Nice example. Actually, whenever you rely on a computer to perform a calculation, you are likewise assuming that the physical structure of the object and the logical structure of the math problem have a degree of isomorphism.
But let’s try to get a little clearer regarding the validity of anthropic reasoning in mathematics… The anthropic principle can never be the reason why a mathematical statement is true, whereas it can be the reason why a particular contingent physical fact is true (true ‘locally’ or ‘indexically’). However, faced with a mathematical uncertainty, it may be that certain possibilities are friendlier to the existence of observers. We might therefore regard our own existence as at least consistent with one of those possibilities being the mathematical truth, and even as favoring those possibilities. This appears to be a form of inductive reasoning.
So to sum up, you cannot anthropically prove a mathematical proposition; but in the absence of more decisive considerations, anthropic induction may provide a reason to favor the hypothesis.
Nice example. Actually, whenever you rely on a computer to perform a calculation, you are likewise assuming that the physical structure of the object and the logical structure of the math problem have a degree of isomorphism.
There is actually a quantum cosmological model that starts with chaos, and a quantum-chaotic encoding of the Riemann hypothesis, so I’m wondering if Roko’s starting point was more than just a whimsical example. :-)
But let’s try to get a little clearer regarding the validity of anthropic reasoning in mathematics… The anthropic principle can never be the reason why a mathematical statement is true, whereas it can be the reason why a particular contingent physical fact is true (true ‘locally’ or ‘indexically’). However, faced with a mathematical uncertainty, it may be that certain possibilities are friendlier to the existence of observers. We might therefore regard our own existence as at least consistent with one of those possibilities being the mathematical truth, and even as favoring those possibilities. This appears to be a form of inductive reasoning.
So to sum up, you cannot anthropically prove a mathematical proposition; but in the absence of more decisive considerations, anthropic induction may provide a reason to favor the hypothesis.