[FOM] CH and mathematics

joeshipman@aol.com joeshipman at aol.com
Mon Jan 21 16:17:07 EST 2008

> How about "we'll never know whether busy-beaver(googol), expressed as 
> base=10 integer, has an even or odd number of digits?"

>Why not Goldbach's Conjecture (GC), or Twin Primes?  These are 
>questions that may turn out not to be knowable at all.

But a proof of GC or TPC is much more conceivable than a proof settling 
my question above.

  For GC and TPC absence of a proof is our only evidence they are hard, 
but we have much stronger theoretical reasons for believing that 
questions about busy-beaver(googol) are unknowable (see Chaitin's work 
showing that no consistent proof systems of size X can decide the value 
of more than approximately X bits of his Omega number (which codes up 
the halting of TMs)).

-- JS
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