3 ms·

http://en.wikipedia.org/wiki/Chaitin%27s_constant http://en.wikipedia.org/wiki/Chaitin%27s_constant But seriously, don't upvote this story, it is written by a

by robertk 18y ago

http://en.wikipedia.org/wiki/Chaitin%27s_constant http://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 Gauss would say that in the 18th century ("Number theory is the Queen of the Sciences"), but obviously it's long been replaced by logic, model, and axiomatic set theory.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_questions 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.

yters 18y ago
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 http://plus.maths.org/issue37/features/omega/feat.pdf His book about getting there: http://arxiv.org/PS_cache/math/pdf/0404/0404335v7.pdf 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 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.
- brl 18y ago
  Wow, thanks for posting those links! I read the first two chapters of the book and I must say that Chaitin is a brilliantly lucid and entertaining writer. I am pretty much mathematically illiterate but I am still enjoying his book immensely.
  - yters 18y ago
    Here is another book of his I found: http://www.umcs.maine.edu/~chaitin/unknowable/ch6.html http://www.umcs.maine.edu/~chaitin/unknowable/ch6.html
yters 18y ago
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.
- 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 ago
    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 18y ago
      [deleted]
  - 18y ago
randomwalker 18y ago
A big part of the problem is that Chaitin is a shameless self-promoter. He is the Bruce Schneier of Algorithmic Complexity. Actually, no, Schneier is not nearly as bad. Let me quote from the highest voted Amazon review of his book: "Let the author speak for himself. From page 7, "Gödel's 1931 work on incompleteness, Turing's 1936 work on uncomputability, and my own work on the role of information, randomness and complexity have shown increasingly emphatically that the role that Hilbert envisioned for formalism in mathematics is best served by computer programming languages[.]" Imagine if a working composer wrote, "Bach's preludes and fugues, Beethoven's symphonies, and my own string quartets have shown increasingly emphatically..." This man's reputation in his declared field is nowhere near his apparent stature in his own mind. The ideas discussed in this book are worthy of late-night musings over a nice brandy, or maybe a Scientific American article, but only after extensive revision. They are not ready for publication in a monograph. "
- jhancock 18y ago
  I assume you weren't really picking on Schneier. He's a self-promotor in a pretty healthy sense. He has written much content on the human aspects of security useful to laymen. He does so without being arrogant or saying "I invented this". All in all, a good educator that doesn't talk down to his audience and can explain things so that his "grandmother could understand" (my favorite Einstein principle). He has interwoven this practice into his business, the beneficiary of his self-promotion, which seems to have done well for him. I might even recommend Schneier as the poster-boy of healthy entrepreneurial self-promotion.
  - randomwalker 18y ago
    No, didn't mean to pick on Schneier. He's a self promoter, but the analogy breaks down after that.
- neilc 18y ago
  This man's reputation in his declared field is nowhere near his apparent stature in his own mind Really? He is one of the coinventors of Kolmogorov complexity, and Kolmogorov complexity certainly does shed a lot of light on the relationship between information, randomness, and complexity. While he is clearly a big ego and a shameless self-promoter, I think it's also fair to say that he is among the foremost experts on K-complexity and related topics.

by robertk 18y ago

yters 18y ago

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 http://plus.maths.org/issue37/features/omega/feat.pdf His book about getting there: http://arxiv.org/PS_cache/math/pdf/0404/0404335v7.pdf 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 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.

brl 18y ago
Wow, thanks for posting those links! I read the first two chapters of the book and I must say that Chaitin is a brilliantly lucid and entertaining writer. I am pretty much mathematically illiterate but I am still enjoying his book immensely.
- yters 18y ago
  Here is another book of his I found: http://www.umcs.maine.edu/~chaitin/unknowable/ch6.html http://www.umcs.maine.edu/~chaitin/unknowable/ch6.html

yters 18y ago

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.

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 ago
  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 18y ago
    [deleted]
- 18y ago

randomwalker 18y ago

A big part of the problem is that Chaitin is a shameless self-promoter. He is the Bruce Schneier of Algorithmic Complexity. Actually, no, Schneier is not nearly as bad. Let me quote from the highest voted Amazon review of his book: "Let the author speak for himself. From page 7, "Gödel's 1931 work on incompleteness, Turing's 1936 work on uncomputability, and my own work on the role of information, randomness and complexity have shown increasingly emphatically that the role that Hilbert envisioned for formalism in mathematics is best served by computer programming languages[.]" Imagine if a working composer wrote, "Bach's preludes and fugues, Beethoven's symphonies, and my own string quartets have shown increasingly emphatically..." This man's reputation in his declared field is nowhere near his apparent stature in his own mind. The ideas discussed in this book are worthy of late-night musings over a nice brandy, or maybe a Scientific American article, but only after extensive revision. They are not ready for publication in a monograph. "

jhancock 18y ago
I assume you weren't really picking on Schneier. He's a self-promotor in a pretty healthy sense. He has written much content on the human aspects of security useful to laymen. He does so without being arrogant or saying "I invented this". All in all, a good educator that doesn't talk down to his audience and can explain things so that his "grandmother could understand" (my favorite Einstein principle). He has interwoven this practice into his business, the beneficiary of his self-promotion, which seems to have done well for him. I might even recommend Schneier as the poster-boy of healthy entrepreneurial self-promotion.
- randomwalker 18y ago
  No, didn't mean to pick on Schneier. He's a self promoter, but the analogy breaks down after that.
neilc 18y ago
This man's reputation in his declared field is nowhere near his apparent stature in his own mind Really? He is one of the coinventors of Kolmogorov complexity, and Kolmogorov complexity certainly does shed a lot of light on the relationship between information, randomness, and complexity. While he is clearly a big ego and a shameless self-promoter, I think it's also fair to say that he is among the foremost experts on K-complexity and related topics.