| Have you also heard about calculators? Every single finance person uses a calculator. How effective do you think a person in any aspect of finance would be if they had never learned what multiplication is? Would they perform their job adequately if they don't know that `X * Y` is `X repeated Y times`? IOW, if you gave a finance person (accountant, asset manager, whatever) a non-deterministic calculator for multiplication, would you trust the person's output if they never learned what multiplication is? This is the situation I am asking about; we aren't talking about whether deterministically automating something that the user already knows how to do is valuable, we're talking about whether non-deterministically generating something that the user is unable to do themselves, even if given all the time in the world, is valuable. All those examples you give are examples of deterministic automation that the user could inspect for accuracy. I'm asking about a near-future where people managing your money have never learned multiplication because "Multiplication has been abstracted away to a tool that gets it right 90% of the time" |
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).