George Levy wrote in part:
Beautiful post, Hal. I have read and reread Rudy Rucker's "Infinity and the Mind" four or five times. This is such a rich book that I enjoy it everytime. His explanation of the infinite always leaves me in awe.
I share the joy. Rudy Rucker's "Infinity and the Mind" is formidable.
Please note that:
Its "excursion II" on Godel's incompleteness theorem is very good. The
excursion ends on a technical note on man-machine equivalence quite
genuine to introduce yourself to ... the consistent machine's elaborations ...
Hal Finney wrote in part:
A multiverse built on computational engines
would be far more limited than one which includes all the endless richnessof mathematical set theory.
I disagree. To disentangle the machine dreams, not *one* grain dust of
Cantor paradise will be too much ...
Mathematics is really like wonderland (or yellow submarine
if you prefer) full of spaces which looks little (countable or even finite)
from the outside and are undefinissably big from inside.
Godel's theorems limits what machines can say and prove about ... machines.
Even machine will need the non mechanical "notions" to speed up their
learning about machines and anticipated their behaviors.