The Omega Man: "Math is built on randomness"
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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"
#2http://en.wikipedia.org/wiki/Chaitin%27s_constant
But seriously, don't upvote this story, it is written by a fifth grader (or at least makes that its audience).
EDIT: In response to the comment below ("just because it's simplification doesn't make it inaccurate"):
Because it's not "simplification." It's--pardon--bullshit. Chaitin's constant has nothing to do with "randomness in mathematics."
Besides, number theory is certainly not "the foundation of pure mathematics." Gauss would say that in the 18th century ("Number theory is the Queen of the Sciences"), but obviously it's long been replaced by logic, model, and axiomatic set theory.
Here, I'll condense the article to one sentence:
In other words, the randomness of the digits of Omega imposes limits on what can be known from number theory--the most elementary of mathematical fields.
There. So what? There are limits on what can be known from anything in mathematics. Nothing to see here.
http://en.wikipedia.org/wiki/Diophantine_equations#Typical_q...
This is just saying that some of those five questions are answerable by Chaitin's constant for that particular huge Diophantine equation.
EDIT2: Disclaimer: I am a graduate student in mathematics.
Re: The Omega Man: "Math is built on randomness"
#3The 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 students among the group Maths masters.
Re: The Omega Man: "Math is built on randomness"
#4http://en.wikipedia.org/wiki/Chaitin%27s_constant But seriously, don't upvote this story, it is written by a fifth grader (or at least makes that its audience). EDIT: In response to the comment below ("just because it's simplification doesn't make it inaccurate"): Because it's not "simplification." It's--pardon--bullshit. Chaitin's constant has nothing to do with "randomness in mathematics." Besides, number theory is…
What's wrong with a simplification if it's accurate? We can't all be geniuses, I know I'm not.
Here's Chaitin's layman's description of his theory:
http://plus.maths.org/issue37/features/omega/feat.pdf
His book about getting there:
http://arxiv.org/PS_cache/math/pdf/0404/0404335v7.pdf
And the halting problem thrown in for good measure:
http://en.wikipedia.org/wiki/Halting_problem
BTW, if someone wants karma, I haven't submitted any of the other Chaitin links. The book, at least, would probably be worth something.
Re: The Omega Man: "Math is built on randomness"
#5http://en.wikipedia.org/wiki/Chaitin%27s_constant But seriously, don't upvote this story, it is written by a fifth grader (or at least makes that its audience). EDIT: In response to the comment below ("just because it's simplification doesn't make it inaccurate"): Because it's not "simplification." It's--pardon--bullshit. Chaitin's constant has nothing to do with "randomness in mathematics." Besides, number theory is…
It's random according to Chaitin's usage of the term. Anyways, I changed the title so that section is in quotes, showing it is what Chaitin thinks, not what is necessarily accepted by all mathematicians.
EDIT
The definition of randomness he uses is the same as Kolmogorov's, something that has a description as complex (containing as many bits) as itself. So, when Chaitin says math is random, he means the basic truths of math cannot be reduced to a simpler system. Godel said such truths exist, Chaitin says they permeate all of math.
Re: The Omega Man: "Math is built on randomness"
#6http://en.wikipedia.org/wiki/Chaitin%27s_constant But seriously, don't upvote this story, it is written by a fifth grader (or at least makes that its audience). EDIT: In response to the comment below ("just because it's simplification doesn't make it inaccurate"): Because it's not "simplification." It's--pardon--bullshit. Chaitin's constant has nothing to do with "randomness in mathematics." Besides, number theory is…
It's random according to Chaitin's usage of the term. Anyways, I changed the title so that section is in quotes, showing it is what Chaitin thinks, not what is necessarily accepted by all mathematicians. EDIT The definition of randomness he uses is the same as Kolmogorov's, something that has a description as complex (containing as many bits) as itself. So, when Chaitin says math is random, he means the basic truths…
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%...
Re: The Omega Man: "Math is built on randomness"
#7Earlier quoted context omitted.
It's random according to Chaitin's usage of the term. Anyways, I changed the title so that section is in quotes, showing it is what Chaitin thinks, not what is necessarily accepted by all mathematicians. EDIT The definition of randomness he uses is the same as Kolmogorov's, something that has a description as complex (containing as many bits) as itself. So, when Chaitin says math is random, he means the basic truths…
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…
Sorry, 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.
Re: The Omega Man: "Math is built on randomness"
#8Earlier quoted context omitted.
It's random according to Chaitin's usage of the term. Anyways, I changed the title so that section is in quotes, showing it is what Chaitin thinks, not what is necessarily accepted by all mathematicians. EDIT The definition of randomness he uses is the same as Kolmogorov's, something that has a description as complex (containing as many bits) as itself. So, when Chaitin says math is random, he means the basic truths…
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…
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 and the TEO is in trouble no matter what part of maths it uses.
Re: The Omega Man: "Math is built on randomness"
#9Earlier quoted context omitted.
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…
Sorry, 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]
Re: The Omega Man: "Math is built on randomness"
#10Earlier quoted context omitted.
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…
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 that.