I've just finished reading Tegmark's "The Mathematical Universe", which I commend for being well written, and also containing enough new ideas on the subject to be worth reading for the old timers.
I only found one obvious mistake. On page 19, he states that "Schmidhuber has hypothesized that all halting programs correspond to physical realities". This is not true, as Schmidhuber is explicitly agnostic in Schmidhuber97 about whether our universe is a halting program, and in Schmidhuber00 explictly deals with the nonhalting case. There is an interesting classification in section VII.D of levels of mathematical realities (there was a spelling error here). I would say that Bruno's COMP, or Schmidhuber's ensemble are basically level 4 mathematical universes (all structures defined by computations not guaranteed to halt). My own "all strings" ensemble lies somewhere between level 4 & 5, in that it has uncountably many elements, but does not cover all mathematical structures. But I would still say the UDA entails the existence of my ensemble (the UD*) as the internal experience of a conscious observer, even if not assumed as a fundamental ontology. However, if what Max calls the Computable Universe Hypothesis is true, then that would rule out the existence of the all strings ensemble. Cheers -- ---------------------------------------------------------------------------- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australia http://www.hpcoders.com.au ---------------------------------------------------------------------------- --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---
