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by fhe
944 days ago
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here's my thought experiment: suppose one builds a generative model that predicts the next digit of pi. if a program can do this perfectly, then it's arguable that it understands what the number pi is. the question is, can such a model be trained by feeding it a large amount of known digits of pi? My intuition is that it's not doable with current approach to building generative models. the number pi arose out of certain constraints and characteristics of the physical world we live in. but if a model ever sees is just an endless stream of digits, without access to the underlying physical model, I don't see a path for it to 'reverse-engineer' and figure out the physical model that gave rise to it. |
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> the number pi arose out of certain constraints and characteristics of the physical world we live in
Pi arose from the notion of a circle, which is an abstractions and axioms. Pi would still be pi in a completely different world under the same axioms and abstractions.
I qualified my statement with 'mostly' because a circular motion can indeed be defined by a differential equation, or in other words by a rule that dictates the 'next' value based on current value (and recent changes). So learning an approximation of a circle is very much in the realms of a sequence learner and it may learn about pi (and made to store the information to retrieve/recognize it later). However learning pi directly from the sequence of digits of pi, which is what you were talking about, that does seem difficult.