this post was submitted on 21 Jul 2023
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If it's a coffee machine that's so advanced it was uninaginable a decade ago, you'd expect it not to perform worse over time.
My point was that a coffee machine is designed to make coffee, not to keep track of time. Maybe it always takes roughly the same amount of time to make a coffee, and so someone uses it as a proxy stopwatch. But it can very well suddenly take more or less time, without anything being wrong about it – maybe different coffee brands, cleaned pipes, or whatnot.
ChatGPT is an algorithm designed to parrot language, not to perform mathematical reasoning based on logic rules.
Mathematical language is a language, ChatGPT has been shown to come up with relationship between very distant elements of language that were not present in the training data... so there is nothing stopping it from, given enough mathematical training data, coming up with whatever relationships we call "logical rules".
Mathematical language is a language, but mathematics is not just a language. It is a structure with internal rules that are not determined by pure convention (as natural languages are). We could internationally agree from tomorrow to call "blue" whatever it's now called "red" and vice versa, but we couldn't agree to say that "2 + 2 = 5", because that would lead to internal inconsistencies (we could agree to use the symbol "5" for 4, but that's a different matter).
This is also related to a staple of science: that scientific and mathematical truth is not determined by a majority vote, but by internal consistency. Indeed modern science started with this very paradigm shift. Quoting Galilei:
If we want to train an algorithm to infer rules from language, we need to give samples of language where the rules are obeyed strictly (and yet this may not be enough). Otherwise the algorithm will wrongly generalize that the rules aren't strict (in fact it'll just see a bunch of mutually inconsistent examples). Which is what happens with ChatGPT.
Edit: On top of this, Gödel's theorem and other related theorems have shown that mathematical reasoning cannot be reduced to pure symbol manipulation, Hilbert's unfulfilled dream. So one can't infer mathematical reasoning from language patterns. Children learn reasoning not only through language training, but also through behaviour training (this was pointed out by Turing). This is why large language models have intrinsic limitations in what they can achieve and be used for.
You are not wrong, but I think public perception is different. It doesn't help, that OpenAI is pushing their models as problem solvers:
I didn't know they made such claims. They're borderline dangerous claims...