For those of you following my series on digital physics (the first part, on the reality of the real line, and the second part on the relevance on cellular automata have been posted), you will like this documentary on the nature of infinity by BBC. It features Gregory Chaitin, whose work I covered in the first part.
Video on Infinity featuring Chaitin
It is long, but worth it, since it is an unusually sophisticated angle for a popular TV documentary. Serves as a pretty neat introduction to this sort of thinking for those new to it.
About Venkatesh Rao
Heh. I chanced upon this video a while back, read the summary and thought, well, let’s hope someone keeps the cutlery away from Chaitin, seeing as how the reward for pushing back the boundaries of math appears to be insanity and/or suicide (Cantor, Godel, Turing).
Then I read his Omega book – the one you reviewed – and was reassured. Chaitin comes across as a chap bursting with enthusiasm, rather than the somber gravitas more suitable to his station. No one who liberally peppers a math book with exclamation points and sexual motifs is going to use cutlery for anything other than taking up extra large helpings of everything.
Gian-Carlo Rota has a great description of the personalities of logicians in ‘Indiscrete thoughts’ (pun intended). The description of Alonzo Church in particular is fantastic — it goes on for a few pages, and includes an extended description of Church’s obsessive compulsive blackboard cleaning ritual and extraordinary precision of speech. The book is on Google Books:
Indiscrete Thoughts by Gian-Carlo Rota
The Australian philosopher colin leslie dean argues
Gödel is a complete failure as he ends in utter meaninglessness. Godels theorems are invalid for 5 reasons: he uses the axiom of reducibility- which is invalid, he uses the axiom of choice, he constructs impredicative statements – which are invalid ,he miss uses the theory of types, he falls into 3 paradoxes
http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf
GODEL’S INCOMPLETENESS THEOREM. ENDS IN ABSURDITY OR MEANINGLESSNESS GODEL IS A COMPLETE FAILURE AS HE ENDS IN UTTER MEANINGLESSNESS CASE STUDY IN THE MEANINGLESSNESS OF ALL VIEWS
Colin leslie dean also argues that mathematics ends in meaninglessness ie contradiction
http://gamahucherpress.yellowgum.com/books/philosophy/Absurd_math_science4.pdf
The absurdities or meaninglessness of mathematics and science: paradoxes
and contradiction in mathematics and science which makes them meaningless,
mathematics and science are examples of mythical thought, case study of the
meaninglessness of all views
thankfully yours
gamla
I think you have missed something. Both of Goedel’s proofs have led to advances in Mathematics and our understanding of the problem. Socrates raised more questions than could be answered in his time. His method showed that many commonly considered notions (concepts, ideas) were not really well understood. Goedel’s proofs do not show at all anything like ‘meaninglessness’. Maybe you should consider the problem yourself and come to your own conclusion.