From: Hara Ra (harara@shamanics.com)
Date: Sat Oct 04 1997 - 14:16:59 MDT
Anders Sandberg wrote:
>
> Geoff Smith <geoffs@unixg.ubc.ca> writes:
>
> > Does Gödel prove that mathematics is infinitely complex, or just
> > incomprehensibly so?
>
> I think infinitely complex is the likely choice. I'm not sure I can
> prove it (metamathematics is not my strong suit), but given the
> results by Chaitin about the random and non-algorithmic structures
> in the natural numbers it seems that the complexity of mathematics
> is infinite, not just incomprehensible.
I suspect the actual answer is "both". The kinds of propositions which
meet Godel's criterion are lengthy, involuted and not the kind of thing
human minds find easy to process. Note that the use of computers to help
mathematical proofs have already produced very lengthy complex proofs
which require teams of mathematicians to verify.
O----------------------------------O
| Hara Ra <harara@shamanics.com> |
| Box 8334 Santa Cruz, CA 95061 |
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