Episode 11: The Turing Principle and Artificial General Intelligence
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Thank you. All right, welcome to the Theory of Anything podcast. How are you doing, Cameo? I'm doing great, Bruce. How are you? Good. So in our previous episode on computational theory, previous two episodes on computational theory, I first described what computational theory was and

Then I got into like, what do they do with computational theory? And I talked about the classes of computations, NPP, things like that, MP hard. And that one was a bit technical, but we've, we've lived in, I've already talked about the Turing principle, but I'm going to go into detail now because I feel like this is one of the single most important

things that there is to know in science that many scientists don't know. And honestly, it's just out of interest. This was the thing that got me into the four strands to David Deutsch's writings, Penrose's writings, things like that, was the discovery of the Turing principle and the implications of it. So I wanted to talk that through, and this is kind of a pivotal thing. And then also, this is the reason I got into AGI, was because of the Turing principle.

So, and the reason I went back to school, started studying machine learning, things like that. So... The robot, over the world. Yes. All right. So got a lot of slides here. For those who can actually see the slides, this is almost more like my notes that I remember. I have like a ton of quotes and such. The slides aren't really important and I'm not going to read everything, all the quotes word for word. They're just to kind of remind me where I got these quotes and what the references are. So...

Let's start into this. So we left off with, this is one of the previous slides that we showed. What is the Church-Turing thesis? So I said, okay, it could be thought of as it's not possible to come up with any sort of computational machine that can perform a logic program that a plain old Turing machine can't.

Or maybe you could say Turing machines and their equivalent are the most powerful possible types of computing machines, and there are no more powerful ones out there that we don't know about yet. This is the Church-Turing thesis. It's a scientific theory. It's not a mathematical proof. It's just a theory. There are no known counterexamples to it. Okay?

Okay. Okay. And then I said, okay, what, what this means then is that all computational machines are functionally equivalent. So if you know how many computations or comparisons that it will take for a Turing machine to do a computation, that is how many it's going to require on any machine you can build because the laws of physics will require it to be that many computations or comparisons.

Right. Okay. Which means that the speed of an algorithm is independent of any specific computing device. Okay. So a competing device might be faster or slower. You have faster computers and slower computers, but the algorithm itself is,

has a speed, if you will, the number of comparisons. And this is where we talked about class P, polynomial time is faster than class NP. Class NP includes class P, but anything that's in NP that isn't P would then be exponential. And exponential just is intractable. You just can't do very much with the algorithm. You have too many, if what you're trying to work with is too large of an input size, then it's just going to take forever. You know, the sun will explode before the computation completes.

So, and then I also mentioned that my interest in artificial intelligence is because it's the study of what do you do when you have an intractable problem. How do you still try to go about solving that problem as best you can. Okay. And so, and so these are all things that kind of get me excited and got me interested and got me going back to school.

Now, I'm going to talk a little bit about the history of the Turing principle. And it's actually kind of funny because David Deutsch was reading his book, The Fabric of Reality, was where I discovered the term, the Turing principle. And in his book, he credits Roger Penrose for the term. But as we'll see here from these quotes, Penrose did not coin the term. David Deutsch did. Penrose called it something else.

He did coin the idea. What did he call it? He called it the Turing thesis is what Penrose called it. Oh, interesting. So Penrose, I've got a couple of quotes here for those who can see the screen. The first one, which I'm not going to read, is basically Penrose. Now, The Emperor's New Mind is the book I'm getting this from. Penrose is the opposite of David Deutsch. He believes that AGI is not possible. He believes

He doesn't accept the Turing principle. His book is to convince you that these are not true scientific theories. It was reading his books, which are super complicated and very technical, that I finally became convinced that David Deutsch was right. Okay.

And it really helped to have someone really smart lay out the counter argument before I could really wrap my mind fully around the full argument and why it just really had to be true, right? So the first thing Penrose is saying in this first quote is he's saying, look, it's not that hard to show that a Turing machine is capable of performing any mechanical operation whatsoever, right? So he accepts that much that...

any mechanical operation you can think of, a Turing machine is a universal machine that is able to do that same mechanical operation. There's an app for that. There's a Turing machine app for that. Oh, is there really? No, I'm kidding. So computers are in fact Turing machines, right? Yeah, sure. So, yeah. So, I mean, there's, there is an app for that. My family has an ongoing joke about like computers,

somebody needed a nail or a hammer and somebody else said, Oh, I think there's an app for that. Anything you can think of, there's probably an app for that somewhere. And I think, all right, I'm sorry. That joke is actually very relevant to the point, right? The very fact that, that a computer is universal, the very fact that a computer can do any mechanical operation whatsoever is why they're completely versatile. You can have an app for everything.

Right. Right. So, and this is really where we're going with the Turing principle. It's the idea of universalities, the idea of a computer can compute anything that computer can compute. That is what the laws of physics allows. Right. There is no anything else out there. So now the second quote from Roger Penrose, he says, some attention has been turned to the matter of whether evolution,

an actual physical system, presumably including human brains, this is where it ties into AGI a little, subject as they are to precise physical laws, are able to perform more than, less than, or precisely the same logical and mathematical operations as a Turing machine. So in plain English, what he's saying here is we're turning our attention to do the laws of physics, laws of physics are precise mathematical laws. So does that mean that the laws of physics match the

what a Turing machine does. Can you simulate all laws of physics on a Turing machine? And since the Turing machine uses the laws of physics to operate, then you have, just like I've showed you with the previous episodes where one is equivalent to this one, this one's equivalent to that one, he's asking, is physical laws equivalent to a Turing machine and is a Turing machine equivalent to physical laws? Right? Right, right, right. Okay. And now Penrose's answer is

No. And I'll explain to you why he says that and why he's probably wrong. But anyhow, so he then goes on to say, and this is where he coins the idea of the Turing thesis, as he calls it, the Turing principle, as Deutsch calls it. He says, the original truth

Church thesis is now seen simply to assert that mathematical algorithms are precisely the things that can be carried out by an idealized computer, which from the definition of the word algorithm that is now usually adopted becomes mere tautology. So he's saying Church is, so you've got Church-Turing thesis, he's splitting them apart. He's saying there's the Church thesis and there's the Turing thesis, that they aren't quite the same, that Church and Turing had a slight

difference of how they looked at the church Turing thesis. Churches was a mere tautology. He's saying, look, the Turing machine or the church lambda calculus was his version of it. That is how you define an algorithm. He wasn't necessarily saying the laws of physics can't do something different than an algorithm, that the laws of physics are algorithmic. Okay. He wasn't going there. All right. Turing did. Okay.

Okay, so he goes, Penrose says, it is, however, probable that Turing himself had something further in mind, that the computational capabilities of any physical device must, in idealization, be equivalent to the action of a Turing machine. Perhaps one should call this physical assertion Turing's thesis in order to distinguish it from the original purely mathematical assertion of Church's thesis. Okay. Okay. So this is the moment that Roger Penrose invented Turing.

the term Turing principle. And in fact, he didn't, but, but it was the idea, the conceptually, it was the same conceptual idea. He just happened to call it the Turing thesis. Okay. Now Deutsch in fabric of reality, he says the mathematic mathematician, Roger Penrose has suggested it should be called the Turing principle. So he uses the wrong term there, but this is how Deutsch then defines the Turing principle. So,

Somewhat differently than I do. There's multiple ways to define it. They're all kind of equipped. They're all equivalent, but he says for abstract computers, simulating physical objects, there exists an abstract universal computer whose repertoire includes any computation that any physically, that's any physically possible object can perform. Okay. He's taking it to its logical conclusion. You can build a computer that can simulate anything, right? There's nothing that can't be simulated. Right. All right. Um,

So based on this, then what is the Turing principle? It's that everything in physical reality is computable on a Turing machine. And we'll see in a moment, we have to actually adopt the idea, not just a Turing machine, but a computational Turing machine, which is actually different, but we often simplify it and say Turing machine, even though we don't mean it. The Turing principle is equivalent to the church Turing thesis. It just follows it to its logical conclusions. And, uh,

Now, you can take the position, there are computers more powerful than the Turing machine, we just haven't discovered them yet. Okay. And in fact, I'm going to show you how to take that position and that people do take that position. All right. However, that does violate Popper's epistemology that we've agreed with in past shows. Because now we're comparing an exploration to a non-explanatory.

Right. We're saying, hey, we have a non-explanation that makes all of this invalidated. Right. Which might be true. It's not that a non-explanation is therefore false. That's not what we're saying. Right. What we're saying is you've got to see that there's a huge difference between those two. Right. We've got this explanation. It's the Turing principle. It's that everything can be simulated on a computer. That is a scientific reality.

well-tested scientific theory that underlies really, honestly, I'm going to show all of science. Okay. But in fact, there's no way to know that definitively know it's true there. You can always take the position that it's not true.

but then you really are just stepping out into things that we have no explanation for, right? You're making up a very easy to vary non-explanation and that's it. That's all you're doing, okay? You're outside of science at this point, right? Now, maybe it's a good research project that might be taken into science at some point and I'll show you an example of that here shortly. But this is, there's a big difference between taking science

accepting the Turing principle saying, okay, look, it is our best scientific theory. Therefore I'm going to tentatively accept it until someone comes along with a better theory for me to accept and simply taking a position that has nothing backing it at all. Okay. Um,

So we can tentatively assume the Turing principle to be true based on trying to test it and our failure to falsify it. Okay, that would be following Popper's epistemology. Likewise, that's the Church-Turing thesis, but for the same reason we can accept the Turing principle, right? We can conjecture that absolutely everything ever discovered by the physical sciences can be broken down into computations. Okay.

We know of no exceptions to that. That's a really good, solid scientific theory. Okay. That's the Turing principle. That's a scientific theory for the same reason church Turing thesis is a scientific principle. Sure. What we're really doing here though, is we're asserting the computational nature of reality. Okay. And this is really an idea that even though you have scientists who will say they don't

agree with that, they're almost always just kind of assuming it, right? It seems to be an inexplicit idea in the background of science that scientists just assume. I mean, when you publish a physics paper, people expect there to be a mathematical explanation for physics, right? Of course. And so, and then, and there... We use math to prove

That's how we use it currently. Right. So the Turing principle sort of underlies the way we think of science, whether you are explicitly accepting the idea or not. Okay. Now I made the claim that it was the best tested theory in a past show. I'm going to just cover that quickly because I feel like it's got some relevance here. Sometimes I've heard the claim that quantum mechanics is the best tested theory in science. Okay. Now, I mean,

I mean, what does that mean to be the best test of theory and science? I've got no idea. It probably, it's probably a meaningless statement. Okay. It's probably a somewhat subjective, depending on what you happen to mean. Right. Well, yeah. And, and yes, what does a test mean? I would say that gravity is the best test of theory and science because all the time. So,

So I'm going to make the case, though, that we can consider the Turing principle the best tested theory in science, even using your gravity example. Okay. So quantum mechanics –

has been tested down to like the ninth and 10th decimal point. I mean, this is a probabilistic theory. So that might be a little surprising that you can test it to the ninth and 10th decimal point. There are no known counter examples to unlike general relativity, where we know black holes defy the theory and break the theory. We don't really know of any places where quantum mechanics breaks other than the obvious that it doesn't encompass gravity.

for some reason. But there are no, we can't go out and do tests and find observations and go, oh yeah, that's a case where the theory breaks down, right? We don't know of anything like that for quantum mechanics. And it's been, there's no other theory where that's really been true of, right? It's just, in that sense, the best tested theory. I can understand why people might call it that.

Okay. And Deutsch's seminal paper, quantum theory, the church Turing principle and the universal quantum computer. He showed that quantum mechanics is perfectly simulatable on a quantum computer. So basically he demonstrated that a quantum computer, which we don't, we don't know how to engineer them well at this point, but a quantum computer is equivalent to quantum mechanics that the two are one in the same. Right. This would seem to be a scientific proof of the Turing principle, but

You can't really prove anything in science, so it's not a proof in that sense. But it's the basis for, it's a stronger scientific basis than what I've explained so far. He's actually laid out, look, all of reality is quantum mechanics. That's the theory. And if that's true, then the Turing principle is true, period, end of story. Okay. Yeah. Now,

This quote here from Roger Penrose, he says, according to Deutsche's analysis, quantum computers cannot be used to perform non-algorithmic operations, i.e. things beyond the power of a Turing machine, but can achieve a greater speed than a standard Turing machine. Now, I said something wrong in one of our past podcasts. I need to correct it here. Oh, okay. I said that a quantum computer can do some things a Turing machine can't.

That's true. Language is loose. And I misunderstood something in, when I was putting this together, I was looking at that paper again, and I misunderstood something that Deutsch had said in that paper. And

He does say that the quantum computer can do things the training machine can't, but what he really means is with greater speed. It can't do anything. The training machine can still, in theory, do anything a quantum computer can do. It's just that some things, it will just be intractable or it's tractable for the quantum computer. I believe in a past podcast, I claimed otherwise that there were some esoteric exceptions. There aren't, according to my now reading of this paper.

Which makes more sense, really, I think. For there not to be, right? Because if we believe that there is nothing beyond the power of a Turing machine, then there shouldn't be anything beyond the power of a Turing machine. Correct.

Now, however, this does mean that there's kind of an exception to the Turing principle. Because one of the things I had said previously is the number of comparisons that a Turing machine needs will be the same for any computing device that you can build. That is not true. That has been violated. That part of the Turing principle has been violated already with quantum computers. Okay. Okay. Now...

In a second, I'll explain to you why that's not really that meaningful, but let's kind of hold that in your mind for the moment. The quote that I just read from Penrose, though, he's effectively admitting that Penrose is admitting that Deutsche's analysis rejects quantum mechanics as a possible way around physics.

um, the Turing principle. Okay. Penrose in his book, this is one of the things that he really gets at is that he rejects quantum mechanics altogether. Part of his belief that the Turing principle isn't true and that you can't build, um, an AGI assumes, I mean, you literally must assume that the theory of quantum mechanics is just wrong. If you're assuming that quantum mechanics is correct,

then the Turing principle holds and Penrose is admitting this. Okay. So, and this is something I think people get confused on. In one of the past podcasts, I talked about a guy who was trying to argue with me about Penrose and Penrose's claim that you can't build an AGI. He didn't even get this right. He didn't even get the basics that Penrose's argument is on the assumption that quantum mechanics is wrong. Okay. That's a huge part of,

of Penrose's argument. So you can't make quantum arguments about consciousness with the existing quantum theory, right? What you're really doing is you're pointing to some future theory that doesn't exist, that we know nothing about, which is a non-explanation, getting back to Popper's epistemology. So what they did is they adapted the Church-Turing thesis to now be called the Church-Turing-Deutsch thesis, and now this includes quantum computers.

And this is why, one of the reasons why I said it doesn't really matter that they violated the Turing principle a little bit. Because as it turns out, as long as, if you can discover a physical phenomenon, and it's still mathematical, right, then you can go build a computer out of that physical phenomenon. And yes, it'll be able to do things a Turing machine can't do. And yes, that will violate, right,

the church-turning thesis in a certain form, but it'll just make a new church-turning thesis, one that's more powerful, right? Interesting. Okay. Okay. And so if that's all you're talking about

That still means we can build an AGI, for example, right? It's, it doesn't, you may not be able to do it on a actual current Turing machine style computer because it may be, it's intractable, but you will just build a quantum computer and then we'll build an AGI, right? And Penrose does believe this. He does believe that even though he's denying that computers can build an AGI,

he still believes we'll be able to physically build them at some point, right? Because he's still a hard-headed scientist. Sure, of course, of course. And scientists believe in the potential of the future and are constantly looking at ways to build it out generally. Right, right.

However, it is important to note from this quote that Penrose is admitting that quantum mechanics is equivalent to the Turing principle. And he's just accepting that. Okay. And he's accepts Deutsch's analysis on that, which is one of the reasons why I think Penrose is just going to turn out to be wrong. Um, he really is stepping off into a non-explanation and this is his whole book is really arguing for a non-explanation. Um,

And now I kind of explained this, but laying out what if we found an exception, Deutsch points out that you could find exceptions in his paper. He says, we could falsify the Turing principle. In principle, we could. It would be exactly the way I just explained. We would find an exception where something physically can be done and the Turing thesis says you can't.

But if we did that, what we would do is we would then use that new physical phenomena to build a new type of computer. And that would then be the new version of the Church-Turing thesis. And we would continue on our merry way. And in fact, that's what happened with quantum computers. We now have the Church-Turing-Deutsch thesis. And I usually just

call it the church-turing thesis. Even Deutsch usually calls it the church-turing thesis, even though his name has been inserted into the end now. It's just easier to refer to it that way. But so, and this is, and a lot of people will say this, they'll say something like, well, you know, humans can be conscious because they're biological and computers aren't biological, so they can't.

Underlying that statement is the assumption that biology is somehow doing some sort of laws of physics that we don't currently understand. Right. Yeah. And if that's true, I mean, let's be honest, biology is still atoms. Right. So is a computer. So there's no real reason to believe that would be the case. Okay. But if it were to be the case,

then that would mean that we can build an AGI using chemical processes that are equivalent to biology. It wouldn't stop us from building an AGI and it wouldn't really invalidate the heart of the Turing principle. It would only invalidate the technicality of the existing Turing principle. It would create a new Turing principle that is more powerful. Okay. So, um, no, this is, I just got to tell you, this is one of the coolest things ever. So, um,

Penrose trying to buoy up his case. He uses Deutsch, one of Deutsch's papers, to explain what he has in mind when he's talking about a non-computable device.

non-computable effect in physics. He gives an example of one from Deutsch, actually, that may actually exist and that may someday lead to a revision of the Church-Turing thesis, just like quantum computing did. Now, unfortunately, the example he uses, I don't think it buys him anything for the rest of his arguments, but it's a super cool example. And this will show how

yes, we accept the Turing principle tentatively, but we do need to be open to there could be a new one in the future. And that would be a good thing, not a bad thing, right? So let me read this whole thing though, and then I'll translate it because it might be a little bit technical. Though it indeed seems reasonable to rule out space-time geometries with closed time-like lines. Now remember we, in a past podcast, we talked about Deutsche's paper about closed time-like lines. That's time travel.

we're talking about. Yes, right. As descriptions of a classical universe, a case can be made that they should not be ruled out as potential occurrences that could be involved in a quantum superposition. This indeed is Deutsch's point. Remember, this is Penrose in Shadows of the Mind, another one of his books arguing against AGI. And then he goes on to say, although the contributions... So let me just explain that quickly because that may not make a ton of sense. It

space, so space-time geometries that are closed time-like lines would be a series of tilted light cones that are in a circle, which would mean that time is in a loop, okay? Because that's the way general relativity works. So you end up with time travel. You end up with some spot in space where you travel there and you're at a different time than you were, you're back in time, but by the time you get there because of time travel, because of these closed time-like loops, okay? What,

Penrose is saying, quoting Deutsch, he's claiming Deutsch claims. The issue here is I've never heard Deutsch claim this. I've only heard Penrose claim this. In the footnotes, Penrose says, I'm getting this from an early draft that I read of Deutsch's paper about closed time-like lines. And

this argument got dropped from his final paper. Although I asked him, I asked Deutsch, is it dropped because you don't think it's right? And he claims Deutsch said, no, I still think it's right. It just wasn't relevant to the argument I was making in this paper. Oh, okay.

Okay. So, but I've never heard Deutsch bring this up, but it's such an interesting idea. So he says, although the contributions of such a geometry to the total state vector may well be utterly minute, their potential presence has, according to Deutsch, a startling effect. If we now consider what it means to perform a quantum computation in such a situation with, in other words, with closed time-like loops,

we apparently come to the conclusion that a non-computable operation can be performed. This arises from the fact that in the space-time geometries with closed time-like lines,

A Turing machine operation can feed on its own output running around indefinitely, if necessary. So the answer to the question, does that computation ever stop, has an actual influence on the final result of the quantum computation. Deutsch comes to the conclusion that in his quantum gravity scheme, quantum oracles are possible,

As far as I can make out, his argument would apply as well to higher order Oracle machines also. Now, you don't know what an Oracle machine is, so I'm going to explain that briefly. What this says in plain English is some future version of quantum mechanics, specifically quantum gravity, the quote theory of everything, misnamed theory of everything, that they're looking for that combines general relativity with quantum mechanics.

Right. Deutsch is arguing that it may well be possible that when we have that theory, we can build cross-sector

quantum computers under this theory, not the existing theory, that use these time loops, an infinite amount of time. And it would allow us to solve the question of does this computation ever stop? Which is, if you'll recall from our last episode, is the halting problem, which is provably incomputable. Okay. Now, in computational theory, we have something called oracle machines, which are physically impossible to build because they violate the laws of physics. Okay. Okay.

An Oracle machine, what they do is they say, what if I had an Oracle that I can attach to this computer and this Oracle can tell me whatever. You then specify what the Oracle can tell you, this non-computable thing. The most obvious one is that it can solve the halting problem. It can say, is this algorithm ever going to halt?

And we know that's an incomputable problem under Turing machines. What if I have this Oracle I could attach that it could solve that. And then the rest of it worked like a regular Turing machine, but it could query the Oracle for an answer to that question. Okay. Like a little mini God. Yes. Well, if you could do that, they they're able to work out.

what that computer could compute differently than what a Turing machine could compute. And they know based on the concept of an Oracle machine, oh, this computer could compute this, this computer. And its repertoire of computations is much larger than Turing machines.

because it can solve the halting problem. Okay. What he's saying is, is that under quantum gravity, it may well be possible to build a quantum Oracle machine, just like these hypothetical machines and that they'll then be real and that we will be able to solve the halting problem. And we'll be able to have a repertoire of computations that goes beyond a terrain machine. However, this is all based on a theory that doesn't exist. And, and,

So we have to wait and see what that theory is. And this is really just speculation at this point. Okay.

But this is kind of a cool idea. The idea that there may be things in physics that do allow us to expand what we consider computable at some future point. And then we will then use those phenomena in physics to build computers that are able to do those computations. Okay. Okay. And you can really see the relationship here between physics and computability. And this is what Deutsch really tries to bring out. The laws of physics are,

dictate what can be computed. That is what computability is. That's why computational theory isn't mathematics. It's a branch of physics. It's the study of what physics allows you to compute.

Okay. Right. Now here's the problem with Penrose's argument here. I love this argument. I wish I knew if Deutch still believed this or not, or if he gave up on this idea. I can't believe he didn't go on to write another paper about it. But Penrose is, he's, he's making the point. See, it is possible to come up with a, you know, to discover some future laws of physics that allow us to, to have a non-computable operation. Okay. And,

But this doesn't really buy him what he's after, right? He's trying to somehow solve Gödel's incompleteness theorem. And the halting problem is the same as Gödel's incompleteness theorem. So this even maybe has the appearance of solving that incompleteness theorem. But really Gödel's theorem would then take that type of computer and then you could reattach Gödel's theorem to that type of computer. And it would turn out that you have a new sort of halting problem

where yes, it can solve the halting problem for a standard Turing machine, but it can't solve the halting problem for this new type of machine, right? And so there's no way around that. And so Penrose is,

This argument, even if you take it completely at face value, even if you just accept it as true, it simply doesn't buy him what he's after, right? Elsewhere in the book, he admits this. But he's really hoping for something that's incomputable in some stronger sense than this, because this type of non-computability is benign, because it just means that you get to make a new type of computer and then it becomes computable.

He's looking for something that's non-computable in some stronger sense. Interesting. Now, it really is hard to imagine science not starting with the assumption of mathematics and computability. Can you imagine someday scientists announcing, we found this strange phenomena that apparently can't be described mathematically?

It closed time like loops everything that Penrose just explained in that past thing those can all be described mathematically, right, we understand the laws of physics we can lay out explanations for them to go one further to what Penrose is after. It seems like what it really would be saying is, oh, we found this phenomenon and there's just there's no way to even describe it mathematically, right, because it's non computable in that sense.

That would be a much, that would not be a benign claim, right? That would be a much different sort of claim. And in fact, we actually view the maturity of science, like social sciences, we don't consider as strongly science as physics, right? And the reason why is because social sciences are far less computable than science.

um physics is right there's they're not a strong mathematical theory so they actually feel to us less scientific and in fact are less scientific yeah in part because they they aren't well laid out mathematically they aren't computable yet we don't know parts of them maybe are but we don't know how to compute those therefore they're far more hand wavy and fuzzy right

We don't understand them as well is what that really means. If you can't write a program that simulates the phenomena in question, it actually is considered less scientific. It means we don't really fully understand it yet. Sure, sure. Okay, now what about like non-mathematical theory? So Darwin's theory of

of natural selection is kind of the quintessential non-mathematical theory. Yeah, sure. But nobody would doubt it's algorithmic, which really just still makes it mathematical, right? It's a series of steps. You've got, you know, you've, you've got, um,

In its current form with neo-Darwinism, you've got these replicators, they're trying to replicate, they're competing with other replicators. The ones that are best at knocking out the other replicators and replicating themselves, those are the ones that survive in the pool and the rest disappear. And, you know, this is really all certain steps and it's algorithmic.

And so you can see that there is a algorithmic nature even to non-mathematical theories. And in fact, when DNA was discovered, that ended up being a huge part of Darwin's theory, you know, modified theory in the future was working DNA into it. Genes on DNA, they are digital information. And in fact, genes are like touring tapes, right? I mean, the quintessential non-mathematical theory of DNA

We already know it's a computable theory. We just don't understand exactly what the computable algorithm is, right? It's, we don't fully understand it yet, but we know it's a computable theory, right? And so I don't think you can use that as a, as a counterexample in science. I agree with that.

So, so then I love this quote from Penrose. This is from a podcast where he was interviewed by Lex Friedman, who's an AI professor who has this really cool podcast. Penrose in that he says, well, if consciousness is not computable, then what the hell is it? What's going on? What physical processes are going on, which are that? So this is what Penrose is asking. And he's a good question too, really? Yeah.

And as I explained, if it's the benign sort of non-computationality, then we'll just build a new type of computer, right? And it wouldn't solve the halt. It wouldn't solve, ultimately solve the halting problem. It might solve it for a certain type of computer, but it wouldn't ultimately solve it, right? And for his argument to make sense, you have to have,

quantum mechanics have some way to once and for all solve gold's incompleteness theorem which i don't think anybody believes is at all possible right and it's it's just you can't even figure out how some future version of quantum mechanics would do that unless it had some completely non-computable and you can't even build a computer out of it right so suppose we do find some sort of process that's non-computable and you can't build a computer out of it um

I guess my first question would be, how would the scientists know that what they discovered was non-computable in the first place? Wouldn't it just be a mystery to them? Right. Yeah. What are they going to publish? Seriously, right? Who would take this paper that says, I've discovered this process and it's non-computable and you can't build a computer out of it. And, you know, there's no way to do anything with it at all. Everyone would just go, no, it's just a mystery. Let's keep trying to figure it out.

Right. And, you know, how would they, how would they even describe it? Right. I mean, it's, you really have to think about,

when people are going this far, what do they have in mind? And it's not clear what they have anything in mind. David Chalmers, who's famously the guy who came up with the, who coined the term hard problem of consciousness, which is, which the hard problem of consciousness is how can a computable program like feel pain, right? And quality.

Right. Okay, well, that is a hard problem. It's definitely a big mystery. Well, his solution to that, his kind of tentative, really speculative proposed solution to that problem is a sort of panpsychism. He thinks that in the future, scientists are going to accept that consciousness is some sort of atomic unit of physics. Right? Okay. If that were true, though, how would you know? Right. Well,

What would you publish? What would you come up with? Right? I mean, it would just, it would really just look like some mystery and scientists would just keep on their merry way trying to figure out consciousness. And when we forever be wondering what consciousness is, it's hard to see how science would suddenly just accept, oh, Penn's psychism is true. And then what would you do with that theory? Where would you go with it from there? And it still wouldn't answer the question of how do you, how do you, how do people have consciousness? How do you build consciousness?

an artificial version of a person, right? And so based on all these arguments, I believe that what we're saying here is, um,

the way I would put this is science studies like laws, right? They're trying to put things into some sort of explainable lawful manner. That's like, that's, that is what science is assuming they're going to find. Right. And if that's the case, there's kind of the assumption that it is going to be described mathematically and is therefore going to be computable on some sort of computer by definition. If there actually is some aspect of consciousness that is

is in no sense computable, not even the benign sense computable. What you've really done is you've disproven science altogether. You've shown that science can't ever figure out that phenomenon. It's going to forever remain a mystery. Okay. And if you, if you're going to accept that that is true of one aspect of reality, then you have to, then how do you explain why the rest of reality is computable and scientific, right? Mm-hmm.

You've ruined the whole explanation behind science. You've ruined all of science completely, if you're going to accept that. I don't want to ruin science, Bruce. Which is why scientists aren't going to ever accept David Chalmers' panpsychism. Yeah, I agree with that. Because they're going to continue to believe in science.

and this is really, I think the strongest form of the Turing principle. Even if we try to accept there could be some future version of the Turing principle, some future version of computational theory, some future definition of computable that's different than what we have today. Okay. Ultimately we're still saying that computation is going to be equivalent to physics, going to be defined by physics. They're going to be what's the term they're going to be reducible to each other. And,

And so they're going to be the same thing. And everything that in physics is going to be simulatable on a computer and a computer is going to use the laws of physics to be able to do that. And they're really one in the same thing. Okay. So the explanation for why all reality that we have ever discovered is

can be described via computations is because all full featured computational machines are equivalent, including any sort of computation that nature does. Right. Now we're getting into the strongest version of the Turing principle. Okay. And since all of nature can be described via math, that means that we will never come across natural phenomenon that can't be simulated on a computer. Our brains are able to do that math. Our brains are able to do the same simulation. Okay.

That is a good reason to believe that therefore everything's going to be comprehensible to us. That argument isn't exactly correct. People would argue that, and rightly so. You could have a computable universe that's still incomprehensible. You could imagine scenarios where that would be true. But this is certainly a minimum argument.

You have to have this. Universe has to be computational for science to work. It has to be computational for explanation to work. There may be more to it than that, but there isn't less to it than that.

Okay. Does that make sense? Interesting. Okay. Now, we're almost done. I want to just explore just for a moment. What would a completely non-computable world look like? Okay. We can actually imagine what that's like. Okay. And in fact, our ancestors believed they lived in such a world.

Okay, so think about like ancient pagans, and to them, the weather's not a lawful computable process, right, that can be fully explained. It's just, it's a live thing, which they think of a live stuff. We know that living things are still following the laws of physics, but they don't know about laws of physics. So living things are just...

have their own agency. They can do whatever they want. So the wind is a capricious God. You can pray to it. You can give a sacrifice to it, but who knows what it's going to end up doing, right? There's, there's no explanation possible. It's completely inscrutable to human rationale. Okay. Um,

This is, the world of the pagans is what a non-scientific, non-computable, non-Turing principle world would look like. At least that's one possible instantiation of it. It would be a simply incomprehensible world. The gods do what they do. Their reasons are incomprehensible.

Okay. It's an unlawful reality where nothing makes sense. There's no reason to believe that it even should make sense. Okay. Logan Chipkin is a friend of mine online. He recently wrote an interesting article where he claimed that the Catholic church actually was responsible for, for part of what led to the scientific revolution. And you'd have to read the article to hear his argument. I won't go into it.

But let's just say that some religions were maybe more open to the idea of a lawful universe than others. And therefore, those were the cultures that were more open to a scientific revolution and to explanations and things like that, to rational explanations.

And so that's his argument. He's actually getting his argument from somebody else who wrote a book. So it wasn't his personal argument, but his article made this argument. And you can kind of see this here, right? The ancient pagan way of looking at the world, it really isn't amenable to the concept of explanation. You have to have cultural beliefs that accept the idea that things do have explanations and that the world is rational and lawful.

Okay. So go ahead. When, when we were talking earlier about, um, you know, really us, I think when, when we're trying to find non-mathematical, uh, explanation for consciousness or, um, I think God is always, you know, have you ever had anybody use the argument that the reason for something like consciousness is simply God?

So yes, I have. I think you'd be surprised how rare that is though. Okay. Right. I mean, it's, I can't speak for every religion in the world and there are many religions I know next to nothing about. But the Mormon religion, they don't call themselves that anymore, which is what my religion is. And Christianity in general, Mormonism is part of Christianity, both have such a long rational history. There isn't, there,

There's kind of an underlying assumption culturally that we should expect scientific explanations. And in fact, they even have something they call God is scientist, which is this idea that actually even God is using scientific knowledge or, and it's, they're very amenable to this idea. And because of that, I haven't generally seen people make that argument.

to me. Interesting. Now, I have sometimes, I mentioned the guy online who made that argument trying to use Penrose as his basis, and he was some sort of Christian religion. So there are religions out there that will make arguments like that. They'll say, well, you know, the explanation is God.

And there is no other explanation. That is what consciousness is. Right. But, you know, I mean, you think about, we're all aware of neuroscience at this point. And the fact that you can, you know, do stuff to a person's brain and their personality changes. And so we're, we're, we're all sort of expecting there to at least be mostly, um,

a scientific explanation for consciousness. And because of that, I mean, like whenever I bring up my interest in AGI to even really devoutly religious people, I could not, I can't even tell you other than online where you can find any kooky idea you want. I can't think of any examples where somebody said, oh, that's not possible because of God. I've had numerous people argue against the Turing principle and just, they simply don't,

believe that they see it as limiting in some way, but they're not really necessarily saying it because they're arguing against AGI, right? And so I think that even religious people have

generally a very open-minded view. We still live in a Western culture, right? And maybe it's different in non-Western cultures. I don't know. But even non-Western cultures are so Westernized today. They still have to rely on scientific theories to build societies and things like that. I

I just think that people in general just accept it, right? They know AGI is coming. There's very few people who just simply completely deny it as far as I can tell. Now, I do think that there's some interesting things. I have had a few people argue with me, well, maybe the brain is more like a transmitter and the actual consciousness exists in the soul. But then I'll usually point out to such person, well, aren't you really just moving the computational...

nature to the soul then. And they usually accept that. They say, oh yeah, okay, I see your point. So, you know, I'm saying the mind's in the soul, but it's still some sort of scientific process that's taking place. Members of the Church of Jesus Christ of Latter-day Saints, formerly known as the Mormons, they actually believe that there's no such thing as non-material matter, which gives them a somewhat more scientific understanding

They do believe in something called intelligences, which maybe goes against some of what I'm saying here, but it's so vaguely defined that most of them don't have any real problem reconciling it to the type of science I'm talking about.

So I have found that there's just zero pushback, really. I just, I feel very comfortable just talking about stuff like this to matter how religious a person is. And I, it's hard for me to even imagine somebody pushing back against me to be perfectly honest. So. Interesting. Okay. I was just curious. Has your, has your experience been different? Yeah. I mean, I, well, and I,

as somebody who identifies as non-Christian and maybe carries some bias from having grown up LDS,

I generally see, and it maybe is more culturally like this. I mean, we always are hearing so much hype about even people denying Darwinism and wanting to teach creationism. It feels like there's this kind of cultural push to move back away from rationality. And so definitely when you look at something like consciousness, if we can't even agree on things that we have

what I, proof not being the right word, but evidence that is strong, it's really hard for me to imagine not seeing pushback on something like this that's almost more conceptually that we're a long way away from having good evidence, you know, mathematically or what we consider scientifically. You know what? You caught me red-handed. I'm going to have to backtrack a little on everything I just said.

So when I was, when I was young and I was growing up in the LDS church, um, I'm still a devout practicing member of the LDS church. People who are listening to the show know that about me. And that's one of the reasons why I'm so religious friendly. Um, and the LDS church is actually very religious friendly to other religions. I think people don't know that they kind of have reputation as the proselyters. They have very, very positive views of other religions. I will agree with that. Yeah. Um,

So growing up in the LDS church, it did used to be that there was an almost expectation that you would disagree with Darwinian evolution. Yes.

And that was true up until maybe I hit college. And then there was a shift that took place. It was like the late 80s. Yeah. I remember it, Bruce. It was about the time that it almost was borderline to start drinking Coke. So they might have been intertwined. I don't know. Darwinism and Coke are definitely intertwined. A little bit of caffeine and some Darwinism. And

Today, people my age and younger pretty much just accept evolution, right? Now, they may accept some modified version of it, right? Or something like that. But they accept enough of it that you can interact with them on evolution and there's zero pushback. Yeah, I agree. I agree. People older than me within the LDS church today still have problems with it. A lot of them. Yeah, and I think that there are, you know...

In the U.S., the evangelical arms of Christianity have a tendency to be super anti-Darwinism and kind of anti-science. Some, really, some Protestants that are... Yeah.

You definitely see arms within Christianity. The Catholic Church kind of has spikes and then they seem to retract and kind of go back. We could do a whole episode on the Catholic Church's stance on evolution. It's very similar to the LDS churches. They're very open about it at this point. They do ultimately deny it as a complete theory.

but that's probably true of most religions, but they accept so much of it at this point that they did more or less accept it. Right. Um, and the Catholic church pushed against evolution for quite a while. One of their, um, monks, um,

Talia de Chardon was one of the people who discovered a lot of the early Neolithic man and things like that. It was the Catholic Church that discovered a lot of these things with evolution, even while officially they were against it. Sure. I think that was part of why they changed over time is they had their own monks doing research into it and finding stuff about it and making advances in it and things like that.

Sure, you pay Galileo to do research and then you lock him up when... Right, and you know what? Galileo was very devout Catholic. Sure he was. He was a Catholic zealot. Yes. I mean, it's...

So it's complicated, right? I do think religion is complicated when it comes to its relationship to science. It's nowhere near as simple as the media makes it look, right? And the reason why the media makes it look this way is because there is this branch, particularly of evangelicalism, that is so fundamentalist and simple-minded about it that is non-representative even of Protestantism, in my opinion. But they're the fun ones to go put on the media, right? Sure, sure.

Now, it's complicated. So the LDS Church has a relationship with evangelicalism, which is itself complicated. The LDS Church on a regular basis picks up doctrines from evangelicalism and then discards them over a period of time. And one of them was Darwin, its stance against Darwinism. That actually came out of LDS Church picking up

evangelical doctrines and then eventually discarding them. There was even a short movement of D&D is satanic that still is around in evangelicalism and Mormonism picked it up for a few years and then just discarded it. I remember that period as well. And it's actually really interesting to watch because it makes sense that religions would be

borrow from each other and would intertwine in interesting ways. I've actually been very comfortable with how quickly the LDS church discards some of these crazier evangelical doctrines that don't make sense, right? The evolution one did last for quite a while.

But it got discarded, right? I mean, and it never became an official doctrine in the sense of, there was definitely a cultural, you should not believe in evolution. But I remember a guy in my congregation, my ward growing up, who was an evolutionist. And I remember reading,

Orson Scott Card, who's a famous Mormon author, and he believed in evolution. I can't think of any time that there weren't substantial forces within the LDS church

that believed in evolution and were championing it, right? They may have been the minority at one point, and now they're kind of more the majority at this point. But there was never, it never got to the point where that view got stamped out, doctrinally speaking. It was always left kind of open for you to make your own opinion, right? Yeah. Okay, so that's my...

That would be, I mean, like, there are probably older members of the church that would have a problem with AGI for exactly the reasons that you're laying out. They're not the people that I'm going to interact with very often. They're not going to be in my circle of friends, right? Because they're not my age. Sure. And I guess that's why I feel like I've just got no problem talking about stuff like this. I think that it's just accepted. It's considered completely legitimate to do research into it.

There just are no religious concerns with it at this point.

All right, let me wrap this up. I've got a couple more slides, and this will tie into AGI now since we're going to talk about it. I got us way off on a side. Yeah. It was an interesting aside, though. Yeah. So Penrose, in Emperor's New Mind, he says, I shall argue strongly that there must be an essentially non-algorithmic element in the action of consciousness. Okay? So this is his viewpoint. He then goes on to argue, and I've shown you some of his arguments, but he goes on to argue consciousness isn't describable by classical physics. Okay?

Consciousness isn't describable by quantum mechanics. He even argues consciousness isn't describable by quantum gravity. Okay. In his interview with Lex Friedman, he openly admits, well, actually quantum gravity is not going to work either. Like quantum gravity, we know enough about it at this point that we know it's not going to be what I'm looking for.

Right. He gives the example of quantum gravity maybe allowing something non-computable, but that's not really what he's looking for either. He's just trying to bolster his case by showing there is such a thing as non-computable in physics. It's not a silly idea, but it's the wrong type of non-computable, unfortunately for him. Right.

It's the benign type that he's giving a description of. He says that there's going to... He believes that there will be some elements of a future theory that will be non-computational and that it's going to solve consciousness using these non-computable elements. Okay? Okay. And this non-computable element will violate Gödel's incompleteness theorem. His whole argument is computers can't violate Gödel's incompleteness theorem and therefore they...

They shouldn't be able to do what humans, he thinks humans can violate goals and completeness theorem. In fact, they can't. There's no sense at all in which humans can violate goals and completeness theorem. His whole argument is on a flawed foundation. Okay. But since he believes humans can, and he believes computers can't, he's looking for this

quantum physics future theory that's beyond quantum gravity that will somehow be able to solve Goldo's incompleteness theorem in some final way that even the example of the close time loops can't. Okay. It's hard to see how, if they even found this, how he would write a paper to describe it. Right. It's, he's looking for something that ultimately would disprove all of science. And that's why it really strikes me as just a waste of time. Right.

right? He's going down the wrong path for this, in my opinion. Now, is it possible that we'll need quantum mechanics, quantum computers, or quantum gravity computers even, to build consciousness? Yeah, that is a possibility. There's reasons why it seems unlikely, though. We understand enough about quantum physics that we know that quantum phenomena are

can't really exist in the brain, right? At least based on our best current understandings of how you engineer quantum phenomenon. Now, Penrose goes to great lengths to talk about microtubules in the brain and the fact that he thinks that there is some sort of quantum phenomenon going on there. But they're just, this is not even really even a good tentative theory at this point. He's a long way off from coming up with an explanation that's really even worthy of taking a hard look at. Okay.

Okay, he's really just kind of rolling the dice saying, I think there could be something, and he's throwing out very vague possible ideas. This is really where he's at at this point with his non-computable theories about consciousness.

And that's one of the reasons why I don't really take his view seriously, right? The brain, the way it operates, our understanding of how it operates, it's all computable on a Turing machine. Therefore, I think the correct theory is AGI only requires a Turing machine, which means that AGI...

can be on a computer, going to be on this computer that I'm running right here. Okay. So the church during thesis, Doug Douglas Hofstadter, who's the author of the Pulitzer prize winning go to Escher Bach and eternal golden braid. That book is a phenomenal book. It's fun. He teaches you little mathematical games. He doesn't tell you what the book's about. And by the end of the book, he, you realize he's taught you the Turing principle. He doesn't call that. He taught you the church Turing thesis. And he,

He then gives his version of the church Turing thesis, the one that got him excited. He's an AGI researcher. And it is all brain processes are derived from a computable substrate. We have very good reason to believe that that is the case for the human brain. That is why AGI is possible. And it's, it's going to be possible. I believe on a regular computer, we don't even need to wait for quantum computers.

So although I'm fine with it turning out to be that we need a quantum computer or something like that, that would still be very cool. But the, and you know, it makes sense. Evolution does not really find super complex algorithms, right? It's this blind process. So the, the intelligence process, whatever it is that the human brain is doing that allows us to be generally intelligent. Okay.

Okay. It's going to turn out to be a simple algorithm and it's gross. Okay. And it's, it's not going to be super complicated and it's going to be obvious once we know what it is. And this is what gets me excited about,

AGI, right? I think it's treated in such a mysterious way. Getting back to your question about religion. It's treated even by atheists, even by scientists. It's treated in such a mysterious way. The real truth is we just haven't discovered it yet and it's going to be easy. Okay.

Okay. That's what gets me excited about trying to study AGI. Now, admittedly, I don't really know which direction to even start researching. And that was why, that was why I went back to school and started starting machine learning. Machine learning, as we're going to see in maybe our next episode is not

is not AGI. It's not even a path to AGI. Yes. Right. But it is a path to understanding computability. It is a path to me learning to program. I do believe, and I know this is heresy to some people who really follow David Deutsch. I do believe it actually does do a very limited form of knowledge creation. Okay. It's super limited. And,

And so it may even give us some really basic hints towards AGI, but there are so many, in so many ways, they're just a completely different branch of study.

And I decided to go into that in part because I wanted to seek a job in that field. I thought it would be interesting. But my real interest is trying to figure out what is intelligence? What is general intelligence? What is it that the human brain is doing that instantiates as software the mind? What is that algorithm that allows us to learn anything, to be a general learner? That's AGI is artificial general intelligence, right? We may not be artificial, but we are general intelligences.

And in our next episode, if it goes the way I'm hoping, we'll have two friends of mine who are researching AGI and probably know more about it than I do. And we will ask them questions and we'll talk about something that Deutsch calls a universal explainer, which is the idea of general intelligence is able to explain anything.

Okay, just as a computer can be universal, you have non-universal computers that can't do every algorithm. Then you have a universal computer that can do every type of algorithm.

there's something called a universal explainer, which is able to explain anything. And that's what a general intelligence is, is a universal explainer. Okay. And at some point humans made this jump to the ancestors of humans and evolution. They were originally animals. Nobody doubts that. And at some point,

something happened and some sort of jump to universality took place that was the algorithm that we're seeking whatever that was that jump was and that's why you suddenly see just out of the blue you suddenly see humanity just pop onto the scene and they almost immediately start having culture they're like us have you ever seen the movie um uh forgotten cave of forgotten dreams no

You need to come over to my house and I have to show it to you in 3D. So you have to actually come over to my house because what it is, is they discovered a 30,000 year old cave with ancient artwork on it from 30,000 year old humans. And,

The humans were very clever because they had culture just like we do. They were universal explainers just like we are, right? And they used the surface of the cave, the 3D surface of the cave as part of their artwork. And the artwork is beautiful. It's not the, you know, when you think of like cave drawings, you think of little stick figures or something. It's not like that. It's very, very beautiful artwork.

And you have to see it in 3D so that you can see how they used the surface of the cave to draw the artwork and things like that, right? And one of the things that is really just stunning about it is the connection, you know, I felt with these people that lived 30,000 years ago. The fact that they were human, just like me, that they were capable of the same thoughts that I am capable of. They didn't have

our understanding of the world. They didn't have our scientific worldview, obviously, but they were us, right? And that group of human beings, I think they popped on into existence like 100,000 years ago. And they almost went extinct, by the way, came very close to an extinction event of human beings. And, yeah,

They lived in a very different world from the world of animals because of the fact that they were universal explainers. And that's really what I want to study is what is that algorithm? What is it that made them so different than their animal ancestors?

Yeah.

their beliefs, but it really didn't, right? Like I said, people just sort of accept this at this point. They were fascinated by the movie. They thought it was so cool. And, you know, it's another example of how religious people, at least the ones I know, just don't seem to have problems with science today. All right. Well, thank you very much, Cameo. Always a pleasure, Bruce.