[FOM] extramathematical notions and the CH

[Vaughan Pratt]

On 1/30/2013 5:13 AM, Joe Shipman wrote:
> in that case ZFC would only decide finitely many bits of the number
 > and if we could measure more than that we would have new mathematical
 > knowledge coming from physics.

Be careful what you wish for.  It takes kT/2 joules to erase one bit 
where k = 13.8 x 10^{-24} is Boltzmann's constant and T is say room 
temperature of 300 K.  This might not seem like much, but if everyone on 
earth had a terabyte drive which they erased that would come to 7 * 10^9 
* 8 * 10^{12} * k * 300 = 232 joules.

The Sun outputs 12.14 * 10^33 joules per year, so if you scale those 232 
joules up by a further factor of 10^33 you've exceeded the annual energy 
output of the Sun by a factor of about twenty.

And you *still* won't have come close to erasing the infinitely many 
bits of your measurement.  The EPA will take a dim view of any such 
measurement that can't be disposed of properly.

Vaughan Pratt