It doesn't matter how clever the AI is: the problem is mathematically impossible. The behaviour of some programs depends on Goldbach's conjecture. The behaviour of some programs depends on properties that have been proven independent of our mathematical systems of axioms (and it really doesn't take many bits: https://github.com/CatsAreFluffy/metamath-turing-machines). The notion of "algorithmic similarity" cannot be described by an algorithm: the best we can get is heuristics, and heuristics aren't good enough to get TDT acausal cooperation (a high-dimensional unstable equilibrium).
In practice, we can still analyse programs, because the really gnarly examples are things like program-analysis programs (see e.g. the usual proof of the undecidability of the Halting problem), and those don't tend to come up all that often. Except, TDT thought experiments posit program-analysis programs – and worse, they're analysing each other…
Maybe there's some neat mathematics to attack large swathes of the solution space, but I have no reason to believe such a trick exists, and we have many reasons to believe it doesn't. (I'm pretty sure I could prove that no such trick exists, if I cared to – but I find low-level proofs like that unusually difficult, so that wouldn't be a good use of my time).
> Remember that infinite precision is an infinity too and does not really exist.
For finite discrete systems, infinite precision does exist. The bytestring representing this sentence is "infinitely-precise". (Infinitely-accurate still doesn't exist.)
In practice, we can still analyse programs, because the really gnarly examples are things like program-analysis programs (see e.g. the usual proof of the undecidability of the Halting problem), and those don't tend to come up all that often. Except, TDT thought experiments posit program-analysis programs – and worse, they're analysing each other…
Maybe there's some neat mathematics to attack large swathes of the solution space, but I have no reason to believe such a trick exists, and we have many reasons to believe it doesn't. (I'm pretty sure I could prove that no such trick exists, if I cared to – but I find low-level proofs like that unusually difficult, so that wouldn't be a good use of my time).
> Remember that infinite precision is an infinity too and does not really exist.
For finite discrete systems, infinite precision does exist. The bytestring representing this sentence is "infinitely-precise". (Infinitely-accurate still doesn't exist.)