The principle is essentially a recognition that, if there were no constraints on energy or other physical limits, then many problems in NP or harder would be tr

The principle is essentially a recognition that, if there were no constraints on energy or other physical limits, then many problems in NP or harder would be tractable. This bridge might be two-way, so we may start from complexity and ask: what bounds might we expect in physics since without, this problem would be tractable? One relevant example is protein folding, which is NP-complete. Why then have we not found arrangements such that protein conformations are solutions to NP-complete problems? It's reasonable to postulate that nature does not actually solve NP-complete problems and that almost all carriers of problematic instances died off (not completely, since prions exist after all). If this is the case then we can make a prediction that there exists some polynomial time algorithm able to predict conformations of biologically encountered instances in reasonable time to high accuracy and that a program search such as deep learning will one day find this algorithm given sufficient data. That would be a huge deal. +++ The following links argue more or less that from a bayesian perspective, a prior weighted heavily on smaller exponents for the case P=NP, is more reasonable given the examples and rarity of realistically intractable polynomial time algorithms (and how quickly they seem to fall to reasonable with focused attention). Paragraph 3 in http://www.scottaaronson.com/democritus/lec6.html http://www.scottaaronson.com/democritus/lec6.html Argument 1 in https://windowsontheory.org/2013/05/06/reasons-to-care-in-honor-of-scott-aaronson/ https://windowsontheory.org/2013/05/06/reasons-to-care-in-ho...