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NancyLebovitz comments on Open Thread: May 2010, Part 2 - Less Wrong
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I'm not dead certain whether "physical" and "mathematical" can be completely disentangled. I'm assuming that gravity following an inverse square law is just a fact which couldn't be deduced from first principles.
I'm not sure what "theory of everything" covers. I thought it represented the hope that a fundamental general theory would be simple enough that at least a few people could understand it.
It may actually be derivable anthropically: exponents other than 2 or 1 prohibit stable orbits, and an exponent of 1, as Zack says, implies 2-dimensional space, which might be too simple for observers.
You can deduce it from the fact that that space is three-dimensional (consider an illustrative diagram), but why space should be three-dimensional, I can't say.
That's a plausible argument. A priori, one could have a three-dimensional world with some other inverse law, and it would be mathematically consistent. It would just be weird (and would rule out a lot simple causation mechanisms for the force.)
Well, we do inhabit a three-dimensional world in which the inverse-square law holds only approximately, and when a more accurate theory was arrived upon, it turned out to be weird and anything but simple.
Interestingly, when the perihelion precession of Mercury turned out be an unsolvable problem for Newton's theory, there were serious proposals to reconsider whether the exponent in Newton's law might perhaps be not exactly two, but some other close number:
Of course, in the sort of space that general relativity deals with, our Euclidean intuitive concept of "distance" completely breaks down, and r itself is no longer an automatically clear concept. There are actually several different general-relativistic definitions of "spatial distance" that all make some practical sense and correspond to our intuitive concept in the classical limit, but yield completely different numbers in situations where Euclidean/Newtonian approximations no longer hold.
Also, I don't know if there's any a priori reason for gravity.
Theory of everything as I see it (and apparently Wikipedia agrees ) would allow us (in principle - given full information and enough resources) to predict every outcome. So every other aspect of physical universe would be (again, in principle) derivable from it.
I think I'm saying that there will be parts of a theory of everything which just won't compress small enough to fit into human minds, not just that the consequences of a TOE will be too hard to compute.
Do you think a theory of everything is possible?
Parts that won't compress? Almost certainly, the expansions of small parts of a system can have much higher Kolmogorov complexity than the entire theory of everything.
The Tegmark IV multiverse is so big that a human brain can't comprehend nearly any of it, but the theory as a whole can be written with four words: "All mathematical structures exist". In terms of Kolmogorov complexity, it doesn't get much simpler than those four words.
For anyone reading this that hasn't read any of Tegmark's writing, you should. http://space.mit.edu/home/tegmark/crazy.html Tegmark is one of the best popular science writers out there, so the popular versions he has posted aren't dumbed down, they are just missing most of the math.
Tegmark predicts that in 50 years you will be able to buy a t-shirt with the theory of everything printed on it.
To be fair, every one of those words is hiding a substantial amount of complexity. Not as much hidden complexity as "A wizard did it" (even shorter!), but still.
(I do still find the Level IV Multiverse plausible, and it is probably the most parsimonious explanation of why the universe happens to exist; I only mean to say that to convey a real understanding of it still takes a bit more than four words.)
Actually, I'm quite unclear about what the statement "All mathematical structures exist" could mean, so I have a hard time evaluating its Kolmogorov complexity. I mean, what does it mean to say that a mathematical structure exists, over and above the assertion that the mathematical structure was, in some sense, available for its existence to be considered in the first place?
ETA: When I try to think about how I would fully flesh out the hypothesis that "All mathematical structures exist", all I can imagine is that you would have the source code for program that recursively generates all mathematical structures, together with the source code of a second program that applies the tag "exists" to all the outputs of the first program.
Two immediate problems:
(1) To say that we can recursively generate all mathematical structures is to say that the collection of all mathematical structures is denumerable. Maintaining this position runs into complications, to say the least.
(2) More to the point that I was making above, nothing significant really follows from applying the tag "exists" to things. You would have functionally the same overall program if you applied the tag "is blue" to all the outputs of the first program instead. You aren't really saying anything just by applying arbitrary tags to things. But what else are you going to do?
What are the Tegmark multiverses relevant to? Why should I try to understand them?
Really? In which parallel universe? Every one? This one?
This one.
Don't we live in a multiverse? Doesn't our Universe splits in two after every quantum event?
How then Tegmark & Co. can predict something for the next 50 years? Almost certainly will happen - somewhere in the Multiverse. Just as almost everything opposite, only on the other side of the Multiverse.
According to Tegmark, at least.
Now he predicts a T shirt in 50 years time! Isn't it a little weird?
All predictions in a splitting multiverse setting have to understood as saying something like "in the majority of resulting branches, the following will be true." Otherwise predictions become meaningless. This fits in nicely with a probabilistic understanding. The correct probability of the even occurring is the fraction of multiverses descended from this current universe that satisfy the condition.
Edit: This isn't quite true. If I flip a coin, the probability of it coming up heads is in some sense 1/2 even though if I flip it right now, any quantum effects might be too small to have any effect on the flip. There's a distinction probability due to fundamentally probabilistic aspects of the universe and probability due to ignorance.
Let's remember that if we're talking about a multiverse in the MWI sense, then universes have to be weighted by the squared norm of their amplitude. Otherwise you get, well, the ridiculous consequences being talked about here... (as well as being able to solve problems in PP in polynomial time on a quantum computer).
Right ok. So in that case, even if we have more new universes being created by a given specific descendant universe, the total measure of that set of universes won't be any higher than that of the original descendant universe, yes? So that makes this problem go away.
How do you know that something will be included in the majority of branches. Suppose that a nuclear war starts in a branch. A lot of radioactivity will be around, a lot of quantum events, a lot of splittings and a lot of "postnuclear" parallel worlds. The majority? Maybe, I don't know. Tegmark knows? I don't think so.
The small amount of additional radioactivity shouldn't substantially alter how many branches there are. Keep in mind that in the standard multiverse model for quantum mechanics, a split occurs for a lot of events that have nothing to do with radioactivity. For example, a lot of behavior with electrons will also cause splitting. The additional radioactivity from a nuclear exchange simply won't matter much.
I think a relatively simple theory of everything is possible. This is however not based on anything solid - I'm a Math/CS student and my knowledge of physics does not (yet!) exceed high school level.