# Pentashagon comments on Natural Laws Are Descriptions, not Rules - Less Wrong

31 08 August 2012 04:27AM

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Comment author: 07 August 2012 06:49:45PM 0 points [-]

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 facts about its nature I think it's at least plausible that we could express the actual rules of the universe within the universe, which would demonstrate a counterexample to your argument. If we cannot express the actual rules of the universe then your argument is correct and only approximate descriptions of the rules can be created and we should use descriptive natural laws with the most benefit for a particular purpose. Amusingly, if the actual rules of the universe are inaccessible then there is no way to rule out immaterial souls or other supernatural phenomena. The inaccessible rules may or may not allow the supernatural, and we will never know.

In the second case our universe happens to exist as if it had rules entirely by chance. Perhaps there are an infinite number of universes where every possible configuration exists and so we (as finite decision theory machines) only experience the universes that appear to have rules. Or perhaps we exist as fleeting instants of time across a sea of an infinite number of universes, our memories and experiences linked only by the similarity between different random patches of universes.

There are a few inferences we can make about how we should be rational depending on which case we think we're in. In the first case we should believe in induction, e.g. the universe probably has mostly-constant rules we can rely on in the future. In the second case one might think induction is invalid and we should have no expectation that the universe will exist or be meaningful in the future, but actually our very existence depends on rule-like formations of the universe existing. We will experience a future instant whenever a random portion of a universe matches what we would expect the rules to predict. A universe that happens to get all the atoms lined up just right to produce an instant of our planet's history will, by definition, line up the atoms very closely to what our current natural laws predict a universe with rules would do. If enough atoms were out of place we would not exist or experience anything. In this sense the natural laws we know would not control the behavior of the universe so much as they controlled (or defined) our continued existence, so behaving as if natural laws existed would still be rational.

There are philosophical theories, modal realism, and mathematical realism, that propose any set of natural laws and initial conditions describe and cause an independent reality, or alternatively stated that any possible universe or world independently exists in reality. The difference (if any) between the class of possible universes and the class of universes defined by natural laws and initial conditions would be the class of universes without rules. The obvious problem is that "possible" is such a nebulous term that it's hard to know what it means. Maybe it means universes that cannot be described with ZFC set theory would qualify as possible universes without rules, or maybe it means that ZFC is insufficient to categorize all possible rules (the latter is more likely, in my opinion).

Intuitively I think we are in a universe that can be fully described using ZFC, since it seems to work so well for modeling what we can experience so far. The question is whether we can derive that full description sometime before the heat death.

Comment author: 08 August 2012 04:35:16PM *  2 points [-]

There are philosophical theories, modal realism, and mathematical realism, that propose any set of natural laws and initial conditions describe and cause an independent reality, or alternatively stated that any possible universe or world independently exists in reality.

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 laws X and null properties Y, a universe will pop out without need for a pre-existing substance" for some X and Y. And then since X and Y are indeed given within that abstracta and are sufficient for a universe, there's a universe, too.)

Comment author: 08 August 2012 12:40:55AM 2 points [-]

Amusingly, if the actual rules of the universe are inaccessible then there is no way to rule out immaterial souls or other supernatural phenomena. The inaccessible rules may or may not allow the supernatural, and we will never know.

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.

Comment author: 08 August 2012 05:48:34PM 1 point [-]

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.

Comment author: 07 August 2012 08:16:07PM 1 point [-]

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.

Comment author: 08 August 2012 06:05:57PM 0 points [-]

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.

Comment author: 07 August 2012 08:16:52PM -2 points [-]

(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.

Comment author: 07 August 2012 09:40:19PM 1 point [-]

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.

Comment author: 09 August 2012 05:14:23PM 1 point [-]

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... ...is true" is true" is true" cannot even be constructed.

Comment author: 09 August 2012 06:46:40PM 1 point [-]

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.