Complexity & Computation (Session 6)

between what computation is, what language is, and what human mind is, basically human mind as being the center of any kind of, as I said, any kind of basically approach, manipulation, of our environment and ourselves, the boundaries between language, computation, and mind completely blurs. Basically, it's not even useful to distinguish them. So it's basically, other than what we get from this in terms of basically massive amount

of tools in how to look suspiciously at any person who talks about complexity, politics, about sociology, philosophy, and smuggle these jargons of complexity into basically the system. We can criticize them. Other than this, the most important one is that it basically puts It basically puts us in a kind of, you know, the right trajectory that we can basically come back to the main problems of philosophy, and especially philosophy of mind and philosophy of intelligence. But without looking at intelligence in that kind of parochial way, we look at intelligence in a completely new way,

that basically it has hierarchical leveling. It has different levels of complexity. It is computational. It's basically, it has, again, different, it works with different models of computation. And basically, this is where basically the central tenets of German idealism lies. German idealism is where, as a kind of a critical philosophy, the first modern critical philosophy, is where philosophy of mind, philosophy of action, and epistemology, philosophy of knowledge, intersected. So basically in this course of

this studying from complexity to computation to language as something that both is complex in the hierarchical sense and also is computational, we see that all of these basically philosophy of action, philosophy of mind, and philosophy of knowledge intersect. So basically, this is, as I said, this is the whole point, other than all of these useful tools and useful purposes, brings us to that very important moment in history of philosophy, whereby philosophy basically was endowed with sufficient critical tools, not to only ask

questions about what to do but also what to think but also why is that we know these kinds of things, how we can manipulate them further. Yeah, I guess my related question is in what sense is it possible to talk about complexity complexity without computation? So I get a sense some of the things that we talk about with complexity are older problems, like a three-body problem, or that basic Newtonian physics can sort of capture some of the issues

and that they've been around for a while. But that it doesn't really make sense to talk about complexity without... or like before sort of mathematical computation, that we didn't really know what it meant, I guess. Is that? Well, I think we know what it meant. But obviously, we did not have sufficient mathematical structures to tackle with it in an appropriate way. But the thing is that this is also something that so many people who are dynamicists, and there are still many physicists who are inclined,

especially of the French school, that are inclined with dynamic approach coming from Henri Poincaré, that they see computation as a threat, basically. Not basically computation in general, the kind of a non-algorithmic, non-sequential computation, but specifically Turing Church computation, because of obvious its connection with digitalism, so on and so forth. For them, this kind of computation has actually put mathematics and physics in the wrong path. So they, basically, they approach to complexity

is still in the kind of a dynamic sense, in the sense of nonlinear dynamic systems, that can, in fact, you can't computationally approach them. But these are kind of subtle issues. I mean, it depends basically what is meant in these arguments about computation, what they mean by computation, and what they basically, what they mean by dynamic complex systems. So there are these kinds of things. But yes, that is true. That's, I mean, when you look at it, the history of physics and how it kind of

influenced history of mathematics, you see that there is this kind of like a very rudimentary account before the introduction of formal systems. you know, modern formal mathematical systems. And in fact, as I will talk a little bit about this today, and I will unfold it throughout the coming sessions, there is this massive enmity, not only in this kind of traditional or classicist physical circles, but also in philosophy, especially in continental philosophy and even somehow in some analytic circles, against modern, formal mathematical approach, especially

of the kind that Hilbert, you know, championed, you know, and kind of the, respectively, Church and Turing, you know, basically reappropriation of that Hilbertian school, which I think is It's an absolutely superbly powerful, excellent, massively exciting, actually, this kind of really stark formalism that he presented. It completely outshines anything that came before it. But nevertheless, yes, it has weak points.

But this whole idea that people have this kind of enmity against formalism and formal systems, especially of the Hilbertian type, it's just kind of dumb. People really don't know what they are talking about when it comes to this stuff. There is this book. She's actually one of, I have read some of her stuff. I read her blog routinely. She's one of the most brilliant people who are working on formal systems and formalism,

especially in particularity with kind of approach to transition from medieval logic to modern and 21st century logic. Her name is Katarina Dottel-Novais. And she has a book on basically formal systems, and especially the kind of axiomatic Hilbertian formalism. She talks about these very extensively,

how basically formal languages are cognitive technologies, or cognitive technologies that you can talk about human civilization and basically this exponential growth of cognitive capacities without the emergence of this kind of system. It's a really excellent thing that she goes and talks about Stanisla Duhan and Shuan and neuroscience, and how basically formal systems, specifically of this computational

kind, Turing Church kind, how basically they become prosthesis, extensional prosthesis of the mind, and how basically they facilitate cognitive capacities. But one other thing is that human cognition is horrendously biased. By cognition I do not mean Kantian sense of cognition as simply concept use and concept manipulation.

But this idea that whatever we do think about has biases of intuition, usually. There are famous problems, for example, this woman is very liberal. She's working at a bank. She's basically a lesbian. And now ask basically the audience, is she, for example,

a Democrat or a Republican? Well, everyone comes up with this answer that, well, she's a Democrat because of these kinds of characterizations. But the thing is that these kinds of forms of cognition, these kinds of judgments are completely biased. They're basically a kind of statistical fallacies and an intuitional fallacies. One of the things that basically these formal systems allowed in the first place is that they completely take out this intervention of human intuition in the process of judgment. Because of that, they really expand this basically what Kant calls the power of judgment to the

point that, for example, Aristotelian Syllologism, you have these kinds of things. For example, all X are, for example, Y, then Z is Y, then Z might be, for example, a species equivalent to X. This is an Aristotelian syllogism. Now, these are, again, kind of intuition, intuitional biases and cognitive biases. What formal systems allow us to do is that to completely, you know, basically circumvent these biases. So there are other than these kinds of prosthetic functionality in the complete sense of extended

mind theories of formal systems, and the formal systems are capable of mitigating human cognitive biases. Adam, she's posting there, but she has also a blog of her own. me an item here. One second.

OK, questions, answers, Aaron observations. Any of you guys? Some of you have been silent the whole course. I'm not in that category, but I was interested in this idea that some of these formal systems or computational insights are sort of retrospectively applicable to some of the problems or problem spaces that we've been grappling with historically, right? So that you have sort of insights coming out of, you know, late 19th century through 20th

century, sort of what we would now see as computational sort of models that you can then take back and apply to historical problems and get new insight, or historical systems and get new insight, which doesn't have to be like a human history, sociology type thing, but it could be other problems that are just historical problems. Yes, yes, yes, certainly. Yes, yes, definitely. And one of the great things about Katarina's work is that she actually does that. She's a historian, you know, she's a philosopher, philosopher of mathematics,

but she's a historian. She actually does this all the time and she starts, you know, she basically applies these to problems of, you know, medieval physics, you know, kind of like 18th century logics. It is absolutely, you know, it's quite, it's kind of a massively powerful retrospective tool of solving some of the kind of like conundrums, the so-called conundrums of different scientific fields other than, you know, the kind of regular philosophical, sociological problems. Yes.

I mean, the thing is that when you look at it, the enmity against formal systems and especially computational formalisms is coming from basically a residue of basically vitalist humanism of the kind that basically favors the centrality of human mind. Now the thing is that formal systems do not basically require you to basically forego

the centrality of human mind, but nevertheless they can be considered as the highest form of assault on human racial syndicity, basically the centrality that only human has the capacity to possess something called reason or judgment. Because of that, I think an argument can be made that not only they do not basically vitiate the centrality of human mind, but also show what is actually central to human mind is not human.

That's, I think, the whole core of basically the computationalist paradigm, which is, I think, exciting. We will talk about this more extensively in the third module, this kind of inhumanist, basically, core to what is exactly cognition computationally understood. I read a nice quote yesterday about this. I posted it by Guattari about what you said about the enhancement of intelligence or whatever. Sure. You can read it. Oh.

Yes. OK. Yeah, well, I mean, the thing is that, I mean, the problem of, for example, some of this of stuff about automation, algorithms, and deployment of sophisticated algorithmic machines. It comes, you know, you can obviously criticize how they are, you know, basically are configured and formed and what kind of purpose they serve.

But the very nature of them, I think, is fundamentally emancipatory. But like everything else, like human mind, they can basically serve completely misguided purposes or configured as such or put into that kind of service. So there is, and that's one of the things that, you know, obviously we can't talk about But you can, in fact, for example, any kind of capitalist system massively use these kinds of technologies, cognitive technologies. But the thing is that how you can re-channel them, how you can re-appropriate them, that's obviously not our task in our sessions to tackle with. But nevertheless, it's something that should be done.

But criticizing, for example, something like capitalist reappropriation of cognitive technologies, especially computational technologies, shouldn't be conflated with the understanding that, for example, these kinds of cognitive technologies are inherently capitalist by nature. I think they are fundamentally emancipated. If other people want to jump in on that point, they can.

I was going to loop back just a little bit. Because my understanding of I'll park are its at at and understand that he was actually one reasons you felt so strongly about intuitionism against for a formalism coming from can't or and stuff like that get use very aggressively against cantor's yes all lessons and set for ones and one of the reasons was a interpretation of Kant, where he saw an intuitionistic understanding of arithmetic as like a synthetic a priori. Yes. Yeah.

So I haven't got a, I don't know, is that getting too often too much of a tangent, or do you see that as... Yes. Yes. But just to kind of make sure that there won't be any confusion is that, for example, when I talked about intuition or bias, I didn't mean it in the sense of Kantian intuition. But yes, I meant it in the common sense understanding of what intuition is. But Kantian intuition, this idea that, as I said, what is exactly Kantian intuition? is basically the relation of cognition to senses, basically. That sensibility, namely receptivity to how objects affect us, play a role in cognition, a fundamental role in

cognition. And you can't really decouple cognition from this intuition. I think there is a grain of truth to this, that you cannot fundamentally decouple cognition from senses. But this does not mean that you cannot—this is basically the lower bound of cognition. Basically, you have in Kantian system, you have sensibility, intuition, and cognition. And the manifold of intuition basically plays a role in what Kant calls imagination, productive imagination

especially. Now this is the lower bound of cognition. But I see, for example, the kind of theoretical or any kind of formalistic system in the sense of modern formalism as not being specifically about a claim about this lower bound of cognition that fundamentally intuition plays a role in it, but being a claim about the upper bound of cognition, how you extend cognition from above rather than from below. And that's, I think, that's one of the, I think, things that people usually align.

Cognition doesn't need to be always about these fundamental aspects of it, but you can, as I said, there are parts of cognition, namely concept manipulation, for example syntactic combinatoriality, specifically in that linguistic core of cognition, that you can basically extend them using these kinds of computational resources, formalistic resources. And that's another part of the argumentation of human cognition. OK, so that's actually quite interesting, because the intuitionistic version of mathematics

of mathematics is that you shouldn't accept certain premises in your system that sort of offend your mathematical intuition or can't be grounded in some very intuitive sense. Yes, yes. What you're describing as Kantian intuition is more about the interface with physical sense systems? Yes, yes. With respect to it. Yeah, okay. That's a very interesting distinction. Yes. However, you see Brouwer, and we will talk about this, especially when we are talking about Howard Curry isomorphism, which basically is a version of Brouwer's constructivism. Brouwer actually has a very sophisticated account of Kant's intuition, and this has

been recently, you know, since I think the 90s, was picked up by French logician Jean-Yves Girard to a kind of refinement of intuitionistic logic called linear logic, which basically preserves the Kantian insight inside Brouwer's system, but also satisfies completely fundamental computational formalistic criteria that need to be in place for a good logical system to be working. So how it preserves the Kantian insight is that it's basically you get a complete constructive

system, but also you get a logical system wherein rules are not a priori given, but are generated through the course of basically your deductive operations, being a priori given in the kind of basically traditional formalistic axiomatic systems. There is no prior route. They emerge as, for example, these logical connectives are interacting with one another. How axioms interact with one another generate routes about how they can basically compose

together. And this is really, I think, really one of the, basically, and actually that's why Girard's basically linear logic has been massively re-appropriated in the last decade or so in computer, fundamental theoretical computer science. Basically has become a canonical tool. Computer scientists hardly ever now talk about, you know, the good ones. hardly ever talk about any kind of classical logic or these structural logical systems. They use basically their tool developments in order to study fundamental computational

phenomena is linear logic. Especially, for example, this is massively, you can see how useful other than studying really fundamental theoretical problems in computer science, it's extremely also useful to understand and work with it into, for example, any kind of interactive framework in computer science and programming. For example, server protocol interaction, functional programming, all of these things, you can do them much easier, much more insightful with linear logic than you could do with other form of structural, non-constructive systems.

So this is one thing, but also you can look into Martin Lowe's homotopy type theory, basically which is extremely, you know, we'll talk a little bit about this, it's an extremely useful approach to, for example, problem of type construction. You can see this, for example, in terms of programming, in the idea of the constructors. Basically constructors say turns ideas or types into objects. So basically how is that possible, how you can approach

this as a form of Kantian constructivism is that Martin Loeb was in fact a Kantian and again he basically took this idea from Corey-Hobard isomorphism and basically turned it into something really, really powerful. We will talk about all of these things, but I think this Kantian Kantian-Browery and intuitionism can be refined without having to deal with or basically preserve

some of its more sloppy, anti-formalistic sensibilities. And as it has been shown by people like Martin Loeb and Jean-Yves Girard and so many people who have worked on these constructive projects, that it can be done. And once it can be done, you can actually have the best of all possible. You can have the excellent axiomatic systems of the four molecular systems, but you can also have the more profound Kantian core of constructivism in your system, where you

don't smuggle in basically a priori any rule, any axiom, any premise, but everything emerges as the system basically is constructed. So I'm trying to link this back to the reading in some of the earlier in the seminar. And there was a reading about the biosemiotics. It was like the symbolic, these revised or something like that, evolved, symbolic species

evolved. Stefan put it in the archive, yes, yes. Yeah, yeah, there's a fellow called Terence Deacon and some other authors. Yeah, Terence Deacon, yes, yes, yes. Yeah, and he has this idea that actually biological systems are symbolic processes at very fundamental levels that you get basic symbolic processing. Not symbolic processing. I don't think that he says symbolic processing. In fact, he said sign processing. Sign basically the interpretation of sign. Symbolic is only reserved for human species, yes. Right, because you have a sense of language there. Yes. Yes. Yeah.

That's the symbolic threshold versus sign processing, which is semiotic. And that sort of biological foundation, again, is the sort of interface that you're talking about when you're talking about intuition and Kant there, that sort of connection or interface between? Yes, I mean, absolutely. You see, what is exactly sensibility in Kant? Sellars defines sensibility as having the sufficient structure, namely wiring. For example, you can think of a robot and basically the sufficient wiring or us, the sufficient neural structure. Having

the sufficient structure in place in order to be capable of two things, reliable differential responsiveness to your environment and adaptive behavior, basically. So in Sellar's interpretation of Kant, the sufficient structure causally intermediates between environmental inputs, which are the sensibility and the senses, and the behavioral outputs, namely adaptivity to the environment. So the thing is that intuition fundamentally plays a role in this causal mediation between

what we get from the environment, how the objects, the items in the environment affect us, and how we adapt to the environment, namely how we adapt to navigate these items in the environment. Now the thing is that at this level of, as I said, this whole idea of basically sensibility and this causal mediation, which is not linguistic mediation. It's purely mechanistic sense you can talk about it. At the level of this causal mediation, specifically at the level of reliable differential responsiveness to the items in the environment as such, we can talk about

basically biosemiotics. And this is something that Ruth Milliken has done splendidly. For For example, you can talk about, at this level, generally about signs. What are signs? In a Persean system, you have three levels of sign, kind of a hierarchical triadic sign. Iconicity, indexicality, and then symbolic, basically, signs. Now the thing is that Decon's and some of these people, rightfully so, talk about that symbols are not signs properly understood. Because signs are referential, whereas symbols are not

referential. In fact, and this basically kind of confirms Sellers claim, you know, theory of meaning in language, that words do not have any relation with world, namely objects in the environment, items in the environment as such, at all. But words only stand in relation to other words, not to words. are the ones that have referential capacities to the items in the world. So at the level of iconicity, which is the level of differential, reliable differential

responsiveness to the environment, you have something like this, that you can discriminate by virtue of arbitrary pattern matching between items in the world. And that's basically all organisms can do that. It's basically reliable stimuli discrimination. And if you do not have this, you basically can't survive for an organism. If you do not have at the level of interpretation of science, at the level of iconicity, namely discrimination of patterns at a very arbitrary level, you can't basically survive. So there is this arbitrary, basically, discrimination

of different stimuli, namely the regime of icon, iconic regime of signs. Then at the upper level, you have the level of indexicality. Indexicality is when, for example, you see with an organism that a certain stimulus repeats for an organism. And the organisms, because of having the sufficient structure in place, again, as I said, causal sufficient structure in place, for example, having memory, having more developed advanced, basically cognitive and nervous systems, is capable of interpreting

computationally, interpreting this, basically, a stimulus as belonging to a regime, a specific regime of causation. For example, you can see it in the sense of, you know, of all opium conditioning, you know, introducing food to a dog and the idea of the bell and, you know, all animal conditionings are working with with the interpretational regime of indexes. Indexes are signs that have causal roots. And these causal roots basically doesn't mean that there should always be a cause behind this, but nevertheless the sign is interpreted as such precisely because of this statistical

frequency of the occurrence of a specific, sorry, the statistical frequency of a specific occurrence with regard to an object in the world. So this is the index. These are all referentials. Now the symbols are different. Symbols are where this referentiality basically is replaced with combinatoriality, namely inferential relations between basically signs themselves. And these are called symbols. They do not have any references. In fact, this is one of the things that he talks about, De Conn, that it basically signals

a shift in cognitive computational memory processing systems. Because if you want to have a word for each item in the world, then it's absolutely, basically computationally not feasible for you to be able to identify things. But if you develop a system in which the signs stand in relation to one another. So if an item is a new item, you come across a new item in the world, you don't need to learn about that item in the world really. But you can only start to talk about it simply within the limited, narrow resources, your combinatorial resources of your symbols. And this has been empirically verified in

training bonobos, especially the famous case of Kansy the bonobo. That's, you know, Kansy, you know, they basically developed this keyboard composed of a limited amount of lexigrams. So Kanzi first started to associate one lexigram, and these lexigrams didn't have any similarity, any kind of pictorial similarity with the actual stuff. So first they taught him to learn the referential relation between the lexigram and, for example,

an object, a banana and a banana. A lexigram stands for vilana and an actual vilana. But once he, they introduced him, for example, with new objects, for example, an orange. It was very difficult for him to understand and talk about an orange, to basically start to work with the lexigrams and show what an orange is. But once they actually put the emphasis on how these lexigrams be combined without any reference with the actual stuff in the environment, they could introduce new, basically, objects, new fruits, new, basically, new actual objects to him,

without him needing to basically make any referential inference between the lexigram and the object. He could simply talk about these objects by combining the lexigrams, by combining the signs. Namely, the combinatorial power of the sign was sufficient to cover a wide range of basically descriptive moves in this kind of system of syntactic combinatoriality. And this is really, I think, interesting, this idea that basically the shift to the syntactic regime, the combinatoriality, basically is the moment where cognition,

the relation between cognition and items in the world, namely the referential regime, is weakened. And that's where basically the computational systems basically underlined, this weakening of the referential link between cognition and items in the world as such. OK, interesting. Thanks. Welcome. OK, let me get a coffee, and then I start this session. One second.

Thank you. Also, did you guys check the Google Classroom for last week? I put some references there for those of you who are interested. Also, I talked a little bit about what

I take to be the weak point of Erisman and Healy's idea of categories, theoretical approach to neural systems. Reza, would you be comfortable putting your lecture notes from some of the previous sessions up on the classroom board? I don't know if there's stuff in there you don't want published or not. Okay, okay, okay. No, I will, absolutely I will. And every time I say, sorry, I'm kind of like beyond my schedule. I promise to talk about this time and stuff.

It's like five, I don't know, like long time ago. So I start to fulfill my promises as they move forward. Yes, definitely. Yeah, that would be . The thing is that I have been trying to wrap up this manuscript I've been working on and it's been a little bit hectic, but especially with preparing material for the class and but I will definitely put them on. So and Sean, I saw you logged in.

And I didn't see you. You said that you will put some article about Boltzmann and Kolmogorov in the drive so we can read. That would be great if you can do that. Yes, I didn't lie. I just didn't do what I said I was going to do. Oh, no, don't worry. I do that all the time. Don't worry. It was one of the references for my homework, But yeah, I'll post it right now as the lecture goes on. Yeah. So talking a little bit about time

before we switch to the computation, because this is kind of why I really think it's important, even though it might not be perceived as important. You know, basically, very briefly, approaches to time are very different in analytic and content of philosophy and also in, basically, philosophy of physics. But there are at least two dominant, two kind of systematic dominant trends in philosophy of time. One is called the linguistic, basically, approach.

And the other one is the physical approach, completely, purely talked about in terms of metaphysics of time. Whereas the linguistic one is the one that usually talks about the metaphysics of time and in terms of basically tensed language. Temporality is an index of tensed language. And we can't really talk about temporality in any sense unless we have a good grasp of tensed language. And a very good example of this and how basically bridges from this tensed language to metaphysics of time, namely the physical conception of time and temporality,

is Célard's, especially his essay, Time and World Order. But nevertheless, one thing that hasn't been questioned by philosophers of time that much is the very idea of temporality. I mean, people take it for granted that there is such a thing as temporality, that there is in fact something called past state, present state, and future state. Or in fact, there is anything called estates in the sense of technical sense that system theory talks about it.

The first person who started to very strongly criticize what he calls the temporality bias was MacTaggart. Magdeburg wrote this long essay called Unreality of Time, where he gave a quite powerful argument to show that talk of temporality is essentially a vicious circle. Basically it has contradictions, it has logical contradictions, not metaphysical, but simply

logical contradictions. Very briefly, you can see the Magdegard's essay online. It's available. He briefly his points can be enumerated as follows. He argues that there is no time without change. He also argues that real change requires that events change with respect to the properties of pastness, presentness, and futurity. They begin as future and become present and then past.

Combined with promise one, namely that there is no time without change, this implies that the reality of time depends on the reality of the properties of pastness, presentness, and futurity. Number three, he then argues that these properties cannot be real, for they are incoherent, in so far as each event must have all three, and yet they are contradictory. So for having past, in order to describe past, you have to describe what is past, what is present, what is future. In order to talk about present, again, you need to have the past, present, future. But talking about the future, again, you need to have basically what is past, what is present,

what is future. So it's basically a self-refrencial contradiction in talk of temporality. And this is basically the kernel of Mactagart's argument. Now, replying to Magdagarth's objection, many physicists came, and it's still ongoing debate, that everyone is coming trying to say that there is, in fact, time. And now, of course, they have different conceptions of time. Some talk about, you know, simply they are trying to preserve the idea of temporality that Magdagarth viciously attacked. And some try to simply argue for the reality of time.

One of these people was Arthur Eddington, British physicist Arthur Eddington. Now before going to Arthur Eddington's objection and the way that he defines and then tying it back to Boltzmann and how Boltzmann really problematizes all of this stuff, is that But as I said, physicists still continue to argue against Magdagart that obviously there is such a thing as time. But Magdagart is a Neokantian, Neohegelian. When he says there is no such a thing as time, it doesn't mean that there is no such a thing

as time as such. He doesn't really specifically target the metaphysics of time. All he argues for, and this is something that I have noticed that so many physicists confuse when they try to object to MacTacquart's argument, is that all he argues is that from our talk of temporality, we cannot draw inference to talk about the metaphysical reality of time. Because the talk of temporality is itself self-contradictory. So we can't talk about temporality in order to draw inference to talk about the metaphysical reality of time. That would be just a wrong move. And in fact, this is not a new thing that Magda Gart championed. In fact, this has been put forward by Kant.

talks about this quite specifically in terms of ideality of time. That the idea of temporal awareness is simply an agential Sorry, suddenly I got disconnected.

So cliffhanger. So basically, this is also Kent's observation that if temporality is an agential pragmatic conception of time, we can't really draw inference from this pragmatic agential conception of time to talk about the reality of time as such, which is completely, I think, a justified move. I mean, any person who tries to make the same friends comes into some sort of contradiction. So this is one, basically, counterargument

to physicists who usually attack Magdegard's challenge. Another one is that some physicists talk about the idea that basically any observer, basically any physical observer, essentially embedded in time. And the structure of time is co-constitutive with the structure of the observer. Now the thing about, I think this is more of a more subtle argument, but I think also it also is a little bit confused, precisely because when physicists talk about observer,

it's absolutely not the human observer. It's the ideal physical observer. But what Kant and Mactagars talk about is simply human temporality. The ideal physical observer is different, fundamentally different epistemologically and metaphysically different from a human agent and also human agential sense of temporality. all Kant and Magdagart are arguing for is that from the perspective of the human agent, we cannot draw inference and talk about the reality of time. Simply we cannot overextend

the temporality, the sense of temporality of the agent, which is simply a pragmatic, you know, conception to metaphysical, basically, talk of time. We can't overextend the term agential temporality talk of time to physical, metaphysical talk about the reality of time. So this is two things. Now, back to Arthur Eddington that I mentioned.

Now, Arthur Eddington talked about, in fact, this human consciousness as a privileged private door to the reality of time. He in fact tried to, as a physicist, tried to argue that in fact human consciousness should be seen as a private door to the structure of time, that there is in fact an intrinsic correspondence between what we call human consciousness, human temporal, spatiotemporal awareness, and the physical reality of time. This is usually called private door argument.

So this is the passage from Addington. The physicist whose method of inquiry depends on sharpening up our sense organs by auxiliary apparatus of precision naturally does not look kindly on private doors, though which all forms of superstitious fancy might enter unchecked. But is he, the physicist who recounts private doors, ready to forego that knowledge of the the going of time which has reached us through the door, and content himself with the time inferred from sense impressions, which is emaciated of all dynamic quality, no doubt some will reply that they are content. To these, I would say, then show your good faith

by reversing the dynamic quality of time, which you may freely do if it has no importance in nature. And just for a change, give us a picture of the universe passing from the more random to the less random state. This is the important part. Give us a picture of the universe passing from the more random to the less random state. If you are an astronomer, tell how waves of light hurry in from the depths of space and condense onto the stars, the complex solar system unwinds itself into the evenness of a nebula. This is the enlightened outlook which you wish to substitute for the first chapter of Genesis.

If you genuinely believe that a contra-evolutionary theory is just as true and as significant as an evolutionary theory, surely it is time that a protest should be made against the entirely one-sided version currently taught. So the kernel of Eddington's argument for the reality of time is basically what he wants to build on is this idea that time has an objective direction. And this is, again, some of the people who talk about, you know, it's, again, basically

it's, again, a version of our temporal system that basically physicists, when they talk about temporality, even though they claim that they don't mean it in terms of human temporality, they nevertheless basically replicate human temporality and talk about the metaphysics, objective reality of time. So when physicists talk about temporality, explicitly it is not about human temporality, it's not about past, present, future, as a human agent talk about it, but it's about objective direction of time.

Now, so this is a more subtle argument. Physicists say that, OK, I'm not talking about human temporality. I don't overextend human temporality to talk about objective reality of time. But I simply talk about objective direction of time as different from human temporality or human temporal direction. Now, the possibility that there may, but the first person who also kind of argued against, put doubt, fundamental doubt, there is in fact such a thing as an objective direction

of time was . The possibility that there may be no objective direction of time, you know, basically was first presented in the following remarks by Boltzmann from his lectures in gas theory. It says, one can think of the world as a mechanical system of an enormously large number of constituents and of an immensely long period of time. So the dimensions of that part containing our own fixed stars are minute compared to the extension of the universe, and times that we call ions are likewise minute compared to such a period. Then in the universe, which is in thermal equilibrium throughout, and therefore dead,

there will occur here and there relatively smaller regions of the same size as our galaxy. We call them single worlds, which during the relatively short time of ions fluctuate noticeably from thermal equilibrium, and indeed the state probability in such cases will be equally likely to increase or decrease. For the universe, the two directions of time are indistinguishable, just as in space there is no up and down. However, just as at a particular place on the Earth's surface we call down the direction toward the center of the Earth, so will a living being in a particular time interval

of such a single world distinguish the direction of time toward the less probable state from the opposite direction, the former toward the past, the latter toward the future. Now, would Boltzmann deny that there is a difference between an asteroid moving from the vicinity of Earth to that of Mars and the same asteroid moving from the vicinity of Mars to that of Earth? Now I think we can be sure that he would not. he would maintain that while, of course, the two cases are different, there is no fact

of the matter as to which is which. And this is basically a metaphor of time, which is which, basically, of these directions of time. Because he taught it, he made an isomorphic, he made a comparison to basically our understanding or objective sense of time is comparable to our, basically, our sense of space. It is basically based on simply local gradients of entropy, namely conditions of local observers in the universe. Rather, Boltzmann would maintain that while, of course, the two cases are different, there

is no fact of the matter as to which is which. At best, there is a fact of the matter relative to a particular temporal perspective or choice of coordinate frame. Basically, just as how we perceive the space is based on our spatial frame of reference, our basically the so-called objective sense of time is based on our choice of temporal frame of reference, which is conditioned by a local entropic gradient in the universe, as basically the necessary condition for observation, simply, in a physical sense. A good analogy is with the issue as to whether, in a Newtonian framework, there is an objective distinction

between an asteroid at rest and an asteroid moving at a uniform non-zero velocity. Boltzmann's view compares to the relationist view There is no such a distinction. Fix a coordinate frame, and you can certainly distinguish between the two cases. But nothing distinguishes a unique correct coordinate frame. Now, when people talk about the direction of time, there is usually a jargon that is

used. It's called temporal anisotropy, basically a property of being directionally dependent, as opposed to isotropy, which implies identical properties basically in all directions. So the thing is that if the argument about the direction of time is an argument about temporal anisotropy, the argument wouldn't be sufficient for a direction, for an argument,

for building an argument for the direction of time. Why? Because not all possible anisotropies have the right character to constitute the direction of time. For example, imagine some simple cases. Suppose time is finite in one direction, infinite in the other, or more granular in one direction than the other, in the sense that, for example, gaps in discrete time get progressively smaller. In both cases, it would seem reasonable to say that time itself was anisotropic. But what relevance with factors like this have for the existence or orientation of an an objective distinction between earlier and later, or for the idea of the so-called passage of time between these temporal instantiations. Why shouldn't it maintain an open question

whether the asymmetrically bounded universe had an objective temporal direction at all, and if so, whether the bounded end was really the past or the future? In order to exercise So do caution at both steps. A defender of the objective direction of time needs to answer to questions such as these, basically. Is time anisotropic at all? And how could we tell? What could constitute good grounds for taking it to be so? And do we have such grounds, in fact, in physics? What kind of temporal anisotropy would be the right kind from the point of view of grounding temporal passage.

And what kind of grounds do we have for thinking that time is anisotropic in this sense? So this was one version, the argument from the anisotropic structure, that a physicist can use this in order to talk about the objective reality of time, sorry, objective direction of time and hence the objective reality of time that is analogous to our temporal sense of time. So this was one argument. There is also another argument from the perspective of initial conditions of the system.

We talked about the initial conditions in the previous sessions. The argument for the initial conditions, the case rests on the argument that the familiar temporal asymmetries of our experience, including the asymmetry of our own memories, turn out to depend on the fact that the universe was in a state of a very low entropy sometime in the distant past. Leading the details entirely to one side, the crucial point for present purposes is the suggestion that it is not accidental that the low entropy boundary at

the beginning of the universe lies in the past. So basically it's the idea that in the up that in the initial condition argument, the physicists start to equate the low entropy gradient with the earlier period, namely the beginning of the universe. And that would be becomes the objective condition of anchoring the past. And in that way, basically creating an objective direction of time from past to present to future according to basically the evolution of the entropy gradient from the low to high.

If past means, inter alia, something like the direction in which we remember things, then it is not an open question why the low entropy boundary condition lies in the past but not in the future. That's the good news. The bad news basically comes in three parts. First, and perhaps most obviously, there is an issue put on the table by Boltzmann, the passage that I just read. What if the required initial conditions are not found uniquely at one temporal extremity of the universe? can occur in multiple locations, in either temporal direction from our own era.

One. Two. Even if we could assume that the required conditions were unique, it is far from clear that a low entropy initial condition need to constitute an anisotropy of time at all. On the contrary, it is usually presented as a temporal asymmetry in the physical arrangement of matter within space and time. In the classical case, it is hard to see how else what could present it. Three, the point of Boltzmann's speculation, which is the origin of this, basically, proposal to tie low entropy boundary conditions with the intuitive idea of the past, is that it

It leads to a picture in which the direction of time is not fundamental. At best, it is something we have locally in appropriate proximity to non-equilibrium regions. With Boltzmann's picture in play, what reason do we have to think that the direction of time is anything more than fundamental, even if low entropy boundary conditions were unique? If Boltzmann's picture could explain the appearance in the non-unique case, why is it something more fundamental needed to do in the unique case? So basically Boltzmann's idea is exactly like Magda Gortz, but constructed not in the kind

of, you know, in the domain of the agential cognition, but basically constructed in the domain of physical necessary conditions for observation. And what was an observation of local entropic gradient? Basically the probability involved in this kind of observation. And the reason that it is isomorphic to Magdegaard's argument is that basically he put a fundamental doubt in the idea that we can simply use the low, basically the low-entropic gradient and

use it as a probability, basically anchor or cue to talk about objective direction of time, simply correlate the low entropy gradient to an earlier state of the universe and then basically construct the objective flow of time from this initial condition. Because for Boltzmann this is completely a relative criteria. Like Mactagart's, temporality is basically simply an agential pragmatic tool, whereas for Boltzmann, this correlation between low entropy, initial condition with the objective

temporality of time is simply a relative to the probabilistic local domain of observation. And because of that, we can draw inference and talk about it in terms of uniqueness or kind of fundamental objective direction of time. Just as MagnaGuard, he made that argument to show that we can draw inference from our temporal awareness to talk about objective reality of time. Now, in answer to the second point, the point, just to repeat it, the point was that even

if we could assume that the required conditions were unique, it is far from clear that the low entropy initial condition needs to constitute an isotropy of time at all. On the contrary, it is usually presented as a temporal asymmetry in the physical arrangement of matter within the space and time. And in the classical case, it is hard to see how else one could present it. So in answer to the second point, it might be pointed out that general relativity introduces other possibilities. For example, Roger Penrose proposes the low entropy boundary condition is a product of a law-like time asymmetric constraint on space-time, namely that it's a wild curvature, Hermann Weill that we talked about.

That's Weill curvature by zero, or at least finite, at initial singularities. Here, the source of the low-entropy path seems explicitly represented as a feature of space-time, and in a way which makes it unique, apparently thus offering a solution to the uniqueness problem, too. Perhaps the simplest way to see how little this helps with the main problem is to ask what difference it would make if we consider a time asymmetric version of Penrose's proposal, with a law-like low-entropy constraint at both ends of a re-collapsing universe, or the middle of a bouncing universe, or simply Boltzmann fluctuations. In that case, for Boltzmann-like reasons, we want

to say that there is no global direction of time, but only local explanations of appearances. There is no global direction of time, but only local explanation of the appearances. But even such an addition takes away nothing from the model in the region in which it coincides with the original model, apparently. There is no objective direction of time which we have to remove from the model in order to make it symmetric. So there is nothing over and above explanation of appearances in the original case either. And that's basically what I briefly talked about. Basically all it comes to this idea of objective direction of time, it becomes simply a matter

of explanations of appearances for the local physical observer. So Boltzmann gives us a picture in which the entropy gradient is a local matter in the universe as a whole, entirely absent in most areas and regions, and with no single preferred direction in those rare locations in which it is to be found. Combined with Arthur Eddington's view that the asymmetries, he challenges his opponents to consider reversing asymmetries of inference and explanation, for example, have their origin

in the entropy gradient. This means that Boltzmann has an immediate answer to basically Arthur Eddington's challenge. Of course we can't reverse the dynamic quality of time around here, for we live within the constraint of the entropy gradient in the region in which we are born. What we can tell you in principle how to find, this is from Boltzmann, what we can tell you in principle how to find a region in the picture is properly reversed. And that shows that the fixity of our own perspective does not reflect a fundamental asymmetry in nature. Analogously, Boltzmann might add to this,

the fact that men in northern Europe cannot live with their feet pointed to the polar star does not prove a spatial anisotropy. The same thing about a temporal anisotropy. If you want to live with your feet pointing that way, you simply need to move elsewhere to another local entropy gradient. Moreover, you know, Eddington associated the entropy gradient directly with basically time of consciousness. So basically, the arguments for local entropy gradient, which we said it's basically the

idea that makes the objective direction of time simply a very relative concept, hence it loses its uniqueness, its global uniqueness. Hence it becomes objective in the first place. Eddington turns this idea, this idea of local gradient, local entropy gradient, into an argument for basically time of consciousness. He says, it seems to me therefore that consciousness with its insistence on time's arrow and its rather erratic ideas of time measurement may

be guided by entropy clocks in some portion of the brain. Entropy gradient is then the direct equivalent of the time of consciousness in both its aspects. Now, the view advocated here is tantamount to an admission that consciousness, looking out through a private door, what, you know, Eddington called the private door, can learn by direct insight an underlying character of the world which physical measurements do not betray. You know, so it becomes basically Eddington's, you know, Mactegaard argued that we can't draw inference from the temporal agent show account of temporality and talk about objective

reality of time. So the lynchpin of Magdegard's argument is this idea that you can't really overextend the talk of human temporality into metaphysical talk about the reality of time. Now, because of this, if this overextending is what is basically the bugbear of, you know, Magdagar's argument, Eddington wants to show that in fact this overextension is justifiable when it comes to basically time of consciousness, to local entropy gradient. As I said, we can learn by direct insight an underlying character of the world which

physical measurements do not betray. But Boltzmann's hypothesis, the idea that there is no uniqueness to the local entropic gradient, and because of that it becomes relativist, and because of that it loses objectivity, and its global, you know, basically, its global import. So Boltzmann hypothesis, because of this, Boltzmann hypothesis also threatens the veracity of Eddington's private door argument. In broader terms, however, Eddington's challenge has not been basically taken up in full so

far. Most advocates of the no-flow view of time, that basically time has no objective direction at all, even those explicit about the possibility that time might have no intrinsic direction, have not explored yet the question as to what insight might follow from Boltzmann-Coperican shift, the idea that simply we are in a relativistic framework when it comes to talking about and talking about the physical structure of time and physical reality of time. Now there are at least three domains in which we can hope to vindicate Boltzmann-Copernican

viewpoints, this idea that the temporal observer basically is tied to a temporal, to an entropic frame of reference. And that's basically the pinnacle of Boltzmann-Copernican viewpoints, just exactly like, you know, a spatial, you know, the actual Copernican viewpoints. So as I said, there are at least three domains in which we can hope to vindicate Boltzmann-Copernican viewpoint by exhibiting the advantages of a temporal perspective it embodies.

So I will come to these points. In order for me to be able to construct this, basically, vindication of the Boltzmann argument, I need to go one step back and talk a little bit about, basically, two other... Two other approaches to time that are quite pervasive when people talk about temporality and objective reality of time. One is modal metaphysics.

Many modal properties and relations, such as chances, powers, dispositions, relations of causal and counterfactual dependencies seem to exhibit a strong past-to-future orientation. Sometimes this passes without comment, but sometimes it's presented as a philosophical puzzle, especially in the light of the apparent temporal symmetry of most of fundamental physics. A natural question is what we should say about these modal asymmetries in the context of Boltzmann's globally symmetric viewpoint. Promoficially, there are several possibilities. we might try to maintain that the modal asymmetries are primitives, not dependent on the local entropy gradient, or the perspective of creatures whose own temporal viewpoint depends on that

gradient in Boltzmann's picture. But this will have the disturbing consequence that some of Boltzmann's intelligent observers will simply be wrong about the direction of these modal arrows. And how could we tell that it wasn't us humans as basically these modal intelligences? For this reason, we might prefer to tie the modal asymmetries either directly to the local entropic gradient or indirectly to it by associating it with the temporal perspective or the observers and agents in question. But it has the consequence that, like the direction of time itself, the modal asymmetries are bound to a lot less fundamental that the pre-Copernican picture assumes in Boltzmann's

model. And this consequence may be of much more than merely a philosophical interest if these asymmetric modal notions are applied unreflectively in science. If their use does reflect a particular contingent temporal perspective, then some parts of science and physics especially may be less objective than they are usually assumed to be. So an important work basically to be done on the relation between modal concepts and the temporal contingence of our physical situation is kind of a rich topic. Another, you know, basically approach to time, you know, other than modal metaphysics is

in terms of microphysics. Most interestingly of all, there is the possibility that the pre-Copernican viewpoint might be standing in the way of progress needed in fundamental physics. That is, that there might be explanation to which this viewpoint is at least a major obstacle, if not an impenetrable barrier. Here the most candidate is the subject of realistic interpretation and extensions of quantum mechanics. Discussions of hidden variable models normally take for granted that in any reasonable model, states will be independent of future interactions to which the system in question might be subject.

The spin of an electron, for example, will not depend on what spin measurement it might be subject to in the future, for example. Obviously, no one expects the same to be true in reverse. On the contrary, we take for granted that the state of the electron may depend on what has happened to it in the past. But how is this asymmetry to be justified if the gross familiar asymmetries of inference, influence, and explanation are to be associated with the entropy gradient? And this is only merely a local matter. What I said, the idea of the Boltzmannian Copernican viewpoint. Are electrons subject to different laws

in one region of the universe and another, or aware, in Eddingtonian sense, of the prevailing entropy gradient in their region. On the contrary, in Boltzmann's picture, we want microphysics to provide the universal background, on top of which statistical asymmetries are superimposed. Sorry.

You know, all of these talk about this local relativity of basically entropy gradient. and how it kind of problematizes these different accounts, talking about the objective direction of time in terms of temporal asymmetries and isotropy, you know, Eddingtonian private

doors, so on and so forth, is that they are all bad news for understanding of complex systems, basically, because they fundamentally problematize our definition of a status space or a state of a system, physical state of a system. Because it requires, because they force us to be careful about what we mean by the state of the physical system. Careful that we don't simply take for granted a conception that cements in place the kind

of time asymmetric modal categories that I just mentioned. We find it very natural to think of the state of a system in terms of its disposition to respond to the range of circumstances it might encounter in the future. What we use estate descriptions for above all else is predicting such counterfactuals or merely possible responses. However we want to allow for the possibility, you know, in line with Baltimore and Vue, that the present estate is affected by future circumstances. This conception of the state, so the traditional concept of the state of the system, this idea

that basically we, you know, the way that basically cemented with that kind of asymmetric view progressing from the past to the future, and we take it as a kind of the objective basically way of talking about how system evolves. I think with this Boltzmannian problematization, need to go. We need to dispense this garden. After all, if different future circumstances produce different present estates, what sense can we make of the idea that the actual present estate predicts the system's behavior

in a range of possible futures. If the future were different, the actual present state wouldn't be here to predict anything. When we explore these issues, it might turn out that the apparently puzzling assumptions that hidden variables cannot depend on future interactions is merely a manifestation of asymmetry of our modal notions, just a kind of perspectival gloss in a kind of Boltzmannian sense or Copernican sense, perspectival gloss on underlying dynamical principles which are symmetric in themselves. If so, there would be no physical mileage to be gained by adopting the Copernican viewpoint in that sense. Certainly, we would understand better what belongs to the physics and what to our basically

linguistic, perspectival viewpoint. But no new physics would be on offer as a result. However, the more intriguing possibility is that there is a new class of physical models on offer here. Models which are being ignored for any genuinely good reason, but only because they seem to conflict with our ordinary asymmetric perspective. And what are these, basically, these models? These are the models that are usually called the block view of time, where basically we do not have an objective direction of time. And people want to look into these kinds of models

and the conceptual framework behind these models. I highly suggest the works of Hugh Price, But also, there's this book, I met the author, skimmed through this book. It's a fantastic book. And it talks extensively about Boltzmann and the way that his statistical idea of local entropy gradient fundamentally problematizes some of our basically phenomenological accounts that we use in, for example, quantum mechanics or in basically general philosophical phenomenology is this book, I have forgotten the title. It's called Phenomenology,

Phenomenalism, and Something About Time. It's by Adam Berg. Let me, and also Hugh Price. So try to come up with these models that no longer has this inbuilt bias of basically time asymmetry or the so-called objective direction of time, which as Boltzmann has argued is basically not objective at all. In fact, it is very comparable to what Magdegard talked about, agential temporal awareness that can draw global inferences

from simply its local temporal instantiation. And as I said, once you use these kinds of new models, the models that do not have this in-built biases about objective direction of time, asymmetric temporal asymmetry, temporal anisotropy, and so on and so forth, then a lot of these stuff that we argued about complexity in terms of causality, determinism, a state of the system, prediction of the behavior become essentially problematic, like basically antiquated almost, as being pre-Copernican in the sense up basically if there is such a thing as a Copernican revolution in philosophy of time.

Talks, arguments, discussions a little bit before we get into our computation stuff. But there are, you know, you can understand, you know, that the thing about, although this is a little bit of a slippery slope, because when it comes to metaphysics of time, you can have all sorts of wacky models of time, you know. But the thing is that I think that you can look simply into the arguments given to justify these models and see exactly what their internal contradictions are, where they fall short.

Nevertheless, once we adopt these non-directional views of time, or basically non-directional models of time. A lot of, you know, basically kind of paradoxes or puzzles in philosophy of time need to be revisited. And in fact, I think they can be solved. And some, Hugh Price actually has targeted some. For example, the idea of time traveling, the idea of retroactive causality, retroactive causation. These are, you know, highly controversial in classical physics or even modern physics when we are talking about the objective direction of time

temporal asymmetry, they become almost paradoxical because of, you know, you can think of this retroactive causality of time traveling paradox in terms of Terminator movies, you know, simply go and kill someone who is supposed to be here, but for example, the example of the grandfather of paradox, like I want to kill my grandfather and then I won't be born. These ideas are usually argued, these are the kind of paradoxes, that if in fact the time doesn't have the kind of direction, and in fact future state of the system can affect the past state of

the system locally understood, locally defined, then it gives rise to these paradoxes. Now Hill Price saw some of these paradoxes to show that either they are incoherent these paradoxes themselves, or in fact there is no basically contradiction that might arise once we apply and start to use these non-directional models of time. Can you give us some kind of intuition or just an example of such a completely different model because it's hard to imagine it?

I think this complexity of models, and especially because of Boltzmann, because Boltzmann did massive amount of work in the idea of the entropy, but also in sense of its correlation with the statistics, the statistical account coupled with basically the physical dynamics of the system. Now the thing is that once we basically take these kinds of models, as I said, we need to basically dispense with some of the accounts of causality, that a system evolves from past,

the present, the future, and basically we use this simply, objectively we have to use the past and present state of the system in order to predict its future. I think using these kinds of new models, one of the areas that you can apply these models in the statistics, in the statistics of how basically have an account of causation, evolution of the system without an account of basically temporal evolution of the system. Bayesians are famous for that.

Bayesians are capable of some... In fact, I think the Bayesian system allows for this kind of Volsmanian viewpoint, very you know, it's kind of like almost fits, suits it, that you can have, you can define a statistical model where you can identify causation in a system, what causes what, without having a temporal direction. And I will get, there is this really interesting article about this, a very short article about, a modeling, a statistical modeling that does not have a directional sense of time.

And why is it useful to model causation in a complex system? I will find it and I will put it on the classroom page. It has diagrams and kind of very stepwise shows basically how you can basically think causation in a system. So I think the first thing that comes to my mind, in a sense of what kind of, you know, basically use these models have is, as I said, is that they give us an account of causation in a system that is a statistical, is robustly a statistical in a Bolsmanian sense, but without having a temporal directionality of basically past, present, future evolution.

But simply you can apply a statistical inference to talk about causation. And because of that, you can basically massively broaden the account of how the system evolved through this interaction of different states of the system, rather than just past is influencing the present, and then inference from the present and the past inferred the future, which we saw basically. In fact, Crutchfield, the statistical complexity, also had this component, also had an inbuilt directionality of time, which is biased, not essentially negatively, but nevertheless temporally biased. Sorry, I did get pulled away from a little bit of that.

So you're talking about situations where you could sort of statistically model all the states of the system and discover some causal relation which goes against the intuitive sort of sense of time. So you could have a sort of future state influencing a past state if you put it into sort of traditional Without having a traditional direction of time. Simply, they do not have a temporal . Because you show a correlation between the, or you show a causation using a statistical technique between that set of states and this other set of states.

Yes. And this is something, strangely, even dynamicists, are you familiar with the work of Renathon? Not really, you mentioned it the other day, though. Yeah, René Thome is a fantastic, all of you should read René Thome. He's a superb, superb thinker and magnificent mathematician. We really foray into everything. He won Fields Medal with Contribution Topology and Catastrophe Theory. The thing is that Thome in fact talks about this. You know, there is this concept in dynamic systems called tendency.

Tendency is simply an abstract, basically, property of the system that is correlated with this future state. Thome talks that the dynamic systems, specifically about this notion of tendency, that tendency is a property of the system correlated to future state, whereby future state basically affects its past states. So you have this basically, again, kind of the Boltzmannian view. So he actually defines and tries to formalize this mathematically, that how basically in a system, or a tendency of the system, is not past oriented. It's

basically the future tendency affects its past and present. And so when basically when it comes to this, as I said, it's not that you do not have any sense of temporality. It's that your sense of temporality does not have a fundamental asymmetry, neither in terms of the future, neither in terms of the past, but simply in the sense of basically its local global interactions. And that, I think that's basically the Bayesian statistical framework in the Bolshevian statistical framework is very useful to basically model this, because it does not have that fundamental

global bias of time asymmetry. And that's important. When we are talking about complex systems, any kind of fundamental time asymmetry in the sense of temporality, whether it is an intuitionistic sense, you know, in the sense of MacTaggart's arguments, or it's in the sense of basically more sophisticated physical metaphysical arguments of modern physics, these I think need to go. These are biased. Or even if they don't need to go, we need to challenge them. Basically we need to show that there is something, you can make an alternative model to these,

Because that's the whole point of Boltzmann, to show that basically they are completely relativistic in a very rudimentary sense. They are bound to basically necessary conditions, entropy conditions of local observation. So that would be a task to, you know, kind of like a two-fold task. to challenge the biases of both the intuitionistic account of fundamental temporal asymmetry and the metaphysical, physical temporal asymmetry, but also providing alternative models that you can have still preserve this intuitionistic sense of temporality, but without its fundamental

uniqueness plus a model of time in which different temporalities of the system, the state of the system, can affect one another without possessing a fundamental time asymmetry, without possessing a fundamental directional conception of time. So I think this is, I think, and this is essentially again becomes a Kantian-Hegelian project. How to preserve our intuitionistic or intuitive idea of time, which is agential temporal awareness,

commensurate this with a block view of time. Simply a view of time that has no fundamental time asymmetry, that has no fundamental direction, that has no global basically anisotropy. So if I try to translate that into a simple example, So if you talk about a system that has a tendency to equilibrium, like a marble rolling around a bowl or something like that, has a tendency to equilibrium where the marble is at the bottom of the bowl, or there is other equilibria where I guess it could get thrown out of the bowl. but the arm is there is

is it is you I I have one where I could phrase it is that equal the real it might be more straightforward to show that equilibrium state is having a causal influence on on decided this deal the states of the system that might actually be a more elegant or a clearer formulation of that system even though that happens at the end of a time series. Yes, I think that's a very good example. Yes, I think and this is actually kind of a, again, Boltzmannian viewpoint that equilibrium can be talked about as a tendency but why is that we need to see this equilibrium as

being emerging directionally from past, present, to future. Well, why not, and this is what Tom really talks about, why not talk about this in terms of a fundamental tendency tied to the future state that basically affects these progressions in kind of a nonlinear way. And that would be a more elegant and more sophisticated account than, you know, the provider. Because the whole idea about this idea of a state of the system progressing from past to present, future, and then we try to explain equilibrium in the sense of this directional asymmetry from the past to the future, is that it is massively, not only itself as a

physical argument has these holes and flaws, but also massively entrenched in our intuitive idea of sense of time. And because of that, you really need to look at it very suspiciously. Anything that has any kind of physical argument that is coupled strongly with our intuitive sense of spatiotemporal perception needs to be looked at very, very suspiciously. Not essentially wrong, but you need to really challenge this. You need to see it as a bias and basically start to provide alternative models to this. But again, that's not really stating the system in those terms isn't necessarily a

fatalistic sort of view. That's... No, absolutely it is not. This is, Hugh Price actually talks about this, that it is absolutely not a fatalistic, whole idea of retrocausation. And in fact, it shows that the kind of objections that are posed by the people who are anti-deterministic, it basically doesn't fall for those things. And Hugh Price, actually, I will try to find his paper on this. He has this long essay to show different varieties of these arguments that are objected against this kind of retrocausation and this account of black

view of time, and usually some of them are equated with fatalism, some minor determinism, some with, as I said, time-traveling paradoxes, contradictions. He refused them one by one. It's a very good one. No, I don't think that this leads to fatalism of any sort. Talks. Aaron, Sean, Stefan, Tal, everyone.

So I guess one thing maybe helpful to, or I guess a problem that I'm having a little bit is that a lot of the way that at least when we first started looking at definitions of complexity. A lot of them were phrased in terms of like an accumulation of historical of like data over time. And that complexity is our ability to formalize and understand this data rather than understanding a system simply as sort of not being influenced by

others sort of local or global factors, sort of considering a system in isolation, as a simple equilibrium system or not, and rather complexity sort of allows us to incorporate time into the system, is sort of like the most basic definition of it, and this obviously comes from... Yeah, in the sense that it's... Yeah. Yeah. I guess is there a way of like reconciling those definitions, or is it... Yeah, that's why I said that. It's a, sorry for being a spoiler sport and giving this at the end of the complexity session which kind of problematizes the entire stuff that we talked about. And that is, I think, that's true. It fundamentally problematizes so many of the stuff that we talked about. And they are taken granted whether in classical physics or in all of the complexity sciences.

I don't think that, we can reconcile them, but I think that would be just a gargantuan task. That would be the task of the modern physics and also modern philosophy of science to talk about these. But at least the problem is there. Complexity in the science is not a function of time or a statement about some part of the system that we understand versus a part that we don't. It seems to be sort of this encompassing notion of configuration space. So some kind of variety amongst the formulation. So whatever we say the system is, we look at sort of the axes of variance or like the variety of states that this formulation can occupy.

And then we find some measure of it. Now, certainly there are... But the notion of complexity, whereas when we talk about complex system, the notion of time becomes essential. And this is, as you say, when we...and I made this distinction between complexity and complex system. When we are talking about complexity, as you say, it's about basically interaction of nonlinear interaction between components of the system, where we do not need essentially a concept of time. But when we are talking about physical complex system, then it becomes much more basically

tangled topic, where the nonlinear interaction, as we talked about, no longer becomes a sufficient condition of how to measure the complexity of a physical complex system. And that's why many measures of complexity basically bring in the concept of time. And that's basically where those measures are basically become, you know, need to face the challenge of basically Boltzmann. It seems to me that time is really deployed to set the axes of sort of like the evolutionary nature of systems. So we know that things are changing, and it's much easier to understand this change as a function of time,

as sort of this false sort of universal scale. Yes. But we don't have that in computation in particular. We just have steps. And I believe that we use time because when we're more concerned with sort of finite, like physics is usually concerned with sort of finite substances, and you get that constraint when you're bound to time. So it's really useful. But I don't... Yeah. Yes, no, it's absolutely true. In the straightforward computational sense, you have just run time. Run time is different from basically time.

But when we talk about physics, whether it's at quantum level or classics, essentially it is under the constraint of time. all of your formulas have one way or another basically have a definition of time in both them. So one thing that would be interesting is when these worlds come together sort of like with Heisenberg uncertainty where we know that the role of the observer is affecting exactly how much information and raw measure of information sort of like on a computability scale what the system is doing.

So it seems like we have these physical notions of position and momentum, right, which are constrained, which are physical, and yet as soon as we introduce an observer, right, then we get information, an amount of information. So like we could make reference to the variety of the configuration space and admit that we're only seeing some subset of it, and that we actually understand the dynamics of this, and we call those dynamics information in this. So there is some overlap between this world in which we have time and physical notions, and this world in which we have computation, we have stages in information. Yes, yes, that's true. Yes, it's absolutely a good point.

Yeah, basically this is why, for example, for people like Bennett and some of the other ones who basically provide so-called computational measures of complex systems, basically this idea of observation and extraction of information. Even though it's provided within the computational framework, classical computational framework, nevertheless it is again coupled with that physical conception of time, which because of that it also brings in, as Adam was pointing out, whether knowingly, intentionally or non-intentionally

bring agential, in the sense of human agent, agential conception of time, which then becomes basically problematic at two levels, not only at the level that Boltzmann points out, simply the physical, fundamental temporal asymmetry argument, but also at the level of Magda Gortz's argument. Yeah, I wanted to go back to the Bennett example of logical depth, because I think that is more what I was saying also with complexity. And also I guess this Kantian difference between sort of just natural time history.

And with Bennett, right, he gives logical depth is sort of indifferent to like the amount of time it takes to compute. Yes! Yes. Instead, it's like the amount of work or the amount of information depth that's there. Yes. The amount of work that had to go into creating this. And that's conceived in a very agential sense. And I associate more with a Kantian history of drawing together the inferential connections between a series of data rather than just understanding the physical process of computing the data. Right? I think with Bennett is a little bit more subtle. As Sean was pointing out, when it comes to computation,

time is simply a step, run time. And Bennett specifically times about time as run time. But when you look at his essay, he makes this unjustified, unwarranted move and crosses over to the physical conception of time and creates this equal class between the runtime and physical time. And basically, that's why he can then talk about physical objects in terms of basically computational time. But again, he kind of overextends computational time to physical time, physical time to computational time. So I think Bennett has basically is subtle,

but also because of this kind of way that he weasels around this basically different concepts of time in the computational sense and the kind of physical sense. And I think for that, we need to be careful about where exactly he talks about which one. Especially, you remember, one of you asked me to talk about Darwin and natural selection, and I said that I will postpone it to when I talk about computation, precisely because of this, because of classically understood,

at least in the Darwinian theory, it seems that evolution in the Darwinian sense is extremely strongly coupled with this intuitive temporal directionality. Hence, it can be problematized massively. But I think there is a way, in fact, to revitalize the Darwinian theory of evolution without bringing into equation such a biased temporal positioning, simply using computational dynamics to reframe Darwinian theory of evolution. And I think that's an exciting task.

But when it comes to Darwin, I think that, at least in the classical framework, you see that even the natural selection, not itself, but the way that evolution basically framed this idea of transition of the states, it has a framework of causality that's tied to our intuitive temporality of time. And for that, we need to find an alternative model that still can preserve the fundamental aspects of Darwinian selection, contingency and finality, but de-emphasize this rule of

directionality, temporal bias. Yeah, that's interesting and helpful. Yeah, I guess jumping off of that, I would also ask more sort of about the applicability of this notion, sort of how it would help us in conceptualizing or making further steps in the task like artificial general intelligence or creating complex models of, yeah, I guess natural selection and evolution is one, or a financial market or I don't know, and what ways would like... I think, as I said to Adam and Tal, that's basically, you know, one of the most prominent

features of how you can use them is basically to talk about causality, basically patterns, the statistical patterns, how they evolve and basically how you can identify tendencies in a system using these models, using these block view models of time that do not have the temporal bias built in them. So anything that involves with some sort of identification of tendencies in a system or or a statistical, basically, conception of causation can massively, basically, enjoy the benefits of these models.

When it comes to AGI and these kinds of stuff, I haven't really, I mean, this is something that I'm thinking, but I really haven't found any answer, you know, kind of like an even intelligible answer. But obviously it is, even speculatively, it is massively interesting, this whole idea that, for example, let's think about not AGI, but also in terms of supposed imaginary terrestrial civilizations. that if they might have a different temporal conception of time, how that intelligence might evolve, in fact,

how it might manipulate the course of evolution if you have a different, completely a different, radically different conception of time and temporality. Then is it possible for us, even in fact, to communicate with such an intelligence? These are, I think, well, speculative topics, but nevertheless, even as mind candies, they are really interesting to entertain. I mean, one of the things is that this is part of Cellar's project, in fact, to show

that the idea of temporal awareness in the Kantian sense, which is basically highly manifested in tense language, is an essential part of how we basically use the natural language, deploy the resources of natural language in terms of modal vocabularies, chain of inferences, dialogue, so on and so forth. So basically, it puts immediate constraints on our communicative, conversational, dialogical capacities, and hence cognitive capacities, in fact. For creatures who have a completely different temporal

perspective, their language can be completely different. the way that they talk about something that functionally, something that has equivalent functional status, for example, modal vocabularies, might be completely different. And because of that, their empirical vocabularies might be completely different. Their base vocabularies of a spatial science might be completely different. So these are really ramifications of this. Because temporal perspective is not just temporal perspective in the sense that you think of this temporality. It manifests in language. And the first thing that manifests in language is the modal vocabularies. And since insofar as modal vocabularies

are part of the fundamental resources of language, in order to deploy other vocabularies in your language, empirical, logical, based vocabularies, If you have a different temporal perspective, you can have different kinds, types, not degrees, types of modal vocabulary, and by extension, completely different empirical based vocabulary, to which you can basically talk about your observations of the universe or the objects in the environment.

Yeah, no, I mean, great. That's all, like, fascinating and interesting. It also seems like the, yeah, the answer is that we're still trying to, I guess, grasp. Yeah, or for something like artificial intelligence, it has to be within the framework of our conception of time, of a gentle time, right? I don't think so. I think that's at least something that I'm trying to think, that basically,

I very briefly mentioned that one of the, I think the task, cognitive tasks of us at this point should be how to reconcile our contingently positioned perspective of time, namely temporality, past, present, future, with an objective view of time that does not essentially have any temporal aspect to it, any global aspect to it. So that would be a cognitive task. Because of that, we can then imagine how to construct an intelligence, a form of cognition

or concept user or linguistic user, but also an artificial reconstruction of mind that basically has both an agential temporal perspectivality, but also allowing this perspectivality to be flexible, not be biased in a kind of global uniqueness. And so, yeah, that sapience. Yes. That is, yeah, time structure of agential thinking is not essential to sapience. It's simply a contingent factor of how we sort of came, our sapience came to develop,

or...? Yes, I mean, yes, absolutely. I mean, it's not a sense, that's exactly, I think, the gist of the argument that this time awareness, a perspective of time awareness in that specific global uniqueness of past, in the present and future is not an essential feature of sapience. It's simply something that has at least two phases that has been built in us. One through basically biological evolution, physical biological evolution bound to this idea, the idea basically of local entropy gradient and local frame of reference that basically

organisms use to differentiate stuff. Basically, it creates accumulations of basically interpretory computational, interpretory indexes that starts to equate a statistical basically accumulation of data in the sense that, for For example, something that has been repeated now has started to equate this with the cause and the cause that lies in the past. So this is one which basically what I called in terms of iconicity, index equality, semiotic interpretation and computational interpretation of statistical, basically, occurrences of events in the environment. You can see it in the course of basically evolution of the nervous system.

It has been coupled with this basically regime of interpretation. And the other one is because this regime of interpretation is then deployed within the evolution of language. And then the language takes the shape and some of the basically intuitions of this interpretation of regime. But that's not how language can essentially needs to function. And that's basically, as I said, it's just not the argument that we shouldn't equate how language has evolved with how language logic conceptually ought to function.

In fact, we can decouple one from that. And that would be part of our cognitive revolution. you know just to be a little bit shows up to get married to sets in my own arm so sorry concepts over these four concepts in human language all things in the future and so into that that so that there are all structures like the structures which are non-systematic and non-scientific around prophecy and oracles and things of that nature, right? So it seems to me that that is also an

adequate mechanism that because you need the sort of scientific sophistication to model these causal arrows systematically, right? So you need that level of scientific sophistication and computational sophistication to be able to recognize these states systematically rather than informally in a folk sense as a prerequisite before you can get at this. Absolutely, yes. And it's not only, I think, massive amounts of new models and studies in sciences, but

also in logics, especially in computational semantics. And I think that's part of fundamental. I don't think that you can, in fact, construct an AI without a massive work yet to be done in computational semantics. how can you develop an artificial language that has the properties, basically the functional capacities of natural language, but also can be debiased from these basic intuitions that are embedded within the natural language because of its evolutionary heritage, namely becoming

more and more in tune with formalistic regime that can basically forego with this intervention of the semantic intervention of this intuitionistic biases in our language. So that would be a task to develop this language that can at least have two sides, two kind of like systematic sides. It functions like a natural language. Namely, it enables agents to communicate linguistic interaction. Let's not even call it communication. Communication, we only reserve it for animal group calls, namely regime of science, referential science.

Simply, it has an interactive dialogical structure. Basically it enables a multi-agent system to function, artificial system to function, to communicate. So basically, it has all the cognitive enhancements, the natural language allows intelligence to possess this on one side. And on the other side, it has basically formalistic flexibility. Namely, it can progressively mitigate, basically, its intralinguistic biases.

And what are these biases? These biases are not essentially the biases of the language, but simply are the biases that's because our language is evolutionary coupled with basically our biological heritage. So that would be two things, you know, the coupling of language from its biological heritage, which is essentially the coupling of mind from its evolutionary heritage, one, and the The other one is the amplification of its logical conceptual capacities. And you can't have one without the other.

That's why I think this whole idea of computation and things are massively important when we talk even at the most fundamental level of just reconstructing language, what a language is. . observations, talks, relation. I know that some of you guys are thinking

about extraterrestrial intelligence and AI and these kinds of stuff. So it would be interesting to give me some comments and talk about some of this stuff in relation to the stuff that we talked about. So I think personally one of the things, and this might be deriving from the discussion of, sorry, earlier at the beginning of the meeting, I'm starting to develop a sort of confusion about maybe the sign relation offered by modeling systems.

I'm trying to think of the best way to put this so I mean in the sense that we're discussing symbolic signification as being in fact producing a sort of structure of reference to other symbols rather than directly to objects in the world how do we start to understand what maybe from that lens how do we start to understand what it means to produce, or I should say maybe to designate and model a system when it comes to the thing that it's supposed to refer to. Does that make any sense? Yes.

Basically, you want to argue that, okay, if the shift from the regime of sign to the regime of symbols discards the referentiality criterion, then how is that when we use the symbols, which symbols absolutely do not have significative, in fact, even significative, significative regime is only part of the sign, not even symbols. So if that's even the case, then how can we talk that, for example, our syntactical language or formal symbolic regime, in fact, has anything to say about an actual system?

Yeah. So the thing is that you see the function of language, the function of basically syntactic formal languages, which also have their semantic levels and pragmatic level as well, is that they do not have referential representational import. Because referential representational import is simply an arbitrary, basically, equivalence between your sign or symbol

and the object in the environment. It's a parochial, basically, relation. It's completely arbitrary. Now when we talk about language at any level, the reference shifts from a causal representation to conceptual representation. Now conceptual representation at the atomic level, at the most atomic level, has in fact the references. Basically, it has a referential capacity. And this is something, for example, we say that this rose is red.

Obviously, the deployment of the word red, we only deploy it when there is a differential, the criteria of reliable differential responsiveness to a red object. Right? But this is only at the atomic level. At the level of the conceptual, which is basically the core of the language, namely the level of inference, inferential relations between the words, namely the concept. Concepts are not discrete entities. Concepts only stand in inferential relations with one another. At this level, we can't basically, basically the atomic fact about the red object is simply an initial point. The point of the

concept, namely the inferential relation, is that for us to be able to make a judgment, a perceptual judgment, but also other forms of judgment about this fact, and to the course Because of this judgment, which is only available to the power of inferential relations, namely inferential networks within the symbolic regime, to basically this power, it's possible for us in fact to revise the atomic statement, which was built on this parochial referential correlation. So it's not that we completely discard it. We just put the emphasis, the main emphasis, on the inferential network between our words,

and that basically becomes the game of assertions or conceptual propositions, while it preserves the atomic statement and the referentials as being a referential, very parochial representational equation. And because of this shift to the conceptual regime, not only we can talk, in fact, about the red object, but also we can revise our judgment about the red object. That might not be a rose, that might not be a red, and that's through the course of interacting through the linguistic resources using the infertile rules of the language. OK, thanks. That helps a lot. OK, guys, if you don't have questions, I think we have to...

Sorry, I actually wanted to start the computation session. Again, it seems that we are way, way behind. I will try to speed it up next week, starting with talking about formalism, formal languages, different concepts of formalisms, how computation is correlated with a specific concept of formalisms in terms of computability theory, then talk about computability theory, formally defined in terms of Church Lambda calculus and Turing machines. And then from that point, we move to listing some of the weaknesses of computability theory

and respectively, church-steering model of computation. And then through the course of later sessions, we provide a different paradigm of computation and that would be computation as interaction. And we will talk about this. And that would be basically the scaffolding for third module, where we talk about linguistic interaction and linguistic picture of mind in terms of computation as interactive regimes. Yes, Sean, do you want to make any comments? I'm super excited for how things are going and I don't mind sort of that we've been running

a little bit longer and maybe taking a little bit more time even though I recognize that other participants might have a class or work or a dinner party. Yeah, I would like, I think I've fallen behind in some of the readings and yeah, need to catch up before I could contribute in sort of a more meaningful way. But yeah. Sure, sure. I mean it gets a little bit, I just, you know, try to, you know, I noticed that I was talking to Tony that the audience, it's really actually exciting that everyone is coming from different backgrounds. So not everyone has the same level of familiarity with every topic.

Some might have more familiarity with one aspect than the other. So it's important, I think, to kind of move from very slow kind of introductory and then build it. And then, unfortunately, the third module, which is the most difficult module, is where basically we all talk about basically the stuff about linear logic and interactive computation and game computational understandings of games and stuff like that, which I think is the most exciting part of it, at least for me, because the whole idea of intelligence and mind and language, these are, I think, the most important things. And we can't really talk about anything unless we grasp of these concepts.

Thank you, Reza, for doing this. You're welcome. Thank you for listening to all of my three-hour-long classes. Yes, thank you, Reza, and thank you, everyone. Thank you, everyone. Thank you. Thanks, Reza. That was great. Thank you very much. So you guys, please, those of you who sent me assignments, give me two dates, considering that I'm living on the East Coast. Give me two dates. I will come back, coordinate with you, so we can have like a 30 minutes discussion. I will give you feedback about your paper.

And those of you who haven't sent me an assignment, feel free to send it to me this week or the next week. I think that would be fine so we can move forward. Fantastic. Great. Thank you. Bye bye. Take care, everyone. Have a great day. Bye bye. Thank you.

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