| Andrew Cooke | Contents | Latest | RSS | Twitter | Previous | Next


Welcome to my blog, which was once a mailing list of the same name and is still generated by mail. Please reply via the "comment" links.

Always interested in offers/projects/new ideas. Eclectic experience in fields like: numerical computing; Python web; Java enterprise; functional languages; GPGPU; SQL databases; etc. Based in Santiago, Chile; telecommute worldwide. CV; email.

Personal Projects

Lepl parser for Python.

Colorless Green.

Photography around Santiago.

SVG experiment.

Professional Portfolio

Calibration of seismometers.

Data access via web services.

Cache rewrite.

Extending OpenSSH.

C-ORM: docs, API.

Last 100 entries

Can't Help Thinking It's Thoughtcrime; Mefi Quotes; Spray Painting Bike Frame; Weeks 10 + 11; Change: No Longer Possible To Merge Metadata; Books on Old Age; Health Tree Maps; MRA - Men's Rights Activists; Writing Good C++14; Risk Assessment - Fukushima; The Future of Advertising and Surveillance; Travelling With Betaferon; I think I know what I dislike so much about Metafilter; Weeks 8 + 9; More; Pastamore - Bad Italian in Vitacura; History Books; Iraq + The (UK) Governing Elite; Answering Some Hard Questions; Pinochet: The Dictator's Shadow; An Outsider's Guide To Julia Packages; Nobody gives a shit; Lepton Decay Irregularity; An Easier Way; Julia's BinDeps (aka How To Install Cairo); Good Example Of Good Police Work (And Anonymity Being Hard); Best Santiago Burgers; Also; Michael Emmerich (Vibrator Translator) Interview (Japanese Books); Clarice Lispector (Brazillian Writer); Books On Evolution; Looks like Ara (Modular Phone) is dead; Index - Translations From Chile; More Emotion in Chilean Wines; Week 7; Aeon Magazine (Science-ish); QM, Deutsch, Constructor Theory; Interesting Talk Transcripts; Interesting Suggestion Of Election Fraud; "Hard" Books; Articles or Papers on depolarizing the US; Textbook for "QM as complex probabilities"; SFO Get Libor Trader (14 years); Why Are There Still So Many Jobs?; Navier Stokes Incomplete; More on Benford; FBI Claimed Vandalism; Architectural Tessellation; Also: Go, Blake's 7; Delusions of Gender (book); Crypto AG DID work with NSA / GCHQ; UNUMS (Universal Number Format); MOOCs (Massive Open Online Courses); Interesting Looking Game; Euler's Theorem for Polynomials; Weeks 3-6; Reddit Comment; Differential Cryptanalysis For Dummies; Japanese Graphic Design; Books To Be Re-Read; And Today I Learned Bugs Need Clear Examples; Factoring a 67 bit prime in your head; Islamic Geometric Art; Useful Julia Backtraces from Tasks; Nothing, however, is lost with less discomfort than that which, when lost, cannot be missed; Article on Didion; Cost of Living by City; British Slavery; Derrida on Metaphor; African SciFi; Traits in Julia; Alternative Japanese Lit; Pulic Key as Address (Snow); Why Information Grows; The Blindness Of The Chilean Elite; Some Victoriagate Links; This Is Why I Left StackOverflow; New TLS Implementation; Maths for Physicists; How I Am 8; 1000 Word Philosophy; Cyberpunk Reading List; Detailed Discussion of Message Dispatch in ParserCombinator Library for Julia; FizzBuzz in Julia w Dependent Types; kokko - Design Shop in Osaka; Summary of Greece, Currently; LLVM and GPUs; See Also; Schoolgirl Groyps (Maths); Japanese Lit; Another Example - Modular Arithmetic; Music from United; Python 2 and 3 compatible alternative.; Read Agatha Christie for the Plot; A Constructive Look at TempleOS; Music Thread w Many Recommendations; Fixed Version; A Useful Julia Macro To Define Equality And Hash; k3b cdrom access, OpenSuse 13.1; Week 2; From outside, the UK looks less than stellar

© 2006-2015 Andrew Cooke (site) / post authors (content).

A Century of Controversy Over the Foundations of Mathematics

From: Manuel Johannes Simoni <csae4529@...>

Date: Mon, 15 Dec 2003 21:16:46 +0100

Historical Introduction --- A Century of Controversy Over the Foundations of 

G J Chaitin

Link: http://www.cs.auckland.ac.nz/CDMTCS/chaitin/cmu.html

G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer 
Science Distinguished Lecture. The speaker was introduced by Manuel Blum. The 
lecture was videotaped; this is an edited transcript which appeared on pp. 12-
21 of a special issue of Complexity magazine on ``Limits in Mathematics and 
Physics'' (Vol. 5, No. 5, May/June 2000).


Now I don't think that Hilbert really wanted us to formalize all of 
mathematics. He didn't say that we should all work in an artificial language 
and have formal proofs. Formal proofs tend to be very long and inhuman and 
hard to read. I think Hilbert's goal was philosophical. If you believe that 
mathematics gives absolute truth, then it seems to me that Hilbert has got to 
be right, that there ought to have been a way to formalize once and for all 
all of mathematics. That's sort of what mathematical logic was trying to do, 
that's sort of what the axiomatic method was trying to do, the idea of 
breaking proofs into smaller and smaller steps. And Leibniz thought about 
this, and Boole thought about this, and Frege and Peano and Russell and 
Whitehead thought about this. It's the idea of making very clear how 
mathematics operates step by step. So that doesn't sound bad. Unfortunately it 
crashes at this point! 

So everyone is in a terrible state of shock at this point. You read essays by 
Hermann Weyl or John von Neumann saying things like this: I became a 
mathematician because this was my religion, I believed in absolute truth, here 
was beauty, the real world was awful, but I took refuge in number theory. And 
all of a sudden Gödel comes and ruins everything, and I want to kill myself! 

So this was pretty awful. However, this 

``This stmt is unprovable!'' 

is a very strange looking statement. And there are ways of rationalizing, 
human beings are good at that, you don't want to face unpleasant reality. And 
this unpleasant reality is very easy to shrug off: you just say, well, who 
cares! The statements I work with normally in mathematics, they're not 
statements of this kind. This is nonsense! If you do this kind of stupidity, 
obviously you're going to get into trouble. 
But that's rationalizing too far. Because in fact Gödel made this 

``This stmt is unprovable!'' 

into a statement in elementary number theory. In its original form, sure, it's 
nonsense, who ever heard of a statement in mathematics that says it's 
unprovable? But in fact Gödel made this into a numerical statement in 
elementary number theory, in arithmetic. It was a large statement, but in some 
clever way, involving Gödel numbering of all arithmetic statements using prime 
numbers, he was writing it so that it looked like a statement in real 
mathematics. But it really indirectly was referring to itself and saying that 
it's unprovable. 

So that's why there's a problem. But people didn't really know what to make of 
this. So I would put ``surprising'' here, surprising, a terrible shock! 


Summary of Gödel's Theorem:

G J Chaitin's homepage: 


Comment on this post