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
Established knowledge.
Established knowledge.
Right.
And now, obviously, for each sort of...
fruitful leap like that.
There probably were thousands of things which went nowhere.
I'm not saying that every leap... It's an open shooting game.
Because, for example, you can try to do the same with three-dimensional space.
So you have coordinates X, Y, and Z. And you can say, oh, if it's one-dimensional, we have a bona fide numerical system called drill numbers.
If it's two-dimensional, which is like, you know, geometrically, it's just like this tabletop extended to infinity in all directions.
These are complex numbers, and we can define addition and multiplication, and they will satisfy the same properties as real numbers that we're used to.
What about three-dimensional space?
Is it possible to also define some operation of addition and multiplication on it so that these operations would satisfy the...
properties that we're used to.
And the answer is no.
You can define addition, but you can't define multiplication, for which there would be an inverse, for instance.
So there is something special about the plane, the two-dimensional case.
And by the way, next question would be, what about four-dimensional?
In a four-dimensional space, again, you can, and you get what's called quaternions, discovered by an Irish mathematician, Hamilton, in the 19th
And then in the eight-dimensional, there is something similar called Actonians, and that's about it.
Showing 581–600 of 2,304 · page 30 of 116
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