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The Omega Man: "Math is built on randomness"

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Re: The Omega Man: "Math is built on randomness"

#11

Post by yters »

robertk wrote: post #10
yters wrote: post #8

Earlier quoted context omitted.

Hey, 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 an…

I 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…

You'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:)

Re: The Omega Man: "Math is built on randomness"

#12

Post by yters »

davido wrote: post #3

The first day at University, my Maths Professor told us: "We will asssume you never knew about Maths and we will start fron the beginning". We defined what a number is, what addition is ... and from theorem to theorem we reached some very high and complex domains in Maths a few years later. The process of understanding each step, each demonstration and ultimatly each concept - starting from scratch - made few student…

That is really neat. I've never had that experience, and I definitely envy you.

Re: The Omega Man: "Math is built on randomness"

#13

Post by cool-RR »

yters wrote: post #12
davido wrote: post #3

The first day at University, my Maths Professor told us: "We will asssume you never knew about Maths and we will start fron the beginning". We defined what a number is, what addition is ... and from theorem to theorem we reached some very high and complex domains in Maths a few years later. The process of understanding each step, each demonstration and ultimatly each concept - starting from scratch - made few student…

That is really neat. I've never had that experience, and I definitely envy you.

You can just attend calculus 101 when the next semester opens, in any university.

Re: The Omega Man: "Math is built on randomness"

#15

Post by jrp »

> Chaitin's discovery implies there can never be a reliable "theory of everything"

Just because gravity works every time we check, there's no certainty that it will work the next time.

Physics disproved - I'll take my Nobel please.

Re: The Omega Man: "Math is built on randomness"

#16

Post by andreyf »

yters wrote: post #12
davido wrote: post #3

The first day at University, my Maths Professor told us: "We will asssume you never knew about Maths and we will start fron the beginning". We defined what a number is, what addition is ... and from theorem to theorem we reached some very high and complex domains in Maths a few years later. The process of understanding each step, each demonstration and ultimatly each concept - starting from scratch - made few student…

That is really neat. I've never had that experience, and I definitely envy you.

Start here: http://en.wikipedia.org/wiki/Set_theory#Basic_concepts

Re: The Omega Man: "Math is built on randomness"

#17

Post by gibsonf1 »

Call me uneducated, but isn't the rock solid foundation for math the real world? To the extent that math corresponds to the real world, it is correct. The "halting problem" sounds like an attempt to predict the future with math, which seems like a futile effort. Maybe the conclusion from the "randomness" in trying to predict the future is that such predictions are simply not possible and a waste of effort?

Re: The Omega Man: "Math is built on randomness"

#18

Post by wensing »

davido wrote: post #3

The first day at University, my Maths Professor told us: "We will asssume you never knew about Maths and we will start fron the beginning". We defined what a number is, what addition is ... and from theorem to theorem we reached some very high and complex domains in Maths a few years later. The process of understanding each step, each demonstration and ultimatly each concept - starting from scratch - made few student…

Sounds a bit like Spivak to me.

http://www.amazon.com/Calculus-Michael-Spivak/dp/0914098896

Re: The Omega Man: "Math is built on randomness"

#19

Post by eru »

gibsonf1 wrote: post #17

Call me uneducated, but isn't the rock solid foundation for math the real world? To the extent that math corresponds to the real world, it is correct. The "halting problem" sounds like an attempt to predict the future with math, which seems like a futile effort. Maybe the conclusion from the "randomness" in trying to predict the future is that such predictions are simply not possible and a waste of effort?

Math has absolutely nothing do with the real world. ;) At least it's not constructed that way.

Re: The Omega Man: "Math is built on randomness"

#20

Post by emmett »

gibsonf1 wrote: post #17

Call me uneducated, but isn't the rock solid foundation for math the real world? To the extent that math corresponds to the real world, it is correct. The "halting problem" sounds like an attempt to predict the future with math, which seems like a futile effort. Maybe the conclusion from the "randomness" in trying to predict the future is that such predictions are simply not possible and a waste of effort?

You are Not Even Wrong, in this instance.

Math is not a simulation of the real world; to take a simple example, both Euclidean and hyperbolic geometry are self-consistent and useful, and yet clearly different. So "the rock solid foundation" of math is not the real world, but rather sets of self-consistent axioms.

The halting problem is not an attempt to predict the future with math; it's a description of a property of algorithms which is inherently non-computable. You cannot, in the general case, prove whether an algorithm halts or not.

So as to your the question of whether the "randomness" comes from trying to predict the future...the answer is not yes, nor is it no. The question is not sensible.

The article was very poorly written though, so I'm not surprised it causes confusion. If you are interested in actually learning about Omega, I recommend http://www.scottaaronson.com/writings/bignumbers.html which is an amazing introduction to all these ideas.

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