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
And so in mathematics, but you see mathematicians are so clever.
It's really kind of like a little kind of a game of mirrors that we often like to say, and I used to say that,
that mathematics is objective.
It's really the only objective science.
But that's because we hide this fact that actually is based on axioms.
And the fact that
that there is no unique choice, that there are many choices.
And so Euclidean geometry is actually a good illustration of this because Euclid had five axioms.
Four of them were kind of obvious, like the one I just mentioned.
And the fifth, which came to be known famously as the fifth postulate, was that if you have a line and you have a point outside of this line,
There is a unique line passing through that point which is parallel to the first line, meaning that doesn't intersect it.
And Euclid himself was uncomfortable about this because he felt that he takes for granted something that is not obvious.
And for many centuries after that, mathematicians were trying to derive this axiom from other axioms, which were more obvious in some sense, and they failed.
And it was only almost 2000 years later that mathematicians realized that you can't, not only you cannot derive, but you can actually replace it with its opposite.
And you will still get a bona fide consistent, not self-contradictory, which is called non-Euclidean geometry.
which of course sounds very complicated, but it's not.
Think of a sphere, just the surface of a basketball or the surface of the earth, idealized.
So you have points, you have analogs of lines, which are meridians.
Every two meridians intersect, unlike parallel lines on a flat space.
There is also a so-called hyperbolic plane, where there are infinitely many lines which do not intersect.
Showing 921–940 of 2,304 · page 47 of 116
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