Meta Math!
by Gregory Chaitin · first published 2005
65% recommend29% neutral6% critical
Why HN recommends it
A short, accessible popular-math book on algorithmic information theory and Chaitin's constant Omega, linking the halting problem and Godel's work. Suited to non-mathematicians curious about incompleteness.
Summarised by Claude from recommending comments
In Meta Math!, Gregory Chaitin, one of the world's foremost mathematicians, leads us on a spellbinding journey of scientific discovery and illuminates the process by which he arrived at his groundbreaking theories.All of science is based on mathematics, but mathematicians have become painfully aware that math itself has serious limitations. This notion was first revealed in the work of two giants of twentieth-century mathematics: Kurt Godel and Alan Turing. Now their successor, Gregory Chaitin, digs even deeper into the foundations of mathematics, demonstrating that mathematics is riddled with
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…discussing not Nature, but our information about Nature. But physics did not have the vocabulary for expressing ideas on that level, hence the groping." >we understand "infinity" just fine. I enjoyed "Meta Math" by Gregory Chaitin: http://arxiv.org/abs/math/0404335 "So the set of real numbers, while natural—indeed, immediately given— geometrically, nevertheless remains quite elusive: Why should I believe in…
on “What I learned as a hired consultant to autodidact physicists” ↗I'm not sure "try not to use [proof by contradiction] unless you really need it" is the optimal conclusion. In "Meta Math"[1], Gregory Chaitin explores the question: "What makes a mathematical concept desirable?" Simplicity was the solution. The best theorems seem obvious in retrospect, because they are reduced into relationships…
on “When is proof by contradiction necessary?” ↗I try to read Godel's Proof once a year or so. You might also be interested in Gregory Chaitin's Meta Math! The Quest For Omega, which relates the halting problem (among other things) to Godel. A word of warning though, the book is rather idiosyncratic, as you might have seen from the title.
on “Gödel and the limits of logic (2006)” ↗Chaitin's "meta math" is also a good read. Less arduous than G.E.B.
on “Kurt Gödel and the Mechanization of Mathematics” ↗…http://www.amazon.com/Concrete-Mathematics-Foundation-Comput... ) by Graham, Knuth & Patashnik - It's based on the course taught at Stanford since 1970 & it's really really good. Another book I think you should get is Meta Math: The quest for Omega( http://www.amazon.com/Meta-Math-Quest-Gregory-Chaitin/dp/140... ) by Gregory Chaitin. It's not really a math course book, and is mostly the authors take on his favorite topics in…
on “Ask HN: Learn Math the Hard Way” ↗Anyone interested in this would immensely enjoy Meta Math! by Gregory Chaitin. Basically, he demonstrates that there are theorems which are randomly true: they're true for no particular reason. It's, of course, deeply connected with Gödel's work. If anyone's…
on “Indescribable numbers: The theorem that made me fall in love with math” ↗For a deep look at Omega (Chaitin's constant) I'd recommend Chaitin's book Meta Math: The Quest for Omega [1]. A fascinating book. Chaitin has also uploaded the full text (pdf) of the book to Arxiv.org [2]. [1] http://www.amazon.co.uk/Meta-Maths-Gregory-J-Chaitin/dp/1843... [2] http://arxiv.org/abs/math/0404335
on “Digital physics” ↗Definitely. I'd recommend his book Meta Math: The Quest for Omega [1]. He posted the full text of the book on arXiv [2]. [1] https://www.amazon.co.uk/Meta-Maths-Gregory-J-Chaitin/dp/184... [2] http://arxiv.org/abs/math/0404335
on “Gödel, Turing and Cantor: The Math” ↗>How do these finitists handle things like the real numbers? You may enjoy "Meta Math" by Gregory Chaitin (jump to Chapter 5 for the impatient): http://arxiv.org/abs/math/0404335 "Finally, and perhaps even more devastatingly, it turns out that the set of all reals that can be individually…
on “Mathematicians Bridge Finite-Infinite Divide” ↗"Meta Math!: The Quest for Omega" by Gregory Chaitin [0] was my introduction to the theory of computability [1]. I found it enjoyable and approachable. [0] https://books.google.com/books?id=Z6FJbwggW1sC [1] https://en.m.wikipedia.org/wiki/Computability_theory
on “The P=?NP Poll (2002) [pdf]” ↗…paper by Wildberger tackling some of the issues in this thread: Set Theory: Should You Believe? http://web.maths.unsw.edu.au/~norman/papers/SetTheory.pdf Some interesting works by Gregory Chaitin Meta Math! The Quest for Omega https://arxiv.org/abs/math/0404335 Exploring Randomness https://www.cs.auckland.ac.nz/~chaitin/ait/ How Real are Real Numbers? https://arxiv.org/abs/math/0411418 People who…
on “A One-Line Proof of the Infinitude of Primes” ↗…good introduction to algorithmic information theory for non-mathematicians. Chaitin's Constant (Omega) is a non-computable number that is equivalent to the halting problem. [0]: https://www.amazon.com/Meta-Math-Quest-Gregory-Chaitin/dp/14...
on “The Axiom of Choice Is Wrong (2007)” ↗A good book to read to get aquainted with these notions is "Meta Math" by Gregory Chaitin. The impatient can jump to chapter 5. https://arxiv.org/abs/math/0404335
on “Are real numbers really real?” ↗This is by Gregory Chaitin, who also published a pretty interesting & related book called "META MATH!" [1] I especially like the Turing / Godel equivalency stuff he discusses. [1] https://arxiv.org/pdf/math/0404335.pdf
on “How to Run Algorithmic Information Theory on a Computer (1995)” ↗…close, yet it's so-so far if you don't remember the password. Just a little difference in your brain state and it flips from trivial to hopeless. PS, if you like thinking about such things, I recommend Meta-Math by Gregory Chaitin, it's very fun (providing an address VS constructing the thing is basically the gist of algorithmic information theory).
on “Show HN: Every single torrent is on this website” ↗