00:00:00.000 Welcome to Topcast, and to chapter 6 of my breakdown of the fabric of reality chapter 6 is called titled
00:00:12.680 Now, David Deutsch is expert in the topics he writes about in the beginning of infinity and in the fabric of reality.
00:00:19.960 But if we were to talk wheelhouses, as people sometimes do,
00:00:24.840 the thing that you spend your career, your life, pursuing,
00:00:30.640 then this is one of those, David Deutsch has a lot of wheelhouses.
00:00:33.680 But this is certainly one, right in the dead center of David Deutsch's professional interests.
00:00:40.160 One of the reasons for David Deutsch's fame among other physicists is because of his contribution to this area of science,
00:00:52.240 In fact, it really was down to David to bring computer science into science itself.
00:01:00.360 Before that, it was treated as an area of mathematics, of pure mathematics, treated in the abstract.
00:01:06.880 And it was David who explained how and why it should be regarded more as a part of physics.
00:01:16.080 Matter of age, the laws of physics, therefore what computers can do is bounded by the laws of physics.
00:01:22.760 This particular chapter is one of my favourites in the entire book.
00:01:27.160 It is inside bomb after inside bomb, which means I am going to take my time with passages here,
00:01:35.840 even more so than what I normally would, in order to break them down or emphasise them.
00:01:41.600 But I'm going to begin just by reading the first paragraph on the first page of the book, and then I'm going to skip rather a lot and I'll explain why in just a moment.
00:01:52.440 And perhaps for those picking it up in this episode, for whatever reason, the last episode was about virtual reality generators.
00:02:01.040 Now, why on earth would one write a book about the fabric of reality about cosmically significant things
00:02:07.760 and concentrate on something seemingly as parochial and as quirky as virtual reality?
00:02:13.000 Well, there is an important reason why, and that is because we human beings, our minds are essentially virtual reality rendering machines.
00:02:21.640 We are minds, and we are connected to the rest of real physical reality via senses, which are creating for us an impression of the environment.
00:02:32.240 It's a virtual reality rendering of whatever real reality happens to be, which we don't have direct access to.
00:02:39.360 So virtual reality, a study of virtual reality not only gives an insight into the workings of people, but things that can do computations more broadly.
00:02:48.080 And hence, David begins the chapter with, quote,
00:02:52.240 the heart of a virtual reality generator is its computer and the question of what environments can be rendered in virtual reality must eventually come down to the question of what computations can be performed.
00:03:04.960 Even today, the repertoire of virtual reality generators is limited as much by their computers as by the image generators.
00:03:11.600 Whenever a new faster computer with more memory and better image processing hardware is incorporated into a virtual reality generator, the repertoire is enlarged.
00:03:21.920 But will it always be so, or will we eventually encounter full universality as I have argued we should expect in the case of image generators?
00:03:31.440 In other words, is there a single virtual reality generator, buildable, once and for all, that could be programmed to render any environment that the human mind is capable of experiencing, end quote.
00:03:44.400 But I might just, I'll just pick up a couple of short paragraphs here, which speak about the limitations of computers, the way in which computers must be limited by the laws of physics.
00:03:55.120 I taste a sort of speak of why it is that there are these limitations placed upon computers.
00:04:02.240 A computer with an effectively unlimited memory capacity can be envisaged in principle, but a computer with an unlimited speed of computation cannot. A computer of given design will always have a fixed maximum speed, which only design changes can increase.
00:04:17.760 End quote. Now, why is this? Well, because we've got this limitation on imposed by the speed of light, stuff can't happen faster than the speed of light.
00:04:27.280 And so signals can't be sent faster than the speed of light. At the speed of light, sure, but not faster than the speed of light. So you have this inherent limitation imposed by the laws of physics.
00:04:36.560 Let's just read on a little bit further, quote,
00:04:38.880 therefore a given virtual reality generator will not be able to perform unlimited amounts of computation per unit time. Will this not limit its repertoire?
00:04:47.280 If an environment is so complex at the computation of what the user should be seeing one second from now takes the machine more than one second to compute, how can the machine possibly render that environment accurately?
00:04:59.360 To achieve universality, we need a further technological trick. To extend it to repertoire as far as this physically possible a virtual reality generator would have to take control of one further attribute of the user's sensory system, namely the processing speed of the user's brain.
00:05:16.000 If the human brain will like an electronic computer, this would simply be a matter of changing the rate at which its clock emits synchronizing pulses.
00:05:24.000 Not out the brain's clock will not be so easily controlled, but again, this presents no problem of principle.
00:05:30.720 The brain is a finite physical object, and all its functions are physical processes which, in principle, can be slowed down or stopped.
00:05:40.480 The ultimate virtual reality generator would have to be capable of doing that end quote.
00:05:46.160 Now, I'm ending the quotation there because then David goes into the details about how virtual reality generators could be built that could even tinker with your own brain.
00:05:59.200 The mechanics of this is interesting, and it's worthwhile if, of course, I presume that people who are listening to this have access to the book, so it might be well worth your while going to the book and reading the few pages that I'm going to gloss over here.
00:06:13.280 I'm just going to skip over because it's about the technical details of how one might go about in the distant future and a technologically enlightened future where we could directly intercept the contents of neurons, let's say.
00:06:27.680 And so give you the experience of whatever is physically possible to experience via that method I've directly intervening in the neurons, the action of the neurons.
00:06:39.040 We don't need to go into that. Please explore this part of the chapter. No doubt, the vast majority of people listening to this have the book if you don't get the book and read the details because they are interesting.
00:06:51.200 But basically, look, the idea is that with an advanced neuroscience with a cybernetic implant, it's going to be possible to tinker with neurons and hence subjective experience given the requisite knowledge knowing how to do that.
00:07:04.800 The laws of physics do not prohibit this from happening, so it must be possible given the right knowledge.
00:07:11.360 So I'm skipping those details. Interesting though, they are glossing over them because the sum of everything David says is basically encapsulated by what he goes under say, quote,
00:07:25.200 for our present purposes technological obstacles are irrelevant. We are not investigating what sorts of virtual reality generator can be built or even necessarily what sorts of virtual reality generator will ever be built by human engineers.
00:07:38.960 We are investigating what the laws of physics do and do not allow in the way of virtual reality.
00:07:44.640 The reason why this is important has nothing to do with the prospects for making better virtual reality generators.
00:07:51.040 It is that the relationship between virtual reality and ordinary reality is part of the deep unexpected structure of the world which this book is about.
00:08:01.040 That's why I begin this episode in the way that I did. It's not an esoteric, quirky sort of bit of technology, this virtual reality stuff.
00:08:10.880 It provides an insight into how it is that knowledge can be constructed about the world and what our situation is, what our relationship is with the rest of physical reality.
00:08:21.680 David goes on, quote, by considering various tricks, nerve stimulation, stopping and starting the brain and so on, we have managed to envisage a physically possible
00:08:30.920 virtual reality generator whose repertoire covers the entire sensory range as fully interactive and is not constrained by the speed or memory capacity of its computer.
00:08:39.480 Is there anything outside the repertoire of such a virtual reality generator?
00:08:44.840 Would it repertoire be the set of all logically possible environments? It would not.
00:08:51.080 Even this futuristic machine's repertoire is drastically circumscribed by the mere fact of its being a physical object.
00:08:58.360 It does not even scratch the surface of what is logically possible as I shall now show, pausing their fire affliction.
00:09:07.400 What he's going to show and what he's about to launch into is the diagonal argument which if you are a long time listener to talk cast you will have encountered before the beginning of infinity also goes through
00:09:17.480 explanations of diagonal arguments. This is a really interesting one. A way of showing how even a machine which
00:09:28.040 can render all environments that can be experienced by a person does not contain it throughout all logically possible environments.
00:09:35.320 There are things it can't do and in fact the things it can't do vastly outnumber the things that it can do.
00:09:40.200 Even though we've begun this whole exercise by trying to define into existence the machine that can do anything when it comes to
00:09:50.680 virtual reality, it can render any environments. We're about to see that in fact the attempt to do that, the attempt to realise that in physical reality is impossible.
00:10:00.680 Why? David explains. The basic idea of the proof, known as a diagonal argument, predates the idea of virtual reality.
00:10:10.920 It was first used by the 19th century mathematician Georg Cantel to prove that there are infinite quantities greater than the infinity of natural numbers.
00:10:20.600 One, two, three, the integers. The same form of proof is at the heart of the modern theory of computation developed by Alan Turing and others in the 1930s.
00:10:30.600 It was also used by Kurt Gertel in his celebrated incompleteness theorem of which more in chapter 10.
00:10:38.120 Each environment in our machines repertoire is generated by some program for its computer.
00:10:44.120 Imagine, the set of all valid programs for this computer, from a physical point of view each such program specifies a particular set of values for physical variables, on the disks or other media that represent the computer's program.
00:10:58.760 We know from quantum theory that all such variables are quantised and therefore that no matter how the computer works, the set of possible programs is discrete.
00:11:08.680 Each program can therefore be expressed as a finite sequence of symbols in a discrete code or computer language.
00:11:15.240 There are infinitely many such programs, but each one can contain only a finite number of symbols.
00:11:21.960 That is because symbols of physical objects made of matter in recognisable configurations and one could not manufacture any infinite number of them.
00:11:29.720 As I shall explain in chapter 10, these intuitively obvious physical requirements that the programs must be quantised and that each of them must consist of a finite number of symbols
00:11:37.960 and can be executed in a sequence of steps are more substantive than they seem.
00:11:43.320 They are the only consequences of the laws of physics that are needed as input for the proof,
00:11:47.880 though they are enough to impose drastic restrictions on the repertoire of any physically possible machine.
00:11:54.840 Other physical laws may impose even more restrictions, but they would not affect the conclusions of this chapter end quote.
00:12:02.680 Okay, so what we've got here is the setup of the concept that we have this computer and the computer can run an infinite number of different programs,
00:12:12.360 but it has a repertoire which means the set of all programs and the set can be infinite, of course,
00:12:17.480 you can have infinite sets, the list that are infinitely long. There's no end to them, so there's no end to the number of programs in this set.
00:12:25.480 It's infinite. Now, some people have a lot of difficulty with this concept that if something is infinite,
00:12:31.080 it might not necessarily contain everything logically possible. But a simple way of understanding this is
00:12:37.240 you just think of the set of all positive numbers, 0, 1, 2, 3, 4, 5, off into infinity.
00:12:44.280 It clearly doesn't contain all the numbers. Okay, specifically if you were to say, well,
00:12:48.920 it's only the integers, well, it doesn't contain a half, a third, and so on and so forth.
00:12:52.200 And it doesn't contain the negative numbers. Okay, so there are things that aren't in that set.
00:12:55.960 There are numbers not in that set even though it's got an infinite number of numbers.
00:12:58.920 Similarly, we're going to get to here. This idea that although there's an infinite number of
00:13:04.920 different logically possible, of possible environments that can be rendered by this computer
00:13:12.360 as a virtual reality generator, it won't contain everything that is logically possible.
00:13:18.520 It won't contain everything that's logically possible. So that's the set up. David goes on to say,
00:13:23.400 quote, now let us imagine this infinite set of possible programs arranged in an infinitely long list
00:13:29.640 and numbered program 1, program 2, and so on. They could, for instance, be arranged in
00:13:35.000 alphabetical order with respect to the symbols in which they are expressed. Because each program
00:13:41.000 generates an environment, this list can also be regarded as a list of all the environments in the
00:13:46.200 machines repertoire. We might call them environment 1, environment 2, and so on. It could be that
00:13:51.320 some of the environments are repeated in the list because two different programs might in effect
00:13:55.720 perform the same calculations. But that will not affect the argument. What is important
00:14:00.280 is that each environment in our machines repertoire should appear at least once in the list.
00:14:05.640 David makes a few more remarks that I'm going to again skip over and pick it up where he says,
00:14:11.080 quote, let me define a class of logically possible environments which I shall call
00:14:17.480 can't go to environments. That's spelt, c-a-n-t-g-o-t-u. Can't go to environments. Partly an honor of
00:14:27.640 can't all, girdle, and touring. And partly for a reason I shall explain shortly, end quote,
00:14:34.360 very clever, clever little name there. Can't go to environments and end you to
00:14:39.560 can't all girdle and touring. Let's keep going. Quote, they are defined as follows,
00:14:45.880 for the first subjective minute, I can't go to environment behaves differently from
00:14:50.680 environment 1, generated by program 1 of our generator. It does not matter how it does behave,
00:14:56.120 so long as it is to the user, recognizably different from environment 1. During the second
00:15:01.080 minute, it behaves differently from environment 2 that what is now allowed to resemble environment
00:15:06.200 1 again. During the third minute, it behaves differently from environment 3 and so on.
00:15:11.080 Any environment that satisfies these rules, I shall call, I can't go to environment.
00:15:17.160 Now, since a can go to environment does not behave exactly like environment 1, it cannot be
00:15:22.360 environment 1. Since it does not behave exactly like environment 2, it cannot be environment 2.
00:15:29.160 Since it is guaranteed sooner or later to behave differently from environment 3, environment 4,
00:15:33.240 and every other environment on the list, it cannot be any of those either. But that list
00:15:38.840 contains all the environments that are generated by every possible program for this machine.
00:15:44.680 It follows that none of the can't go to environments are in the machines repertoire.
00:15:49.640 The can't go to environments are environments that we can't go to using this virtual reality
00:15:54.680 generator end quote pausing there. That's the diagonal argument. It illustrates a couple of things
00:16:04.520 that this infinitely long list that can of programs that can render any environment at all,
00:16:10.200 all the environments that are possible, limited only by the memory capacity of the computer.
00:16:15.960 Let's say you've got environment 1 that it can render. Maybe it looks like earth it is today.
00:16:22.840 Environment 2 maybe it is earth as it was yesterday and repeat for all the days and the past and
00:16:28.440 then for environments on Mars and so on and so forth. This infinitely long list of environments
00:16:34.680 that the computer can generate based upon programs in the computer. But the ones that
00:16:41.960 it can't render are infinitely greater in number. There's many, many more after all.
00:16:48.120 Environment 1 is one such environment that can be rendered. Now all that we require is that
00:16:53.480 our first can't go to environment differs from environment 1 in any way, shape or form.
00:16:59.720 But there's an infinite number of ways in which it could differ from environment 1.
00:17:03.720 So already we've got an infinite number of ways it could differ and there you can
00:17:06.760 even number of ways it could differ from environment 2 and so on and so forth. So the ones that
00:17:10.600 can't be rendered, the can't go to environments vastly outnumber the number of environments that
00:17:16.040 can be rendered, even though the ones that can be rendered are infinite number.
00:17:25.960 clearly there are enormously many can't go to environments because the definition leaves enormous
00:17:30.600 freedom in choosing how they should behave. The only constraint being that during each minute
00:17:36.040 they should not behave in one particular way. It can be proved that for every environment
00:17:41.160 in the repertoire of a given virtual reality generator there are infinitely many can't go to
00:17:45.880 environments that it cannot render. Nor is there much scope for extending the repertoire
00:17:51.080 by using a range of different virtual reality generators. Okay, no, end quote I won't go on and read
00:17:56.520 the expansion of that. Leave that as an exercise to the reader. Instead I'll pick it up where David
00:18:02.280 writes, quote, thus our hypothetical project of building the ultimate virtual reality generator
00:18:08.120 which had been going so well has suddenly run into a brick wall. Whatever improvements may be made
00:18:13.640 in the distant future, the repertoire of the entire technology of virtual reality will never grow
00:18:18.200 beyond a certain fixed set of environments. Admittedly, this set is infinitely large and very diverse
00:18:25.880 by comparison with human experience prior to virtual reality technology nevertheless. It is only
00:18:32.680 an infinitesimal fraction of the set of all logically possible environments. What it feel like to
00:18:39.560 be in a can't go to environment. Although the laws of physics do not permit us to be in one,
00:18:43.720 it is still logically possible and so it is legitimate to ask what it would feel like.
00:18:48.040 Certainly it could give us no new sensations because a universal image generator is possible
00:18:53.320 and is assumed to be part of our high technology virtual reality generator. So a can't go to
00:18:57.640 environment would seem mysterious to us only after we had experienced it and reflected on the
00:19:02.520 results. It would go something like this. Suppose you are a virtual reality buff in the distant ultra
00:19:08.520 high technology future. You have become jaded for it seems to you that you've already tried
00:19:13.080 everything interesting. But then one day a genie appears and claims to be able to transport you
00:19:17.720 to a can't go to environment. You are skeptical but you agree to put the claim to the test.
00:19:23.560 You are whisked away to the environment. After a few experiments you seem to recognize it,
00:19:28.040 it responds just like one of your favorite environments which on your home virtual reality system has
00:19:33.320 program number X. However, you keep experimenting and eventually during the X's subjective minute
00:19:40.360 of the experience the environment responds in a way that is markedly different from anything
00:19:45.720 that environment X would do. So you give up the idea that this is environment X. You may then notice
00:19:52.040 that everything that has happened so far is also consistent with another renderable environment
00:19:56.120 environment Y but then during the white subjective minute you approve wrong again the characteristic
00:20:01.480 of a can't go to environment is simply this. No matter how often you guess, no matter how complex
00:20:06.760 a program your content plate is being the one that might be rendering the environment you will
00:20:11.160 always be proved wrong because no program will render it on your virtual reality generator
00:20:16.840 or on any other. Soon or later you will have to bring the test to a close. As that point you may
00:20:22.520 well decide to concede the genie's claim that is not to say that you could have approved
00:20:27.720 that you had been in a can't go to environment for there is always an even more complex program
00:20:33.720 that the genie might have been running which would match your experience so far. That is just the
00:20:39.640 general feature of virtual reality that I've already discussed. Namely that experience cannot
00:20:45.800 prove that one is in a given environment. Be it the center-caught at Wimbledon or an environment of
00:20:51.880 the can't go to type end quote. So that that that that harks back to previous chapter talking about
00:20:59.800 not knowing that you are not being able to confirm that you are on an actual rendering of the real
00:21:05.640 Wimbledon which is to say you can't confirm you can only ever disconfirm logically speaking.
00:21:12.680 Moving on David writes quote. Anyway there are no such genies and no such environments so we must
00:21:20.120 conclude that physics does not allow the repertoire of a virtual reality generator to be anywhere
00:21:24.920 near as large as logical loan would allow. How large can it be? Since we cannot hope to render all
00:21:31.160 logically possible environments let us consider a weaker but ultimately more interesting sort of
00:21:36.440 universality. Let us define a universal virtual reality generator as one whose repertoire
00:21:43.000 contains that of every other physically possible virtual reality generator. Can such a machine exist?
00:21:49.240 It can. Thinking about futuristic devices based on computer controlled nerve stimulation makes this
00:21:55.880 obvious. In fact almost two obvious. Such a machine could be programmed to have the characteristics
00:22:02.120 of any rival machine. It could calculate how that machine would respond under any given program
00:22:07.560 to any behavior by the user and so could render those responses with perfect accuracy. From the
00:22:13.800 point of view of a given user any given user. Just perfect accuracy there. Remember that was
00:22:21.560 defined in the previous chapter and it's basically where the user themselves is unable to distinguish
00:22:26.200 and if you're unable to distinguish you know x from y then to you to the perfect degree of accuracy
00:22:34.360 x is equal to y. That's all it's just a subjective perfect accuracy. It's not perfect accuracy
00:22:40.440 in real life in sort of an unobjective sense which doesn't exist. Let's get going quote.
00:22:47.240 I say this is almost too obvious because it contains an important assumption about what the proposed
00:22:51.720 device or more specifically its computer could be programmed to do given the appropriate program
00:22:57.160 and enough time and storage media. It could calculate the output of any computation performed by
00:23:02.520 any other computer including the one in the rival virtual reality generator. That's the
00:23:07.720 feasibility of a universal virtual reality generator depends on the existence of a universal
00:23:13.640 computer. A single machine that can calculate anything that can be calculated as I have said.
00:23:21.640 This sort of universality was first studied not by physicists but by mathematicians. They were
00:23:27.480 trying to make precise the intuitive notion of computing or calculating or proving something in
00:23:33.560 mathematics. They did not take on board the fact that mathematical calculation is a physical
00:23:39.000 process. In particular as I've explained it is a virtual reality rendering process so it is
00:23:45.320 impossible to determine by mathematical reasoning what can or cannot be calculated mathematically.
00:23:51.080 That depends entirely on the laws of physics but instead of trying to deduce their results from
00:23:56.840 physical laws mathematicians postulated abstract models of computation and defined calculation
00:24:05.000 and proof in terms of those models. I should discuss this interesting mistake in chapter 10.
00:24:11.400 That is how it came about that over a period of a few months in 1936.
00:24:17.400 Three mathematicians and will post Alonso Church and most importantly Alan Turing independently
00:24:22.760 created the first abstract designs for universal computers just pausing their my reflection. I might
00:24:27.080 just go back and just to mention that this argument here, this explanation about the fact that
00:24:35.560 mathematics consists of explanations but it requires calculations, it uses proofs and computations
00:24:46.120 and these things are completed by physical systems whether the mathematician themselves
00:24:55.640 or computers and pocket calculators and that kind of thing. A bound necessarily by the laws of
00:25:01.480 physics so what is able to be proved is limited by the set of things that the laws of physics
00:25:10.760 say is provable because your building computers out of matter, the matter obeys laws of physics,
00:25:19.960 and those laws of physics only allow certain kinds of things to be proved. The laws of physics
00:25:25.400 bound what can be mathematically proved. Many mathematicians don't like that, that doesn't matter,
00:25:31.880 doesn't affect the fact that it's true. Many people don't like that, they think that somehow
00:25:36.040 mathematics has to be prior to physics in some sense. Now all that said, the precise
00:25:44.760 of the same argument applies even more broadly. To reasoning in general, reasoning in general,
00:25:52.120 you can't get outside of the laws of physics. What can be known is bounded by the laws of
00:25:59.000 physics and so philosophy, epistemology, reasoning itself is done by physical things, human beings,
00:26:09.880 brains, minds, and they obey laws of physics. So it is the laws of physics that constrain
00:26:17.320 the possibility of what we can think, what we can know, what we can reason. This is not a problem
00:26:24.760 as such, but it's just worth keeping in view and understanding. It does come to bear on
00:26:33.320 capacity to know, but it doesn't come on our, it doesn't come to bear on our capacity to
00:26:39.960 solve problems that we're interested in. In particular, it's the very thing that allows us to know
00:26:45.720 that problems are solvable. Problems are solvable precisely because, well, the physical structure of
00:26:51.960 our brain, what it's able to do uniquely is generate explanations, which can be in one-to-one
00:27:00.280 correspondence with the rest of physical reality. That's what the laws of physics allow.
00:27:07.480 It provides, the laws of physics provide constraints but allow for that, and therefore allow
00:27:12.680 for the solving in principle of any possible problem we could encounter. Problems are soluble.
00:27:18.360 And David's going to get to that, essentially get to that in this chapter. But I do think one
00:27:25.880 reason I'm also saying that is that philosophers who are sometimes disconnected to some extent
00:27:32.600 from physics, the file to take this into account and think that the physics can be irrelevant
00:27:39.880 to what they're doing, but it's not, not at a linear relevant. There's not to say that everything
00:27:45.240 reduces to physics, I'm not being reductionist in this sense, or that the philosopher needs to
00:27:49.960 refer to what's going on in physics now and again. But the reasoning itself has to be understood
00:27:58.040 is itself bounded by what the laws of physics permit us to reason about.
00:28:05.000 If you're trying to, the common area here that really, I guess I'm circling, is the prophecy,
00:28:13.320 that philosophers, epistemologists, others who don't take this on board fully,
00:28:20.040 think that there must be a mechanism whether by induction or something else that allows them to
00:28:23.880 forecast the future perfectly accurately. But that is in contravention to laws of physics.
00:28:29.160 It's that kind of thing that importantly is constrained by laws of physics. Laws of physics
00:28:35.560 set a bound on what is noble, and one thing that's not noble is the creation of knowledge,
00:28:42.120 knowledge creation. The future cannot be known with perfect fidelity. Also because of laws of physics
00:28:47.240 as well as the fact that people create explanatory knowledge which changes the future in ways that
00:28:54.680 cannot be known ahead of time. That's a major theme of beginning of infinity, a theme throughout
00:29:00.840 topcast as well. So I'll just point to earlier work on that kind of stuff rather than going down
00:29:08.520 the road of making that argument again. But just to say that a knowledge of this kind of
00:29:13.400 physics can help with the philosopher and the epistemologist, or people who are interested in knowledge,
00:29:18.760 rather than being utterly disconnected from things. And I think that where
00:29:24.120 where some philosophers go wrong, especially when they fall into pessimism, it can be because of this.
00:29:28.920 Okay, back to the book. We're talking about how Emma will post Alonzo's search and
00:29:34.120 Alan Turing most importantly, created the first abstract designs for universal computers. Okay,
00:29:38.920 so abstract designs, important to know. Not a physical design, abstract, mathematical theory
00:29:45.560 of the computer. Without being concerned about the physical laws that actually control these
00:29:51.080 things, David Wright's on this. Each of them conjecture that his model of computation
00:29:56.600 did indeed correctly formalize the traditional intuitive notion of mathematical computation.
00:30:01.400 Consequently, each of them also conjecture that his model was equivalent to had the same
00:30:06.120 repertoire as any other reasonable formalization of the same intuition. This is now known as the
00:30:13.000 Church Turing conjecture. Turing's model of computation, and his conception of the nature of the
00:30:18.040 problem he was solving, was the closest to being physical. His abstract computer, the Turing
00:30:24.280 machine, was abstracted from the idea of a paper tape divided into squares with one of
00:30:31.320 a finite number of easily distinguishable symbols written on each square. Computation was performed
00:30:37.240 by examining one square at a time, moving the tape backwards or forwards, and erasing or writing
00:30:42.360 one of the symbols according to simple unambiguous rules, pausing their my reflection.
00:30:48.040 This is one of the most jarring insights that goes unsaid, untold, unlearned, I think, these days.
00:30:56.120 Unless one takes on pure mathematics course, takes an interest in this kind of thing,
00:31:02.280 goes into computer science, whatever. That no matter how diverse this technology of
00:31:08.120 computer becomes, how ubiquitous it becomes, that all of it can be modeled. Okay,
00:31:14.600 but modular what David is about to say and the insights that David brings with quantum
00:31:19.560 computational and other stuff, but it can be modeled by, reduced to, the action of reading
00:31:28.280 and infinitely, well, not infinite, but a very long tape divided into squares with symbols
00:31:34.040 written on it. That's what computers do. It doesn't matter how complicated the program it could
00:31:39.160 be running a word processor, it could be simulating the collision of galaxies, it could be
00:31:43.960 running a computer game, it could be, you know, Facebook or Twitter or a flight simulator,
00:31:50.360 whatever the program is, whatever the thing is that the computer can do is based upon code,
00:31:55.560 a program, and that itself can be represented as symbols of zeros and ones on a long strip
00:32:05.240 of paper, remarkable, absolutely remarkable. And when you get into the details of this,
00:32:10.520 that and how this, in principle, could be done for any program is perhaps jarring to people,
00:32:17.400 that a complicated computer program could reduce to such a simple thing,
00:32:23.320 such a simple idea. And this is the first model of computation, which predated the existence of
00:32:29.320 any actual computer that had been built, an electronic computer. Let's keep going. And David writes,
00:32:36.120 quote, cheering proved that one particular computer of this type, the universal Turing machine,
00:32:43.640 had the combined repertoire of all other Turing machines. He conjectured that this repertoire
00:32:49.320 consisted precisely of every function that would naturally be regarded as computable. He meant
00:32:56.120 computable by mathematicians. But mathematicians are rather untypical physical objects.
00:33:01.480 Why should we assume that rendering them in the act of performing calculations is the ultimate
00:33:07.240 in computational tasks? It turns out that it is not. As I shall explain in chapter nine,
00:33:12.920 quantum computers can perform computations of which no human mathematician will ever,
00:33:18.840 even in principle, be capable, pausing their my reflection. Now, why should there be things that
00:33:25.240 a human mathematician cannot even in principle calculate? Does this violate the universality
00:33:31.480 of the human mind? It doesn't. Why? Well, because calculation is not explanation. Now, quantum
00:33:38.760 computers harness something called entanglement and interference phenomena. I go to topcast that are
00:33:44.760 about the multiverse to go into that or to read sections of the fabric of reality or the beginning
00:33:50.760 infinity to understand or have have more insight into entanglement and interference phenomena.
00:33:55.480 But anyway, quantum computers use this. But this is not how brains presumably do what they do.
00:34:02.280 That's not how they do their computations. So, although a person cannot calculate what a
00:34:07.320 quantum computer can, a person can't quickly do the prime factorization of a 15 digit number
00:34:15.800 or calculate the position, let's say, of electrons in some uranium atom, this does not prevent
00:34:21.960 us from understanding those things and what is going on there and using technology to do it.
00:34:28.760 We can still understand it. We can still explain those things that that phenomena.
00:34:33.640 There is a difference between calculation, which in physics allows some precise prediction
00:34:40.040 and understanding the explanation that allows for that prediction to be made. We're still universal,
00:34:46.600 human beings are people, people are universal, universal, explainers, not universal calculators.
00:34:52.200 Indeed, I don't think there can be a universal calculator. After all, all we need to do is to just
00:34:58.280 think of a number large enough whose prime factorization could never be done, even in the multiverse,
00:35:05.080 no matter how much time you go. Whatever number that is, I don't know, 10 to the power of 10
00:35:10.440 to the power of a million to the power of seven or something. I don't know, there must be some number
00:35:14.840 out there which it's just so large that the prime factorization would just take longer than the
00:35:20.920 life of the universe, but maybe the universe goes on forever. Maybe if the universe is eternal
00:35:26.440 and this computer lasted forever and had an eternal and an infinite amount of energy,
00:35:30.760 maybe then you could have this universal calculator. But put aside that, there are
00:35:36.760 non-computable functions as cheering a particular girdle proof. There are these non-computable
00:35:42.440 things anyway. Okay, let's go back to the book. It is implicit in Turing's work that he
00:35:48.360 expected what would naturally be regarded as computable to be also what could, at least in
00:35:53.320 principle, be computed in nature. This expectation is tantamount to a stronger physical version
00:35:59.880 of the Church Turing conjecture. The mathematician Roger Penrose has suggested that it should be
00:36:04.760 called the Turing principle, the Turing principle, for abstract computers simulating physical objects.
00:36:11.960 There exists an abstract universal computer whose repertoire includes any computation
00:36:17.800 that any physically possible object can perform. So that's the Turing principle.
00:36:23.080 There goes on to say. Turing believed that the universal computer in question
00:36:28.200 was the universal Turing machine. To take account of the wider repertoire of quantum computers,
00:36:33.800 I have stated the principle in a form that does not specify which particular abstract computer
00:36:39.800 does the job, Paul's name reflects. Yes, this is David's addition to Turing's work. The
00:36:45.800 generalization of what Turing started Turing's principle, David proved and which laid the
00:36:55.080 foundations for quantum computation. That there is such a physical object that can be constructed,
00:37:01.160 that is able to do the computations of anything. Any computable thing can be computed by this
00:37:09.560 particular thing. And that includes anything made of matter, buying laws or physics,
00:37:17.080 is going to be, it's behavior is going to be computable. It goes on to say, quote,
00:37:22.360 the proof I've given of the existence of can't go to environments is essentially due to Turing.
00:37:27.000 As I said, he was not thinking explicitly in terms of virtual reality, but in an environment
00:37:31.400 that can be rendered does correspond to a class of mathematical questions whose answers can be
00:37:37.720 calculated. Those questions are computable. The remainder, the questions for which there is no
00:37:43.560 way of calculating the answer are called non-computable. If a question is non-computable,
00:37:49.320 that does not mean that it has no answer or that its answer is in any sense ill-defined or ambiguous.
00:37:55.480 On the contrary, it means that it definitely has an answer. It is just that there physically
00:38:00.280 is no way even in principle of obtaining that answer or more precisely, since one could always
00:38:05.560 make a lucky unverifiable guess of proving that is the answer. For example, a prime pair is a pair
00:38:12.120 of prime numbers whose differences too, such as 3 and 5 or 11 and 13. Mathematicians have tried
00:38:18.520 in vain to answer the question whether there are infinitely many such pairs or only a finite number
00:38:25.080 of them. It is not even known whether this question is computable. Let us suppose that it is not.
00:38:31.800 That is to say that no one and no computer can ever produce a proof either that there are only
00:38:37.080 finitely many prime pairs or that there are infinitely many. Even so, the question does have an answer.
00:38:44.040 One can say with certainty that either there is a highest prime pair or there are infinitely many
00:38:48.520 prime pairs. There is no third possibility. The question remains well defined, even though we may
00:38:54.840 never know the answer. In virtual reality terms, no physically possible virtual reality generator
00:39:00.440 can render an environment in which answers to non-computable questions are provided to the user on
00:39:06.120 demand. Such environments are of the can't go to type. And conversely, every can't go to
00:39:11.640 environment corresponds to a class of mathematical questions. What would happen next in an
00:39:16.760 environment defined in such and such a way, which it is physically possible to answer?
00:39:21.560 Although non-computable questions are infinitely more numerous than computable ones,
00:39:25.960 they tend to be more esoteric. That is no accident. It is because of the parts of mathematics
00:39:30.760 that we tend to consider the least esoteric are those we see reflected in the behavior of physical
00:39:35.800 objects in familiar situations. In such cases, we can often use those physical objects to answer
00:39:42.360 questions about the corresponding mathematical relationships. For example, we can count on our
00:39:47.080 fingers because the physics of fingers naturally mimics the arithmetic of the whole numbers from
00:39:52.600 zero to ten, pausing their more reflection. So, pure mathematics doesn't need to concern itself
00:39:59.960 about whether it applies to physical stuff. They can, the pure mathematicians can consider
00:40:06.520 pure abstractions, the things that aren't made out of material at all and don't obey the laws of
00:40:11.880 physics. Even though what can be known is constrained by the laws of physics, that's a separate issue,
00:40:17.160 quite a separate issue. The constraints placed on mathematics by the laws of physics aren't
00:40:24.280 constraints that prevent mathematics from delving into non-physical stuff. Indeed, pure mathematics
00:40:30.280 is largely about non-physical stuff. There's a great YouTube video of Richard Fine when talking
00:40:37.080 about mathematics and physics, the relationship between them and the mathematicians and the
00:40:42.680 physicists. It's almost like a stand-up routine. The man was just so engaging, so entertaining,
00:40:48.440 and so funny when he talks about certain things. That particular one I'll try and remember to provide
00:40:53.960 a link in the description to this video to that one. I can't put a clip here, I'd like to be
00:40:58.760 able to put a clip here, but it seems when I do that, they take down the entire video and it's
00:41:03.560 such a hassle, so I have to avoid putting clips in these days. But in a, you know, like,
00:41:08.440 Feynman's basically saying, you look, your physicist is sort of interested in specific cases. He's
00:41:13.800 not interested in general cases. He goes along to the mathematician and then he says, I'm interested
00:41:19.160 in, you know, the laws of gravity, for example, in three-dimensional space. I just need
00:41:25.000 the three-dimensional space and the mathematical, pure mathematician will say, well, for an
00:41:28.840 n-dimensional space, here are the theorems that follow and the physicists will say, I'm not interested
00:41:33.400 in n-dimensions. I'm not interested in just the arbitrary, you know, sort of force. I'm not
00:41:37.240 interested in arbitrary spaces of n-dimensions. I'm interested in a specific case and the pure
00:41:43.800 mathematician will say, well, just substitute n equals three then. And then, of course, I find
00:41:50.040 me goes on to say something like, then, of course, the physicist has to go crawling back to the
00:41:54.280 pure mathematician at some point and say, you know, you're talking about those n-dimensional spaces.
00:41:59.800 What about the case of n equals four? Sometimes these, the general case turns out to be very
00:42:08.280 useful for the physicist. And there is this cross-pollination that happens between physics and
00:42:13.320 mathematics, of course. What is done in math in pure mathematics sometimes is thought to be
00:42:18.280 utterly irrelevant. And, you know, I've mentioned before, the case of G.H. Hardy and a mathematician's
00:42:23.880 apology wrote this book about, you know, meeting romanogen, another famous mathematician. And
00:42:28.840 Hardy said, Hardy said of his own work that he didn't think it would ever have any applications to
00:42:34.120 anything ever, and he was quite proud of it, he regarded as more being like art. Okay? Just to
00:42:39.800 just exploring the space of mathematics for its own sake. But in fact, his own work, I think,
00:42:45.400 went on to be used in electrical engineering and, you know, had had applications anyway, had
00:42:50.280 proper applications later on. And, you know, that's the unpredictability of the growth of
00:42:54.360 knowledge. And it can happen in the other direction as well, you know, physicists can do work in
00:42:58.840 physics, which then goes on to have a bearing on what happens in mathematics. I think, you know,
00:43:03.800 things like chaos theory, you know, there's first investigator biophysicists about how
00:43:09.960 seemingly purely deterministic systems, bang, you know, the simple laws can actually become chaotic.
00:43:16.360 Even if you assume that the classical laws of physics, the perfectly deterministic laws of
00:43:21.640 things, they can lead to these extremely complex behavior. A double pendulum is one such thing,
00:43:27.480 which has this interestingly chaotic behavior. So that comes from physics and goes into
00:43:34.120 pure mathematics, and the pure mathematicians can explore that kind of thing. But, yes, if you want
00:43:38.440 to laugh, definitely look up Feynman talking about mathematics and physics. Let's keep going,
00:43:46.040 David Wright's. Quite. The reptiles of the three very different abstract computers defined
00:43:50.840 by Turing, Church, and Post were soon proved to be identical. So have the
00:43:55.560 repertoire of all abstract models of mathematical computation that have since been proposed.
00:44:00.200 This is deemed to lend support to the Church Turing conjecture and to the universality
00:44:04.760 of the universal Turing machine. However, the computing power of abstract machines
00:44:09.960 has no bearing on what is computable in reality, pausing their myreflection. Yes, so here,
00:44:16.760 this is the genius of David Deutsch. This is where it comes in, right? I mean,
00:44:21.640 if you regard Turing as a genius for the insight about all of this computation stuff,
00:44:27.720 which he certainly was, then so is this insight by David, okay? It may seem simple in retrospect,
00:44:32.680 you know, like so much of science just seems simple like, well, why couldn't I think of that?
00:44:36.840 Well, because you're not thinking about this particular problem all the time. You could,
00:44:42.600 any of us could, but we didn't. It's the people that are passionately curious and interested
00:44:48.920 in these particular problems and push the frontier of science, in this case, physics and computation
00:44:53.960 forward. This whole idea that thinking about computation as actually being physical,
00:45:00.440 and not merely an abstract thing, it takes insight, questioning assumptions, and that can be hard,
00:45:07.480 which assumptions do you question? And once you question those assumptions, what do you replace
00:45:14.200 them with? What's better? It's no point you're saying, oh, let's assume that's false. Well, then
00:45:20.040 what are you going to put in its place? If nothing does it lead to something better or not?
00:45:25.320 Even recognizing, noticing in the first place that something is an assumption at all is hard,
00:45:31.560 computation is assumed to be abstract and not physical. Oh, is it? Yeah, that sense in
00:45:37.080 assumption. And I guess a lot of the mathematicians who were doing this didn't realize the assumptions
00:45:40.920 they were making. Who notices that kind of thing? What is the consequence of that? It's like,
00:45:47.400 oh, physics is about dynamical laws. You plug in the initial conditions and you calculate
00:45:52.440 what goes on next. But that's an assumption as well. What if we relaxed that assumption and
00:45:58.120 considered something deeper about what is possible and impossible? Why would we have a question
00:46:05.000 the very foundations of physics? Who would ever do that? Well, these things take creative leaps,
00:46:10.520 don't they? And those creative leaps can be the hard part. You have to sit down and you have to
00:46:15.720 be creative and you have to think about these things. They're hard and yet not hard. You know,
00:46:21.320 like they're hard and once someone's done it, you can look back and you go, oh, you know, how could
00:46:25.320 it have been otherwise? It's that kind of thing. But it's beforehand before the creative actors
00:46:30.600 take in place that, you know, people are struggling to make the progress. And yet it always seems
00:46:35.400 in retrospect. Oh, that was so simple. I could have done that. Yeah, you could have. But you weren't
00:46:41.080 focused on that problem. Were you? And yet this is the kind of thing that anyone interested in
00:46:45.720 progress needs to strive for. It's not to say, well, you just go around assuming everything is false
00:46:51.480 and then you're done, question everything and then you're done. No, you need an alternative. This is
00:46:56.680 the hard part. You need to, yeah, take what is known now, regard it as the best explanation now, figure
00:47:05.720 out what could possibly be false about it and replace that with something better, something that
00:47:12.520 is going to have consequences that you can investigate and pursue or that others can, perhaps.
00:47:20.280 And then you might have a whole new field of physics, let's say. You might have a whole field
00:47:25.960 of quantum computation, say. Okay, let's keep going. David writes, quote, the scope of virtual
00:47:32.040 reality and its wider implications for the comprehensibility of nature and other aspects of the
00:47:36.680 fabric of reality depends on whether the relevant computers are physically realizable.
00:47:41.960 In particular, any genuine universal computer must itself be physically realizable. This leads
00:47:47.640 to a stronger version of the cheering principle, the cheering principle for physical computers
00:47:53.000 simulating each other. It is possible to build a universal computer, a machine that can be
00:47:58.600 programmed to perform any computation that any other physical object can perform. It follows
00:48:05.240 that if a universal image generator were controlled by a universal computer, the resulting
00:48:09.480 machine would be a universal virtual reality generator. In other words, the following principle
00:48:14.760 also holds the cheering principle for virtual reality generators rendering each other.
00:48:20.520 It is possible to build a virtual reality generator whose repertoire includes that of every other
00:48:26.280 physically possible virtual reality generator. Now any environment can be rendered by a virtual
00:48:31.160 reality generator of some sort. For instance, one could always regard a copy of that very environment
00:48:37.160 as a virtual reality generator with perhaps a very small repertoire. So it also follows
00:48:42.440 from this version of the cheering principle that any physically possible environment can be rendered
00:48:47.640 by the universal virtual reality generator. Hence, to express the very strong self-similarity that
00:48:53.560 exists in the structure of reality embracing not only computations but all physical processes,
00:48:59.880 the cheering principle can be stated in this all embracing form. The cheering principle,
00:49:06.680 it is possible to build a virtual reality generator whose repertoire includes every physically
00:49:13.080 possible environment. This is the strongest form of the cheering principle. It not only tells us
00:49:19.000 that various parts of reality can resemble one another. It tells us that a single physical object,
00:49:25.960 buildable once and for all, apart from maintenance and a supply of additional memory when needed,
00:49:30.600 can perform with unlimited accuracy, the task of describing or mimicking any other part of the
00:49:36.760 multiverse. This set of all behaviors and responses that one object exactly mirrors the set of all
00:49:42.440 behaviors and responses of all other physically possible objects and processes. The set of all
00:49:47.800 behaviors and responses of that one object exactly mirrors the set of all behaviors and responses
00:49:54.600 of all other physically possible objects and processes, pausing the MRI reflection. So this is
00:50:00.920 the basis of quantum computation. This says that you can build this thing, this computer,
00:50:07.080 quantum computer, which as long as you have the program, as long as you know what to feed into
00:50:14.600 this computer, it can represent that environment. It can represent that world. In particular,
00:50:21.960 if you have a theory of physics, then you can program it in, you can model the rest of physical
00:50:30.120 reality. And it also implies the existence of people who can understand because they also are
00:50:39.320 rendering these environments with their models of science that this can be done too, that this is
00:50:47.160 the comprehensibility of physical reality as well. It allows for the comprehensibility of physical
00:50:55.000 reality as well. Let's go on, David writes. On this exact point, David goes on, right, quote,
00:51:01.800 this is just the sort of self similarity that is necessary if, according to the hope I expressed in
00:51:06.200 chapter one, the fabric of reality used to be truly unified and comprehensible. If the laws of
00:51:11.400 physics as they apply to any physical object or process are to be comprehensible, they must be
00:51:17.160 capable of being embodied in another physical object, the Noah, pausing the MRI reflection. So that's
00:51:24.200 the universal explanation. Now, this particular passage is where I say David's just dropping
00:51:31.880 insight bombs. It's just so much of the beginning of infinity yet to come. Even stuff of the
00:51:38.920 science of Canon can't be the constructive theory. And it's just deep deep stuff. So I'll go on,
00:51:46.040 okay, and then I'm going to go back and I'm going to read some of this again, for emphasis,
00:51:50.440 it's important. David writes, quote, it is also necessary that processes capable of creating such
00:51:56.600 knowledge be physically possible. Such processes are called science. Science depends on experimental
00:52:03.640 testing, which means physically rendering a law's predictions and comparing it with a rendering
00:52:09.720 of reality. End quote. So we've moved from the existence of the universal computer, the sharing
00:52:17.480 principle, to the idea that Noah's are able to come to a and understanding of physical reality
00:52:27.320 that's entailed within this. And also that science therefore is possible and physically testing
00:52:36.840 theories is possible. This is all coming from the same thing. I apologize if anyone feels
00:52:41.720 patronised that I'm just laboring the labouring the point, but it's just for anyone who's new to
00:52:49.080 this, these can be deep insights. And it's one reason why because of the density of consequences
00:52:59.640 that flow from, and David pursues these consequences, but the density of them, the number of them,
00:53:04.680 the depth of them means that sometimes the world view is difficult to convey and let's say a few
00:53:11.480 tweets that it's all built in a sense as a web of these interconnected explanations about reality,
00:53:25.480 which have these connections between physics, mathematics, epistemology, science, more broadly,
00:53:35.160 philosophy. Let's keep going, David writes. It also depends on explanation and that requires
00:53:41.160 abstract laws themselves, not merely their predictive content, to be capable of being rendered in
00:53:47.800 virtual reality. End quote. So there we have David in the fabric of reality, again, you know,
00:53:55.960 laying out the deep themes of the beginning of infinity. And again, the idea of the Noah here,
00:54:02.840 okay, and the purpose of science, that abstract laws themselves being explained,
00:54:10.600 not merely being about their predictive content, being able to predict stuff, instrumentalism
00:54:15.480 as false. David goes on, quote, this is a tall order, but reality does meet it. That is to say
00:54:21.400 the laws of physics meet it. The laws of physics by conforming to the Turing principle make it
00:54:26.040 physically possible for those same laws to become known to physical objects. Thus, the laws of physics
00:54:32.920 may be said to mandate their own comprehensibility end quote. So it's that kind of passage that
00:54:38.760 sets the book apart from other books. It is not merely the science. It's philosophical exploration
00:54:49.480 of these ideas and hence provides a whole world of view, a way of thinking about reality that
00:54:57.000 is coherent, as far as we can tell, it's the deepest one that we can tell, providing for cosmic
00:55:06.760 significance of people and comprehensibility of that cosmos. And it goes on with more insight,
00:55:13.960 bombs, but really I just have to, without interruption, without interruption, go back and just read
00:55:23.640 through that, okay, because David's talking about self-similarity. What is this self-similarity is,
00:55:28.040 well, and I'll talk about this in my Nexus video, the idea here is that in a person's mind,
00:55:34.360 they represent the rest of physical reality. There's a self-similarity, there's relationships between
00:55:40.200 ideas you have in your mind that correspond to some degree of accuracy with physical reality.
00:55:51.080 That's what self-similarity is. And so that connection between us and the cosmos,
00:55:58.040 or all of reality rather, you know, every single thing that can be known, makes us unique and
00:56:05.320 important. So let's just go through and read that again because it is just one of the reasons
00:56:12.040 why this is one of my favorite chapters. It's the wheelhouse of David Deutsch. It underscores
00:56:19.080 the world you presented to us in both of these books here too. It's optimistic, all-encompassing,
00:56:26.360 weighing which these findings, like that you're in principle, allow for comprehensibility,
00:56:35.320 infinite progress, solving of problems. Let's just read it again. Let's just read it again.
00:56:39.800 And enjoy it without my interruption. Quote, this is just the sort of self-similarity that is
00:56:46.840 necessary. If according to the hope I expressed in Chapter 1, the fabric of reality is to be truly
00:56:51.800 unified and comprehensible. If the laws of physics as they apply to any physical object or process
00:56:57.080 are to be comprehensible, they must be capable of being embodied in another physical object,
00:57:01.400 the Noah. It is also necessary that processes capable of creating such knowledge,
00:57:06.200 be physically possible. Such processes are called science. Science depends on experiment testing,
00:57:11.720 which means physically rendering a law's predictions and comparing it with a rendering of reality.
00:57:16.440 It also depends on explanation, and that requires the abstract laws themselves,
00:57:20.680 not merely their predictive content, to be capable of being rendered in virtual reality.
00:57:25.160 This is a tall order, but reality does meet it. That is to say, the laws of physics meet it.
00:57:30.120 The laws of physics by conforming to the Turing principle make it physically possible for those
00:57:35.080 same laws to become known to physical objects. Thus, the laws of physics may be said to mandate
00:57:41.480 their own comprehensibility. Amazing stuff. The scientific view of the
00:57:49.720 deep importance of human beings as people, the scientific view, the rejection of
00:57:58.600 parochialism and the principle of mediocrity, and pessimism about people as a chemical scum.
00:58:05.000 That's all there, that we are unique, and in some sense,
00:58:11.000 written into the laws of physics. Okay, let's keep going. David Wright is quite
00:58:16.120 since building a universal virtual reality generator is physically possible. It must actually be
00:58:21.000 built in some universes. A caveat is necessary here. As I explained in chapter three, we can
00:58:26.280 normally define a physically possible process as one that actually occurs somewhere in the multiverse.
00:58:31.400 But strictly speaking, a universal virtual reality generator is a limiting case that requires
00:58:36.520 arbitrarily large resources to operate. So what we mean by saying that it is physically possible
00:58:42.520 is that virtual reality generators would repertoire arbitrarily close to the set of all physically
00:58:48.200 possible environments exist in the multiverse. Similarly, since the laws of physics are capable
00:58:53.560 of being rendered, they are rendered somewhere. Thus it follows from the Turing principle in the
00:58:58.360 strong form for which I have argued that the laws of physics do not merely mandate their own
00:59:02.680 comprehensibility in some abstract sense. Comprehensibility by abstract scientists as it were,
00:59:08.200 they imply the physical existence somewhere in the multiverse of entities that understand them
00:59:14.440 arbitrarily. Well, I should have discussed this implication further in later chapters,
00:59:18.280 pausing that as my reflection. Yes, so when it says there, just be aware,
00:59:23.400 now I'm not speaking, this is me talking, this is not David talking. I could be wrong,
00:59:28.040 mistakes my own. This could be one of them I'm about to make. But my understanding over that there
00:59:33.240 is when he says they imply the physical existence somewhere in the multiverse of entities that
00:59:38.920 understand them arbitrarily well. He's not saying that here right now at the same time as us,
00:59:45.480 somewhere there are aliens that exist that understand them arbitrarily well. It's that we could be
00:59:51.640 those entities. If we're not then someone else will be, some other species will be,
00:59:57.400 but we could be that species. We could be those entities that understand the physical laws
1:00:03.720 arbitrarily well. In other words, people are mandated by the laws of physics. If they're
1:00:09.400 possible they exist somewhere, well here we are, here we are. Now, it could be the case that a
1:00:14.520 great catastrophe wipes us out, that the bostromes and reases and various other intellectuals who
1:00:22.040 think the civilization could come to an end. We all think it could come to an end, but they
1:00:28.360 tend to be putting their eggs into that basket, civilization crumbling. They could be right.
1:00:35.720 If they are right then we won't be the ones that go on to understand the physical laws
1:00:40.280 arbitrarily well, but other people will. That's my understanding of that. We could be the ones.
1:00:48.520 I think we will be. I think we will be. It appears to be the case. There needs to be a history
1:00:56.520 of optimism written that things are getting better, not irrevocably, not necessarily,
1:01:05.640 but there are explanations that go into allowing for the dynamic society which we are occupying
1:01:14.040 right now. The resilience of this society is growing, not diminishing. Of course,
1:01:23.240 hyperbole and pessimism is increasing to some extent in some places, but optimism is increasing
1:01:29.080 in other places as well. In the West, sometimes we end up having a blanket of view because our
1:01:36.440 intellectuals have a certain cultural demand. I think it's transient. I think that there will be
1:01:43.720 a resurgence of optimism. People are going to get bored. They're going to get bored with
1:01:49.400 the constant pessimism, the constant weighing which people, human beings, talk down human beings,
1:01:55.720 talk up the environment. It's can't last. It's can't last. I'm hopeful.
1:02:01.960 Okay, let's keep going. Let me get to off track. David writes, quote,
1:02:07.320 Now I return to the question I posed in the previous chapter,
1:02:10.040 namely whether if we only had a virtual reality rendering based on the wrong laws of physics
1:02:15.320 to learn from, we should expect to learn the wrong laws. The first thing to stress is that we do
1:02:21.000 have only virtual reality based on the wrong laws to learn from. As I've said, all our external
1:02:26.040 experiences are of virtual reality generated by our own brains. And since our concepts and theories
1:02:33.400 whether in born or learned are never perfect, all our renderings are indeed inaccurate. That is to
1:02:39.000 say, they give us the experience of an environment that is significantly different from the environment
1:02:43.880 that we are really in. Marriages and other optical illusions are examples of this.
1:02:48.440 Another is that we experience the earth to be at respinate our feet despite its rapid and
1:02:52.200 complex motion in reality. Another is that we experience a single universe and a single instance
1:02:56.840 of our own conscious selves at a time while in reality there are many. But these inaccurate and
1:03:01.400 misleading experiences provide no argument against scientific reasoning. On the contrary,
1:03:05.400 such deficiencies are its very starting point, pausing their my reflection. Yes, so this is the
1:03:10.680 reputation of empiricism. Our senses don't provide us with accurate information. We need science.
1:03:16.760 Science is about explaining what we see in terms of what we don't see. It's the scene in terms of
1:03:22.280 the unseen. My desk here made of wood, solid, continuous matter, it feels like, feels nice and smooth.
1:03:31.400 We know it's bumpy atoms. I can't see the atoms. My senses are not going to be able to tell me
1:03:38.760 that. But we have theories and we had theories of atoms before we had scanning electron microscopes
1:03:44.120 that could produce images for us of those atoms. No image is possible. No way of seeing
1:03:52.840 what is going on in the center core of the sun. The core of the sun is not directly observable.
1:03:59.640 We said surface. But we know what's going on there. We know what's going on there because of our
1:04:05.720 explanations. Big bang. No one's going to be there to observe it. No one was there to observe it.
1:04:11.080 But we know what happened. No one's going to see a dinosaur. Almost everything in science is like this.
1:04:18.040 We don't see the stuff that really explains what we do see, whether because it's too small,
1:04:26.040 too vast, too far back in time, so on and so forth. Science is about the scene in terms of the
1:04:35.720 unseen. We get an inaccurate experience of reality. Our experience is virtual reality.
1:04:45.640 Real reality. We can come to approximate that more and more over time, more and more closely over time.
1:04:52.600 And we do. But still, I mean, we're just barely scratching the surface as the beginning of
1:04:57.400 infinity emphasizes. They're always at the beginning of infinity, right? Just scratching the surface.
1:05:02.840 Our virtual reality rendering, understanding improves out of time. That science, that's that kind
1:05:09.480 of virtual reality. And then there's the virtual reality of us just being minds, running on brains
1:05:15.400 in the darkness of our of our skulls. That's where we really are. But we are connected to
1:05:21.640 the rest of physical reality via these imperfect, sense gathering things, eyes and ears and hands
1:05:28.600 and so on. Okay, let's kick it. David writes, quote, we are embarked upon solving problems about
1:05:33.720 physical reality. If it turns out that all this time, we have merely been studying the programming
1:05:39.400 of a cosmic planetarium, then that would merely mean that we have been studying a smaller portion
1:05:44.360 of reality than we thought. So what? Such things have happened many times in the history of science
1:05:49.240 as our horizons have expanded beyond the earth to include the solar system, our galaxy,
1:05:53.800 other galaxies, clusters of galaxies and so on. And of course, parallel universes.
1:05:58.600 Another such broadening may happen tomorrow. Indeed, it may happen according to any one of an
1:06:03.480 infinity of possible theories or it may never happen. Logically, we must concede to
1:06:08.200 solar system and related doctrines that the reality we are learning about might be an
1:06:13.960 unrepresentative portion of a larger inaccessible or incomprehensible structure. But the general
1:06:18.760 refutation I've given of such doctrines shows that it is irrational to build upon that possibility.
1:06:24.680 Following Occam, we shall entertain such theories when and only when they provide better explanations
1:06:29.640 than simple rival theories pausing their more affection. Yeah, exactly. Reality, realism, rather,
1:06:35.160 realism allows for progress to be made, problems to be solved. But the opposite,
1:06:41.880 solubism. Well, how do you build on that? What follows? Okay, it's all a dream. Okay, what follows?
1:06:50.040 If what follows, Geron Lenny Makes is probably, if what follows is, well, science still works
1:06:54.200 in the same way it would under realism. You've just got an unnecessary assumption, don't you?
1:06:59.320 You know, realism is just works, but let's add on top of that, but it's all a dream.
1:07:05.800 Why don't just do away with the but it's all a dream, but it's all a simulation and just get
1:07:09.720 on with science because that's the most parsimonious way of working, assume things are real.
1:07:17.000 David goes on to write, quote, however, there is a question we can still ask.
1:07:21.160 Suppose that someone were imprisoned in a small, unrepresentative portion of our own reality,
1:07:26.040 for instance, inside a universal virtual reality generator that was programmed with the wrong
1:07:31.480 laws of physics. What could such prisoners learn about our external reality?
1:07:36.200 At first sight, it seems impossible that they could discover anything at all about it.
1:07:41.480 It may seem that the most they could discover would be the laws of operation, i.e. the program
1:07:47.960 of the computer that operated their prison. But that is not so. Again, we must bear in mind that
1:07:53.960 if the prisoners are scientists, they will be seeking explanations as well as predictions.
1:08:00.600 In other words, they will not be content with merely knowing the program that operates their
1:08:04.600 prison, they will want to explain the origin and attributes of the various entities, including
1:08:09.640 themselves, that they observe in the reality they inhabit. But in most virtual reality environments,
1:08:15.480 no such explanation exists for the rendered objects do not originate there, but have been designed
1:08:20.600 in the external reality. Suppose that you are playing a virtual reality video game,
1:08:25.480 for the sake of simplicity, suppose that the game is essentially chess.
1:08:29.400 A first-person perspective version perhaps, in which you adopt the persona of the king,
1:08:34.680 you will use the normal methods of science to discover this environment,
1:08:38.120 laws of physics, and their emergent consequences. You will learn that checkmate and
1:08:43.000 stalemate are physically possible events, a possible under your best understanding of how the
1:08:48.520 environment works. But that a position with nine white pawns is not physically possible.
1:08:54.520 Once you had understood the laws sufficiently well, you would notice that the chess board is
1:08:58.760 too simple an object to have, for instance, thoughts. And consequently, that your own thought
1:09:05.000 processes cannot be governed by the laws of chess alone. Similarly, you could tell that during any
1:09:11.880 number of games of chess the pieces can never evolve into self-reproducing configurations,
1:09:17.320 and if life cannot evolve on the chess board, far less can intelligence evolve. Therefore,
1:09:22.600 you would also infer that your own thought processes could not have originated in the universe,
1:09:27.080 in which you found yourself. So even if you had lived within the rendered environment or your life
1:09:32.680 and did not have your own memories of the outside world to account for as well,
1:09:36.200 your knowledge would not be confined to that environment. You would know that,
1:09:39.880 even though the universe seemed to have a certain layout and a base certain laws,
1:09:43.720 there must be a wider universe outside it obeying different laws of physics,
1:09:48.200 and you could even guess some of the ways in which those wider laws would have to be different
1:09:53.320 from the chess board laws. Arthur C. Clarke, once remarked that any sufficiently advanced technology
1:09:59.160 is indistinguishable from magic. This is true, but slightly misleading. It is stated from the point
1:10:05.160 of view of a pre-scientific thinker, which is the wrong way around. The fact is, that to anyone
1:10:11.960 who understands what virtual reality is, even genuine magic would be indistinguishable from technology.
1:10:17.800 For there is no room for magic in a comprehensible reality. Anything that seems incomprehensible
1:10:24.120 is regarded by science merely as evidence there is something we have not yet understood,
1:10:28.600 be it a conjuring trick, advanced technology, or a new law of physics. Posing there just
1:10:35.560 that seems like a tweetable quote, doesn't it? I'll read it again. Anything that seems
1:10:40.520 incomprehensible is regarded by science merely as evidence that there is something we have not
1:10:45.320 yet understood, be it a conjuring trick, advanced technology, or a new law of physics.
1:10:50.760 And it goes on to say, reasoning from the premise of one's own existence is called
1:10:55.800 anthropic reasoning. Although it has some applicability in cosmology, it usually has to be
1:11:00.840 supplemented by substantive assumptions about the nature of one's self before it yields definite
1:11:06.520 conclusions. But anthropic reasoning is not the only way in which the inmates of our hypothetical
1:11:12.200 virtual reality prison could gain knowledge of an outside world. Any of their evolving
1:11:18.120 explanations of their narrow world could at the drop of a hat reach into an outside reality.
1:11:23.880 For instance, the very rules of chess contain what I thought for player may realize is
1:11:28.840 fossil evidence of those rules having had an evolutionary history. There are exceptional moves,
1:11:34.120 such as casting and capturing on-personge, which increase the complexity of the rules but improve
1:11:39.640 the game. In explaining that complexity, one justifiably concludes that the rules of chess
1:11:45.800 were not always as they are now. In the Papurian scheme of things, explanations always lead to new
1:11:52.040 problems which in turn require further explanations. If the prisoners fail after a while to improve
1:11:58.440 upon their existing explanations, they may of course give up, perhaps falsely concluding that
1:12:03.240 there are no explanations available. But if they do not give up, they will be thinking about those
1:12:07.880 aspects of their environment that seem inadequately explained. Thus if the high technology
1:12:13.240 jailers wanted to be confident that their rendered environment would forever fool their prisoners
1:12:18.520 into thinking there is no outside world, they would have their work cut out for them.
1:12:22.920 The longer they wanted the illusion to last, the more ingenious the program would have to be.
1:12:27.880 It is not enough that the inmates be prevented from observing the outside, the rendered environment
1:12:33.240 would also have to be such that no explanations of anything inside would ever require one to
1:12:38.920 postulate an outside. The environment, in other words, would have to be self-contained as regards
1:12:45.800 explanations. But I doubt that any part of reality should of the whole thing has that property.
1:12:53.320 End quote. End of the chapter. Long one today. But as I think I hope you will agree, this
1:13:00.280 just is so dense and deep and sort of has feelers into the rest of the book and the beginning
1:13:07.560 of infinity and the world viewers I say. This is way of understanding the place of human beings and
1:13:15.000 people in the cosmic scheme of things. How it is that we can go about creating an infinite stream
1:13:21.720 of solutions to the problems that we encounter via creating knowledge. And there's the bounds imposed
1:13:27.960 by laws of physics are there and they're real, but they don't prevent us from making infinite progress.
1:13:33.400 Which is what optimism is all about. But because this has been a long one, I won't have a long
1:13:38.440 outro today. And instead I'll just say, until next time, bye-bye. Of course, if you would like to
1:14:00.360 support this endeavor of me exploring the world view, that is contained within the philosophy
1:14:07.640 of Karl Popper, the science and philosophy of David Deutsch, construct a theory, infinite progress,
1:14:15.640 rational optimism, so I want to say for all the good stuff that we talk about here then,
1:14:20.120 please go to my website www.renthall.org and there there are links to Patreon paper. Until next time, bye-bye.
