On 29-04-2023 22:39, John Clark wrote:
On Sat, Apr 29, 2023 at 4:28 PM smitra <smi...@zonnet.nl> wrote:
https://nyti.ms/3VlIBDo#permid=124757243 [1]
You say that GPT4 doesn't understand what it is saying, but did you
read my post about what happened when Scott Aaronson gave his final
exam on Quantum Computers to GPT4? The computer sure acted as if it
understood what it was saying!
John K Clark
If I read his account of the xam on posted here:
https://scottaaronson.blog/?p=7209
Then while I'm impressed about how much progress has been made with AI
systems being able to communicate in plain language, I don't see much
evidence that it understands anything at all. Even though the exact same
questions with answers are not posted on the Internet, a student with
poor knowledge of the subject who could very fast search the entire
Internet would be able to score a similar result and you would then see
a similar patters in ha questions it got right and wrong.
The way we evaluate students who we suspect of have cheated, is to
invite them at the office for some questioning, We then ask the student
to do some problems on the blackboard and try to get to the bottom of
whether or not the student has a proper understanding of the subject
consistent with the exam score.
That's why I think that the only proper way to evaluate GPT is via such
a dialogue where you ask follow up questions that go to the hart of the
matter.
If we want to test of GPT has properly mastered contour integration, I
would first start with asking to give me the derivation of the integral
of sin(x)/x dx from minus to plus infinity. It will probably blurt out
the standard derivation that involves integrating exp(i z)/z that
bypasses the origin along a small circle of radius epsilon and you then
have to subtract that contribution of that half circle and take the
limit of epsilon to zero.
This is the standard textbook derivation which is actually quite a bit
more complicated with all this fiddling with epsilon than a different
derivation which is not widely published. All you need to do is right at
th start when you write the integral as the limit of R to infinity of
the integral from minus to plus R of sin(x)/x dx, to ud]se Cauchy's
theorem to change to integration path from along the real axis to one
which bypasses the origin You can do that in any arbitrary way, we can
let the contour pass it from above. But because sin(z) for complex z
cannot be written as the imaginary part of exp(i z), we must now use
that sin(z) = [exp(i z) - exp(- i z)]/(2 i). And we then split the
integral into two parts for each of these terms. The integral, from the
first term is then completed by an arc of radius R in the upper
half-plane and this integral yields zero, while the integral for the
second term is completed in the lower half-plane and this then picks up
the contribution from the pole at zero.
Clearly this is a much simpler way of computing the integral, no
fiddling with epsilon involved at all but GPT may struggle doing the
problem in that much simpler way even if you walk it through most of the
details of how to do it, because it's not widely published and it
doesn't understand anything at all about complex analysis at all.
Saibal
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