0:00 Uh, there was something that I wanted to talk about if if um everyone's okay with that. And thanks very much for for having us here. Nice to meet all of you. Let me go ahead and share um something here. I want to show you all a couple of slides. Not very long at all. Go for it. But if everyone's seeing this stuff about strong anticipation. So, basically there's this phenomenon I want to share with you all that I think is structurally analogous to Platonic space in Gresham, but something that happens in a totally mundane familiar way. So, strong anticipation is a process where anticipatory behavior emerges via the coupling of elements within a system rather than through some kind of internal model that's like doing computations and making forecasts. So, a classic example of this is a baseball
0:47 fielder catching a baseball. One way that they might try to to predict where the baseball is going to go is to have some internal model of the physics that says this is the baseball's computed trajectory. So, that's where we need to run to catch the ball. And basically the problem with this is that that's really very hard to do in real life. There's a lot of factors to consider. It's hard to understand what that internal machinery would look like. So, another much simpler, much more natural way for a baseball player to catch a baseball is to visually couple to the ball. Where if you run in a way that maintains a certain visual relationship with the ball, you just hold your visual relationship with it constant doing whatever actions are necessary to make that happen, you will end up uh at the place where the ball is going to
1:33 end up. And this is anticipatory behavior because the only stable way to maintain that relationship is to to be basically phase shifted ahead of the ball because then delayed feedback because it takes you time to see what the ball is doing and to figure out how that should update your actions, that's going to then push your phase back so you end up coupled to the ball. So, the only stable way to track the ball and end up where it's going to go is to adopt an anticipatory relationship with respect to it. So it's this much more computationally simple, perceptually natural way of trying to catch a ball, and what this produces is a process that in dynamic systems is called enslavement. There's way too much text on this cuz ChatGPT made this and it likes to go kind of crazy with it. But if you just look at this fourth point
2:19 here on enslavement, which it has misspelled, um basically what happens is is this term gets used where basically the degrees of freedom that the person has to how they're going to move their body end up being governed by the trajectory of the baseball. If you just know what the baseball is going to do, you can just see the person's movement as a function of that. So they don't like literally lose their free will, but effectively you can think of them as just being controlled by this other pattern that the So the ball controls the person, but the person of course cannot control the ball, only their relationship with it. And so my argument is that if baseballs were invisible, then fielding would look like pattern ingression. So here's the symmetry.
3:05 Platonic space, you have whatever patterns like prime numbers. These can influence the physical world in the form of cicada cycles and so forth, but the physical world cannot influence Platonic space back. So Platonic space, you know, controls the physical world, but not vice versa, and this creates this apparent dualism. But this is analogous to the trajectory of the fly ball. You have this pattern that enslaves the person, controls what the person does, but the person cannot influence the fly ball back. And so, you know, if the ball was invisible, it would all look the same. We have this evolving behavior in the physical world, and we're like, "Why is that? There must be some kind of external pattern that we can't quite perceive, but somehow is affecting our behavior." The strong anticipation version of this with the the fly ball
3:51 and the baseball uh player basically goes in the opposite direction of dualism though where it says that this stuff happened precisely because the organism and the environment are coupled parts of one system. So, the kind of dynamic system perspective that this comes from the work of people like Michael Turvey and Esther Thelen explicitly rejects a dualism between organism and environment. Rather than seeing these as separate systems, we can see them as coupled elements of a single larger system and that's how you can get these kinds of natural dynamics. We get this anticipatory behavior. And so, basically, that's exactly this argument where platonic spaces influence the physical world, but the physical world can't influence them by back. It's structurally identical to a baseball player tracking a fly ball. The ball
4:38 enslaves the player's trajectory. But in the baseball case, there's no dualism. The player's anticipation isn't some kind of internal model predicting an external world. Rather, it's an emergent property of good coupling. It's precisely because they're all in the same system that this is able to happen. And so, the same logic, because this appears to be structurally similar, may apply to platonic space. Pattern ingression might be in fact an example of dynamic enslavement occurring between coupled elements of a single larger system. I've been blogging about this on my website interesting essays where I've been writing a whole bunch of things about strong anticipation lately. So, that's just been something on my mind because I think it's been super interesting to observe a something in just a normal mundane thing that seems
5:24 to have the same dynamics as pattern ingression. So, I wanted to share all of that with you and get your thoughts. That's a good question. Well, >> [clears throat] >> first just a quick comment. The the first the first point of of that list, that's so so some people believe that that isn't my model. So, just just to say that I do I do think it's a bidirectional interface. But my question is this, when you say, um, you couldn't see the baseball, you mean we as third-person observers couldn't see it, or you mean the the guy trying to catch it can't see it? Cuz if Yeah, if we were scientists studying the system and we had no way to directly perceive a baseball, but we can just see if this guy keeps moving in this way as if he's trying to catch a baseball, but we don't know really what baseballs are, where they come from, we might say there's some kind of baseball realm or there's
6:10 some kind of pattern that the guy's body is coupled to, even though we don't really know how that happens. Okay. I I mean, fair enough, but but he needs I mean, the ball the the ball has to actually be physically maybe, you know, maybe he has a different visual system or something, but but physically the ball has to be there for him to see it, even if we don't even if we don't see it as third-person observers. Yes, perceptual coupling is absolutely key to how this process works, and so if this analogy is going to hold, there would have to be this whole big empirical question about how exactly do we perceptually couple to these, uh, platonic patterns. Mhm. And regarding the question of the bidirectional influence, there is a kind of bidirectional influence in the strong anticipation baseball catching, where
6:56 you can't control the trajectory of the ball, but you can control your relationship with the ball. So, in that sense, you can exert a a direct effect on what you're seeing about the ball, which is in fact key to how the catch the anticipatory behavior occurs by maintaining a certain relationship. Uh, so in that sense, there's a very clear bidirectional effect, which is actually crucial to producing the whole effect. I'll say I agree with Michael on the bidirectional issue. I mean, we've spoken on that. I'm not 100% sure as to why there couldn't or wouldn't be, um, an option for influence
7:41 the other direction. Um, I think there's a lot of implications if you suggest that there is not uh if we go that road, but there's a lot of important stuff here, especially about like the big issues of whether or not we're really talking about dualism is the best approach generally or idealism or what? I think there's a lot of I guess maybe difference of opinion probably or lack of clarity amongst the many people involved, so I'd love to hear what people's thoughts are on these sort of big issues. Yeah, I guess I guess for me I I agree. I I like the the the functional force of your example then is is really useful for me cuz it kind of helps tease tease apart and interrogate that notion of
8:26 what is a pattern to begin with. What do we count as a as a possible pattern? If we're going to talk about all possible mathematical cues, right? That are guiding some kind of physical instantiation, which of those mathematical structures are going to be counted as platonic quasi-platonic patterns and which ones are going to be potentially not discounted, right? That's kind of a a boundary dispute that I don't personally I don't have a good intuition about. Yeah, for sure. I I mean the whole point of basically why I wanted to to share this in this conversation is cuz I don't really know where to go with this in terms of the platonic, you know, how to answer these questions. Like you have something that very much looks analogous then like, okay, I don't know what the next step is. Mhm. I guess in the sort of
9:13 obvious case of like numbers, right? As a prototypical platonic example, right? The perception would be kind of my ability to think about them or to calculate or things like that. So instead of the visual perception, it would be like a a conceptual perception, right? And then maybe you know how like different people use different sort of visual or cognitive metaphors to do calculations, right? So it's like it could be different ways to shift your relation to the ball. Here would be using different kind of computational techniques uh in order to see that. And then uh it seems like in that case the heavy work is done by this, you know, how I orient myself or how I relate myself to the numbers and to the ball. And in some sense, you know, uh people could say
9:58 that uh the way I think about numbers actually creates numbers. So, they're not preexisting. It's, you know, my perception of them or my thinking about them that that uh gives them existence. And so, the way I relate to the ball actually is like the crucial piece that makes it bidirectional rather than ingression, right? Yeah. So, I I guess that would be the analogy and stuff. Have any of you seen what Lisa Feldman Barrett put out about relational realism? And so, she's a Yeah, I saw I I watched a video about that the other day, yeah, where she's saying that it you can go ahead and and summarize about it. Something to do with the fact that all of all of these traditionally realistic claims can only really be grounded through the uh not just the ball itself, but the relationship between my hand and the
10:44 ball, right? It only becomes real through the relation. Kind of similar to what Miguel has been saying, right, about uh relations and reality preexisting each other, that type of thing. But yeah, go ahead. Yeah, yeah, yeah, no, exactly. I mean, she's a neuroscientist and, you know, there's basically two levels to the argument. One is in the context of neuroscience specifically, the meaning of internal signals is entirely relational. So, like you get one signal that means this, another signal means that, and the brain's job is to like add it all up. Rather, no individual signal means anything except in the context of the larger ensemble. And sort of by extension, there's this argument that that's how everything works. It's always relational realism, you know, everywhere all around. And so, that yeah, may well be what we're dealing with with platonic space, that there's some kind of relational coupling, maybe as a generalization of perceptual coupling.
11:31 But um yeah, the question is how to get that to cash out. But, I think it's super interesting. I'll share a link in the chat. I mean, one thing one thing to say about one particular version of this model that I like is that I don't see this as here we are as primarily physical beings and then we somehow connect to these forms once in a while. I I I think we're forms, too. So, the whole point is that that space is extremely wide in the the range of of of patterns that are inhabited. And so, you get simple low, you know, sort of simple things that may not be able to be changed like the value of E and things like that. That's not going to change. And then you have these sort of much more complex higher agency forms, which are us. And so, in the case of because as earlier was saying, in the case that, um, you know, you are
12:18 perceiving when when you're perceiving mathematical structures, that may be some sort of direct lateral interaction, right? Because, you know, two, I don't know, resonance or some some kind of lateral interaction between the forms that doesn't have to sort of go through the go through the physical interface unlike most of the perception that we do here. So, that's that's another another piece of this. Yeah. Yeah, all of this to to me all of this is is in is fundamentally an interaction between these patterns and then some of it also sort of reflects into into this world that we can we can see in third person. I guess when you think about Platonic space, Ben, what sort of scope do you give it in terms of, you know, is it numbers? Is it more than that? Is it
13:05 every single independent conceptual object like the minimal form of it or the reduced form of it? Or is it a narrower set because they're already sort of even Michael with morphogenetic space is clearly a subset of like the broader possibility space just like assembly space is effectively a chemical analog. And here, if you've got Platonic space ingressing, I sort of sit with Michael that it has to be sort of enmeshed in one integrated map and that Mhm. the ontology or sort of the metaphysics I think is quite a good or at least has history is sort of a dual aspect monism where this sort of realm of ideas or those Platonic spaces kind of constituted as information. Like you
13:51 can't really say that what's the currency of it. At least in some, you know, coarse way. And I think it's how you how you compose those things together. So, what does Platonic space do in this concept? Well, it bounds the possibility and you get upward feedback and it's sort of like Iain McGilchrist's sort of right brain, left brain idea. The whole is a distinct thing and then the parts kind of try to build up to the whole and we get a thin wedge of that whole space here in our bodies, but, you know, there are other types of information with their accessible to us, like imagination where things don't have to be physically possible. Are those ideas also sitting in your form of Platonic space and are they ingressing in a minimal way in just a thought?
14:37 You know, it's how real are those things in that context? No clue, but let me show you one other thing which is a totally made-up evidence-free cosmology that I just think is kind of um suggestive. So, um I think we'll just maybe help indicate what a perspective could look like here. So, this is another lovely AI-made image and basically um what this is sort of presenting is a picture the world in which all of the sciences, uh you know, chemistry, physics, and so on are are not natural kinds, they're just ways that humans kind of break up the world. Uh and they're sort of within um the sort of these patterns of constraints that end up defining what kinds of patterns can form and what
15:23 kinds of patterns won't form, which in mathematics would be like your, you know, your axioms that basically end up defining and all the rules of logic as to, you know, what kinds of things can actually end up being true and what kinds of things can be, what kind of patterns can perpetuate and what can't, which in economics, which is my background, is analogous to scarcity, which is the fundamental concept in economics that, you know, some things are possible but some things aren't. You have trade-offs. If you do this, you can't get that. So, you have this like for somehow this pattern of constraints that ends up defining like the dynamical trajectories of all the the things that we could possibly observe. And then outside of that would be a larger space of of just truly everything. So, contradiction as the opposite of logical consistency, abundance as the opposite
16:10 of scarcity in economics, where there are no limits, there are no such rules, and so you have everything all at once like as in the principle of explosion without logical consistency. Everything is true and false simultaneously. And so, this is all totally made up. This is not anything I like believe is true and certainly would have no empirical evidence for, but it's just sort of this perspective I've been playing around with a little bit. So, if I were to try to offer some kind of, you know, realism dualism idealism whatever kind of take, this is my kind of take. It's something about webs of constraints that end up defining what patterns can evolve and what can't. That's where I am with that. Is it I mean, that sort of form of argument is very classically theologian. So, it goes back thousands of years and in the metaphysics of
16:56 pretty much every single persistent religion, that exact structure with different categorical grounding is used to describe that sort of infinite ground or that unbounded ground restricting itself down to categorical things that we understand and the category they they do this in different variations with sort of different levels of sophistication. So, Hinduism has sort of 26 or seven different subcategories, and they basically say each category has more restrictions on state within the category. So, there are sort of cardinality less objects or choices, and that applies across every consistent, you know, system. These constraint-based dynamics uh
17:43 you know, tool that a tool that we use to make sense of objects, I think, throughout history is like a thinking mechanic because the nature of observers or you know, the people sampling these spaces is that they are bounded and finite. So, economics naturally sits at the edge of that structure because there's a scarce amount of computational power at the bare minimum. It's like a model Even if you're just saying you're doing non-computational stuff, you're reporting on it computationally. So, if you've got computation, you've got boundedness, then you instantly have scarcity when faced with sort of an internet ground an infinite groundswell of every possible thing you know, so you have to narrow it to make sense of the world. And so, these sorts of ontologies are you can do them in lots of different
18:29 ways, but they're very, very common um throughout history. Um are you referencing um Samkhya philosophy when you mentioned 26? Uh I I'm I'm not a Hinduism expert, but I think it's uh the Vedanta. That's probably probably what you're ref cuz it means like enumeration, I think, and they do have like 26. But, what's interesting is Samkhya is a notoriously dualistic in that particular as opposed to say like Advaita Vedanta, which is very Yeah, so I'm not a I'm not a great expert on Hinduism, so you have to apologize for me getting getting getting getting getting getting getting getting
19:14 getting getting getting >> Hey, Sam, I muted you. So, there was a problem with you. But, that was that wasn't just me, right? No, yeah. Sorry, Sam, but it the audio got very wonky for a minute there as you were talking. Yeah, it still is. I think you should mute yourself or something. Yeah. Now we're done. Sam, you might need to just like leave and come back or something. Every time you seem to unmute, there's this repeated noise that blocks whatever else you're saying. That Zoom is going to be the the new printer where we have this amazing AI technology and it still never works,
20:00 right? Glad that wasn't just me hearing that. >> [laughter] >> Got to be careful talking about non-dualism, you know. >> [laughter] >> I'm trying to take this to be more experimental in that sense. You said that there is no communication between the platonic space to the the other way, but I'm maybe there is a way to do some communication. If there is a communication like that, what will how can we test it? Because again, if I interpreted correctly the neuroscience, uh there are people that did a
20:45 split-brain surgery and they're reporting on two different personalities. One in the left hemisphere and the right and the right hemisphere. And each part of the brain receive different sensory input and also shared input. If the split-brain have no there is a the corpus callosum is completely severed so they don't have shared input so they have completely split. And at that point they create or forming different personalities but in normal people we we do have connect connection. So in a way we do have two personalities
21:31 but have a shared connection. Yeah, I mean that's people argue about that is there there are some people that think that the second personality is formed at the time you cut, right? That it wasn't there before but I don't think that's the right Elliot like I don't think that's the majority view. I No, I was going to say yeah, the majority view is is the other option, right? That it's yeah, a co-mingling that's already existed, yeah. Yeah. So we we cannot claim that it's a shared platonic space in that sense. Um what I'm inclined to to say about that in terms of of shared personalities are any of you all familiar with the the A not B experiment experiments done by Esther Thelen and her group back in the
22:16 1990s and early 2000s? So what she was able to do is basically she wasn't the one who started this but sort of came to I think the best understanding of this is there are experiments that show these kind of split brain results where you have these multiple competing personalities but rather than being in some brain damaged person they actually happen in normal healthy infants. So you can you take a normal healthy infant this is originally Piaget's experiments and you you have them play with a toy and then you hide it in one of two locations right in front of them two opaque boxes and you show them what you're doing there's no tricks. You show them I'm hiding it under box A here where is it? And of course the baby reaches for box A and then once they've done that a bunch of times you then hide it under box B showing them exactly what
23:01 you're doing. They see exactly where you've hidden it. They clearly know how to reach the boxes to get what they want cuz they've just been doing it successfully. And yet, instead of reaching to box B now to get the toy, the infant continues to reach to box A. And that's it's called the A not B error. And then there was this whole flurry of experiments over decades basically showing when this would and wouldn't happen under various conditions. And what um And it does all it's all kinds of it's very sensitive to a lot of different things. And what Thalen and her group basically were able to show experimentally is that there's always these multiple competing dynamics inside of you. And uh infants basically And there's very particular reasons for this. It's not just because they're less developed. Like the dynamics are are kind of particular. But they're they're
23:48 bad at resolving those internal competing dynamics compared to a mature adult. So like the kind of potential inference to make from that is there's always split personality stuff going on inside of us, but just our systems are better at resolving those dynamics to cohere to some system-level plan. And um And it's entirely And basically, if the strong anticipation analogy to Platonic spaces correct, then like somehow these competing dynamics get resolved into the kinds of relational patterns we see, but I don't really know where that goes. So like internal family systems? Yeah, it's it's it's related to stuff like that. Um I've been trying to to
24:33 push these ideas further cuz you see the same things in the economy, I think. And um And in neuroscience as well. And so um But the the families I don't like how the dynamics are much more like ever-present. Like there's always a lot of things going on in like all systems. And so I don't know. Somehow some of the systems dynamics stuff somehow takes it a little too seriously. So, I was just thinking about how processes resolve. That's kind of where I am on that. What's it since we're talking about the brain? Um I had a couple of notes to maybe present if that's okay, Mike. Please. Yeah, please do. Great. Sure. Um so, I don't have any slides, but I just made a couple of notes this afternoon.
25:18 Kind of um that offer what I'm trying to think of as maybe kind of like an antidote to the common but pretty uh confused objection that finite brain and infinite process, namely something like uh human language grammar are incompatible right? Cuz I think that kind of hits at the center of how the themes of uh the Platonic Symposium are kind of relevant to the neurosciences. That's what I've trying to be think about the last year or so, like how the general themes that have been talked about in the Symposium could be like useful to people working within departments of like uh neuroscience and and neurosurgery. So, one of the things that I care about is like whether the formal properties of language, so you know, Ben mentioned the example of the of the baseball player, um whether or not there are other kind of formal properties that you might say that human language has, like constituent structure,
26:04 or the fact that language doesn't chunk words together in a linear sequence, but rather in a kind of a recursive hierarchical manner, whether or not that process emerges from some system akin to a deep learning architecture, like fully connectionist modern connectionist neural nets approach, or whether there are some kind of inductive biases that help constrain connections architectures from the very beginning that happen to be more tailored toward how human infants acquire their grammar, say, right? I I currently lean much stronger in the second direction uh for the reasons that I've written like a lot about. Um but I'm interested in using these formal or quasi Platonic models of linguistic knowledge, like the fact that a human grammar is driven by a compositional operator that via category theory we can formalize in a very specific way. For example, a free commutative
26:49 non-associative magma operation, uh sometimes called merge in the linguistic literature, basically recursively combining structures together, some way of forming tree structures. I'm using that formal set of instructions to see if there are neural processes that comply with and hence might be able to instantiate and derive these aspects of language. So we might not be looking for a kind of crude isomorphism like we likely won't get neurons and nouns to meet together in a totally sympathetic formal space. But I think over the past decade, the field of theoretical neurolinguistics, which is where I inhabit, has been able to move towards some candidate neural mechanisms like phase amplitude coupling, phase synchronization, other forms of well-documented neural measurements. Um So I'm just a quick note here. The algebraic recipe that I just mentioned
27:36 to formally characterize human language is chosen because each property corresponds to a like a load-bearing empirical generalization about natural language. And dropping any of these algebraic formal uh you know bullet points either leads to over-generating or under-generating possible human grammars, like possible forms of human language essentially. Um so the argument is essentially that this is like the weakest algebraic structure minimal consistent with the core observations, which is exactly the one that you want under standard like methodological norms of of minimal commitments. So that's a kind of background of my comments here, but the reason why I say all this is because I don't want to necessarily move the conversation towards linguistics, but I kind of want to use this as an interesting case study to make a different point that's maybe more relevant. So in the literature, some authors when
28:23 critiquing the cognitive neuroscience of language, which is how you know the human brain neurally enforces the properties of language, they've assumed incorrectly, and this is very common in the field, kind of one of my my chief bugbears, that any object constructed by a physical system must also be physical, right? So hence speaking about the biology of language is kind of nonsensical by definition. So the claim by these many of these figures is that language is either physical or it's platonic. Right? It can't be both. Um and of course as some of you guys uh talked about in of the last few months, this is a false dilemma. The rules of arithmetic are also multiply uh realizable, right? From the analog abacus to the digital computer to the brain. Uh same for the like, you know, functions and sets and things like that. And also
29:08 the same for abstract objects definable as mathematical at the proper level of analysis like a computer program. Right? So, think of our computer program explicitly representing the Euclidean axioms encodes only a finite number of bits. It does not and cannot encode the infinite number of bits that could be derived from the postulates. But it would be a bit obtuse to say that um such an infinity is implicit or compressed in the explicit axioms. So, while it's true that physically we can't perform indefinite computation, we are endowed physically with a competence. We are seemingly endowed neurally with a competence that does generate a set that could be produced by indefinite computation. So, the idea that This goes back to a lot of von Neumann's, you know, claims as well in the in the '50s and '60s. So, uh uh '50s. So, the idea of in linguistic
29:55 theory that humans are endowed with the ability to recursively generate an unbounded array of hierarchically structured expressions is not incompatible with the idea that neural tissue can directly execute a sympathetically targeted operator. Right? So, Turing's model of computation already showed famously why a finite physical system can encode a rule that generates an unbounded domain. And similarly, you can consider a computer capable of simulating a game of chess. A chess-playing program is abstract, but it's instantiated in silicon, radio waves, memory states, etc. So, a recursive linguistic function can be abstract in kind and biologically realized in the brain. So, the fact that a rule is mathematical doesn't mean it can't be physically implemented, right? So, one of the interesting arguments that even figures like Dawkins have
30:40 recently argued actually uh as being reasonable is the idea that natural language grammar has within it a kind of all-or-nothing component to it. So, there are some aspects of language that are we share with other species and are associative and sequential and graded. But, other components like the capacity for digital infinity or unbounded, you know, recursive infinity seem to be a kind of all-or-nothing capacity, right? Like, you can't really have half of that or a third of that. Um it's hard to it's kind of hard hard to think of how you can um uh capture that in existing gradualist accounts. And, in fact, any of these existing gradualist accounts of language evolution have had a hard time dealing with these sorts of invariant mathematical formal properties of language. They kind of get brushed under. Or, they get claimed as just
31:26 being, you know, emergent, right? It's just something that surprises us and we don't really know how to explain it from the actual first principles of our models. Um so, the issue is not that every aspect of the broad language faculty appears all-or-nothing, but that certain formal properties, as I just said, unbounded recursive formation, look less like a mere increase in associative capacity and more like an entry into a different generative regime. So, we arrive at concerns of complexity science here, right? Uh Anderson's more is different. People like David Krakauer have spoken about this quite a lot. In physics and chemistry, it's taken for granted that, you know, more can be different. Three different types of, you know, if you want to call it emergence or not. But, in the cognitive neuroscience, one of the things that kind of frustrates me is that there's
32:11 still a strong bias, and you could even call it dogma, that all explanations for human behavior must be yoked to the same reductionist level of explanation. Everything from touch to music perception to consciousness to language must be reduced to the same model, 20th century style model of neural function, right? And, of course, a lot of these assumptions are derived from 20th century models of motor function, cat visual processing, and and and all the rest of it. But, there's no reason why the same strictures will be wholly relevant for neural theories of language and higher cognition, especially in parts of the brain that are clearly outside of primary, you know, sensorimotor cortex. So, one of my kind of main gripes and the reasons why the Platonic themes are important is because a lot of contemporary neuroscientists kind of have that I think problematic assumption that all
32:58 of what we've learned from the brain in 20th century, late 20th century textbooks about cortical computation have to be uh explanatory relevant for all of our human cognitive capacities, including our perception and our understanding of linguistic and even like mathematical um geometric reasoning, right? So, people like Stanislas Dehaene in France has done some really good work where he's trying to figure out um how the human brain processes core knowledge functions like mathematics, you know, number, and morality, and music, and language, and all these sorts of symbolic or seemingly like discrete symbolic domains. Um But, that that may not be incompatible with other models of of of biology. Um So, cognitive neuroscience has kind of privileged these forms of explanation,
33:43 which which have been inherited from sensorimotor systems like coding, prediction, and things like that. Um but, it's not obvious that these explanatory templates are sufficient for the algebraic or generative capacities of a of human language. So, for these reasons I think that the thesis that human unique intellectual capacities emerge purely from an expanded capacity for information processing can't be the whole story. That's a kind of a common explanation in like human evolution, right? An expanded information capacity. Um but, so for example, in a one of Steven Pinker and Ted Sizer's recent papers, he has a discussion of relational reasoning, and they acknowledge in this paper that symbol training dramatically helps non-human primates succeed at quaternary uh tasks. But, this is actually a problem for the pure capacity story because if it were just about holding more items in working
34:29 memory, then why would an externally provided symbol like unlock performance so dramatically? Like the symbol seems to be doing like representational work. Like I have a compression or reform I think the problem in some way. I'm not I'm not sure exactly, but the the presence of the symbol does seem to change performance in an interesting way. It's not just offloading memory. So again, I think this kind of speaks to the importance of these platonic symbolic concerns of intelligence like with within human neuroscience that is. Now I'm not talking about the rest of of physics and biology. Um I'm just focusing narrowly here. Um so I just want to briefly I'll just finish by connecting this with some of uh Mike's ideas too, right? So Mike's suggestions about a temporal mathematical laws ingressing into biology and offering universal constraints on forms of life is not entirely dissimilar from some of these ideas in in linguistics about enabling constraints for natural
35:16 language. Like Professor Chomsky's idea about efficient computation having a causal role in the formation of linguistic grammaticality judgments and inferences. So the idea that there is there exists deep organizational motifs for organic forms strongly speaks to this kind of uh traditional concern of of linguistics. Right? So Mike's assumed some kind of latent space um that structures in the natural world seem to draw from and be constrained by the universe as as Ben was just saying, right? The universe draws from this latent space and not the other way around. Um so are there laws of mathematics that seem to be thoroughly invariant physical law, etc. These sorts of questions. And these sorts of questions encourage folk like me um who may be partially, you know, sympathetic to send a brutally platonic theories not in the traditional sense, but also in this modern sense in philosophy of
36:02 mathematics to assume that life has evolved through being sculpted not simply by selectional logic, but by a latent space of mathematical forms. And for me personally, I'm interested in thinking more in my work about to what extent these like formal properties of language that I just vaguely mentioned do seem to be rather unique at least in the cognitive science space. Um so uh you know, contrary to many misconceptions, I think the notion that language as a system of discrete infinity is not incompatible or inconsistent with the assumption that language has a finite biological basis, right? The consilience is affected by Turing's proof of the coherency of a finite procedure, right? I eat defining the computable numbers as those determinable by his mathematical machine, generative of infinite sets. And many neuroscientists in the present era have
36:48 however kind of limited their operational definition of language. And not just language by the way, but also other forms of cognition to the sorts of algorithms and structures that are safely neurobiologically plausible. So that's kind of a common theme, right? We have to figure out what is neurobiologically plausible. And if there are certain theories of cognition that don't seem to be neurobiologically plausible, then we query them and potentially dismiss them. But of course that has a large presupposition about what exactly is neurobiologically plausible in the same way that physicists used to debate and still do what is physically plausible. That those sorts of open debates are less common in the in the neurosciences, right? At least in my kind of view, right? Um, even if there's no regard to whether or not those neurobiologically plausible structures of from predictive sequential processing
37:34 bear any principled relation to the behavior of forms like linguistic forms under investigation, right? So language is plainly not just about next token prediction right? Um, despite what someone might might tell you. So we don't yet know enough about how the physical and computational properties of neurons uh, make any strong to make any strong preliminary conclusions that I would say about the formal properties of language being incompatible with with matter essentially. Um, so I guess what I'm trying to say is that biology may implement operators whose formal profile is best described at an abstract level like recursive composition, etc. But that doesn't mean that biology itself is incompatible with these abstract notions, right? From from mathematics. Um, biology repeatedly seems to realize as, you you people like
38:20 Sam have written about very nicely. Um, abstract spaces of possibility, morpho spaces, behavioral space, cognitive space, and then language and syntactic spaces. And then natural sciences need accounts of how like physical systems navigate those spaces and how the brain neurally enforces these algebraic properties of of intelligence. Um, so the formal properties of language are not rendered biologically suspect, I'm kind of arguing, not simply because they are abstract, right? Like a finite neural system may implement a finite geometric procedure whose consequences define an unbounded space of possible structures. The question is not whether language is physical or platonic, but it's how a biological system comes to realize, approximate, or exploit a particular region of formal possibility space. That's kind of the topic of the formal neuroscience, right? Like theoretical neuroscience. And I think
39:05 this makes language a really interesting case study for broader questions about morpho space, cognition, and biological organization. Because with language you have a really rich formal recipe for the the forms and the behavior that you're interested in. And you happen to be the object of study happens to be the human brain. So it's a really nice mix of both of these formal concerns and these biological neurochemical types of of of concerns as well. Um, of course like a neural system doesn't need to literally contain nouns and verbs and things like that as I said, right? But it may need to respect certain invariants like hierarchy, non-associativity, variable binding, and things like that. What kind of biological organization allows neural tissue to become sensitive to such abstract invariants? That's the question that my Rose model of of language um of the brain attempts to grasp and it's kind of what my contribution to the
39:52 platonic symposium was all about. Um, but yeah, that's kind of what I wanted to offer as a general set of questions and concerns. Um, I wanted to just go back to your example with the you know, the monkey being taught um a letter or symbol and how that improved the performance generally. One of the things I'm thinking about within sort of this network or sort of like really add style model or computational model of this possibility space is that certain objects admit more morphisms, more potential embeddings than other objects. So language or a letter or a symbol for the observer or for the thing that's
40:38 sampling it could admit more possible reductions, more possible compressions. So that symbol in the in this sort of formalism frees up computational space for the you know for the monkey or the yeah or to to do other things and that extra computation because he's been able to basically reduce a bunch of objects or a bunch of things that it comes across regularly to that symbol more than one or it has more variability than say a stick on the ground or a tool. That might be one one potential mechanic for or explan- explanatory option that fits within sort of this idea of computational boundedness as a sort of core drop like in sort of
41:24 that computational model of how so like a sort of selection criteria for Platonic space. So the idea is that these ideas are competitive and you know embedding or observers working with them or being you know directed or pulled by them that ingression works both ways. So observers sculpt the idea like this idea of you know co-creators or interactions or the latter is you're enforcing some you know carving around the edges of an idea to try and get it down to that minimal hole and math is very good at that and so is science cuz it's effectively gradient following or following lots of variants. As you go up the curve to more complex objects in latent space maybe it's an emotion or maybe it's you know the the way a book the the way a book feels when you read it cuz of the rhythm. That is not
42:11 reducible in the same way. So, when you're using language to kind of carve the edges of that concept, there's more variability. There are more potential ways of expressing that concept. So, that's kind of one thing I'm playing with at the moment, trying to figure out how to design experiments to do that and all for the experiment itself. I I'm not I'm not that sort of pink I'd say. It's not very I'm not very good at it, but it's something I'd love to try and explore cuz I think it's a rational mechanism that fits with a lot of the sort of core things that are true about computation in the sort of very abstract of how it works, particularly in Steven's model, but also in things like Church-Turing and also applies to things like construct constructive theory in a
42:59 sort of oblique second-hand way. Yeah, it it definitely connects to constructive theory. I I totally agree with that. Um I would recommend the work of Stan Dehaene, who's done some really cool experiments on like uh minimal description of auditory working memory, uh visual, linguistic, and uh tone, uh the different kind of like linguistic and non-linguistic modalities. And he's shown that in using intracranial recordings in in humans and in also extracranial recordings that the patterns that they may be formally distinct across music and language and what have you, right? But they still adhere to the they they comply to some of these broader Fristonian concerns about, you know, minimal um description length, etc. And the ones that do are the ones that are recognized most saliently and arise to consciousness and
43:46 also derive a lot of other aesthetic preferences, which one thing that I've been thinking about recently, which I think you might like some actually, given your background, is like um there's a debate in in linguistics, which is more of a philosophical debate, but really about how um why the Great Leap Forward happened, um and if the evolution of language was linked to some of these other higher order capacities, right? So, Chomsky had an idea that language might be causally linked to the emergence of the successive function and and and then the natural numbers, right? So, they both evolved at the same time. I'm not sure if that if I necessarily agree with that, but there's some other ideas that um uh when language emerged, it seemed have a functional use, of course, for communication and and sharing ideas with with other
44:31 conspecifics, but it also seems to be very linked for like formally linked to our notion of beauty. So, Chomsky also had this idea that language evolved for beauty in a very vague sense, and that's kind of hard to cash out in and and explain in in ways that, you know, we could um hash out here maybe, but there's some kind of intuition that the the formal characterization of language is compatible and helps facilitate the creative expression of other non-linguistic forms of of beauty and expression. Um, and there's been some pushback in the literature because some people from the stroke side and then the psychology side say that language is functionally segregated in the brain from other systems like, you know, music and and morality and domain general cognition and and the salience network and um the tension frontoparietal attention network. So,
45:17 therefore, language has to be some kind of separate system. But again, that's a there's a lot of controversy about just because a certain part of the brain might be a certain function might be in a different part of the brain, it could still be doing a similar um computation. So, the obvious example that people always ignore is motor cortex, right? So, dorsal versus ventral motor cortex are different parts of the brain, but they are still subserved by the same beta phase disynchronization um neurocomputational mechanism, right? Whether or not you're doing uh motor coordination for your your hands or your face, it's the same kind of algorithm essentially, even if it's a different part of the brain. So, a lot of strange inferences have been made about, "Oh, because this part of the brain is, you know, this function's over here and this other slightly different function's over here, they have to be subserved by wildly different modular the and etc." So, that's that's a that's a real
46:02 ongoing topic. But, yeah, I do I do like this idea and I can't really explain why I like it, but the idea that language evolves for um beauty and is is itself a form of you know, a beautiful form of object seems to cash and you know, it gels with me for reasons that I think people who have a similar instinct working in this platonic kind of space will probably recognize even if it's you know, same aesthetic preference but different kind of domain, right? Yeah, I I I mean like I tend to agree. I think these sorts of sort of psychotechnologies like like language and as you move to you know, writing and they're all tools to increase our ability to access you know, you know, if you
46:49 think this sort of platonic space in whatever format you decide to have it is real, then every one of those technologies is like an exponential increase in the amount of that space we that's accessible to us. Therefore, the amount of possible objects that we can you know, bring into this world and we search for objects that are coherent or across whatever sort of piece of that we sample and that coherence where we discover those those I think it's linked to aesthetic aesthetics and beauty and symmetry [snorts] like you know, objects develop you know, lots of things in this world involved by broken symmetries and symmetries in some respects seem to be a big component of that and you're
47:35 talking about sort of an auto recursive function a recursive function is effectively like an operation operating on itself is as close to symmetrical as you can get with different ratios you can get to like because that's how you get to the golden ratio, right? So, these are things that seem baked into the structure that we're sort of sensitive to or sensitive to the finding and you see it passively in other forms of life like, you know, peacocks, like things things trend to beauty to signal things are good. And that can be in, you know, bird song, can be in anything. But we just have much more of a range of ways and languages like we can now do that much much cleaner. And I think there's all those technologies and now we're sitting at the point where yeah, we've got the next one which is basically like
48:20 you know, might be inside all of the things we know. There are lots of connections between the things we know already that are very hard for us to map that these systems are quite good at. And my guess is that it's going to be you know, I think the function of people in this new world where you can search, you know, effectively LLMs let you do a very lossy search of platonic space, you direct it to a gradient, you direct it to a space and you say and your taste is knowing which of those sort of sinks or attractors in that loss landscape are actually reasonable to link together and the mechanisms to do it. And what's going to happen is as these systems get better, they might get better at mapping the inter inside of that space more and more. And I my guess is that humans will go to the edge of that space
49:06 where they compose new things from the inside. And that's sort of that recursiveness in language being sort of accelerated by something that's recursively generating it internally now feeding something that's at the edge of that space recursively generating new things or finding new things if you think space are permanent. And that's a I have a sort of quite, you know, romantic, you know, it's like romantic or yeah, romantic relationship with that idea because I think it's quite a meaningful idea. And we're sitting in a world where these systems seem to be, you know, there was an article today that like, was it nature, like science is scientists are going to be gone in 5 years or 10 years or something like that. And that just seems one wholly stupid and two that they're not understanding what these systems are or what the component parts
49:52 are, and you know, you have really brilliant people like Karl Friston, like you know, cuz it's not like it's not out there. These things don't do the explore part. We're very good at that, and these things are very good at the gradient part. And I think that that that sort of break is going to be how these things can work together, and why how these sort of things will kind of come together through that aesthetic relationship between that process. Like you can use it to chuck out all of the crap, which is what most of the internet does, or you can do something a bit more interesting. Um hey Elliot, uh do those the the way that you've described the language, does that does that help us, or or what what tools exist to try to look for it in unconventional data sets?
50:38 So, if we what whether whether it be a neural like data set, or the actual output that may or may not contain language, like what I mean I guess it's a subset of the SETI problem sort of, right? But but but what what tools are available to ask whether like if you have a system let's say we have two systems that are clearly communicating, we can do the mutual, you know, the the transfer entropy, whatever. Like we know we know that we know they're talking to each other. But now the question comes, okay, are they using some sort of a some sort of a some level of language? Is there a a grammar, whatever. Are there are there tools available to analyze it and and make a claim on that? Um yeah, um the the field of NLP, like natural language processing, has done a lot of work trying to figure out, for
51:24 example, if you give some [snorts] transformer architectures the ability to to to train and and learn some basic grammatical, very basic grammatical properties. Um like the way you form questions, the way that pronouns relate to the nouns, etc. Really basic relational stuff. Um it turns out that they can uh they can often approximate some of these um uh structures, but they do so much better and much cleaner if you add like a what's called a uh transformational grammar. So, you So, you add some kind of explicit grammatical rules inside the you know, you feed the transformer some explicit kind of uh prior and inductive bias, I guess, about the grammatical rules. And so, with transformational grammars, you get a lot
52:09 a lot a lot closer in the space that's being explored right now to figuring out and sussing out relevant linguistic patterns um uh that's out there. The issue that I have, though, is that mo- a lot of people try and do this for this this approach, and they look in the non-language non-human space, right? So, whales, there's lots of papers about do whales have language, right? Um do other form of of of uh species have language? And I guess the question you're asking would be a similar type of search like like which other kind of structures in nature could have a a possible language? The The The real problem here is that um the The focus is There's been too much focus, I think, on the kind of uh sequential um probabilistic properties of parsing,
52:56 which human language does do, for sure, and not enough focus on the kind of more invariant um So, Sa- Sam mentioned broken symmetries. One of the core algorithms in human language is symmetry breaking, where you form two objects together into a into a set, and then one of them kind of becomes the the the head or the label of the phrase. So, every time you put two words together, one of them seems to lead and and kind of drive semantic inference. There's never kind of Ex- Outside of like compound noun phrases like swordfish, I guess. Swordfish is a rare example, but most phrases in human language, when you put things together, there's like uh uh the the tree either leans left or leans right, right? The kind of branching left or right. There's some kind of uh forced symmetry breaking. So, that's kind of the core algebraic component that I would look for, I guess, in other systems. Like, if you say, okay, do
53:42 these things have language? Do they have a similar type of symmetry breaking algorithm that would be predicted based on the algorithm that all human beings have. So like the fact that you know, there's some examples are the fact that different languages have different surface orders like SVO, SOV, OSV, etc. You know, subject verb object. But the underlying kind of semantic instructions in conceptual space are invariant. So when I talk about a whiskey glass or a big brown bottle of whiskey, the the linear order of those words is different from the way a Japanese speaking person would say those words, but the underlying conceptual instructions are the same. And the way that the symmetry is broken is also identical. So the underlying
54:27 kind of semantic configuration, if you like, in the is identical. But the surface form is different. So there's been too much focus on the patterns in the surface form in human language, which is why you'll if you do that, you end up concluding that whales have language, too. And you end up concluding that dolphins have language because they also adhere statistically to some of the similar surface patterns like Zipf's law, for example, and other sorts of, you know, foundational laws, right, in in linguistics and cog science. And you say well, because they have the same kind of statistical compressions or the same they adhere to the same statistical constraints on sequential chunking rules, then therefore whale communication systems are just a different form of language. The the the the risky move there is that you kind of conflate the expressive
55:14 medium with the underlying kind of state. So I assume that whale language may be safe on the surface form complex, and it may have some of the same statistical regularities that human language does, but I would assume, and we don't know for sure because we can't get we obviously can't, you know, test this for sure, but we assume that, at least I assume, that a whale's conceptual apparatus is not being regulated in the same complex ways that humans concept of apparatus is being regulated by human linguistic instruction, right? So that when I hear a sentence, I'm not just parsing this the the linear order of words, I'm I'm having a very specific revision to my world model based on where I'm navigating my world model, I should say, based on the kind of instructions that I parse together.
56:00 So, it's hard to it's it's it's often easy to conclude that non-human species do have a form of language because oh, it look looks like they you know, they the the expressive modalities adhere to the same kind of statistical biases you know, that we do. Um same there's been some work on pigeon communication systems and how how our pigeon communication also adheres to some of these patterns too. But um like I said, it it's And this is one of the problems that large language models have too, right? Because you know, I've I've published some papers with with Gary Marcus and some other people um showing that uh language large language models will often uh generate a particular structure uh because they think it's it's the most it's the most common or likely uh kind of construction to a particular linguistic question. Though it may not
56:46 adhere to grammatical rules. So there's a lot of work showing that large language models don't um uh they can't parse they can parse I'm I'm sorry. They can parse impossible uh languages that a human for a human being in ways that are pretty much just as as good for them. So they would learn a impossible grammar just as much as a human uh an impossible grammar, right? So whereas human beings would never you know, adhere to these kinds of impossible constraints. So the so the real searchlight I think should not necessarily be on the surface distributional forms, but on this very simple underlying algorithmic set of of instructions that you that you then you know, lead into this more expressive kind of of landscape. I don't know if that helps with the question, but it's it's generally where I kind of would
57:33 would would land, yeah. Can I ask a question? Just sort of do with the sort of animals, is it is it like a composability point like human language has composability? Animals calls or however they speak, they're not composable. Does that have anything to do with it? It's outside of anything I know about, so it's just Yeah, so it it's this this is where I um it's it's very common in the philosophy literature for people to talk about um combining [snorts] concepts, right? Humans combine concepts. Um when you In fact, let me just pull up an example that I was uh working on. Um uh today. >> I mean more simply like the composability of like the symbol of like the single letter. I don't mean Yeah, I mean down to like the letter level like
58:20 a call is not the same chunk ability as like that we have more ability to make more distinct things and therefore we get to this thing. That That's kind of what I'm going getting at. Yeah, I I So I So monkeys um you know, they can combo can do minimal morphological composition. They can, you know, um say uh a call like crack or a call like hawk for, you know, an airborne or a landborne uh predator, and then they can also emphasize it like ooh. So they say crack ooh or hawk ooh, and they'll emphasize it based on pragmatic considerations like whether or not the predator is close by or far away, right? So um but that seems to be the full expressive range, the combinatorial expressive range, at least externally. Internally, um it is possible that they
59:05 are combining in conceptual space a much more rich array of of features, but they're just not externalizing that. Whereas humans, we externalize fairly complex expressions, and then we map it to an even more complex underlying space underlying space. There's been some work by um Tecumseh Fitch uh in Vienna uh in the last decade
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