Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
So by doing that, the energy inches forward scale by scale in such a way that it's always localized at one scale at a time.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
And then it can resist the effects of viscosity because it's not dispersed.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
So in order to make that happen,
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
yeah, I had to construct a rather complicated non-linearity.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
Um, and it was basically like, um, you know, like it was constructed like an electronic circuit.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
So I, I actually thank my wife for this because she was trained as a electrical engineer.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
Um, and, um, you know, she talked about, um,
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
He had to design circuits and so forth.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
And if you want a circuit that does a certain thing, like maybe have a light that flashes on and then turns off and then on and then off, you can build it from more primitive components, capacitors and resistors and so forth.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
And you have to build a diagram.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
And these diagrams, you can sort of follow it with your eyeballs and say, oh yeah, the current will build up here and then it will stop and then it will do that.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
So I knew how to build the analog of basic electronic components, like resistors and capacitors and so forth, and I would stack them together in such a way that I would create something that would open one gate, and then there would be a clock, and then once the clock hits a certain threshold, it would close it.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
It was kind of a Rube Goldberg-type machine, but described mathematically.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
And this ended up working.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
So what I realized is that if you could pull the same thing off for the actual equations, so if...
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
The equations of water support a computation.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
You can imagine a steampunk, but it's really a waterpunk type of thing.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
Modern computers are electronic.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
They're powered by electrons passing through very tiny wires and interacting with other electrons and so forth.
Lex Fridman Podcast
#472 β Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI
Instead of electrons, you can imagine these pulses of water moving at a certain velocity.