B (75:50)
I think Don's work is very interesting. For the purposes of what I'm about to say, we don't need to worry about it. Let's assume a perfectly conventional physics. I think Don's onto something, I think for sure. But let's assume that we don't need to worry about that, a perfectly conventional physics. One thing that scientists nowadays like is a view called physicalism. Physicalism says that, look, there's only one realm that we need to worry about, but it's this physical realm. Physics tells us everything you need to know about this realm. And there it is. A lot of people like that. But I actually think that view is a non starter for the following reason. There are all kinds of important facts that are simply not facts about physics. They are not discovered by physicists, they will never be discovered by physicists. They are not changed by anything we do in physics. And those are certain facts of mathematics. So, for example, the exact value of E, the natural logarithm, the fact that complex numbers behave differently than quaternions, that behave differently than octunions, the truths of number theory, certain facts of topology and the distribution of prime numbers. You can't just dissolve the math department and hope that don't worry, the physicists will figure out why this is. This is not what they will ever do. The math department does things that are different and additive to what physics does. And both in physics and biology, and I think in cognitive science too, there's an interesting phenomenon which is that if you're like a five year old and you do that thing where you keep asking, but why? Right? So this is the. Yeah, but, but why? If you keep asking, but why long enough, eventually you always end up in the math department. It's the damnedest thing. Like imagine cicadas, right? They come out every, whatever, 13 and 17 years or something. They come out, right? You say, hey, hey. Why is. The biologist says, hey, why is that? Ah, because that way they don't time their predators. Because if it was every 12 years, then every two year, three or four year, six year predator would get you right? So 13 and 17, like, like, you know, okay, but that's cool. Why are those numbers so special? Ah, they're prime numbers. But why 13 and 17? Why isn't there one in between? Ah, now you got to go to the math department because they're the only ones that understand why that is. So it's like this with everything, with physics, you, you know, you keep digging, but why do the fermions do this or that? Oh, because this like amplitude Hedron has like this symmetry group or whatever. So there's something interesting going on where even from the basic, most basic math that you learn in high school up through these very complicated things, there are a bunch of facts that are simply not facts of physics. Now this I think is just how it is. Now from here you have a choice to make. You could say, well, these are just random regularities that are true in our world. It's just a random grab bag of interesting things. Mathematicians don't treat it that way, right? They think it's an ordered structure space that they are exploring. They think they're especially Platonist. Mathematicians think they are discovering, they're not inventing that you don't have a choice. You start with set theory, eventually you find out the value of E. You didn't have a choice about that. That's what you found out. You discovered that. So I think more optimistically that this is not a random grab bag of stuff. This is some kind of structured space of patterns, mathematical patterns. Now you can take one other step and you say, interesting. How do we know that these patterns are only of relevance to math? Is it possible? Well, we know they're of relevance to Physics, because they constrain how physics go. What about biology? Well, biology is interesting. Imagine that there's some planet, and on this planet the highest fitness belongs to a triangle of a very specific shape. So here comes evolution, and it cranks a bunch of generations and it finds the first angle. Cool. And cranks a bunch more generations, finds a second angle. Does it need to do it again to find a third angle? Why no, because once you know two angles of the triangle, you know the third one. Why did evolution just get to save one third of the time that it would take to figure this out while you get a free gift for mathematics? And so I think that physics is what we call things that are constrained by these patterns. Biology are the things that are enabled or facilitated by these patterns. I think biology uses the hell out of these things. And we'll talk about what they are momentarily. But now you say, okay, so they're relevant in physics, they're relevant in biology. What kinds of patterns are there? Well, there are passive things like the value of E and some fractals and things like that. But could it be that there are other patterns in the space that, that look a lot like things that are not studied by mathematicians? Maybe they look a lot like things that are studied by behavioral scientists. Could they be patterns that have some capacity for memory or patterns that have capacity for problem solving? Could they be recognizable as kinds of minds? And so this is the kind of crazy claim that I'm making. Maybe the relationship between the mind and the body is exactly the same relationship as between the truths of mathematics and physics. So this is an old idea. Descartes, you know, for example in the west is associated with this, that, okay, the mind is this like non material thing somewhere. And then of course immediately, you know, the princes of Bohemia and other people immediately nailed him on this idea. Yeah, but how does the interaction happen? How do you have a non physical pattern making the brain sort of damp like a puppet? Energy conservation laws, like how, how could that possibly work? And I don't think he said this, and I don't know why he didn't say this, because he was a mathematician. He could have said, I think you already have this problem because since the time of Pythagoras you have this problem that you have. These immaterial truths of mathematics are constraining the physics of our universe. We already have this interaction. This is not new, this has been around forever. This is a kind of interaction where some of these truths that come from a different space of facts absolutely constrain and enable things that happen in the physical world. So one thing you might think about is whether some of these patterns and we have right now, if anybody's interested, I give you a link to it. We're having this thing I organized called the Symposium on the Platonic Space. And we've got about 26 people. I initially thought it was going to be three people, me and these two other groups. It turned out there's like 26 people that gave awesome talks about this stuff, talking about this notion. I think it's going to be huge. And I think it has all kinds of very practical implications because what do you get? Well, maybe you get static patterns, but maybe you get dynamic patterns that are more like behavioral policies or even competencies. But maybe you also get compute. And if you get compute, and we can talk about this because we've actually done some experiments on this. If you actually get compute this way, maybe the way we've been totally adding up the cost of computation isn't right because we've been looking at the front end and I actually think this is what's happening here, is that the theories of computation that we have are mostly about the front end interface and they're kind of been neglecting some stuff that happens on the backend. And we've just begun. We published a couple things on it. There's lots more coming. So I think that's an exciting new area that may have all kinds of implications for cognition and behavioral science more generally.