What is the Universe made of? By Gregory Chaitin

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You are one of the proponents of Digital Philosophy. What does it imply?

Digital Philosophy is a kind of neo-Pythagorean view. It’s an ontology, it’s a metaphysics. And it’s sort of Pythagorean. Pythagoras said “all is number”, God is a mathematician, the Universe is built of one, two, three, four, five. And the new version of this Pythagorean idea, this new view which is Digital Philosophy, says the world is discrete, it’s built out of zeros and ones, out of bits, and God is a computer programmer. So the new version is “all is algorithm” instead of “all is number.” And a number of us are sort of enthusiastic about an approach of this kind, and each of us has a slightly different version of it, but we’re basically doing pre-Socratic philosophy. We’re saying “it would be nice if the world were this way.” But the world doesn’t have to be this way, just because we find it more beautiful intellectually. So we’re kind of doing the stuff that pre-Socratics did, saying “the world is fire” , “the world is number”, “the world is one” or “everything is change”: they were doing ontology. They were trying to understand the world by pure thought, pretty much. So that’s essentially what Digital Philosophy is, but there are some encouraging aspects in the real world, on the empirical side: there is of course computer technology, which is digital and discrete; there’s also the modern approach to Quantum Mechanics, called Quantum Information and Quantum Computation. Another thing I left out, which is part of Digital Philosophy, is the idea that the world is a giant computer program, or the Universe is a giant computer, which is calculating its future state from its present state all the time, it’s a giant calculation. And there is a physical theory which is very fashionable now and doing very well, which is called Quantum Information and Quantum Computation, and that’s a very exciting field which is uniting Quantum Mechanics, which is theoretical physics, with theoretical computer science, which is pure mathematics, and this is sort of along the lines of Digital Philosophy. There’s also more tentative work, dealing with General Relativity, connected to work on black holes by people like Stephen Hawking and Jacob Bekenstein, which has to do with Quantum Gravity, the attempts to unify Quantum Mechanics and General Relativity. String theory is one attempt to solve this problem; there are other people who work in a more phenomenological way, such as the work on the thermodynamics of black holes, by people like Stephen Hawking. Jacob Bekenstein, using this work on the thermodynamics of black holes, tentatively arrived at the conclusion of what has now been generalized into something called “the holographic principle”, by people like Gerhard ’t Hooft, a Nobel price winner in Physics, and Leonard Susskind, at the Stanford University. These are fine physicists, all of these people. And the general idea of the holographic principle is that every physical system can only contain a finite amount of information. And that comes, originally, from the thermodynamics of black holes, but you can generalize it to other physical systems. There’s a formula to calculate the number of bits, and the important thing is that this number grows with the surface area of the system, not with its volume. That’s why it’s called the holographic principle: it suggests that, in some funny way, the physical world is actually 2-dimensional, not 3-dimensional. That part interests physicists a lot, but what interests me -because I’m a pure mathematician, so I’m further away from the physics- is just the fact that this suggests that every physical system only contains a finite number of bits of information and therefore, in a sense, that the physical universe is discrete.

This would imply that the Universe is computable.

Right. If information is finite and discrete, then these models of the world as a computation work better, because computers are discrete and they work better with finite numbers of bits. Not with real numbers or field theory. In classical physics and field theory, quantum field theory, an arbitrary small piece of space-time contains an infinite amount of information. And, as Feynman says in his little book The character of the physical law, that’s a little implausible. So he says, based on pure thought, that a checkerboard model of the physical universe would avoid that problem. It would create other problems, like anisotropy -there might be preferred directions- but it would solve the problem of the infinite amount of information that you need for an arbitrarily small space-time cube. This new phenomenological work on Quantum Gravity, connected with the thermodynamics of black holes, already suggests that there’s only a finite amount of information, which I view as encouraging. For example, algorithmic information theory works better if everything is discrete, it doesn’t work so well for continuous systems, because the computer is the basis in which information is measured in it: it’s the size of the smallest program to calculate something, the size in bits, that’s the fundamental measure of algorithmic information. So you can apply that to physical systems if physical systems are really discrete. You can’t talk about the complexity of a physical system if you need continuous mathematics, not using algorithmic information theory, which looks at the size in bits of a computer program, because you need an infinite number of bits to calculate a continuous system.

That’s the reason I like Digital Philosophy, but the question is: does God like Digital Philosophy? I mean, is the physical universe that way? Just because I would prefer it, it doesn’t mean it’s that way. But there are some encouraging signs from Quantum Gravity, thermodynamics of black holes and the holographic principle. Also, I would say that Quantum Information Theory is encouraging to a certain extent. So that’s real physics.

On the other hand, from the side of technology, the most important technology of our time is computer technology, which is completely digital and discrete, and DNA, which is clearly discrete software. That’s encouraging also, as a metaphor. So I think there’s a lot of things encouraging people to think about Digital Philosophy. There are a few of us who would like to think in more specific terms: Stephen Wolfram – the author of A new kind of science- is certainly an important man to mention; Edward Fredkin has been working on this for many years and has a website (www.digitalphilosophy.org), apart from many papers; and I have my book Metamath!; so in a way what we’re doing is pre-Socratic philosophy, although part of the reason we’re doing it is because there are some encouraging signs from physics. But it’s sort of trying to learn about the world by pure thought… which is also theoretical physics, as I’ve read somewhere. Every good theoretical physicist, in a way, is doing metaphysics. A good theoretical physicist, as Einstein says in one of his essays, is basically a reformed metaphysicist: a metaphysicist is someone who thinks he can understand the world by pure thought, which is a little extreme; theoretical physicists have that in their blood, but they know that you have to look at experiments also. They’re sort of reformed metaphysicists. You won’t come up with a new physical theory unless you’re willing to take a leap into the unknown, based on pure thought. The experiments don’t force you to come up with a new theory. They do in some routine cases, but the big jumps require a big leap of imagination.

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