## Mathematics: the foundation of reality

“Our universe is not just described by mathematics — it is mathematics.” That’s the conclusion of Max “Peg Leg” Tegmark, an astrophysicist at the Massachusetts Institute of Technology. But he ain’t nuts, even if he sounds as if he’s a couple of planets short of a solar system.

His argument is actually kinda convincing. In a paper that he says is a director’s cut of an article that he wrote for New Scientist which in turn was based on an earlier paper of his called The Mathematical Universe, he starts with a question: if we accept that the universe has a reality independent of ourselves, then what sort of reality is it?

Peg Leg Tegmark argues that it has to be free of any kinda of physical or cultural bias so that it is the same for all aliens wherever they may be in the universe. The only logical system that fits this description is the one that underlies mathematics, he says. Therefore the universe is mathematics.

Peg Leg Tegmark reckons that this line of thought leads to a number of curious predictions that are actually testable by observation. F0r example, he says that a measurement of the distribution of dark energy within our universe would be a decent test.

Just how we might make that measurement and what *exactly *we would be looking for is harder to say.

Still we can hardly expect the trifling details behind the actual observation and measurement of the universe to trouble a thinker like Tegmark. All in all, his paper makes a fine addition to the general framework of ~~untestable philosophy~~ cosmology.

Ref: arxiv.org/abs/0709.4024: Shut Up and Calculate

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What reason is there to assume that it must be possible to represent the laws of nature algorithmically, or by any symbolic system at all? Other than the fact that some people find the idea that it might not be possible upsetting, I mean.

The idea that “universe has a reality independent of ourselves” and the idea that it must be fully describable via any symbolic system are two separate propositions. The first is a nearly a given to most scientifically minded people despite the fact that it is a statement of metaphysics. The second is, as far as I know, supported by no actual evidence or rigorous logical theory whatsoever and is simply an assumption.

The idea that “universe has a reality independent of ourselves” and the idea that it must be fully describable via any symbolic system are two separate propositions. The first is a nearly a given to most scientifically minded people despite the fact that it is a statement of metaphysics. The second is, as far as I know, supported by no actual evidence or rigorous logical theory whatsoever and is simply an assumption.The Tegmark papers build exactly the bridge between those two apparently independent assumptions.

Still arguable, of course, but his arguments are nonetheless interesting.

Another possibility is that mathematics is the result of our abiliy to spot patterns, something we’ve got from evolution not reality.

This amazing pattern recognition capability allows us to classify the world by certain rules.

But that don’t mean the universe is built from those rules.

KFC, did you even read what you wrote. “but that doesnt mean the universe is built from those rules”, but that the universe kinda fell into alignment with patterns we kinda came up with.

there are rules building everything, even if we know the formulas currently or not.

you shouldnt reply on physics websites ever again

The Tegmark papers build exactly the bridge between those two apparently independent assumptions.Still arguable, of course, but his arguments are nonetheless interesting.

Yes, I have been following up on this with more reading. The “director’s cut” paper itself makes more sense than the above summary would indicate. I find it unconvincing in the end, but it it at least is attempting to address the core issue.

Taco, nice to know who is the referee for allowed postings. I sure hope I have not offended your infinite wisdom…

What reason is there to assume that it must be possible to represent the laws of nature algorithmically, or by any symbolic system at all?Indeed. I’ve always thought to be a major over-assumption. Math seems little more than a human means to abstract and explain the universe (math is bound by the universe, not vice versa), much the same way that language is used to abstract human expression.

Horace,

You’re on to something. I’m no mathematician, but to assume that everything can be broken down algorithmically/mathematically seems to run head on into Godel’s incompleteness theorem or Turing’s halting problem.

Jgraham,

No, it doesn’t run head on into Godel’s incompleteness theorem or Turing’s halting problem at all. Godel and Turing basically say that “there are some scientific facts that we will never know for sure to be true (, even in an algorithmic world)”. With a slightly off analogy: Concluding from Turing that the universe can’t be broken down algorithmically is like concluding from our inability to predict next year’s weather that weather can’t be broken down mathematically.

The limitations of an internal observer of the universe are not to be confused with the properties of the universe itself.

It has often been mussed, “Why does mathematics work so well to describe the universe.”.

In mathematics one has input operation output, that is to say that the nature of mathematics is fundamentally causal.

That mathematics works so well (though not proof) may be taken to indicate that the universe is causal, but if the universe is causal then indeed “the universe has a reality independent of ourselves”.

But a causal universe does not sit well with many involved in QM (”The first is a nearly a given to most scientifically minded people”???)

The is also a reason to wonder if QM is complete, as QM leads to a philosophical collision between the nature of mathematics and why it would work so well to describe a non causal universe.

The universe can be seen as an homogeneous, gradient driven environment composed of penetrating waves with non-commutative geometry & algebra, both like multi-components system composed of colliding particles, fulfilling the Peano algebra and Fermi-Dirac statistics.

These perspectives are mutually exclusive, therefore I don’t think, the Universe is strictly causal. The only reason, why we are seeing’ it deterministic is the fact, the chaotic environment doesn’t spread the energy at the distance. By AWT the Universe appears like dense Perlin (scale invariant) noise, from which we can see only causal gradients, which are enabling the energy spreading at the distance.

http://superstruny.aspweb.cz/images/fyzika/aether/perlin1.jpg