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Yes, for example Solomonoff induction (SI) requires infinite computational capacity. If SI is representative of the human mind, then the human mind cannot be p
by yters 8y ago
Yes, for example Solomonoff induction (SI) requires infinite computational capacity. If SI is representative of the human mind, then the human mind cannot be physical.
- tlb 8y agoThe human mind isn't exactly Solomonoff, because we often hold theories that are more complicated than necessary. Working towards simpler scientific or mathematical theories takes decades. So it seems like we don't just have SI in the inner loop. People have made plausible attempts to approximate SI with practical amounts of computing, like AIXI (https://arxiv.org/abs/0909.0801 https://arxiv.org/abs/0909.0801).
- yters 8y agoIt is not so much whether we identify the simplest theory, but that we are so good at inferring principles and predicting, whether in science or in day to day life. SI is a formalization of this general capability. Perhaps a finite TM can approximate SI to some degree, but to what degree, and is this degree equivalent to human capability? I don't know of any evidence of the latter. If you do, let me know!