[FOM] extramathematical notions and the CH
Vaughan Pratt
pratt at cs.stanford.edu
Wed Jan 30 21:04:22 EST 2013
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
More information about the FOM
mailing list