Comments

  • A Comparison of Fox News with McDonald's Advertising
    Is there anything to this approach, other than just advertising?jasonm

    You mean, when someone is trying to sell you something, whether a product or a point of view, they'll do whatever they can to persuade you? Well, of course they would.

    However, these companies are beginning to lose many of their viewers. It appears that audiences are tiring of combative and demeaning dialogue.jgill

    I think it's just polarization. Fox viewers aren't getting tired of Fox and CNN viewers aren't getting tired of CNN. But Fox gets few CNN viewers and CNN gets few Fox viewers. It's a tradeoff between loyalty and reach.
  • Techno-optimism is most appropriate
    Well, both positions, as stated, are stupid caricatures. Or the first one is a caricature; the second is just stupid.
  • Idiot Greeks
    Yanis Varoufakis, belov'd of German bankers, sparked my curiosity by claiming that idiotis, in ancient Greek, was a derogatory term for one who refuses to think in terms of the common goodBanno



    Funny, I just heard another unsourced version of this factoid: as the story went, there was a law in Sparta (rather than Athens) concerning political conflicts in the polis. Every citizen was obligated to choose a side; those who didn't were called ideos. They were subject to the seizure of property and exile.
  • Infinites outside of math?
    This is getting painful to watch.jgill

    This is the same crank whose banning you were lamenting earlier because (he says) he is a physicist and we should be grateful for him being here to educate us... Be wary of unhinged bullshitters confidently throwing around specialist terminology.
  • How is this not Epiphenomenalism
    I'll take the bow on behalf of the late Jerry Fodor :)
  • How is this not Epiphenomenalism
    By the way, I am afraid that when they talk about "Fodors’s anxieties" [over epiphenomenalism] they are misrepresenting him. Perhaps they mistook a rhetorical setup for his actual position. For example, here is the opening of the essay that concludes with that vivid wanting-reaching-itching-scratching passage ("Making Mind Matter More"):

    An outbreak of epiphobia (the fear that one is turning into an epiphenomenalist) appears to have much of the philosophy of mind community in its grip. Though it is generally agreed to be compatible with physicalism that intentional states should be causally responsible for behavioral outcomes, epiphobics worry that it is not compatible with physicalism that intentional states should be causally responsible for behavioral outcomes qua intentional. So they fear that the very successes of a physicalistic (and/or a computational) psychology will entail the causal inertness of the mental. Fearing this makes them unhappy. In this chapter, I want to argue that epiphobia is a neurotic worry; if there is a problem, it is engendered not by the actual or possible successes of physicalistic psychology, but by two philosophical mistakes: (a) a wrong idea about what it is for a property to be causally responsible, and (b) a complex of wrong ideas about the relations between special science laws and the events that they subsume. — Fodor

    Fodor exposes the causal exclusion argument (as it is used here) for the obvious nonsense that it is with a couple of examples, such as:

    Consider, for example, the property of being a mountain; and suppose (what is surely plausible) that being a mountain isn't a physical property. (Remember, this just means that "mountain" and its synonyms aren't items in the lexicon of physics.) Now, untutored intuition might suggest that many of the effects of mountains are attributable to their being mountains. Thus, untutored intuition suggests, it is because Mount Everest is a mountain that Mount Everest has glaciers on its top; and it is because Mount Everest is a mountain that it casts such a long shadow; and it is because Mount Everest is a mountain that so many people are provoked to try to climb it... and so on. But not so, according to the present line of argument. For, surely the causal powers of Mount Everest are fully determined by its physical properties, and we've agreed that being a mountain isn't one of the physical properties of mountains. So then, Mount Everest's being a mountain doesn't affect its causal powers. So then - contrary to what one reads in geology books - the property of being a mountain is causally inert. Geoepiphobia! — Fodor

    It should be noted that Fodor explicitly stipulates "property dualism" as a precondition for the line of argument that he mocks. That's why he says in this example that "being a mountain" is a non-physical property: just as mental or intentional properties are held to be non-physical because they aren't "items in the lexicon of physics," any property that is not in the lexicon of physics must be ipso facto treated as non-physical on this account.

    Fodor's own solution rejects the principle of causal exclusion in favor of causal sufficiency:

    P is a causally responsible property if it's a property in virtue of the instantiation of which the occurrence of one event is nomologically sufficient for the occurrence of another. — Fodor

    On his "covering law" account there can be multiple causes for the same event, and the epiphenomenalist worry stemming from causal exclusion is dissolved. Thus, if we accept that there are mental, or intentional laws of some sort, then the mental is not epiphenomenal. That there are such laws is implicit in the very attitude towards the epiphenomenalist threat that Fodor satirizes: "if it isn’t literally true that my wanting is causally responsible for my reaching ... it’s the end of the world." That is, we ordinarily assume that it is true my wanting is causally responsible for my reaching. We treat this connection between wanting and reaching as a law-like regularity. You don't have to call these laws physical if you don't like, but that doesn't matter for the argument.
  • Mathematical universe or mathematical minds?
    What motivates all those math people? Tenure/promotion considerations. Prestige within a community. Delight in the exploratory aspects of a subject with few constraints arising from the physical world - free rein for one's imagination.jgill

    Yeah, I think imagination, curiosity and play are underestimated in these reductionist accounts of mathematics, even though they are as much a feature of our psyche as anything else.

    From my vantage point as a very senior citizen, the first thing I note is the huge number of people pursuing activities compared with 60 years ago. I haven't a clue as to numbers of mathematicians then and now. But at that time the outdoor sport I became involved with had perhaps a couple of thousand fairly serious devotees here in the USA. Now there are well over six million. World-wide there may be ten million or more. It staggers the mind.jgill

    Ha! You think there is a connection? :) From my own experience, I've known a few physicist and astronomer climbers, but can't recall any mathematicians off the top of my head.
  • How is this not Epiphenomenalism
    In the quoted passage Brown and Ladyman give only a brief outline of a solution; do they go on to say more? From this one paragraph it's difficult to tell just where their solution is situated, but it does have some resemblance with identity theories (see for instance Mental Causation in the SEP).

    They are being a bit coy though in that it is not clear how seriously they take the causal exclusion argument and whether they think that mental causation does have its place. When they switch from subvenient to supervenient, from physical to mental, they no longer talk about causation and instead use the word "description." But is it a causal description that parallels a description in terms of physical causes?

    They also use the word "express," which hints at realization.
  • How is this not Epiphenomenalism
    There is an article on supervenience in the SEP - probably more than you want to know, but relevant to this topic. Here is a handy definition from the opening:

    A set of properties A supervenes upon another set B just in case no two things can differ with respect to A-properties without also differing with respect to their B-properties. In slogan form, “there cannot be an A-difference without a B-difference”.Supervenience
  • Mathematical universe or mathematical minds?
    The question seems a correspondent of the most popular question “Was mathematics invented or discovered?” and relates to the nature of mathematics as well as to the philosophical problem of applicability of mathematics. However, there are anthropocentric and evolutionary features that the philosophical investigations on this topic have not focused on muchDoru B

    The idea of naturalizing mathematics is not new. It is how the thesis that mathematics and mathematical truth are discovered (as opposed to constructed or pulled from an ideal Platonic realm) is often cached out.

    Though the research in "perceptual mathematics" cited in the article is recent, the general finding that there are innate proto-mathematical capacities should not come as a surprise. This doesn't resolve the question of whether mathematics is invented or discovered, but perhaps the question should be dissolved as a false dilemma. We might gravitate towards certain mathematical structures due to innate predispositions. We also invent mathematics to deal with empirical problems. We also invent mathematics with no practical goal in mind and then, having a ready-made tool at our disposal, opportunistically find a use for it. Nowadays we also invent a load of completely useless mathematics, of which perhaps a small fraction will ever find an application, and the rest will gather dust in mathematical journals and specialist books. Then again, pure mathematicians share the same cognitive apparatus with the rest of humans, they develop in largely the same environment, and their work is influenced by past mathematical culture.

    So, what to make of this tangle? That it's not either-or - it's both and then some.
  • Personal Identity over time and Causal Continuity
    Here’s a copy of the paper, I responded to a post about it on Reddit

    https://scholarworks.sjsu.edu/cgi/viewcontent.cgi?article=1391&context=comparativephilosophy
    Ignoredreddituser

    Well, the paper doesn't give any detail about the causal continuity theory beyond what you've summarized here, and I don't feel like delving into Buddhist philosophy to find out more. Perhaps there is a more tenable version of the model than just a hand-wavy "causal stream"? Otherwise it's hardly worth talking about.
  • Personal Identity over time and Causal Continuity
    I don't really have a stake in this argument, since I don't subscribe to the causal continuity theory of personal identity. As a metaphysical theory, I would even object to the presumption that identity has to be grounded (reduced to) something else. As a summation of its semantics (i.e. how the concept is ordinarily deployed in speech and thought) it doubt that it works well.

    That said, it would be good to see a fuller exposition of the thesis before considering the criticism. Obviously, personal identity can't be all and only about causality, else it would entrain your entire past lightcone, let alone people around you.

    As a possible defense though it could be argued that people and other influential events in (and even preceding) your life do contribute to the development of your personal identity and to how you and others perceive it.
  • What are you listening to right now?
    This cracked me up. So you want to write a fugue...



    Written (yes, written) by Glenn Gould.
  • On the Effectiveness of Mathematics in the Natural Sciences (By Way of Analogy)
    it has been asserted by a number of philosophers that the predicational logic underlying mathematics is not irreducible. There may be more ‘precise’ ways to render
    the world than via a mathematical language.
    Joshs

    Can you plain this a bit more? "Not irreducible" = reducible? To what? And has anything been proposed as an alternative to a mathematical language?
  • On the Effectiveness of Mathematics in the Natural Sciences (By Way of Analogy)
    I must admit that I was kind of playing devil's advocate here. I do not honestly believe that we systematically confabulate structure where none exists. Peirce famously quipped: "Let us not pretend to doubt in philosophy what we do not doubt in our hearts." Taken at face value, I think this is exactly wrong. Like many people raised in the same rationalist, scientific tradition, I do not doubt in my heart the vision of a rule-bound world. And this complacency is what worries me sometimes, so I want to push back against it.

    I can think of two arguments against this possibility.

    1. Consider just how implausible it would be for the development of structure in the world--any structure, never mind galaxies, solar systems, complex molecules, life, or intelligent life--without regularity.
    Asphodelus

    Well, structure and regularity are related notions, but yes, of course I wasn't arguing for a solipsist vision in which none of the apparent regularity is real. The world has to be regular enough to produce all these things.

    2. On the fundamental level of matter, space, and time, the world has proved to be extremely regular.Asphodelus

    Yes, this is what convinces the most. It is all right to talk about alternative possibilities in the abstract, but when you actually study nature, especially at its most basic, you see just how tightly it constrains our explanations. And the more closely we look, the less room there is for error, which begs the conclusion that any apparent slack is due to our lack of understanding.

    This doesn't hold equally well across all inquiries though. The larger and more complex the object of study, the poorer the data, the more we have to rely on statistics and plausible extrapolation to make the best of a bad situation. And this is where our optimistic, pattern-seeking nature can get the best of us (not to mention systemic flaws in our scientific institutions). We tend to oversimplify and overexplain in the face of messy or insufficient information.
  • On the Effectiveness of Mathematics in the Natural Sciences (By Way of Analogy)
    I agree that with the above, but that does t necessarily mean the below follows from it.Joshs

    Saying the world is mathematical is like saying that it consists of propositional statements.Joshs

    I was just loosely referencing the idea of a clockwork universe, structured world, mathematics being "embedded" in the world - however you want to express it. This general idea has been widely shared by rational-minded people, but caching it out with more philosophical precision opens up a metaphysical Pandora's box, as I am sure you are well aware.
  • Why do people hate Vegans?
    Why do people hate Vegans?

    They taste like broccoli.
    Banno

    Nonsense! I love vegans, especially those health-conscious, exercise- and diet-obsessed ones. They taste like high-end gourmet pork.
  • On the Effectiveness of Mathematics in the Natural Sciences (By Way of Analogy)
    It isn't "formulated in a priori necessity in the armchairs and heads of mathematicians".

    That's a relatively recent image of mathematics, a consequence of the advent of modern academia.

    Mathematics is embedded in the world.
    Banno

    You make like you are objecting to the OP, but here you are just restating the same thesis. Yes, the game analogy is a bit awkward, but the idea is the same: mathematics fits the world so well because the world just is "mathematical."

    The game analog breaks down, because any move can be made to fit into the rules of a game in which part of the game is to re-write the rules.Banno

    Not any move, surely. The world is rich enough to exhibit multiple regularities, depending on how you look at it, and those regularities can be modeled in multiple ways. Still, when you get into the nitty-gritty of said modeling, you will quickly discover just how tightly nature constrains our efforts - ask any working scientist! For better or for worse, scientists aren't free to make any moves they wish.

    Which, of course, forms the essence of the OP question. When people wonder at how well mathematics fits the world, there are two seemingly opposing aspects to this observation. On the one hand, yes, we've had a lot of success with mathematical modeling. On the other hand, you can't just make up anything and apply it anything equally successfully. It's a very tight fit, especially at the most basic (aka fundamental) level. This is what makes the fit seem to remarkable.

    Still, there's this nagging doubt that I referred to earlier and that perhaps you had in mind as well: how much of that fit is down to our desires, prejudices and biases?
  • On the Effectiveness of Mathematics in the Natural Sciences (By Way of Analogy)
    This is easy to see in a simplified situation of games, but harder to see in the situation of mathematics and the natural world.Asphodelus

    To be honest, I thought it was rather the opposite: the game analogy is overly complicated for the point it is making, which is that the world has a certain structure and we, being part of the world, are constrained by that structure. And that the world being structured is what explains the effectiveness of (some) mathematics in describing it, since mathematics is a way to build or describe abstract structures.

    Of course, that's one possible explanation. Another is that we expect to find structure, are constrained by our mental constitution to find structure, and that is why we find it. This isn't as neatly self-contained as the first explanation, since it doesn't explain why we are constituted this way and how it is that we exist at all, in contrast to this:

    So here's a kind of anthropological explanation for the effectiveness of mathematics to the natural sciences. Of course our cosmos yields to the great book of mathematics, because a cosmos that didn't wouldn’t have us in it. In short, only a regular universe can harbor intelligence, and a regular universe is mathematically describable.Asphodelus

    But what if there is some truth to the second possibility? What if the world is not quite as regular as our science implies, but we are biased against noticing this fact, because we have evolved to seek out and take advantage of regular structures?
  • Synonymity, Shannon Entropy, Complexity, and the Library of Babel
    1. The total number of meaningful messages is less than the total number of possible messages. The proof of this is that the same message can be sent using different codes, such that, once transcribed into meaning by the receiver, it is the same message. For an example, we can imagine whole books of English where every letter is simply shifted one space down, A becomes B, Z becomes A, etc.Count Timothy von Icarus

    This is assuming that there is a strict mapping from code to meaning (a surjection in this case). In reality, of course, the interpretation of a text ("code") is not unambiguous, which is to say that the same code can generate multiple meanings for different receivers (readers) or even for the same receiver.
  • Transitivity of causation
    My question is: isn't this just a debate about the definition of 'causality'? Does it really matter which definition we accept? Can't we simply decide the definition?clemogo

    And by 'definition of causation' I don't mean the literal dictionary definition or scientific definition. I'm referring to whether or not causation is transitive... can we just decide whether or not it is? Or is it something that needs to be discovered somehow?clemogo

    Your question is odd. Surely, if causality is more than an idle fantasy that we are making up here on the spot, then the question of whether causality is transitive is not independent of what we believe causality to be?
  • Gettier Problem.
    JTB is posited not as a dictionary definition of the word 'knowledge' but as a specialist philosophical definition. Like you though, I am not sure how useful it is for that purpose. Sometimes it seems that it has no other use than for people to argue over it, but perhaps my perception is skewed by these perennial Gettier-type debates on the internet.
  • Gettier Problem.
    It's better to let go of this constraint and simply use the word knowledge as we tend to do in ordinary life, which usually does not pose much problems in discussion, outside of specific cases like this.Manuel

    The thing is that ordinary use varies, and there is a sense of knowledge that answers the JTB criteria. The truth criterion is justified by locutions such as "I thought I knew that P, but I was wrong" (i.e. I didn't actually know that P). Or "A thinks that she knows that P, but she is mistaken."

    But I agree that JTB picks out at best some, but not all ordinary senses of knowledge.
  • Bannings
    One good thing that's come out of this discussion is that I've learned, partly thanks to Banno, that espouse does not mean advocate.jamalrob

    It's the difference between living with your spouse and prostituting him/her.
  • The dark room problem
    Well, not quite. We want a theory that rules out things that are contradicted by the evidence.Banno

    The thing is that when you reduce a theory to very general and rough slogans, like "minimizing surprise" or "survival of the fittest," you will readily find both apparent examples and apparent counterexamples, which then prompts complaints that the theory is either contradictory or explains too much, or even both (@Kenosha Kid). The devil is in the details, as you acknowledge. Without getting into those details you can't really say anything one way or another.

    I am sympathetic to your attitude towards totalizing theories. But there is a difference between a general unifying idea and a detailed treatment of a subject. Evolutionary biology as a whole is a complex and diverse field, appropriate for its complex and diverse subject. And yet Darwin's basic insight pervades it throughout. I think there is room for more such insights in cognitive science and biology.

    By the way, looking Friston's publications, you can see a rather typical pattern where the further he gets from his own field, the wider he casts his net, the more diffuse and light on details and empirical support are his (team's) works, shading into pop-science and philosophy-lite. (There is also an inverse correlation with the number of citations...) Then again, if he got something essentially right, then these kinds of big-picture narratives can be valuable as setting directions for future research and providing an insight into large-scale patterns.
  • The dark room problem
    Again the point is made that an explanation for everything is an explanation for nothing.Banno

    This - not so much this article, but your complaint that PP/PEM seems to have an explanation for everything - reminds me of a common creationists' complaint about the theory of evolution, which often follows a series of failed challenges to its ability to explain evidence. The fact that a theory can explain all evidence doesn't distinguish between a good theory and a vacuous theory. And there is no way to establish which is the case other than scrutinizing the theory and how it purports to explain evidence. There are no easy shortcuts here to dismissive judgements.

    Another thing to note is that there are different ways to respond to a challenge. One is to make a positive argument that the challenge misses its target, e.g. by conducting a decisive test, or by showing that what is alleged to be the case necessarily is not the case. Another is to argue that the challenge may not hit the target. For example, when creationists rhetorically ask "what good is half a wing?" one response is to argue that the equivalent of "half a wing" can be adaptive (maybe not for flying). This second mode of response doesn't provide an additional argument for the theory, but it does forestall the challenge and tasks the challenger (or alternatively the defender) with going deeper and doing more work. This is how we can view Friston's response to the "dark room" challenge in the comment article that you shared.
  • The dark room problem
    Point being, despite some protestations to the contrary, it is still not clear how this fits in with thermodynamics and information theory.Banno

    You picked a rather peripheral article, a comment. Friston's background is in fMRI and computational neuroscience, and that is the inspiration and the main source of evidence for his free energy model, not so much high-level psychology. These would be a better place to start if anyone is looking for more substance:

    A free energy principle for the brain (2006)

    The free-energy principle: a unified brain theory? (Nature Reviews 2010)
  • The dark room problem
    Here's an article that attempts to provide a summation of the thinking around this problem: Free-energy minimization and the dark-room problemBanno

    When I read that sentence I immediately thought of Friston (who is indeed the lead author). Sean Carroll had a podcast with him, where they touched upon the dark room (non-)problem, among other things. It's pretty complicated stuff (at least for someone with no relevant background) that's hard to grasp without getting into some details of information theory, probability, Markov blankets and all that. People shouldn't jump to conclusions based on a short paraphrase.

    It may be worth mentioning that the idea of prediction error (surprise) minimization and predictive processing in general has been kicking around in cognitive science for some time. Other notable people actively working on it are Andy Clark (of The Extended Mind) and Jakob Hohwy. Friston's particular contribution is in bringing the Helmholtz free-energy approach to bear on the problem, and then trying to extend it beyond cognitive science to living systems in general.

    The problem is in trying to model all human behaviour according to one general rule when in fact it is an interplay between many physical processes evolved at different times in different environments, some overriding.Kenosha Kid

    Sure, but also keep in mind that there can be multiple subsystems that can be described by that model, of varying complexity and operating concurrently on different timescales.
  • A common problem in philosophy: The hidden placeholders of identity as reality
    I think that is the point.Philosophim

    I still don't get the point. Yes, most people don't have the background to understand a complex scientific theory, and popularizations can be misleading by way of instilling a false sense of comprehension. We probably agree on that. But I don't see a connection from this to the topic that you are trying to develop.

    But do we know its out there? All that a dimension is, is a variable. We don't really know what the variable represents in reality, because we can't observe it in reality. The fact that we abstract it out to spatial dimensions is the problem.Philosophim

    What exactly do you see as the problem? Abstract thought?
  • A common problem in philosophy: The hidden placeholders of identity as reality
    First, I am a bit puzzled by your choice of the words "identity" and "placeholder": I don't think I've seen them used like this before. From the context, you seem to be referring to models, concepts, representations, abstractions, maps (as in "the map is not the territory"). Is that what you mean?

    Second, I am struggling to discern your point here. The most specific example that you give concerning the use of extra dimensions in string theories is poorly chosen, since neither you nor most of the readers understand the background enough to have a reasonable discussion about it. That these dimensions are "not representations of reality or dimensions as we believe them to be" is obviously true in one sense: we the common people are used to thinking about space as three-dimensional (and that only because Descartes' invention has been drilled into us from an early age). But what of it?
  • Double Slit Experiment.
    assigns an objective existence to a mathematical entity (the wavefunction), which is absurdCartuna

    Do you know of any theory in physics or other sufficiently mathematized science that doesn't do exactly that?

    What's left is assigning a physical reality of what the wavefunction describes.Cartuna

    So... MWI then?
  • Only nature exists
    I suggest the categories "biological" and "artificial".

    They essentially explain the same differentiation that is commonly understood between "natural" and "unnatural" but they are much more precise in doing so.
    Hermeticus

    How about "natural rock formation"?


    Why is it that some people can't wrap their head around the fact that words can have multiple meanings/uses? Have they ever opened a dictionary? Merriam-Webster gives something like 20 distinct meanings of the word 'natural'.
  • Consciousness, Mathematics, Fundamental laws and properties
    It seems that we can easily observe informational correlates of consciousness (such as integrated information theory), and from there construct mathematical theories to quantify the degree of consciousness within a system.tom111

    I don't know what mathematical models you are referring to, but it seems to me that it is unwarranted to jump to any metaphysical conclusions from the mere fact that some descriptive mathematical models of conscious systems don't give you certain features of consciousness.
  • Does the Multiverse violate the second law of thermodynamics?
    Where did you get that from? 90%? No way. Hooks law doesn't apply to most materials. Even with shear it can't be applied to most materials. Maybe for very small forces, or tiny displacements. Mostly though, a linear algebra just isn't applicable. For a metal spring in the physics class it will do. For an atomic nucleus inside an electron cloud, a Hooke approximation will do.Cartuna

    The 90% figure is rhetorical, but yes, much of engineering mechanics is based on the linear elastic model, with plasticity accounting for most of the rest. Applications of non-linear elasticity, rate-dependence, etc. are much less common.

    (Relatively) tiny displacements characterize the operating range of most buildings and machinery, and linear elasticity works well in that range. (Of course, the fact that it is computation-friendly is also a big factor in its popularity.) Forces don't have to be so tiny, since materials like steel and concrete have a high elastic modulus.
  • Does the Multiverse violate the second law of thermodynamics?
    Sure, it's much more useful for more ideal mechanical oscillators like atoms. Not very universal for springs and stuff like Hooke had in mind.Kenosha Kid

    It's very useful for practical stuff though: from ball bearings to bridges to tectonic plates. Take Hooke's law into 3D (with shear) and you get linear elasticity, the backbone of 90% of engineering mechanics from 19th century through the present day.
  • Coronavirus
    Since the vaccines don't prevent transmission of the virus, I'm not sure if they reduce the risk of mutations.Count Timothy von Icarus

    They significantly reduce transmission.

    On the one hand, yes, people who have been vaccinated get infected at lower rates. On the other hand, evidence from livestock shows that partial immunizations that reduce the severity of a disease but still allow transmission between the immunized tends to make diseases more lethal. Variants that would otherwise die out due to killing their hosts too quickly are allowed to proliferate.Count Timothy von Icarus

    You have one example from livestock, and it doesn't look like what we are seeing with COVID. This virus has produced more transmissible variants, but there is no evidence so far that it is becoming more lethal. The general trend with infectious diseases is to become less lethal over time: there is no evolutionary advantage for an infection in killing off its vector.
  • Does the Multiverse violate the second law of thermodynamics?
    I don't see how.Kenosha Kid

    I was kidding, of course. But you could trace the ancestry to the Hooke's law from the stress components of the tensor. I am not sure, but that may have been the first example of a constitutive material equation, which evolved into continuum mechanics, and from there it's a hop, skip and a jump to GR :)
  • Does the Multiverse violate the second law of thermodynamics?
    Shouldn't the second law of thermodynamics be called a "habit" instead of a law? It seems to me to speak of a tendency to disorder, not an iron-clad rule.Manuel

    Hey, if Hooke's law gets to be a law, thermodynamics is a cert!Kenosha Kid

    Hey, Einstein field equations are basically a glorified Hooke's law :)

    The second law is a statistical law, so yes, it doesn't deliver absolutely certain predictions. It works well with probabilistic epistemology though: its predictions should be treated as rational expectations. Yes, it is possible for all the air in your room to spontaneously bunch up in one corner, but you should not take that possibility seriously, on account of its vanishingly low probability.

    Right, you could have it, but obviously we don't have it at the macroscopic level, as entropy is observably increasing.Count Timothy von Icarus

    Well, it has been increasing so far, in our corner of the universe...

    However, given many worlds, the almost infinitely improbable universe of non-increasing entropy is one of the (almost?) infinite worlds and actually exists.

    Whereas you as an observer in one world could expand the volume of a container of gas all day for a billion years and not see entropy remain static a single time, because the probability is incredibly low.
    Count Timothy von Icarus

    A thermodynamic anomaly could still happen in our world, for all we know. Thermodynamics describes our expectations of what we are likely to observe, and that is not affected by there being many other worlds, because we are only experiencing one world.

    Besides, you shouldn't conflate the many branches of the universal wavefunction with the many microstates of each and every statistical ensemble described by thermodynamics. There is no one-to-one correspondence between them, since they describe very different things.