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Tic-Tac-Universe

June 22nd, 2008 · 3 Comments

Is the universe made of math? That’s a question going around internet science-fan circles of late, and it’s a pretty difficult question. Roughly, a cosmologist named Max Tegmark believes in a very concrete form of mathematical Platonism - the idea that math is “real” in some sense. Now I and many other people agree that math isn’t just something we humans made up out of thin air (the formalist position) because math simply works too well. The richness of mathematics and mathematical physics is not something that was planned out from the start, which leads me to think mathematics is built in to the universe independently of anyone in the universe to write it down.

Now that’s a much weaker statement than “the universe is made of math”. Take Tegmark’s view:

I said there could be a whole universe that is nothing more than a dodecahedron, a 12-sided figure the Greeks described 2,500 years ago. Of course, I was just fooling around, but later, when I thought more about it, I got excited about the idea that the universe is really nothing more than a mathematical object. That got me thinking that every mathematical object is, in a sense, its own universe.

Tic-tac-toe is formally and completely described by math (as is the machine code of the Barbie Fashion Show computer game, for that matter), but the idea that somehow there’s an actual tic-tac-toe universe out there seems… far-fetched. At the very minimum there’s a lack of corroborating evidence, and not much hope of getting any.

He has a factual error as well:

But if space goes on forever, then there must be other regions like ours—in fact, an infinite number of them. No matter how unlikely it is to have another planet just like Earth, we know that in an infinite universe it is bound to happen again.

Not quite.  There’s an infinite number of prime numbers, none of them are the number 15.  Infinite trials do not necessarily lead to every result.  There could be an infinite number of earths, but there doesn’t have to be even if the universe is infinite in extent.  I notice John Derbyshire on (of all places) the National Review website has also pointed this out.

It’s not a bad attempt at an answer to Hawking’s “How come existence?” question, but for the moment I think it’s better to take the wet blanket stance on this particular idea.  There aren’t any experimental ways to check it, and so it’s speculative philosophy but not yet anything approaching science.

Tags: Looking Beyond

3 responses so far ↓

  • 1 Uncle Al // Jun 22, 2008 at 5:38 pm

    Depends on which infinity you pick. Countable infinities like the number of integers are pipsqueaks. An infinitely larger infinity is the number of points on a line. Infinitely larger still is the number of functions through a point. Perhaps Max Tegmark thought large.

    Is the value of pi contained within the value of pi? Of course not! 314159265358 starting 1,142,905,318,634 digits after the decimal is merely coincidence. Ditto 271828182845 starting 1,016,065,419,627 digits after the decimal. Interested readers may go looking for the Feigenbaum constants.

    Matt replies: It doesn’t matter which transfinite cardinal number describes the infinity in question. Just because a set is infinite doesn’t mean it contains every element. This is true no matter which infinity you choose. If I may extend the great Russell a bit: Consider the universe of all universes that do not contain themselves. Does it contain itself?

  • 2 Markk // Jun 26, 2008 at 7:03 pm

    Actually if you read his papers Tegmark is correct assuming the Copernican principle, pigionhole principle and the Holographic principle. The Holographic principle states that all the information in a volume can be described as a function of the surface area of the volume and that there is a finite number of bits per piece of surface area. That is, a finite number bits will wholly describe the exact state of a volume of space. This seems ridiculous to me, but the math is there (assuming some particular kind of quantum gravity). This doesn’t mean automatically that there are copies - there could be all of a few similar low energy states everywhere but around us, similar to what you describe. But if you assume Copernican principle or that inflation went on for some time, then he makes the case that there will be very very many duplicates of our “Hubble zone” around. If you query for his papers you’ll find this one. It makes me doubt the holographic principle.

    Matt replies: True enough, as far as I can tell. Though there’s no reason to doubt the Copernican principle, there’s also no observational evidence for it being true beyond our Hubble zone. There’s equally no evidence that it’s not, but I wouldn’t want to make firm statements about the nature of existence based on the truth of something we can’t get evidence about even in theory.

  • 3 Marybeth Lowery // Nov 12, 2008 at 4:52 pm

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