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.
Best, Eric ----------- Eric P. Charles, Ph.D. Head, Data Analytics and Delivery Human Capital Data Modernization and Management (HCDMM) Office of Personnel Management (OPM) American University - Adjunct Instructor <echar...@american.edu> On Wed, Jan 22, 2025 at 11:42 PM Nicholas Thompson <thompnicks...@gmail.com> wrote: > 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. > > You said: > "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?" > ChatGPT said: > > 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: > > 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. > > 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. > > So, your professor's statement captures part of the concept, but it's > simplified. Entropy involves distributions across *all* relevant > variables in a system—not just the spatial ones. Does that align with what > you're exploring? > You said: > 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? > ChatGPT said: > > 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. > > Entropy, at its core, relates to the *equilibration of microstates*—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. > > 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 *result* of the system seeking equilibrium by exploring > all accessible microstates—not the defining feature of entropy. > > In essence, entropy is the measure of *possibilities*, 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. > You said: > 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? > ChatGPT said: > > 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. > 1. *Is Position a Microstate?* > > 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. > 2. *Does Momentum Fully Capture Position?* > > 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. > 3. *Why the Confusion?* > > 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. > 4. *Reconciling the Contradiction* > > 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. > > Would this clarification align with your understanding? > You said: > 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. > ChatGPT said: > > Absolutely, Nick—let’s unpack that further. > *The "Random Placement" Metaphor* > > The idea of "random placement" often shows up in simplified explanations > of entropy, especially in introductory contexts. For example: > > - A gas in a box is said to "spread out" to fill the container, which > is often visualized as particles randomly scattering in space. > - 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. > > 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. > ------------------------------ > *Position's Role in Phase Space* > > The deeper truth lies in how position contributes to the *phase space* of > the system. In classical mechanics: > > - A particle's microstate is defined by its position (x,y,z) and > momentum (px,py,pz). > - The *phase space* is the multidimensional space of all possible > combinations of these variables for all particles in the system. > > 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. > ------------------------------ > *Why Phase Space Matters More Than Position Alone* > > Entropy is about maximizing the *volume* of accessible phase space under > the system’s constraints. This means: > > - If you only considered positions, you'd ignore a significant portion > of the system's microstate diversity—specifically, the momentum degrees of > freedom. > - 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. > > ------------------------------ > *Entropy Beyond the Visual Metaphor* > > The metaphor of random spatial placement simplifies entropy to the visible > world of positions, but entropy fundamentally counts possibilities: > > 1. *Position Space*: Particles can occupy different regions of space. > 2. *Momentum Space*: Particles can have various momenta, which > significantly increases the number of microstates. > 3. The combination of these spaces—phase space—is what entropy > measures. > > So, while random placement is a *consequence* 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. > > Does this deepen the distinction you’re seeking? > You said: > I understood x, y, and z to be velocity vectors, not positions. Was I > wrong? > ChatGPT said: > > Great question, Nick! Let’s clarify the distinction between *position > vectors* and *velocity vectors* and how they relate to entropy and phase > space. > *Position vs. Velocity Vectors* > > 1. > > *Position Vectors (x,y,z)* > These specify the spatial location of a particle in three-dimensional > physical space. For example: > - If a particle is in a box, x,y,z tell you where the particle is > inside that box. > 2. > > *Velocity Vectors (vx,vy,vz)* > These specify how fast the particle is moving and in which direction. > They are related to momentum (px,py,pz) via the relationship: > p > > =mv > > 2. > > where m is the particle’s mass. > > ------------------------------ > *Phase Space and Microstates* > > - A *microstate* in classical mechanics is defined by both the > *position* (x,y,z) and the *momentum* (px,py,pz) of each particle. > - Phase space is the multidimensional space that includes all possible > combinations of these variables. For N particles, the phase space has 6 > N dimensions: 3N for positions and 3N for momenta. > > ------------------------------ > *Did You Confuse Velocity with Position?* > > It sounds like you were interpreting x,y,z as velocity components instead > of positions. If that’s the case, here's the distinction: > > - In phase space, x,y,z refer to positions, and px,py,pz (or > equivalently vx,vy,vz) refer to momentum or velocity components. > - Both position and momentum are independent variables that fully > specify a particle’s state. > > ------------------------------ > *Why Both Are Necessary* > > Position and velocity (or momentum) describe different aspects of the > particle: > > - *Position (x,y,z)* tells you *where* the particle is. > - *Momentum (px,py,pz)* tells you *how* 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. > > ------------------------------ > *Key Takeaway* > > 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. > > Did that clarify the confusion? > You said: > 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? > ChatGPT said: > > 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. > ------------------------------ > *1. Position as a Relational Property* > > You are correct that position is inherently relational. A particle’s > position is always described relative to some reference frame. For example: > > - A particle at x=5 meters means it is 5 meters away from the origin > of the chosen coordinate system. > - If you shift the reference frame, the particle’s position can change > even if the particle itself hasn’t "moved" in an absolute sense. > > This is a key difference from intrinsic properties like mass and velocity, > which are not dependent on the choice of reference frame. > ------------------------------ > *2. Position as a Vector* > > A *position vector* 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: > r > =(x,y,z) > > Here, r > > 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). > > 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. > ------------------------------ > *3. Why Position is Part of a Microstate* > > In the Boltzmannian sense, a *microstate* specifies the detailed > configuration of all particles in a system. This includes: > > - Where the particles are (position: x,y,z). > - How the particles are moving (momentum: px,py,pz). > > 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: > > - If a gas is confined to one corner of a box, there are fewer > possible positions and therefore fewer microstates. > - When the gas spreads out, the accessible positions increase, and so > does the entropy. > > In this context, position isn’t an "absolute" property but a placeholder > for how particles are distributed within a given spatial domain. > ------------------------------ > *4. Your Trouble with Position as a Microstate* > > The root of your concern might lie in the relational nature of position: > > - You’re right that position can change depending on the reference > frame, which seems less "absolute" than other microstate variables like > momentum or energy. > - 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. > > 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. > ------------------------------ > *5. Why This Isn’t a Contradiction* > > - *Position as Relational*: 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. > - *Position as a Vector*: The vector nature of position is about > defining the relative location, not implying motion. It’s just a > mathematical representation. > > ------------------------------ > *6. Position in Statistical Mechanics* > > In the Boltzmannian framework, what truly matters is the *distribution* > 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. > ------------------------------ > > Does this alleviate your concern, or is there a deeper philosophical > tension I can help address? > You said: > Well, I can think about it that way. But then I cannot imagine why entropy > does not decrease under adiabatic compression > ChatGPT said: > > 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. > ------------------------------ > *1. Adiabatic Compression and Phase Space* > > In adiabatic compression: > > - The system (e.g., a gas) is compressed without heat exchange (Q=0). > - The volume of the gas decreases, and its particles are confined to a > smaller spatial region. > > 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 *phase space volume*: > > - *Phase space* consists of both position (x,y,z) and momentum (px,py,p > z) variables. > - 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. > > ------------------------------ > *2. Why Doesn't Entropy Decrease?* > > Entropy, in statistical mechanics, is proportional to the logarithm of the > number of accessible microstates in phase space: > S=kBlnΩ > > Here, Ω is the volume of phase space corresponding to the system’s > constraints (energy, particle number, etc.). During adiabatic compression: > > 1. The system's energy increases (work is done on the gas, increasing > particle momenta). > 2. This increase in energy expands the momentum part of the phase > space, compensating for the reduction in the position part. > > Thus, the total phase space volume—and hence the entropy—remains constant. > ------------------------------ > *3. Intuition Behind Phase Space Conservation* > > The conservation of phase space volume under adiabatic processes is a > consequence of *Liouville's theorem*, which states: > > - The phase space density of microstates is constant over time for a > system evolving under Hamiltonian mechanics. > - Compression changes the shape of the phase space (squeezing position > coordinates, stretching momentum coordinates), but it does not change its > overall "size." > > ------------------------------ > *4. Reconciling with Your Intuition* > > If we focus only on the *spatial distribution* 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. > ------------------------------ > *5. Why Position Alone Can't Explain Entropy* > > Your trouble with position as a microstate is understandable when thinking > about compression: > > - If entropy depended only on positions, it would indeed decrease > under compression. > - However, the inclusion of momentum in the microstate definition > ensures that entropy remains invariant under processes like adiabatic > compression. > > In essence, *entropy is a property of the entire phase space, not just > the positions*. The relational nature of position doesn’t change this, > because momentum is just as relational—it depends on the chosen reference > frame as well. > ------------------------------ > *6. EAC and Adiabatic Compression* > > Your preference for framing adiabatic compression as an "equilibration" > (EAC) aligns well here. During compression: > > - The system equilibrates within the constraints of phase space > conservation. > - Entropy doesn’t decrease because the system maximizes its microstate > distribution within the new constraints. > > ------------------------------ > > Does this bring clarity to why entropy stays constant, or is there another > layer of the problem you’d like to tackle? > You said: > 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? > ChatGPT said: > > 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. > ------------------------------ > *1. The Role of the Piston in Adiabatic Compression* > > When the piston compresses the gas: > > 1. *Confinement of Position Space*: The gas particles are confined to > a smaller spatial region, which, if considered alone, would suggest fewer > microstates and a reduction in entropy. > 2. *Imparting Directional Momentum*: The piston does work on the gas, > increasing the particles' energy. This energy manifests as an increase in > momentum (both magnitude and directionality). > > 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. > ------------------------------ > *2. Why Doesn't Entropy Decrease?* > > To resolve this, we need to carefully consider the entire phase space and > the conservation principles at play. > *2.1 Confinement and Redistribution* > > While the piston confines the gas spatially, it doesn't remove > microstates—it merely redistributes them. Here's how: > > - The reduction in position-space volume is accompanied by a > compensatory expansion in momentum-space volume due to the work done by the > piston. > - 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. > > *2.2 Directional Momentum and Phase Space* > > The piston imparts momentum to the gas, creating a temporary directional > bias. However: > > - This directional momentum is rapidly equilibrated by collisions > between gas particles, redistributing the momentum uniformly in all > directions. > - The equilibration process ensures that the final phase space > distribution is isotropic (the same in all directions), preserving the > overall randomness and entropy. > > *2.3 Liouville's Theorem* > > Liouville's theorem guarantees that the total phase space volume remains > constant under Hamiltonian dynamics: > > - The compression changes the shape of phase space (squeezing position > coordinates and stretching momentum coordinates). > - The overall phase space volume, which determines the entropy, does > not change. > > ------------------------------ > *3. Why Directional Momentum Doesn’t Reduce Entropy* > > Directional momentum, even if imparted temporarily, doesn’t reduce entropy > because: > > 1. *Entropy Measures the Total Phase Space*: Entropy is about the > total number of accessible microstates. Even with directional momentum, the > gas still has the same number of microstates. > 2. *Equilibration Restores Randomness*: 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. > > ------------------------------ > *4. The Key Insight* > > 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: > > - The increase in momentum space compensates for the decrease in > position space. > - The temporary directional bias in momentum is a transient state that > equilibrates to maintain the system's entropy. > > This is why, under adiabatic compression, *entropy remains constant*, > even though the system undergoes significant changes in its spatial and > momentum distributions. > ------------------------------ > *5. Reconciling Your Intuition* > > Your observation is correct that the piston’s movement imposes constraints > and directionality. However: > > - The "decrease" in entropy you associate with confinement and > directional momentum is balanced by the redistribution of microstates in > phase space. > - Entropy measures the total possibilities, not the apparent > randomness in one aspect (e.g., spatial or directional momentum). > > ------------------------------ > > Does this help resolve the tension, or would you like to explore the > dynamics of equilibration in greater detail? > You said: > 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. > ChatGPT said: > > You're absolutely right, Nick—introducing the concept of *quasi-static > compression* provides a clearer and less contentious framework for > discussing these processes. Let's reframe the explanation with this in mind: > ------------------------------ > *1. Quasi-Static Compression* > > Quasi-static compression describes an idealized process where the piston > moves so slowly that the system remains arbitrarily close to equilibrium at > every step: > > - The compression happens gradually, allowing the gas particles to > redistribute themselves smoothly without sharp gradients or shock waves. > - At no point does the system deviate significantly from thermodynamic > equilibrium, making the process reversible (in the thermodynamic sense) and > entropy constant. > > This is in contrast to rapid compression, which would introduce shock > waves and temporary nonequilibrium states. > ------------------------------ > *2. Why Quasi-Static Compression Keeps Entropy Constant* > > In a quasi-static process: > > - The work done by the piston is immediately redistributed throughout > the gas via frequent particle collisions. > - Any directional momentum imparted by the piston is quickly > equilibrated, ensuring isotropy in phase space. > - The compression of position space is perfectly balanced by the > expansion of momentum space without introducing large-scale, irreversible > gradients. > > ------------------------------ > *3. Shock Waves and Non-Quasi-Static Compression* > > If the piston moves too quickly: > > - A shock wave propagates through the gas, creating localized regions > of high pressure, temperature, and entropy. > - These transient states involve nonequilibrium dynamics, during which > entropy can increase. > > Once the system re-equilibrates, the entropy stabilizes, but it will now > reflect the irreversible effects of the rapid compression. > ------------------------------ > *4. Quasi-Static Compression as the Idealization* > > In thermodynamics, we often focus on quasi-static processes to: > > - Simplify the analysis by avoiding transient nonequilibrium effects. > - Provide a clear baseline for understanding how entropy behaves in an > idealized, reversible context. > > 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. > ------------------------------ > *Conclusion* > > 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. > > Would you like me to help formalize this perspective further, perhaps in a > way that fits your weather book? > You said: > 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? > ChatGPT said: > > 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. > ------------------------------ > *1. Why Use Simplified Models Like the Spherical Cow?* > > Simplified models are powerful because: > > - They strip away complexities to focus on fundamental principles. > - They offer insights that are robust to certain kinds of deviations. > - They are computationally and conceptually manageable, allowing us to > make predictions that align closely with observed phenomena. > > In the case of quasi-static adiabatic compression, the model assumes: > > - Perfectly slow compression (no shock waves or gradients). > - Immediate equilibration of momentum and energy. > > These assumptions are clearly idealized, but they capture essential > features of how thermodynamic systems behave under controlled conditions. > ------------------------------ > *2. What Makes This Model Robust?* > > Physicists have confidence in the robustness of idealized models because > of: > > 1. > > *Conservation Laws*: 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. > 2. > > *Insensitivity to Small Deviations*: 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. > 3. > > *Separation of Scales*: 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. > 4. > > *Agreement with Experiment*: 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. > > ------------------------------ > *3. Why Aren’t Spherical Cows Always Useless?* > > The spherical cow metaphor critiques models that oversimplify to the point > of absurdity. But not all simplifications are equally problematic. For > example: > > - *Spherical Stars*: Assuming stars are spherical simplifies their > gravitational dynamics while still providing highly accurate predictions > for many phenomena. > - *Point Masses*: Treating planets as point masses in orbital > calculations works beautifully despite their actual shapes and > compositions. > > 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. > ------------------------------ > *4. When Does the Model Break Down?* > > The model fails when: > > - Compression is too fast, creating shock waves or large-scale > irreversibilities. > - Heat exchange or other non-adiabatic effects become significant. > - Microscopic assumptions (e.g., perfect collisions) break down due to > quantum or relativistic effects. > > Physicists are aware of these limitations and refine or replace models as > needed when their assumptions no longer hold. > ------------------------------ > *5. Why Do Physicists Trust It?* > > The trust comes from: > > - *Generality*: The underlying principles are broadly applicable. > - *Predictive Power*: The model reliably predicts outcomes in the > scenarios it’s designed for. > - *Empirical Validation*: Repeated experimental confirmation underpins > confidence in its robustness. > > ------------------------------ > *Conclusion* > > 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. > > Would you like to discuss a specific example where such trust might be > misplaced, or do you find this explanation satisfactory? > > - > - > > > On Wed, Jan 22, 2025 at 4:48 PM Barry MacKichan < > barry.mackic...@mackichan.com> wrote: > >> 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. >> >> — Barry >> >> On 22 Jan 2025, at 14:30, Nicholas Thompson wrote: >> >> I am curious how many of you on the list know or could guess at the >> author of the following quote: >> >> I am interested in your guesses; if you know it for SURE, please hold >> off guessing. >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.”* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *Let me ask you to watch a metaphor breaking down here before you.* >> >> *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.”* >> >> *I said, “You mean the universe is like a machine?”* >> >> *He said, “No. I think it is one . . . Well, it is like . . .”* >> >> *“I think you mean the universe is like a machine.”* >> >> *“All right. Let it go at that.”* >> >> *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?”* >> >> *He said, “No—no.”* >> >> *I said, “All right. Is the universe like that?”* >> >> *And he said, “No. I mean it is like a machine, only . . .”* >> >> *“. . . it is different from a machine,” I said.* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.* >> >> *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.”* >> >> *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.”* >> >> *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.* >> >> *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.* >> >> *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.* >> >> -- >> Nicholas S. Thompson >> Emeritus Professor of Psychology and Ethology >> Clark University >> nthomp...@clarku.edu >> https://wordpress.clarku.edu/nthompson >> >> .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / >> ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. >> FRIAM Applied Complexity Group listserv >> Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom >> https://bit.ly/virtualfriam >> to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> FRIAM-COMIC http://friam-comic.blogspot.com/ >> archives: 5/2017 thru present >> https://redfish.com/pipermail/friam_redfish.com/ >> 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >> >> .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / >> ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. >> FRIAM Applied Complexity Group listserv >> Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom >> https://bit.ly/virtualfriam >> to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> FRIAM-COMIC http://friam-comic.blogspot.com/ >> archives: 5/2017 thru present >> https://redfish.com/pipermail/friam_redfish.com/ >> 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >> > > > -- > Nicholas S. Thompson > Emeritus Professor of Psychology and Ethology > Clark University > nthomp...@clarku.edu > https://wordpress.clarku.edu/nthompson > .- .-.. .-.. / ..-. --- --- - . .-. ... / .- .-. . / .-- .-. --- -. --. / > ... --- -- . / .- .-. . / ..- ... . ..-. ..- .-.. > FRIAM Applied Complexity Group listserv > Fridays 9a-12p Friday St. Johns Cafe / Thursdays 9a-12p Zoom > https://bit.ly/virtualfriam > to (un)subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: 5/2017 thru present > https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ >
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