Stuart_Armstrong comments on The mathematics of reduced impact: help needed - Less Wrong
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I don't understand much of this, and I want to, so let me start by asking basic questions in a much simpler setting.
We are playing Conway's game of life with some given initial state. An disciple AI is given a 5 by 5 region of the board and allowed to manipulate its entries arbitrarily - information leaves that region according to the usual rules for the game.
The master AI decides on some algorithm for the disciple AI to execute. Then it runs the simulation with and without the disciple AI. The results can be compared directly - by, for example, counting the number of squares where the two futures differ. This can be a measure of the "impact" of the AI.
What complexities am I missing? Is it mainly that Conway's game of life is deterministic and we are designing an AI for a stochastic world?
The game of life is interesting, because it's not reversible. It would then be possible to design an AI that does something (brings happiness to a small child or whatever) such that in a million iterations, the board is exactly as it would have been had the AI not existed.
But yes, counting the squares different might work in theory, though it might be too chaotic to be much use in practice. In our world, we use 'chaos' to get non-reversiblity, and coarse graining to measure the deviation.