Gregory Chaitin is a mathematician who thinks that the universe is itself a computer, or similar...

He has written papers closely related to the field of hypercomputation (For example, he invented the "Chaitin Constant" which is related to hypercomputers and the Halting Problem: https://en.wikipedia.org/wiki/Chaitin%27s_constant).

He has also written a book where, at some point, analyzes hypercomputation and hypercomputers (https://books.google.es/books?id=EEXRBQAAQBAJ&pg=PA116&lpg=PA116&dq=%22gregory+chaitin%22+%22hypercomputer%22&source=bl&ots=axkLAE8kGq&sig=ACfU3U2POCgo4uVT-SKFeF0PT3jShv67Vg&hl=es&sa=X&ved=2ahUKEwilk-if2ujiAhWQGBQKHWMTC2AQ6AEwAHoECAkQAQ#v=onepage&q=%22gregory%20chaitin%22%20%22hypercomputer%22&f=false)

Or in this paper (https://arxiv.org/pdf/math/0404335.pdf) it is again implied that Chaitin is a proponent of hypercomputation

According to Gregory Chaitin vision, they reveal the open logic of mathematics if regarded from a more general viewpoint, the super-Turing possibilities of oracles emerge from a vision which links physics, geometry and information.

Or, in this article: https://www-2.dc.uba.ar/staff/becher/notes/ns.html, it is indicated that Chaitin could even believe that oracles are not only mathematical artifacts but also physically real

I was pretty sure then that Chaitin was a proponent of a model of a hypercomputational universe

But then I found this page (http://www.philosophytogo.org/wordpress/?p=1876) written by Chaitin himself, which says:

(Talking about his propositions)

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.

That is apparently absolutely contradictory with his works about hypercomputation...

So, could you clarify this? Does he propose a completely computational or a hypercomputational universe? And if he proposes a 100% computational universe, then, what about all these studies about hypercomputation? WHy did he study concepts related to this?

And, also, does Chaitin bases his arguments in some kind of hypothesis/model/theory in physics? I was thinking that he based his ideas in Kolmogorov's complexity or Algorithmic Information Theory, but these concepts are purely mathematical ones and are not models of physics/cosmology... So, do you know of any theory/model in physics that would be compatible with Chaitin's views?

1 Answer 1


I don't think Chaitin is committed to either a (Turing) computational or hypercomputational universe.

Quoting Chaitin from a live panel discussion on digital physics:

Look, I’d like to be aggressive about this — the best way for me to think about something is to make claims that are much too strong (at least it brings out the idea). So the universe has to be a computer, as Stephen [Wolfram] said, because the only way to understand something is to program it. [...] So the only possible working model of the universe has to be a computer — a computational model. I say a working model because that’s the only way we can understand something: by writing a program, and getting it to work and debugging it. And then trying to run it on examples and such. So you say that you understand something only if you can program it. Now what if the universe decides however that it’s not a — that you can’t do a computational model about it. Well, then: no problem. It just means we used the wrong computers. You know, if this universe is more powerful than a computer model of it can be, that means that our notion of what a computer is is wrong and we just need a notion of computer that is more powerful, and then things are in sync.

On the question of epistemology vs ontology, Chaitin is equally forceful:

In other words when you say the Universe looks like a computer, that this is a model that is helpful — that’s an epistemological point of view, it helps us to understand, it gives us some knowledge. But a deeper question is what is the universe really. [...] And fundamental physics also wants to answer ontological questions: “What is the world really built of at the fundamental level?” So, it’s true, we very often modestly work with models, but when you start looking at fundamental physics and you make models for that and if a model is very successful — you start to think [that] the model is the reality. That this is really an ontological step forward. And I think modern philosophy doesn’t believe in metaphysics and it certainly doesn’t believe in ontology. It’s become unfashionable.

(My emphasis).

  • "... if this universe is more powerful than a computer model of it can be, that means that our notion of what a computer is is wrong and we just need a notion of computer that is more powerful ..." Replace computer with tunafish sandwiches and you see how circular this argument is. You have to fix a notion of computation and then make your argument that the universe is a computation. You can't just say that a computation is whatever the universe does and therefore the universe is a computation, and by the way I've redefined computation to mean something other than what it means.
    – user4894
    Commented Jun 14, 2019 at 23:43
  • @user4894 Yes, just one of many howlers courtesy of Mr Chaitin. I just wish that he was making operatic gestures with his hands throughout the discussion.
    – nwr
    Commented Jun 14, 2019 at 23:57
  • @user4894 Are you criticizing the post or Chaitin's quote? What Chaitin says is not an argument but a typical turn of phrase among mathematicians: such and such theorem comes out wrong because we have not properly generalized such and such notion. And yes, one can commit to adjusting their notions to keep specified theorems true as a methodological heuristic for building new theories.
    – Conifold
    Commented Jun 15, 2019 at 0:02
  • @Conifold Thanks for clarifying that point. I must confess I had read it in a much more one-dimensional light.
    – nwr
    Commented Jun 15, 2019 at 1:21
  • @Conifold That particular post was almost entirely composed of the Chaitin quote, and it's Chaitin's point I'm questioning. Redefining computation to be "whatever the universe does" is not IMO an instance of mathematical generalization. We have a mathematical concept of computation from Turing 1936 and nobody has found a better one. Perhaps the universe is some sort of oracle machine, but that would require new physics. This would fall into the category of speculation, not math. I take your point about math, but I don't think it really applies here.
    – user4894
    Commented Jun 16, 2019 at 1:04

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