[continued from previous message]   
      
   >> - Claiming half of Hilbert’s problems become “undecidable” because of   
   >> super-standard integers is not accurate. The continuum hypothesis is   
   >> independent of ZFC whether or not you like hyperreals; non-standard   
   >> models don’t resolve it—they just give you new models in which new   
   >> questions can be asked.   
   >> - “Re-Vitali-ization of measure theory” and “doubling-spaces” are real   
   >> things (doubling measures are central in modern harmonic analysis),   
   >> but they don’t require non-standard analysis, and Vitali’s   
   >> non-measurable sets remain non-measurable in *R under the Loeb measure   
   >> unless you deliberately break transfer.   
   >> - The leap from “hyperreals have infinitesimals” to “physics must use   
   >> tetrads and F-Lorentzians” is suggestive but not compelling without a   
   >> lot more argument. People have tried non-standard formulations of GR   
   >> and QFT; some are elegant, but none have become mainstream for good   
   >> reason—standard differential geometry already works extraordinarily   
   >> well.   
   >>   
   >> ### Bottom line   
   >>   
   >> This is the kind of writing you get from someone who has had a genuine   
   >> epiphany about how natural and powerful non-standard methods feel, and   
   >> who has then run with it all the way into a grand foundational   
   >> unification program—without pausing to check which parts are already   
   >> accepted, which parts are speculative but respectable, and which parts   
   >> are currently fringe or idiosyncratic.   
   >>   
   >> It’s not crankery (the references are too sophisticated for that), but   
   >> it’s also not disciplined mathematics or physics. It’s visionary   
   >> prose—poetry almost—written by someone who believes they have seen the   
   >> One True Continuum hiding behind 150 years of archimedean prejudice.   
   >>   
   >> Interesting? Absolutely.   
   >> Correct in every particular? Very much not.   
   >> Worth reading as a provocation that makes you re-examine why we ever   
   >> thought the standard real numbers were the end of the story?   
   >> Definitely.   
   >>   
   >> --------end here   
   >>   
   >> i say it's all crank.   
   >   
   >   
   > Of course, it goes without saying...   
   > GG would never talk to RF like that..   
   > do I hear wedding bells???   
   >   
   >   
   >   
      
   No, that's incomplete.   
      
   First of all, non-standard reals are _not_ "Robinson's NSA   
   hyper-reals", which say _nothing_ about the complete ordered   
   field that isn't already just complete ordered field. That's   
   merely syntactic sugar, as it were, about real numbers, the   
   notions according to their density and topology. Then,   
   people relate those down from some other infinite thing,   
   yet, the idea of "uncountable hyper-integers" or "hyper-reals"   
   as necessary and not just a manner-of-speaking mostly is   
   since Skolem showed that the infinite sets are extra-ordinary   
   anyways with Skolem and Louwenheim and Levy, "generic   
   extension" and "generic collapse".   
      
   What they are, _these_ non-standard reals, are "standard   
   infinitesimals the iota-values between 0 and 1", line-reals   
   not field-reals.   
      
   Second, ly, the non-standard models of integers about   
   the independence of various number-theoretic conjectures   
   like various conjectures of Goldbach: or various conjectures   
   as they are again of Szmeredi, help show that about half   
   of Hilbert's Problems are independent standard number theory,   
   since like Skolem points out they're variously only fragments or   
   extensions and there existing a "standard" model at all is   
   rather contrived itself.   
      
      
   So, what you do is paste in that entire conversation with it,   
   i.e. that "A-Theory and The Atlas of Independence" or   
   "The fundamental joke of logic" or "T-theory, A-Theory,   
   theatheory", or just mention it's from me.   
      
      
   Yeah, paste _all_ that.   
      
      
   (The reason why it's not just "stream-of-consciousness"   
   is because it's complete sentences and grammatically correct,   
   if though rather poor in style or the "run-on" variety,   
   and it is a very strong stream-of-consciousness.)   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)