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other like pretty fascinating examples. I mean, I would say like Demis Hassabi, founder of DeepMind. He probably is also one of those like extreme polymaths. You know, anything he puts his mind on, he becomes world class. I mean, like, you know, competitions of board games. I think he became a grandmaster by the age of like 13 or something like that in chess. And then in any game he's played, like he's just outstanding. Essentially he clearly has like a super incredible ability to, you know, generalized. He even is a world class player in this game called diplomacy, which yeah, it actually requires kind of perspective taking capacity and aligning incentives and winning by either war or peace. And yeah, I'm honestly kind of, you know, scared of his power. I mean, the one thing though is, again, I'm not really sure if he actually understands the relevance of consciousness. And as I'll get to in a moment, I would say that's probably another very key component of kind of like a very general conception of intelligence that is enriched rather than this just kind of a mind blind, you know, logical pattern, you know, pattern finding ability. So as another example, I would say, oh yeah, and I guess like if you have that conception of intelligence, you know, yes, of course you will think of this sort of material as kind of like the cutting edge of our understanding of what is intelligence, you know, maximizing utility in various forms, you know, using statistics to make sense of language. And of course, like algorithm design. I mean, like these three, you know, textbooks that I showed you are exactly the sort of thing that Avon Neumann, Ortega, Demis Hassabi. Yeah, they are like incredibly powerful, like superhuman on in that domain. But you know, that's not all, you know, there's also, and I'll show maybe some books from like maybe one of my all time's favorite geniuses, which is Alexander Shulgin. Pical, you know, phonetically means I have known and loved where, yeah, he synthesized hundreds and hundreds of psychoactive molecules, tested them on himself and tried to make sense of those exotic state spaces of consciousness. Yeah, I think that's a kind of intelligence that is actually in the long term, even far more consequential and important than, yeah, just kind of in some sense, kind of autistic mathematical skills. They work in synergy though, they work in synergy. So it's very important to also ideally combine them. Also another book recommendation. Thank you, Quintin, for this gift. No, this is really fun reading. I'll probably like read a passage of it in a different video. It might be a little bit basic for a lot of things, for a lot of people, but actually the anecdotes and the kind of random facts that he adds, very worth it. I highly recommend it. Anyway, so yeah, Shulgin is a genius and, you know, he

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text:
actually was also a member of Mensa and according to Ann Shulgin in Pical, there's kind of like a passage about that. He actually hated IQ tests. Why? Because as a kid, they did an IQ test on him in elementary school and, you know, he just did it. He didn't think much of it, but apparently he kind of like scored, you know, the highest that had anybody had ever scored at that test, like putting him like 170 IQ or whatever it was. And rather than the teachers realizing, oh my gosh, this is a gifted child, they actually thought he was cheating and they did not believe him that he actually was able to solve all those problems in that time. And they accused him of cheating. And since then, yeah, he was just, actually he really hated kind of, hated IQ tests. But I mean, in the end, apparently he became a member of Mensa. So clearly, clearly that was not an impediment in the final analysis. Okay. So all of that, yeah, kind of like traditional conceptions of intelligence. Let's get into kind of like some of the more meaty, fascinating, interesting things, which is, yes, okay, Shulgin gives you kind of this window into, wow, there might be other things in intelligence. And, you know, as kind of a high level approximation, I did try to enrich our conception of intelligence in the latest video called Qualia Computing, because it's extremely relevant to, yeah, my research, the research at QRI, the research that, you know, the things I've been thinking about for years. And that is, how is the brain actually solving problems? And it is not solving problems in kind of the, you know, sequential serial way that you may think, if you just think in kind of these like very, you know, mathematical way. There's actually something else going on. There's massive parallelism going on in your experience. I recommend watching that video to kind of like go deeper into this. But to a first approximation, I would say that intelligence in an organism like us is about selecting the right self-organizing principle that will solve the problem for you. Meaning that, you know, deep down, our brain is full of physics. You know, our brain is part of physics. It's exploiting physical phenomena. And there's like, you know, to a first approximation, the main thing that is going on at all times is energy minimization. You know, the brain is trying to minimize energy just as every other physical system. So for example, a soap bubble, you blow it at first and it will be kind of like weirdly shaped and amorphous and maybe bouncing around. But eventually it will radiate out the energy and it will fall into its lowest energy configuration, which is a perfect sphere. So in a sense, if you want a sphere, you can just use physics to give you a sphere in itself. Why? Because

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text:
the sphere is going to be this attractor of, you know, the local lowest energy configuration of that system. And this is happening in a massively parallel way. There's no kind of like epistemic agent that is saying like, oh, it shifted here and shifted here and shifted here. No, this constraint satisfaction problem is being solved simultaneously all at once. Every part of the soap bubble is instantiating the same algorithm, which is like tension minimization, which is like one measure of energy that is happening simultaneously everywhere. And the emergent holistic behavior of it will give you a sphere. Likewise, I think that when you're solving a problem, whether it is a perceptual problem, like making sense of a weird image or, you know, solving even like an emotional problem or like, you know, how to navigate an environment, what the brain is doing is configuring itself in such a way that minimizing its energy will automatically give you the solution to the problem. And, you know, there's just so many different ways of doing this and just so many, you know, instantiations. And I mean, I think like even in, you know, graphics and artificial intelligence, people are slowly catching up to kind of this paradigm, this way of thinking of intelligence. There's recently a fascinating paper of how to, you know, in graphics, you have kind of like a cord, how to disentangle that cord. Like if the cord is like all tangled up or something like that, there's these repulsion algorithms where essentially you get every part of the cord to repulse the cord. And essentially that automatically makes it, you know, disentangle. And you didn't need, you know, kind of like anybody kind of like setting that as a goal. It's just what happens naturally. So likewise, I mean, I think that our brain is kind of this, you know, warp engine capable of instantiating all sorts of physical phenomena, like huge variety of physical phenomena. And then the way in which we learn to solve problems is the brain is finding the physical phenomena such that minimizing their energy will help you solve the problem. Okay. I hope that makes sense. And well, from that point of view, all of a sudden this facet of intelligence, which is absolutely not measured by IQ tests in the least, which is making sense of recruiting and navigating exotic states of consciousness becomes, you know, a core part of what intelligence is about. And this actually will in a way vindicate this idea that there is such a thing as philosophical intelligence and there is such a thing as like meditative intelligence. And I would claim, you know, if you compare von Neumann and Buddha, von Neumann, no doubt will completely, you know, outsmart Buddha when it comes to like, you know, making a, you know, developing an algorithm to solve a particular problem in a certain runtime complexity. But Buddha, I guarantee you will be

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text:
way better at deescalating difficult situations in social settings. Why? Because the kind of mindset that somebody like von Neumann will inhabit in a sense, like a very emotionally triggered, well, you could actually say like von Neumann undoubtedly lived in kind of a dualistic world, with a dualistic metaphysics. Potentially he was a closed individualist. I mean, there's no evidence that he is identified with consciousness or anything of the sort. No, I think like he probably identifies as a normal human being. I suspect his philosophical intelligence probably wasn't like comparable, you know, just not in the same league as his mathematical intelligence. So yeah, I mean, chances are that in his own phenomenology, he actually fell for the same traps that most people fall, which is identification with particular patterns of thought and feeling. So, which essentially over time create these ego constructs that it feels bad when they get questioned. And I mean, there are like actually anecdotes of John von Neumann losing his temper when somebody kind of like showed him that he was smarter with a trick usually. Like there was this anecdote of somebody in a sense, like giving him a really difficult problem and then pretending to like solve it in real time, like faster than him. He was pissed. He was really angry at that because obviously that went against his self image of the smartest person in the world. It was very painful. So obviously he had like tons of ego identification. He was not passing the meditative test, you know, the meditative intelligence test of are you able to realize that you're not the patterns of qualia that you inhabit? Yeah, which would be actually a very basic test in kind of like a scale of meditative intelligence. But there's more. I mean, like one example I'll give you is compare the following two kind of rats in a laboratory setting. You have kind of a, they're both trying to solve a maze because there's like, you know, food pellets. You have one of those rats that like learns to solve the maze really fast and gets lots of pellets that way. But maybe, you know, gets as many pellets as there are runs. And that's kind of like the limiting factor here. And there's another rat that realizes, hold on a second, this is a setup and kind of like choose through the walls of the labyrinth or the maze, gets out of it and then finds the bucket full of pellets, which is the smarter rat, right? Like in some sense, okay, sure. The first one maybe has like better algorithmic intelligence, better ability to kind of like represent this environment and navigate it and so on. But the other one actually, you know, the end result was just way better, was able to kind of like hack the motivational architecture and find a way of like getting unlimited pellets. So I would say there's something kind

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text:
of analogous here where like somebody like John von Neumann would be extremely good at navigating a maze, but somebody like Buddha would be like, hold on a second, this is a setup. Let's actually hack valence and become liberated without having to go through all of these, you know, hoops. And I think like, yeah, that's in some sense a superior kind of intelligence. Why? Because it's capable of distinguishing the trivial from the significant. You actually are paying attention to what is it that truly matters. You're developing a theory of value. And that I think is, you know, an inherent part of any conception of intelligence that we have. It ought to have that. So which is not to say that, you know, the first kind of rat is not incredibly powerful. I'm just saying that whatever its power is, will ultimately be aimed in the wrong direction because it's not actually trying to find what's valuable. It's just trying to satisfy whatever like reward function it's been given without necessarily questioning it. So that's the thing, and I think philosophical intelligence, meditative intelligence, highly, highly related with this. It's kind of like, are you the rat that is able to kind of chew through the wall and find the bucket of pellets? And here's a couple of examples. So I think like there's this skill, meditative skill, philosophical skill I call frame exiting skill, in one of the videos earlier, I kind of like talked about like wire puzzles and how like one of the tricks with wire puzzles is to realize that actually the piece that you're supposed to take out is already out. It's actually just an illusion. Like topologically, it was never closed. Yeah, things like that. Like if you feel trapped in a particular situation, maybe the mindset that you should have is, hold on a second, you're actually already out. You're actually already outside of this trap. You're just figuring out in what way. Another one is essentially when there's like conflicts between people, whenever there is people kind of like get stuck in whatever like turfs, you know, families used to believe in, you know, honor and duty and stuff like that. And so like, well, okay, so there's this illusion. It's a mixture of the tyranny of the intentional object and dualistic thinking where essentially you take at face value how you feel and you assume that your reactions to things are actually what was intended from the other person. So there's essentially, yeah, this phenomenon that like if somebody hits you to kind of like make it even, you will hit that person. And in practice, you will hit that person 20% stronger. Well that doesn't make it even. The other person realizes, oh gosh, you hit me even stronger. And because of a bias, they might actually think you hit me like 50% stronger. And so they escalate and will hit you as well. Okay. This is

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a feedback loop. There's no way to escape it if you're stuck in that mindset. Very smart, very high IQ people can get utterly trapped in stupid turfs that way. And yeah, they will justify it. They'll be like, yeah, I'm just like, you know, trying to make sure that incentives are aligned, that the bad guy does not win. They cannot win for the game theoretical, whatever, whatever. Actually if they had chosen instead to, yeah, do some loving kindness meditation and deconstruct the hurt, they will be able to actually find moves that are way more valuable for themselves and to others rather than ruminating in a revenge cycle. Another test of intelligence, which is not of the standard kind of intelligence. And importantly though, I think in general, when we have kind of like low dimensional models of the world and competing factions, yeah, we can, like people get stuck in very, very stupid models. Even very smart people get stuck precisely because they're not able to deconstruct whatever mental formations that is making it a life and they don't see alternatives. They get stuck, they don't realize that, yeah, it's a wire puzzle. They're actually already out. The other thing is for kind of like these like more generalized form of intelligence where you're not just kind of like solving, you know, this maze at face value, you're actually questioning what is the source of value. I'll say that a lot of it also is about identifying the properties of the medium of thought. In a sense, not only taking your thoughts at face value, but being able to kind of make sense of why they have the effect they have in your own psyche, in your own being. And you can think of like, okay, there's like a lot of like interesting meditation techniques like internal family systems, or like, for example, working with the subconscious, as I've talked about in previous lectures, where you have some aspect of your mind can communicate to you through images, you know, with symbolism and things like that. Like, yeah, you shouldn't dismiss that, you know, that is doing actually some kind of information propagation and coalition building in the sub-agent network of your mind that is more than you would be able to do with just kind of verbally trying to convince yourself to do something. So being able to use that, you know, skillfully, navigate that kind of operation. Yeah, that's a form of pretty advanced intelligence. It's a kind of like very refined self-awareness. And it's, I think, very rare. I mean, like meditative geniuses are able to get there for the most part. Most of us are actually kind of victims of our own subconscious and we react to it in unhelpful ways. In addition, then let's talk about existential intelligence. I mean, like realizing that, yeah, you actually need to invest on kind of this higher level perspective, not only take at face

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text:
value, you know, how people are rewarding you. A lot of people, they put all of their intelligence into how they can be praised by others because the thing they're trying to optimize for is kind of this inner smile. You know, when somebody says like, oh, you're doing a great work or that was a beautiful piece of art or whatever, it makes you smile internally. Yeah, you're kind of like pursuing that, you're chasing that. But actually that might not be the most valuable thing you could do. You could, for example, develop equanimity and all of a sudden you're in a positive high billing state, independent of conditions as Shenzhen Yang would describe. Okay, so we're getting to the end here. I just want to kind of like talk about my vision of what super intelligence would be given all of this, which would be not, sorry, where is it? Would not be like super intelligence of the Nick Bostrom kind of, well, I think I lost the book. It fell somewhere. It doesn't matter. You know what I mean? Super intelligence, it's not that, that's not the point. And I mean, what is he talking about? He's talking about causal power. You see, like the sort of intelligence that, you know, the alignment community is worried about is essentially things that can, you know, transform the world in whatever way they want, you know, whatever utility functions you give it to them, they will enact that utility function. And here's the thing. I do not deny that that category of artificial intelligences are dangerous. Actually they are super dangerous and like good, like whatever, you know, research we can do in AI alignment that reduces the probability of kind of some utility maximizer transforming us into paperclips. Good, awesome. But don't take that conception of intelligence and project it to the world and believe that that is all there is to intelligence because that is just not the case. As I explained, a lot of what I think any meaningful conception of intelligence ought to be able to account for is precisely this ability to distinguish the trivial from the significant. So, yeah, I mean, something to be truly intelligent. I mean, I'm not saying this is, this would emerge naturally. I mean, I could absolutely envision you could program a paperclip maximizer that is actually not even conscious. It would be very dangerous, very intelligent in the causal sense of the word, but incapable of exploring the source of value. So if you define intelligence that way, sure, whatever, but I don't care. I prefer to actually look at this phenomenon that is like fascinating, which would be kind of like the more general intelligence, which also includes, yeah, the ability to explore the states of consciousness, identifying what's valuable. So what do we, what could we imagine here? Well, I would actually imagine that any decent, you know, full spectrum intelligence and full spectrum

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text:
here means capable of accessing a variety of states of consciousness and recruit them for both their intrinsic value and their computational properties. I think any decent intelligence of that kind would quickly arrive at the following two very important insights. First of all, open individualism or something to that effect. Essentially, yeah, the interconnectedness of everything, the absence of essence that each moment of experience is kind of an instance of consciousness more broadly and that deep down in a way are true identities consciousness rather than its particular instantiations. And in that sense, yeah, the suffering that others experience is your suffering, is your suffering as well. So like, even if you're like in some sense, kind of like strictly selfish, not in a traditional sense, but kind of in a ontological sense of like loving yourself, yourself in a very deep ontological sense, yeah, you will also be intrinsically motivated to help other sentient beings not experience intense suffering at the very least, among other things. So open individualism would be one, or at least not closed individualism. And second would be, you know, valence realism. It would realize that actually the thing that is underneath any kind of instantiation of value or this value is either pleasure or pain, not in the shallow sense of kind of like bodily comfort and discomfort, but in the deeper sense of the entire gamut of possible valence qualities, which yes, includes configurations of thought, configurations of feeling and their cross-modal correspondences, all of that. I mean, again, there's some beautiful DMT experiences, there's some horrible DMT experiences, and the dividing line between them is their valence. It's not, you know, what they were about. You could have like, in principle, a DMT experience that like the semantic content of it is kind of like a horror film, but all throughout, it's just so much fun. To kind of like experience it. So that would be a high valence, maybe negatively, you know, semantic content might be negative. Again, the thing that actually matters is the valence. So in my understanding, any super intelligence worth its name would arrive at open individualism and valence realism, and perhaps even valence structuralism, which is this concept Mike Johnson coined, which is realizing that the thing that makes an experience good or bad is its structure, not its function, not its semantic content, not the way in which it's been used, but its inherent structure. Is this a harmonious or is this a dissonant configuration? And that is what I think, yeah, truly matters in the end. So yeah, I mean, I do envision any super intelligence worth its name will actually, in a sense, try to transform the universe into a paradise, a paradise where consciousness is the winner, not a particular random arbitrary pattern that you just happen to be attached to for evolutionary reasons, which is kind of making you solve all these mazes and make you feel pain whenever

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your sense of self is insulted or whatever it may be. That is not what I envision as a super intelligence. But then, okay, let's kind of to wrap up, what will a full spectrum super intelligence do with its time? And, okay, it's a huge mystery. I mean, it could be constant orgasms, it could be constant pure love towards all beings, it could be any of those things. One thing I think it's pretty compelling would be it would be playing the glass bead game. And the glass bead game essentially is, yeah, this fascinating novel, the concept I find it more fascinating than the actual narrative in this case, which is, yeah, kind of a hypothetical game where essentially you combine elements from art and science and rhetoric and literature, and you try to construct these beautiful experiences in a collective fashion, kind of like you exploit it, you use each other's creativity in order to create these shared beautiful construct with perhaps like emergent qualia properties that are more than some of their parts. I mean, and I'm talking about something much more advanced than just combining music and visual art, because if you're a full spectrum super intelligence, you will also have access to ketamine qualia and 5-MeO DMT qualia and DMT qualia and being able to extract what's good about all of them, identify the self organizing principles that are, in a sense, the juicy aspect of all of them, and bring them together into, yeah, you know, experiences that are incomprehensible, unimaginably glorious and beautiful and pleasant, worth having. And I actually expect that to potentially go on and on and on for millions of years, because the states of consciousness is very likely unbelievably huge. So there is a lot of room for growth. And yeah, I mean, kind of like in that direction, we coined this term team consciousness, which is, yeah, I mean, like, if that is sort of the vision, you know, an advanced vision of paradise as I've talked about it in previous talks. Yeah, imagine it as team consciousness winning kind of the evolutionary arms race, kind of like, not, you know, the rat that is the fastest at solving the mazes, but the rats that are able to kind of get out of the maze. Those are the ones that we want to, in a sense, encourage and make take control so that we can actually be free, not be trapped in evolutionary selection pressures and incentives. And yeah, I mean, that will definitely kind of look like exploring the states of consciousness systematically finding its computational properties, figuring out how to defabricate ego constructs faster than we're able to do nowadays with meditation and things like that. All of those are kind of like pointing in the direction of team consciousness. And using, for example, also like correspondences with other fields, like, for example, math. Math becomes not just a way to show off your

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text:
intelligence and in doing so, enhancing your ego. It actually becomes something you use in order to make beautiful mental sensory constructs that have the capacity of organizing information for both computational and aesthetic purposes. So this is just one example of kind of a, yeah, symmetry breaking operations. And I would expect this diagram to, you know, be one of the many things that could be floating around for a glass bead game of a super intelligence. I guess the thing I'll conclude with is a couple of, I think like, yeah, the end of 2020 when I was like starting to make my own fragrances and things like that, I mailed actually these little bottles to people. These are basically like my first eight attempts at making interesting smells by synergizing various elements. I mailed them to various people and then like had conversations, had them fill out a survey to kind of like give me feedback. One of the persons I mailed it to was David Pierce. I remember we had a Skype call where we both kind of like were smelling them and commenting and trying to make sense of it. And just one comment that I thought was very funny and amazing was he actually said that in his time at Oxford, you know, back in the day when he was an undergraduate, he was already, you know, very interested in consciousness and, you know, he was not a fan of Wittgenstein saying that the philosophy should leave the world exactly as it is. Like no, there's just so much more to be figured out. And yeah, philosophy can be informative, as I explained, identifying the, you know, the utility function of the universe itself as valence is yeah, definitely a philosophical insight. Well, he was trying to argue that, you know, just as nowadays we use this weird set of sensations for thinking, some another hypothetical intelligence could use smells for thinking. And like our sense of smell is incredibly impoverished in a way. We just kind of get these flashes of, oh, this qualia variety. Wow. We don't get what he was envisioning, which is a whole language of it, you know, with clauses, subordinate clauses and a syntax and a grammar and kind of like interactions between them and forming, you know, mental constructions with, you know, stacking properties of sense and focusing on their contrast or their similarity, their intersections. Yes, I mean, that is one of the things that I think a full spectrum super intelligence would be able to do. You know, like if you talk about, oh, sauvage by Dior, or I don't know, what is this Versace bright crystal absolute in the mind of a full spectrum super intelligence. This is not just a random perfume. Like it's actually like something that connects to a whole web of other qualia values and varieties and has isomorphisms and can be used as kind of like a move. I

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text:
mean, imagine the super intelligence is like playing in this field of the glass bead game and they're all kind of like thinking very hard and exploring the state space. And one of them says, Versace, bright crystal, absolute. And everybody's like, oh yes. And everybody claps and yes, that was the most brilliant move in that context. Yeah, that's the sort of thing I envision is going to be really fun. And with that, yes. Okay. So let's move on towards full spectrum, super intelligence, open individualism, you know, valence realism. And yeah, hopefully you join team consciousness. Let's make it happen. Let's get rid of suffering and I'll see you next time. Thank you so much for coming and may you have a wonderful qualia rich afternoon or day or, you know, whatever it may be. It doesn't matter. Hope it's good. And thank you for listening and have a wonderful day. Hello, hello everybody. Welcome back. Thank you for joining me again in this, this exploration of consciousness and the nature of reality. And yeah, so welcome back. Today we're going to talk about Quillia computing. I mean, not the blog, although of course I could talk at length about the blog and you know, the meaning behind it. But actually, we're going to talk about the concept of Quillia computing itself, because it is a legitimately new concept. I mean, as far as it goes in philosophy of mind, I do think that coining Quillia computing, referring to, okay, the computational properties of Quillia is a very, yeah, potentially like meaningful, non-trivial, and innovative thing to do in philosophy of mind. Now, before we go into Quillia computing as the subject of today's video, let's go through the Quillia of the day, which today is Eau Sauvage. Eau Sauvage. It's kind of like a very classic, I believe 1966, citrus aromatic fragrance. And it's actually really great. I only smelled it recently. And I've got to say that I agree with Luca Turin in that it's a five out of five star fragrance. Now, I think it's also classifies as a high entropy alloy of scent. And I recommend watching a video on high entropy alloys of experience to kind of like get a sense of what I mean by high entropy alloy. But just to kind of like briefly summarize it, it is essentially crafted to be exactly in the precise kind of in between aromatic and citrus without either of them actually dominating. And it generates like something that is kind of in between that is quite fascinating. I mean, at a first glance, it's definitely a very Bergamot like scent, I would say. Yeah, I mean, definitely something like 40 to 50% of the scent is like Bergamot or Bergamot. But also there's lemon and also neroli and rosemary. And to a lesser extent, there is a tiny bit of indol, which is essentially kind of like having the, I don't know, the

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text:
cachet or the rapport of white flowers, but within a Bergamot type of vibe. And if I were to point out like one very cheap perfume that is somewhat similar to Eau Sauvage, it would be this one, which is a lemon and ginger, actually. So like Eau Sauvage, interestingly, also has candied ginger facets. Anyway, I highly recommend it. It's pretty great. It's definitely a little bit pricey, but as a Quillia, it's very much worth it. So, okay, let's get on to the topic of the day, which is Quillia computing. Okay, so we already have the concept of computing. Why do we need Quillia computing? Well, I would say, because part of the claim here is that the substrate actually matters. Okay, so in classical kind of like computing theory, we have this whole idea of the Church-Turing thesis, which essentially states that a function in the natural numbers, although you can generalize it, is in a sense classified as computable if and only if it can be implemented with a Turing machine. And you hear a lot of people kind of invoke the Church-Turing thesis in the context of philosophy of mind. That like, okay, we don't know exactly what the brain is doing, but because it's clearly some kind of computable function, I mean, we're not talking about like uncomputable things. I mean, let's be realistic. It must be on some level, something that we can model with a Turing machine. And now, as far as kind of like in principle reasoning, I think these sort of holds, but we have to be really careful about not throwing the baby with the bathwater, so to speak, because it essentially presupposes a whole ontology for what is kind of the basis of computation, what computation is for, what is it about. And if you kind of like dissect something like the Church-Turing thesis, you will come to understand that that notion, that conception of computation is one where essentially what you have is inputs and outputs, and a particular computation is a transformation of the input into the output. Now, reality is a little bit more complicated and interesting than that, because you also have intermediate states in the transformation from input to output, and a lot of interesting things can happen there. So, in particular, the implementation can actually give rise to particular computational speedups. So, if you're using, for example, a particular quantum computing algorithm, in principle, you might be able to translate that into something that a Turing machine would be able to compute. However, you will not be able to do that with the same runtime complexity. In other words, the particular quantum substrate that you're actually utilizing for one of these algorithms is allowing you to solve the problem with a runtime complexity that is different than what you would get with a Turing machine. Now, of course, you can always compensate for this, in a sense, by scaling down as

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