Kaj_Sotala comments on Value of Information: Four Examples - Less Wrong
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Side question: Why are these called "small world" assumptions? I've heard the term before but didn't understand it there either.
I presume it's because actually having a complete model about a problem requires looking at a problem that is small enough that you can actually know all the relevant factors. This is in contrast to e.g. problems in the social sciences, where the amount of things that might possibly affect the result - the size of the world - is large enough that you can never have a complete model.
As another example, many classic AI systems like SHRDLU fared great when in small, limited domains where you could hand-craft rules for everything. They proved pretty much useless in larger, more complex domains where you ran into a combinatorial explosion of needed rules and variables.