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If I may play the devil's advocate, nothing is deterministic. A neutrino could cause a bit flip in your calculator. More commonly, the lower abstractions we build upon without knowing their innards can have bugs. Even the most popular compilers (say, g++) have bugs, for instance. I am personally incapable of fixing a bug within gcc, despite the tool being a vital requirement of my work. IMO the dichotomy should not be deterministic/stochastic, but proved/unproved reliable. gcc has been shown reliable, for instance, so I don't need to know whether it was built by deterministic (clever engineers) or stochastic (typewriting monkeys) processes. I'm certain the former are more efficient, but this is ultimately not what makes the tool valuable. As a bit of an artificial example, there's stochastic processes that can be proved to converge to a desired result (say, a stochastic gradient descent, or Monte-Carlo integration), in the same way that deterministic methods can (say a classic gradient descent or quadrature rules). In practical cases, the only proof that matters is empirical. I write (deterministic) mathematical algorithms for a living, yet they very rarely come out correct on first iteration. The fact there is a mathematical proof that a certain algorithm yields certain results lets me arrive at a working program much faster than if I left it to typewriting monkeys, but it is ultimately not what guarantees a valid program. I could just as well, given enough time, let a random text file generator write the programs, and do the same testing I do currently, it would just be very inefficient (an understatement). |