Edward Frenkel
speaker
2,304 appearances
1 recordings
1 series
first heard Apr 2023
last heard Apr 2023
Edward Frenkel’s voice in public audio — every appearance, attributed to the second.
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Appearances
Boom, the glass is full.
And then I come up with a discovery.
No, it's always felt as a jump, as a leap.
And I have actually been studying various examples in history of mathematics of some fundamental discoveries, like discovery of complex numbers, like square root of negative one.
I wonder if a large language model could actually ever come up with the idea that square root of negative one is something that is essential or meaningful.
Because if all the information that you get, all the knowledge that had been accumulated up to that point, tells you that you cannot have a square root of a negative number.
Why?
Because if you had such a square root,
We know that if you square it, you get a negative number.
But we know that if you square any real number, positive or negative, you will always get a positive number.
So checkmate.
It's over.
Square root of negative one doesn't exist.
Yet we know that these numbers make sense.
They're called complex numbers.
And in fact, quantum mechanics is based on complex numbers.
They are essential and indispensable for quantum mechanics.
Could one discover that?
So to me, that sounds like a discontinuity in the process of discovery.
It's a jump.
Showing 501–520 of 2,304 · page 26 of 116
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