><span class="font" style="font-family:Calibri, sans-serif;">equilibration of microstates</span></i>—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.<u></u><u></u><br></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 <i><span class="font" style="font-family:Calibri, sans-serif;">result</span></i> of the system seeking equilibrium by exploring all accessible microstates—not the defining feature of entropy.<u></u><u></u><br></p><p>In essence, entropy is the measure of <i><span class="font" style="font-family:Calibri, sans-serif;">possibilities</span></i>, 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.<u></u><u></u><br></p></div></div></div></div></div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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?<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></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.<u></u><u></u><br></p><h3>1. <b><span class="font" style="font-family:Calibri, sans-serif;">Is Position a Microstate?</span></b><u></u><u></u><br></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 (x,y,z) and the momenta (px,py,pz) 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.<u></u><u></u><br></p><h3>2. <b><span class="font" style="font-family:Calibri, sans-serif;">Does Momentum Fully Capture Position?</span></b><u></u><u></u><br></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.<u></u><u></u><br></p><h3>3. <b><span class="font" style="font-family:Calibri, sans-serif;">Why the Confusion?</span></b><u></u><u></u><br></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.<u></u><u></u><br></p><h3>4. <b><span class="font" style="font-family:Calibri, sans-serif;">Reconciling the Contradiction</span></b><u></u><u></u><br></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.<u></u><u></u><br></p><p>Would this clarification align with your understanding?<u></u><u></u><br></p></div></div></div></div></div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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.<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></h6><div><div><div><div><div><p>Absolutely, Nick—let’s unpack that further.<u></u><u></u><br></p><h3><b><span class="font" style="font-family:Calibri, sans-serif;">The "Random Placement" Metaphor</span></b><u></u><u></u><br></h3><p>The idea of "random placement" often shows up in simplified explanations of entropy, especially in introductory contexts. For example:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">A gas in a box is said to "spread out" to fill the container, which is often visualized as particles randomly scattering in space.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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.<u></u><u></u></span><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Position's Role in Phase Space</span></b><u></u><u></u><br></h3><p>The deeper truth lies in how position contributes to the <i><span class="font" style="font-family:Calibri, sans-serif;">phase space</span></i> of the system. In classical mechanics:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">A particle's microstate is defined by its position (x,y,z) and momentum (px,py,pz).<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The <i><span class="font" style="font-family:Calibri, sans-serif;">phase space</span></i> is the multidimensional space of all possible combinations of these variables for all particles in the system.<u></u><u></u></span><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Why Phase Space Matters More Than Position Alone</span></b><u></u><u></u><br></h3><p>Entropy is about maximizing the <i><span class="font" style="font-family:Calibri, sans-serif;">volume</span></i> of accessible phase space under the system’s constraints. This means:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">If you only considered positions, you'd ignore a significant portion of the system's microstate diversity—specifically, the momentum degrees of freedom.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Entropy Beyond the Visual Metaphor</span></b><u></u><u></u><br></h3><p>The metaphor of random spatial placement simplifies entropy to the visible world of positions, but entropy fundamentally counts possibilities:<u></u><u></u><br></p><ol start="1" type="1"><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Position Space</span></span></b><span class="size" style="font-size:11pt;">: Particles can occupy different regions of space.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Momentum Space</span></span></b><span class="size" style="font-size:11pt;">: Particles can have various momenta, which significantly increases the number of microstates.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The combination of these spaces—phase space—is what entropy measures.<u></u><u></u></span><br></li></ol><p>So, while random placement is a <i><span class="font" style="font-family:Calibri, sans-serif;">consequence</span></i> 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.<u></u><u></u><br></p><p>Does this deepen the distinction you’re seeking?<u></u><u></u><br></p></div></div></div></div></div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">I understood x, y, and z to be velocity vectors, not positions. Was I wrong?<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></h6><div><div><div><div><div><p>Great question, Nick! Let’s clarify the distinction between <b><span class="font" style="font-family:Calibri, sans-serif;">position vectors</span></b> and <b><span class="font" style="font-family:Calibri, sans-serif;">velocity vectors</span></b> and how they relate to entropy and phase space.<u></u><u></u><br></p><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Position vs. Velocity Vectors</span></b><u></u><u></u><br></h3><ol start="1" type="1"><li><div><b><span class="font" style="font-family:Calibri, sans-serif;">Position Vectors (x,y,z)</span></b><br></div><div>These specify the spatial location of a particle in three-dimensional physical space. For example:<u></u><u></u><br></div></li></ol><ol start="1" type="1"><ul type="circle"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">If a particle is in a box, x,y,z tell you where the particle is inside that box.<u></u><u></u></span><br></li></ul></ol><ol start="2" type="1"><li><div><b><span class="font" style="font-family:Calibri, sans-serif;">Velocity Vectors (vx,vy,vz)</span></b><br></div><div>These specify how fast the particle is moving and in which direction. They are related to momentum (px,py,pz) via the relationship:<u></u><u></u><br></div></li></ol><p class="qt-MsoNormal" style="margin-left:0.5in;"><span class="size" style="font-size:11pt;">p<u></u><u></u></span><br></p></div></div></div></div></div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">=mv<u></u><u></u></span><br></p><div><div><div><div><ol start="2" type="1"><li>where m is the particle’s mass.<u></u><u></u><br></li></ol><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Phase Space and Microstates</span></b><u></u><u></u><br></h3><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">A <b><span class="font" style="font-family:Calibri, sans-serif;">microstate</span></b> in classical mechanics is defined by both the <b><span class="font" style="font-family:Calibri, sans-serif;">position</span></b> (x,y,z) and the <b><span class="font" style="font-family:Calibri, sans-serif;">momentum</span></b> (px,py,pz) of each particle.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Phase space is the multidimensional space that includes all possible combinations of these variables. For N particles, the phase space has 6N dimensions: 3N for positions and 3N for momenta.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Did You Confuse Velocity with Position?</span></b><u></u><u></u><br></h3><p>It sounds like you were interpreting x,y,z as velocity components instead of positions. If that’s the case, here's the distinction:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">In phase space, x,y,z refer to positions, and px,py,pz (or equivalently vx,vy,vz) refer to momentum or velocity components.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Both position and momentum are independent variables that fully specify a particle’s state.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Why Both Are Necessary</span></b><u></u><u></u><br></h3><p>Position and velocity (or momentum) describe different aspects of the particle:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Position (x,y,z)</span></span></b><span class="size" style="font-size:11pt;"> tells you <i><span class="font" style="font-family:Calibri, sans-serif;">where</span></i> the particle is.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Momentum (px,py,pz)</span></span></b><span class="size" style="font-size:11pt;"> tells you <i><span class="font" style="font-family:Calibri, sans-serif;">how</span></i> 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.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Key Takeaway</span></b><u></u><u></u><br></h3><p>The x,y,z 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.<u></u><u></u><br></p><p>Did that clarify the confusion?<u></u><u></u><br></p></div></div></div></div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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?<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">1. Position as a Relational Property</span></b><u></u><u></u><br></h3><p>You are correct that position is inherently relational. A particle’s position is always described relative to some reference frame. For example:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">A particle at x=5 meters means it is 5 meters away from the origin of the chosen coordinate system.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">If you shift the reference frame, the particle’s position can change even if the particle itself hasn’t "moved" in an absolute sense.<u></u><u></u></span><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">2. Position as a Vector</span></b><u></u><u></u><br></h3><p>A <b><span class="font" style="font-family:Calibri, sans-serif;">position vector</span></b> 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:<u></u><u></u><br></p><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">r<u></u><u></u></span><br></p></div></div></div></div></div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">=(x,y,z)<u></u><u></u></span><br></p><p>Here, r<u></u><u></u><br></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).<u></u><u></u><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">3. Why Position is Part of a Microstate</span></b><u></u><u></u><br></h3><p>In the Boltzmannian sense, a <b><span class="font" style="font-family:Calibri, sans-serif;">microstate</span></b> specifies the detailed configuration of all particles in a system. This includes:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Where the particles are (position: x,y,z).<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">How the particles are moving (momentum: px,py,pz).<u></u><u></u></span><br></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:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">If a gas is confined to one corner of a box, there are fewer possible positions and therefore fewer microstates.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">When the gas spreads out, the accessible positions increase, and so does the entropy.<u></u><u></u></span><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">4. Your Trouble with Position as a Microstate</span></b><u></u><u></u><br></h3><p>The root of your concern might lie in the relational nature of position:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">You’re right that position can change depending on the reference frame, which seems less "absolute" than other microstate variables like momentum or energy.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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.<u></u><u></u></span><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">5. Why This Isn’t a Contradiction</span></b><u></u><u></u><br></h3><ul type="disc"><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Position as Relational</span></span></b><span class="size" style="font-size:11pt;">: 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.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Position as a Vector</span></span></b><span class="size" style="font-size:11pt;">: The vector nature of position is about defining the relative location, not implying motion. It’s just a mathematical representation.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">6. Position in Statistical Mechanics</span></b><u></u><u></u><br></h3><p>In the Boltzmannian framework, what truly matters is the <b><span class="font" style="font-family:Calibri, sans-serif;">distribution</span></b> 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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><p>Does this alleviate your concern, or is there a deeper philosophical tension I can help address?<u></u><u></u><br></p></div></div></div></div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Well, I can think about it that way. But then I cannot imagine why entropy does not decrease under adiabatic compression<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">1. Adiabatic Compression and Phase Space</span></b><u></u><u></u><br></h3><p>In adiabatic compression:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The system (e.g., a gas) is compressed without heat exchange (Q=0).<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The volume of the gas decreases, and its particles are confined to a smaller spatial region.<u></u><u></u></span><br></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 <b><span class="font" style="font-family:Calibri, sans-serif;">phase space volume</span></b>:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Phase space</span></span></b><span class="size" style="font-size:11pt;"> consists of both position (x,y,z) and momentum (px,py,pz) variables.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">2. Why Doesn't Entropy Decrease?</span></b><u></u><u></u><br></h3><p>Entropy, in statistical mechanics, is proportional to the logarithm of the number of accessible microstates in phase space:<u></u><u></u><br></p><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">S=kBlnΩ<u></u><u></u></span><br></p><p>Here, Ω is the volume of phase space corresponding to the system’s constraints (energy, particle number, etc.). During adiabatic compression:<u></u><u></u><br></p><ol start="1" type="1"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The system's energy increases (work is done on the gas, increasing particle momenta).<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">This increase in energy expands the momentum part of the phase space, compensating for the reduction in the position part.<u></u><u></u></span><br></li></ol><p>Thus, the total phase space volume—and hence the entropy—remains constant.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">3. Intuition Behind Phase Space Conservation</span></b><u></u><u></u><br></h3><p>The conservation of phase space volume under adiabatic processes is a consequence of <b><span class="font" style="font-family:Calibri, sans-serif;">Liouville's theorem</span></b>, which states:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The phase space density of microstates is constant over time for a system evolving under Hamiltonian mechanics.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Compression changes the shape of the phase space (squeezing position coordinates, stretching momentum coordinates), but it does not change its overall "size."<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">4. Reconciling with Your Intuition</span></b><u></u><u></u><br></h3><p>If we focus only on the <b><span class="font" style="font-family:Calibri, sans-serif;">spatial distribution</span></b> 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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">5. Why Position Alone Can't Explain Entropy</span></b><u></u><u></u><br></h3><p>Your trouble with position as a microstate is understandable when thinking about compression:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">If entropy depended only on positions, it would indeed decrease under compression.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">However, the inclusion of momentum in the microstate definition ensures that entropy remains invariant under processes like adiabatic compression.<u></u><u></u></span><br></li></ul><p>In essence, <b><span class="font" style="font-family:Calibri, sans-serif;">entropy is a property of the entire phase space, not just the positions</span></b>. The relational nature of position doesn’t change this, because momentum is just as relational—it depends on the chosen reference frame as well.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">6. EAC and Adiabatic Compression</span></b><u></u><u></u><br></h3><p>Your preference for framing adiabatic compression as an "equilibration" (EAC) aligns well here. During compression:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The system equilibrates within the constraints of phase space conservation.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Entropy doesn’t decrease because the system maximizes its microstate distribution within the new constraints.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><p>Does this bring clarity to why entropy stays constant, or is there another layer of the problem you’d like to tackle?<u></u><u></u><br></p></div></div></div></div></div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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?<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">1. The Role of the Piston in Adiabatic Compression</span></b><u></u><u></u><br></h3><p>When the piston compresses the gas:<u></u><u></u><br></p><ol start="1" type="1"><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Confinement of Position Space</span></span></b><span class="size" style="font-size:11pt;">: The gas particles are confined to a smaller spatial region, which, if considered alone, would suggest fewer microstates and a reduction in entropy.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Imparting Directional Momentum</span></span></b><span class="size" style="font-size:11pt;">: The piston does work on the gas, increasing the particles' energy. This energy manifests as an increase in momentum (both magnitude and directionality).<u></u><u></u></span><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">2. Why Doesn't Entropy Decrease?</span></b><u></u><u></u><br></h3><p>To resolve this, we need to carefully consider the entire phase space and the conservation principles at play.<u></u><u></u><br></p><h4><b><span class="font" style="font-family:Calibri, sans-serif;">2.1 Confinement and Redistribution</span></b><u></u><u></u><br></h4><p>While the piston confines the gas spatially, it doesn't remove microstates—it merely redistributes them. Here's how:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The reduction in position-space volume is accompanied by a compensatory expansion in momentum-space volume due to the work done by the piston.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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.<u></u><u></u></span><br></li></ul><h4><b><span class="font" style="font-family:Calibri, sans-serif;">2.2 Directional Momentum and Phase Space</span></b><u></u><u></u><br></h4><p>The piston imparts momentum to the gas, creating a temporary directional bias. However:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">This directional momentum is rapidly equilibrated by collisions between gas particles, redistributing the momentum uniformly in all directions.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The equilibration process ensures that the final phase space distribution is isotropic (the same in all directions), preserving the overall randomness and entropy.<u></u><u></u></span><br></li></ul><h4><b><span class="font" style="font-family:Calibri, sans-serif;">2.3 Liouville's Theorem</span></b><u></u><u></u><br></h4><p>Liouville's theorem guarantees that the total phase space volume remains constant under Hamiltonian dynamics:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The compression changes the shape of phase space (squeezing position coordinates and stretching momentum coordinates).<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The overall phase space volume, which determines the entropy, does not change.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">3. Why Directional Momentum Doesn’t Reduce Entropy</span></b><u></u><u></u><br></h3><p>Directional momentum, even if imparted temporarily, doesn’t reduce entropy because:<u></u><u></u><br></p><ol start="1" type="1"><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Entropy Measures the Total Phase Space</span></span></b><span class="size" style="font-size:11pt;">: Entropy is about the total number of accessible microstates. Even with directional momentum, the gas still has the same number of microstates.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Equilibration Restores Randomness</span></span></b><span class="size" style="font-size:11pt;">: 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.<u></u><u></u></span><br></li></ol><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">4. The Key Insight</span></b><u></u><u></u><br></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:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The increase in momentum space compensates for the decrease in position space.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The temporary directional bias in momentum is a transient state that equilibrates to maintain the system's entropy.<u></u><u></u></span><br></li></ul><p>This is why, under adiabatic compression, <b><span class="font" style="font-family:Calibri, sans-serif;">entropy remains constant</span></b>, even though the system undergoes significant changes in its spatial and momentum distributions.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">5. Reconciling Your Intuition</span></b><u></u><u></u><br></h3><p>Your observation is correct that the piston’s movement imposes constraints and directionality. However:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The "decrease" in entropy you associate with confinement and directional momentum is balanced by the redistribution of microstates in phase space.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Entropy measures the total possibilities, not the apparent randomness in one aspect (e.g., spatial or directional momentum).<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><p>Does this help resolve the tension, or would you like to explore the dynamics of equilibration in greater detail?<u></u><u></u><br></p></div></div></div></div></div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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.<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></h6><div><div><div><div><p>You're absolutely right, Nick—introducing the concept of <b><span class="font" style="font-family:Calibri, sans-serif;">quasi-static compression</span></b> provides a clearer and less contentious framework for discussing these processes. Let's reframe the explanation with this in mind:<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">1. Quasi-Static Compression</span></b><u></u><u></u><br></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:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The compression happens gradually, allowing the gas particles to redistribute themselves smoothly without sharp gradients or shock waves.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">At no point does the system deviate significantly from thermodynamic equilibrium, making the process reversible (in the thermodynamic sense) and entropy constant.<u></u><u></u></span><br></li></ul><p>This is in contrast to rapid compression, which would introduce shock waves and temporary nonequilibrium states.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">2. Why Quasi-Static Compression Keeps Entropy Constant</span></b><u></u><u></u><br></h3><p>In a quasi-static process:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The work done by the piston is immediately redistributed throughout the gas via frequent particle collisions.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Any directional momentum imparted by the piston is quickly equilibrated, ensuring isotropy in phase space.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">The compression of position space is perfectly balanced by the expansion of momentum space without introducing large-scale, irreversible gradients.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">3. Shock Waves and Non-Quasi-Static Compression</span></b><u></u><u></u><br></h3><p>If the piston moves too quickly:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">A shock wave propagates through the gas, creating localized regions of high pressure, temperature, and entropy.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">These transient states involve nonequilibrium dynamics, during which entropy can increase.<u></u><u></u></span><br></li></ul><p>Once the system re-equilibrates, the entropy stabilizes, but it will now reflect the irreversible effects of the rapid compression.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">4. Quasi-Static Compression as the Idealization</span></b><u></u><u></u><br></h3><p>In thermodynamics, we often focus on quasi-static processes to:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Simplify the analysis by avoiding transient nonequilibrium effects.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Provide a clear baseline for understanding how entropy behaves in an idealized, reversible context.<u></u><u></u></span><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Conclusion</span></b><u></u><u></u><br></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.<u></u><u></u><br></p><p>Would you like me to help formalize this perspective further, perhaps in a way that fits your weather book?<u></u><u></u><br></p></div></div></div></div><h5>You said:<u></u><u></u><br></h5><div><div><div><div><div><div><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">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?<u></u><u></u></span><br></p></div></div></div></div></div></div></div></div></div><h6>ChatGPT said:<u></u><u></u><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">1. Why Use Simplified Models Like the Spherical Cow?</span></b><u></u><u></u><br></h3><p>Simplified models are powerful because:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">They strip away complexities to focus on fundamental principles.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">They offer insights that are robust to certain kinds of deviations.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">They are computationally and conceptually manageable, allowing us to make predictions that align closely with observed phenomena.<u></u><u></u></span><br></li></ul><p>In the case of quasi-static adiabatic compression, the model assumes:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Perfectly slow compression (no shock waves or gradients).<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Immediate equilibration of momentum and energy.<u></u><u></u></span><br></li></ul><p>These assumptions are clearly idealized, but they capture essential features of how thermodynamic systems behave under controlled conditions.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">2. What Makes This Model Robust?</span></b><u></u><u></u><br></h3><p>Physicists have confidence in the robustness of idealized models because of:<u></u><u></u><br></p><ol start="1" type="1"><li><b><span class="font" style="font-family:Calibri, sans-serif;">Conservation Laws</span></b>: 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.<u></u><u></u><br></li><li><b><span class="font" style="font-family:Calibri, sans-serif;">Insensitivity to Small Deviations</span></b>: 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.<u></u><u></u><br></li><li><b><span class="font" style="font-family:Calibri, sans-serif;">Separation of Scales</span></b>: 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.<u></u><u></u><br></li><li><b><span class="font" style="font-family:Calibri, sans-serif;">Agreement with Experiment</span></b>: 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.<u></u><u></u><br></li></ol><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">3. Why Aren’t Spherical Cows Always Useless?</span></b><u></u><u></u><br></h3><p>The spherical cow metaphor critiques models that oversimplify to the point of absurdity. But not all simplifications are equally problematic. For example:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Spherical Stars</span></span></b><span class="size" style="font-size:11pt;">: Assuming stars are spherical simplifies their gravitational dynamics while still providing highly accurate predictions for many phenomena.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Point Masses</span></span></b><span class="size" style="font-size:11pt;">: Treating planets as point masses in orbital calculations works beautifully despite their actual shapes and compositions.<u></u><u></u></span><br></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.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">4. When Does the Model Break Down?</span></b><u></u><u></u><br></h3><p>The model fails when:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Compression is too fast, creating shock waves or large-scale irreversibilities.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Heat exchange or other non-adiabatic effects become significant.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Microscopic assumptions (e.g., perfect collisions) break down due to quantum or relativistic effects.<u></u><u></u></span><br></li></ul><p>Physicists are aware of these limitations and refine or replace models as needed when their assumptions no longer hold.<u></u><u></u><br></p><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">5. Why Do Physicists Trust It?</span></b><u></u><u></u><br></h3><p>The trust comes from:<u></u><u></u><br></p><ul type="disc"><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Generality</span></span></b><span class="size" style="font-size:11pt;">: The underlying principles are broadly applicable.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Predictive Power</span></span></b><span class="size" style="font-size:11pt;">: The model reliably predicts outcomes in the scenarios it’s designed for.<u></u><u></u></span><br></li><li class="qt-MsoNormal"><b><span class="font" style="font-family:Calibri, sans-serif;"><span class="size" style="font-size:11pt;">Empirical Validation</span></span></b><span class="size" style="font-size:11pt;">: Repeated experimental confirmation underpins confidence in its robustness.<u></u><u></u></span><br></li></ul><div class="qt-MsoNormal" align="center" style="text-align:center;"><span class="size" style="font-size:11pt;"><hr size="0" width="96%" align="center"></span><br></div><h3><b><span class="font" style="font-family:Calibri, sans-serif;">Conclusion</span></b><u></u><u></u><br></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.<u></u><u></u><br></p><p>Would you like to discuss a specific example where such trust might be misplaced, or do you find this explanation satisfactory?<u></u><u></u><br></p></div></div></div></div></div><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><u></u> <u></u></span><br></li></ul><div><ul type="disc"><li class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><u></u> <u></u></span><br></li></ul></div></div></div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><u></u> <u></u></span><br></p><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">On Wed, Jan 22, 2025 at 4:48 PM Barry MacKichan <<a href="mailto:barry.mackichan@mackichan.com" target="_blank">barry.mackichan@mackichan.com</a>> wrote:<u></u><u></u></span><br></p></div><blockquote style="border-top-width:medium;border-top-style:none;border-top-color:currentcolor;border-right-width:medium;border-right-style:none;border-right-color:currentcolor;border-bottom-width:medium;border-bottom-style:none;border-bottom-color:currentcolor;border-left-width:1pt;border-left-style:solid;border-left-color:rgb(204, 204, 204);padding-top:0in;padding-right:0in;padding-bottom:0in;padding-left:6pt;margin-left:4.8pt;margin-right:0in;"><div><div><div><p><span class="font" 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.<u></u><u></u></span><br></p><p><span class="font" style="font-family:Arial, sans-serif;">— Barry<u></u><u></u></span><br></p><p><span class="font" style="font-family:Arial, sans-serif;">On 22 Jan 2025, at 14:30, Nicholas Thompson wrote:<u></u><u></u></span><br></p></div><blockquote style="border-top-width:medium;border-top-style:none;border-top-color:currentcolor;border-right-width:medium;border-right-style:none;border-right-color:currentcolor;border-bottom-width:medium;border-bottom-style:none;border-bottom-color:currentcolor;border-left-width:1.5pt;border-left-style:solid;border-left-color:rgb(119, 119, 119);padding-top:0in;padding-right:0in;padding-bottom:0in;padding-left:4pt;margin-left:0in;margin-right:0in;margin-bottom:3.75pt;"><div id="qt-m_1722174043489856872m_-1513511458509069282m_-156084093925917569m_4537490940269728881m_843719540042853379736CB688D-9A87-4C02-ACA1-67845F9B5EEB"><div><div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;">I am curious how many of you on the list know or could guess at the author of the following quote: <u></u><u></u></span></span></span><br></p></div><div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;"><u></u> <u></u></span></span></span><br></p></div><div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;">I am interested in your guesses; if you know it for SURE, please hold off guessing.<u></u><u></u></span></span></span><br></p></div><div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;"><u></u> <u></u></span></span></span><br></p></div><div><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Aptos, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">Let me ask you to watch a metaphor breaking down here before you.</span></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">I said, “You mean the universe is like a machine?”</span></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">He said, “No. I think it is one . . . Well, it is like . . .”</span></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">“I think you mean the universe is like a machine.”</span></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">“All right. Let it go at that.”</span></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">He said, “No—no.”</span></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">I said, “All right. Is the universe like that?”</span></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">And he said, “No. I mean it is like a machine, only . . .”</span></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">“. . . it is different from a machine,” I said.</span></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p><p class="qt-MsoNormal" style="margin-bottom:8pt;line-height:115%;"><b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:garamond, serif;"><span class="size" style="font-size:12pt;">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></span></span></b><span style="line-height:115%;color:rgb(119, 119, 119);"><span class="font" style="font-family:Aptos, sans-serif;"><span class="size" style="font-size:12pt;"><u></u><u></u></span></span></span><br></p></div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;"><br><span>--</span><u></u><u></u></span></span></span></p><div><div><div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;">Nicholas S. Thompson<u></u><u></u></span></span></span><br></p></div><div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;">Emeritus Professor of Psychology and Ethology<u></u><u></u></span></span></span><br></p></div><div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;">Clark University<u></u><u></u></span></span></span><br></p></div><div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;"><a href="mailto:nthompson@clarku.edu" target="_blank">nthompson@clarku.edu</a><u></u><u></u></span></span></span><br></p></div><p class="qt-MsoNormal"><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;"><span class="size" style="font-size:11pt;"><a href="https://wordpress.clarku.edu/nthompson" target="_blank">https://wordpress.clarku.edu/nthompson</a><u></u><u></u></span></span></span><br></p></div></div></div></div></blockquote><div><blockquote style="border-top-width:medium;border-top-style:none;border-top-color:currentcolor;border-right-width:medium;border-right-style:none;border-right-color:currentcolor;border-bottom-width:medium;border-bottom-style:none;border-bottom-color:currentcolor;border-left-width:1.5pt;border-left-style:solid;border-left-color:rgb(119, 119, 119);padding-top:0in;padding-right:0in;padding-bottom:0in;padding-left:4pt;margin-left:0in;margin-right:0in;margin-bottom:3.75pt;"><p><span style="color:rgb(119, 119, 119);"><span class="font" style="font-family:Arial, sans-serif;">.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. <br>FRIAM Applied Complexity Group listserv <br>Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://bit.ly/virtualfriam" target="_blank"><span style="color:rgb(119, 119, 119);">https://bit.ly/virtualfriam</span></a> <br>to (un)subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank"><span style="color:rgb(119, 119, 119);">http://redfish.com/mailman/listinfo/friam_redfish.com</span></a> <br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank"><span style="color:rgb(119, 119, 119);">http://friam-comic.blogspot.com/</span></a> <br>archives: 5/2017 thru present <a href="https://redfish.com/pipermail/friam_redfish.com/" target="_blank"><span style="color:rgb(119, 119, 119);">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:rgb(119, 119, 119);">http://friam.383.s1.nabble.com/</span></a><u></u><u></u></span></span></p></blockquote></div></div></div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..<br>FRIAM Applied Complexity Group listserv<br>Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://bit.ly/virtualfriam" target="_blank">https://bit.ly/virtualfriam</a><br>to (un)subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a><br>archives: 5/2017 thru present <a href="https://redfish.com/pipermail/friam_redfish.com/" 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><u></u><u></u></span></p></blockquote></div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><u></u><u></u></span><br></p></div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><br><span>--</span><u></u><u></u></span></p><div><div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Nicholas S. Thompson<u></u><u></u></span><br></p></div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Emeritus Professor of Psychology and Ethology<u></u><u></u></span><br></p></div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">Clark University<u></u><u></u></span><br></p></div><div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><a href="mailto:nthompson@clarku.edu" target="_blank">nthompson@clarku.edu</a><u></u><u></u></span><br></p></div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;"><a href="https://wordpress.clarku.edu/nthompson" target="_blank">https://wordpress.clarku.edu/nthompson</a><u></u><u></u></span><br></p></div></div><p class="qt-MsoNormal"><span class="size" style="font-size:11pt;">.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..<br>FRIAM Applied Complexity Group listserv<br>Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://bit.ly/virtualfriam" target="_blank">https://bit.ly/virtualfriam</a><br>to (un)subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" target="_blank">http://friam-comic.blogspot.com/</a><br>archives: 5/2017 thru present <a href="https://redfish.com/pipermail/friam_redfish.com/" 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><u></u><u></u></span></p></blockquote></div></div></div><div>.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..<br></div><div> FRIAM Applied Complexity Group listserv<br></div><div> Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://bit.ly/virtualfriam" rel="noreferrer" target="_blank">https://bit.ly/virtualfriam</a><br></div><div> to (un)subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com" rel="noreferrer" target="_blank">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br></div><div> FRIAM-COMIC <a href="http://friam-comic.blogspot.com/" rel="noreferrer" target="_blank">http://friam-comic.blogspot.com/</a><br></div><div> archives: 5/2017 thru present <a href="https://redfish.com/pipermail/friam_redfish.com/" rel="noreferrer" target="_blank">https://redfish.com/pipermail/friam_redfish.com/</a><br></div><div> 1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/" rel="noreferrer" target="_blank">http://friam.383.s1.nabble.com/</a><br></div></blockquote></div><div>.- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-..<br></div><div>FRIAM Applied Complexity Group listserv<br></div><div>Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom <a href="https://bit.ly/virtualfriam">https://bit.ly/virtualfriam</a><br></div><div>to (un)subscribe <a href="http://redfish.com/mailman/listinfo/friam_redfish.com">http://redfish.com/mailman/listinfo/friam_redfish.com</a><br></div><div>FRIAM-COMIC <a href="http://friam-comic.blogspot.com/">http://friam-comic.blogspot.com/</a><br></div><div>archives: 5/2017 thru present <a href="https://redfish.com/pipermail/friam_redfish.com/">https://redfish.com/pipermail/friam_redfish.com/</a><br></div><div> 1/2003 thru 6/2021 <a href="http://friam.383.s1.nabble.com/">http://friam.383.s1.nabble.com/</a><br></div><div><br></div></blockquote><div style="font-family:Arial;"><br></div></body></html>