Here's a thought experiment:
1) Let us assume that the total amount of energy in the universe is finite. Or at least, the total amount of available energy.
2) And let us assume that in order to perform any sort of calculation, energy is required.
3) Let us use all the energy (and/or mass) in the universe to construct an optimally-designed computer, which could then perform calculations at the fastest possible rate.
4) Let us employ the computer to calculate a sequence of digits, say the decimal expansion of an irrational number such as pi. I think this is an example where one can prove that there is no simple algorithm to calculate the nth digit based on a simple formula, rather one needs to laboriously calculate the preceding digits first.
5) Then, let us use all the energy in the universe to calculate as many digits as possible in this sequence, and suppose we end up with "p" digits.
6) Then the (p+1)st digit is calculable in theory, but unknowable in the universe!
Yes / No ?
2006-07-13
06:07:58
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10 answers
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asked by
garth_d
1