Laws as Rules

We speak casually of the laws of nature determining the distribution of matter and energy, or governing the behavior of physical objects. Implicit in this rhetoric is a metaphysical picture: the laws are rules that constrain the temporal evolution of stuff in the universe. In some important sense, the laws are prior to the distribution of stuff. The physicist Paul Davies expresses this idea with a bit more flair: "[W]e have this image of really existing laws of physics ensconced in a transcendent aerie, lording it over lowly matter." The origins of this conception can be traced back to the beginnings of the scientific revolution, when Descartes and Newton established the discovery of laws as the central aim of physical inquiry. In a scientific culture immersed in theism, it was unproblematic, even natural, to think of physical laws as rules. They are rules laid down by God that drive the development of the universe in accord with His divine plan.

Does this prescriptive conception of law make sense in a secular context? Perhaps if we replace the divine creator of traditional religion with a more naturalist-friendly lawgiver, such as an ur-simulator. But what if there is no intentional agent at the root of it all? Ordinarily, when I think of a physical system as constrained by some rule, it is not the rule itself doing the constraining. The rule is just a piece of language; it is an expression of a constraint that is actually enforced by interaction with some other physical system -- a programmer, say, or a physical barrier, or a police force. In the sort of picture Davies presents, however, it is the rules themselves that enforce the constraint. The laws lord it over lowly matter. So on this view, the fact that all electrons repel one another is explained by the existence of some external entity, not an ordinary physical entity but a law of nature, that somehow forces electrons to repel one another, and this isn't just short-hand for God or the simulator forcing the behavior.

I put it to you that this account of natural law is utterly mysterious and borders on the nonsensical. How exactly are abstract, non-physical objects -- laws of nature, living in their "transcendent aerie" -- supposed to interact with physical stuff? What is the mechanism by which the constraint is applied? Could the laws of nature have been different, so that they forced electrons to attract one another? The view should also be anathema to any self-respecting empiricist, since the laws appear to be idle danglers in the metaphysical theory. What is the difference between a universe where all electrons, as a matter of contingent fact, attract one another, and a universe where they attract one another because they are compelled to do so by the really existing laws of physics? Is there any test that could distinguish between these states of affairs?

Laws as Descriptions

There are those who take the incoherence of the secular prescriptive conception of laws as reason to reject the whole concept of laws of nature as an anachronistic holdover from a benighted theistic age. I don't think the situation is that dire. Discovering laws of nature is a hugely important activity in physics. It turns out that the behavior of large classes of objects can be given a unified compact mathematical description, and this is crucial to our ability to exercise predictive control over our environment. The significant word in the last sentence is "description". A much more congenial alternative to the prescriptive view is available. Instead of thinking of laws as rules that have an existence above and beyond the objects they govern, think of them as particularly concise and powerful descriptions of regular behavior.

On this descriptive conception of laws, the laws do not exist independently in some transcendent realm. They are not prior to the distribution of matter and energy. The laws are just descriptions of salient patterns in that distribution. Of course, if this is correct, then our talk of the laws governing matter must be understood as metaphorical, but this is a small price to pay for a view that actually makes sense. There may be a concern that we are losing some important explanatory ground here. After all, on the prescriptive view the laws of nature explain why all electrons attract one another, whereas on the descriptive view the laws just restate the fact that all electrons attract one another. But consider the following dialogue:

A: Why are these two metal blocks repelling each other?

B: Because they're both negatively charged, which means they have an excess of electrons, and electrons repel one another.

A: But why do electrons repel one another?

B: Because like charges always repel.

A: But why is that?

B: Because if you do the path integral for the electromagnetic field (using Maxwell's Lagrangian) with source terms corresponding to two spatially separated lumps of identical charge density, you will find that the potential energy of the field is greater the smaller the spatial separation between the lumps, and we know the force points in the opposite direction to the gradient of the potential energy.

A: But why are the dynamics of the electromagnetic field derived from Maxwell's Lagrangian rather than some other equation? And why does the path integral method work at all?


Is the last link in this chain doing any explanatory work at all? Does it give us any further traction on the problem? B might as well have ended that conversation by saying "Well, that's just the way things are." Now, laws of nature do have a privileged role in physical explanation, but that privilege is due to their simplicity and generality, not to some mysterious quasi-causal power they exert over matter. The fact that a certain generalization is a law of nature does not account for the truth and explanatory power of the generalization, any more than the fact that a soldier has won the Medal of Honor accounts for his or her courage in combat. Lawhood is a recognition of the generalization's truth and explanatory power. It is an honorific; it doesn't confer any further explanatory oomph.

The Best System Account of Laws

David Lewis offers us a somewhat worked out version of the descriptive conception of law. Consider the set of all truths about the world expressible in a particular language. We can construct deductive systems out of this set of propositions by picking out some of the propositions as axioms. The logical consequences of these axioms are the theorems of the deductive system. These deductive systems compete with one another along (at least) two dimensions: the simplicity of the axioms, and the strength or information content of the system as a whole. We prefer systems that give us more information about the world, but this greater strength often comes at the cost of simplicity. For instance, a system whose axioms comprised the entire set of truths about the world would be maximally strong, but not simple at all. Conversely, a system whose only axiom is something like "Stuff happens" would be pretty simple, but very uninformative. What we are looking for is the appropriate balance of simplicity and strength [1].

According to Lewis, the laws of nature correspond to the axioms of the deductive system that best balances simplicity and strength. He does not provide a precise algorithm for evaluating this balance, and I don't think his proposal should be read as an attempt at a technically precise decision procedure for lawhood anyway. It is more like a heuristic picture of what we are doing when we look for laws. We are looking for simple generalizations that can be used to deduce a large amount of information about the world. Laws are highly compressed descriptions of broad classes of phenomena. This view evidently differs quite substantially from the Davies picture I presented at the beginning of this post. On Lewis's view, the collection of particular facts about the world determines the laws of nature, since the laws are merely compact descriptions of those facts. On Davies's view, the determination runs the other way. The laws are independent entities that determine the particular facts about the world. Stuff in the world is arranged the way it is because the laws compelled that arrangement.

One last point about Lewis's account. Lewis acknowledges that there is an important language dependence in his view of laws. If we ignore this, we get absurd results. For instance, consider a system whose only axiom is "For all x, x is F" where "F" is defined to be a predicate that applies to all and only events that occur in this world. This axiom is maximally informative, since it rules out all other possible worlds, and it seems exceedingly simple. Yet we wouldn't want to declare it a law of nature. The problem, obviously, is that all the complexity of the axiom is hidden by our choice of language, with this weird specially rigged predicate. To rule out this possibility, Lewis specifies that all candidate deductive systems must employ the vocabulary of fundamental physics.

But we could also regard lawhood as a 2-place function which maps a proposition and vocabulary pair to "True" if the proposition is an axiom of the best system in that vocabulary and "False" otherwise. Lewis has chosen to curry this function by fixing the vocabulary variable. Leaving the function uncurried, however, highlights that we could have different laws for different vocabularies and, consequently, for different levels of description. If I were an economist, I wouldn't be interested (at least not qua economist) in deductive systems that talked about quarks and leptons. I would be interested in deductive systems that talked about prices and demand. The best system for this coarser-grained vocabulary will give us the laws of economics, distinct from the laws of physics.

Lawhood Is in the Map, not in the Territory

There is another significant difference between the descriptive and prescriptive accounts that I have not yet discussed. On the Davies-style conception of laws as rules, lawhood is an element of reality. A law is a distinctive beast, an abstract entity perched in a transcendent aerie. On the descriptive account, by comparison, lawhood is part of our map, not the territory. Note that I am not saying that the laws themselves are a feature of the map and not the territory. Laws are just particularly salient redundancies, ones that permit us to construct useful compressed descriptions of reality. These redundancies are, of course, out there in the territory. However, the fact that certain regularities are especially useful for the organization of knowledge is at least partially dependent on facts about us, since we are the ones doing the organizing in pursuit of our particular practical projects. Nature does not flag these regularities as laws, we do.

This realization has consequences for how we evaluate certain forms of reductionism. I should begin by noting that there is a type of reductionism I tentatively endorse and that I think is untouched by these speculations. I call this mereological reductionism [2]; it is the claim that all the stuff in the universe is entirely built out of the kinds of things described by fundamental physics. The vague statement is intentional, since fundamental physicists aren't yet sure what kinds of things they are describing, but the motivating idea behind the view is to rule out the existence of immaterial souls and the like. However, reductionists typically embrace a stronger form of reductionism that one might label nomic reductionism [3]. The view is that the fundamental laws of physics are the only really existant laws, and that laws in the non-fundamental disciplines are merely convenient short-cuts that we must employ due to our computational limitations.

One appealing argument for this form of reductionism is the apparent superfluity of non-fundamental laws. Macroscopic systems are entirely built out of parts whose behavior is determined by the laws of physics. It follows that the behavior of these systems is also fixed by those fundamental laws. Additional non-fundamental laws are otiose; there is nothing left for them to do. Barry Loewer puts it like this: "Why would God make [non-fundamental laws] the day after he made physics when the world would go on exactly as if they were there without them?" If these laws play no explanatory role, Ockham's razor demands that we strike them from our ontological catalog, leaving only the fundamental laws.

I trust it is apparent that this argument relies on the prescriptive conception of laws. It assumes that real laws of nature do stuff; they push and pull matter and energy around. It is this implicit assumption that raises the overdetermination concern. On this assumption, if the fundamental laws of physics are already lording it over all matter, then there is no room for another locus of authority. However, the argument (and much of the appeal of the associated reductionist viewpoint) fizzles, if we regard laws as descriptive. Employing a Lewisian account, all we have are different best systems, geared towards vocabularies at different resolutions, that highlight different regularities as the basis for a compressed description of a system. There is nothing problematic with having different ways to compress information about a system. Specifically, we are not compelled by worries about overdetermination to declare one of these methods of compression to be more real than another. In response to Loewer's theological question, the proponent of the descriptive conception could say that God does not get to separately specify the non-fundamental and fundamental laws. By creating the pattern of events in space-time she implicitly fixes them all.

Nomic reductionism would have us believe that the lawhood of the laws of physics is part of the territory, while the lawhood of the laws of psychology is just part of our map. Once we embrace the descriptive conception of laws, however, there is no longer this sharp ontological divide between the fundamental and non-fundamental laws. One reason for privileging the laws of physics is revealed to be the product of a confused metaphysical picture. However, one might think there are still other good reasons for privileging these laws that entail a reductionism more robust than the mereological variety. For instance, even if we accept that laws of physics don't possess a different ontological status, we can still believe that they have a prized position in the explanatory hierarchy. This leads to explanatory reductionism, the view that explanations couched in the vocabulary of fundamental physics are always better because fundamental physics provides us with more accurate models than the non-fundamental sciences. Also, even if one denies that the laws of physics themselves are pushing matter around, one can still believe that all the actual pushing and pulling there is, all the causal action, is described by the laws of physics, and that the non-fundamental laws do not describe genuine causal relations. We could call this kind of view causal reductionism.

Unfortunately for the reductionist, explanatory and causal reductionism don't fare much better than nomic reductionism. Stay tuned for the reasons why!



[1] Lewis actually adds a third desideratum, fit, that allows for the evaluation of systems with probabilistic axioms, but I leave this out for simplicity of exposition. I have tweaked Lewis's presentation in a couple of other ways as well. For his own initial presentation of the view, see Counterfactuals, pp. 72-77. For a more up-to-date presentation, dealing especially with issues involving probabilistic laws, see this paper (PDF).

[2] From the Greek meros, meaning "part".

[3] From the Greek nomos, meaning "law".

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A: But why are the dynamics of the electromagnetic field derived from Maxwell's Lagrangian rather than some other equation? And why does the path integral method work at all?

B: What do you mean by "why"?

A: Hey, wait a minute, I'm asking the questions here! Um ... I mean ... I want an explanation of what makes the world that way.

B: Really, you do? You didn't like the last three explanations I gave you. What was wrong with them?

A: They didn't go deep enough. They explained things in the world in terms of deeper and deeper levels, but there was always something left to explain.

B: What would it feel like to have a deep-enough explanation? What are some things for which you think you do have a deep-enough explanation?

A: I don't know. Arithmetic, maybe? I don't feel the need to have a deeper explanation of 1 + 1 = 2, I'm happy saying that it just does equal two, and if you set it up to be different you'd just be talking about some operation other than addition on the naturals.

B: I wonder why arithmetic feels adequately explained to you, but electromagnetism doesn't? What would it feel like if arithmetic were as problematic to you as electromagnetism is?

A: ... I'd be asking why ... (read more)

B: Regarding arithmetic, I know they're truths because I've defined the underlying territory. I - collectively speaking - decided on axioms from which the whole tree of lemmata and corollaries spawns. Granted, I cannot fully track all the branches of the tree due to Goedel, there will be true statements that follow from my axioms that I'll never be able to trace back to the roots (which would be the proof), but the statements that I do prove I can rely upon to be true. Why? Because it is I who made up the whole system, I don't need to match it to any external system of unknowns. Unlike my model of physics.
For the record, Tegmark 4 feels "deep enough" for me because it's a TOE without any arbitrary choices.
Metaphysics is when one tries to understand macrophysics. Symbols are from how conscious beings process and use info, which they do in different places and with different bodies/processors encoded with info from all their previous places all the way back to the beginning or infinity. All these differences are what I refer to as "perspectivism," which we have to correct for in trying to understand macrophysics and in helping beings. I can think of only one way in which a human can output a TOE useful to other humans: there being plenty of cosmic info encoded in him to express through symbols that can be easily decoded by other humans. But if there's plenty of info in them, what about in other bodies? People are realizing that there's more encoded in, sought, and processed by beings than they previously realized (e.g. consciousness in non-humans, latent savant skills, latent creativity, etc. In the case of Derek Amato, an acquired savant, what would've happened if he didn't have a piano with which to process and express info? Would he have been stuck with racing thoughts or considered crazy, lame, or autistic, like in Yellow Wall Paper or as with Cassandras, who have trouble communicating info to left-brains to use? LessWrongers have so far been left-brainy, using symbolism, rather than realistic or even representational imagery, despite using the word "map." This website lacks multimedia for conveying more than words or numbers can and preventing symbolic framing bias. To the extent that brains manipulate symbols, or "symbol polish" as Seth Godin would say and those manipulations don't connect to and activate much sense-data, the symbols can be useless or misleading, like listening to what the GPS says without sensing much else while driving. So what happens if one doesn't sense much about beings' inner workings, yet still must work with or write about those beings? The left-brain can end up treating the beings like objects that came out of nothing, like when Yvain

This seems to be taking down a straw man, and far from "challenging a central tenet of LW: reductionism", you perfectly describe it and expound on it, if a bit wordily. At least in my mind, it's very obvious that physical 'law' is a map-level concept. Physicists themselves have noticed that for a map-level concept, physical 'law' fits the territory so amazingly well, that they have written articles such as "The Unreasonable Effectiveness of Mathematics in the Natural Sciences"

I don't claim that this post in particular challenges the consensus (at least, I don't intend to claim that, but I can see how my phrasing in the intro suggests it). It's mostly just setup. I think the LW consensus is probably closer to what I call "explanatory reductionism" at the end of this post, but attacking that position required that I make it clear how I think about laws of nature. The ultimate position I want to defend is that the only tenable reductionism is the extremely weak mereological kind. Surely this is different from the position generally advocated here. That said, I don't think the position I'm attacking in this post is a straw man. As I point out, Paul Davies (hardly a fringe figure in physics) explicitly embraces it. He also says (in the linked excerpt) that "most physicists working on fundamental topics inhabit the prescriptive camp, even if they won't own up to it explicitly." In addition, I've seen nomic reductionism defended (and upvoted) on LW more than once. As an example, see some of the comments on this thread. Even people who would, if pressed, agree that laws are description often unconsciously infer things that only work if you think of laws as rules. Do you think the points made in this post are common enough knowledge around here for the post to be of not much use?

I don't claim that this post in particular challenges the consensus

That would be the bit where you said "This is the first in a planned series of posts challenging a central tenet of the LessWrong consensus". When you say that you're challenging the consensus, it appears to the reader as though you're challenging the consensus.

Hence my parenthetical concession in the grandparent. But you're right, I should edit the post itself. Doing that right now.

I hereby nominate this for the 2012 Understatement Award.
How was it an understatement? I acknowledge that it feels like one when you read it, but defining that way lies madness! Just ask the words "ironic" and "literally".
I agree with David_Gerard: when I say I'm doing something, it appears to the reader as though I'm doing that thing. I would also agree with various more-strongly-worded equivalents, such as "when I say I'm doing X in a series of acts that includes Y, it's disingenuous to later claim that Y wasn't intended to do X." Hence, understatement. That is, an expression worded less strongly than, in my opinion, the situation justifies.
Is "challenge the consensus" a performative utterance? By saying "I challenge the consensus regarding foo", do you thereby challenge the consensus regarding foo? Consider: If I said, "I challenge the Less Wrong consensus that 2 + 2 = 5. I assert that it's 4," by saying this I wouldn't actually challenge a consensus that 2 + 2 = 5, because there isn't one to challenge. Rather, all I would be doing is setting up a straw man: falsely asserting the existence of a consensus, and then disagreeing with that imagined consensus.
What is, actually, the difference between laws as rules and laws as descriptions of regularity, except the choice of language? There is in fact a pretty strong LW consensus that beliefs should be distinguishable from each other by different anticipated experiences; I am not sure whether nomic and mereological reductionism predict different observations. (I agree with the gist of the post, in the sense that it is more elegant to view physical laws as descriptions of regularities in observed universe, rather than rules that push matter around.)
See my comment here. Thinking of laws as rules vs. descriptions may not predict different observations, but they do lead to different cognitive attitudes about scientific inquiry and explanation (e.g. we often think of rules as explaining behavior, but we don't think of descriptions as explanatory in the same way), and in this regard I think the prescriptive perspective is a recipe for confusion. One could say the same thing about the kind of empiricism advocated on LW as opposed to rationalism (of the traditional philosophical variety, not the LW variety). These two philosophical stances don't predict different observations, but that doesn't mean the choice between them is merely a linguistic one. They are associated with different pragmatic attitudes, and the empiricist attitude is a lot more valuable that the rationalist one.
What concrete differences in e.g. scientific achievements would you expect to stem from the difference between the descriptive and prescriptive attitudes?
See this comment for an example.
Not really.
I know that post and don't think it invalidates my point. Its main point is that for a proposition to be meaningful it is not necessary that it can be verified directly, but it is often sufficient if the proposition is part of a logically coherent theory that is tested as a whole. This is not in conflict with the demand on difference in anticipated experiences from different beliefs: the hypothesis that a cheesecake materialised in the centre of the Sun may not be falsified by direct observation, but still is incompatible with the picture of the world dictated by perfectly testable and verified physical theories. As a side note, the linked post has been criticised as strawmanning logical positivism.
So what testable logically coherent theory is your main point a part of?
Do you want to read about the testable consequences of the belief that beliefs should have testable consequences, or was your question only rhetorical?
I'd actually find that fascinating :)
Are they similar to this?
One testable consequence of the belief that beliefs should have testable consequences (let's call it T) is that people who believe T will have higher percentage of true beliefs than people who don't. Although this is not much a consequence of T as a more precise reformulation thereof.
You do realize you can apply that procedure to give any metaphysical belief testable consequences, including the one you were asking about here.
Well, yes. That was basically pragmatist's answer to my question which I have accepted. It is a little bit disturbing since I am forced to give metaphysics more credit that I used to. The possible way out is to limit the testability criterion only to direct logical consequences of beliefs so that it doesn't apply to "psychological" consequences of form "believing X increases likelihood of believing Y (even if there is no logical connection between X and Y)". This might be a good idea but I am not sure where precisely to draw the line between direct and psychological consequences of beliefs.
Why do you care?
To have an objective criterion for evaluating ideas in case my intuition is ifluenced by bias. To find out what exactly makes most metaphysics appear unsatisfactory and empty to me. Why are people concerned with formalising epistemology, after all? By the way, you don't need to link to the Sequences articles for me, I have read them all.
What do any of those have to do with where you "draw the line between direct and psychological consequences of beliefs"?
If I aim to apply the criterion "a theory is worthy only if it has direct logical testable consequences", I better know what do I mean by "direct consequence".

A: But why are the dynamics of the electromagnetic field derived from Maxwell's Lagrangian rather than some other equation? And why does the path integral method work at all?


What do you think of Max Tegmark's answer, that it's because universes with every possible (i.e., non-contradictory) set of laws of physics exist and we happen to be in one with electromagnetic dynamics derived from Maxwell's Lagrangian? (Or alternatively, every mathematical structure exist in a platonic sense and we happen to inhabit one that looks like this from the inside.)

I'm not sure if this can be called a LW consensus, but it has at least a large minority following here. One important reason is that this view seems to make it much easier to do decision theory, because it means that goals/values can be stated in terms of preferences about how mathematical structures turn out or unfold, instead of about "physical stuff". In particular, UDT was heavily influenced by Tegmark's ideas and there seems to be a consensus among people interested in decision theory here that UDT is a step in the right direction. If you're not already familiar with Tegmark's ideas, user ata wrote a post that can serve as an introduction.

This seems like a trivial idea, interesting mostly insofar as it dispels unnecessary mysteriousness of physical world, but not particularly meaningful or helpful otherwise. I'll try to summarize the context in which the idea of mathematical universe looks to me this way. When abstract objects or ideas are thought about with mathematical precision, it turns out that they are best described by their "structure", which is a collection of properties that these things have (like commutativity of multiplication on a complex plane or connectedness of a sphere), rather than some kind of "reductionistic" recipe for assembling them. These properties imply other properties, and in many interesting cases, even based on a fixed initial definition it's possible to explore them in many possible ways, there is no restriction to a single direction in finding more properties (like new laws of number theory or geometry, as opposed to running a computer program to completion). At the same time, it's not possible, either in principle or in practice, to infer all interesting properties following from given defining properties that specify a sufficiently complicated structure, so there is perpetual logical uncertainty. When two structures (or two "things" having these respective structures, described by them to some extent) share some of their properties in some sense, it's possible to infer new facts about one of the structures by observing the other. This way, for example, a computer program can reason about an infinite structure: if we know that a certain property stands or falls for the program and for the structure together, we can conclude that the property holds for the structure if its counterpart does for the program and so on. Also, setting up a structure that reflects properties of another one doesn't require knowing all defining properties of that structure, knowing only sufficiently accurate approximations to some of them may be sufficient to make useful inferences. Physic
Every existing thing has a structure, but it is not clear that every logically consistent structure is the structure of an existing thing. The distinction between instantiated and uninstantiated mathematical structures is not obviously meaningless. The Tegmark hypothesis is that this distinction is meaningless. Since this meaninglessness is not obvious, the Tegmark hypothesis is nontrivial.
Define instantiated.
What would constitute a definition for your purposes?
A way to tell an instantiated mathematical-structure-containing-sentient-beings from an uninstantiated one. (That doesn't sound very different from telling conscious beings from philosophical zombies to me.)
I don't know whether the concept of existence is meaningful. If it is, then something like the following should work: To determine whether a mathematical structure M is instantiated, examine every thing that exists. If M is the structure of something that you examine, then M is instantiated. Otherwise, M is not instantiated. Thus, whether the concept of existence is meaningful is the heart of the problem. I don't claim to know that this concept is meaningful. I claim only not to know that it is meaningless.
I think it's more like there are several concepts which share the same label. If a tree falls in the forest, and no one hears it, does it make a sound?
The tree in the forest is a case of various clear concepts (of sound) clearly implying different true answers. The problem of Being is a problem of finding a clear concept that implies answers that many people find intuitively plausible. It is more like the problem of being perfectly confident that various mathematical statements are true, while finding it very difficult to say just what it is that those statements are true about.
*points at objects which are instances of a class* Those are instantiated (classes). *points at classes that are unused at runtime, do not have any real object instances, perhaps were never even coded, but are simply logically consistent* Those are uninstantiated (classes). Perhaps that'll help seeing it.
I'm making a distinction between saying "physical world is a structure" and "physical world has structure": the first form seems to demand something unclear, and the latter seems to suffice for all purposes. Suppose things may either exist or not; but structure of things is abstract math, so it does seem clear that the properties of a structure don't care whether it's "instantiated" or not: the math works out according to what the structure is, regardless of which things have it. And since we only reason about things in terms of their structure, a distinction that isn't reflected in that structure can't enter into our reasoning about them. (It might be possible to cash out "existence" of the kind physical world has as a certain property of structures, probably something very non-fundamental, like human morality, but this interpretation seems unlike the kind of confusion the argument is meant to counter.)
3Wei Dai12y
I can't find anything to disagree with after this quoted sentence, but "this seems like a trivial idea" certainly isn't something I'd say if someone else wrote the comment you're replying to. My guess is that you think "makes decision theory much easier" gives Tegmark too much credit because decision theory is far from solved, there are lots of hard problems left, and Tegmark's ideas represent only a small step, in a relative sense, compared to the overall difficulty of the project. If my guess is right, I could offer the defense that it feels like a large amount of progress to me, in an absolute sense, but it might be a good idea to just rephrase that sentence to avoid giving the wrong impression. Or, let me know if I'm totally off base and you intended a different point entirely.
I mean only that the description I sketched (which might be seen as referring the the idea of "mathematical universe", but also deconstructs some of it, suggesting that it's meaningless to insist that something "is a mathematical structure"), isn't saying much of anything, and uses only standard ideas from mathematics; in this sense the idea of "mathematical universe" doesn't say much of anything either (i.e. is trivial). It might be a useful point to the extent that understanding it would banish useless ways of metaphysical theorizing about the physical world and free up time for more fruitful activities. So, my comment is unrelated to your point about decision theory, although the simplification (back to triviality) may be useful there and probably more relevant than for most other problems.
I'm aware of Tegmark's ideas, although I haven't thought about them much. I was not aware that they have a following on this site, probably because I haven't read much of the decision theory material on here. I'll read up on the idea and think about it more. My immediate uninformed inclination is skepticism, mainly on the grounds that I doubt the anthropics will work out in Tegmark's favor without some gerrymandering of the ensemble. Also, being able to conceive of a mathematical structure as an independently existing entity rather than a formal description of the structure of some material system seems to require a Gestalt switch that I haven't yet been able to attain.

LW discussions of anthropics in Tegmark's multiverse:

If you look in the comments of these posts you'll find more links to earlier discussions.

I think Tegmark's idea is either tautological or preposterous, depending on what he means by exist. If exist means ‘exist in an abstract, mathematical sense’ (as it does in the sentence There exist infinitely many prime numbers) then it's tautological, and if it means ‘physically exist in this particular universe (i.e., the set of everything that can interact or have interacted with us, or interact or have interacted with something that can interact or have interacted with us, etc.)’ (as it does in the sentence Santa does not exist), it's preposterous. The last chapter in Good and Real by Gary Drescher elaborates on this. Once again, we badly need different words for ‘be mathematically possible’ and ‘be part of this universe’.
I assume he means they exist in the same sense as observers can only find themselves in places that exist. Which does not require any possibility of interaction between any two things that happen to exist.
From what I can tell, Tegmark doesn't mean either of the options you provide. It is closer to the first option ('exist in the abstract') but without all the implied privilege for the universe that happens to have you in it. The difference seems significant.
I don't know too much about Tegmark, but I'm pretty sure he doesn't have your second meaning in mind. That said, I'm not sure your first meaning is actually tautological, given that for Tegmark's idea to be an answer as Wei_Dai suggests, whatever "exist" means it has to encompass the kind of thing that you are doing right now. The idea that things which "exist in an abstract mathematical sense" can, solely by virtue of that, do what you're doing right now is perhaps tautological, but if so the tautology is not one that most humans will readily recognize as one.
Yes, I was unintentionally implicitly assuming that this universe is a mathematical structure. (OTOH, ISTM that this is a somewhat standard assumption on LW, e.g. Solomonoff induction wouldn't make that much sense without it.)
Perhaps. But the connotations of saying that something exists in an abstract, mathematical sense tend to run counter to that.
Escape the first underscore by putting a backslash before it. (Why does the MarkDown italics mark-up work even within words, anyway? I think the situations where someone would want to italicize only part of a word are far fewer than those where one would want to use a word with an underscore in the middle of it.)
I would think a lot less of a language that introduced an arbitrary limitation on its syntax like that. Italics of parts of a word come up occasionally and bold letters of a word more frequently than that. The language arbitrarily deciding it doesn't want to execute the formatting commands unless you do whole words the same would be irritating, confusing and inelegant.
It's probably less work to read character-by-character than to split on words and read the first and last character of each.
And it makes the rare-but-still-occasionally-desired case doable without escaping into HTML (which is not possible in LW's no-HTML subset of Markdown).
You'd only need, whenever you see an underscore, to check whether the previous character is whitespace (or punctuation, e.g. a left parenthesis). Arundelo's point seems more valid to me (though you might allow to escape spaces, e.g. _n_\ th... but that'd be more complicated).
True! I do not know why MarkDown italics works within words.
If I can be frank, this is insane. This is the ontological argument for god revisited. Possibility does not imply necessity, and to think it does means you can rationally posit entities by defining them: defining them into existence.
I don't know why you retracted this, but I mostly agree with your comment. Tegmark IV and the ontological argument for god are, if not identical, at least closely enough related that anyone accepting the one and not the other should at least pause and consider carefully what exactly the differences are, and why exactly these differences are crucial for them...
I retracted it because when I wrote it I hadn't known Tegmarkism was part of Yudkowskian eclecticism. In that light, it deserves a less flippant response. While it strikes me as being as absurd as the ontological argument, for some of the same reasons, I can dispositively refute the ontological argument; so if they're really the same, I ought to be able to offer a simple, dispositive refutation of Tegmark. I think that's possible to, but it's instructive that the refutation isn't one that applies to the ontological argument. So, contrary to what I said, they're not really the same argument. Arguably, even, I committed what Yvain (mistakenly) considers a widespread fallacy, his "worst error," since I submerged Tegmark in the general disreputability of inference from possibility to necessity. Briefly, Tegmark's analysis is obfuscatory because: A. The best (most naturalistic) analyses of knowledge hold that it results from our reliable causal interactions with its objects. Thus, if Tegmark universes exist, we could have no knowledge of them (which leaves us with no reason to think they do exist). I don't know how Tegmark addresses this objection. Or even if he does, but this objection seems to me the basic reason Tegmark's constructs seem so dismissible. B. It's easy to "solve" many metaphysical and cosmological problems by positing an infinite number of entities, whether parallel universes or an infinite cosmos, but the concept of an actually realized infinity is incoherent. [Side question: Does anyone happen to know whether the many-worlds interpretation of q.m. posits infinitely many worlds--or only a very, very large number?]
It's simpler to postulate that all possible worlds exist, rather than just one of them. Also, postulating an ensemble can be predictive, if you add the further postulate that you are a "typical observer in a typical world". Panactualists need to hear the protests of more practical-minded people, to occasionally remind them that they really don't know whether the other worlds exist. The doctrine is either unprovable, undisprovable, or can be decided by a sort of insight we don't presently possess, such as one that can tell us why there is something rather than nothing. No, it's not. Maybe it blows your mind to imagine space stretching away without limit, but if space is there independent of you, and if it has no edge, and if it doesn't close back on itself, then it's an actually realized infinity.
The second independent clause is true, but if (as I contend) actually realized infinities are incoherent, the proper conclusion is that the three assumptions cannot all hold. Of course, having one's mind blown doesn't prove the concept entertained in incoherent; I must demonstrate that the concept really contains a logical contradiction. The contradiction in actual infinity is revealed by a question such as this one: Assume there are an infinite number of quarks in the universe. Then, are there any quarks that aren't contained in the set of all the quarks in the universe? Suggestion: Answer the question thoughtfully for yourself before proceeding to my answer. By definition, they're all in the set. But, you can add a finite number to an infinite set and not change the number of elements. So, there are at the same time other quarks than are contained in the set of all quarks. (I accept that Cantor demonstrated that infinities are consistent. The incoherence doesn't lie in the mathematics of infinity but in conceiving of them as actually realized. This was also the stance of mathematician and philosopher of mathematics David Hilbert, who devised the Hilbert's Hotel thought experiment to bring out the absurdity of actually realized infinities--while warmly welcoming Cantor's achievements in infinity taken strictly mathematically. Or as we might say, infinity as a limit rather than as a number). Important changes for clarity Sept. 2.
Could you clarify this inference, please? How does the second sentence follow from the first? Here's my interpretation of what you're saying: Let the set of all quarks be Q, and assume Q has infinite elements. Now pick a particular quark, let's call it Bob, and remove it from the set Q. Call the new set thus formed Q\Bob. Now, it's true that Q\Bob has the same number of elements as Q. But your claim seems to be stronger, that Q\Bob is in fact the same set as Q. If that is the case, then Q\Bob both is and isn't the set of all quarks and we have a contradiction. But why should I believe Q\Bob is identical to Q? I agree that belief in the existence of actually infinite sets leads to all sorts of very counterintuitive scenarios, and perhaps that is adequate reason to be an infinite set atheist like Eliezer (although I'm unconvinced). But it does not lead to explicit contradiction, as you seem to be claiming.
Because there is no difference between Q and Q/Bob besides that Q/Bob contains Bob, a difference I'm trying to bracket: distinctions between individual quarks. Instead of quarks, speak of points in Platonic heaven. Say there are infinitely many of them, and they have no defining individuality. The set Platonic points and the set of Platonic points points plus one are different sets: they contain different elements. Yet, in contradiction, they are the same set: there is no way to distinguish them. Platonic points are potentially problematic in a way quarks aren't. (For one thing, they don't really exist.) But they bring out what I regard as the contradiction in actually realized infinite sets: infinite sets can sometimes be distinguished only by their cardinality, and then sets that are different (because they are formed by adding or subtracting elements) are the same (because they subsequently aren't distinguishable).
If Q genuinely has infinite cardinality, then its members cannot all be equal to one another. If you take, at random, any two purportedly distinct members of Q u and w, then it has to be the case that u is not equal to w. If the members were all equal to each other, then Q would have cardinality 1. So the members of Q have to be distinguishable in at least this sense -- there needs to be enough distinguishability so that the set genuinely has cardinality infinity. If you can actually build an infinite set of quarks or Platonic points, it cannot be the case that any arbitrary quark (or point) is identical to any other. If one accepts the principle of identity of indistinguishable, then it follows that quarks or points must be distinguishable (since they can be non-identical). But you need not accept this principle; you just need to agree with me that the members of the set Q cannot all be identical to one another. Now, the criterion for identity of two sets A and B is that any z is a member of A if and only if it is a member of B. In other words, take any member of A, say z. If A = B you have to be able to find some member of B that is identical to z. But this is not true of the sets Q and Q\Bob. There is at least one member of Q which is not identical to any member of Q\Bob -- the member that was removed when constructing Q\Bob (which, remember, is not identical to any other member of Q). So Q is not identical to Q\Bob. There is no separate criterion for the identity of sets which leads to the conclusion that Q is identical to Q\Bob, so we do not have a contradiction. Believe me, if there was an obvious contradiction in Zermelo-Fraenkel set theory (which includes an axiom of infinity), mathematicians would have noticed it by now.
I accept the principle, but I think it isn't relevant to this part of the problem. I can best elaborate by first dealing with another point. True, but my claim is that there is a separate criterion for identity for actually realized sets. It arises exactly from the principle of the identity of indistinguishables. Q and Q/Bob are indistinguishable when the elements are indistinguishable; they should be distinguishable despite the elements being indistinguishable. What justifies "suspending" the identity of indistinguishables when you talk about elements is that it's legitimate to talk about a set of things you consider metaphysically impossible. It's legitimate to talk about a set of Platonic points, none distinguishable from another except in being different from one another. We can easily conceive (but not picture) a set of 10 Platonic points, where selecting Bob doesn't differ from selecting Sam, but taking Bob and Sam differs from taking just Bob or just Sam. So, the identity of indistinguishables shouldn't apply to the elements of a set, where we must represent various metaphysical views. But if you accept the identity of indistinguishables, an infinite set containing Bob where Bob isn't distinguishable from Sam or Bill is identical to an infinite set without Bob. I'll take your word on that, but I don't think it's relevant here. I think this is an argument in metaphysics rather than in mathematics. It deals in the implications of "actual realization." (Metaphysical issues, I think, are about coherence, just not mathematical coherence; the contradictions are conceptual rather than mathematical.) I don't think "actual realization" is a mathematical concept; otherwise--to return full circle--mathematics could decide whether Tegmark's right. Among metaphysicians, infinity has gotten a free ride, the reason seeming to be that once you accept there's a consistent mathematical concept of infinity, the question of whether there are any actually realized infinities
Let me restate it, as my language contained miscues, such as "adding" elements to the set. Restated: If there are infinitely many quarks in the universe, then I can form an infinite set of quarks. That set includes all the quarks in the universe, since there can be no set of the same cardinality that's greater and because, from the bare description, "quarks," I have no basis for establishing a subset/superset relationship (HT JoshuaZ) within the set of quarks. But that set does not include all the quarks in the universe because finding other quarks is consistent with the set's defining [added 9/02] requirement that it contain infinitely many elements. Could you (or anyone else) possibly provide me with a clue as to how I might find E.Y.'s opinions on this subject or on what you base that he's an infinite set atheist? I'm also interested in how E.Y. avoids infinite sets when endorsing Tegmarkism or even the Many Worlds Interpretation of q.m. [In another thread, one poster explained that "worlds" are not ontologically basic in MWI, but I wonder if that's correct for realist versions (as opposed to Hawking-style fictitional worlds).] If intuitions have any relevance to discussions of the metaphysics of infinity, I think they would have to be intuitions of incoherence: incomplete glimmerings of explicit contradiction. The contradiction that seems to lurk in actually realized infinities is between the implications of absence of limit provided by infinity and the implications of limit implied by its realization.
I'm still confused by this argument. Are you arguing in the second sentence that "any infinite set of quarks must be the set of all quarks"? But for example I could form the set of all up quarks, which is an infinite set of quarks, yet does not include any down quarks, and so is not the set of all quarks. Are you implicitly using the following idea? "Suppose A and B are two sets of the same cardinality. Then A cannot be a proper subset of B." This is true for finite sets but false for infinite sets: the set of even integers has the same cardinality as the set of all integers, but the even integers are a proper subset of the set of all integers.
The key is the qualification "from the bare description, 'quarks.'" To elaborate--JoshuaZ's comment brought this home--you can distinguish infinite sets by their cardinality or by their subset/superset relationship, and these are independent. The reasoning about quarks brackets all knowledge about the distinctions between quarks that could be used to establish a set/superset relationship.
By default, sets are different. You can't argue "two sets are the same because they have the same cardinality and we don't know anything else about them" which I think is what you're doing. If there are infinitely many quarks, then we can form infinite sets of quarks. One of these sets is the set of all quarks. This set is infinite, includes all quarks, and there are no quarks it doesn't include, and saying anything else is patent nonsense whether you're talking about quarks, integers, or kittens.
Sets with different elements are different. But, unfortunately for actually realized infinities, you can argue that two sets with different elements are the same when those infinite sets are actually realized--but only because actually realized infinities are incoherent. That you can argue both sides, contradicted only by the other side, is what makes actual infinity incoherent. You can't defeat an argument purporting to show a contradiction by simply upholding one side; you can't deny me the argument that the two sets are the same (as part of that argument to contradiction) simply based on a separate argument that they're different.
Suppose I restate your argument for integers instead of quarks: "If there are infinitely many integers, then I can form an infinite set of integers. That set includes all the integers, since there can be no set of the same cardinality that's greater and because, from the bare description, "integers," I have no basis for establishing a subset/superset relationship (HT JoshuaZ) within the set of integers. [I don't follow this sentence, so I've just copied it.]. But that set does not include all the integers because the existence of other integers outside the set is consistent with the set's defining requirement that it contain infinitely many elements." As I mentioned above, we can form infinite sets of integers that do not include all integers, for example the set of even numbers, so the argument cannot be valid when it's made about integers. What about the argument makes it valid for quarks but not for integers? I imagine it must have to do with your distinction between an abstract infinity and an "actually realized" infinity. Perhaps you can clarify where you are using this distinction in your argument? To help us better understand what you're claiming, suppose the universe is infinite and I form an infinite set of quarks, any infinite set of quarks. Is it your contention that we can prove that this set of quarks equals the set of all quarks? Also, regarding this key sentence: I don't follow this sentence, I didn't follow the clarification you made three posts up. Perhaps you could expand this sentence into a paragraph or two that a five year old could understand?
We don't need to assume there are infinitely many integers, only that integers are unlimited. Some Platonists may think that an infinite set of integers is realized, and I think the arguments does pertain to that claim. The distinction is relevant to why I have no quarrel with potential infinities as such. No. It's only the case if (per stipulation) you know nothing about properties that distinguish one quark from another. Then, the only way you can form an infinite set of quarks is by taking all of them. So, I'm not assuming that any infinite set of quarks I can form is the only infinite set of quarks I can form; I'm setting up the problem so there's only one way to form an infinite set of quarks. Any set conforming to that description "should" be the only set. That set includes all the quarks, since there can be no set of the same cardinality that's greater and because, from the bare description, "quarks," I have no basis for establishing a subset/superset relationship (HT JoshuaZ) within the set of integers. The only way you can form an infinite set of quarks--given that you can't distinguish one quark from another--is by selecting for inclusion all quarks indiscriminately. This is because there are only two ways that infinite subsets can be distinguished from their supersets: 1) the subset is of lower cardinality than the superset or 2) the elements are distinguishable to create a logical superset/set relationship (such as exists in quarks/upside-down quarks).
OK, suppose I grant this. I now feel like I might be able to formulate your argument in my own words. Here's an attempt; let me know if and when it diverges from what you're actually arguing. -- "Suppose I have sworn to give up the hateful practice of discriminating between quarks based on their differences. Henceforth I shall treat all quarks as utterly indistinguishable from one another. Having made this solemn vow, I now ask you to bring me an infinite set of quarks (note that I do not specify which quarks, for that would violate my vow!). You oblige, and provide me with a set called S. "I inspect the set S and try to see whether it's different from the set of all quarks, which we call Q. First I look at the cardinalities of S and Q. If their cardinalities were different, then obviously S and Q would be different sets. But their cardinalities are the same. Next I look for a quark that is contained in Q, but not contained in S. If there were such an element, then obviously S and Q would be different sets. But in order to successfully find such an element, I would have to make use of the distinctions between quarks. After all, how would I know that a given quark was in Q, but not in S? I would have to show that the quark in Q was distinct from each quark in S, but I have agreed to regard all quarks as indistinguishable. Therefore my search for an element of Q that is not in S will fail. I conclude that the set S is the same as the set Q. That is the set you gave me must be the set of all quarks. "But this conclusion is obviously wrong. All I asked you for was an infinite set of quarks. There are many infinite sets of quarks, not all of which are the same as Q, the set of all quarks. You might have left some quarks out of S, and still provided me with an infinite set of quarks, which was all I asked for. "Therefore we have a contradiction: I have proved something that is not necessarily true. Therefore the set of quarks cannot be infinite." -- The response to
I take issue with your translation at only a single point: My version contains a further constraint: When you ask me to bring you an infinite set of quarks, you instruct me to be as blind as you to the features that distinguish between quarks. The_Duck tells metaphysicist to gather together an infinite set of quarks while remaining blind to their individuality. Metaphysicist, having no distinctions on which to carve infinite subsets, can respond to this request in only one way; include every quark. (I want to resist calling this the "set of all quarks," because the incoherence of that concept with infinite quarks is what I argue.) The_Duck then goes out and finds another quark, and scolds metaphysicist, "You missed one." The_Duck is unjustified in criticizing metaphysicist, who must have picked "all the quarks," given that metaphysicist succeeded—without knowing of any proper subsets—in assembling an infinite set . Having "selected all the quarks" doesn't preclude finding another when they're infinite in number and the only criterion for success is the number. You will say that there is a fact of the matter as to whether the first set I assembled was all the quarks. Unblind yourself to the quarks' individuating features, you say, and you get an underlying reality where the sets are different. I agree, but I think a more limited point suffices. When I follow the same procedure—gather all the quarks—I will be equally justified in gathering a set and in gathering a superset consisting of one other quark. There's no way for me to distinguish the two sets. The contradiction is that following the procedure "gather all the quarks" should constrain me to a single set, "all the quarks," rather than allowing a hierarchy of options consisting of supersets.
I'm making progress then. :) No. If what you gathered is a proper subset of what you could have gathered, then you didn't gather all the quarks, and you're not justified in claiming that you did. How did you decide to leave out that one other quark? You must have made a distinction between it and the others that you did gather. Of course there is. The superset contains a quark that the subset doesn't. If you refuse to notice the differences that single that quark out from the others, that's your loss. I think that maybe you're trying not to distinguish between quarks, but are implicitly distinguishing between "quarks that you know about" and "quarks that you don't know about." So you might assemble all the quarks you know about--an infinite number--and not have any evidence that this isn't all the quarks there are. But later, you worry, you might find some other quarks that you didn't know about before, so that your original set didn't actually contain all quarks. This is not contradictory. If there was a chance that there existed quarks you didn't know about, then you weren't justified in saying that you had gathered all the quarks. It does. If you're not at the top of the hierarchy, you haven't gathered all the quarks. And you can't justify claiming that you're at the top of the hierarchy by blinding yourself to evidence that would prove otherwise.
Well, " 'infinite set atheist'" is a clue, but is also a place to start.
No, then there are the same number of quarks in both cases in the sense of cardinality. Your intuition just isn't very good for handling how infinite sets behave- adding more to the an infinite set in some sense doesn't necessarily make it larger. Failure at having a good intuition for such things shouldn't be surprising; we didn't evolve to handle infinite sets.
Yes, I understand that; in fact, it was my express premise: "You can always add a finite number to an infinite set and not change the number of elements." That is, not change the number of quarks from one case to another. Please read it again more carefully. My argument may be wrong, but it's really not that naive. Added. I see what you might be responding to: "So, there are more quarks than are contained in the set of all quarks." The second sentence, not the first. It's stated imprecisely. It should read, "So, there are other quarks than are contained in the set of all quarks." Now changed in the original.
You've collapsed the distinction between two possible worlds. You started out by saying, consider a universe containing infinitely many quarks. Then you say, consider a universe which has all the quarks from the first universe, plus a finite number of extra quarks. The set of all quarks in the second scenario indeed contains quarks that aren't in the set of all quarks in the first scenario, but that's not a contradiction. It's like saying: Consider the possible world where Dick Cheney ended up as president for the last two years of Bush's second term. Then that would mean that there was a president who wasn't an element of the set of all presidents.
Replying separately to this now added comment. it still seems like this is an issue of ambiguous language. It isn't that there are other quarks that aren't contained in the set of all quarks." Is is that there's a set of quarks and a superset that have the same cardinality.
The problem seems to be that you are using the word "more" in a vague way that reflects more intuition than mathematical precision.
I think you responded before my correction, where I came to the same conclusion that my use of "more" was imprecise. Added I remember reading an essay maybe five years ago by Eliezer Yudkowsky where he maintained that the early Greek thinkers had been right to reject actual infinities for logical reasons. I can't find the essay. Has it been recanted? Is it a mere figment of my imagination? Does anyone recall this essay?
A "world" is not an ontologically fundamental concept in MWI. The fundamental thing is the wave function of the universe. We colloquially speak of "worlds" to refer to clumps of probability amplitude within the wave function.

I feel like there's a distinction being made I don't entirely understand. What's the difference between something describing behavior perfectly and determining behavior? If one person says (x-1)(x-2) determines x^2-3x+2, and another person says (x-1)(x-2) perfectly describes x^2-3x+2, do they disagree? Similarly, is there a meaningful way in which "the laws of physics govern reality" is false if the laws of physics perfectly describe reality?

(Our current understanding of the laws of physics is, of course, not complete, and the above paragraph should be assumed to refer a hypothetical set of laws of physics that do describe every phenomenon with perfect accuracy).

Maybe you can convince me that, in some deep philosophical sense, there is no substantive difference between determination and description of physical facts. But it is certainly true that rules and descriptions play very different roles in the social context, and that we are wired to think about and respond to rules and descriptions in very different ways. Conceiving of laws as rules activates all sorts of unconscious inferences stemming from the part of our brain that processes social rules, such as the intuitions that motivate nomic fundamentalism. So whether or not there is a genuine distinction between determination and description, there is certainly a cognitive difference in how we respond to those concepts.
Can you give an example specifically relating to physics? (That is to say, some scenario which would play out differently if the participants thought of physics one way versus the other?)
There's a widely acknowledged problem involving the Second Law of Thermodynamics. The problem stems from the fact that all known fundamental laws of physics are invariant under time reversal (well, invariant under CPT, to be more accurate) while the Second Law (a non-fundamental law) is not. Now, why is the symmetry at the fundamental level regarded as being in tension with the asymmetry at the non-fundamental level? It is not true that solutions to symmetric equations must generically share those same symmetries. In fact, the opposite is true. It can be proved that generic solutions of systems of partial differential equations have fewer symmetries than the equations. So it's not like we should expect that a generic universe describable by time-reversal symmetric laws will also be time-reversal symmetric at every level of description. So what's the source of the worry then? I think it comes from a commitment to nomic reductionism. The Second Law is, well, a law. But if you really believe that laws are rules, there is no room for autonomous laws at non-fundamental levels of description. The law-likeness, or "ruliness", of any such law must really stem from the fundamental laws. Otherwise you have overdetermination of physical behavior. Here's a rhetorical question taken from a paper on the problem: "What grounds the lawfulness of entropy increase, if not the underlying dynamical laws, the laws governing the world's fundamental physical ontology?" The question immediately reveals two assumptions associated with thinking of laws as rules: the lawfulness of a non-fundamental law must be "grounded" in something, and this grounding can only conceivably come from the fundamental laws. So we get a number of attempts to explain the lawfulness of the Second Law by expanding the set of fundamental laws, Examples include Penrose's Weyl curvature hypothesis and Carroll and Chen's spontaneous eternal inflation model. These hypotheses are constructed specifically to account for
Probably because it does not have testable consequences?
Yes it does. For one it predicts that the explanations being pursued by physicists are likely to turn out to be false.
Yes. One might worry that the second law, which is clearly not fundamental, doesn't seem to be grounded in a fundamental law. The usual solution to this is to realize that we are forgetting an important fundamental law, namely the boundary conditions on the universe. Then we realize that the non-fundamental law of entropy increase is grounded in the fundamental law that gives the initial conditions of the universe. I don't think this is "[coming] up with an elaborate hypothesis whose express purpose is accounting for why [the second law] is lawful," as you seem to imply. Even if we didn't need to explain the second law we would expect the fundamental laws to specify the initial conditions of the universe. The second law is just one of the observations that provide evidence about what those initial conditions must have been.
First of all, thank you for your detailed reply. I think this is near to the core of our disagreement. It seems self-evident that two true laws/descriptions cannot give different predictions about the same system; otherwise, they would not both be true. If two mathematical objects (as laws of physics tend to be) always yield the same results, it seems natural to try and prove their equivalence. For example, when I learned Lagrangian mechanics in physics class, we proved it equivilent to Newtonian mechanics. So the question arises, "why should the Second Law of Thermodynamics be proved in terms of more "fundamental" laws, rather than the other way around?" (this, if I'm interpreting you correctly, is the double standard). This is simply because the Second Law's domain in which it can make predictions is much smaller than that of more fundamental laws. The second law of thermodynamics is silent about what happens when I dribble a ball; Newton's laws are not. As such, one proves the Seccond law in terms of non-thermodynamic laws. "Fundamentalness" seems to simply be a description of domain of applicability. I'm not qualified to assess the validity of the Weyl curvature hypothesis or of the spontaneous eternal inflation model. However, I've always understood that the increase in entropy is simply caused by the boundry conditions of the universe, not any time-asymmetry of the laws of physics.
It's self-evident that that two true laws/descriptions can't give contradictory predictions, but in the example I gave there is no contradiction involved. The laws at the fundamental level are invariant under time reversal, but this does not entail that a universe governed by those laws must be invariant under time reversal, so there's nothing contradictory about there being another law that is not time reversal invariant. What do you mean by "yield the same results"? The Second Law makes predictions about the entropy of composite systems. The fundamental laws make predictions about quantum field configurations. These don't seem like yielding the same results. Of course, the results have to be consistent in some broad sense, but surely consistency does not imply equivalency. I think the intuitions you describe here are motivated by nomic reductionism, and they illustrate the difference between thinking of laws as rules and thinking of them as descriptions. No. I don't take it for granted that either law can be reduced to the other one. It is not necessary that the salient patterns at a non-fundamental level of description are merely a consequence of salient patterns at a lower level of descriptions. Well, yes, if the Second Law holds, then the early universe must have had low entropy, but many physicists don't think this is a satisfactory explanation by itself. We could explain all kinds of things by appealing to special boundary conditions but usually we like our explanations to be based on regularities in nature. The Weyl curvature hypothesis and spontaneous eternal inflation are attempts to explain why the early universe had low entropy. Incidentally, while there are many heuristic arguments that the early universe had a low entropy (such as appeal to its homogeneity), I have yet to see a mathematically rigorous argument. The fact is, we don't really know how to apply the standard tools of statistical mechanics to a system like the early universe.
The entropy of a system can be calculated from the quantum field configurations, so predictions about them are predictions about entropy. This entropy prediction must math that of the laws of thermodynamics, or the laws are inconsistent.
This is incorrect. Entropy is not only dependent upon the microscopic state of a system, it is also dependent upon our knowledge of that state. If you calculate the entropy based on an exact knowledge of the microscopic state, the entropy will be zero (at least for classical systems; quantum systems introduce complications), which is of course different from the entropy we would calculate based only on knowledge of the macroscopic state of the system. Entropy is not a property that can be simply reduced to fundamental properties in the manner you suggest. In any case, even if it were true that full knowledge of the microscopic state would allow us to calculate the entropy, it still wouldn't follow that knowledge of the microscopic laws would allow us to derive the Second Law. The laws only tell us how states evolve over time; they don't contain information about what the states actually are. So even if the properties of the states are reducible, this does not guarantee that the laws are reducible.
I'm a bit skeptical of your claim that entropy is dependent on your state of knowledge; It's not what they taught me in my Statistical Mechanics class, and it's not what my brief skim of Wikipedia indicates. Could you provide a citation or something similar? Regardless, I'm not sure that matters. Let's say you start with some prior over possible initial microstates. You can then time evolve each of these microstates separately; now you have a probability distribution over possible final microstates. You then take the entropy of the this system. I agree that some knowledge of what the states actually are is built into the Second Law. A more careful claim would be that you can derive the Second Law from certain assumptions about initial conditions and from laws I would claim are more fundamental.
Sure. See section 5.3 of James Sethna's excellent textbook for a basic discussion (free PDF version available here). A quote: "The most general interpretation of entropy is as a measure of our ignorance about a system. The equilibrium state of a system maximizes the entropy because we have lost all information about the initial conditions except for the conserved quantities... This interpretation -- that entropy is not a property of the system, but of our knowledge about the system (represented by the ensemble of possibilities) -- cleanly resolves many otherwise confusing issues." The Szilard engine is a nice illustration of how knowledge of a system can impact how much work is extractable from a system. Here's a nice experimental demonstration of the same principle (see here for a summary). This is a good book-length treatment of the connection between entropy and knowledge of a system. Yes, but the prior over initial microstates is doing a lot of work here. For one, it is encoding the appropriate macroproperties. Adding a probability distribution over phase space in order to make the derivation work seems very different from saying that the Second Law is provable from the fundamental laws. If all you have are the fundamental laws and the initial microstate of the universe then you will not be able to derive the Second Law, because the same microscopic trajectory through phase space is compatible with entropy increase, entropy decrease or neither, depending on how you carve up phase space into macrostates. EDITED TO ADD: Also, simply starting with a prior and evolving the distribution in accord with the laws will not work (even ignoring what I say in the next paragraph). The entropy of the probability distribution won't change if you follow that procedure, so you won't recover the Second Law asymmetry. This is a consequence of Liouville's theorem. In order to get entropy increase, you need a periodic coarse-graining of the distribution. Adding this ingredient m
Dang, you're right. I'm still not entirely convinced of your point in the original post, but I think I need to do some reading up in order to: * Understand the distinction in approach to the Second Law you're proposing is not sufficiently explored * See if it seems plausible that this is a result of treating physics as rules instead of descriptions. This has been an interesting thread; I hope to continue discussing this at some point in the not super-distant future (I'm going to be pretty busy over the next week or so).
Thanks for that comment, I very much enjoy these topics. Why would we not be able to accurately describe and process the occasional phenomenon that went counter to the Second Law? Intermittent decreases in entropy might even make the evolution of complex brains more likely, at least it does not make the existence of agents such as us less likely prima facie. If you want to rely on the Anthropic Principle, you'd need to establish why it would prefer such strict adherence to the Second Law. Are you familiar with Smolin's paper on the AP? "It is explained in detail why the Anthropic Principle (AP) cannot yield any falsifiable predictions, and therefore cannot be a part of science." For a rebuttal see the Smolin Susskind dialogue here. Even if there were a case to be made that agency would only be possible if the partition generally follows the Second Law, it would be outright unexpected for the partition to follow it as strictly as we assume it does. Out of the myriad trajectories through phase space, why would the one perfectly (in the sense of as yet unfalsified) mimicking the Second Law be taken? There could surely exist agencies if there were just a general, or even very close, correspondence. Which would be vastly more likely for us to observe, if we were iid chosen from all such worlds with agency (self sampling assumption).
I am familiar with Smolin's objections, but I don't buy them. His argument hinges on accepting an outmoded Popperian philosophy of science. I don't think it holds if one adopts a properly Bayesian perspective. In any case, I think my particular form of anthropic argument counts as a selection effect within one world, a form of argument to which even he doesn't object. As for the ubiquity of Second Law-obeying systems, I admit it is something I have thought about and it does worry me a little. I don't have a fully worked response, but here's a tentative answer: If there were the occasional spontaneously entropy decreasing macroscopic system in our environment, the entropy decrease would be very difficult to corral. As long as such a system could interact with other systems, we could use it to extract work from those other systems as well. And, as I said, if most of the systems in our environment were not Second Law-obeying, then we could not exercise our agency by learning about them and acting on them based on what we learn. So perhaps there's a kind of instability to the situation where a few systems don't obey the Second Law while the rest do that explains why this is not the situation we're in.
Interesting idea, but doesn't it lead to something akin to the Boltzmann Brain problem? This asymmetry would hold for an agent's brain and its close environment, but I don't see a reason why it should hold in the same way for the wider universe. So shouldn't we predict that when we make new observations with information coming from outside our previous past lightcone, we will not see the same Second Law holding? Or maybe I have misunderstood you completely...
The Boltzmann brain problem usually arises when your model assigns a probability distribution over the universal phase space according to which an arbitrary observer is more likely to be a Boltzmann brain than an ordinary observer. There are various reasons why my model does not succumb to this probabilistic kind of Boltzmann brain problem which I'd be happy to go into if you desire. However, your particular concern seems to be of a different kind. It's not that Boltzmann brains are more likely according to the model, it is that the model gives no reason to suppose that we are not Boltzmann brains. The model does not tell us why we should expect macroscopic regularities to continue to hold outside our immediate environment. Is this an accurate assessment of your worry? If it is, I think it is demanding too much of a physical model. You are essentially asking for a solution to the problem of induction, I think. My view is that we should expect (certain) macroscopic regularities to persist for the same sorts of reasons that we expect microscopic regularities to persist. Of course, if there were specific probabilistic arguments against the persistence of macroscopic regularities, I would have a problem. But like I said above, those don't arise for my model the same way they do for Boltzmann's.
Yes, your second paragraph gets at what I was thinking (and you are right that it is not exactly the Boltzmann Brain problem). But I don't think it is the same as the general problem of induction, either. On your model, if I understand correctly, there are microscopic, time symmetric laws that hold everywhere. (That they hold everywhere and not just on our experience we take for granted--we are not allowing Humean worries about induction while doing physics, and that's fine.) But on top of that, there is a macroscopic law that we observe, the Second Law, and you are proposing (I think--maybe I misunderstand you) that its explanation lies in that we are agents and observers, and that the immediate environment of a system that is an agent and observer must exhibit this kind of time asymmetry. But then, we should not expect this macroscopic regularity to hold beyond our immediate environment. I think this is ordinary scientific reasoning, not Humean skepticism.
Do you have a similar concern about Tegmark's anthropic argument for the microscopic laws? It only establishes that we must be in a universe where our immediate environment follows those laws, not that those laws hold everywhere in the universe.
I am not really familiar with the details of Tegmark's proposal. If your two-sentece summary is accurate, then yes, I would have concerns.
Hmmm... I'm not yet sure how bothered I should be about your worry. Possibly a lot. I'll have to think about it.
The Second Law includes the definition of the partitions to which it applies- it specifically allows 'local' reductions in entropy, but for any partition which exhibits a local decrease in entropy, the complementary partition exhibits a greater total increase in entropy. If you construct your partition creatively, consider the complementary partition which you are also constructing?
I think we're using the word "partition" in two different senses. When I talk about a partition of phase space, I'm referring to this notion. I'm not sure exactly what you're referring to.
How can that be implemented to apply to Newtonian space?
The partition isn't over Newtonian space, it's over phase space, a space where every point represents an entire dynamical state of the system. If there are N particles in the system, and the particles have no internal degrees of freedom, phase space will have 6N dimensions, 3N for position and 3N for momentum. A partition over phase space is a division of the space into mutually exclusive sub-regions that collectively exhaust the space. Each of these sub-regions is associated with a macrostate of the system. Basically you're grouping together all the microscopic dynamical configurations that are macroscopically indistinguishable.
Now, describe a state in which entropy of an isolated system will decrease over some time period. Calculate entropy at the same level of abstraction as you are describing the system; (if you describe temperature as temperature, use temperature. If you describe energy states of electrons and velocities of particles, use those instead of temperature calculate entropy. When I checked post-Newtonian physics last, I didn't see the laws of thermodynamics included. Clearly some of the conservation rules don't apply in the absence of others which have been provably violated; momentum isn't conserved when mass isn't conserved, for example.
The entropy of a closed system in equilibrium is given by the logarithm of the volume of the region of phase space corresponding to the system's macrostate. So if we partition phase space differently, so that the macrostates are different, judgments about the entropy of particular microstates will change. Now, according to our ordinary partitioning of phase space, the macrostate associated with an isolated system's initial microstate will not have a larger volume than the macrostate associated with its final volume. However, this is due to the partition, not just the system's actual microscopic trajectory. With a different partition, the same microscopic trajectory will start in a macrostate of higher entropy and evolve to a macrostate of lower entropy. Of course, this latter partition will not correspond nicely with any of the macroproperties (such as, say, system volume) that we work with. This is what I meant when I called it unnatural. But its unnaturalness has to do with the way we are constructed. Nature doesn't come pre-equipped with a list of the right macroproperties. Here's an example: Put a drop of ink in a glass of water. The ink will gradually spread out through the water. This is a process in which entropy increases. There are many different ways the ink could initially be dropped into the water (on the right or left side of the cup, for instance), and we can distinguish between these different ways just by looking. As the ink spreads out, we are no longer able to distinguish between different spread out configurations. Even though we know that dropping the ink on the right side must lead to a microscopic spread out configuration different from the one we would obtain by dropping the ink on the left side, these configurations are not macroscopically distinguishable once the ink has spread out enough. They both just look like ink uniformly spread throughout the water. This is characteristic of entropy increase: macroscopically available distinctions g
No, you can't redefine the phase state volumes so that more than one macrostate exists within a given partition, and you can't use a different scale to determine macrostate than you do for entropy. Of course, to discuss a system not in equilibrium, you need to use formulas that apply to systems that aren't in equilibrium. The only time your system is in equilibrium is at the end, after the ink has either completely diffused or settled to the top or bottom. And the second law of thermodynamics applies to isolated systems, not closed systems. Isolated systems are a subset of closed systems.
We still seem to be talking past each other. Neither of these is an accurate description of what I'm doing. In fact, I'm not even sure what you mean here. I still suspect you haven't understood what I mean when I talk about a partition of phase space. Maybe you could clarify how you're interpreting the concept? Yes, I recognize this. None of what I said about my example relies on the process being quasistatic. Of course, if the system isn't in equilibrium, it's entropy isn't directly measurable as the volume of the corresponding macroregion, but it is the Shannon entropy of a probability distribution that only has support within the macroregion (ie. it vanishes outside the macroregion). The difference from equilibrium is that the distribution won't be uniform within the relevant macroregion. It is still the case, though, that a distribution spread out over a much larger macroregion will in general have a higher entropy than one spread out over a smaller volume, so using volume in phase space as a proxy for entropy still works. Fair enough. My use of the word "closed" was sloppy. Don't see how this affects the point though.
Now you've put yourself in a position which is inconsistent with your previous claim that diffuse ink can be defined to have a lower entropy than a mixture of concentrated ink and pure water. One response is that they have virtually identical entropy. That's also the correct answer, since the isolated system of the container of water reaches a maximum entropy when temperature is equalized and the ink fully diffuse. The ink does not spontaneously concentrate back into a drop, despite the very small drop in entropy.
How so? Again, I really suspect that you are misunderstanding my position, because various commitments you attribute to me do not look at all familiar. I can't isolate the source of the misunderstanding (if one exists) unless you give me a clear account of what you take me to be saying.
This is where you tried to define the entropy of diffuse ink to be lower. The highest entropy phase state is the one in which the constraints on each variable are least restrictive. That means that the state where each ink can be in any position within the glass is (other things being equal) higher entropy than a state where each ink is constrained to be in a small area. Entropy is a physical property similar to temperature, in that at a certain level it becomes momentum. If you view a closed Carnot cycle, you will note that the source loses heat, and the sink gains heat, and that the source must be hotter than the sink. There being no method by which the coldest sink can be made colder, nor by which the total energy can be increased, the gap can only decrease.
You're applying intuitions garnered from classical thermodynamics, but thermodynamics is a phenomenological theory entirely superseded by statistical mechanics. It's sort of like applying Newtonian intuitions to resist the implications of relativity. Yes, in classical thermodynamics entropy is a state function -- a property of an equilibrium state just like its volume or magnetization -- but we now know (thanks to stat. mech.) that this is not the best way to think about entropy. Entropy is actually a property of probability distributions over phase space, and if you believe that probability is in the mind, it's hard to deny that entropy is in some sense an agent-relative notion. If probability is in the mind and entropy depends on probability, then entropy is at least partially in the mind as well. Still, the agent-relativity can be seen in thermodynamics as well, without having to adopt the probabilistic conception of entropy. The First Law tells us that any change in the internal energy of the system is a sum of the heat transferred to the system and the work on the system. But how do we distinguish between these two forms of energy transfer? Well, heat is energy transferred through macroscopically uncontrollable degrees of freedom, while work is energy transferred through macroscopically controllable degrees of freedom. Whether a particular degree of freedom is macroscopically controllable is an agent-relative notion. Here is the fundamental equation of thermodynamics: dE = T dS + F1 dX1 + F2 dX2 + F3 dX3 + ... The Fs and Xs here are macroscopic "force" and "displacement" terms, representing different ways we can do mechanical work on the system (or extract work from the system) by adjusting its macroscopic constraints. Particular examples of these force-displacement pairs are pressure-volume (usually this is the only one considered in introductory courses on thermodynamics), electric field-polarization, tension-length. These work terms -- the controllable d
The maximum work you can extract from a system does not depend on knowledge- greater knowledge may let you get work done more efficiently, and if you operate on the scale where raising an electron to a higher energy state is 'useful work' and not 'heat', then you can minimize the heat term. But you can't have perfect knowledge about the system, because matter cannot be perfectly described. If the state of the box becomes more knowable than it was (per Heisenberg uncertainty), then the state of outside the box must become less knowable than it was. You could measure the knowability of a system by determining how may states are microscopically indistinguishable from the observed state: As energies of the particles equalize, (such that the number of possible plank-unit positions is more equally divided between all the particles), there are more total states which are indistinguishable (since the total number of possible states is equal to the product of the number of possible states for each particle, and energy is conserved.) if you can show where there are spontaneous interactions which result in two particles having a greater difference in total energy after they interact than they had before they interact, feel free to win every Nobel prize ever.
It seems likely to me that the the laws of motion governing the time evolution of microstates has something to do with determining the "right" macroproperties -- that is, the ones that lead to reproducible states and processes on the macro scale. (Something to do with coarse-graining, maybe?) Then natural selection filters for organisms that take advantage of these macro regularities.
maybe you're thinking of partitions of actual space? He's talking about partitions of phase space.
Isn't that exactly what hidden-variable theories try to do? There have been a lot of people dissatisfied with the probabilistic nature of quantum mechanics, and have sought something more fundamental to explain the probabilities.
Hidden variable theories are not an attempt to ground the lawfulness of quantum mechanics. The Schrodinger equation isn't reduced to something deeper in Bohmian mechanics. It appears as a basic unexplained law in the theory, just as it does in orthodox interpretations of QM. The motivation behind hidden variable theories is to repair purported conceptual defects in standard presentations of QM, not to account for the existence of the laws of QM. I do think my claim is wrong, though. People do ask what grounds quantum field theory. In fact, that's a pretty common question. But that's mainly because people now realize that our QFTs are only effective theories, valid above a certain length scale. So the question is motivated by pretty much the same sort of reductionist viewpoint that leads people to question how the lawfulness of the Second Law is grounded.
That's question begging, in that the question is just what are those differences when applied to physics rather than sociology. The connotation of 'rule' that survives transfer to physics might be just the one that's useful: choose from the parts of the intuition and discard the irrelevant. The distinction that physics seems to have retained from the original intuition is that between a determinate and finite set of rules (or laws or universals of a particular kind) and an infinitely large set of potential descriptions. To collapse the distinction between rules and descriptions as you suggest is to invite gliding over what the distinction really represents. The empiricist armory may not have the conceptual equipment to distinguish our restrictive expectations for laws of physics from the broad pragmatic tolerance in other fields and in ordinary description. You have to mark that distinction, and that's accomplished with 'rules' and 'descriptions.' If you choose to mark it some other way, then the difference is merely rhetorical. But the empiricists really don't want to mark it--they have seemingly principled objections to the distinction's coherence--have you noticed? That's what the dispute about rules and descriptions is really about. To say the universals are 'causes' of physical events under realism really does introduce connotations into your descriptions that I'd be surprised to see Lewis himself endorse.
First of all, I don't think this is anthropologically accurate. I have seen a number of cases of (what appears to me to be) confusion in physics (and probably even more in philosophy) engendered by thinking of laws as rules in a sense more robust than what you describe here. I gave one example in this comment, and I could give others if you desire. The reason I brought up the effect of social cognition is that concepts have power. Someone may insist that by "rule" they really just intend the attenuated definition you've given, just as someone may insist that by "human" they literally just mean "featherless biped", but when one tries to redefine established concepts in this way, the original conceptions have an insidious way of sneaking into one's inferences. Someone tells you Natalie Portman has feathers, and you insist that this is conceptually impossible because she is human and humans are featherless bipeds. Second, I don't see how thinking of laws as rules is necessary to establish that the laws are finite. On my modification of Lewis's view, the laws are the axioms (Lewis himself says "axioms and theorems", but I think that's clearly the wrong way to go) of the best deductive system, where "best" depends on some balance of simplicity and strength (and presumably some other virtues as well). These systems will at the least be recursively axiomatizable, and in most actual cases finitely axiomatizable. If not, your system will take a HUGE hit on the simplicity metric. So Lewis's descriptive view itself gives warrant for constraining the set of laws. We don't need help from prescriptive intuitions, as far as I can see. As for the claims about the completeness of physical law, these might correctly characterize the expectations of physicists, but the expectations of physicists are not dispositive in this case. If you look at what's actually going on in physics, it's not at all clear that those expectations are being borne out. Our best current theories (such as th

"Arguments end where questions begin." How I wish I could remember where I read that sentence. It helped me reduce my use of rhetorical questions. Since then my writing is more clear (sometimes more clearly wrong I'm sure) and more friendly.

Instead of thinking of laws as rules that have an existence above and beyond the objects they govern, think of them as particularly concise and powerful descriptions of regular behavior.

The rest is commentary. I might emphasize the predictive utility of natural laws more than their descriptive utility.

Thanks for this. It seems like very sound advice, and I'll endeavor to keep it in mind in the future.
See, I read that quote, and come to a completely different conclusion: You -should- ask questions. But then, I think good questions are more valuable, and harder to come by, than good answers. Everybody has answers. Questions are where interesting things happen.
I may have been unclear. The quote "arguments end where questions begin" addresses the use of rhetorical questions as a substitute for building an argument or the use of rhetorical questions as a way to change the subject. The quote does not address questions in general. We are in agreement that questions in general are good.

First: upvoted.

On this descriptive conception of laws, the laws do not exist independently in some transcendent realm. They are not prior to the distribution of matter and energy. The laws are just descriptions of salient patterns in that distribution.

I'd also like to point out the flip side of the coin: by the same arguments, it doesn't make sense to talk about matter and energy separate from how it behaves - matter isn't some primordial grey blob, which, by its inaction, forces laws to be separate objects. What we'd call "matter" and "physical law" don't have to exist independently just because we have two words for them.

Note that whether things are separate or not is pretty map-level, but I think the above is necessitated if we accept the foundation of your post.

If the fundamental laws of physics are already lording it over all matter, there is no room for another locus of authority. However, the argument fizzles [...] if we regard laws as descriptive.

I'm confused why you would argue that physical law can't be some separate thing, "lording it over all matter," but still leave room in your picture for a really existing, similarly separate &q... (read more)

Agreed. Was this just meant to be an observation or do you think it creates a problem for my view? If the latter, I don't see it yet. That particular sentence was uttered from the perspective of a prescriptivist. If I believed that laws were rules, and I also believed that non-fundamental laws were real, then I would be committed to there being multiple loci of authority. But I don't believe that any laws are rules, so on my picture there are no loci of authority. I've added the words "On this assumption,..." in front of the sentence. Hopefully that makes my point less confusing. I intend to address the specific point you bring up in my post on explanatory reductionism. I do see your point about the rhetorical question, though. I've edited that section. Thanks!
Just thought it would be interesting. Though I guess it makes things complicated if you go full on "therefore it's totally reasonable to think that God created the pattern of events in space-time, implicitly fixing all the laws." Somehow I don't think that's where you're headed though.


I cannot imagine a real physicist saying something like that. Sounds more like a bad physics teacher... or a good judge.

To me, that sounds like just about every physics teacher I've ever spoken to (for cases where I was aware that they were a physics teacher).

I remember once going around to look for them so that one of them could finally tell me where the frak gravity gets its power source. I got so many appeals to authority and confused or borked responses, and a surprisingly high number of password guesses (sometimes more than one guess per teacher - beat that!). One of them just pointed me to the equations and said "Shut up and plug the variables" (in retrospect, that was probably the best response of the lot).

Basically, if you want to study physics, don't come to Canada.

Yeah, that's sad. Here's a positive example from my school, which was in Russia. At some point in our "advanced" math classes we learned the concept of open and closed sets. The idea grew in my young mind and eventually I asked our physics teacher whether actual physical objects were more like closed sets (i.e. include points on their boundary), or more like open sets. That led to an amazingly deep discussion of what happens at the boundary of a physical object. My school was nice =)

My physics instructor in college didn't answer any questions like that. He barely lectured, in point of fact. He gave us a mountain of assignments, chosen by selecting from the state database of Physics problems by the criteria of being in the top X% (I don't recall the exact number; I'm inclined to think 5) of questions gotten wrong; many of the problems were -way- beyond the scope of the book we were nominally learning from. It took me longer to complete two weeks' worth of assignments than it took me to do the homework for every other class throughout the entire semester, including research papers. That was the whole of the class. It was the most effective class I have ever taken. There were a few problems where the state database had the wrong formula for calculating solutions (which explains how -they- got into the "hardest problem" set; nobody could ever get them right); I remember one in particular was off by a multiplicative factor of 4pi. Those were quite possibly the absolute best learning experiences; not only did you have to solve the problem, you had to -understand- it, on a very deep level, in order to first realize that they, not you, are wrong, and then figure out exactly why their solution was wrong.
That sounds like a good way to learn, but it could be made more efficient by removing useless parts, like a teacher.
This tends to work for the top students, and frustrate the hell out of the rest. Was this the intention of the lecturer, to weed out the weaklings?
4Eliezer Yudkowsky12y
That is amazingly sad and we should use that as a test question on some SPARC unit somewhere.
A decent answer (exploring potential vs dissipative forces) probably requires more of a physics background than you want to presume.
Not giving an answer is also a valid answer.
I'm not a physicist, but I am an engineer interested in things like this. I've wondered this kind of question too. After a bit of online research, I think I understand it well enough to explain it. Since DaFranker, EY, and shiminux all seem to know, I'd like to run this by you and get your edits. Question: "Where the frak does gravity get its power source?" Answer: "It's not really a source like a battery or a motor. What you're seeing is the changing of energy from one kind to another. The fact that masses curve space creates a way for the positions of potential energy to be changed into the motions of kinetic energy. Since it's not a dissipative force like friction there's no need to keep "pushing power into the system" like with a car's motor or an airplane's jet. Just like a spacecraft only needs to fire rockets at the beginning and the end to change direction and doesn't need to keep engines going all the time to stay moving. Oh, wait, you weren't talking about the equations of power, right? If that was it I'll need to go read up some more." Upvotes! I've had the space travel and the gravity pieces of the puzzle for a long time. A special thanks to shminux for mentioning potential and disipative forces. That's how I was prompted to come to an answer. Also, this really seems like a question that needs to be dissolved. I think it's based on a misunderstanding and not a real problem. That may be why professors have a hard time explaining it - there isn't a power source for gravity in the sense that was being asked.
I'd like to help you out, but I'm afraid I don't understand gravity beyond rote application of the inverse-square law and a metaphor about rubber sheets.
Someone who has a hard time answering questions based on incorrect understandings is not well qualified to be a teacher. Handling that sort of question is a major part of the job. The other sort of question, those that are based on a clear and correct understanding, are the questions that teachers ask their students. Although as Eliezer suggests above, asking students the first sort could be awesome teaching material.
True, but college professors are often not expert teachers. I agree that ideally all teachers should be experts at understanding what the student is asking, but they often aren't. Having a PhD means you have great depth of knowledge in your subject, but teaching skills only have to be acceptable, not stellar. And this question is an uncommon and challenging one. It doesn't surprise me that he got answers that he personally felt didn't answer the question. In one of the other splinter conversations that came out of this post someone told me that the answer to the question in relativity is an actual true unknown. Which means no average college professor would be expected to be able to answer. As far as asking questions that deliberately lead the students the wrong way, I only think that's acceptable if you VERY SOON tell them why, and what the real circumstance is. If you're trying to teach people to challenge assumptions, yes, I agree, it's a very valuable tool. Thanks for the comment. I was fascinated by the question he had, and still am.
In that case the right answer would consist of explaining conservative force fields and potential energy, and then to say something along the lines of "but nobody knows what this potential energy is." Feynman tells a story of his father explaining inertia in the same way: things in motion tend to keep moving and things at rest tend to stay at rest, and we call this inertia, but no-one really knows why this happens. One can always correctly answer a question. It's just that sometimes, the correct answer is "I don't know."
I completely agree with you that an accurate answer to a student is "I don't know" But teaching in general, and PhD's in particular are specifically trainined never to say that. I mean look at how much effort they have to put into proving that they DO know. Oral examinations are NOT a place to say "I don't know." Just in general smart people don't like to say it, and authority figures don't like to say it. But I've heard it said that the one thing a PhD will never say is "I don't know" A great story about that from the opposit direction is one about astronaut John Young. Apparently he would ask instructors question after question until he reached "I don't know" and if he never got to it you would never gain his trust. Is it important? Yes. Should teachers say it? Absolutely. Is it one of the hardest things for people to say? Oh yes. I mean, even my kids teachers never say it. I've met with my son's teachers a lot over the years, and I ask tons of detailed questions. It's really, really hard to get them, or any authority figure to say "I don't know." I tell my kids lots of things. They ask me all kinds of questions and I give them all the info I've got to give. They're like me and keep asking more and asking more. I did that so much growing up (and still do!) that I annoyed the heck out of people with my questions. So I'm generous when my kids do it and don't get frustrated and keep giving the next answer I've got. Eventually I get to "I don't know." I've started saying things like "That's one of the mysterious scientists are still trying to figure out" because I've said "I don't know" so much that it's gotten monotonous. My point is that it's not surprising to me that a questioning student gets frustrating answers from frustrated college professors. Even if the best answer in a perfect world should have been "I don't know."
I know a lot of PhDs and haven't noticed any tendency for such people to be more reluctant than others to say "I don't know". By whom have you heard it said that that's one thing a PhD will never say? (Disclaimer: Some of those PhDs are friends are mine. One of them is me.)
Sorry, how did you form this impression?
That's pretty good, though you could probably settle for the Newtonian version of gravity, relativity tends to complicate things. It is interesting to dig deeper, however: Why is friction dissipative? After all, no fundamental forces are.
Thanks! I wouldn't be able to answer using Newtonian gravity, I've never seen the theory explained (that I remember). I see more reading in my near future. I obviously don't understand the words "dissipative force" in the same way you do. I thought I had that part down too. I thought it means that the energy you are concerned about is getting changed into energy not useful to you, like "waste" heat. So then friction would be dissipative. Please point me in a direction to learn more.
Well, a more poetic description of Newtonian gravity (which may or may not also be reusable for relativity with some edits) goes that: "The entire Universe longs to be in equilibrium, in balance. This equilibrium was disrupted some 13.75 billion years ago, and since then all the splinters have been trying to reunite into a single whole, the distance between them and various other forces hampering their quest to become one again. It is the natural equilibrium that all masses attract eachother in the same way that opposite electromagnetic charges must attract eachother. "
What is waste heat and why is it less useful than any other form of energy? What's the mechanism that changes useful energy into waste heat? These are some of the many of the questions you can still ask and find answers to, before you hit the limits of what is currently known.
Waste heat is an increase in entropy that doesn't do something that we want it to. It differs from useful energy in that it has effects either irrelevant to or opposed to what we want. Friction sometimes generates waste heat (as in the case where we want something to move) and sometimes generates useful work (as in the case where we want two things to stop moving relative to each other, and cause them to interact via friction to a common momentum. The mechanism is electrical forces- given two crystal or ceramic matrices close to each other and moving, electrical forces near the interface cause electrons near the interface to enter different energy levels (heat). The electrons transfer the impulse to other particles in the same ceramic or crystal through other forces, slowing the relative movement of the macro objects. Asking where gravity gets its power source is like asking where the electron gets its power source. After all, electrons exhibit a force on each of them, and so do baryons.
Then what makes you think you know enough to use GR for anything besides a fake explanation?
Maybe I don't. I think I do. I think I have a general, summarized, understangin of how gravity works. I would say I have a starting point of knowledge, and If I ever need to get more specific to solve specific problems, I know where to go research the details, and then run experiements to solve a specific problem. Or to challege the Fake Explanations. I'm not set on Relativity, for example, and I don't accept it as some kind of gospel. I love thories that try to poke holes in Reltivity. The day I posted this I read about several that tried and were demonstratably worse at predicting reality that Relitivity. As far as I can tell my mental map of the universe works pretty well, but I'm ok to revise it if that turns out not to be true. I'm putting this out there to clarify my understanding and get comments on it, so I accept your comment, but how would YOU phrase your answer to the question of how gravity works, in a better, non-Fake-Explanation way? Or, alternatively, how would you rewrite my answer in a better, non-Fake-Explanation way? Because if you mean that I need to send up my own Gravity Probe B to verify frame-dragging before I can help other students try to understand gravity, you're out of luck. I'm planning on trusting teir results. (although I have to admit to being a bit disappointed when they confirmed Einstein instead of challenging him! )
Do you regularly encounter situations where your map of GR is tested? Sure: Question: "Where the frak does gravity get its power source?" Newtonian Answer: "It's not really a source like a battery or a motor. What you're seeing is the changing of energy from one kind to another. The fact that masses [creates a gravitational field] creates a way for the positions of potential energy to be changed into the motions of kinetic energy. ... GR Answer: "This question is related to a major unsolved problem in general relativity.
Indeed. Three relevant posts for how a good answer could be constructed.
Feel free to elaborate.
"I don't know." or "This seems impossible." or even "My teacher mumbled something about gravity being canceled by the ground's opposite upwards reaction once an object is at rest, but that still feels incomplete. I'm sure there's a better explanation that I just don't know about yet." (that third one is me verbatim five years ago, so it might not fit the golden standard of a SPARC model student)
I can't parse the question. There are plenty of great physicists in Canada.
This has to be seen from a (earlyhighschool student)'s perspective, a student that is suffering through the Forces, Mechanical Motion and Electromagnetism introductory courses to physics. Physicist =/= Physics teacher. I made no significant statement about canadian physicists. Only two of the physics teachers I spoke to/of were actually university-level physics teachers, and only one of which was an actual physicist. After all, it's pretty hard for a mere compulsory-ed student to even get an email reply from a physicist on something so obviously below their status.
It's a reasonable question, if your intuition comes from engines and muscles, where every intentionally applied force must have a power source. A reasonable answer would be to explore the origins of this intuition, and to consider some familiar examples, like magnets and springs, which don't have an obvious power source. But few physics departments with decent instructors. And, as you well know, good scientists are not necessarily good teachers.
My point is that if you ask an incoherent question (i.e., think of gravity as an agent) you're bound to get an incoherent answer. At the rate at which the number of countries with apparently no good physics teachers is expanding, given the other comments in this thread, there will be nowhere to study physics on Earth by tomorrow.
For clarification: At the time, the question was by no means incoherent. I had been taught some of the basics of Newton's Laws of Motion, the maths needed to compute standard problems directly relevant to those laws, and very little else. I was, personally, extremely skeptical of the validity of some of the material being taught, but I was quite willing to adjust in favor of the material if I could find answers to my core doubts about it. With the material that I was taught at the time, it wasn't as trivial of an issue as you try to make it seem. There was this weird Force being created out of nowhere that created violations of momentum for no apparent reason and with zero energy conversion, which effectively would mean blatant violations of nearly all the "Laws" of physics I had been given so far (and I had to agree and take them as the Holy Word Of Supremely Divine Truth, lest I become a failure of society begging for bread near the local strip club, according to His Authority The Great Teacher). As far as I can tell, you're essentially arguing against a strawman. I fully agree, now, in hindsight, that the question, with my current knowledge, seems incoherent. However, the story wasn't about how a stupid student asked a stupid question to a bunch of Great Authorities and the Great Authorities didn't immediately know how to fix this poor broken tall-monkey. It was about how "BECAUSE IT IS THE LAW", as a major stopsign, sounded very much like what I actually got from teachers, along with related failure modes of physics pedagogy. That you or the teachers aren't able to apply reductionism techniques taught here to the question and match the reduced question to your model of physics is a different matter altogether. The model I was given was flawed, but within this model, the question - and inherent inconsistency regarding gravity - was perfectly legitimate relative with the rest of the model. It just didn't match the territory all that perfectly, despite what I
So, if they had clarified your question as "How does gravity violate momentum with no power source" and responded with "Momentum is conserved with gravity, it's just that the effect of the column of water on the velocity of the Earth is negligible because of the difference in scale of scales between the two.", would you have been less confused? Or did they also fail to explain the Newtonian "One type of potential energy is what you have due to height, and is equal to mass times height times acceleration due to gravity."? THAT would be a failure to teach Newtonian physics.
I disagree with the "bound" part. A competent and patient teacher would attempt to identify and explore the issue you are really struggling with, not the surface question that is being asked.
If you're talking about high schools... don't come to Italy either. (Especially because they allow people with a degree in maths to teach physics; those with a physics degree are typically at least kind-of passable, but there are many fewer of them.)
Actually, the only physics teacher I officially had at the time (all the others I actually had to look for in other schools or through other contacts) was previously a History and Art teacher, who then got transmuted into a Biology teacher out of sheer "We need one so let's put this guy" (the guy had no background in science whatsoever). Then his experience as a Biology teacher granted him status as a Sciences teacher, which qualifies them pretty much to teach Physics, Chemistry, Maths, Geology, Biology, and any other "Science-ish" thing throughout all middle and high school levels, including local "accelerated learning" courses and programs. I was essentially taught that material by an art critic with a teaching license and some experience at throwing formulas and exercises towards helpless students. I still have much to unlearn, to this day.
Glad to know that my country is further away from as-fucked-up-as-plausibly-possible than I previously thought, but still... WTF?
Haha. To be fair, even here those are the exceptions, and this is in Québec, which has notoriously fucked-up public education. If you've never heard of CÉGEPs before, now is the time to take out your barf bag. Cégeps are essentially what is normally the last year of high school (or grade 12) everywhere else in the world, but split into two years and is non-compulsory. Calculus is not even mentioned until Cégep. Most people here, even with cégep diplomas, have never done any Calculus course whatsoever - there are many Cégep courses that don't have Calculus in them. In general, education here is still superior to many (most?*) developing / "third world" countries, and it's much less horrible in the rest of Canada. There are plenty of good scientists throughout Canada and a relatively decent amount of good teachers, but as for good science teachers... I generally hold the whole lot in lower expected esteem and expect lower competence, doubly so in Québec. * (I have no comparative statistics whatsoever, so I'm guessing based mostly on availability of skilled labor, professionals and PhDs.)
Heh. In Florida, USA, Calculus wasn't typically allowed until the last year of fully-subsidized schooling, and there was only one class of ~15 students in a graduating class of 300 that took it. I managed to get into (and complete) that class in my penultimate year, but for my final year there was literally no math offered at the school which was an appropriate progression.
D(redd): I AM THE LAW!

If I were an economist, I wouldn't be interested (at least not qua economist) in deductive systems that talked about quarks and leptons. I would be interested in deductive systems that talked about prices and demand. The best system for this coarser-grained vocabulary will give us the laws of economics, distinct from the laws of physics.

There's this difference between economics and physics. The axioms of economics don't come close to completely explaining prices and demand, and we don't expect them to, even in principle. It would be a miracle if they did: finding coarse-grained descriptions at different levels of abstraction that are exceptionless would be miraculous.

We want a complete physics; we know we can't have a complete economics. The expectation that physics can be complete reflects an assumption that we can cut physical reality at its seams, but we have no similar expectation for economics. Physical descriptions are more than mere descriptions because we expect a finite number of them to describe the (physical) universe; we don't expect axiomatized economics to describe the coarse grain of the economics universe, only what's really a small part.

Accusing realists abou... (read more)

I haven't put my finger on it exactly, but I am somewhat concerned that this post is leading us to argue about the meanings of words, whilst thinking that we are doing something else.

What can we really say about the world? What we ought to be doing is almost mathematically defined now. We have observations of various kinds, Bayes' theorem, and our prior. The prior ought really to start off as a description of our state of initial ignorance, and Bayes' theorem describes exactly how that initial state of ignorance should be updated as we see further observat... (read more)

I'm not sure this dichotomy you've set up is quite so binary. Essentially, I agree with metaphysicist's comment (see also rocurley's) -- a fundamental set of laws is descriptive, but it's also more -- but I'd like to add to it.

It's well accepted that physical laws are descriptive, in the sense that there can be multiple equivalent descriptions (consider all the different descriptions of classical mechanics). On the other hand, we expect that it is possible to find a set of laws which can be called "fundamental", and that these are not just desc... (read more)

On the completeness of physics, see my response to metaphysicist here. As for the determinism of physical law, I'm afraid that's not looking too good these days either. Initial value problems for the gravitational field equations satisfy existence and uniqueness conditions only within the domain of dependence of the initial data surface, and this need not extend across all of spacetime. In particular, if the spacetime is not globally hyperbolic, the initial value problem will not (in general, although there are specific exceptions) have a unique solution. Global hyperbolicity fails if, for instance, there are naked singularities (singularities without event horizons). It is for this sort of reason that Penrose came up with the cosmic censorship conjecture, outlawing naked singularities. Unfortunately, the conjecture seems to be in tension with what we know about quantum gravity. Consider Hawking radiation, the process by which black holes gradually evaporate away. If (and this is a pretty big if) the evaporation can be described by a classical general relativistic spacetime, then it must eventually result in a momentarily naked singularity, violating cosmic censorship (and global hyperbolicity). There are also problems involving quantum mechanics, even if you don't adopt a collapse interpretation. There are configuration spaces that possess singularities. In the classical case, these singularities are usually protected by a potential barrier, preventing the system from falling into them. But in the quantum case, it is possible for the system to tunnel through the barrier, leading to non-unitary evolution. Mathematically, this corresponds to a Hamiltonian operator that is not essentially self-adjoint (its closure is not self-adjoint). This problem would arise if we were doing quantum mechanics on a spacetime with a timelike or naked singularity. There are also interesting issues related to the failure of narratability in relativistic quantum theory, discussed in
While I put consideration of the "block-universe" concept and directly-related statements until I understand them (and what you mean by them) properly, I find the rest of this post to be a very good description* of my own current model of nature. I'd like to know more about this "block-universe" concept, though. I'm not sure if it would clash with my own model of relativity interactions, and if so, I want to know how. My understanding of relativity is, admittedly, rather limited and untrained/uneducated, so any non-trivial evidence at this point is very much worth it. If you could point me to a paper or book on the subject, that would be even better. * (insert immature pun along the lines of "I rule!")

In a scientific culture immersed in theism, it was unproblematic, even natural, to think of physical laws as rules.

It wasn't just theism that made talk of natural law seem warranted. Many of the pioneers of the scientific revolution (as much as there was such a thing) were, in fact, lawyers.

Posts written by people exercising the thought processes you are exercising are the kind of posts I am most interested in reading on LessWrong, as a category. However, the specific content of this post (possibly in part because it is an introduction) did not make me super interested in this post.

I do think that this is exactly the sort of thing that Main needs more of.

Upvoted; I like where (I think) this is going.

To your distinction between mereological and nomic reductionism, I would add a third kind of reductionism ("ontic reductionism" would be a good name) that goes beyond the mereological claim, to say that the only things that really exist are the entities of fundamental physics. In this view, quarks/strings/wavefunctions or whatever is posited in the ultimate theory are real, but high-level entities like trees and people are only "real": they are certain combinations of fundamental entities t... (read more)

I call that view "metaphysical penis envy". Less descriptive, but deliciously derisive.
It would be more accurate to say "Trees are special cases of waveforms" and "Bark is special cases of waveforms", in that you can now describe the properties of trees (they have bark) without claiming that trees are more or less or equally as real as quarks.
I used "quarks" as a placeholder for whatever "fundamental" physical entities are posited as "truly real" by the reductionist. You seem to be using "waveforms" in a similar way, so I am confused as to whether we have a disagreement or not. If the fundamental concept in physical theory is "waveform", then I'd say: there is a map in which you can describe all reality as waveforms. There is a map, less comprehensive but more useful for many purposes, in which you can describe some aspects of reality as trees. I don't like saying "Trees are special cases of waveforms" because it seems to place the reductionism at the ontic level (territory) instead of in the maps: it is a short distance from it to "only waveforms really exist", which I regard as confused.

A: But why are the dynamics of the electromagnetic field derived from Maxwell's Lagrangian rather than some other equation? And why does the path integral method work at all?

The way I usually answer such questions is “If I knew, I'd have a friggin' Nobel Prize!”

"Here is an accurate map of the city. To get from this location to this location, follow these roads"

"Why those roads and not the highway?"

"Because the highway doesn't go anywhere near the start or end point of the proposed journey."

"Why is that?"

"The highway is located at the place indicated by the blue line. The start point and end point are represented by these symbols. The blue line never gets closer to either of the symbols than they are to each other."

"But why is the blue line there instead of so... (read more)

According to Lewis, the laws of nature correspond to the axioms of the deductive system that best balances simplicity and strength. He does not provide a precise algorithm for evaluating this balance, and I don't think his proposal should be read as an attempt at a technically precise decision procedure for lawhood anyway.

This is just minimum message length.

I guess I would say that MML is one way of precisifying the general Lewisian view. But yeah, it's the same sort of idea, except Lewis's view is intended as an account of what laws of nature are, rather than a scheme for model selection. The plausibility of the view, of course, stems from the fact that model selection (and therefore law discovery) in science seems to follow the sort of criteria he describes.

laws of nature do have a privileged role in physical explanation, but that privilege is due to their simplicity and generality, not to some mysterious quasi-causal power they exert over matter. The fact that a certain generalization is a law of nature does not account for the truth and explanatory power of the generalization, any more than the fact that a soldier has won the Medal of Honor accounts for his or her courage in combat.

That's a self-defeating analogy. So long as the process of pinning a medal on someone is epistemically valid, it does indica... (read more)

One reason for privileging the laws of physics is revealed to be the product of a confused metaphysical picture.

I have a fix for others' "confused metaphysical pictures." It's another (moving) picture: an updated, more complex, dynamic version of Powers of Ten (that includes info that came out of different humans and at least one non-human animal and a computer -- to convey perspectivism). But it's in my head and I don't have the skills to express it through multimedia production & distribution. Help?

I'm reading an introduction to perspectives on free will for an introductory philosophy course, which contains a lot of discussion of determinism. I found this article immensely clarifying as an accompaniment.

From the free will thing:

Assuming determinism, the laws of physics completely determine what happens in the universe, including all of your actions. So in principle, everything you do could have been predicted before you were even born. It seems that, if this is true, you are wrong to suppose that you are sometimes able to choose between different o

... (read more)
I think this is exactly right. Arguments that physical determinism is incompatible with free will usually assume that your behavior is controlled by physical law, so it cannot also be controlled by you: "The laws of nature (in conjunction with the initial conditions of the universe) made you raise your hand, so how could it be a free choice?" But this sort of argument relies on thinking of laws as somehow controlling physical systems, and this is wrong. While it is entirely accurate to think of the relationship between certain aspects of your mental state and your muscular activity as one of control, it is inaccurate to think of the relationship between the laws of nature and your muscular activity as one of control. You control your actions, the laws don't.
I have to make one comment and disagree in one aspect. The comment is about determinism. The description we have of nature at the highest energies is based on quantum mechanics, which is deterministic in the sense that the wave function obey a well defined differential equation, but predictions of measurements are only probabilistic. Even considering this degree of determinism you would still not be able to make precise predictions. Of course, you might consider prediction of probabilities deterministic enough to threaten free will. Now, I have to disagree that the views of the "laws of physics" as compressed descriptions of nature imply free will in the described way. All evidence points to the fact that there are, let's say, patterns in nature that are not disobeyed. Any decision one makes has to obey those patterns and the collected evidence up to now supports this. For instance, no matter what you decide to do, the firing of your neurons will obey the patterns we call collectively electrodynamics. Although that does not completely decides your actions, it put limits on it. Call it a partial lack of free will if you like, but it is not completely free.
In a similar vein, Hume argues that determinism is essential for the concept of free will to exist, I believe. I think the argument is that if our actions aren't controlled by our thoughts, then they're controlled by a random diceroll of bizarreness from another ontological dimension without meaning to us. I used fanciful terms to describe that, of course, but essentially its saying that since our physical thoughts are what matter to us and are what are associated with free will traditionally, the traditional concept of free will depends on physical determinism once we accept that we are not magic ghost angel souls in human bodies. For will to cause things to happen determinism must be true, since wills are physical things.

This is a better explanation than I could have given for my intuition that physicalism (i.e. "the universe is made out of physics") is a category error.

The issue is not whether there are "laws", the issue is whether there are causes. A descriptive approach to physics amounts to saying "wherever you see A, you also see B". But is there a reason why B always accompanies A? If there is no reason, then the regularities of reality are just one big coincidence. If there is a reason, the next question is, is causality the reason? Is B caused to accompany A? If the answer is yes, there are causes, then we have to worry about what a cause is. If the answer is no, there are no causes, then we ha... (read more)

Yes, this is a question I intend to address. As I say at the end of the post: I have to say, though, I don't see how saying "causality" is supposed to explain the existence of regularity. It seems like the same sort of thing as the "BECAUSE IT IS THE LAW" move I criticize in this post. If someone asks "Why do like charges always repel one another?" and you respond with something like "Because there is a causal relationship which forces the charges apart" have you done anything other than restate the existence of the regularity with some new words that sound satisfying? I guess you have also conveyed the further information that the regularity is robust under interventions, but that doesn't seem to be an explanation for why the regularity holds in the first place. ETA: This comment might clarify what I think about the sort of issue you raise.

The problem with descriptivism in modern physics is that you say physical theory describes something independent, but you end up postulating the things that it describes as part of the description language, you do not provide any additional denotation for them. I.e. you claim that it describes the real stuff, but in fact it only describes the constants of its language. So the descriptive view forces anti-realism. But it seems your mereological reductionism is a form of realism.

Under prescriptivism, the theory postulates reality. So we can remain realists, ... (read more)

I'm having trouble following your argument here. Could you clarify how descriptivism commits me to anti-realism?
I hope everyone understands that anti-realism is not a statement that "reality is not real", i.e. it is not nihilism, but it is a statement that the predication of existence is relative to the theory which gives it (this predication) validity, so to say. ETA: I think I'll withdraw my comments here regarding "anti-realism" because it seems the term is not defined this way... See Anti-realism and metaphysical nihilism.
Correct me where I might go "off the rails". I think that descriptivism+realism implies that the theory has a denotational semantics, where the terms are part of the theory and the objects are part of reality. This goes without problem in case of mechanics applied to billiard ball dynamic, or of crowd dynamic theory, etc. But one cannot give denotational semantics to the "Standard Model" theory, because there is no outside-theory means of individuation of its objects like the elementary particles.
Presumably the reason you think it's unproblematic in the billiard ball case is that we can see billiard balls, so we have independent non-theoretical access to them. But we can also "see" the particles in the Standard Model, or at least we can see their experimental signatures. Now it's true that our observations in this case are much more obviously theory-laden than they are in the billiard ball case, but I would argue that this is a difference in degree, not a difference in kind. In neither case do we have some kind of direct access to the object itself, unmediated by any model of the world. It's just that in the billiard ball case the mediation isn't so blatant. So I don't think the distinction you're drawing here holds up. Anyway, if this is what you mean by anti-realism -- no access to the object unmediated by a model -- then I guess I'm fine with that kind of anti-realism. It doesn't seem to compel me to say things like "The Higgs boson doesn't actually exist."
Now my comments feel silly to me, I withdraw criticism. But I'd like to elicit the semantics under which we say we have a description. We don't have a description of the Higgs boson but of the experimental results, right?
I think that "explanation" sits between "description" and "prescription" and is most fitting.
Let me take a different stab at it. Do you mean by "The Higgs boson actually exists" that you believe that in every theory at least as good as the standard model, we could naturally delineate a structure that corresponds to the Higgs boson?
Note that the condition was not to have "access to the object unmediated by a model", but to have an independent model, the model which is being described.
Also, continuing to allow cruder levels can help to validate the more fundamental ones, or even falsify them (which would help refine the fundamental ones). If a description that bases its predictions on fundamental axioms turns out to be unreliable, that can point to a problem in the axioms themselves, even if they look flawless to us, it could be clear where the problem is coming from.

I think it is good to be somewhat agnostic with regard to metaphysics, acknowledging those metaphysics that work: the realist, the positivist, and the neopragmatist.

Everyone who says 'metaphysics' could explain the same thing without saying. Mostly talk about ontology are extremely social prone, with explain the overall skepticism present here.
Metaphysics as the generally accepted paintbrush handle is not a natural, nor well-formed thingspace cluster, that is correct. However, while Physics are about the world of causal interactions that we call the territory, there are things like cosmology that heavily rests on belief in the implied invisible w.r.t. the cosmological horizon. There are also things like speculating why the universe has simple mathematical descriptions, how to apply the anthropic principle to multiverses and so on and forth. All of those I would consider less physics and more maths.

Complete summary of post for the traditionally minded philosopher: Yay Aristotle! Boo Plato!

One of the main problems with a purely descriptive account of laws is that it renders those laws epistemic. In and of itself, this is not a bad thing. Certainly, our expressions of laws (whether or not there is an underpinning metaphysical reality to them) are entirely epistemic. When I say, "Gravity is a result of the curving of space-time by mass," I am expressing an idea, an epistemic state.

I agree that saying something "Is a Law" can be used as a curiosity-stopper, just as you suggest. Particularly when the speaker is talking with s... (read more)

Oh, I don't pretend to be presenting an explanation for the existence of regularities. I don't think any philosophical account of the laws of nature can do that. The right sort of response to a question like "Why does this regularity exist?" is going to come from science. It's going to appeal to some deeper theoretical understanding of the relevant system. All-purpose philosophical explanations like "Because it is a law of nature" or "Because of the causal structure of the universe" aren't really explanations at all. I think one of the reasons for the persistence of the prescriptive view of laws is the illusory promise of a universal explanation of regularity. Once we give up the hope that philosophy is going to save us from the unavoidable curse of unexplained explainers, we can set about the business of figuring out the actual scientific role of the concept "laws of nature". So I'm not picking any of the bad answers you propose to the question of why there is a regularity. I don't think you can get any useful answer at that level of generality. The right answer is going to depend on what regularity you're talking about and is going to look like science, not philosophy.
Interesting. How do you get around the problem that not all regularities are something we would consider a law of nature, even when generalizable? (Trivial example: I buy a pair of jeans and immediately put 3 quarters in them and keep these jeans until I throw them out. We would not say that "Those jeans have 3 quarters in them when belonging to me" is a law of nature, but it takes the form of a complete regularity. Even if the jeans lasted until the heat death of the universe and always had 3 quarters in them, we wouldn't say it is a law that they do.)
Regularities of the kind you describe would very plausibly not be the axioms of the best system for any vocabulary we care about. Adding the jeans regularity to the list of axioms in a system would give up simplicity for a trivial gain in information content.
So it comes down to laws being separated from other regularities because of some ratio of parsimony to information? Without some reason to declare a particular boundary on that, that seems like a rather arbitrary distinction.
What does "being epistemic" (or "purely descriptive", for that matter) mean? Taking a photo of a man doesn't render the man "purely photographic", nor is the image "purely photographic"; the image of the world describes the world, and both have the properties reflected in the photo. Predictions inferred from known physical laws coincide with the events in physical world, and this systematic coincidence reflects the presence of common structure between the world and its description. It is this common structure that makes known laws useful, and if it were imprinted on a different description it would remain so, but being shared with the world (and many other things) it doesn't exclusively belong to our descriptions.
I'm not sure what point you are trying to make here.

How exactly are abstract, non-physical objects -- laws of nature, living in their "transcendent aerie" -- supposed to interact with physical stuff? What is the mechanism by which the constraint is applied? Could the laws of nature have been different, so that they forced electrons to attract one another?

I feel I should link to my post The Apparent Reality of Physics right now. To summarise: both the "descriptions" and "rules" views are wrong as they suppose there is something to be described or ruled. The (to me, obvious) dissolution is to state that a Universe is its rules.

I propose a following form of reductionism, which I call positivism:

For a theory to count as knowledge, it has to fit into the body of knowledge, there have to be links that can be mathematically traced to the "core theories". The total, firm knowledge postulates a possible reality. There is no claim that the possible reality is real (therefore anti-realism). But for it to count as knowledge it has to be metaphysically possible, there could be reality exactly as described. Where we are not led to believe that a part of our experience or experimen... (read more)


Physical laws push matter around in the same sense that decision-theory-implementing algorithm pushes an agent around. In both cases we have an abstract entity that enables coherent behavior of a concrete entity.

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Lawhood Is in the Map, not in the Territory

Excellent, you are half way to the basic instrumentalist model: territory is in the map, not in the territory.


The problem is that people ask why about physics.

There is no why of like charges repelling. They just do.

There are two ways I can see your argument going.

  • Physical laws are descriptions of a universe that has its own (potentially inaccessible to us) rules.
  • Physical laws are descriptions of a universe that has no rules at all.

In the first case either we can write down the actual rules of the universe inside the universe, or we cannot. Whether the rules can be expressed within the universe as correct natural laws depends on its nature. Given that the rules of a system as simple as arithmetic can be fully described within the system and can be used to prove... (read more)

The account of reality that seemed plausible enough to finally switch me over from theism to atheism is related to mathematical realism. I don't know its standard name, but I might call it mathematical nihilogenesis: the set of real universes are those describable by continuous lawful evolution from null initial conditions. The motivation in this case is twofold. First, it would come extremely close to a satisfactory explanation of why there is something rather than nothing. Second, it has already been argued that our universe may have zero total energy and may have originated via quantum effects from what Vilenkin describes as a spherical vacuum of zero radius and certain other null properties. That may not be nothingness, but it's close. If that were true, it would imply that, in Aristotelian terms, the world is all form and no substance. It could be disproved by discovery of some fundamental thing not fully describable in terms of its relations to other things. If it were conclusively found that universe has probably always had nonzero total energy, that would be a disproof. Some people argue that qualia have precisely the characteristics of a disproof, though I'm going to hold out hope for a reductionist explanation of them. In any case, an all-form world is an extremely Platonic notion. Though I am not a mathematician, I share the sense of many mathematicians that mathematical truths have a kind of necessary Platonic existence, because if abstracta only existed in their physical instantiations, it would feel extremely odd, for example, that we could nevertheless prove various properties of how a physical computer will perform a nonexistent algorithm regardless of the physical principles by which the computer operates. (Casually paraphrased, here's a rough explanation of the thought behind "mathematical nihilogenesis". If mathematical truths have necessary Platonic existence, then it appears some abstract reality exists corresponding to the statement "Given la
I think you're misunderstanding what he's saying about rules. He's arguing that the concept of "rule" doesn't belong to the territory, but to the map. The territory is only possessed of patterns, or regularities as he refers to them; we can divine a rule that explains this pattern, but this doesn't mean that this rule is the reason for this pattern. The pattern may simply exist.
I thought the post was using the word "rules" to refer to the cause of the patterns and regularities apparent in the territory and "laws" to refer to the map we create. If the patterns simply exist acausally then I would call that a "no-rules" scenario.
This is also true even if the actual rules of the universe are accessible since we can never be sure that this is in fact the case or that the rules we have are the fundamental ones.
Quite so. There will just be a greater absence of evidence for the supernatural if we find natural laws that make predictions that always match our observations perfectly. E.g. in a discrete universe (say Conway's Life) beings would be able to exactly reproduce the phenomena they experienced, although I am not sure what limits on measurement might exist in a discrete universe.
(Splitting my comments out into different points.) In reference to your comments on arithmetic, I'm pretty sure Godel's Incompleteness Theorem states that you -can't- have a fully self-describing mathematical system. But I may be misunderstanding what you're saying there.
Godel created a numbering scheme for statements in a formal system that was strong enough to contain arithmetic. The syntactic rules of the logic could be represented as statements in that logic using only arithmetic operations on the numeric representation of statements. Each statement could also be numbered according to the same scheme, and the system was now self-describing because its definition was in the same language that it operated on. From there it was a matter of encoding the statement Y="There does not exist a sequence of valid derivations in X that results in Y" using the numbering scheme and replacing X and Y where they appear in the statement with the numerical representations of X and Y. In short, Godel used a self-describing formal system to prove that all formal systems capable of arithmetic were either inconsistent or incomplete. Self-description is not a problem in general, but Godel's construction works at a meta-level above the system itself. From inside the universe we will only have evidence that our natural laws match or do not match the actual rules.
Specifically, he proved that there is a true statement in a formal system that cannot be proven by the formal system. There is an additional option: that of a formal system which is incapable of self-reference or self-description. That would be a system in which "There does not exist a valid proof that "There does not exist a valid proof that the statement "There does not exist a valid proof that the statement ""There does not exist a valid proof that the statement... true" is true" is true" cannot even be constructed.
I should have been more careful when I said "arithmetic" too, because if I recall correctly a system that has only addition and not multiplication is insufficient to construct a self referencing statement. I guess I am making the assumption that if the rules of the universe exist, they at least contain addition and multiplication since we can construct both of them.

mere correlation is not causation, descriptions can never provide complete explanations of reality since they only summarize relationships between things (correlations) without establishing an actual causal hierarchy (causation)

more complex things are explained by decomposing them into simpler things, so for a full explanation of reality mere data compression is not enough. we also need additional information about how a potentially infinite number of things could be ordered within a causal hierarchy. without this missing information no fully reductioni... (read more)

I agree that "Laws" are descriptions. I think it boils down to, we don't 'know' anything we simply assume.

The purpose of a rule is to make or recognize something as regular, or predictable for us as humans. (We even extend this to the physical world, other humans and to ourselves. To the extent that we even use various substances to make our bowel movements "regular")

regular and rule share similar latin origin (read more)