Terence Tao: uncertainty

Transcript context

…ing, maybe have a light that flashes on and then turns off and then on and off. You can build it from more primitive components, capacitors and resistors and so forth, and you have to build a diagram. And these diagrams, you can sort of follow up your eyeballs and say, “Oh yeah, the current will build up here and it will stop, and then it will do that.” So, I knew how to build 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’d be a clock, and then once the clock hits a certain threshold, it would close it. It would become a Rube Goldberg type machine, but described mathematically. And this ended up working. So, what I realized is that if you could pull the same thing off for the actual equations, so if the equations of water support a computation… So, you can imagine a steampunk, but it’s really water-punk type of thing where… So, modern computers are electronic, they’re powered by electrons passing through very tiny wires and interacting with other electrons and so forth. But instead of electrons, you can imagine these pulses of water moving a certain velocity. And maybe there are two different configurations corresponding to a bit being up or down. Probably that if you had two of these moving bodies of water collide, they would come out with some new configuration, which would be something like an AND gate or OR gate, that the output would depend in a very predictable way on the inputs. And you could chain these together and maybe create a Turing machine. And then you have computers which are made completely out of water. And if you have computers, then maybe you can do robotics, so hydraulics and so forth. And so you could create some machine which is basically a fluid analog, what’s called a von Neumann machine. So, von Neumann proposed if you want to colonize Mars, the sheer cost of transporting people in machines to Mars is just ridiculous, but if you could transport one machine to Mars, and this machine had the ability to mine the planet, create some more materials, smelt them and build more copies of the same machine, then you could colonize a whole planet over time. So, if you could build a fluid machine, which yeah, so it’s a fluid robot. And what it would do, its purpose in life, it’s programmed so that it would create a smaller version of itself in some sort of cold state. It wouldn’t start just yet. Once it’s ready, the big robot configuration of water would transfer all its energy into the smaller configuration and then power down. And then they clean itself up, and then what’s left is this newest state which would then turn on and do the same thing, but smaller and faster. rgy into the smaller configuration and then power down. And then they clean itself up, and then what’s left is this newest state which would then turn on and do the same thing, but smaller and faster. And then the equation has a certain scaling symmetry. Once you do that, it can just keep iterating. So, this, in principle, would create a blowup for the actual Navier-Stokes. And this is what I managed to accomplish for this average Navier-Stokes. So, it provided this sort of roadmap to solve the problem. Now, this is a pipe dream because there are so many things that are missing for this to actually be a reality. So, I can’t create these basic logic gates. I don’t have these special configurations of water. There’s candidates, these include vortex rings that might possibly work. But also analog computing is really nasty compared to digital computing because there’s always errors. You have to do a lot of error correction along the way. I don’t know how to completely power down the big machine, so it doesn’t interfere the writing of the smaller machine, but everything in principle can happen. It doesn’t contradict any of the laws of physics, so it’s sort of evidence that this thing is possible. There are other groups who are now pursuing ways to make Navier-Stokes blow up, which are nowhere near as ridiculously complicated as this. They actually are pursuing much closer to the direct self-similar model, which can… It doesn’t quite work as is, but there could be some simpler scheme they want to just describe to make this work. There is a real leap of genius here to go from Navier-Stokes to this Turing machine. So, it goes from what the self-similar blob scenario that you’re trying to get the smaller and smaller blob to now having a liquid Turing machine gets smaller and smaller and smaller, and somehow seeing how that could be used to say something about a blowup. That’s a big leap.…

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