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Scott Aaronson: The Greatest Unsolved Problem in Math
December 11, 2023
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Is there always a clever shortcut for every problem where we can efficiently recognize a correct answer? I think it's now recognized as one of the central unsolved problems in all of mathematics.
Scott Aronson is a professor of theoretical computer science at UT Austin, particularly known for his work on quantum computing and complexity theory. Today we talk about free will, we talk about consciousness, complexity classes, super determinism, and even quantum computing, that last one in particular, we talk about what quantum supremacy actually means rather than how it's promulgated by people like Michio Kaku and other popularizers of science.
Scott explores and teaches these ideas with extreme simplicity, as well as joy, which is a rare combination. Welcome to this channel. My name is Kurt Jaimungal. And for those of you who are unfamiliar, this is Theories of Everything, where we delve into the topics of mathematics, physics, artificial intelligence, and consciousness with depth and rigor. This commitment stems from a recognition that popular science articles often peddle superficial falsehoods, leaving a discerning audience like yourself yearning for technical accuracy and substantive discourse.
In other words, the audience of Toe is the audience that's willing to invest the extra time to understand the nature of reality and not be stuck in the mysticism that characterizes, say, Neil deGrasse Tyson, explaining that, whoa, quantum mechanics is both a wave and a particle. Cool, bro. Like, what does that mean? In order to understand how that's misleading, one needs to know what a complex linear combination is. And so we'd rather explain that than broadcast that a particle is both up and down at the same time. Enjoy this podcast with Scott Aaronson.
Welcome, Professor. It's an honor to speak with you. I've been following you for a few years. Thanks. Great to be here. I mean that in a non creepy way. What got you interested in computational complexity? Well, I mean, I got into computer science as an adolescent because I wanted to create my own video games mostly. And so I learned, you know, what I could about programming.
You know, and really it was a revelation to find out that, you know, engineering, you know, a video game, you know, just reduces to, you know, writing these lines of code. That was not what I had expected. I like to say that for me, it was like learning where babies come from, you know, like, why didn't I find that out before? But as I learned more about it, I realized that while I like programming, I was really not any good at software engineering.
at making my code work with other people's code, getting it done by a deadline, documenting it. And if I had any comparative advantage, then it was probably on the more theoretical side, thinking about what
What kinds of programs could be written, you know, couldn't be written at all, you know, and, and, and, you know, I kept wondering about that. I mean, I, when I first saw Apple basic or, you know, and then GW basic and Q basic and, you know, these, these ancient languages, I figured, okay, but to make a really sophisticated program, clearly you would need a more powerful language, right?
It was a second revelation to me that no, you just very rapidly hit this ceiling of touring universality where just a very simple programming language becomes capable in principle of expressing anything that any programming language could express.
One of the biggest remaining questions is about efficiency. Among all of the problems that computers can solve, which ones can they solve in a reasonable amount of time or a reasonable amount of memory?
15 or 16, I would have learned what is the P versus NP problem. And you know, and that problem is just so stunning, you know, that humans could ask something, you know, so basic and yet, you know, so concrete, you know, that has a definite answer one way or the other.
And, you know, I had fantasies for, you know, a few months that, well, you know, all of these, these experts, you know, must have gotten, you know, stuck in a rut and I'll come in as a 15 year old and, you know, with no preconceptions and I'll polish this problem off. You know, I think it was good to have that experience once in my life, you know, once was enough to get, you know, to get disabused of that.
At some point I learned about quantum computing, which we can talk about more, but that actually changes the rules of computational complexity based on our best current theory of physics. That was then irresistible to understand because somehow these very basic questions in physics and in computer science were merging with each other.
And it was all a story about computational complexity. If you don't care about complexity, then there's basically no reason to build a quantum computer. Anything it can do can be simulated by a classical computer, albeit exponentially slower. So you need complexity theory to even pose the questions about what are quantum computers good for. But this was a field where there was a lot of low-hanging fruit in the
late 1990s when I started really getting into it. And, you know, I was also extremely interested in AI. I thought maybe I would do that. But, you know, again, there was the difficulty that AI so often boils down to in practice to software engineering, which I wasn't so good at. Now it was when I saw I was an undergrad at Cornell.
When I applied for grad school, I got into where I really wanted to go, which was UC Berkeley. But it was the AI people who recruited me there, not the theory people. But I secretly, I guess, wanted to do quantum complexity theory. So after a year of doing AI, I switched. And then I ended up
You know, computational complexity in quantum computing ended up being interesting enough that I've spent more than 20 years of my life on them. And only now, finally, in the last couple of years, I'm circling back to AI with the stuff that I'm doing for OpenAI. Yeah, I'd love to speak with you about your work at OpenAI. First, is computational complexity, algorithmic complexity, and quantum complexity distinct?
Well, I would say that computational complexity is the whole field that studies the inherent computational resources that are needed to solve problems, and that includes time,
memory it could it could include energy randomness parallelism and quantum computing is is a part of that right you know you could say or you could say quantum this is another computational resource that you can throw you know throw into the mix and then see how it changes things so so so yeah but but but it is the field that studies sort of the inherent
capabilities and limitations of algorithms. Sometimes people who are only interested in just solving a practical problem with the best algorithm that they can find for that problem, they might not call themselves complexity theorists. They might just be algorithms people. But as soon as you start asking the question, what is the best algorithm for this task?
In terms of the scaling of resources as the input gets larger and larger, how do I know that it's the best algorithm? What else would it imply if there were a faster algorithm? As soon as you start asking things like that, then you're doing complexity theory.
It sounds like it's easy to show that something is a more efficient algorithm than another, but to show that something is the best. Yeah. How do you go about doing that? Yes. Well, a good question. You know, the field has been struggling with that for half a century. So, yeah, in order to give a faster, you know, in order to show that there is a faster algorithm to solve a given problem, typically the way you do it is you just give that algorithm.
You know, you, you give it, you know, and that could already be very non-trivial because you have to analyze the algorithm. You have to prove that it works and you have to prove that it actually terminates after this reasonable amount of time. Okay. So that can, that can already be, be non-trivial. Okay. But, but now, you know, if you ask, is this the best algorithm, you know, how do we know it's the best? Okay. Now you're trying to prove a negative, right? And that is inherently
The main reason why we view it as a goal to strive for at all
is that computer science was born with knowledge about its own limitations. When Alan Turing introduced the Turing machine, which is the mathematical model for what a computer is in the 1930s,
He also, as the key application of his new theory, proved that certain problems are not solvable by any Turing machine in any amount of time. This was the famous unsolvability of the halting problem. It built on Gödel's incompleteness theorem, which had been proved just five years prior.
I give you a program and you have to determine whether it ever stops running when run on a blank input.
And Turing showed that there is no program to solve this problem in any amount of time. And the argument is basically self-referential. You say, well, suppose that there were such an algorithm, then we could contrive things in such a way that that algorithm would be fed its own code as input. And then it would have to do the opposite of whatever it does. It's like if it halts, then it would have to, you know, when run on itself as input, then it would have to run forever.
And if it runs forever when run on itself as input, then it would have to halt. And since that's a contradiction, the only conclusion is that the program can't have existed. And so we've known since the beginning of computer science that you can use these sort of self-referential methods to understand something about the limitations of any algorithm.
In a kind of magical way, without having to roll up your sleeves and delve into the details of what the Turing machine is doing. And then in the 1960s, some of the first complexity theorists, like Joris Hartmanis, who passed away recently, and Richard Stearns, managed to go further. And they used similar self-referential arguments to show, for example,
There are problems involving n-bit inputs that are solvable in n-cubed steps but are not solvable in n-squared steps. There are other problems that are solvable in n to the fourth steps but not in n-cubed steps. Can you give an example? Yeah, the simplest example would just be I give you a program and now you have to decide whether it halts in n to the fourth steps or not. That is solvable in slightly more than n to the fourth steps.
But, you know, a sort of scaled down version of Turing's argument shows that it is not solvable in N cubed.
And basically, basically, because if it were, then the program could predict what it itself is going to do faster than it can do it. Okay, and it's kind of like, you know, the like, like, you know, this is like a paradox that a five year old can understand. It's like, you know, if I could, you know, if I if I knew for certain, you know, whether I'm going to raise one finger or two fingers, you know, 10 seconds from now, then I could just resolve to do the opposite of whatever I predicted I would do. And so, you know, so and so and so that's not possible.
To you, does this touch on free will? Some people think it does. I mean, I mean, I tend to think that, you know, if if if there were a computer in another room, you know, and you know, it ran faster than my brain does, and it perfectly predicted what I was going to do before I do it. And, you know, maybe it just it leaves its prediction in a sealed envelope, you know, but then after I take the action, then we can open the envelope and we can see that it
Perfectly predicted what I would do I would say you know that that would that would really profoundly shake my sense of free will you know just speaking speaking personally right and and I would say that based on the known laws of physics we don't actually know whether that prediction machine can exist or not
It comes down to questions about how accurately would you have to scan someone's brain? Would you have to go all the way down to the quantum mechanical level? Would that not be necessary? I would say that the thing that most people don't realize is that this is an empirical question. Maybe whose answer will someday know, but we don't know it yet.
Why is the sealed envelope important? Because if I saw the prediction, then I could resolve to do the opposite.
Yeah, so if this machine existed, does it still say something about your free will if you weren't able to look at it and you could go against the wishes of the machine or the predictions of it? Well, yeah, I mean, you could say if that machine cannot be reliably built, you know, if any attempt to build it consistent with the laws of physics, you know, fails, then that seems to me like about as far as science, you know, could possibly go in saying that, well, you know, there seems to be something that, you know,
You know that corresponds to part of what we mean by free will right there is this inherent unpredictability to our actions. And you know and conversely if the machine did exist and that seems to be.
to me like about as far as science could possibly go to towards saying, you know, actually, you know, free will is an illusion, right? Not, you know, not just begin in some abstract metaphysical way, but because, you know, here is the machine that predicts what you will do, you know, look at it, try it out.
Yeah, you had a blog post on Newcombe's paradox. Yes. Can you please outline it and then what your proposed resolution is, if it exists? Sure. A Newcombe's paradox is the thing where, you know, we imagine this super intelligent predictor, you know, just like I was talking about before, you know, that this this sort of machine or being that that, you know, knows what what, you know, you're going to do before you do it. And it puts two boxes on a table.
Okay.
Or you can take both of the boxes. But now the catch is that the predictor has told you in advance that if it predicts that you're going to take both boxes, then it will leave the first box empty. So it punishes greed. Yes, right. If it predicts that you're going to take only the first box, then it puts a million dollars in it.
Okay, so, and let's say that the predictor has played this game with, you know, a thousand people before you and it's never been wrong. Right. So then, then, you know, what do you do? Do you, do you, you know, as, as, you know, people have actually made it into verbs, you know, do you one box or do you two bucks in the, in the, in the new comb paradox. And, uh, uh, you know, and there seemed to be like basic principles of rationality that, you know, that you could use to, to, to prove either answer is correct.
On the one hand, everyone who takes only the first box ends up about a million dollars richer.
than the people who try to take both, right? And, you know, by the whole setup of the problem is that, you know, that's because the predictor knew and, you know, it's over. But on the other hand, you know, by the time you're contemplating your decision, the million dollars is either in the box or not, right? And so how could your decision possibly affect, you know, what is in the box? It would seem like it would have to be a backwards in time causation.
Right. And therefore, you know, you know, whatever is in the first box, you're going to have a thousand dollars more than that if you take both boxes and therefore you should take both. Right. So, you know, so we can prove two contradictory answers. You know, that is the basic setup of a paradox. And, you know, and people have argued about this for half a century. There is an enormous literature on this problem and many different points of view.
I had a blog post back in 2006 where I suggested what seemed to me like the natural resolution of this. Since then, I've learned that other people have had broadly similar ideas. Some of them do cite that blog post of mine.
But, you know, my resolution of the Paranax was, okay, I think that, you know, in this scenario, you should take one box, right? You should one box. Okay, but the question is why, right? The question is, how can we possibly explain how your decision to one box could affect the predictor, could affect, you know, whether the predictor puts the money in the box? Okay, and now the key is, well, you know, we have to think
harder about what the world would be like with this predictor in it. The predictor contains within it a perfect simulation of you. Whatever you're going to base your decision on, whatever childhood memory, whatever detail of your brain function, the predictor knows all of it by hypothesis. But the way that I would describe that,
is that the predictor has effectively brought into being a second copy of you, a second instantiation of you, right? And now, you know, the key is that as you're contemplating your decision, whether it's a one box or two box, you know, you have to think of yourself as somehow, you know, being both versions of you at once.
or perhaps you don't know which one you are. If you are the simulation being run by the predictor, well then of course your decision can affect what the predictor does. In the scenario that was hypothesized, you have to be radically uncertain about where you physically are, about what time it is,
These are the kinds of things that you have to worry about in a world where there really could be perfect predictors of yourself. A much more boring resolution would be to say, well, I'm not going to worry about Newcombe's paradox because I believe that this predictor cannot exist at all.
You know, as I said, I regard that as an empirical question to which we don't yet know the answer.
Two concepts that I see as related are the no cloning theorem and computational irreducibility.
So this is something popularized by Wolfram, which I know, you know, so I'll get you to explain it to the audience. But the no cloning may have implications that such a machine can't exist because it can't be a perfect copy of you. Yeah. OK. So so so yeah. So by the way, no cloning and computational irreducibility are two totally different things. You know, we can we can we can talk about both of them. But the no cloning theorem
is just a very, very basic fact about quantum mechanics. And it says that there is no physical operation that you can do that takes as input an arbitrary quantum state, an unknown quantum state, like let's say a qubit, a quantum bit, a superposition of a zero and a one, and that produces as output two identical copies of that state.
I'm sorry to interrupt. I'm sure you've heard of Leibniz's law of indiscernible.
This is a fact about physics that could have been false, but it is true because
For a century, every experiment has told us that quantum mechanics is true. As long as quantum mechanics remains the basis of physics, then this is true, but it's not something that is a priori knowable. The sense of copying that I mean is copying the information. Think about classical bits. We all know that classical bits can be copied.
Okay, so Napster exists because the no cloning theorem is purely quantum precisely.
Yeah, so so classical information can be copied. Okay, but what we're saying is that is that in quantum mechanics, you know, even the information cannot be copied. Okay, so so quantum, we have to take a step back and say, you know, what is quantum information, right? It's
The basic building block in quantum information is what's called this quantum bit or qubit. This is a bit that doesn't have to be definitely zero or definitely one.
We know how to deal with that classically. We could have a random bit that has a
40% chance of being one and a 60% chance of being zero and until you look you don't know which it is So you kind of have to think about both possibilities, but then once you look you know, right? Okay now now that is not a qubit right qubit is more interesting than that Okay, because what the key thing that quantum mechanics says is that to every possible? configuration that a system could be in is
like zero or one in the case of a bit, you have to assign not just a probability, you have to assign a complex number. These complex numbers are called amplitudes. They're the basic quantities of quantum mechanics. For example, a quantum bit might have a square root of a half amplitude to be zero.
and it might have a minus square root of a half amplitude to be one. They could actually be complex numbers, a real plus an imaginary number. And now when I make a measurement, then these amplitudes convert into probabilities. And the way they do that is one of the most famous rules in all of physics. It's called the Born rule.
It says that the probability that I see a particular outcome is equal to the square of the absolute value of the amplitude for that outcome. So if I had an equal superposition, zero plus one divided by the square root of two, the qubit zero plus the qubit one divided by the square root of two, and then I measure it, then I'm going to see zero or one equally likely.
There are other things that I can do besides just measuring the qubit to ask it whether it is zero or one. When the qubit is isolated, then these amplitudes can change in time by rules that are not familiar to our experience. I can take the list of all the amplitudes of all the possible states
And I can do something to my system, my particles or whatever, that has the effect of doing a linear transformation on that list of amplitudes. So you could say in some sense what quantum mechanics tells us is that
The operating system of the universe is linear algebra. It's matrices and vectors. My states are these vectors of amplitudes, these lists of complex numbers. My time evolution, the way the state changes over time while it's isolated,
is that I apply what's called a norm preserving linear transformation, also called a unitary transformation. These are linear transformations, matrices that always map unit vectors to other unit vectors. So they always preserve the length of the vector. But an example would be a rotation.
I could take a qubit that is some intermediate state between 0 and 1, somewhere on the unit circle, where here's 0, here's 1, here's minus 0, here's minus 1, and I could rotate by a certain fixed angle, or I could reflect about an axis. These are unitary transformations that I can do.
You know, and then I measure and then I, you know, measurement is a destructive operation. It sort of collapses me to a single outcome. But, but now, you know, the key phenomenon that, you know, that, you know, told physicists, you know, that the world works this way in the first place a century ago. Okay. And that, you know, and it is sort of the signature that something quantum is going on.
is called interference. Okay, so now if I want to know, let's say, you know, how likely is a particle to get a certain spot on a screen, right? Then, you know, I have to, well, I have to calculate the amplitude for that thing to happen, right? You know, and then take the squared absolute value and that gives me the probability. Okay, but the amplitude is a sum of a whole bunch of contributions. Okay, one from every possible path
that the photon could have taken or the particle could have taken in order to reach this endpoint. And now if some of those paths that it could have taken make a positive contribution and others make a negative contribution, then they can interfere destructively and cancel each other out.
meaning like the total amplitude will be zero and then the particle will never be found there at all. Whereas, and here's the even crazier part, if I close off one of the paths, like the famous two-slit experiment, or there are two slits that this particle could go through, if I block one of the two slits, well now I only have a positive contribution or only a negative contribution, depending on which slit I block.
So now the particle can appear at that at that end point. OK, so to say it again, by decreasing the number of paths that a particle can take to get somewhere, I can increase the chance that it gets there. That is something that, you know, just just just, you know, forget about all the low level details of physics. Right. That could never happen if the world were described by conventional probability theory. Right. That, you know, that is sort of the sign that we have
you know, that to actually describe what physics is doing, we need different rules of probability, okay, which is a much more fundamental thing than you might have imagined the laws of physics even talking about at all. But they do. And so now, you know, okay, now we can come back to the no cloning theorem, since you asked about it. Now, you know, a qubit is going to have some state like
a times the qubit zero plus b times the qubit one, where a and b are amplitudes. So the state of one qubit is described by a two-dimensional vector, a list of two complex numbers, a and b. Now, what would it mean to make a copy of the qubit? It would mean that, well, now at the other end, I should have two qubits that are both in the state, a zero plus b one.
Okay. And the way that in quantum mechanics, the way that we describe sort of two systems that are just sitting there next to each other and that are, you know, separate from each other that haven't interacted, right? It's a mathematical operation called the tensor product. Okay. But it basically just means, you know, we, we take like component wise multiplication. So if I have a zero plus B one,
you know, for my first qubit times a zero plus b one for my second qubit. Okay. Then I can, you know, just like in, in, uh, middle school algebra, you know, I can expand it out and I can say that's an amplitude of a squared for the qubits to both be zero. That's an amplitude of a B for the qubits to be zero and then one. It's an amplitude of a B for the qubits to be one and then zero. And it's an amplitude of B squared for the qubits to both be one.
So now I have a new vector. I want you A squared, AB, AB, and B squared. But now that we know that, now we've proved the no cloning theorem. Why have we proved it? Well, because that transformation that we just asked for is a nonlinear transformation.
The amplitudes A and B were not replaced by linear functions of A and B. They were replaced by nonlinear functions such as A squared or B squared. That is a thing that unitary evolution in quantum mechanics cannot do. There are other ways to prove the no cloning theorem, but one way to prove it is really as simple as that.
i see now computational irreducibility and then also what all this has to do with new comes paradox all right all right all right so i i mean computational irreducibility is just you know a term that steven wolfram uses for uh uh you know i would say you know a basic phenomenon that was you know known to many people uh before wolfram you know he likes to
uh, you know, treat everything as, as, as, as, as his invention. But, uh, you know, it is, um, you know, the, the, the fact that, that, you know, for many, many, uh, systems that are computationally universal, like, you know, we cannot figure out how to, you know, predict their behavior faster than just by simulating the whole thing. Right. So, you know, there, there are, you know, in some sense, science has gotten all, you know, as much leverage as it has.
over the past 400 years because often we can model a system by something that is simpler than the system itself. So the orbits of the planets around the sun, the orbit of the moon around the earth. Kepler said these look like ellipses. And then Newton explained from a single simple law of gravitation,
And from laws of motion, he explained why they should look like ellipses. And then you can predict, in some cases, what the planets are going to be doing millions of years from now, because the system is simple enough. But there are many other systems. We could take a lava lamp, for example, or the weather, where there is just
so much dependence on the fine details of the system state at any one time that if you try to run a prediction to a future time, then your prediction will before long diverge from reality. This is the famous butterfly effect.
Right? That, you know, unless you know, you know, the exact state of every particle and can then feed that into your computer, right? Then, you know, like a small, you know, whatever small error you make in, in, in knowing the current state is going to blow up exponentially over time. Hey, that's the, you know, basic phenomenon of chaos and computational irreducibility. I mean, I think it's just, you know, the term that Wolfram uses for like, you know, the analog of chaos in, in discrete systems, like cellular automata.
Great. And so what does that have to do with free will and new comes? Well, okay. I mean, I mean, what I would say is that if there is a, you know, some deep reason why the prediction machine cannot be built, you know, why the new com predictor cannot exist, then you know, the the only candidate that I can put forward, you know, based on
you know, the physics and neuroscience and so forth that I know about is to say, well, maybe, you know, in order to make, you know, a well calibrated prediction of what a person is going to do, you know, you would really have to know, you know, not just like a crude approximation of the state of their brain, you know, which could mean like, like knowing the connectivity pattern of the neurons, you know, knowing the strengths of each synaptic
You know, and so forth, right? Maybe that's not good enough. Okay. You know, maybe you need to know like, like, you know, is this individual neuron going to fire or not? Right. At this time.
I mean, a single neuron firing or not firing could certainly trigger a cascade of chaotic effects. Maybe if this neuron fires, it causes 10 neurons to fire, which in turn cause 100 neurons to fire and so forth and before long, you're going
Yeah, so a cosmic ray is responsible for Scott not being a quant. I mean, this is the question, right? You know, what is the smallest change that you could have made? You know, and this is a standard trope of like,
you know, time travel stories and science fiction, right? Like when you go back in time, you know, if you change even the tiniest thing, I mean, you know, like usually they, you know, they're like, oh, we have to walk very carefully and not kick any of the rocks. So, you know, that's kind of silly. If you believe this at all, then, you know, the very fact that you're there, you know, disturbing the air molecules, you know, you're, you know, it's like, forget it, you know, you've already completely changed the future.
If we really need to know whether a single neuron fires or not, we know that the sodium ion channels that control that are modeled in neuroscience by something called the Hodgkin-Huxley equation, which is a stochastic differential equation. It has a noise component.
Right and you know the neuroscientist will probably say well you know we just treated as thermal noise right we just treated as you know a bunch of molecules are bumping around randomly and that you know somehow you know sometimes it makes the sodium ion channel open and other times it makes it close right but if you really needed to
I don't know if that is true. I regard this as at least partly an empirical question.
There is also a philosophical question here, I should admit,
How accurate does the copy have to be before you will accept that copy as being a new version of you? The famous thought experiment here is, imagine that someone has built a teleportation machine that can teleport you to Mars. You can visit Mars in only 10 minutes transit time.
But the way that it works is that your brain will get scanned in as pure information. That information will get sent to Mars. On Mars, a machine will reconstitute you from that information. And then the original version of you on Earth, well, that'll just be painlessly euthanized or something. And so now the question is, do you agree to go in that machine? Is that a means of travel that you are comfortable with?
Uh, and you know, I think, well, you know, it might, you know, depend on the details of, you know, just how accurate is this copy, right?
Is it really perfect? Is it just good enough? There have been philosophical thought experiments about this kind of thing for generations, but we can already see with GPT, for example, with the AIs that have come online within the last few years,
These questions are going to come up. Take a person who has some giant corpus of work, tens of thousands of postings on the internet, and then you can train a language model to emulate that person as well as it can. As character.ai and companies like that are already doing in a kind of crude way, they let you talk to Einstein.
Talk to Taylor Swift, talk to Socrates or whatever. I didn't find it that engrossing. They all kind of sounded the same to me. They all kind of sounded just like different language models. Imagine that that gets better. Imagine that you make this doppelganger of yourself and then you lay in bed all day and you get up and you see what it's done and you say, yeah, those are totally the things that I would have done.
You know, how good does it have to be before you accept it as a replacement for yourself? Do we need to go as far as a teleportation thought experiment to Mars? Because even when you move a sub-millimeter amount, it could technically be that you just got destroyed in an instant and then was just reconstituted a sub-millimeter further. Well, yeah, I mean, so there is that philosophical question, right?
Are we constantly just being destroyed and recreated, or should we think about it that way? Certainly in ordinary life, we don't think about, I get on a bus, I get on a plane, I move around as something that is destroying and reconstituting me. But now, if you really want to get confused about this, you can think about quantum teleportation.
Right. So there is a protocol by which you can transfer, you know, a quantum state from one place to a different place. Okay. If you have two resources, you know, number one is just classical communication. You know, the ability to send conventional bits, like let's say over the internet, for example. Right. That's pretty. And the second resource is you need pre-shared quantum entanglement.
So you need the sender and the receiver location to have pre-shared entangled quantum states that were correlated with each other beforehand. But if you have both of those things, there is this amazing protocol that was discovered 30 years ago where you measure your quantum state, let's say Alice over on the left side,
measures her state together with her entangled particle and then she gets two bits of information that she sends over the internet to Bob and then Bob using those bits applies some correction operations to his entangled particle and now voila he now has exactly the same quantum state that
Did this violate the no-cloning theory?
Right. Because I had my quantum state and now somehow a new copy of the quantum state has popped up over at Bob's head. But the key is in order for this to work, Alice had to make a measurement that destroyed her copy of the state. And does Alice know her copy of the state before? No, she doesn't. She doesn't even know what she's sending. Right. Exactly. She doesn't have to know. She doesn't have to know.
She can know, but she doesn't have to. Bob just ends up with a new copy of the same state, whatever it was. You could say, would you agree to be quantumly teleported to Mars? Well, in that case,
You know, that sounds potentially better or safer than just being sent as classical information because in that case, it really is the same quantum state that would be reconstituted on Mars, right? You know, just like it would have been if you would just gotten into a spaceship and traveled to Mars in a conventional way. Yeah. All right. Great. Do you have a preferred interpretation of quantum mechanics? Well,
Actually, if your views on this have changed, then it would be great to outline what they were prior and what changed them.
When I teach quantum mechanics to undergrads in my quantum computing and information class, I try to teach it like comparative religion. I try to not tip my hand about which interpretation I'm leaning toward, but I've discovered something interesting.
in recent years, which is that it's really hard to not make the majority of the students into many-worlders. Once they see the pros and cons laid out, then we ask as an ungraded question on the final, we ask what's your favorite interpretation, and then consistently a majority
Just to back up, many worlds interpretation is just the one that says that the wave function, which is this list of amplitudes for all the possibilities that you could get, that is the fundamental reality.
That is what the universe is. It is this list of amplitudes. And it evolves in time just by this unitary evolution. And the many-worlders would say that measurement is not real. Measurement is our local perception from our local point of view. But it's not really a fundamental law of physics.
Hey, so, so, so if you know, and there's a sense in which that is, you know, the, the, the mathematically simplest or nicest picture that you could have, right, where it just all unitary evolution, which is continuous, it's reversible, it's, um, um,
It's deterministic. You don't have these weird probabilistic irreversible jumps. You don't have any of that. But the cost for saying that is that now if let's say there's some qubit that's in a superposition of zero and one and then we make a measurement of it, then the way you have to describe that by unitary evolution is that the whole system
Consisting of, you know, the qubit and the measuring device and me, you know, are now going to evolve to a new quantum state. Okay. And that state will have two components. And in one of the components, the qubit is zero and the measuring device registered it as zero. And my brain, you know, I looked at it and I saw the zero. Right. And in the other branch, you know, the qubit was in the state one and the measuring device registered it as one. And my brain, you know, saw that.
Okay, so you're led to this prediction, you know, that the universe is sort of constantly splitting into branches, you know, as it were, or at least, you know, what we would regard as sort of different, approximately classical universes, okay, and where, you know, our lives could turn out differently, right?
If you were to treat the qubit plus all of the atoms in the measuring device and all of the atoms in your body as just all quantum mechanical systems,
all just obeying the same Schrodinger equation, the same laws of, you know, of unitary physics, and nothing ever gets singled out as being an observer, or, you know, or having this sort of special role, then like that, that is the prediction that you, you know, that you would get, you know, and so now, like, in some sense, the whole interpretation problem of quantum mechanics is what do you do with that fact?
Okay. And so now, you know, there are, you know, a few different approaches. The original approach of, you know, Niels Bohr and Werner Heisenberg and most of the other founders of quantum mechanics was to say, well, then, you know, this wave function, this list of amplitudes is not real.
It's just a mental device in our heads that we are using in order to calculate the probability that we will see this outcome or that one. What is real is what we see when we make a measurement. They would tend to say there is the classical world that we live in, and then there is the quantum world, which is the subatomic world, and measurement is somehow an interface between the two worlds.
The problem that Copenhagen has always had is where do you actually draw the boundary between the quantum world and the classical world?
Right? You know, like nowadays, we can take much bigger systems and we can put them in superposition states, like even molecules with, you know, thousands of atoms in them, we can put in a superposition of going one way and going another way. Nothing as big as a Schrodinger cat, you know, yet. But, you know, but but like after a century, no one has discovered any fundamental obstruction to, you know, scaling up superpositions arbitrarily.
And quantum computing feeds into this discussion as well, because if you can build a scalable, error-corrected quantum computer, then you could have millions or billions of qubits that are all in a superposition of two different states. If you even loaded an AI program onto that quantum computer,
and if the AI were conscious, then it could even be in a superposition of thinking one thought and thinking a different thought. Which was the original thought experiment that sort of led David Deutsch to propose the ideas of quantum computing in the first place in the late 1970s. So the question is like, where does the buck stop? And the Copenhagen approach has basically been to say, well, there are certain questions that you're not allowed to ask.
We know a priori what it means to measure something and get a classical outcome. This is just a precondition of doing science and so we have to just assume this. That was an answer that was bound to not satisfy everyone forever.
But, you know, you could say that sort of option one, I view it as kind of the giving up option, right? You just say, you know, the theory, you know, it works for experiments and we're not going to treat the whole universe, including ourselves quantum mechanically. We're not even going to try to understand that. And then a second approach would be to say, yes, there is this whole wave function, right? There is this whole
a list of amplitudes for every possible outcome, but also there is one particular branch that is the real one, that is the one of actual experience. And so you have this giant ocean of amplitudes, but then there's also a cork in the ocean that just gets pushed around by the waves.
in a way that matches the predictions of quantum mechanics, the Bohr and Ruhl. That is what David Bohm tried to do and Louis de Broglie. This is called the pilot wave or the de Broglie-Bohm interpretation of quantum mechanics.
okay and you know and and there are many different versions of it because you know you can write down like thousands of different such rules for how the cork is going to go that will all make that will all end up with the same predictions for any experiment that we can do
And then a third point of view would be many worlds where you just bite the bullet and you say the wave function is real and I refuse to introduce any additional ingredient, like any quark in this ocean, which means I'm not going to regard the other branches as any less real than my branch.
I regard all of them as existing. I can't talk to the other branches. The fact that quantum mechanics is linear is the thing that prevents me from communicating with the other branches. But if they're there in the equations, if they're there in the theory, then I'm going to say that they're just as real as whichever branch you and I happen to experience.
And then the fourth option would be to say, well, none of these ideas are any good. None of these interpretations is acceptable. And therefore, there must be something wrong with quantum mechanics itself. And hopefully in the future, we'll discover a better theory of physics that says, OK, here is when the quantum state collapses. It happens when it gets this big or this massive.
And there will just be some objective testable law of physics that describes the collapse process. OK, now that would be something new, right? That would be that's not an interpretation. That would be a new and different physical theory that would overturn quantum mechanics as we know it today. Right. But you can say, well, you know, then then that that has to be the truth. You know, quantum mechanics has to just be an approximation to some better theory that hasn't been discovered yet.
So, you know, you ask what I'm partial to, you know, I'm kind of partial to an idea by the physicists Lenny Susskind and Raphael Bussot from a decade ago, which is that cosmology might be an important part of the story, right? So like you could say that, you know, the big, you know, one of the main problems, you know, for anyone who is trying to interpret
quantum mechanics is to specify when does a measurement happen? When does the buck stop and when should I regard the superposition of outcomes as having resolved into one or the other definite outcome? The many-worlders might say, well, there's no one right answer to that question. It's kind of like asking,
How many grains of sand do I have to put together until it's a heap of sand? Even they might want a rough and ready rule for when we can treat an outcome as definite. Here is one possibility for such a rule. When you make a measurement, it's not just your brain that becomes entangled with the qubits or the particles that you measure.
It's the air in the room that you're in, in the radiation in the room. There's a butterfly effect that happens. Each particle starts knocking around the nearby particles and so there's a whole bubble of effects of whatever the outcome of that measurement was that spreads outward from you.
No faster than the speed of light, but as soon as the information gets encoded into photons, then possibly this sphere of effects is expanding around you at the speed of light. Once the information about which measurement outcome you saw is encoded into photons that are leaving the earth,
right and that are flying away from the earth at the speed of light right which eventually they will be then you could say well even in principle we could never catch those again you know as we would need if we wanted to re-cohere the superposition.
you know, if we wanted to like show that, you know, see any effect of the other outcome of the one that we didn't measure, right? So, you know, in order to get interference, you have to collect all of the qubits that were affected, right? And, you know, if many of those qubits are flying away from us at the speed of light, well, then you could say, you know, how could we ever catch them again? Well,
If there were some extraterrestrials who would thought to like enclose the solar system in perfectly reflecting mirrors, right? Well, then okay, then the photons are going to bounce back and then maybe we could go here and we could see that this is still a quantum superposition. But, you know, I will assume that aliens have not done that, right? That does not seem to be the case in our universe.
And then you get into questions about cosmology. There's this cosmological constant that was discovered in 1998, also known as the dark energy. It's the thing that is pushing the galaxies away from each other at an exponential rate.
You know, one of the most important discoveries in all of physics for decades, right? And certainly in cosmology, right? The fact that this dark energy exists, what Einstein a century ago called the cosmological constant. It's actually not zero. We now know that, right? But now, if that constant had been negative, which it could have been, a universe with a negative cosmological constant
is one that in some sense does have a reflecting boundary. It's called an anti-decider universe. In that kind of universe, we would be trapped in a bubble where everything would be unitary. Any photons that are flying away from the Earth, eventually they can come back.
Right. And so so no loss of quantum coherence would truly be permanent in that kind of universe. OK. But, you know, since 1998, we know that we don't live in that kind of universe. Right. We live in a universe with a positive cosmological constant, a de Sitter universe. And in that universe, you know, things really, you know, at least as far as anyone knows, no one knows for sure. But it's, you know, it seems possible that things can can fly off to infinity.
And we could just take that as our criteria for when a measurement has happened. So in some sense, you know, we could say like it doesn't, you know, we could sort of
harmonize the many worlds in the Copenhagen points of view by saying like, yeah, at some formal level, yes, you know, we, you know, there is this whole wave function of the universe or, you know, we're, we're willing to talk about it. That does include all of these branches where all these other things happen. Right. But, uh, you know, there's also a criterion, you know, uh, uh, uh, for, for loss of quantum coherence, right. The, you know, the photons flying away from me at the speed of light.
Where after that happens, then I might as well say that the other branches are gone. They are now not empirically accessible to me, even in principle.
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So in other words, when you're teaching this in the comparative religion sense, you're the Baha'i faith.
I think they called it the multiverse interpretation. And by the way, I just saw Lenny Suskind a couple of weeks ago and he doesn't seem to believe his own interpretation anymore. But I still like it though.
Great, so the multiverse interpretation is separate from the many worlds, because those sound similar. That's right, yes. And the many worlds, when you said that you measured, forgive the pun, your students at the end and then they said that they like the many worlds, 80% or so. I think it was probably more like 55%.
What does it even matter or shut up and calculate or that there has to be new physics?
Yeah, it's surprising to me that number four, the provisional one that, hey, we don't have the current fundamental law and so who cares about it, isn't more popular given that gravity isn't integrated into quantum mechanics. I mean, it does have adherence, right? I mean, Roger Penrose is one very famous adherent, right? But I think he sort of hurts his case by tacking onto it like a whole enormous chain of speculations, right?
He thinks that quantum gravity causes an objective collapse of the wave function and this collapse is uncomputable. It cannot be simulated by a Turing machine and the microtubules in our brains are somehow sensitive to this quantum gravitational collapse and this is implicated in consciousness.
So that's the Penrose view and you can say even if you might go with him to the first stop of that train, most of us are going to get off before the later stops. Okay, we're going to explore uncomputability shortly. Oh yeah, what I was getting at was did you measure the students initially and say, hey, what is your preferred interpretation in order for you to establish a difference? Yeah, that's a good question.
Like to do a controlled experiment, you want to do that. The trouble is that until I expose the students to all these interpretations, they don't even know what they are. Most of them have not even heard of them, or if they have heard of them, then I'm not sure if they could define them.
The reason is because in the popular press, many worlds is prominent and so it may just be an effect of, hey, I like Sean Carroll. I listen to his podcast. Yeah. Yeah. Well, I mean, I mean, I mean, Sean makes very, you know, I've, you know, he's been a good friend of mine since, you know, 2006 or so. And I think he does make very strong arguments for many worlds. And I say that even though, you know, I am not nearly as, as hardcore of a many world or as Sean is.
Isn't there still the issue of having a globally well-defined measure in order to even state what the probability distribution is of different branches of the wave function? But can you explain what that is? Yeah, so I mean, you could say that the basic problem for if you want to be a many-worlder is you have to explain, well, why do we only perceive one world? And not only that, but why do we perceive each world
with these particular probabilities, these born rule probabilities. I have to say, I don't regard that as a problem for only the many worlds interpretation. You could ask the same question with any interpretation. Where did these probabilities come from? It's just that question takes on a different character depending on which interpretation you like.
If you believe in new physics, then you have to postulate some new law of physics that will then give rise to these probabilities. You can check whether it does or it doesn't. Ideally, you wouldn't just stick them in. In physics, it's always better if you can derive something rather than just assuming it from the outset.
If you are a bohemian, you postulate a rule for your hidden variable, for your quirk in the ocean.
that happens to always give you agreement with this born rule, right? But then you could say, you know, why should it have been a rule of that kind, right? And then, you know, if we started out in some other distribution, would we reach that born distribution as an equilibrium, right? So that's what the question looks like to a bohmian. To a many-worlder, you know, the issue is that a many-worlder is committed to the view that all of the outcomes are real, right?
All of the outcomes are experienced by someone. And so then they have to say, then what does it even mean to say that this outcome has this probability and that one has that probability? How do you even make sense of that statement? It's like, you have to imagine that all of these beings are real, but somehow one of them is going to be picked to be your experience. And so somehow there is some
You know, metal law that governs that, right? And so there is a long history, you know, ever, you know, since Everett himself in the 1950s of many worlders, um, trying to, uh, or claiming to derive the bourne rule, right? Derive the probabilities. Okay. They always have to make some auxiliary assumption, you know, in, in these derivations, right? Because it's like, you're starting with a picture.
That is just the wave function, you know, that has no probabilities in it. And then in the end, you know, you get a statement about probability. Right. And so, so, you know, there, there, there, there has to be some step where, where you're just postulating that, yes, something is random. Right. And, you know, and for a many-worlder, what that kind of looks like is it's this thing called indexical uncertainty or self-locating belief.
So basically, imagine that you didn't know your own blood type. You just hadn't gotten tested yet. But then you say, well, look, there's this many people in the world who are type O, there's this many people who are type A. So I'm going to just assume that I was a randomly chosen person. And there's something fundamentally weird about that. As soon as you start thinking about yourself,
As chosen randomly from the set of all people. Yeah, there's also a reference classes. Yeah, exactly. Exactly. Then you can start wondering about things like, you know, why was I born in the, you know, late 20th century as opposed to, you know, in medieval Spain or, you know, or at some other time, right? Why am I on earth? Why am I not an alien on a different planet? Right. And, you know, it's not, it's not obvious if these questions have well-defined answers at all.
Right. But what the many worlders need to do is to say, you know, there are all of these branches of the wave function.
that are all real, they all have real copies of you, but now you have to think of yourself as a randomly selected member of that ensemble. And then once you decide to do that, then you actually can give many mathematical arguments that the born probabilities are pretty much the only probabilities that would make sense.
You can show that any other choice for what the probabilities would be, like if instead of the absolute square of the amplitude, suppose it were the absolute cube.
of the amplitude or the absolute value to the 2.8 power or something like that. You can show that that would give you nonsensical things. It would lead to faster than light communication. It would lead to massive violations of the laws of physics that we understand. You can give arguments for once you've decided to
Now, it's been a while since I've studied this, but it's my understanding that the space of pure quantum states is a projective Hilbert space, which is a Kahler manifold. The symplectic structure gives rise to the dynamics.
That's probably all true. Those are already much fancier words than the ones that I ever use to talk about these things. Right. Well, fancy words with a specific mathematical meaning. Some say that computability or quaternions are fancy words.
Right. Exactly. Yeah. What I mean is that when one says, well, where does the Born rule come from in a symplectic, sorry, in a scalar manifold? If you have two of those structures to get the third. So why isn't the question then? Well, why do we have a complex structure or why do we have that? That is a different superb question. You could say like, why should quantum mechanics have been based on complex numbers? You know, and you actually can define a variant of quantum mechanics that would only use real amplitudes, right?
And that version turns out to be pretty good for many purposes. Like it would lead to exactly the same power of quantum computers, you know, as our ordinary, you know, complex quantum mechanics, right? It would lead to, you know, basically all of the same, you know, information and communication protocols, you know, such as quantum teleportation, you know, you'd have the same no cloning theorem, the same, all of that stuff. It just that there are certain things
that would be less elegant in the, in the universe with, with real quantum mechanics. Okay. And we know some of those arise just because the real numbers are not algebraically closed. You know, you can't take square roots of them. Right. And so like, if I have a unitary transformation that, you know, operates over, let's say one second of time, and now I want to know, okay, but now what was the piece of it that operated only over the first half second? Right.
Well then, yeah, as long as I have complex matrices, then I can just take a square root, right? And, you know, I'll get an answer to that question. Okay. With real matrices, there might not be a square root, you know, in the same number of dimensions. So for example, there's no, there's no two by two real square root of the matrix one, zero, zero, negative one, right? That would be, that would be an example, right? And we, we can see that because it has a negative one determinant, right?
So that breaks various things about the way that physicists use quantum mechanics. And then there are other more subtle things that also break, like the number of parameters that you need to describe a composite state. In complex quantum mechanics, it's exactly just the number of parameters that you need to describe the first piece times the number of parameters that you need to describe the second piece.
Okay, but in real quantum mechanics, that's no longer true. By the way, it's also not true in quantum mechanics based on quaternions, right? With real numbers, you get an undercount, with quaternions, you get an overcount, and only with complex numbers does it work out exactly right. Okay, so there are these subtle things.
that just work out perfectly when quantum mechanics is defined over the complex numbers. But I've asked mathematicians this question, if you were God designing the universe on a blackboard, do you know why you would have chosen the complex numbers for this? In some sense, the deepest laws of physics that we know. And the mathematicians were like, come on, they're algebraically closed.
I think you said this that we used to think there were two logical operations and or or but then we found out with quantum mechanics there's complex linear combinations. Well yeah okay so I was saying like like in terms of how you can combine multiple possibilities right like like it's
Like when someone says that an electron, for example, it's not in its ground state, it's not in its excited state, it's in some kind of superposition of the two. Often the first thing that they think that you mean is well then you must be saying that it's in both simultaneously.
And you know and the trouble is if you take that too literally that it leads to like for example a vision of what a quantum computer is where it would just try all of the different solutions in parallel.
Right. And that's that's that's wrong. Right. That's just like that leads you to to like leads people to importantly wrong expectations of how useful a quantum computer would be if they really think that it could try all the answers in parallel, you know, in the in the in the naive way. Right. So then you correct that. And then they say, oh, so then so then what you must be saying instead is that, you know, the electron is in one state or the other and we just don't know which one.
Do you believe there to be a fourth ontological category that involves the quaternions?
I mean, you could define quantum mechanics over the quaternions or over the reals for that matter, and that would give a subtly different answer. But what would that look like? So quantum mechanics over the quaternions turns out to be sick in various ways. Sick as in cool? Let me tell you what I mean and then you can decide. At least naively,
In quaternion quantum mechanics, you could send information faster than light. And in fact, if Alice and Bob are far away, even if Alice is on Earth and Bob is on Mars, it could matter which one of them does an operation first. Does Alice act first or does Bob act first? And this is because the quaternions are non-commutative.
So, you know, it matters in, you know, even for separated events, it can matter, you know, sort of which operation we put there first. And now this is in flagrant contradiction with special relativity, right? Which says that, you know, when two events are, you know, space-like separated, then it can't matter in which order, you know, they're done because, you know, to some observers, you know, Alice will be first and to other observers, Bob will be first.
And these two perspectives have to be consistent with each other. So quaternionic quantum mechanics breaks that because the quaternions are not commutative. So if you want to believe in it, then you need some way of making that effect go away at large enough distance scales or something like that. There's a physicist named Steve Adler who spent decades trying to make that work.
I talked to him a few years ago and he said that he doesn't really believe it anymore. Real quantum mechanics, like I said, that one does make a lot more sense, but a real superposition philosophically I would think of is almost the same sort of thing.
as a complex superposition. You know, they're just kind of different in detail. Now the octonians have been chopped liver in this conversation. Yeah, octonians don't even get started, right? Yeah, do you mind getting a tiny bit started? Just explain because that's a popular subject. Well, okay, the the the the the the the the octonians are so you know, so there are these four, what are they complete division algebras, the norm division, norm division algebras, excuse me, the the the reals, the complex numbers, the
You know, which have two parameters, the quaternions, which have four parameters and the octonions, which have eight parameters. And, you know, and like naively you would expect that it would, you know, it must just keep going after that point. But, you know, it was a very important theorem from the 19th century that says that these are the only four.
right? So it's sort of the progression stops after that. So there are these, these four norm division algebras that are kind of special, but you know, as you go to the larger and larger ones, you, you know, you lose certain properties. So like, you know, the reels are ordered, right? No, the complex numbers and beyond are not ordered. Okay. But with the complex numbers, you could say, you know, you, you, you lose something, but you gain something, right? You get, you gain that they're algebraically closed.
Right. But now when you go to the, you know, and the complex numbers are also, you know, commutative, they're associative, they satisfy pretty much all of the basic properties that you would want in algebra. Right. But now, you know, with the caternions, that already starts falling apart because the caternions are associative, but they're not commutative.
Okay, so A times B can be different from B times S. Which doesn't sound terrible because non-commutativity is a hallmark of quantum mechanics. No, no, no. I mean, look, and anectoneons still have, you know, they have applications in, you know, even in computer graphics, in math, in physics, you know, they are actually used, right? As I said, you know, if you want to use them as amplitudes in quantum mechanics, then there is stuff that goes wrong. You have to then somehow make that consistent with
with relativity. But now the octonians are not commutative and they're not even associative. It's funny, it's like in fifth or sixth grade, kids learn all these terms. This is the commutative property, this is the associative property. But until you've seen any examples of things that are not commutative or not associative, then this is just a bunch of words to memorize.
I think that the time when you want to teach these terms is the time when you want to teach things that don't satisfy them. For my daughter, my 10-year-old daughter just the other day, I gave the example of something non-commutative, getting dressed, putting your pants on and then your underwear is not the same as the reverse.
So there are examples for non-commutativity that even a small child can understand. Non-associativity is a little bit harder. Well, you're lucky this camera is only here, otherwise you'd see that I don't pay much attention to the non-commutativity of the pants and underwear. Before we get on to consciousness, I want to talk about IIT and I want to talk about P equals NP. Which, by the way, what I learned as a teenager, I just learned the equation P equals NP.
21 years ago when you know one of the first things I ever wrote as a student was a review of his new kind of science book.
And what I spent half of that review doing is just explaining why his kind of model cannot account for the known phenomena of quantum mechanics. And this is not a fuzzy statement. This is a thing that one can prove.
What he wants basically is to reduce everything in the universe to cellular automata, to a bunch of bits, maybe at the Planck scale or something like that, that are undergoing some sort of simple computational rules. That far along, yeah, I think that's great.
That's like, you know, the whole physics community would like that, right? They would like, you know, especially a theory of quantum gravity that would explain why, you know, what's called the Bekenstein-Hawking entropy is finite, right? Why are there only finitely many degrees of freedom in a black hole, right? Or apparently in any physical system, right? Like what is it, you know, when you get down to the Planck scale of 10 to the minus 33 centimeters or 10 to the minus 43 seconds,
Something seems to break in our picture of a smooth, continuous space-time. We can see that from thought experiments where, for example, if you tried to
Right. So there are these
Thought experiments that tell us that something breaks at the Planck scale, but can you actually explain that by giving a theory where space and time are discrete or sort of discrete at the Planck scale? That is, I would say, a central part of the problem of quantum gravitation.
But now Wolfram wants to do something else. He wants to say, no, it's not that we have quantum mechanics with a finite dimensional Hilbert space and with a discrete space and time. He wants to in some sense get rid of quantum mechanics and have it be a classical cellular automata. And then the problem is, well, we have
a mountain of evidence that quantum mechanics is both true and unavoidable. And so what does he do with that evidence? And he kind of handwaves it away. This is the key problem. In a new kind of science, he said, well, it's true that there are these experiments that you can do on entangled particles that could be very far away.
that lead to these phenomena like the violation of the Bell Inequality, which is famously a thing that you could not explain in a classical universe. And that's just a very crisp statement. It doesn't matter what additional assumptions you make as long as they're reasonable ones or sane ones.
So, you know, Alice and Bob, who are far away from each other, they measure their halves of this entangled pair and the statistics of the outcomes could not have been explained by any theory where the particles just secretly agreed in advance on whether to be spin up or spin down or whatever, right? It can only be explained by
saying, well, until Alice and Bob made the measurements, it was an entangled superposition state. So this is one of the strongest arguments that, yes, the world is really quantum mechanical. And we can't just replace it by something else, certainly not by a local hidden variable theory.
But then what Wolfram says, and this is in chapter 9 of A New Kind of Science, he just says, well, okay, you know, this is no problem. Just imagine that sometimes there were long range threats.
between the particles, right? So usually space is local, but when two particles become entangled, then there's kind of like a thread that allows instantaneous communication between them, right? Problem solved, right? This is like the Wolfram method, right? If you can imagine a way that the problem could be solved, then it's solved, right? And so what I spend a lot of my review doing is just explaining, sorry, it still doesn't work.
It's sort of a statement that
If the measurements that Alice and Bob are going to make on the entangled particles have not been pre-decided, sort of were not known in advance, then the outcomes of the measurements on the particles also cannot have been pre-decided. They cannot be explained by hidden variables that go back to the beginning of time. They must be sort of genuine new randomness.
or otherwise you get a violation of locality. So that was kind of the argument. And like I said, I just made that in 2002, buried in my review of Wolfram's book. Now that same conclusion a few years later became famous when John Conway and Simon Cotion said something very similar in 2006 and they called it the free will theorem.
If humans have free will, then subatomic particles must also have free will. That got all over the popular press. I would never have used the term free will here because I would say we could equally well just talk about randomness. I might have called it the freshly generated randomness theorem.
the the
Wolfram never really accepted that. I think most of the community did. He did not. But if you look at what he's done more recently with the Wolfram, I think he called it the Wolfram model of physics, what he basically does is he just says, okay, well, wherever we have a result that we can't explain classically, then we'll just graft on the relevant part of quantum mechanics.
Right.
You know, and also like we will say we can derive general relativity except the derivation basically be we like crib from a general relativity textbook. We just find out what the Einstein's equations are and we say, okay, well, whatever is the cellular automaton, it's presumably it's something that satisfies those equations.
Right? So it's like, you know, it's not sort of playing by the rules of physics, right? Where you have to, you have to actually, you know, mathematically derive these things, right? From some simple starting postulate. And then ideally, you know, make a novel prediction, right? That's the that's the gold standard.
One thing that I talked to Wolfram in person a couple years ago when he was in Austin. One thing that I kept trying to get clarity from him about was does he predict that scalable quantum computers can work or not? He would not give a clear prediction.
This multi-way theory suggests that maybe quantum computers can't work, but if it turns out that they do work then the theory can accommodate that also.
Have you read any of the papers by Jonathan Gerard?
P and NP are two of the most fundamental complexity classes, which are just classes of problems that are solvable with different kinds of computational resources. P stands for polynomial time.
And it's the class of all of the yes or no problems that a conventional computer, you know, a deterministic digital computer like the one that we're using could solve using a number of steps that grows like a polynomial function of the of the number of input bits. OK, so yeah, and that's our sort of rough and ready criterion for when an algorithm is efficient.
If it's running time scales polynomially with the length of the input. This is not a perfect criterion because an algorithm that took n to the 10,000 time would be wildly impractical. But what justifies it is that usually when something is solvable in polynomial time, the polynomial is something like
and
So that's why from the 1960s onward, the polynomial versus exponential distinction kind of became fundamental to complexity theory. And so P is just all of the yes or no problems that are solvable by some algorithm that has polynomial scaling.
What are some examples of problems in P? If I give you a string of text and I ask, is it a palindrome or not? Any kind of basic arithmetic. Most of the things we do with our computers, to be honest, are things that are in P.
More interesting examples like, given a map, is every city reachable from every other one? Given a graph, is it connected? That's in P. Given a bunch of boys and girls and who is willing to date whom, can you pair them off so that everyone is happy with their partner? That's called the matching problem.
That's also in P. And graphics like ray tracing, are you able to say whether that's P? Yeah, I think the basic problems underlying ray tracing would be in P also, yes. And these are all things that one can learn as an undergraduate in computer science, right? There are also much more non-trivial examples. Given a number written in binary, is it prime or composite?
That's in P. It was only discovered to be in P 20 years ago. That's called the Agrawal-Kyle-Saxena or AKS theorem. So they gave a breakthrough algorithm. Before that, we had known probabilistic algorithms, but they gave the first deterministic polynomial time algorithm for primality testing. If the number is composite, then these fast algorithms do not tell you the factors.
Finding the factors seems to be a much, much harder problem, which we can come back to. But determining primality is in P. Given a bunch of linear constraints, is there a way to satisfy all of them? That's called the linear programming problem. Again, it's in P for very nontrivial reasons.
Okay, so a lot of interesting things are NP. Okay, but now there's this potentially larger class, which is called NP. Now that does not stand for not polynomial, which, you know, some people think it stands for non-deterministic polynomial time. Okay, so what does that mean? So NP is the class of all the problems where sort of if there is a solution, then you can check the solution in polynomial time.
So if the answer is yes, there is a solution, then there is some witness, some proof that if it's given to you, then you can check in polynomial time that, yeah, I guess that works. So let's go through some examples. Solving a jigsaw puzzle. Imagine a jigsaw puzzle with no picture on it.
You're just trying to fit all the pieces together. That might be incredibly cumbersome to do. You might have exponentially many possible ways of fitting the pieces together to try. But if someone has solved the puzzle, then they just have to show it to you. You can easily see that, yes, they have solved it. The famous traveling salesman problem where you're given a bunch of cities and you're asked, let's say,
Is there a route that visits every city with at most 5,000 miles of total travel distance? Again, if there are N cities, there might be N factorial different routes that you would have to try out. With hundreds of cities, that could be massively expensive, but if someone finds a route that works, then they just have to show it to you, and it's easy to check. That's also an NP problem.
You know, I ask, let's say, does this number have a prime factor that ends with a three? Or some, you know, question like that, right? Where, again, you know, the fastest algorithms that we know for factoring take some sort of exponential time, at least the algorithms for classical computers, okay?
I actually take time that's like exponential in the cube root of the number of digits. That's called the number field sieve. And that's extremely important for cryptography.
I agree. If you just want to know if the number is divisible by three, that isn't big.
In fact, if you want to know if it's divisible by any fixed number, that's NP. But if I don't tell you the prime factors and they're like, let's say they're all enormous and now you have to find them, then that we don't know how to do in P. But it still is an NP problem because if someone succeeds in factoring the number, then they just have to show you the prime factors.
And at least with a computer, it's easy enough to multiply them. And as I said, it's even easy enough to check that those numbers are prime. So factoring is another NP problem. OK, so now the P versus NP question is just the question, well, how do these classes relate to each other? So it's pretty clear that P is contained in NP.
Right. So, you know, if you can solve a problem yourself in polynomial time, then you don't even need this witness. Right. You just, you know, you just have the answer to it. Right. But now the profound question is, is NP contained in P? Okay. So if I can efficiently recognize the solution to a problem, then does that imply that I can efficiently find the solution? Okay.
And so that's the P versus NP question. And as soon as you see this question, some people, it takes time to convince them of why it's even a question at all. Because they would say, well, obviously not. Obviously, there are cases where you're going to need brute force search. And brute force search is going to take exponential time.
The trouble is that as we discussed with the example of the matching problem or the linear programming problem or the primality problem, there are cases where naively it looks like you have to try exponentially many possibilities. But if you think about it more, then there is a clever shortcut that only takes polynomial time. So what P versus NP is asking is, is there always a clever shortcut?
for every problem where we can efficiently recognize a correct answer. And so you know that is for half a century that's been sort of the central unsolved problem of theoretical computer science and I think it's now recognized as one of the central unsolved problems in all of mathematics.
So, two questions. One, why is this the largest unsolved problem to you? You think this is the greatest unsolved problem in math and potentially even physics? And then number two, this sounds... It's not a physics question, right? I mean, we could find a related physics question by asking, for example, can the all NP problems be solved in polynomial time by any physical means?
Right. Which could include a quantum computer or could even include, you know, a hypothetical quantum gravity computer or whatever. Right. You know, then we'd be asking a physics question. Right. But, you know, P versus NP is a question that can be purely stated mathematically. Right. Meaning it has some platonic answer. Right. We just we just haven't we just haven't proven what it is.
What I meant was that I heard you say something along the lines of, look, the Clay Institute has many problems. Yes. And one of the problems is a physics problem, the Yang-Mills problem. Yeah. Well, you could say it's a mathematical physics problem. It's a math problem that came from physics. But I mean, the argument that I give is just that if P equaled NP,
And furthermore, if the algorithm were really efficient in practice, so not like n to the 10,000, but you know, n squared or n or something, then that would not only let you solve the P versus NP problem, that would let you solve all of the other clay problems, you know, the Riemann hypothesis, the Yang-Mills problem, right, and all the other ones. And why is that? Because it would mean that we could just ask our computer, right, say like, like,
Is there a proof of this theorem in this formal language, like Zermelo-Frankel set theory, that is at most a million symbols long or at most a billion symbols long? What it would mean if P equal to NP would be that if such a proof existed, then you could find it using a number of steps that only scaled polynomially with the length of the
Right. So like in, you know, only polynomially more time than it would take to write down the proof, you could actually find the proof. Right. And so in some sense, you know, mathematical creativity, uh, would have been automated. So a proof of P equals NP would automatically have well, well, okay. I mean, I mean, I mean, the, the, the, the, the caveat is that the algorithm would have to be efficient in practice. Right. But, but, you know, the, the question like, you know,
Is there a proof of this theorem in some purely formal language, like first order logic, ZF set theory, with at most this number of symbols? That is an NP problem, literally. And so that means that if P equaled NP, then it would also be a P problem. Can you explain what quantum supremacy is?
So quantum supremacy is a term that was coined by the physicist John Preskill in 2012 and it's just referring to sort of the first experiment that you can do with a quantum computer that solves some benchmark problem.
much faster than we believe that it could be solved with a classical computer.
Okay, so like it can't just be like simulate this physical system with all of its noise, right? You have to give a mathematical specification of what calculation you want so that that same calculation could be done either on a quantum computer or on a classical computer. Okay. And what we want to see is that the quantum computer is faster, you know, not just in classical brute force, but the fastest classical algorithm that anyone can can design.
And we want to see that that is so for sort of inherent scaling reasons, you know, not just for sort of accidental reasons of hardware, but you know, the quantum running time is sort of scaling polynomially in a way that the classical run time is scaling exponentially with the size of the problem. Okay, so that's quantum supremacy. And so Preskill coined this term in order to describe sort of the kind of thing
that I and others had been talking about in the year or so prior. My then student Alex Arkhipov and I, in 2011, we had a proposal called Boson Samplet, which was a proposal for a very rudimentary kind of quantum computer.
For example, it could be built using photonic components. You just generate a bunch of single photons, you send them through a network of beam splitters, and then you measure where they end up. And that's it.
That's all you do here. So this is we don't think that this is universal for quantum computation or even universal for classical computation for that matter, right? It's like in some ways it's a very, very limited model of computation. And yet if you ask like, okay, what is it doing? Well, it's sampling from a probability distribution.
Each time you run the experiment, you feed in the photons, they will typically end up in different places.
right because you know they sort of move around randomly you know and you know i mean they they they they they or or rather they evolve in a superposition state but then when you make a measurement you collapse the superposition okay and you just see one outcome uh so you probably never even see the same outcome twice you know sometimes there's two photons here one here zero here you know sometimes there's zero here zero here you know three here and so forth all right so
So you see these different distributions, sorry, you see these different lists of photon occupation numbers, numbers of photons in each sort of output port. But then you ask the question, okay, you could ask, well, what is this useful for? We don't really have a good answer to that. But then you can ask a different question, which is how hard would it be for a classical computer
to
If there were a classical algorithm that could sample from exactly the same probability distribution as the sort of ideal version of this photonic experiment, then we say that would have sort of staggering implications for complexity classes. It wouldn't quite mean that P equal to NP, but it would mean something that's sort of morally almost as bad as that, which is called the collapse of the polynomial hierarchy.
It's sort of like a more abstract version or higher up version of P equaling N. We showed that that would follow if you had a fast, exact classical simulation of boson sampling. And then if your classical simulation is only approximate,
Which is the more physically relevant case, because after all the experiment itself isn't perfect either, right? In the approximate case, we believe that that would collapse the polynomial hierarchy, but there we had to make yet another conjecture. And I would say the status of that remains unresolved to this day.
okay but but you know it's it's at least it's at least seems very plausible that you know and we showed that like you know here is some well stated problem about a function of matrices called called the permanent and if this problem is sufficiently hard then boson sampling is hard to simulate using a classical computer even approximate okay so
Yes, so we did that and then independently from us there were others like Bremner, Joseph and Shepard who were having related ideas about different kinds of rudimentary quantum computers that were not obviously useful for anything but that at least seemed to give rise to these probability distributions that are hard to sample using a classical computer.
Can you encode these hard problems into the amplitudes of a quantum computer? But then we realized more and more as we worked on it that
Maybe the experimentalists will care about this because what we're talking about are devices that seem potentially much, much easier to build than a full error corrected quantum computer.
Basically, if you could just generate 50 to 100 photons and send them through a beam splitter network and then measure where they end up, that should already be enough to do a boson sampling experiment that is hard for a classical computer, hard for the biggest supercomputers in the world to simulate. Then we explicitly talked about that and then the quantum optics experimentalists got very excited about it.
and you know they decided to start doing it you know initially like in 2013 it was like with three photons four photons this is all you know of course trivial for a classical computer to simulate right yeah yeah the difficulty ideally you know you would expect it to go maybe like two to the power of the number of photons
But then what happened was that in 2014, Google hired John Martinez, who was maybe the top superconducting qubits experimentalist in the world.
and he said we want to build a 50 to 70 qubit quantum computer that's programmable using superconducting qubits and we want to do something cool with it. And what is there to do with 50 qubits that's cool? Well, there's not a whole lot, unfortunately. Most of the actually useful things, they might need like
you know, hundreds to thousands of qubits and then crucially, you know, of a much higher quality than, than Google was able to make where you could do like thousands of layers of gates, you know, and they couldn't do that. They can do maybe 20 layers of gates, right? Uh, but so, so, so, so what you could do while they, they realized, okay, we can do some version of those on sampling, right? Except, you know, except now more, more adapted to their hardware.
So we talked to them about that, and we said, yeah, that sounds reasonable. But we then had to adapt the theory from boson sampling to superconducting qubits, to the kind of thing that they were building. So we did that in 2016, 2017. And then in 2019, Google announced that they had actually done this.
So they built a 53 qubit device called Sycamore and they used it to sample from some probability distribution over 53 bit strings that you get by just applying like a random sequence of quantum operations to these qubits.
And then, you know, at first they were saying, well, with the best classical algorithm that we can think of, it would take 10,000 years to do the same thing on a supercomputer. Right. And the press loved that. Right. And they ran with that number and that, and that turned out to be wildly overoptimistic. Right. So I could imagine Mishio Kaku would love that. Yes. Oh, I'm sure he would. Right. But, but you know, the, the, the, the hard part in quantum computing, if you want to be intellectually honest about it,
is that you always have to compare against what is the best thing that anyone can do with a classical computer. And you're only winning if you do better than that. And what's the best thing that you can do with a classical computer is often far from obvious. After all, that's what the P versus NP question is about.
Right? Right. So so so so and indeed what happened over the next couple of years is that people got better and better at simulating the Google type of experiment with classical computers by, you know, taking advantage of the noise and taking advantage of the fact that each qubit can only sort of talk to its nearest neighbors. You know, so you can you can sort of take advantage of all the the current technological limitations of Google's experiment.
in order to simulate it faster with a classical computer. I would say that the current situation is that the Google chip is still somewhat better than any classical solution that we have for the task of simulating itself. If you measure, let's say, by the total energy cost,
Right or by you know the the money that it takes to run it or the co2 that's emitted by steps well by the the trouble with steps is that you know you like with a Classically you can always roughly have the number of steps by just using twice as many cores Okay, so these problems are very very parallelizable
Right. So, you know, you can always do it faster if you're willing to like go to AWS or whatever and just say, you know, I want, you know, this, this massive number of cores, right. But then, you know, it's interesting, right. But then at some point for the comparison to be fair, you know, you should maybe be talking about money or you should be talking about, you know, the energy, you know, the electricity that gets spent.
And if you look at metrics like that, then I think that the quantum computer still wins on some tasks, but only by a couple orders of magnitude at this point. That sounds a bit human though, because if we're measuring it by money, firstly, that's human. But if we're measuring it by energy, isn't it then not based on the algorithm, but based on our current cores and maybe in the future, Apple comes out with M5? Of course it is. Of course it is. So you could say that you are fighting against a moving target, right?
like quantum supremacy could be achieved and then unachieved because you know the classical classical hardware and software will both get better you know and so if you want to claim that a quantum computer is better for something right then you know you may have to keep improving the quantum computer you know just for for that statement to still be true okay now now the hope let's be clear okay the hope is that eventually you have an error corrected
you know programmable quantum computer and at that point you can scale up to as many operations as you want on as many qubits as you want okay and at that point you know you could use like millions of qubits to factor some enormous number right that like unless there's a breakthrough in classical algorithms that just cannot be done classically within the whole lifetime of the universe right so that's the eventual goal okay but we're not there yet okay
And what we can do today are these sorts of sampling experiments, where we're solving problems that don't have a single right answer. We're sampling from a distribution over possible answers. And a key drawback of these problems is that
Even just to verify what the quantum computer is doing already appears to take exponential time with a classical computer. Which means that we're sort of inherently limited in how far we can scale this. Like, you know, if you scale it to 300 qubits, even if it worked, how would you ever prove it? How would you ever convince a skeptic of what you had done? So we're sort of forced to stay in this regime where the advantages that we can get over classical computers are relatively marginal ones.
But at least we can now do that. Five years ago, we could not even do that. And now we can. I think it's a step forward. I think it's taught the experimentalists a lot about how to actually integrate large numbers of qubits. And maybe scientifically, the most important thing that they learned from these quantum supremacy experiments
was that like the total amount of signal you get what's called the circuit fidelity is well it's falling off exponentially with the number of operations you know which sounds kind of bad right but it's but the good news is that it's merely falling off exponentially and not faster than that.
Okay. So basically the total fidelity, you know, like let's say, you know, each individual two qubit operation has a fidelity in Google's experiment of about 99.5%. Right. And there's about a thousand such operations. Okay. And so, so then the total fidelity that you get for the circuit, it looks like just 0.995 to the power of a thousand. Right. Uh, you know, which is like the simplest prediction that you could possibly make.
And as long as that remains true, then ultimately quantum error correction should work. So the people who believe that scalable quantum computers are impossible, such as Gil Kalai is a famous one, what they basically have to believe is that either quantum mechanics itself is going to break, which let's face it, that would be far more exciting than a mere success in building a quantum
Sure. That would be a revolution in physics, or else they have to believe that there's some sort of conspiratorially correlated errors that will violate all the assumptions of the theory of quantum error correction. But from the quantum supremacy experiments, we can now say we see no sign of those conspiratorially correlated errors. You're referring to super determinism?
No, I'm not. Super determinism is so bizarre that it's not even clear that that would have any empirical consequences at all. That's just saying there's a giant cosmic conspiracy theory that just predetermined everything that would happen from the beginning of time. It was like, you can always believe that, but it's sort of explanatorily worthless. It has no power to explain anything.
The more interesting thing, if there were these conspiracies in the errors affecting qubits, that would be something that would be empirically observable. And if the correlations were strong enough, then conceivably that could even kill quantum computation. But there are some basic difficulties here. One is that it's very, very hard
design a model of correlated errors that only kills quantum computation and that wouldn't also kill classical computation. If you kill classical computation then you've proved too much because we know that scalable classical computers can be built. But then the other thing you can say is that from the quantum supremacy experiments we see no sign of these correlated errors. The errors look pretty independent and in that case
it's you know as long as that remains true then it's just a quantitative question you just have to get the the accuracy of each operation to be high enough like instead of .995 maybe .9999 right and then and then at that point quantum error correction should work
Now we both got to get going shortly and I want to end on the topic of consciousness. So why don't you talk about your critiques for IIT and then also what the pretty hard problem of consciousness is. But before you do that, I just wanted to ask you a yes or no question about if you saw Tim Palmer's
response to your critiques on super determinism in his recent article, Tim Palmer's article on super determinism without conspiracy is listed in the description. And you should know that Tim Palmer was on the theories of everything podcast. And that link is also in the description. He was on with Tim modeling at the same time talking about the interpretations of quantum mechanics. Yeah, I mean, I say I think I think it is a conspiracy. I mean, I think that he redefines terms in an utterly perverse way.
in order to
like orders of magnitude more plausible to me than these right these are just you know these people have succeeded at like getting out to the public right and putting their message before the public but like scientifically i regard these as worthless ideas so um uh so so okay um yeah uh but but but now uh uh consciousness yeah so so so so integrated information theory is another thing that i think
has, you know, okay, you know, maybe like it was worth trying, it was worth thinking about, but that has also become, you know, a worthless idea, a pathological idea. Okay. So it's a proposed, you know, theory of, of consciousness, or at least of what things are conscious and what things are not, uh, that was, uh, um, originated, originated by Giulio Tononi. Okay. And, uh, you know, also,
uh... pursued by you know a bunch of other people such as christoph coke uh... i think you know max tagmark uh... was into it and and basically what it says is that there is some you know you could take any complex system and then there is some quantitative measure that you know that that that you can calculate uh... for that system that somehow measures how interconnected all of its components are right and and the war you know that they call that fee
The larger is that fee measure, the more conscious the system is. You could say, what is this fee? Well, the actual definition of it keeps changing. There's not actually the one fixed thing that you can critique. They keep fiddling with the definition of it.
And if you read the papers about it, what they say is, well, we have these axioms of conscious experience and then we derive phi from these axioms. But actually, there's no derivation at all. It's sort of like pseudo mathematics. It's like they state the axioms and then at some point,
The axioms are not even clear enough for me to really understand what they are saying. But at least the fee measure seems reasonably clear. Once you've decided what are the subsystems, what does it mean for a subsystem to be connected to each other, and so forth.
then you know and you decided which version of fee you're working with then you know you can actually calculate these numbers okay and then you know their their case you know they're like they were neuroscientists and they said well there seems to be much higher connectivity in the cerebrum than in the cerebellum for example right and the cerebrum is associated with consciousness and the cerebellum is not right so that was
That was the kind of evidence that they gave. I wrote a blog post about this nine years ago where I pointed out that we could easily invent systems that have massively higher fee than the human cerebrum.
Right. But that are just like a gigantic grid of XOR gates or something like that. Right. Without processing. Yeah. Well, OK. Yeah. Maybe, you know, they do process something like they compute the XOR of a bunch of bits. Right. But but it's all like completely regular. It's like there's not even anything interesting or intelligent going on there, let alone anything conscious. Right. And yet, you know, if you calculate this number that they put forward, then you'll get
that the connectivity between the different components can be arbitrarily large, just depending on how big you make the thing. To me, that seems like a reductio ad absurdum. The theory is just making an utterly wrong or absurd prediction.
and therefore, this connectivity, it might be correlated with consciousness in various cases, but it cannot be identical with consciousness.
The problem is that you're just using your intuition but you have to rely on the theory and what the theory tells you is that this grid of
This giant grid of XOR gates is conscious. In fact, it's much more conscious than you are, right? And you have to be bold and just believe what the theory says. And, you know, and my response at that point was like, okay, if a theory is sort of getting right, you know, the things that, you know, the cases where we already thought, you know, we knew the answers, right, then you might be interested in, you know, what does the theory say about the really hard cases? Like, let's say,
about a fetus or about a coma patient or about an earthworm or about an AI program, right? But if the, if the, you know, your measure of consciousness is already, you know, telling you that a potato chip bag is conscious, right? Or that, you know, any old, you know, sort of uninteresting physical system, you know, is conscious just, you know, because of this sort of, you know, this sort of, you know,
This theory has just continued
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A bunch of philosophers and neuroscientists who said that integrated information theory is pseudoscience and then there was a response and I didn't even wade into this because I felt like I had said my piece a decade ago.
It's like, yeah, these are ideas that are worth exploring, but then once you see that you make a prediction that's that badly wrong, then I think you have to go back to the drawing board. You have to say, okay, well, then this is not a measure of consciousness. Instead, they just keep trying to rescue the theory, and at some point, that kind of thing does degenerate into pseudoscience.
So it sounds like what he's saying is that what you think of as a reductio ad absurdum is actually a productio ad correctum. You're proving something correct and we should listen to the theory. Yeah. So why can't we follow that same logic when it comes to the many worlds and say, look, on one hand, some people can say it's a reductio ad absurdum. You're predicting all of these other worlds. Yeah. But then Sean Carroll may say, no, no, we should be listening. Well, I would say that the difference is that quantum mechanics gets, you know, every single case that we can check, it gets the right answer. Right.
right? You know, that's been true for 100 years. There was zero counterexamples, right? And that's now even with very, very complicated, entangled quantum systems. And so then, you know, it is natural to just want to do the extrapolation and say, you know, assume that this continues to be true up to arbitrary scales, then what does that mean? Because we've seen no sign otherwise, right? But like with consciousness, like I feel like if you want to decide what is or isn't conscious,
Or at least not having anywhere near as much.
Right. Yes. Yes, exactly. It's not having nearly as much. If you say that this glasses cloth has much more consciousness than I do, then I say, what do you even mean anymore by the word consciousness? I don't think you're talking about the same thing that I was trying to talk about. Right. Right. Yeah. Okay. And then the pretty hard problem consciousness is... Yeah. That's just the problem of... Okay. So the hard problem of consciousness is, you know,
Articulated by the philosopher David Chalmers in the 90s is to explain why there is ever anything that it is like to be. Explain how subjective experience can arise out of mere matter or mere physical systems obeying the laws of physics. In some sense, this is a problem.
that goes all the way back to Democritus in like 400 BC. And you have a book on this. I do. I do. Yeah. I mean, I mean, Democritus already stated this problem in a remarkably modern way. Right. And, you know, and certainly Descartes, you know, asked this question centuries ago. So this is, you know, one of the great problems of philosophy or maybe, you know, the great problems of all of human existence. And it's not even clear what an answer would look like.
What kind of thing could be an answer, let alone how to find that answer? Whenever you encounter something that is just way too hard, whether it's the hard problem of consciousness or whether it's P versus NP, then it's natural to want to scale back and say, is there an easier related problem that we can make progress on? What I call the pretty hard problem is just the question,
which physical systems are associated with consciousness and which are not. You could imagine answering that without having to answer among the ones that are conscious, like why are they conscious or how. You could imagine just giving a criterion that agrees with intuition in all the cases that we can think of and that actually calculates
Well, professor, thank you for spending so long with me. Sure. It was so much fun. Yeah. All right. I hope to speak with you again. Yeah. All right. Take care. Talk to you later. Bye bye.
If you enjoyed this podcast, then one that I recommend is the one with Tim Palmer and Tim Modlin as they're both superlative explicators of quantum theory and super determinism was a central tenet of that conversation. The link is in the description. Also, if you'd like to donate as we've had trouble monetizing the channel with sponsorship, then please do so.
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▶ View Full JSON Data (Word-Level Timestamps)
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"text": " Scott Aronson is a professor of theoretical computer science at UT Austin, particularly known for his work on quantum computing and complexity theory. Today we talk about free will, we talk about consciousness, complexity classes, super determinism, and even quantum computing, that last one in particular, we talk about what quantum supremacy actually means rather than how it's promulgated by people like Michio Kaku and other popularizers of science."
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"text": " Scott explores and teaches these ideas with extreme simplicity, as well as joy, which is a rare combination. Welcome to this channel. My name is Kurt Jaimungal. And for those of you who are unfamiliar, this is Theories of Everything, where we delve into the topics of mathematics, physics, artificial intelligence, and consciousness with depth and rigor. This commitment stems from a recognition that popular science articles often peddle superficial falsehoods, leaving a discerning audience like yourself yearning for technical accuracy and substantive discourse."
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"text": " Welcome, Professor. It's an honor to speak with you. I've been following you for a few years. Thanks. Great to be here. I mean that in a non creepy way. What got you interested in computational complexity? Well, I mean, I got into computer science as an adolescent because I wanted to create my own video games mostly. And so I learned, you know, what I could about programming."
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"text": " What kinds of programs could be written, you know, couldn't be written at all, you know, and, and, and, you know, I kept wondering about that. I mean, I, when I first saw Apple basic or, you know, and then GW basic and Q basic and, you know, these, these ancient languages, I figured, okay, but to make a really sophisticated program, clearly you would need a more powerful language, right?"
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"text": " It was a second revelation to me that no, you just very rapidly hit this ceiling of touring universality where just a very simple programming language becomes capable in principle of expressing anything that any programming language could express."
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"text": " One of the biggest remaining questions is about efficiency. Among all of the problems that computers can solve, which ones can they solve in a reasonable amount of time or a reasonable amount of memory?"
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"text": " 15 or 16, I would have learned what is the P versus NP problem. And you know, and that problem is just so stunning, you know, that humans could ask something, you know, so basic and yet, you know, so concrete, you know, that has a definite answer one way or the other."
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"text": " And, you know, I had fantasies for, you know, a few months that, well, you know, all of these, these experts, you know, must have gotten, you know, stuck in a rut and I'll come in as a 15 year old and, you know, with no preconceptions and I'll polish this problem off. You know, I think it was good to have that experience once in my life, you know, once was enough to get, you know, to get disabused of that."
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"text": " At some point I learned about quantum computing, which we can talk about more, but that actually changes the rules of computational complexity based on our best current theory of physics. That was then irresistible to understand because somehow these very basic questions in physics and in computer science were merging with each other."
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"text": " And it was all a story about computational complexity. If you don't care about complexity, then there's basically no reason to build a quantum computer. Anything it can do can be simulated by a classical computer, albeit exponentially slower. So you need complexity theory to even pose the questions about what are quantum computers good for. But this was a field where there was a lot of low-hanging fruit in the"
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"text": " late 1990s when I started really getting into it. And, you know, I was also extremely interested in AI. I thought maybe I would do that. But, you know, again, there was the difficulty that AI so often boils down to in practice to software engineering, which I wasn't so good at. Now it was when I saw I was an undergrad at Cornell."
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"text": " When I applied for grad school, I got into where I really wanted to go, which was UC Berkeley. But it was the AI people who recruited me there, not the theory people. But I secretly, I guess, wanted to do quantum complexity theory. So after a year of doing AI, I switched. And then I ended up"
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"text": " You know, computational complexity in quantum computing ended up being interesting enough that I've spent more than 20 years of my life on them. And only now, finally, in the last couple of years, I'm circling back to AI with the stuff that I'm doing for OpenAI. Yeah, I'd love to speak with you about your work at OpenAI. First, is computational complexity, algorithmic complexity, and quantum complexity distinct?"
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"text": " Well, I would say that computational complexity is the whole field that studies the inherent computational resources that are needed to solve problems, and that includes time,"
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"text": " memory it could it could include energy randomness parallelism and quantum computing is is a part of that right you know you could say or you could say quantum this is another computational resource that you can throw you know throw into the mix and then see how it changes things so so so yeah but but but it is the field that studies sort of the inherent"
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"text": " capabilities and limitations of algorithms. Sometimes people who are only interested in just solving a practical problem with the best algorithm that they can find for that problem, they might not call themselves complexity theorists. They might just be algorithms people. But as soon as you start asking the question, what is the best algorithm for this task?"
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"text": " In terms of the scaling of resources as the input gets larger and larger, how do I know that it's the best algorithm? What else would it imply if there were a faster algorithm? As soon as you start asking things like that, then you're doing complexity theory."
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"text": " It sounds like it's easy to show that something is a more efficient algorithm than another, but to show that something is the best. Yeah. How do you go about doing that? Yes. Well, a good question. You know, the field has been struggling with that for half a century. So, yeah, in order to give a faster, you know, in order to show that there is a faster algorithm to solve a given problem, typically the way you do it is you just give that algorithm."
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"text": " You know, you, you give it, you know, and that could already be very non-trivial because you have to analyze the algorithm. You have to prove that it works and you have to prove that it actually terminates after this reasonable amount of time. Okay. So that can, that can already be, be non-trivial. Okay. But, but now, you know, if you ask, is this the best algorithm, you know, how do we know it's the best? Okay. Now you're trying to prove a negative, right? And that is inherently"
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"text": " The main reason why we view it as a goal to strive for at all"
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"text": " is that computer science was born with knowledge about its own limitations. When Alan Turing introduced the Turing machine, which is the mathematical model for what a computer is in the 1930s,"
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"text": " He also, as the key application of his new theory, proved that certain problems are not solvable by any Turing machine in any amount of time. This was the famous unsolvability of the halting problem. It built on Gödel's incompleteness theorem, which had been proved just five years prior."
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"text": " I give you a program and you have to determine whether it ever stops running when run on a blank input."
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"text": " And Turing showed that there is no program to solve this problem in any amount of time. And the argument is basically self-referential. You say, well, suppose that there were such an algorithm, then we could contrive things in such a way that that algorithm would be fed its own code as input. And then it would have to do the opposite of whatever it does. It's like if it halts, then it would have to, you know, when run on itself as input, then it would have to run forever."
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"text": " And if it runs forever when run on itself as input, then it would have to halt. And since that's a contradiction, the only conclusion is that the program can't have existed. And so we've known since the beginning of computer science that you can use these sort of self-referential methods to understand something about the limitations of any algorithm."
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"text": " In a kind of magical way, without having to roll up your sleeves and delve into the details of what the Turing machine is doing. And then in the 1960s, some of the first complexity theorists, like Joris Hartmanis, who passed away recently, and Richard Stearns, managed to go further. And they used similar self-referential arguments to show, for example,"
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"text": " There are problems involving n-bit inputs that are solvable in n-cubed steps but are not solvable in n-squared steps. There are other problems that are solvable in n to the fourth steps but not in n-cubed steps. Can you give an example? Yeah, the simplest example would just be I give you a program and now you have to decide whether it halts in n to the fourth steps or not. That is solvable in slightly more than n to the fourth steps."
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"text": " But, you know, a sort of scaled down version of Turing's argument shows that it is not solvable in N cubed."
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"text": " And basically, basically, because if it were, then the program could predict what it itself is going to do faster than it can do it. Okay, and it's kind of like, you know, the like, like, you know, this is like a paradox that a five year old can understand. It's like, you know, if I could, you know, if I if I knew for certain, you know, whether I'm going to raise one finger or two fingers, you know, 10 seconds from now, then I could just resolve to do the opposite of whatever I predicted I would do. And so, you know, so and so and so that's not possible."
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"text": " To you, does this touch on free will? Some people think it does. I mean, I mean, I tend to think that, you know, if if if there were a computer in another room, you know, and you know, it ran faster than my brain does, and it perfectly predicted what I was going to do before I do it. And, you know, maybe it just it leaves its prediction in a sealed envelope, you know, but then after I take the action, then we can open the envelope and we can see that it"
},
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"text": " Perfectly predicted what I would do I would say you know that that would that would really profoundly shake my sense of free will you know just speaking speaking personally right and and I would say that based on the known laws of physics we don't actually know whether that prediction machine can exist or not"
},
{
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"start_time": 895.623,
"text": " It comes down to questions about how accurately would you have to scan someone's brain? Would you have to go all the way down to the quantum mechanical level? Would that not be necessary? I would say that the thing that most people don't realize is that this is an empirical question. Maybe whose answer will someday know, but we don't know it yet."
},
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"text": " Why is the sealed envelope important? Because if I saw the prediction, then I could resolve to do the opposite."
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"text": " Yeah, so if this machine existed, does it still say something about your free will if you weren't able to look at it and you could go against the wishes of the machine or the predictions of it? Well, yeah, I mean, you could say if that machine cannot be reliably built, you know, if any attempt to build it consistent with the laws of physics, you know, fails, then that seems to me like about as far as science, you know, could possibly go in saying that, well, you know, there seems to be something that, you know,"
},
{
"end_time": 994.497,
"index": 41,
"start_time": 978.916,
"text": " You know that corresponds to part of what we mean by free will right there is this inherent unpredictability to our actions. And you know and conversely if the machine did exist and that seems to be."
},
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"end_time": 1010.213,
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"start_time": 994.991,
"text": " to me like about as far as science could possibly go to towards saying, you know, actually, you know, free will is an illusion, right? Not, you know, not just begin in some abstract metaphysical way, but because, you know, here is the machine that predicts what you will do, you know, look at it, try it out."
},
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"start_time": 1010.674,
"text": " Yeah, you had a blog post on Newcombe's paradox. Yes. Can you please outline it and then what your proposed resolution is, if it exists? Sure. A Newcombe's paradox is the thing where, you know, we imagine this super intelligent predictor, you know, just like I was talking about before, you know, that this this sort of machine or being that that, you know, knows what what, you know, you're going to do before you do it. And it puts two boxes on a table."
},
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"end_time": 1054.445,
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"start_time": 1038.319,
"text": " Okay."
},
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"start_time": 1054.735,
"text": " Or you can take both of the boxes. But now the catch is that the predictor has told you in advance that if it predicts that you're going to take both boxes, then it will leave the first box empty. So it punishes greed. Yes, right. If it predicts that you're going to take only the first box, then it puts a million dollars in it."
},
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"end_time": 1107.995,
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"text": " Okay, so, and let's say that the predictor has played this game with, you know, a thousand people before you and it's never been wrong. Right. So then, then, you know, what do you do? Do you, do you, you know, as, as, you know, people have actually made it into verbs, you know, do you one box or do you two bucks in the, in the, in the new comb paradox. And, uh, uh, you know, and there seemed to be like basic principles of rationality that, you know, that you could use to, to, to prove either answer is correct."
},
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"end_time": 1115.333,
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"start_time": 1108.387,
"text": " On the one hand, everyone who takes only the first box ends up about a million dollars richer."
},
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"end_time": 1141.288,
"index": 48,
"start_time": 1116.049,
"text": " than the people who try to take both, right? And, you know, by the whole setup of the problem is that, you know, that's because the predictor knew and, you know, it's over. But on the other hand, you know, by the time you're contemplating your decision, the million dollars is either in the box or not, right? And so how could your decision possibly affect, you know, what is in the box? It would seem like it would have to be a backwards in time causation."
},
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"end_time": 1168.916,
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"start_time": 1141.613,
"text": " Right. And therefore, you know, you know, whatever is in the first box, you're going to have a thousand dollars more than that if you take both boxes and therefore you should take both. Right. So, you know, so we can prove two contradictory answers. You know, that is the basic setup of a paradox. And, you know, and people have argued about this for half a century. There is an enormous literature on this problem and many different points of view."
},
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"end_time": 1189.411,
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"text": " I had a blog post back in 2006 where I suggested what seemed to me like the natural resolution of this. Since then, I've learned that other people have had broadly similar ideas. Some of them do cite that blog post of mine."
},
{
"end_time": 1217.637,
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"text": " But, you know, my resolution of the Paranax was, okay, I think that, you know, in this scenario, you should take one box, right? You should one box. Okay, but the question is why, right? The question is, how can we possibly explain how your decision to one box could affect the predictor, could affect, you know, whether the predictor puts the money in the box? Okay, and now the key is, well, you know, we have to think"
},
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"end_time": 1247.568,
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"text": " harder about what the world would be like with this predictor in it. The predictor contains within it a perfect simulation of you. Whatever you're going to base your decision on, whatever childhood memory, whatever detail of your brain function, the predictor knows all of it by hypothesis. But the way that I would describe that,"
},
{
"end_time": 1269.326,
"index": 53,
"start_time": 1247.739,
"text": " is that the predictor has effectively brought into being a second copy of you, a second instantiation of you, right? And now, you know, the key is that as you're contemplating your decision, whether it's a one box or two box, you know, you have to think of yourself as somehow, you know, being both versions of you at once."
},
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"end_time": 1296.578,
"index": 54,
"start_time": 1269.65,
"text": " or perhaps you don't know which one you are. If you are the simulation being run by the predictor, well then of course your decision can affect what the predictor does. In the scenario that was hypothesized, you have to be radically uncertain about where you physically are, about what time it is,"
},
{
"end_time": 1324.94,
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"start_time": 1296.834,
"text": " These are the kinds of things that you have to worry about in a world where there really could be perfect predictors of yourself. A much more boring resolution would be to say, well, I'm not going to worry about Newcombe's paradox because I believe that this predictor cannot exist at all."
},
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"end_time": 1337.159,
"index": 56,
"start_time": 1325.435,
"text": " You know, as I said, I regard that as an empirical question to which we don't yet know the answer."
},
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"end_time": 1368.285,
"index": 57,
"start_time": 1341.135,
"text": " Two concepts that I see as related are the no cloning theorem and computational irreducibility."
},
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"end_time": 1393.541,
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"start_time": 1368.677,
"text": " So this is something popularized by Wolfram, which I know, you know, so I'll get you to explain it to the audience. But the no cloning may have implications that such a machine can't exist because it can't be a perfect copy of you. Yeah. OK. So so so yeah. So by the way, no cloning and computational irreducibility are two totally different things. You know, we can we can we can talk about both of them. But the no cloning theorem"
},
{
"end_time": 1419.241,
"index": 59,
"start_time": 1393.797,
"text": " is just a very, very basic fact about quantum mechanics. And it says that there is no physical operation that you can do that takes as input an arbitrary quantum state, an unknown quantum state, like let's say a qubit, a quantum bit, a superposition of a zero and a one, and that produces as output two identical copies of that state."
},
{
"end_time": 1438.558,
"index": 60,
"start_time": 1419.923,
"text": " I'm sorry to interrupt. I'm sure you've heard of Leibniz's law of indiscernible."
},
{
"end_time": 1452.022,
"index": 61,
"start_time": 1438.78,
"text": " This is a fact about physics that could have been false, but it is true because"
},
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"end_time": 1476.852,
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"start_time": 1452.295,
"text": " For a century, every experiment has told us that quantum mechanics is true. As long as quantum mechanics remains the basis of physics, then this is true, but it's not something that is a priori knowable. The sense of copying that I mean is copying the information. Think about classical bits. We all know that classical bits can be copied."
},
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"end_time": 1506.476,
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"start_time": 1476.852,
"text": " Okay, so Napster exists because the no cloning theorem is purely quantum precisely."
},
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"index": 64,
"start_time": 1506.476,
"text": " Yeah, so so classical information can be copied. Okay, but what we're saying is that is that in quantum mechanics, you know, even the information cannot be copied. Okay, so so quantum, we have to take a step back and say, you know, what is quantum information, right? It's"
},
{
"end_time": 1539.258,
"index": 65,
"start_time": 1523.951,
"text": " The basic building block in quantum information is what's called this quantum bit or qubit. This is a bit that doesn't have to be definitely zero or definitely one."
},
{
"end_time": 1559.855,
"index": 66,
"start_time": 1539.616,
"text": " We know how to deal with that classically. We could have a random bit that has a"
},
{
"end_time": 1585.367,
"index": 67,
"start_time": 1559.855,
"text": " 40% chance of being one and a 60% chance of being zero and until you look you don't know which it is So you kind of have to think about both possibilities, but then once you look you know, right? Okay now now that is not a qubit right qubit is more interesting than that Okay, because what the key thing that quantum mechanics says is that to every possible? configuration that a system could be in is"
},
{
"end_time": 1611.442,
"index": 68,
"start_time": 1585.606,
"text": " like zero or one in the case of a bit, you have to assign not just a probability, you have to assign a complex number. These complex numbers are called amplitudes. They're the basic quantities of quantum mechanics. For example, a quantum bit might have a square root of a half amplitude to be zero."
},
{
"end_time": 1639.07,
"index": 69,
"start_time": 1611.732,
"text": " and it might have a minus square root of a half amplitude to be one. They could actually be complex numbers, a real plus an imaginary number. And now when I make a measurement, then these amplitudes convert into probabilities. And the way they do that is one of the most famous rules in all of physics. It's called the Born rule."
},
{
"end_time": 1667.278,
"index": 70,
"start_time": 1639.411,
"text": " It says that the probability that I see a particular outcome is equal to the square of the absolute value of the amplitude for that outcome. So if I had an equal superposition, zero plus one divided by the square root of two, the qubit zero plus the qubit one divided by the square root of two, and then I measure it, then I'm going to see zero or one equally likely."
},
{
"end_time": 1691.561,
"index": 71,
"start_time": 1667.637,
"text": " There are other things that I can do besides just measuring the qubit to ask it whether it is zero or one. When the qubit is isolated, then these amplitudes can change in time by rules that are not familiar to our experience. I can take the list of all the amplitudes of all the possible states"
},
{
"end_time": 1711.135,
"index": 72,
"start_time": 1691.92,
"text": " And I can do something to my system, my particles or whatever, that has the effect of doing a linear transformation on that list of amplitudes. So you could say in some sense what quantum mechanics tells us is that"
},
{
"end_time": 1728.08,
"index": 73,
"start_time": 1711.357,
"text": " The operating system of the universe is linear algebra. It's matrices and vectors. My states are these vectors of amplitudes, these lists of complex numbers. My time evolution, the way the state changes over time while it's isolated,"
},
{
"end_time": 1750.094,
"index": 74,
"start_time": 1728.387,
"text": " is that I apply what's called a norm preserving linear transformation, also called a unitary transformation. These are linear transformations, matrices that always map unit vectors to other unit vectors. So they always preserve the length of the vector. But an example would be a rotation."
},
{
"end_time": 1774.633,
"index": 75,
"start_time": 1750.503,
"text": " I could take a qubit that is some intermediate state between 0 and 1, somewhere on the unit circle, where here's 0, here's 1, here's minus 0, here's minus 1, and I could rotate by a certain fixed angle, or I could reflect about an axis. These are unitary transformations that I can do."
},
{
"end_time": 1800.162,
"index": 76,
"start_time": 1774.821,
"text": " You know, and then I measure and then I, you know, measurement is a destructive operation. It sort of collapses me to a single outcome. But, but now, you know, the key phenomenon that, you know, that, you know, told physicists, you know, that the world works this way in the first place a century ago. Okay. And that, you know, and it is sort of the signature that something quantum is going on."
},
{
"end_time": 1826.51,
"index": 77,
"start_time": 1800.367,
"text": " is called interference. Okay, so now if I want to know, let's say, you know, how likely is a particle to get a certain spot on a screen, right? Then, you know, I have to, well, I have to calculate the amplitude for that thing to happen, right? You know, and then take the squared absolute value and that gives me the probability. Okay, but the amplitude is a sum of a whole bunch of contributions. Okay, one from every possible path"
},
{
"end_time": 1846.493,
"index": 78,
"start_time": 1826.749,
"text": " that the photon could have taken or the particle could have taken in order to reach this endpoint. And now if some of those paths that it could have taken make a positive contribution and others make a negative contribution, then they can interfere destructively and cancel each other out."
},
{
"end_time": 1874.087,
"index": 79,
"start_time": 1846.8,
"text": " meaning like the total amplitude will be zero and then the particle will never be found there at all. Whereas, and here's the even crazier part, if I close off one of the paths, like the famous two-slit experiment, or there are two slits that this particle could go through, if I block one of the two slits, well now I only have a positive contribution or only a negative contribution, depending on which slit I block."
},
{
"end_time": 1902.193,
"index": 80,
"start_time": 1874.428,
"text": " So now the particle can appear at that at that end point. OK, so to say it again, by decreasing the number of paths that a particle can take to get somewhere, I can increase the chance that it gets there. That is something that, you know, just just just, you know, forget about all the low level details of physics. Right. That could never happen if the world were described by conventional probability theory. Right. That, you know, that is sort of the sign that we have"
},
{
"end_time": 1931.032,
"index": 81,
"start_time": 1902.449,
"text": " you know, that to actually describe what physics is doing, we need different rules of probability, okay, which is a much more fundamental thing than you might have imagined the laws of physics even talking about at all. But they do. And so now, you know, okay, now we can come back to the no cloning theorem, since you asked about it. Now, you know, a qubit is going to have some state like"
},
{
"end_time": 1961.323,
"index": 82,
"start_time": 1931.357,
"text": " a times the qubit zero plus b times the qubit one, where a and b are amplitudes. So the state of one qubit is described by a two-dimensional vector, a list of two complex numbers, a and b. Now, what would it mean to make a copy of the qubit? It would mean that, well, now at the other end, I should have two qubits that are both in the state, a zero plus b one."
},
{
"end_time": 1988.029,
"index": 83,
"start_time": 1961.937,
"text": " Okay. And the way that in quantum mechanics, the way that we describe sort of two systems that are just sitting there next to each other and that are, you know, separate from each other that haven't interacted, right? It's a mathematical operation called the tensor product. Okay. But it basically just means, you know, we, we take like component wise multiplication. So if I have a zero plus B one,"
},
{
"end_time": 2017.927,
"index": 84,
"start_time": 1988.353,
"text": " you know, for my first qubit times a zero plus b one for my second qubit. Okay. Then I can, you know, just like in, in, uh, middle school algebra, you know, I can expand it out and I can say that's an amplitude of a squared for the qubits to both be zero. That's an amplitude of a B for the qubits to be zero and then one. It's an amplitude of a B for the qubits to be one and then zero. And it's an amplitude of B squared for the qubits to both be one."
},
{
"end_time": 2036.459,
"index": 85,
"start_time": 2018.507,
"text": " So now I have a new vector. I want you A squared, AB, AB, and B squared. But now that we know that, now we've proved the no cloning theorem. Why have we proved it? Well, because that transformation that we just asked for is a nonlinear transformation."
},
{
"end_time": 2066.152,
"index": 86,
"start_time": 2037.671,
"text": " The amplitudes A and B were not replaced by linear functions of A and B. They were replaced by nonlinear functions such as A squared or B squared. That is a thing that unitary evolution in quantum mechanics cannot do. There are other ways to prove the no cloning theorem, but one way to prove it is really as simple as that."
},
{
"end_time": 2089.121,
"index": 87,
"start_time": 2066.937,
"text": " i see now computational irreducibility and then also what all this has to do with new comes paradox all right all right all right so i i mean computational irreducibility is just you know a term that steven wolfram uses for uh uh you know i would say you know a basic phenomenon that was you know known to many people uh before wolfram you know he likes to"
},
{
"end_time": 2118.831,
"index": 88,
"start_time": 2089.121,
"text": " uh, you know, treat everything as, as, as, as, as his invention. But, uh, you know, it is, um, you know, the, the, the fact that, that, you know, for many, many, uh, systems that are computationally universal, like, you know, we cannot figure out how to, you know, predict their behavior faster than just by simulating the whole thing. Right. So, you know, there, there are, you know, in some sense, science has gotten all, you know, as much leverage as it has."
},
{
"end_time": 2148.063,
"index": 89,
"start_time": 2119.07,
"text": " over the past 400 years because often we can model a system by something that is simpler than the system itself. So the orbits of the planets around the sun, the orbit of the moon around the earth. Kepler said these look like ellipses. And then Newton explained from a single simple law of gravitation,"
},
{
"end_time": 2175.367,
"index": 90,
"start_time": 2148.336,
"text": " And from laws of motion, he explained why they should look like ellipses. And then you can predict, in some cases, what the planets are going to be doing millions of years from now, because the system is simple enough. But there are many other systems. We could take a lava lamp, for example, or the weather, where there is just"
},
{
"end_time": 2195.333,
"index": 91,
"start_time": 2175.657,
"text": " so much dependence on the fine details of the system state at any one time that if you try to run a prediction to a future time, then your prediction will before long diverge from reality. This is the famous butterfly effect."
},
{
"end_time": 2224.633,
"index": 92,
"start_time": 2195.606,
"text": " Right? That, you know, unless you know, you know, the exact state of every particle and can then feed that into your computer, right? Then, you know, like a small, you know, whatever small error you make in, in, in knowing the current state is going to blow up exponentially over time. Hey, that's the, you know, basic phenomenon of chaos and computational irreducibility. I mean, I think it's just, you know, the term that Wolfram uses for like, you know, the analog of chaos in, in discrete systems, like cellular automata."
},
{
"end_time": 2245.469,
"index": 93,
"start_time": 2225.077,
"text": " Great. And so what does that have to do with free will and new comes? Well, okay. I mean, I mean, what I would say is that if there is a, you know, some deep reason why the prediction machine cannot be built, you know, why the new com predictor cannot exist, then you know, the the only candidate that I can put forward, you know, based on"
},
{
"end_time": 2273.217,
"index": 94,
"start_time": 2245.742,
"text": " you know, the physics and neuroscience and so forth that I know about is to say, well, maybe, you know, in order to make, you know, a well calibrated prediction of what a person is going to do, you know, you would really have to know, you know, not just like a crude approximation of the state of their brain, you know, which could mean like, like knowing the connectivity pattern of the neurons, you know, knowing the strengths of each synaptic"
},
{
"end_time": 2284.002,
"index": 95,
"start_time": 2273.575,
"text": " You know, and so forth, right? Maybe that's not good enough. Okay. You know, maybe you need to know like, like, you know, is this individual neuron going to fire or not? Right. At this time."
},
{
"end_time": 2304.565,
"index": 96,
"start_time": 2284.292,
"text": " I mean, a single neuron firing or not firing could certainly trigger a cascade of chaotic effects. Maybe if this neuron fires, it causes 10 neurons to fire, which in turn cause 100 neurons to fire and so forth and before long, you're going"
},
{
"end_time": 2332.722,
"index": 97,
"start_time": 2304.565,
"text": " Yeah, so a cosmic ray is responsible for Scott not being a quant. I mean, this is the question, right? You know, what is the smallest change that you could have made? You know, and this is a standard trope of like,"
},
{
"end_time": 2356.084,
"index": 98,
"start_time": 2333.012,
"text": " you know, time travel stories and science fiction, right? Like when you go back in time, you know, if you change even the tiniest thing, I mean, you know, like usually they, you know, they're like, oh, we have to walk very carefully and not kick any of the rocks. So, you know, that's kind of silly. If you believe this at all, then, you know, the very fact that you're there, you know, disturbing the air molecules, you know, you're, you know, it's like, forget it, you know, you've already completely changed the future."
},
{
"end_time": 2378.097,
"index": 99,
"start_time": 2356.084,
"text": " If we really need to know whether a single neuron fires or not, we know that the sodium ion channels that control that are modeled in neuroscience by something called the Hodgkin-Huxley equation, which is a stochastic differential equation. It has a noise component."
},
{
"end_time": 2397.619,
"index": 100,
"start_time": 2378.097,
"text": " Right and you know the neuroscientist will probably say well you know we just treated as thermal noise right we just treated as you know a bunch of molecules are bumping around randomly and that you know somehow you know sometimes it makes the sodium ion channel open and other times it makes it close right but if you really needed to"
},
{
"end_time": 2419.189,
"index": 101,
"start_time": 2397.619,
"text": " I don't know if that is true. I regard this as at least partly an empirical question."
},
{
"end_time": 2441.237,
"index": 102,
"start_time": 2419.411,
"text": " There is also a philosophical question here, I should admit,"
},
{
"end_time": 2469.377,
"index": 103,
"start_time": 2441.613,
"text": " How accurate does the copy have to be before you will accept that copy as being a new version of you? The famous thought experiment here is, imagine that someone has built a teleportation machine that can teleport you to Mars. You can visit Mars in only 10 minutes transit time."
},
{
"end_time": 2497.125,
"index": 104,
"start_time": 2469.684,
"text": " But the way that it works is that your brain will get scanned in as pure information. That information will get sent to Mars. On Mars, a machine will reconstitute you from that information. And then the original version of you on Earth, well, that'll just be painlessly euthanized or something. And so now the question is, do you agree to go in that machine? Is that a means of travel that you are comfortable with?"
},
{
"end_time": 2506.015,
"index": 105,
"start_time": 2497.295,
"text": " Uh, and you know, I think, well, you know, it might, you know, depend on the details of, you know, just how accurate is this copy, right?"
},
{
"end_time": 2531.032,
"index": 106,
"start_time": 2506.374,
"text": " Is it really perfect? Is it just good enough? There have been philosophical thought experiments about this kind of thing for generations, but we can already see with GPT, for example, with the AIs that have come online within the last few years,"
},
{
"end_time": 2559.804,
"index": 107,
"start_time": 2531.032,
"text": " These questions are going to come up. Take a person who has some giant corpus of work, tens of thousands of postings on the internet, and then you can train a language model to emulate that person as well as it can. As character.ai and companies like that are already doing in a kind of crude way, they let you talk to Einstein."
},
{
"end_time": 2588.882,
"index": 108,
"start_time": 2560.077,
"text": " Talk to Taylor Swift, talk to Socrates or whatever. I didn't find it that engrossing. They all kind of sounded the same to me. They all kind of sounded just like different language models. Imagine that that gets better. Imagine that you make this doppelganger of yourself and then you lay in bed all day and you get up and you see what it's done and you say, yeah, those are totally the things that I would have done."
},
{
"end_time": 2614.957,
"index": 109,
"start_time": 2589.241,
"text": " You know, how good does it have to be before you accept it as a replacement for yourself? Do we need to go as far as a teleportation thought experiment to Mars? Because even when you move a sub-millimeter amount, it could technically be that you just got destroyed in an instant and then was just reconstituted a sub-millimeter further. Well, yeah, I mean, so there is that philosophical question, right?"
},
{
"end_time": 2644.957,
"index": 110,
"start_time": 2614.957,
"text": " Are we constantly just being destroyed and recreated, or should we think about it that way? Certainly in ordinary life, we don't think about, I get on a bus, I get on a plane, I move around as something that is destroying and reconstituting me. But now, if you really want to get confused about this, you can think about quantum teleportation."
},
{
"end_time": 2670.623,
"index": 111,
"start_time": 2644.957,
"text": " Right. So there is a protocol by which you can transfer, you know, a quantum state from one place to a different place. Okay. If you have two resources, you know, number one is just classical communication. You know, the ability to send conventional bits, like let's say over the internet, for example. Right. That's pretty. And the second resource is you need pre-shared quantum entanglement."
},
{
"end_time": 2698.251,
"index": 112,
"start_time": 2671.084,
"text": " So you need the sender and the receiver location to have pre-shared entangled quantum states that were correlated with each other beforehand. But if you have both of those things, there is this amazing protocol that was discovered 30 years ago where you measure your quantum state, let's say Alice over on the left side,"
},
{
"end_time": 2722.517,
"index": 113,
"start_time": 2698.251,
"text": " measures her state together with her entangled particle and then she gets two bits of information that she sends over the internet to Bob and then Bob using those bits applies some correction operations to his entangled particle and now voila he now has exactly the same quantum state that"
},
{
"end_time": 2746.817,
"index": 114,
"start_time": 2723.456,
"text": " Did this violate the no-cloning theory?"
},
{
"end_time": 2769.411,
"index": 115,
"start_time": 2747.227,
"text": " Right. Because I had my quantum state and now somehow a new copy of the quantum state has popped up over at Bob's head. But the key is in order for this to work, Alice had to make a measurement that destroyed her copy of the state. And does Alice know her copy of the state before? No, she doesn't. She doesn't even know what she's sending. Right. Exactly. She doesn't have to know. She doesn't have to know."
},
{
"end_time": 2789.991,
"index": 116,
"start_time": 2769.735,
"text": " She can know, but she doesn't have to. Bob just ends up with a new copy of the same state, whatever it was. You could say, would you agree to be quantumly teleported to Mars? Well, in that case,"
},
{
"end_time": 2817.978,
"index": 117,
"start_time": 2790.179,
"text": " You know, that sounds potentially better or safer than just being sent as classical information because in that case, it really is the same quantum state that would be reconstituted on Mars, right? You know, just like it would have been if you would just gotten into a spaceship and traveled to Mars in a conventional way. Yeah. All right. Great. Do you have a preferred interpretation of quantum mechanics? Well,"
},
{
"end_time": 2828.097,
"index": 118,
"start_time": 2819.002,
"text": " Actually, if your views on this have changed, then it would be great to outline what they were prior and what changed them."
},
{
"end_time": 2851.442,
"index": 119,
"start_time": 2828.746,
"text": " When I teach quantum mechanics to undergrads in my quantum computing and information class, I try to teach it like comparative religion. I try to not tip my hand about which interpretation I'm leaning toward, but I've discovered something interesting."
},
{
"end_time": 2877.841,
"index": 120,
"start_time": 2851.749,
"text": " in recent years, which is that it's really hard to not make the majority of the students into many-worlders. Once they see the pros and cons laid out, then we ask as an ungraded question on the final, we ask what's your favorite interpretation, and then consistently a majority"
},
{
"end_time": 2896.169,
"index": 121,
"start_time": 2877.841,
"text": " Just to back up, many worlds interpretation is just the one that says that the wave function, which is this list of amplitudes for all the possibilities that you could get, that is the fundamental reality."
},
{
"end_time": 2923.49,
"index": 122,
"start_time": 2896.408,
"text": " That is what the universe is. It is this list of amplitudes. And it evolves in time just by this unitary evolution. And the many-worlders would say that measurement is not real. Measurement is our local perception from our local point of view. But it's not really a fundamental law of physics."
},
{
"end_time": 2943.097,
"index": 123,
"start_time": 2923.712,
"text": " Hey, so, so, so if you know, and there's a sense in which that is, you know, the, the, the mathematically simplest or nicest picture that you could have, right, where it just all unitary evolution, which is continuous, it's reversible, it's, um, um,"
},
{
"end_time": 2972.125,
"index": 124,
"start_time": 2943.985,
"text": " It's deterministic. You don't have these weird probabilistic irreversible jumps. You don't have any of that. But the cost for saying that is that now if let's say there's some qubit that's in a superposition of zero and one and then we make a measurement of it, then the way you have to describe that by unitary evolution is that the whole system"
},
{
"end_time": 3001.988,
"index": 125,
"start_time": 2972.125,
"text": " Consisting of, you know, the qubit and the measuring device and me, you know, are now going to evolve to a new quantum state. Okay. And that state will have two components. And in one of the components, the qubit is zero and the measuring device registered it as zero. And my brain, you know, I looked at it and I saw the zero. Right. And in the other branch, you know, the qubit was in the state one and the measuring device registered it as one. And my brain, you know, saw that."
},
{
"end_time": 3025.862,
"index": 126,
"start_time": 3001.988,
"text": " Okay, so you're led to this prediction, you know, that the universe is sort of constantly splitting into branches, you know, as it were, or at least, you know, what we would regard as sort of different, approximately classical universes, okay, and where, you know, our lives could turn out differently, right?"
},
{
"end_time": 3044.65,
"index": 127,
"start_time": 3026.135,
"text": " If you were to treat the qubit plus all of the atoms in the measuring device and all of the atoms in your body as just all quantum mechanical systems,"
},
{
"end_time": 3070.759,
"index": 128,
"start_time": 3045.009,
"text": " all just obeying the same Schrodinger equation, the same laws of, you know, of unitary physics, and nothing ever gets singled out as being an observer, or, you know, or having this sort of special role, then like that, that is the prediction that you, you know, that you would get, you know, and so now, like, in some sense, the whole interpretation problem of quantum mechanics is what do you do with that fact?"
},
{
"end_time": 3093.848,
"index": 129,
"start_time": 3071.152,
"text": " Okay. And so now, you know, there are, you know, a few different approaches. The original approach of, you know, Niels Bohr and Werner Heisenberg and most of the other founders of quantum mechanics was to say, well, then, you know, this wave function, this list of amplitudes is not real."
},
{
"end_time": 3119.531,
"index": 130,
"start_time": 3094.138,
"text": " It's just a mental device in our heads that we are using in order to calculate the probability that we will see this outcome or that one. What is real is what we see when we make a measurement. They would tend to say there is the classical world that we live in, and then there is the quantum world, which is the subatomic world, and measurement is somehow an interface between the two worlds."
},
{
"end_time": 3133.968,
"index": 131,
"start_time": 3119.889,
"text": " The problem that Copenhagen has always had is where do you actually draw the boundary between the quantum world and the classical world?"
},
{
"end_time": 3162.159,
"index": 132,
"start_time": 3134.48,
"text": " Right? You know, like nowadays, we can take much bigger systems and we can put them in superposition states, like even molecules with, you know, thousands of atoms in them, we can put in a superposition of going one way and going another way. Nothing as big as a Schrodinger cat, you know, yet. But, you know, but but like after a century, no one has discovered any fundamental obstruction to, you know, scaling up superpositions arbitrarily."
},
{
"end_time": 3188.746,
"index": 133,
"start_time": 3162.517,
"text": " And quantum computing feeds into this discussion as well, because if you can build a scalable, error-corrected quantum computer, then you could have millions or billions of qubits that are all in a superposition of two different states. If you even loaded an AI program onto that quantum computer,"
},
{
"end_time": 3218.336,
"index": 134,
"start_time": 3188.951,
"text": " and if the AI were conscious, then it could even be in a superposition of thinking one thought and thinking a different thought. Which was the original thought experiment that sort of led David Deutsch to propose the ideas of quantum computing in the first place in the late 1970s. So the question is like, where does the buck stop? And the Copenhagen approach has basically been to say, well, there are certain questions that you're not allowed to ask."
},
{
"end_time": 3240.879,
"index": 135,
"start_time": 3219.036,
"text": " We know a priori what it means to measure something and get a classical outcome. This is just a precondition of doing science and so we have to just assume this. That was an answer that was bound to not satisfy everyone forever."
},
{
"end_time": 3269.872,
"index": 136,
"start_time": 3241.271,
"text": " But, you know, you could say that sort of option one, I view it as kind of the giving up option, right? You just say, you know, the theory, you know, it works for experiments and we're not going to treat the whole universe, including ourselves quantum mechanically. We're not even going to try to understand that. And then a second approach would be to say, yes, there is this whole wave function, right? There is this whole"
},
{
"end_time": 3294.889,
"index": 137,
"start_time": 3270.845,
"text": " a list of amplitudes for every possible outcome, but also there is one particular branch that is the real one, that is the one of actual experience. And so you have this giant ocean of amplitudes, but then there's also a cork in the ocean that just gets pushed around by the waves."
},
{
"end_time": 3310.879,
"index": 138,
"start_time": 3295.094,
"text": " in a way that matches the predictions of quantum mechanics, the Bohr and Ruhl. That is what David Bohm tried to do and Louis de Broglie. This is called the pilot wave or the de Broglie-Bohm interpretation of quantum mechanics."
},
{
"end_time": 3325.589,
"index": 139,
"start_time": 3310.879,
"text": " okay and you know and and there are many different versions of it because you know you can write down like thousands of different such rules for how the cork is going to go that will all make that will all end up with the same predictions for any experiment that we can do"
},
{
"end_time": 3348.302,
"index": 140,
"start_time": 3326.323,
"text": " And then a third point of view would be many worlds where you just bite the bullet and you say the wave function is real and I refuse to introduce any additional ingredient, like any quark in this ocean, which means I'm not going to regard the other branches as any less real than my branch."
},
{
"end_time": 3373.882,
"index": 141,
"start_time": 3348.592,
"text": " I regard all of them as existing. I can't talk to the other branches. The fact that quantum mechanics is linear is the thing that prevents me from communicating with the other branches. But if they're there in the equations, if they're there in the theory, then I'm going to say that they're just as real as whichever branch you and I happen to experience."
},
{
"end_time": 3403.951,
"index": 142,
"start_time": 3374.326,
"text": " And then the fourth option would be to say, well, none of these ideas are any good. None of these interpretations is acceptable. And therefore, there must be something wrong with quantum mechanics itself. And hopefully in the future, we'll discover a better theory of physics that says, OK, here is when the quantum state collapses. It happens when it gets this big or this massive."
},
{
"end_time": 3433.473,
"index": 143,
"start_time": 3404.206,
"text": " And there will just be some objective testable law of physics that describes the collapse process. OK, now that would be something new, right? That would be that's not an interpretation. That would be a new and different physical theory that would overturn quantum mechanics as we know it today. Right. But you can say, well, you know, then then that that has to be the truth. You know, quantum mechanics has to just be an approximation to some better theory that hasn't been discovered yet."
},
{
"end_time": 3462.961,
"index": 144,
"start_time": 3434.462,
"text": " So, you know, you ask what I'm partial to, you know, I'm kind of partial to an idea by the physicists Lenny Susskind and Raphael Bussot from a decade ago, which is that cosmology might be an important part of the story, right? So like you could say that, you know, the big, you know, one of the main problems, you know, for anyone who is trying to interpret"
},
{
"end_time": 3493.131,
"index": 145,
"start_time": 3463.439,
"text": " quantum mechanics is to specify when does a measurement happen? When does the buck stop and when should I regard the superposition of outcomes as having resolved into one or the other definite outcome? The many-worlders might say, well, there's no one right answer to that question. It's kind of like asking,"
},
{
"end_time": 3522.005,
"index": 146,
"start_time": 3493.37,
"text": " How many grains of sand do I have to put together until it's a heap of sand? Even they might want a rough and ready rule for when we can treat an outcome as definite. Here is one possibility for such a rule. When you make a measurement, it's not just your brain that becomes entangled with the qubits or the particles that you measure."
},
{
"end_time": 3548.524,
"index": 147,
"start_time": 3522.193,
"text": " It's the air in the room that you're in, in the radiation in the room. There's a butterfly effect that happens. Each particle starts knocking around the nearby particles and so there's a whole bubble of effects of whatever the outcome of that measurement was that spreads outward from you."
},
{
"end_time": 3575.486,
"index": 148,
"start_time": 3548.78,
"text": " No faster than the speed of light, but as soon as the information gets encoded into photons, then possibly this sphere of effects is expanding around you at the speed of light. Once the information about which measurement outcome you saw is encoded into photons that are leaving the earth,"
},
{
"end_time": 3590.947,
"index": 149,
"start_time": 3576.032,
"text": " right and that are flying away from the earth at the speed of light right which eventually they will be then you could say well even in principle we could never catch those again you know as we would need if we wanted to re-cohere the superposition."
},
{
"end_time": 3619.343,
"index": 150,
"start_time": 3591.271,
"text": " you know, if we wanted to like show that, you know, see any effect of the other outcome of the one that we didn't measure, right? So, you know, in order to get interference, you have to collect all of the qubits that were affected, right? And, you know, if many of those qubits are flying away from us at the speed of light, well, then you could say, you know, how could we ever catch them again? Well,"
},
{
"end_time": 3648.012,
"index": 151,
"start_time": 3619.633,
"text": " If there were some extraterrestrials who would thought to like enclose the solar system in perfectly reflecting mirrors, right? Well, then okay, then the photons are going to bounce back and then maybe we could go here and we could see that this is still a quantum superposition. But, you know, I will assume that aliens have not done that, right? That does not seem to be the case in our universe."
},
{
"end_time": 3668.387,
"index": 152,
"start_time": 3648.251,
"text": " And then you get into questions about cosmology. There's this cosmological constant that was discovered in 1998, also known as the dark energy. It's the thing that is pushing the galaxies away from each other at an exponential rate."
},
{
"end_time": 3698.524,
"index": 153,
"start_time": 3668.729,
"text": " You know, one of the most important discoveries in all of physics for decades, right? And certainly in cosmology, right? The fact that this dark energy exists, what Einstein a century ago called the cosmological constant. It's actually not zero. We now know that, right? But now, if that constant had been negative, which it could have been, a universe with a negative cosmological constant"
},
{
"end_time": 3719.206,
"index": 154,
"start_time": 3698.848,
"text": " is one that in some sense does have a reflecting boundary. It's called an anti-decider universe. In that kind of universe, we would be trapped in a bubble where everything would be unitary. Any photons that are flying away from the Earth, eventually they can come back."
},
{
"end_time": 3749.326,
"index": 155,
"start_time": 3719.616,
"text": " Right. And so so no loss of quantum coherence would truly be permanent in that kind of universe. OK. But, you know, since 1998, we know that we don't live in that kind of universe. Right. We live in a universe with a positive cosmological constant, a de Sitter universe. And in that universe, you know, things really, you know, at least as far as anyone knows, no one knows for sure. But it's, you know, it seems possible that things can can fly off to infinity."
},
{
"end_time": 3761.271,
"index": 156,
"start_time": 3749.718,
"text": " And we could just take that as our criteria for when a measurement has happened. So in some sense, you know, we could say like it doesn't, you know, we could sort of"
},
{
"end_time": 3788.319,
"index": 157,
"start_time": 3761.544,
"text": " harmonize the many worlds in the Copenhagen points of view by saying like, yeah, at some formal level, yes, you know, we, you know, there is this whole wave function of the universe or, you know, we're, we're willing to talk about it. That does include all of these branches where all these other things happen. Right. But, uh, you know, there's also a criterion, you know, uh, uh, uh, for, for loss of quantum coherence, right. The, you know, the photons flying away from me at the speed of light."
},
{
"end_time": 3804.206,
"index": 158,
"start_time": 3788.575,
"text": " Where after that happens, then I might as well say that the other branches are gone. They are now not empirically accessible to me, even in principle."
},
{
"end_time": 3821.305,
"index": 159,
"start_time": 3804.582,
"text": " Football fan, a basketball fan, it always feels good to be ranked. Right now, new users get $50 instantly in lineups when you play your first $5. The app is simple to use. Pick two or more players. Pick more or less on their stat projections."
},
{
"end_time": 3836.681,
"index": 160,
"start_time": 3821.305,
"text": " Anything from touchdown to threes, and if you're right, you can win big. Mix and match players from any sport on PrizePix, America's number one daily fantasy sports app. PrizePix is available in 40 plus states including California, Texas,"
},
{
"end_time": 3864.343,
"index": 161,
"start_time": 3836.92,
"text": " So in other words, when you're teaching this in the comparative religion sense, you're the Baha'i faith."
},
{
"end_time": 3884.974,
"index": 162,
"start_time": 3865.555,
"text": " I think they called it the multiverse interpretation. And by the way, I just saw Lenny Suskind a couple of weeks ago and he doesn't seem to believe his own interpretation anymore. But I still like it though."
},
{
"end_time": 3903.814,
"index": 163,
"start_time": 3886.425,
"text": " Great, so the multiverse interpretation is separate from the many worlds, because those sound similar. That's right, yes. And the many worlds, when you said that you measured, forgive the pun, your students at the end and then they said that they like the many worlds, 80% or so. I think it was probably more like 55%."
},
{
"end_time": 3919.599,
"index": 164,
"start_time": 3904.138,
"text": " What does it even matter or shut up and calculate or that there has to be new physics?"
},
{
"end_time": 3944.974,
"index": 165,
"start_time": 3919.599,
"text": " Yeah, it's surprising to me that number four, the provisional one that, hey, we don't have the current fundamental law and so who cares about it, isn't more popular given that gravity isn't integrated into quantum mechanics. I mean, it does have adherence, right? I mean, Roger Penrose is one very famous adherent, right? But I think he sort of hurts his case by tacking onto it like a whole enormous chain of speculations, right?"
},
{
"end_time": 3966.988,
"index": 166,
"start_time": 3944.974,
"text": " He thinks that quantum gravity causes an objective collapse of the wave function and this collapse is uncomputable. It cannot be simulated by a Turing machine and the microtubules in our brains are somehow sensitive to this quantum gravitational collapse and this is implicated in consciousness."
},
{
"end_time": 3996.203,
"index": 167,
"start_time": 3967.722,
"text": " So that's the Penrose view and you can say even if you might go with him to the first stop of that train, most of us are going to get off before the later stops. Okay, we're going to explore uncomputability shortly. Oh yeah, what I was getting at was did you measure the students initially and say, hey, what is your preferred interpretation in order for you to establish a difference? Yeah, that's a good question."
},
{
"end_time": 4015.52,
"index": 168,
"start_time": 3996.408,
"text": " Like to do a controlled experiment, you want to do that. The trouble is that until I expose the students to all these interpretations, they don't even know what they are. Most of them have not even heard of them, or if they have heard of them, then I'm not sure if they could define them."
},
{
"end_time": 4039.991,
"index": 169,
"start_time": 4016.271,
"text": " The reason is because in the popular press, many worlds is prominent and so it may just be an effect of, hey, I like Sean Carroll. I listen to his podcast. Yeah. Yeah. Well, I mean, I mean, I mean, Sean makes very, you know, I've, you know, he's been a good friend of mine since, you know, 2006 or so. And I think he does make very strong arguments for many worlds. And I say that even though, you know, I am not nearly as, as hardcore of a many world or as Sean is."
},
{
"end_time": 4067.056,
"index": 170,
"start_time": 4040.674,
"text": " Isn't there still the issue of having a globally well-defined measure in order to even state what the probability distribution is of different branches of the wave function? But can you explain what that is? Yeah, so I mean, you could say that the basic problem for if you want to be a many-worlder is you have to explain, well, why do we only perceive one world? And not only that, but why do we perceive each world"
},
{
"end_time": 4096.92,
"index": 171,
"start_time": 4067.056,
"text": " with these particular probabilities, these born rule probabilities. I have to say, I don't regard that as a problem for only the many worlds interpretation. You could ask the same question with any interpretation. Where did these probabilities come from? It's just that question takes on a different character depending on which interpretation you like."
},
{
"end_time": 4124.94,
"index": 172,
"start_time": 4097.193,
"text": " If you believe in new physics, then you have to postulate some new law of physics that will then give rise to these probabilities. You can check whether it does or it doesn't. Ideally, you wouldn't just stick them in. In physics, it's always better if you can derive something rather than just assuming it from the outset."
},
{
"end_time": 4136.954,
"index": 173,
"start_time": 4125.23,
"text": " If you are a bohemian, you postulate a rule for your hidden variable, for your quirk in the ocean."
},
{
"end_time": 4167.073,
"index": 174,
"start_time": 4137.227,
"text": " that happens to always give you agreement with this born rule, right? But then you could say, you know, why should it have been a rule of that kind, right? And then, you know, if we started out in some other distribution, would we reach that born distribution as an equilibrium, right? So that's what the question looks like to a bohmian. To a many-worlder, you know, the issue is that a many-worlder is committed to the view that all of the outcomes are real, right?"
},
{
"end_time": 4197.073,
"index": 175,
"start_time": 4167.278,
"text": " All of the outcomes are experienced by someone. And so then they have to say, then what does it even mean to say that this outcome has this probability and that one has that probability? How do you even make sense of that statement? It's like, you have to imagine that all of these beings are real, but somehow one of them is going to be picked to be your experience. And so somehow there is some"
},
{
"end_time": 4223.763,
"index": 176,
"start_time": 4197.363,
"text": " You know, metal law that governs that, right? And so there is a long history, you know, ever, you know, since Everett himself in the 1950s of many worlders, um, trying to, uh, or claiming to derive the bourne rule, right? Derive the probabilities. Okay. They always have to make some auxiliary assumption, you know, in, in these derivations, right? Because it's like, you're starting with a picture."
},
{
"end_time": 4250.111,
"index": 177,
"start_time": 4223.951,
"text": " That is just the wave function, you know, that has no probabilities in it. And then in the end, you know, you get a statement about probability. Right. And so, so, you know, there, there, there, there has to be some step where, where you're just postulating that, yes, something is random. Right. And, you know, and for a many-worlder, what that kind of looks like is it's this thing called indexical uncertainty or self-locating belief."
},
{
"end_time": 4279.65,
"index": 178,
"start_time": 4250.401,
"text": " So basically, imagine that you didn't know your own blood type. You just hadn't gotten tested yet. But then you say, well, look, there's this many people in the world who are type O, there's this many people who are type A. So I'm going to just assume that I was a randomly chosen person. And there's something fundamentally weird about that. As soon as you start thinking about yourself,"
},
{
"end_time": 4307.637,
"index": 179,
"start_time": 4280.077,
"text": " As chosen randomly from the set of all people. Yeah, there's also a reference classes. Yeah, exactly. Exactly. Then you can start wondering about things like, you know, why was I born in the, you know, late 20th century as opposed to, you know, in medieval Spain or, you know, or at some other time, right? Why am I on earth? Why am I not an alien on a different planet? Right. And, you know, it's not, it's not obvious if these questions have well-defined answers at all."
},
{
"end_time": 4315.043,
"index": 180,
"start_time": 4307.944,
"text": " Right. But what the many worlders need to do is to say, you know, there are all of these branches of the wave function."
},
{
"end_time": 4339.172,
"index": 181,
"start_time": 4315.367,
"text": " that are all real, they all have real copies of you, but now you have to think of yourself as a randomly selected member of that ensemble. And then once you decide to do that, then you actually can give many mathematical arguments that the born probabilities are pretty much the only probabilities that would make sense."
},
{
"end_time": 4350.401,
"index": 182,
"start_time": 4339.616,
"text": " You can show that any other choice for what the probabilities would be, like if instead of the absolute square of the amplitude, suppose it were the absolute cube."
},
{
"end_time": 4378.592,
"index": 183,
"start_time": 4350.691,
"text": " of the amplitude or the absolute value to the 2.8 power or something like that. You can show that that would give you nonsensical things. It would lead to faster than light communication. It would lead to massive violations of the laws of physics that we understand. You can give arguments for once you've decided to"
},
{
"end_time": 4401.203,
"index": 184,
"start_time": 4378.848,
"text": " Now, it's been a while since I've studied this, but it's my understanding that the space of pure quantum states is a projective Hilbert space, which is a Kahler manifold. The symplectic structure gives rise to the dynamics."
},
{
"end_time": 4421.664,
"index": 185,
"start_time": 4401.374,
"text": " That's probably all true. Those are already much fancier words than the ones that I ever use to talk about these things. Right. Well, fancy words with a specific mathematical meaning. Some say that computability or quaternions are fancy words."
},
{
"end_time": 4448.985,
"index": 186,
"start_time": 4421.664,
"text": " Right. Exactly. Yeah. What I mean is that when one says, well, where does the Born rule come from in a symplectic, sorry, in a scalar manifold? If you have two of those structures to get the third. So why isn't the question then? Well, why do we have a complex structure or why do we have that? That is a different superb question. You could say like, why should quantum mechanics have been based on complex numbers? You know, and you actually can define a variant of quantum mechanics that would only use real amplitudes, right?"
},
{
"end_time": 4478.08,
"index": 187,
"start_time": 4449.377,
"text": " And that version turns out to be pretty good for many purposes. Like it would lead to exactly the same power of quantum computers, you know, as our ordinary, you know, complex quantum mechanics, right? It would lead to, you know, basically all of the same, you know, information and communication protocols, you know, such as quantum teleportation, you know, you'd have the same no cloning theorem, the same, all of that stuff. It just that there are certain things"
},
{
"end_time": 4505.828,
"index": 188,
"start_time": 4478.285,
"text": " that would be less elegant in the, in the universe with, with real quantum mechanics. Okay. And we know some of those arise just because the real numbers are not algebraically closed. You know, you can't take square roots of them. Right. And so like, if I have a unitary transformation that, you know, operates over, let's say one second of time, and now I want to know, okay, but now what was the piece of it that operated only over the first half second? Right."
},
{
"end_time": 4534.07,
"index": 189,
"start_time": 4506.22,
"text": " Well then, yeah, as long as I have complex matrices, then I can just take a square root, right? And, you know, I'll get an answer to that question. Okay. With real matrices, there might not be a square root, you know, in the same number of dimensions. So for example, there's no, there's no two by two real square root of the matrix one, zero, zero, negative one, right? That would be, that would be an example, right? And we, we can see that because it has a negative one determinant, right?"
},
{
"end_time": 4561.63,
"index": 190,
"start_time": 4534.445,
"text": " So that breaks various things about the way that physicists use quantum mechanics. And then there are other more subtle things that also break, like the number of parameters that you need to describe a composite state. In complex quantum mechanics, it's exactly just the number of parameters that you need to describe the first piece times the number of parameters that you need to describe the second piece."
},
{
"end_time": 4585.435,
"index": 191,
"start_time": 4562.005,
"text": " Okay, but in real quantum mechanics, that's no longer true. By the way, it's also not true in quantum mechanics based on quaternions, right? With real numbers, you get an undercount, with quaternions, you get an overcount, and only with complex numbers does it work out exactly right. Okay, so there are these subtle things."
},
{
"end_time": 4614.309,
"index": 192,
"start_time": 4585.759,
"text": " that just work out perfectly when quantum mechanics is defined over the complex numbers. But I've asked mathematicians this question, if you were God designing the universe on a blackboard, do you know why you would have chosen the complex numbers for this? In some sense, the deepest laws of physics that we know. And the mathematicians were like, come on, they're algebraically closed."
},
{
"end_time": 4635.998,
"index": 193,
"start_time": 4614.633,
"text": " I think you said this that we used to think there were two logical operations and or or but then we found out with quantum mechanics there's complex linear combinations. Well yeah okay so I was saying like like in terms of how you can combine multiple possibilities right like like it's"
},
{
"end_time": 4658.814,
"index": 194,
"start_time": 4636.937,
"text": " Like when someone says that an electron, for example, it's not in its ground state, it's not in its excited state, it's in some kind of superposition of the two. Often the first thing that they think that you mean is well then you must be saying that it's in both simultaneously."
},
{
"end_time": 4670.589,
"index": 195,
"start_time": 4659.104,
"text": " And you know and the trouble is if you take that too literally that it leads to like for example a vision of what a quantum computer is where it would just try all of the different solutions in parallel."
},
{
"end_time": 4699.326,
"index": 196,
"start_time": 4670.845,
"text": " Right. And that's that's that's wrong. Right. That's just like that leads you to to like leads people to importantly wrong expectations of how useful a quantum computer would be if they really think that it could try all the answers in parallel, you know, in the in the in the naive way. Right. So then you correct that. And then they say, oh, so then so then what you must be saying instead is that, you know, the electron is in one state or the other and we just don't know which one."
},
{
"end_time": 4724.718,
"index": 197,
"start_time": 4699.326,
"text": " Do you believe there to be a fourth ontological category that involves the quaternions?"
},
{
"end_time": 4753.695,
"index": 198,
"start_time": 4724.991,
"text": " I mean, you could define quantum mechanics over the quaternions or over the reals for that matter, and that would give a subtly different answer. But what would that look like? So quantum mechanics over the quaternions turns out to be sick in various ways. Sick as in cool? Let me tell you what I mean and then you can decide. At least naively,"
},
{
"end_time": 4781.459,
"index": 199,
"start_time": 4753.899,
"text": " In quaternion quantum mechanics, you could send information faster than light. And in fact, if Alice and Bob are far away, even if Alice is on Earth and Bob is on Mars, it could matter which one of them does an operation first. Does Alice act first or does Bob act first? And this is because the quaternions are non-commutative."
},
{
"end_time": 4810.196,
"index": 200,
"start_time": 4781.869,
"text": " So, you know, it matters in, you know, even for separated events, it can matter, you know, sort of which operation we put there first. And now this is in flagrant contradiction with special relativity, right? Which says that, you know, when two events are, you know, space-like separated, then it can't matter in which order, you know, they're done because, you know, to some observers, you know, Alice will be first and to other observers, Bob will be first."
},
{
"end_time": 4837.176,
"index": 201,
"start_time": 4810.316,
"text": " And these two perspectives have to be consistent with each other. So quaternionic quantum mechanics breaks that because the quaternions are not commutative. So if you want to believe in it, then you need some way of making that effect go away at large enough distance scales or something like that. There's a physicist named Steve Adler who spent decades trying to make that work."
},
{
"end_time": 4855.708,
"index": 202,
"start_time": 4837.363,
"text": " I talked to him a few years ago and he said that he doesn't really believe it anymore. Real quantum mechanics, like I said, that one does make a lot more sense, but a real superposition philosophically I would think of is almost the same sort of thing."
},
{
"end_time": 4885.367,
"index": 203,
"start_time": 4855.776,
"text": " as a complex superposition. You know, they're just kind of different in detail. Now the octonians have been chopped liver in this conversation. Yeah, octonians don't even get started, right? Yeah, do you mind getting a tiny bit started? Just explain because that's a popular subject. Well, okay, the the the the the the the the octonians are so you know, so there are these four, what are they complete division algebras, the norm division, norm division algebras, excuse me, the the the reals, the complex numbers, the"
},
{
"end_time": 4904.838,
"index": 204,
"start_time": 4885.606,
"text": " You know, which have two parameters, the quaternions, which have four parameters and the octonions, which have eight parameters. And, you know, and like naively you would expect that it would, you know, it must just keep going after that point. But, you know, it was a very important theorem from the 19th century that says that these are the only four."
},
{
"end_time": 4933.234,
"index": 205,
"start_time": 4905.35,
"text": " right? So it's sort of the progression stops after that. So there are these, these four norm division algebras that are kind of special, but you know, as you go to the larger and larger ones, you, you know, you lose certain properties. So like, you know, the reels are ordered, right? No, the complex numbers and beyond are not ordered. Okay. But with the complex numbers, you could say, you know, you, you, you lose something, but you gain something, right? You get, you gain that they're algebraically closed."
},
{
"end_time": 4955.93,
"index": 206,
"start_time": 4933.558,
"text": " Right. But now when you go to the, you know, and the complex numbers are also, you know, commutative, they're associative, they satisfy pretty much all of the basic properties that you would want in algebra. Right. But now, you know, with the caternions, that already starts falling apart because the caternions are associative, but they're not commutative."
},
{
"end_time": 4986.049,
"index": 207,
"start_time": 4956.254,
"text": " Okay, so A times B can be different from B times S. Which doesn't sound terrible because non-commutativity is a hallmark of quantum mechanics. No, no, no. I mean, look, and anectoneons still have, you know, they have applications in, you know, even in computer graphics, in math, in physics, you know, they are actually used, right? As I said, you know, if you want to use them as amplitudes in quantum mechanics, then there is stuff that goes wrong. You have to then somehow make that consistent with"
},
{
"end_time": 5014.889,
"index": 208,
"start_time": 4986.391,
"text": " with relativity. But now the octonians are not commutative and they're not even associative. It's funny, it's like in fifth or sixth grade, kids learn all these terms. This is the commutative property, this is the associative property. But until you've seen any examples of things that are not commutative or not associative, then this is just a bunch of words to memorize."
},
{
"end_time": 5042.449,
"index": 209,
"start_time": 5015.623,
"text": " I think that the time when you want to teach these terms is the time when you want to teach things that don't satisfy them. For my daughter, my 10-year-old daughter just the other day, I gave the example of something non-commutative, getting dressed, putting your pants on and then your underwear is not the same as the reverse."
},
{
"end_time": 5071.51,
"index": 210,
"start_time": 5042.858,
"text": " So there are examples for non-commutativity that even a small child can understand. Non-associativity is a little bit harder. Well, you're lucky this camera is only here, otherwise you'd see that I don't pay much attention to the non-commutativity of the pants and underwear. Before we get on to consciousness, I want to talk about IIT and I want to talk about P equals NP. Which, by the way, what I learned as a teenager, I just learned the equation P equals NP."
},
{
"end_time": 5101.8,
"index": 211,
"start_time": 5071.92,
"text": " 21 years ago when you know one of the first things I ever wrote as a student was a review of his new kind of science book."
},
{
"end_time": 5127.21,
"index": 212,
"start_time": 5102.329,
"text": " And what I spent half of that review doing is just explaining why his kind of model cannot account for the known phenomena of quantum mechanics. And this is not a fuzzy statement. This is a thing that one can prove."
},
{
"end_time": 5152.773,
"index": 213,
"start_time": 5128.029,
"text": " What he wants basically is to reduce everything in the universe to cellular automata, to a bunch of bits, maybe at the Planck scale or something like that, that are undergoing some sort of simple computational rules. That far along, yeah, I think that's great."
},
{
"end_time": 5181.732,
"index": 214,
"start_time": 5153.012,
"text": " That's like, you know, the whole physics community would like that, right? They would like, you know, especially a theory of quantum gravity that would explain why, you know, what's called the Bekenstein-Hawking entropy is finite, right? Why are there only finitely many degrees of freedom in a black hole, right? Or apparently in any physical system, right? Like what is it, you know, when you get down to the Planck scale of 10 to the minus 33 centimeters or 10 to the minus 43 seconds,"
},
{
"end_time": 5195.981,
"index": 215,
"start_time": 5181.971,
"text": " Something seems to break in our picture of a smooth, continuous space-time. We can see that from thought experiments where, for example, if you tried to"
},
{
"end_time": 5216.323,
"index": 216,
"start_time": 5196.169,
"text": " Right. So there are these"
},
{
"end_time": 5234.923,
"index": 217,
"start_time": 5216.664,
"text": " Thought experiments that tell us that something breaks at the Planck scale, but can you actually explain that by giving a theory where space and time are discrete or sort of discrete at the Planck scale? That is, I would say, a central part of the problem of quantum gravitation."
},
{
"end_time": 5262.5,
"index": 218,
"start_time": 5235.094,
"text": " But now Wolfram wants to do something else. He wants to say, no, it's not that we have quantum mechanics with a finite dimensional Hilbert space and with a discrete space and time. He wants to in some sense get rid of quantum mechanics and have it be a classical cellular automata. And then the problem is, well, we have"
},
{
"end_time": 5291.323,
"index": 219,
"start_time": 5262.978,
"text": " a mountain of evidence that quantum mechanics is both true and unavoidable. And so what does he do with that evidence? And he kind of handwaves it away. This is the key problem. In a new kind of science, he said, well, it's true that there are these experiments that you can do on entangled particles that could be very far away."
},
{
"end_time": 5311.51,
"index": 220,
"start_time": 5291.527,
"text": " that lead to these phenomena like the violation of the Bell Inequality, which is famously a thing that you could not explain in a classical universe. And that's just a very crisp statement. It doesn't matter what additional assumptions you make as long as they're reasonable ones or sane ones."
},
{
"end_time": 5336.92,
"index": 221,
"start_time": 5311.732,
"text": " So, you know, Alice and Bob, who are far away from each other, they measure their halves of this entangled pair and the statistics of the outcomes could not have been explained by any theory where the particles just secretly agreed in advance on whether to be spin up or spin down or whatever, right? It can only be explained by"
},
{
"end_time": 5359.787,
"index": 222,
"start_time": 5337.858,
"text": " saying, well, until Alice and Bob made the measurements, it was an entangled superposition state. So this is one of the strongest arguments that, yes, the world is really quantum mechanical. And we can't just replace it by something else, certainly not by a local hidden variable theory."
},
{
"end_time": 5371.101,
"index": 223,
"start_time": 5360.162,
"text": " But then what Wolfram says, and this is in chapter 9 of A New Kind of Science, he just says, well, okay, you know, this is no problem. Just imagine that sometimes there were long range threats."
},
{
"end_time": 5396.817,
"index": 224,
"start_time": 5371.34,
"text": " between the particles, right? So usually space is local, but when two particles become entangled, then there's kind of like a thread that allows instantaneous communication between them, right? Problem solved, right? This is like the Wolfram method, right? If you can imagine a way that the problem could be solved, then it's solved, right? And so what I spend a lot of my review doing is just explaining, sorry, it still doesn't work."
},
{
"end_time": 5410.538,
"index": 225,
"start_time": 5397.108,
"text": " It's sort of a statement that"
},
{
"end_time": 5438.575,
"index": 226,
"start_time": 5410.862,
"text": " If the measurements that Alice and Bob are going to make on the entangled particles have not been pre-decided, sort of were not known in advance, then the outcomes of the measurements on the particles also cannot have been pre-decided. They cannot be explained by hidden variables that go back to the beginning of time. They must be sort of genuine new randomness."
},
{
"end_time": 5465.572,
"index": 227,
"start_time": 5438.78,
"text": " or otherwise you get a violation of locality. So that was kind of the argument. And like I said, I just made that in 2002, buried in my review of Wolfram's book. Now that same conclusion a few years later became famous when John Conway and Simon Cotion said something very similar in 2006 and they called it the free will theorem."
},
{
"end_time": 5495.469,
"index": 228,
"start_time": 5466.032,
"text": " If humans have free will, then subatomic particles must also have free will. That got all over the popular press. I would never have used the term free will here because I would say we could equally well just talk about randomness. I might have called it the freshly generated randomness theorem."
},
{
"end_time": 5515.93,
"index": 229,
"start_time": 5495.691,
"text": " the the"
},
{
"end_time": 5545.213,
"index": 230,
"start_time": 5516.22,
"text": " Wolfram never really accepted that. I think most of the community did. He did not. But if you look at what he's done more recently with the Wolfram, I think he called it the Wolfram model of physics, what he basically does is he just says, okay, well, wherever we have a result that we can't explain classically, then we'll just graft on the relevant part of quantum mechanics."
},
{
"end_time": 5564.531,
"index": 231,
"start_time": 5545.964,
"text": " Right."
},
{
"end_time": 5586.049,
"index": 232,
"start_time": 5564.974,
"text": " You know, and also like we will say we can derive general relativity except the derivation basically be we like crib from a general relativity textbook. We just find out what the Einstein's equations are and we say, okay, well, whatever is the cellular automaton, it's presumably it's something that satisfies those equations."
},
{
"end_time": 5604.241,
"index": 233,
"start_time": 5586.578,
"text": " Right? So it's like, you know, it's not sort of playing by the rules of physics, right? Where you have to, you have to actually, you know, mathematically derive these things, right? From some simple starting postulate. And then ideally, you know, make a novel prediction, right? That's the that's the gold standard."
},
{
"end_time": 5632.295,
"index": 234,
"start_time": 5604.582,
"text": " One thing that I talked to Wolfram in person a couple years ago when he was in Austin. One thing that I kept trying to get clarity from him about was does he predict that scalable quantum computers can work or not? He would not give a clear prediction."
},
{
"end_time": 5647.09,
"index": 235,
"start_time": 5632.619,
"text": " This multi-way theory suggests that maybe quantum computers can't work, but if it turns out that they do work then the theory can accommodate that also."
},
{
"end_time": 5672.637,
"index": 236,
"start_time": 5647.449,
"text": " Have you read any of the papers by Jonathan Gerard?"
},
{
"end_time": 5701.032,
"index": 237,
"start_time": 5672.978,
"text": " P and NP are two of the most fundamental complexity classes, which are just classes of problems that are solvable with different kinds of computational resources. P stands for polynomial time."
},
{
"end_time": 5728.865,
"index": 238,
"start_time": 5701.51,
"text": " And it's the class of all of the yes or no problems that a conventional computer, you know, a deterministic digital computer like the one that we're using could solve using a number of steps that grows like a polynomial function of the of the number of input bits. OK, so yeah, and that's our sort of rough and ready criterion for when an algorithm is efficient."
},
{
"end_time": 5751.425,
"index": 239,
"start_time": 5729.224,
"text": " If it's running time scales polynomially with the length of the input. This is not a perfect criterion because an algorithm that took n to the 10,000 time would be wildly impractical. But what justifies it is that usually when something is solvable in polynomial time, the polynomial is something like"
},
{
"end_time": 5772.346,
"index": 240,
"start_time": 5751.732,
"text": " and"
},
{
"end_time": 5794.821,
"index": 241,
"start_time": 5772.978,
"text": " So that's why from the 1960s onward, the polynomial versus exponential distinction kind of became fundamental to complexity theory. And so P is just all of the yes or no problems that are solvable by some algorithm that has polynomial scaling."
},
{
"end_time": 5814.206,
"index": 242,
"start_time": 5795.077,
"text": " What are some examples of problems in P? If I give you a string of text and I ask, is it a palindrome or not? Any kind of basic arithmetic. Most of the things we do with our computers, to be honest, are things that are in P."
},
{
"end_time": 5839.292,
"index": 243,
"start_time": 5815.333,
"text": " More interesting examples like, given a map, is every city reachable from every other one? Given a graph, is it connected? That's in P. Given a bunch of boys and girls and who is willing to date whom, can you pair them off so that everyone is happy with their partner? That's called the matching problem."
},
{
"end_time": 5868.063,
"index": 244,
"start_time": 5839.582,
"text": " That's also in P. And graphics like ray tracing, are you able to say whether that's P? Yeah, I think the basic problems underlying ray tracing would be in P also, yes. And these are all things that one can learn as an undergraduate in computer science, right? There are also much more non-trivial examples. Given a number written in binary, is it prime or composite?"
},
{
"end_time": 5897.398,
"index": 245,
"start_time": 5868.575,
"text": " That's in P. It was only discovered to be in P 20 years ago. That's called the Agrawal-Kyle-Saxena or AKS theorem. So they gave a breakthrough algorithm. Before that, we had known probabilistic algorithms, but they gave the first deterministic polynomial time algorithm for primality testing. If the number is composite, then these fast algorithms do not tell you the factors."
},
{
"end_time": 5922.432,
"index": 246,
"start_time": 5897.79,
"text": " Finding the factors seems to be a much, much harder problem, which we can come back to. But determining primality is in P. Given a bunch of linear constraints, is there a way to satisfy all of them? That's called the linear programming problem. Again, it's in P for very nontrivial reasons."
},
{
"end_time": 5951.886,
"index": 247,
"start_time": 5922.756,
"text": " Okay, so a lot of interesting things are NP. Okay, but now there's this potentially larger class, which is called NP. Now that does not stand for not polynomial, which, you know, some people think it stands for non-deterministic polynomial time. Okay, so what does that mean? So NP is the class of all the problems where sort of if there is a solution, then you can check the solution in polynomial time."
},
{
"end_time": 5975.572,
"index": 248,
"start_time": 5952.227,
"text": " So if the answer is yes, there is a solution, then there is some witness, some proof that if it's given to you, then you can check in polynomial time that, yeah, I guess that works. So let's go through some examples. Solving a jigsaw puzzle. Imagine a jigsaw puzzle with no picture on it."
},
{
"end_time": 6005.811,
"index": 249,
"start_time": 5975.811,
"text": " You're just trying to fit all the pieces together. That might be incredibly cumbersome to do. You might have exponentially many possible ways of fitting the pieces together to try. But if someone has solved the puzzle, then they just have to show it to you. You can easily see that, yes, they have solved it. The famous traveling salesman problem where you're given a bunch of cities and you're asked, let's say,"
},
{
"end_time": 6035.35,
"index": 250,
"start_time": 6006.135,
"text": " Is there a route that visits every city with at most 5,000 miles of total travel distance? Again, if there are N cities, there might be N factorial different routes that you would have to try out. With hundreds of cities, that could be massively expensive, but if someone finds a route that works, then they just have to show it to you, and it's easy to check. That's also an NP problem."
},
{
"end_time": 6059.667,
"index": 251,
"start_time": 6035.691,
"text": " You know, I ask, let's say, does this number have a prime factor that ends with a three? Or some, you know, question like that, right? Where, again, you know, the fastest algorithms that we know for factoring take some sort of exponential time, at least the algorithms for classical computers, okay?"
},
{
"end_time": 6070.794,
"index": 252,
"start_time": 6060.009,
"text": " I actually take time that's like exponential in the cube root of the number of digits. That's called the number field sieve. And that's extremely important for cryptography."
},
{
"end_time": 6097.329,
"index": 253,
"start_time": 6070.964,
"text": " I agree. If you just want to know if the number is divisible by three, that isn't big."
},
{
"end_time": 6124.445,
"index": 254,
"start_time": 6098.029,
"text": " In fact, if you want to know if it's divisible by any fixed number, that's NP. But if I don't tell you the prime factors and they're like, let's say they're all enormous and now you have to find them, then that we don't know how to do in P. But it still is an NP problem because if someone succeeds in factoring the number, then they just have to show you the prime factors."
},
{
"end_time": 6146.749,
"index": 255,
"start_time": 6124.753,
"text": " And at least with a computer, it's easy enough to multiply them. And as I said, it's even easy enough to check that those numbers are prime. So factoring is another NP problem. OK, so now the P versus NP question is just the question, well, how do these classes relate to each other? So it's pretty clear that P is contained in NP."
},
{
"end_time": 6174.224,
"index": 256,
"start_time": 6147.261,
"text": " Right. So, you know, if you can solve a problem yourself in polynomial time, then you don't even need this witness. Right. You just, you know, you just have the answer to it. Right. But now the profound question is, is NP contained in P? Okay. So if I can efficiently recognize the solution to a problem, then does that imply that I can efficiently find the solution? Okay."
},
{
"end_time": 6202.108,
"index": 257,
"start_time": 6174.548,
"text": " And so that's the P versus NP question. And as soon as you see this question, some people, it takes time to convince them of why it's even a question at all. Because they would say, well, obviously not. Obviously, there are cases where you're going to need brute force search. And brute force search is going to take exponential time."
},
{
"end_time": 6231.203,
"index": 258,
"start_time": 6203.029,
"text": " The trouble is that as we discussed with the example of the matching problem or the linear programming problem or the primality problem, there are cases where naively it looks like you have to try exponentially many possibilities. But if you think about it more, then there is a clever shortcut that only takes polynomial time. So what P versus NP is asking is, is there always a clever shortcut?"
},
{
"end_time": 6248.319,
"index": 259,
"start_time": 6231.408,
"text": " for every problem where we can efficiently recognize a correct answer. And so you know that is for half a century that's been sort of the central unsolved problem of theoretical computer science and I think it's now recognized as one of the central unsolved problems in all of mathematics."
},
{
"end_time": 6274.104,
"index": 260,
"start_time": 6249.138,
"text": " So, two questions. One, why is this the largest unsolved problem to you? You think this is the greatest unsolved problem in math and potentially even physics? And then number two, this sounds... It's not a physics question, right? I mean, we could find a related physics question by asking, for example, can the all NP problems be solved in polynomial time by any physical means?"
},
{
"end_time": 6298.285,
"index": 261,
"start_time": 6274.599,
"text": " Right. Which could include a quantum computer or could even include, you know, a hypothetical quantum gravity computer or whatever. Right. You know, then we'd be asking a physics question. Right. But, you know, P versus NP is a question that can be purely stated mathematically. Right. Meaning it has some platonic answer. Right. We just we just haven't we just haven't proven what it is."
},
{
"end_time": 6319.753,
"index": 262,
"start_time": 6298.575,
"text": " What I meant was that I heard you say something along the lines of, look, the Clay Institute has many problems. Yes. And one of the problems is a physics problem, the Yang-Mills problem. Yeah. Well, you could say it's a mathematical physics problem. It's a math problem that came from physics. But I mean, the argument that I give is just that if P equaled NP,"
},
{
"end_time": 6344.787,
"index": 263,
"start_time": 6319.753,
"text": " And furthermore, if the algorithm were really efficient in practice, so not like n to the 10,000, but you know, n squared or n or something, then that would not only let you solve the P versus NP problem, that would let you solve all of the other clay problems, you know, the Riemann hypothesis, the Yang-Mills problem, right, and all the other ones. And why is that? Because it would mean that we could just ask our computer, right, say like, like,"
},
{
"end_time": 6369.804,
"index": 264,
"start_time": 6345.06,
"text": " Is there a proof of this theorem in this formal language, like Zermelo-Frankel set theory, that is at most a million symbols long or at most a billion symbols long? What it would mean if P equal to NP would be that if such a proof existed, then you could find it using a number of steps that only scaled polynomially with the length of the"
},
{
"end_time": 6399.821,
"index": 265,
"start_time": 6371.271,
"text": " Right. So like in, you know, only polynomially more time than it would take to write down the proof, you could actually find the proof. Right. And so in some sense, you know, mathematical creativity, uh, would have been automated. So a proof of P equals NP would automatically have well, well, okay. I mean, I mean, I mean, the, the, the, the, the caveat is that the algorithm would have to be efficient in practice. Right. But, but, you know, the, the question like, you know,"
},
{
"end_time": 6421.459,
"index": 266,
"start_time": 6400.299,
"text": " Is there a proof of this theorem in some purely formal language, like first order logic, ZF set theory, with at most this number of symbols? That is an NP problem, literally. And so that means that if P equaled NP, then it would also be a P problem. Can you explain what quantum supremacy is?"
},
{
"end_time": 6442.21,
"index": 267,
"start_time": 6421.886,
"text": " So quantum supremacy is a term that was coined by the physicist John Preskill in 2012 and it's just referring to sort of the first experiment that you can do with a quantum computer that solves some benchmark problem."
},
{
"end_time": 6457.858,
"index": 268,
"start_time": 6442.5,
"text": " much faster than we believe that it could be solved with a classical computer."
},
{
"end_time": 6488.097,
"index": 269,
"start_time": 6458.319,
"text": " Okay, so like it can't just be like simulate this physical system with all of its noise, right? You have to give a mathematical specification of what calculation you want so that that same calculation could be done either on a quantum computer or on a classical computer. Okay. And what we want to see is that the quantum computer is faster, you know, not just in classical brute force, but the fastest classical algorithm that anyone can can design."
},
{
"end_time": 6514.94,
"index": 270,
"start_time": 6488.49,
"text": " And we want to see that that is so for sort of inherent scaling reasons, you know, not just for sort of accidental reasons of hardware, but you know, the quantum running time is sort of scaling polynomially in a way that the classical run time is scaling exponentially with the size of the problem. Okay, so that's quantum supremacy. And so Preskill coined this term in order to describe sort of the kind of thing"
},
{
"end_time": 6535.503,
"index": 271,
"start_time": 6515.196,
"text": " that I and others had been talking about in the year or so prior. My then student Alex Arkhipov and I, in 2011, we had a proposal called Boson Samplet, which was a proposal for a very rudimentary kind of quantum computer."
},
{
"end_time": 6553.456,
"index": 272,
"start_time": 6536.459,
"text": " For example, it could be built using photonic components. You just generate a bunch of single photons, you send them through a network of beam splitters, and then you measure where they end up. And that's it."
},
{
"end_time": 6577.022,
"index": 273,
"start_time": 6553.729,
"text": " That's all you do here. So this is we don't think that this is universal for quantum computation or even universal for classical computation for that matter, right? It's like in some ways it's a very, very limited model of computation. And yet if you ask like, okay, what is it doing? Well, it's sampling from a probability distribution."
},
{
"end_time": 6584.531,
"index": 274,
"start_time": 6577.346,
"text": " Each time you run the experiment, you feed in the photons, they will typically end up in different places."
},
{
"end_time": 6611.954,
"index": 275,
"start_time": 6584.821,
"text": " right because you know they sort of move around randomly you know and you know i mean they they they they they or or rather they evolve in a superposition state but then when you make a measurement you collapse the superposition okay and you just see one outcome uh so you probably never even see the same outcome twice you know sometimes there's two photons here one here zero here you know sometimes there's zero here zero here you know three here and so forth all right so"
},
{
"end_time": 6640.026,
"index": 276,
"start_time": 6612.944,
"text": " So you see these different distributions, sorry, you see these different lists of photon occupation numbers, numbers of photons in each sort of output port. But then you ask the question, okay, you could ask, well, what is this useful for? We don't really have a good answer to that. But then you can ask a different question, which is how hard would it be for a classical computer"
},
{
"end_time": 6661.22,
"index": 277,
"start_time": 6640.247,
"text": " to"
},
{
"end_time": 6689.582,
"index": 278,
"start_time": 6661.596,
"text": " If there were a classical algorithm that could sample from exactly the same probability distribution as the sort of ideal version of this photonic experiment, then we say that would have sort of staggering implications for complexity classes. It wouldn't quite mean that P equal to NP, but it would mean something that's sort of morally almost as bad as that, which is called the collapse of the polynomial hierarchy."
},
{
"end_time": 6707.875,
"index": 279,
"start_time": 6690.503,
"text": " It's sort of like a more abstract version or higher up version of P equaling N. We showed that that would follow if you had a fast, exact classical simulation of boson sampling. And then if your classical simulation is only approximate,"
},
{
"end_time": 6731.561,
"index": 280,
"start_time": 6708.217,
"text": " Which is the more physically relevant case, because after all the experiment itself isn't perfect either, right? In the approximate case, we believe that that would collapse the polynomial hierarchy, but there we had to make yet another conjecture. And I would say the status of that remains unresolved to this day."
},
{
"end_time": 6752.159,
"index": 281,
"start_time": 6731.817,
"text": " okay but but you know it's it's at least it's at least seems very plausible that you know and we showed that like you know here is some well stated problem about a function of matrices called called the permanent and if this problem is sufficiently hard then boson sampling is hard to simulate using a classical computer even approximate okay so"
},
{
"end_time": 6782.005,
"index": 282,
"start_time": 6753.217,
"text": " Yes, so we did that and then independently from us there were others like Bremner, Joseph and Shepard who were having related ideas about different kinds of rudimentary quantum computers that were not obviously useful for anything but that at least seemed to give rise to these probability distributions that are hard to sample using a classical computer."
},
{
"end_time": 6802.005,
"index": 283,
"start_time": 6782.005,
"text": " Can you encode these hard problems into the amplitudes of a quantum computer? But then we realized more and more as we worked on it that"
},
{
"end_time": 6817.022,
"index": 284,
"start_time": 6802.193,
"text": " Maybe the experimentalists will care about this because what we're talking about are devices that seem potentially much, much easier to build than a full error corrected quantum computer."
},
{
"end_time": 6846.357,
"index": 285,
"start_time": 6817.312,
"text": " Basically, if you could just generate 50 to 100 photons and send them through a beam splitter network and then measure where they end up, that should already be enough to do a boson sampling experiment that is hard for a classical computer, hard for the biggest supercomputers in the world to simulate. Then we explicitly talked about that and then the quantum optics experimentalists got very excited about it."
},
{
"end_time": 6867.415,
"index": 286,
"start_time": 6846.732,
"text": " and you know they decided to start doing it you know initially like in 2013 it was like with three photons four photons this is all you know of course trivial for a classical computer to simulate right yeah yeah the difficulty ideally you know you would expect it to go maybe like two to the power of the number of photons"
},
{
"end_time": 6889.497,
"index": 287,
"start_time": 6867.841,
"text": " But then what happened was that in 2014, Google hired John Martinez, who was maybe the top superconducting qubits experimentalist in the world."
},
{
"end_time": 6914.121,
"index": 288,
"start_time": 6889.923,
"text": " and he said we want to build a 50 to 70 qubit quantum computer that's programmable using superconducting qubits and we want to do something cool with it. And what is there to do with 50 qubits that's cool? Well, there's not a whole lot, unfortunately. Most of the actually useful things, they might need like"
},
{
"end_time": 6940.555,
"index": 289,
"start_time": 6914.514,
"text": " you know, hundreds to thousands of qubits and then crucially, you know, of a much higher quality than, than Google was able to make where you could do like thousands of layers of gates, you know, and they couldn't do that. They can do maybe 20 layers of gates, right? Uh, but so, so, so, so what you could do while they, they realized, okay, we can do some version of those on sampling, right? Except, you know, except now more, more adapted to their hardware."
},
{
"end_time": 6967.534,
"index": 290,
"start_time": 6940.828,
"text": " So we talked to them about that, and we said, yeah, that sounds reasonable. But we then had to adapt the theory from boson sampling to superconducting qubits, to the kind of thing that they were building. So we did that in 2016, 2017. And then in 2019, Google announced that they had actually done this."
},
{
"end_time": 6987.961,
"index": 291,
"start_time": 6967.534,
"text": " So they built a 53 qubit device called Sycamore and they used it to sample from some probability distribution over 53 bit strings that you get by just applying like a random sequence of quantum operations to these qubits."
},
{
"end_time": 7016.817,
"index": 292,
"start_time": 6988.422,
"text": " And then, you know, at first they were saying, well, with the best classical algorithm that we can think of, it would take 10,000 years to do the same thing on a supercomputer. Right. And the press loved that. Right. And they ran with that number and that, and that turned out to be wildly overoptimistic. Right. So I could imagine Mishio Kaku would love that. Yes. Oh, I'm sure he would. Right. But, but you know, the, the, the, the hard part in quantum computing, if you want to be intellectually honest about it,"
},
{
"end_time": 7036.596,
"index": 293,
"start_time": 7017.09,
"text": " is that you always have to compare against what is the best thing that anyone can do with a classical computer. And you're only winning if you do better than that. And what's the best thing that you can do with a classical computer is often far from obvious. After all, that's what the P versus NP question is about."
},
{
"end_time": 7066.561,
"index": 294,
"start_time": 7036.988,
"text": " Right? Right. So so so so and indeed what happened over the next couple of years is that people got better and better at simulating the Google type of experiment with classical computers by, you know, taking advantage of the noise and taking advantage of the fact that each qubit can only sort of talk to its nearest neighbors. You know, so you can you can sort of take advantage of all the the current technological limitations of Google's experiment."
},
{
"end_time": 7087.858,
"index": 295,
"start_time": 7066.869,
"text": " in order to simulate it faster with a classical computer. I would say that the current situation is that the Google chip is still somewhat better than any classical solution that we have for the task of simulating itself. If you measure, let's say, by the total energy cost,"
},
{
"end_time": 7109.326,
"index": 296,
"start_time": 7088.183,
"text": " Right or by you know the the money that it takes to run it or the co2 that's emitted by steps well by the the trouble with steps is that you know you like with a Classically you can always roughly have the number of steps by just using twice as many cores Okay, so these problems are very very parallelizable"
},
{
"end_time": 7132.551,
"index": 297,
"start_time": 7109.48,
"text": " Right. So, you know, you can always do it faster if you're willing to like go to AWS or whatever and just say, you know, I want, you know, this, this massive number of cores, right. But then, you know, it's interesting, right. But then at some point for the comparison to be fair, you know, you should maybe be talking about money or you should be talking about, you know, the energy, you know, the electricity that gets spent."
},
{
"end_time": 7161.237,
"index": 298,
"start_time": 7132.79,
"text": " And if you look at metrics like that, then I think that the quantum computer still wins on some tasks, but only by a couple orders of magnitude at this point. That sounds a bit human though, because if we're measuring it by money, firstly, that's human. But if we're measuring it by energy, isn't it then not based on the algorithm, but based on our current cores and maybe in the future, Apple comes out with M5? Of course it is. Of course it is. So you could say that you are fighting against a moving target, right?"
},
{
"end_time": 7189.582,
"index": 299,
"start_time": 7161.578,
"text": " like quantum supremacy could be achieved and then unachieved because you know the classical classical hardware and software will both get better you know and so if you want to claim that a quantum computer is better for something right then you know you may have to keep improving the quantum computer you know just for for that statement to still be true okay now now the hope let's be clear okay the hope is that eventually you have an error corrected"
},
{
"end_time": 7220.196,
"index": 300,
"start_time": 7190.452,
"text": " you know programmable quantum computer and at that point you can scale up to as many operations as you want on as many qubits as you want okay and at that point you know you could use like millions of qubits to factor some enormous number right that like unless there's a breakthrough in classical algorithms that just cannot be done classically within the whole lifetime of the universe right so that's the eventual goal okay but we're not there yet okay"
},
{
"end_time": 7242.193,
"index": 301,
"start_time": 7220.52,
"text": " And what we can do today are these sorts of sampling experiments, where we're solving problems that don't have a single right answer. We're sampling from a distribution over possible answers. And a key drawback of these problems is that"
},
{
"end_time": 7273.046,
"index": 302,
"start_time": 7243.183,
"text": " Even just to verify what the quantum computer is doing already appears to take exponential time with a classical computer. Which means that we're sort of inherently limited in how far we can scale this. Like, you know, if you scale it to 300 qubits, even if it worked, how would you ever prove it? How would you ever convince a skeptic of what you had done? So we're sort of forced to stay in this regime where the advantages that we can get over classical computers are relatively marginal ones."
},
{
"end_time": 7302.654,
"index": 303,
"start_time": 7273.473,
"text": " But at least we can now do that. Five years ago, we could not even do that. And now we can. I think it's a step forward. I think it's taught the experimentalists a lot about how to actually integrate large numbers of qubits. And maybe scientifically, the most important thing that they learned from these quantum supremacy experiments"
},
{
"end_time": 7321.084,
"index": 304,
"start_time": 7302.978,
"text": " was that like the total amount of signal you get what's called the circuit fidelity is well it's falling off exponentially with the number of operations you know which sounds kind of bad right but it's but the good news is that it's merely falling off exponentially and not faster than that."
},
{
"end_time": 7350.725,
"index": 305,
"start_time": 7321.493,
"text": " Okay. So basically the total fidelity, you know, like let's say, you know, each individual two qubit operation has a fidelity in Google's experiment of about 99.5%. Right. And there's about a thousand such operations. Okay. And so, so then the total fidelity that you get for the circuit, it looks like just 0.995 to the power of a thousand. Right. Uh, you know, which is like the simplest prediction that you could possibly make."
},
{
"end_time": 7379.753,
"index": 306,
"start_time": 7351.169,
"text": " And as long as that remains true, then ultimately quantum error correction should work. So the people who believe that scalable quantum computers are impossible, such as Gil Kalai is a famous one, what they basically have to believe is that either quantum mechanics itself is going to break, which let's face it, that would be far more exciting than a mere success in building a quantum"
},
{
"end_time": 7402.432,
"index": 307,
"start_time": 7379.872,
"text": " Sure. That would be a revolution in physics, or else they have to believe that there's some sort of conspiratorially correlated errors that will violate all the assumptions of the theory of quantum error correction. But from the quantum supremacy experiments, we can now say we see no sign of those conspiratorially correlated errors. You're referring to super determinism?"
},
{
"end_time": 7429.36,
"index": 308,
"start_time": 7402.756,
"text": " No, I'm not. Super determinism is so bizarre that it's not even clear that that would have any empirical consequences at all. That's just saying there's a giant cosmic conspiracy theory that just predetermined everything that would happen from the beginning of time. It was like, you can always believe that, but it's sort of explanatorily worthless. It has no power to explain anything."
},
{
"end_time": 7455.538,
"index": 309,
"start_time": 7430.486,
"text": " The more interesting thing, if there were these conspiracies in the errors affecting qubits, that would be something that would be empirically observable. And if the correlations were strong enough, then conceivably that could even kill quantum computation. But there are some basic difficulties here. One is that it's very, very hard"
},
{
"end_time": 7485.776,
"index": 310,
"start_time": 7455.896,
"text": " design a model of correlated errors that only kills quantum computation and that wouldn't also kill classical computation. If you kill classical computation then you've proved too much because we know that scalable classical computers can be built. But then the other thing you can say is that from the quantum supremacy experiments we see no sign of these correlated errors. The errors look pretty independent and in that case"
},
{
"end_time": 7503.763,
"index": 311,
"start_time": 7485.998,
"text": " it's you know as long as that remains true then it's just a quantitative question you just have to get the the accuracy of each operation to be high enough like instead of .995 maybe .9999 right and then and then at that point quantum error correction should work"
},
{
"end_time": 7520.213,
"index": 312,
"start_time": 7504.753,
"text": " Now we both got to get going shortly and I want to end on the topic of consciousness. So why don't you talk about your critiques for IIT and then also what the pretty hard problem of consciousness is. But before you do that, I just wanted to ask you a yes or no question about if you saw Tim Palmer's"
},
{
"end_time": 7545.35,
"index": 313,
"start_time": 7520.213,
"text": " response to your critiques on super determinism in his recent article, Tim Palmer's article on super determinism without conspiracy is listed in the description. And you should know that Tim Palmer was on the theories of everything podcast. And that link is also in the description. He was on with Tim modeling at the same time talking about the interpretations of quantum mechanics. Yeah, I mean, I say I think I think it is a conspiracy. I mean, I think that he redefines terms in an utterly perverse way."
},
{
"end_time": 7568.797,
"index": 314,
"start_time": 7545.64,
"text": " in order to"
},
{
"end_time": 7597.688,
"index": 315,
"start_time": 7569.019,
"text": " like orders of magnitude more plausible to me than these right these are just you know these people have succeeded at like getting out to the public right and putting their message before the public but like scientifically i regard these as worthless ideas so um uh so so okay um yeah uh but but but now uh uh consciousness yeah so so so so integrated information theory is another thing that i think"
},
{
"end_time": 7624.582,
"index": 316,
"start_time": 7598.063,
"text": " has, you know, okay, you know, maybe like it was worth trying, it was worth thinking about, but that has also become, you know, a worthless idea, a pathological idea. Okay. So it's a proposed, you know, theory of, of consciousness, or at least of what things are conscious and what things are not, uh, that was, uh, um, originated, originated by Giulio Tononi. Okay. And, uh, you know, also,"
},
{
"end_time": 7653.558,
"index": 317,
"start_time": 7624.889,
"text": " uh... pursued by you know a bunch of other people such as christoph coke uh... i think you know max tagmark uh... was into it and and basically what it says is that there is some you know you could take any complex system and then there is some quantitative measure that you know that that that you can calculate uh... for that system that somehow measures how interconnected all of its components are right and and the war you know that they call that fee"
},
{
"end_time": 7673.985,
"index": 318,
"start_time": 7653.848,
"text": " The larger is that fee measure, the more conscious the system is. You could say, what is this fee? Well, the actual definition of it keeps changing. There's not actually the one fixed thing that you can critique. They keep fiddling with the definition of it."
},
{
"end_time": 7696.049,
"index": 319,
"start_time": 7674.394,
"text": " And if you read the papers about it, what they say is, well, we have these axioms of conscious experience and then we derive phi from these axioms. But actually, there's no derivation at all. It's sort of like pseudo mathematics. It's like they state the axioms and then at some point,"
},
{
"end_time": 7725.845,
"index": 320,
"start_time": 7696.305,
"text": " The axioms are not even clear enough for me to really understand what they are saying. But at least the fee measure seems reasonably clear. Once you've decided what are the subsystems, what does it mean for a subsystem to be connected to each other, and so forth."
},
{
"end_time": 7752.09,
"index": 321,
"start_time": 7726.135,
"text": " then you know and you decided which version of fee you're working with then you know you can actually calculate these numbers okay and then you know their their case you know they're like they were neuroscientists and they said well there seems to be much higher connectivity in the cerebrum than in the cerebellum for example right and the cerebrum is associated with consciousness and the cerebellum is not right so that was"
},
{
"end_time": 7770.691,
"index": 322,
"start_time": 7753.131,
"text": " That was the kind of evidence that they gave. I wrote a blog post about this nine years ago where I pointed out that we could easily invent systems that have massively higher fee than the human cerebrum."
},
{
"end_time": 7799.906,
"index": 323,
"start_time": 7771.049,
"text": " Right. But that are just like a gigantic grid of XOR gates or something like that. Right. Without processing. Yeah. Well, OK. Yeah. Maybe, you know, they do process something like they compute the XOR of a bunch of bits. Right. But but it's all like completely regular. It's like there's not even anything interesting or intelligent going on there, let alone anything conscious. Right. And yet, you know, if you calculate this number that they put forward, then you'll get"
},
{
"end_time": 7822.978,
"index": 324,
"start_time": 7800.162,
"text": " that the connectivity between the different components can be arbitrarily large, just depending on how big you make the thing. To me, that seems like a reductio ad absurdum. The theory is just making an utterly wrong or absurd prediction."
},
{
"end_time": 7833.336,
"index": 325,
"start_time": 7823.063,
"text": " and therefore, this connectivity, it might be correlated with consciousness in various cases, but it cannot be identical with consciousness."
},
{
"end_time": 7861.903,
"index": 326,
"start_time": 7833.831,
"text": " The problem is that you're just using your intuition but you have to rely on the theory and what the theory tells you is that this grid of"
},
{
"end_time": 7888.848,
"index": 327,
"start_time": 7861.903,
"text": " This giant grid of XOR gates is conscious. In fact, it's much more conscious than you are, right? And you have to be bold and just believe what the theory says. And, you know, and my response at that point was like, okay, if a theory is sort of getting right, you know, the things that, you know, the cases where we already thought, you know, we knew the answers, right, then you might be interested in, you know, what does the theory say about the really hard cases? Like, let's say,"
},
{
"end_time": 7917.261,
"index": 328,
"start_time": 7889.087,
"text": " about a fetus or about a coma patient or about an earthworm or about an AI program, right? But if the, if the, you know, your measure of consciousness is already, you know, telling you that a potato chip bag is conscious, right? Or that, you know, any old, you know, sort of uninteresting physical system, you know, is conscious just, you know, because of this sort of, you know, this sort of, you know,"
},
{
"end_time": 7947.073,
"index": 329,
"start_time": 7917.739,
"text": " This theory has just continued"
},
{
"end_time": 7974.241,
"index": 330,
"start_time": 7948.08,
"text": " With TD Early Pay, you get your paycheck up to two business days early, which means you can go to tonight's game on a whim, check out a pop-up art show, or even try those limited edition donuts. Because why not?"
},
{
"end_time": 8001.852,
"index": 331,
"start_time": 7975.06,
"text": " A bunch of philosophers and neuroscientists who said that integrated information theory is pseudoscience and then there was a response and I didn't even wade into this because I felt like I had said my piece a decade ago."
},
{
"end_time": 8028.985,
"index": 332,
"start_time": 8002.244,
"text": " It's like, yeah, these are ideas that are worth exploring, but then once you see that you make a prediction that's that badly wrong, then I think you have to go back to the drawing board. You have to say, okay, well, then this is not a measure of consciousness. Instead, they just keep trying to rescue the theory, and at some point, that kind of thing does degenerate into pseudoscience."
},
{
"end_time": 8059.411,
"index": 333,
"start_time": 8029.445,
"text": " So it sounds like what he's saying is that what you think of as a reductio ad absurdum is actually a productio ad correctum. You're proving something correct and we should listen to the theory. Yeah. So why can't we follow that same logic when it comes to the many worlds and say, look, on one hand, some people can say it's a reductio ad absurdum. You're predicting all of these other worlds. Yeah. But then Sean Carroll may say, no, no, we should be listening. Well, I would say that the difference is that quantum mechanics gets, you know, every single case that we can check, it gets the right answer. Right."
},
{
"end_time": 8088.507,
"index": 334,
"start_time": 8059.582,
"text": " right? You know, that's been true for 100 years. There was zero counterexamples, right? And that's now even with very, very complicated, entangled quantum systems. And so then, you know, it is natural to just want to do the extrapolation and say, you know, assume that this continues to be true up to arbitrary scales, then what does that mean? Because we've seen no sign otherwise, right? But like with consciousness, like I feel like if you want to decide what is or isn't conscious,"
},
{
"end_time": 8107.602,
"index": 335,
"start_time": 8088.78,
"text": " Or at least not having anywhere near as much."
},
{
"end_time": 8135.128,
"index": 336,
"start_time": 8107.858,
"text": " Right. Yes. Yes, exactly. It's not having nearly as much. If you say that this glasses cloth has much more consciousness than I do, then I say, what do you even mean anymore by the word consciousness? I don't think you're talking about the same thing that I was trying to talk about. Right. Right. Yeah. Okay. And then the pretty hard problem consciousness is... Yeah. That's just the problem of... Okay. So the hard problem of consciousness is, you know,"
},
{
"end_time": 8159.599,
"index": 337,
"start_time": 8135.299,
"text": " Articulated by the philosopher David Chalmers in the 90s is to explain why there is ever anything that it is like to be. Explain how subjective experience can arise out of mere matter or mere physical systems obeying the laws of physics. In some sense, this is a problem."
},
{
"end_time": 8188.797,
"index": 338,
"start_time": 8159.821,
"text": " that goes all the way back to Democritus in like 400 BC. And you have a book on this. I do. I do. Yeah. I mean, I mean, Democritus already stated this problem in a remarkably modern way. Right. And, you know, and certainly Descartes, you know, asked this question centuries ago. So this is, you know, one of the great problems of philosophy or maybe, you know, the great problems of all of human existence. And it's not even clear what an answer would look like."
},
{
"end_time": 8217.79,
"index": 339,
"start_time": 8189.189,
"text": " What kind of thing could be an answer, let alone how to find that answer? Whenever you encounter something that is just way too hard, whether it's the hard problem of consciousness or whether it's P versus NP, then it's natural to want to scale back and say, is there an easier related problem that we can make progress on? What I call the pretty hard problem is just the question,"
},
{
"end_time": 8245.896,
"index": 340,
"start_time": 8218.012,
"text": " which physical systems are associated with consciousness and which are not. You could imagine answering that without having to answer among the ones that are conscious, like why are they conscious or how. You could imagine just giving a criterion that agrees with intuition in all the cases that we can think of and that actually calculates"
},
{
"end_time": 8269.002,
"index": 341,
"start_time": 8246.118,
"text": " Well, professor, thank you for spending so long with me. Sure. It was so much fun. Yeah. All right. I hope to speak with you again. Yeah. All right. Take care. Talk to you later. Bye bye."
},
{
"end_time": 8288.046,
"index": 342,
"start_time": 8269.394,
"text": " If you enjoyed this podcast, then one that I recommend is the one with Tim Palmer and Tim Modlin as they're both superlative explicators of quantum theory and super determinism was a central tenet of that conversation. The link is in the description. Also, if you'd like to donate as we've had trouble monetizing the channel with sponsorship, then please do so."
},
{
"end_time": 8304.241,
"index": 343,
"start_time": 8288.046,
"text": " at Patreon.com slash Kurt Jaimungal or the PayPal link is in the description as well as a crypto link. Your support helps Toe Delve this much in depth with each episode, keeping it high quality and helps us continue. Thank you so much. Every dollar helps."
},
{
"end_time": 8328.422,
"index": 344,
"start_time": 8304.241,
"text": " The podcast is now concluded. Thank you for watching. If you haven't subscribed or clicked that like button now would be a great time to do so as each subscribe and like helps YouTube push this content to more people. You should also know that there's a remarkably active discord and subreddit for theories of everything where people explicate toes, disagree respectfully about theories and build as a community our own toes."
},
{
"end_time": 8346.442,
"index": 345,
"start_time": 8328.422,
"text": " Links to both are in the description. Also, I recently found out that external links count plenty toward the algorithm, which means that when you share on Twitter, on Facebook, on Reddit, etc., it shows YouTube that people are talking about this outside of YouTube, which in turn greatly aids the distribution on YouTube as well."
},
{
"end_time": 8371.596,
"index": 346,
"start_time": 8346.442,
"text": " Last but not least, you should know that this podcast is on iTunes, it's on Spotify, it's on every one of the audio platforms, just type in theories of everything and you'll find it. Often I gain from re-watching lectures and podcasts and I read that in the comments, hey, toll listeners also gain from replaying. So how about instead re-listening on those platforms? iTunes, Spotify, Google Podcasts, whichever podcast catcher you use."
},
{
"end_time": 8396.493,
"index": 347,
"start_time": 8371.596,
"text": " If you like to support more conversations like this then do consider visiting patreon.com slash Kurt Jai Mungle and donating with whatever you like again it's support from the sponsors and you that allow me to work on toe full time you get early access to add free audio episodes there as well for instance this episode was released a few days earlier every dollar helps far more than you think either way your viewership is generosity enough."
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]
}No transcript available.