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Show Notes
This is a brief (~17 minute) introduction to my argument about Platonic space in biology, using a 1-page simplified argument format and then a quick overview of the research program entailed by it.
CHAPTERS:
(00:00) Specific mathematical patterns
(01:46) Math explaining physical patterns
(03:25) Causality from mathematical properties
(04:34) Physicalism and Platonic space
(06:14) Structured space of patterns
(07:49) Minds in pattern space
(10:03) Dualism as scientific option
(11:08) Non-biological pattern interfaces
(12:33) Patterns as cognitive goals
(13:44) Interfaces for Platonic patterns
(16:00) Empirical Platonic space research
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Transcript
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[00:00] To make this as simple as possible, the parts in green, I think, as odd as they may sound, I think are pretty, pretty hard to argue with. I think they're just pretty, pretty set. The blue is an optional thing, and then I suggest some wilder things that are up for discussion.
So here's my argument. There are, as we know, specific facts of mathematics. These are properties of certain numbers. These are things like Feigenbaum's constant and all kinds of facts of number theory. Let's call them patterns or other people have called them forms. Here are some examples: facts about what the amplituhedron does and doesn't do, symmetry groups, and so on.
Okay, so that's the first thing. We know this is the case.
The second thing we know is that there are many of these specifics that are surprising and forced on you once you choose some very basic assumptions. For example, my understanding, and I'm no mathematician, is that once you start with logic or set theory, you then can build up mathematics, and then you get things like the very specific value of E. You don't get a choice about it. You couldn't have set it to something else. Once you start with some specific assumptions, you could have started with other assumptions, but once you start with specific assumptions, you then inherit all kinds of actual facts that are what they are. You discover them, and there's nothing you can do about them. That seems also to be true.
For some such patterns, there are aspects of math and physics that are explained by those patterns. For example, if you want to know why the cicadas come out at 13 years and 17 years, you're going to eventually get a story about prime numbers because they're trying to avoid predators and cycles. The pattern that you see in biology, for example, is explained by the distribution of primes. Or if you want to know why certain particles do this or that, the answer is going to be because there's this group that has certain symmetries and the amplituhedron does this and that, and that's why the particles are how they are.
So it seems to me that if you ask why long enough, eventually you end up in the math department. You start in biology or you start in physics, and if you keep asking why, eventually it turns into some kind of mathematical fact.
However, in contrast, it doesn't work backwards. For example, if you wanted E to be different, or if you wanted Feigenbaum's constant to be a different number, there's, to my knowledge, nothing you can do in the physical world to change that.
The facts from the mathematical world affect what happens in the physical world, but the reverse is not true. You could change all the constants at the beginning of the Big Bang, and still the patterns of those Halley plots that I always show still look the way they look, and the facts of number theory still are what they are. There's nothing you can do in physics to change that. If the facts of these patterns were different, biology and math would be different. In a certain sense, it doesn't work in reverse.
In a certain sense, you can say that causality flows from these mathematical properties to the physical world. When I say causality, I don't mean in the physical, in the temporal sense of first the A happened and it was the cause for B happening. I don't mean there's a sense of time here. I mean that if you want to explain what's going on in biology or physics and you want to do better than explain—if you want to build new things, if you want to control what happens, you want to make new capabilities—you have to understand what's happening, what these properties of these mathematical objects are. That's what I mean by causality. The properties of those mathematical objects determine what you're going to be doing in the physical world. They cannot be ignored.
These things play instructive roles, instructive in a very pragmatic sense: you can't ignore these things. If you want to understand evolution, biomedicine, engineering, whatever, you're going to have to understand that these are inputs into the system you care about.
All of that, I think, is pretty hard to argue with. I think those are things we know.
But now it has some conclusions, which people may or may not like. The first conclusion, it seems to me, is that physicalism is dead on arrival. It is simply a non-viable theory because there are facts that are not in the physical world in any useful sense of physics. There are no theories of physics that will tell you why E has the value that it has or why certain other abstract mathematical properties are what they are. These things comprise a set of truths that are not in the physical world. Pythagoras knew this already; many ancient thinkers have already said this. Plato, of course, said it. For that reason, I call the space of possible properties the Platonic space.
[05:18] I'm not trying to stick close to how Plato thought about these things. In particular, I don't believe that these are immutable, unchanging, permanent forms. I don't know if we really know what he thought about some of these things. That's not what I'm trying to do. The only reason I call it Platonic space is to try to stick close to the mathematician's view of what's going on and point out that this is already an existing view. I make this up, although I make a couple of important changes. Even in Newton's classical world with no quantum mechanics and no weirdness, physicalism was dead because the objects of that physical world had to obey rules that were not set in that world.
Here are some optional hypotheses. This is a metaphysical claim. I can't prove this, but I think it's a good way to go because it's optimistic and it leads to research, which is that if we look at the space of possible patterns, this Platonic or latent space of patterns, I propose that we don't think that it is a random collection of facts that we just have to live with, which is what a lot of scientists say when they want to be physicalists. When I point out how come this thing has this property, they say it's emergent. It just means that it's a fact that holds in our world. We're going to build up a catalog of facts that hold in our world, and that'll be that. I think that's a mysterian and pessimistic way of looking at it. I would rather think the way that many mathematicians think, which is that this is not a random collection of facts. They form a structured, ordered space such that when you've understood one, that helps you to move in some direction to understand the next one. They come from an ordered, systematically tractable space of patterns.
That's an assumption. You don't have to believe that, but all of science, having a research agenda at all, means that you've already bought into the belief that you're studying a systematic space of truths that has a structure to it. From there, I will draw two skeptical positions. The first position is that I don't think we can assume that the models of mathematics, which are formal ways of understanding low-agency patterns, encompass everything that exists in this space. You could say mathematics is all there is. The only things this space contains are the kinds of things that math is good at dealing with. But that's an assumption, and I don't think we can assume that. I'm taking the skeptical position that maybe that space also contains other patterns that are more complex, more dynamic, higher agency. When you study those things, it doesn't look like math anymore. It starts to look like behavioral science. The formal tools of mathematics only apply to one layer of the contents of that space. There are other contents that are better dealt with by tools we recognize as behavioral science tools. That is an empirical claim. We should find out if that's the case, and that's what we've been doing.
Therefore, if you follow that skeptical position, you would say that some of these patterns that are making their way into physics and biology actually look like kinds of minds. They look like behavioral propensities or competencies. They don't look like just the properties of mathematical objects. A couple of engineers and mathematicians at our Platonic Space symposium have pointed out to me that even the assumption that mathematical objects are low-agency tools is a bad assumption. In their own space, those things may have more on the ball than I give them credit for, which I think is possible and is consistent with my idea that you can't just decide these things, you have to do experiments. There's some interesting work those people are doing.
Once we've said that patterns from this non-physical space make a difference in physics and biology, then dualism is basically viable. This is a model that's been unpopular in modern science. Everybody wants a physicalist perspective where you don't have influence from other spaces.
[10:27] It seems to me that we already knew that some aspect of dualism was true in physics and biology, because both of those areas get inputs from a space of patterns that is not the physical space. We already knew that physics and biology has this dualist aspect, but I'm suggesting it may also be relevant in cognitive science. In other words, some of these are not just patterns of form and function, they're also patterns of behavior. These are also kinds of minds. That gets us closer to the original dualist model by Descartes.
The final skeptical position that I want to suggest is that I don't think we can assume that biological materials, evolutionary processes, et cetera, have any monopoly on hosting the ingression of these patterns. In other words, we can all see that complex biology is really good at taking advantage of these spaces, the patterns from this space, but I don't think you can assume that there's any magic in the complexity in the biological materials in the random search of evolution. I don't think you can assume that any of that is essential for this. For that reason, it might behoove us to look at simple model systems, AKA machines, algorithms, to see if they also host some ingressions, maybe not as complex and agential as what we see in biology, but still not zero.
We've done experiments in this space and shown that even extremely minimal deterministic kinds of things actually do become the interfaces for these intrinsic motivations of behavior and these patterns in general that are not just complexity, not just unpredictability, but actually well-recognizable cognitive competencies. That's my simple argument about where these patterns come from and some optional implications.
What I have after that are a couple of summaries of the talk. We'll point you to a long talk that I gave on this. The summary of that talk is that these patterns of form and behavior are ubiquitous. These patterns serve as cognitive targets or goals for all kinds of agents. Physics, genetics, and the notion of emergence, which just means surprise, are insufficient to take advantage of all this.
Especially the novel forms that we and others have made, the xenobots, anthropots, cannot be well dealt with by the kinds of things that biologists are used to, which is history of selection. There are all sorts of speculations and implications, which I have said at one point or another.
I think that all physical objects, including machines, cells, embryos, cyborgs, swarms, robots, AIs, human bodies, are basically interfaces. They're pointers into that space of patterns through which these non-physical patterns ingress into the physical world. I think evolution exploits the fact that you get more than you put in. The whole point here is you make an interface and spend some amount of effort making that interface, but the patterns that ingress through it provide massive functionality beyond what you've done.
I think that physics is what we call the things that are constrained by these patterns. When we say the fermions do this or that because of some mathematical property of some kind of structure, that's a constraint. Biology is what we call the things that exploit these patterns. They're enabled by them. They do new things because the patterns are coming through.
I don't think this magic is quantum, although maybe quantum biology puts new bells and whistles on it. I think the classical world was informed by the truths of mathematics, which are determining what's going to happen.
I think that the mind-brain problem really is the same as the math-physics problem. In exactly the way that physical objects are haunted by these weird patterns that don't come from the physical space, I think brains and bodies in general are front ends, thin-client interfaces for the real show, which is the patterns from that space. I think we are the patterns.
[15:34] In other words, I don't think we are physical bodies that are occasionally subjected to various forms coming through. We are the forms. And our minds, maybe that's what consciousness is, the view from the Platonic space outwards. We are the patterns looking out into the world through these various interfaces. We can talk about what this means for reasons and causes and free will.
What I think is important about all of this is that it leads to a practical research program. So my goal is not to only do philosophy. This has to impact the empirical sciences. And so this is our research program.
We're building new interfaces to try to understand what forms are coming through. We use these interfaces as vehicles to explore the space. We want to understand via rigorous mapping the properties of the pointers we build and the patterns we get. So when I make a Zenobot or I make an Anthrobot, and the Anthrobots have four types of behavior and the Zenobots have this many new gene expressions and they do kinematic replication, we need to be able to say why. Is it that we're pulling down these specific behavioral propensities once we've made a certain interface?
We're doing work now on the compute side to quantify this free lunch aspect. When you've made an interface and you're getting ingressions through it, it's pretty clear to us that you're getting more than you paid for in the physical world. How much more? We're actually trying to quantify that. Are we getting free compute, which I suspect we are? We're trying to understand the metric of that space. Is it dense? Is it sparse? Why is it under positive pressure? Why are these ingressions so eager to come through the interfaces?
These are much harder questions to address. I don't think these patterns are purely passive. I don't think they're eternal and unchanging. I think there is some kind of, for lack of a better word, chemistry of a dynamic that they do on their own in that space, in parallel with whatever they're doing through the physical interfaces. I think there's actually action on both spaces.
