How can we trust reality? How can anybody know that they're not just a brain in a vat, being fed artificial neural impulses by some mad scientist running a supercomputer simulation of the world?
Perhaps (if one can rely on one's own reason) there is a solution. Are there natural problems so computationally intensive that they can't successfully be solved in real time, even with the largest conceivable future computers? If so, could one use such problems to tell the difference between a simulation and reality? That is, could you know that you were just a brain in a vat by the breakdown of such a complex simulation? And contrariwise, could you trust the evidence of your senses, if you observed situations too rich in detail ever to be faked?
Imagine raising a pair of binoculars to your eyes, to look more closely at a waterfall, and seeing the cascade resolve itself into a wire-mesh framework rather than a chaotic torrent of droplets and eddies. Imagine flipping the pages of a book and noticing a delay before the words of the next chapter appear. Imagine tuning a radio across the RF spectrum and hearing perceptible stutters at each different station before its music resolves into continuity.
To cause such a breakdown of the simulation, the challenge problem has to have real-time elements — otherwise, it might be precomputed at the leisure of the evil genius who is out to trick us. It has to incorporate directly observable features — otherwise, the readouts of complex instruments could be faked without doing the underlying hard computational work. And the challenge problem has to have an answer that can be reliably checked, after the fact, by trustworthy human mental operations.
What are examples of such complex and noncomputable problems? Could explicit ones be exhibited, perhaps involving issues of number theory or the chaotic behavior of deterministic physical systems? Or do no such problems exist in the real world? If not, is that a coincidence, or ...?
Saturday, June 19, 1999 at 06:22:11 (EDT) = 1999-06-19