I'm tinkering with an argument based on algorithmic complexity that if it were possible to make something like an "automated mathematician" or "automated scientist", then these would be expected to eventually produce outputs that we humans would be unable to distinguish from random noise.
Getting the whole argument just right is fiddly, but the basic idea is this. You feed some kind of theory into the AM/AS, which is a black box. It churns on this and spits out a result, which is added to the theory (I'm neglecting the case that the result is inconsistent with the theory). It can now churn on theory + result 1. For any given and potentially very large N, after doing this long enough, it's churning on theory + result 1 + result 2 + ... + result N. Whatever it spits out will be dependent in particular on results 1 - N. When N is large enough, unless you know these results you will not be able to understand what it outputs because the output will almost surely depend critically on one or more of results 1 - N. In other words, the output will look like noise to you. If the AM/AS is appreciably faster at producing results than people are at understanding them, there will be an N beyond which no one can understand the output up to that point. It'll become indistinguishable (unable to be distinguished) from random noise.
If you're into software development, this would be analogous to a software system that generates syntactically-correct code and then adds that code as a new call in a growing software library. If you were to run this long enough, virtually all the programs it generated that were short enough for human beings to have any hope of reading and understanding would consist almost entirely of library calls to code generated by the system. You'd have no idea what any of this code did unless you studied the library calls, which you wouldn't be able to do beyond a certain scale. If the system were expanding the library faster than you could read and understand it, there'd be no hope at all.
I'll leave it as an exercise to the reader whether this is a desirable thing to do and whether it's happened yet. I would offer, though, a question to ponder: what reason is there to believe that a random number generator hooked up to an inscrutable interpreter produces human flourishing, for any given meaning of "human flourishing" you care to use?
#tech #dev #mathematics #AutomatedMathematician #AutomatedScientist #AI #GenAI #GenerativeAI #ThoughtExperiment
Scott A.W Lewin
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