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So a Theory of Everything would be a set of axioms from which we can deduce all mathematical truths and derive all mathematical objects. A Theory of Everything
by robertk 18y ago
So a Theory of Everything would be a set of axioms from which we can deduce all mathematical truths and derive all mathematical objects.
A Theory of Everything was meant in the physical sense. One that fully describes the nature of spacetime (or what appears to us as spacetime).
Obviously the above can't be true. You can't have a consistent and complete theory, come on, that's Godel already.
This is exactly what I'm saying. Chaitin might have a clue to what he's talking about, but obviously the author has nought. I rest my case for people to stop upmodding the article. You may not know it's sensationalist and innacurate, so I'm just letting you know.
I thought we wanted to avoid articles like this on HN?
EDIT: Parent edited his comment.
EDIT2: What basic truths? The only "basic truth" is first-order predicate logic. After that you assume some axioms (ZFC), and then it's not basic anymore. If you had used different axioms, you'd end up with a different mathematics, .e.g.
http://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory http://en.wikipedia.org/wiki/Von_Neumann%E2%80%93Bernays%E2%...
- yters 18y agoSorry, I should have waited for your response. Anyways, they are saying different things from what I can tell, as mentioned in the edit. So, I'm not seeing the case that the article is innacurate.
- deleted 18y ago[deleted]
- yters 18y agoHey, no need for downvoting. robertk knows more about what he's talking about than I do. Anyways, here's what I gather the article is saying: Pysics depends on maths. Godel's incompleteness theorem (GIT) doesn't necessarily impact physics because physics can just use the untouched part of maths. However, Chaitin says his Omega number impacts all of maths with the same kind of consequence as GIT. Therefore, physics and the TEO is in trouble no matter what part of maths it uses.
- robertk 18y agoI didn't realize the goal was to talk about physics. Consider the first sentence: He shattered mathematics with a single number. And that was just for starters, says Marcus Chown. Certainly reading about uncomputable numbers like Chaitin's constant is interesting reading, but my case is that this article is not the right start. Anyways, foundations and information theory isn't my area of research, so I'll leave it at that.
- yters 18y agoYou're right, physics is just part of it, and some of the other links we've posted will give people a better grounding in his theory. Anyways, I appreciate your input, criticism is always welcome, especially from grad students. Best of luck on your studies:)