Human beings can not do most math without pencil and paper and a lot of pondering. Whereas there are a number of papers showing specialized transformers can do math and code at a more sophisticated level than I would have expected before seeing the results.
I literally noted that GPT-J, which uses said 7GB of math (assuming that number is right), usually fails at ‘2 + 2 =’. People can do several digit addition without pencil and paper. ’763 + 119 =’ probably doesn’t require pencil and paper to get ’882′. We do require it for many step algorithms, but this is not that. ‘Dumb’ computers do 64-bit addition trivially (along with algebra, calculus, etc.). I haven’t seen specialized math models, but I’m dumbfounded that general models don’t do math way better.
I haven’t tried coding using ‘AI’ tools, so have no real opinion on how well it compares to basic autocomplete.
The basic problem of arithmetic is this: You can’t be informal in math, and every single step needs to be checked. Language, while complicated can allow a degree of informality, as long as you can communicate well. Math does not allow this.
This is obviously correct math, but formally you would do each step separately. The steps don’t necessarily need to be checked either, because it is an easy enough one that you can just check the result.
Math is a language, just a rigorous one, where it is simple to be right or wrong. It is a simple way to abstract away things that don’t matter, and talk about the underlying relations. Math is a subset of language with easier relations. For something with a pure general intelligence, math is probably much easier than a normal language.
I hold that we are story telling intelligences [and consciousness is us telling ourselves our own story as we compose it] that have been generalized through a deep understanding of the patterns in stories, which is why normal languages are easier for us -they were made to tell stories. (I also hold that you story of math is technically incorrect.)
Human beings can not do most math without pencil and paper and a lot of pondering. Whereas there are a number of papers showing specialized transformers can do math and code at a more sophisticated level than I would have expected before seeing the results.
I literally noted that GPT-J, which uses said 7GB of math (assuming that number is right), usually fails at ‘2 + 2 =’. People can do several digit addition without pencil and paper. ’763 + 119 =’ probably doesn’t require pencil and paper to get ’882′. We do require it for many step algorithms, but this is not that. ‘Dumb’ computers do 64-bit addition trivially (along with algebra, calculus, etc.). I haven’t seen specialized math models, but I’m dumbfounded that general models don’t do math way better.
I haven’t tried coding using ‘AI’ tools, so have no real opinion on how well it compares to basic autocomplete.
The basic problem of arithmetic is this: You can’t be informal in math, and every single step needs to be checked. Language, while complicated can allow a degree of informality, as long as you can communicate well. Math does not allow this.
You kind of can be informal though?
Suppose, 5x − 2 = 3b +9, thus
x = (3b + 11)/5 or b = (5x −11)/3
If b = 2, then
x = 17⁄5
If x = 2, then
b = −1/3
This is obviously correct math, but formally you would do each step separately. The steps don’t necessarily need to be checked either, because it is an easy enough one that you can just check the result.
Math is a language, just a rigorous one, where it is simple to be right or wrong. It is a simple way to abstract away things that don’t matter, and talk about the underlying relations. Math is a subset of language with easier relations. For something with a pure general intelligence, math is probably much easier than a normal language.
I hold that we are story telling intelligences [and consciousness is us telling ourselves our own story as we compose it] that have been generalized through a deep understanding of the patterns in stories, which is why normal languages are easier for us -they were made to tell stories. (I also hold that you story of math is technically incorrect.)