On Sun, Apr 2, 2023 at 5:58 PM smitra <smi...@zonnet.nl> wrote:
> > *> While GPT hooked up to Mathematica may greatly improve its performance, > I would not be impressed when judging that in terms of approaching human > level cognition.* > > > > > > *A long time ago I was teaching a statistical mechanics class, the > students had to do a certain calculation for homework that involved doing > the series expansion of 1/sinh(x) to order x. I was shocked to see that > none of the students could do it. But some did come up with the right > answer, they had shown some failed attempts and then wrote that they used > Mathematica and Mathematica says that the answer is 1/x - x/6 ...* > > > > *The students couldn't do it because they could not use the Taylor > expansion formula due to the singularity at x = 0. Most students had not > bothered to think about how to bypass that problem, otherwise at least a > few would have written down the correct derivation* > Forget algebra, trigonometry and calculus, even when a human performs something as basic as long division he's usually just blindly following an algorithm that he learned in grade school and is not consciously thinking about why it works. But GPT4 is certainly capable of providing mathematical proofs if necessary and can show it understands them by correctly answering questions about them and even giving the proof in a very different way. I just asked GPT3.5 to give me Euclid's proof of the infinity of the primes but do so in the form of a poem, and in less than two seconds this is what it produced, no doubt GPT4 could do even better. And this is before Mr.GPT got hooked up with Mathematica: *"In Euclid's time, a great debate was rife,About the primes that fill the number line, * *Some claimed that their count must end in time,* *But Euclid proved them wrong with reason's might.Suppose we have a finite set of primes, * *And multiply them all to get a line, * *We add one to this product, quite sublime, * *A new number appears, that's not confined.This number is not divisible * *by Any of the primes in our finite set, * *For if it were, we'd reach a sorry lie, * *That contradicts the number line's duet.So this new number must be prime indeed, * *And thus we've found a new one to concede, * *Adding it to our set, we then proceed, * *To find another prime with the same breed.And thus we prove there's infinite primes to find, * *A truth that stands the test of space and time, * *The primes are infinite, in number and kind, * *Thanks to Euclid's proof, so clear and divine."* John K Clark -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv09YkJG82KYoyKTy30cLtO4mdehs-%3DbOa0CUtC4CqMGYw%40mail.gmail.com.
