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:
1/sinh(x) = 1/(x + x^3/6 +...) = 1/x 1/(1 + x^2/6 + ...) = 1/x (1 -
x^2/6 + ...) = 1/x - x/6 +...
Now, I do think that GPT is a great leap forward, I don't want to
downplay the progress made. But I'm quite skeptical about the idea that
such systems are approaching human level cognition. The human brain is
an enormously powerful system, but we don't have free access to use the
power of our brains to do whatever we want. For example, most people
cannot multiply two 5 digit numbers in their head, but a simple pocket
calculator has no problems with that task.
However, some autistic savants do have more of a privileged access to
use the power of the our brains to do arithmetic. Some of them can do
calculations that most other people cannot do. In certain tests
involving magnetic stimulation or inhibition of certain brain parts
performed on ordinary people, it has been shown that people can
temporarily gain certain abilities that they normally don't have. For
example, if you look at a screen with a few hundreds dots on it, can you
count the number of displayed dots in one second? Most people can't,
some autistic savants can do this. But in the
experiment with magnetic stimulation or inhibition, the test subjects
were also able to do this.
When we are consciously using our brains doing complicated things e.g.
mathematics, then we are using our brains in an extremely inefficient
way. If we could have an artificial brain similar to our brain but one
which is completely dedicated to doing mathematics instead of what our
brains are dedicated to do, then it would be enormously better at math
than we are. It's then likely that something like the brain of a lizard
that is fully dedicated to math would already completely outclass the
world's best mathematicians. Perhaps even the brain of insects could
perform at the same level of most mathematicians when fully dedicated to
doing math.
Saibal
On 28-03-2023 23:32, John Clark wrote:
Apparently I'm not the only one who has become obsessed with the
developments in AI that have occurred in the last few weeks, Stephen
Wolfram, the man who developed Mathematica, started Wolfram Alpha, and
wrote the book A New Kind Of Science about cellular automation, has
given two very interesting interviews on the subject. Wolfram wrote a
plug-in to connect GPT4 with Mathematica because calculation was the
one thing that GPT4 was not very good at but Mathematica is superb at
it; he describes the experience as "poking at an alien intelligence".
GPT + Wolfram: The Future of AI is Here! [1]
GPT, AI, and AGI with Stephen Wolfram [2]
John K Clark See what's on my new list at Extropolis [3]
9eq
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[4].
Links:
------
[1] https://www.youtube.com/watch?v=z5WZhCBRDpU
[2] https://www.youtube.com/watch?v=szxiPMyuMGY
[3] https://groups.google.com/g/extropolis
[4]
https://groups.google.com/d/msgid/everything-list/CAJPayv2%3D_vDQ1fhCpoa3nv20TC66iWGLb1oiEtEmpGfb3YOQiA%40mail.gmail.com?utm_medium=email&utm_source=footer
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