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RomeoStevens comments on What is optimization power, formally? - Less Wrong Discussion
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String A and B are descriptions of worldstates. A is the received string, B is the desired string. It is not clear that there is a simple operation that generates a string "between" A and B. It seems intuitively like we should look to the VNM-axioms for a simple formal model of "betweeness" I think. Not sure.
A powerful optimizer can perform transforms between more disparate As and Bs maybe.
You could compare the structure of the compression (minimal program to represent) of the two strings. Though this asks the same question only on another level.