00:00:24.480 Welcome to Topcast, in episode 4 of the site of Cannon Cart.
00:00:29.680 Although we're only at chapter 3, previous episode was an introduction to this chapter.
00:00:36.080 So I don't really need to do an introduction today, so I'm going to launch straight in to the reading.
00:00:41.520 And Kiara begins in chapter 3, titled information.
00:00:46.080 With an explanation of what she's going to do in this chapter, and I shall read that, quote,
00:00:51.120 Where I explain how information can be completely captured within physics with two
00:00:55.600 counterfactuals, the possibility of copying and of flipping, where you encounter the
00:01:02.240 counterfactual properties of universality, and learn how it enables universal computers.
00:01:08.240 And then we get into the main part of the chapter. And this first part of the chapter is a lovely
00:01:13.360 description, which sets a literal scene of things that she's going to discuss later on in the
00:01:20.640 chapter. She begins, quote, When the night falls on Centosa, a small satellite island of Singapore,
00:01:28.720 a remarkable spectacle takes place. The best location to witness it is somewhere along the bridge
00:01:34.800 connecting Centosa to Singapore. That bridge is made of smooth wooden tiles. It also has a panoramic
00:01:41.840 spot where one can rest, leaning on a balustrade while enjoying the view that spans the whole day.
00:01:47.920 As the twilight turns into night, distinctive kinds of lights and sounds fill the air.
00:01:53.360 The surroundings gradually become darker and darker until the whole backdrop is pitch black,
00:01:58.480 both the sky and the sea. At that point, the spectacle reaches its peak,
00:02:03.520 suspended several dozen metres above the sea, green lit cable cars run smoothly through the
00:02:08.320 air back and forth in constant gentle motion, boats and ships move lazily across the bay,
00:02:13.920 their signalling lights, cutting through the darkness. The music from the bars on the shore
00:02:19.040 spreads around whispering in the warm equatorial night, for the back in the distance a lighthouse
00:02:25.280 flashes on and off, on and off. The objects populating that nocturnal landscape display
00:02:31.680 extremely diverse behaviours, each explained by a different branch of physics,
00:02:36.800 cable cars, boats and ships are powered by engines explained by the laws of thermodynamics.
00:02:42.320 The music and its propagation are explained by the theory of sound,
00:02:45.680 sound is composed of waves of molecules of air which travel to one's ease,
00:02:50.080 and are then converted into electrochemical signals in the brain. Molecules are in turn
00:02:54.640 composed of atoms and atoms are made of subatomic particles such as protons, electrons and neutrons.
00:03:01.600 Light has explained by the laws of electromagnetism, Maxwell's equations,
00:03:06.640 at the most fundamental level, all these phenomena are explained by quantum theory and general
00:03:11.520 relativity, the two deepest explanations of physical reality we possess at present.
00:03:17.280 Despite being so different in their specific details, those systems have something in common,
00:03:22.640 which is not explained by any of the existing branches of physics. The music, the boats,
00:03:27.760 lights, the lighthouse, they are all signals, they are capable of carrying information.
00:03:34.320 This property is a key trait they all share, one that contrary to what one might think
00:03:39.520 is possessed only by a particular class of systems in our universe. In a short while,
00:03:44.880 I should give you examples of systems that cannot carry information.
00:03:49.120 What is the property that makes those systems, and many others like them,
00:03:54.880 Entering this question involves counterfactuals and it will keep us occupied in this chapter,
00:03:59.520 it will reveal the way to express information as a fundamental entity in physics,
00:04:03.520 and the fundamental physical laws that rule the physical system capable of instantiating information.
00:04:09.040 This is crucially important, not only from the point of view of understanding the universe
00:04:12.800 in a deeper way, but also because information and its connection with physics
00:04:17.840 is at the heart of information technologies that could further revolutionize our civilization,
00:04:22.880 such as the universal quantum computer that we will discuss in chapter 4.
00:04:27.840 At first, it may seem that information does not really have anything to do with physics.
00:04:32.160 In fact, in everyday language, the word information is used to refer to all sorts of things.
00:04:36.720 For instance, many systems contain information, books, newspapers, and magazines,
00:04:41.520 emails, and messages. The words we utter when speaking to friends and family,
00:04:45.520 poems, and songs, and ballads. The biosphere contains information too,
00:04:49.120 as I mentioned in chapter 1, encoded in DNA molecules.
00:04:52.640 But even though all those systems are plainly part of physical reality,
00:04:56.720 it is hard to identify information with a particular physical system.
00:05:00.560 Information looks more like an abstract entity, and it is hard to pin down its connection with
00:05:05.360 physics. For a start, information does not have a specific embodiment,
00:05:09.360 but it can be embodied by many diverse physical systems.
00:05:13.360 Is it then some kind of property that systems have, such as say colour?
00:05:17.600 That allows the light as green, for instance, means that the photons it emits.
00:05:22.080 The contour of energy it is composed of have a particular frequency or energy content.
00:05:26.720 Could information be something like energy or frequency?
00:05:29.920 Not quite. Those are factual properties, because they are specified exclusively
00:05:34.400 by the system state at a certain time and in a certain location in space.
00:05:39.600 But when it comes to information, the story is different.
00:05:42.080 As I shall explain in detail, one cannot say that some systems contain information
00:05:47.280 just by stating a full description of its state and its factual properties,
00:05:50.960 because the fact that it does has to do with certain transformations being possible on it.
00:05:56.400 Then what do we mean when we say that a computer or smartphone is carrying information?
00:06:01.520 Rather than seeking to define information as a physical entity,
00:06:06.240 or as a property of physical systems, the key is to change our focus and ask a slightly different question.
00:06:14.080 What is different in the state of affairs of a physical system between when it does carry information
00:06:20.320 and when it doesn't? It is, as I shall explain, a set of
00:06:24.640 counterfactual properties. Once we pin those down, we will have established
00:06:28.960 what is required of a system in order for it to contain information and the connection between
00:06:34.320 information and physics without ever actually having to define information directly,
00:06:40.160 just pausing their more reflections. This is a crucial point to make,
00:06:45.600 is that Cara saying that we don't need to define information. If instead, we pin down as she says,
00:06:54.480 what is required of the system in order for it to contain information? And that of course,
00:06:58.560 is Paparian people get absolutely hooked on trying to define certain things in science.
00:07:04.800 And definitions are misleading. Definitions are ultimately ambiguous. And also, if you're talking
00:07:10.480 more philosophically, definitions are just a way to reduce philosophy to talking about words,
00:07:15.920 which is not what philosophy is about. And it's certainly not what science is about.
00:07:19.520 Science is not about trying to define precisely what any given physical thing happens to be.
00:07:25.840 My favorite example is the electron. You can try and define what an electron is.
00:07:30.000 But that definition is going to rule out what you're going to learn about the electron tomorrow.
00:07:35.520 So it's going to be a useless definition tomorrow upon learning some new property about the
00:07:40.560 electron because your previous definition can't possibly have included the knowledge that you're
00:07:45.280 going to gain tomorrow that you're going to create tomorrow. So instead, it's better to talk about
00:07:50.240 understandings. And so we can have an understanding about information without needing to necessarily
00:07:54.960 define it. We can say, this system can carry information. This system can't carry information.
00:07:59.840 And that gives you some insight into how to understand what information is,
00:08:04.400 even if you can't put a precise definition on it. Moving on, and Chiara writes,
00:08:10.400 let's use a thought experiment to identify the counterfactual properties that a system must have
00:08:15.440 to carry information. First, we take a system that can carry information,
00:08:20.720 such as a lamp that can be used to signal. Then we gradually subtract its key properties until
00:08:26.480 it stops being capable of doing so. At that point, we will know that the properties we removed
00:08:31.520 in our thought experiment are necessary for carrying information. Supposed that you were standing
00:08:37.040 on the Centosa Bridge's viewing point at night, and you had the task to communicate
00:08:41.680 with an approaching boat using a lamp. The lamp is green, say, and it can be switched on or off.
00:08:47.440 And the code of communication is that if the lamp is on, then the boat can proceed. If it is off,
00:08:52.800 then the boat should stop. Now, imagine the color of the lamp changed. Clearly,
00:08:58.000 that would not modify its ability to convey the signal. Nor would changing its shape,
00:09:02.640 or similar other properties of its state. But suppose now you modified some of its
00:09:07.520 functionalities. For instance, suppose that once you switched the lamp on, it could no longer
00:09:13.360 be switched off. Would this lamp work as a signal? Clearly no. Given that it cannot be in any
00:09:20.160 other state, it is useless for signaling one of two alternatives. It has only one state available.
00:09:26.400 Now, imagine you wrap the lamp in a completely opaque covering, which does not allow the light
00:09:30.640 to come through and to be seen at a distance. With this modification, the lamp would not be able
00:09:35.760 to signal either because it could not be seen from the approaching boat. This example of the
00:09:40.160 lesson you can then generalize. The fact, the light, when it is on, carries information, is due
00:09:45.920 to the fact that it could be set to a different value of. And the difference between on and off can
00:09:51.520 be perceived by the approaching boat. Both of these properties of the lamp are counterfactuals.
00:09:56.640 Abstracting from the example, you can assume or perceive a general fundamental,
00:10:01.280 regularity in nature. Any system containing information must have these two properties.
00:10:07.680 Property one is that it can be set to one of at least two states. For example, if it has two
00:10:14.080 possible states, let's call them zero on one, generalizing on and off, these two states can be
00:10:19.680 changed from one into another like this, one into zero, zero into one. This notation specifies
00:10:27.120 the following transformational task. If given one, turn it to zero, if given zero, turn it into one.
00:10:33.920 A machine can perform this task. If it can indeed obey both these requests, I shall call this
00:10:39.600 transformation a flip, a special case of a permutation. But if you're familiar with computer science,
00:10:45.200 you will know that in the jargon of that field, it is called a not operation. The name could
00:10:50.080 not be more appropriate. The operation describes exactly the behavior of someone with a
00:10:54.080 contrarian personality. If you say yes, they will always flip your statement to its negation and
00:10:58.240 say no and vice versa. Likewise, this operation flips the state of a system to zero if it is in one
00:11:04.560 and one to if it is zero. We've already seen the flip operation appear in several places in
00:11:09.840 that view from the centosa bridge. It is in the lighthouse whose lamp flips its on-off-on-off
00:11:16.800 pattern. It is in the signaling light from the boats which also operate like switches. It is
00:11:21.760 realized to a high degree of accuracy in any computer when a transistor switches on and off.
00:11:27.520 It is even realized to a lower degree of accuracy in our brain when a neuron fires and then becomes
00:11:34.320 quiet again. And as we have seen from the lamp example, it is the counterfactual property that is
00:11:40.240 necessary to send the most elementary signal a binary one. Property two required for some system to
00:11:47.120 contain information is that it states, for example, on and off states of the lamp on the bridge,
00:11:53.120 can be received and distinguished in some other location. For example, by the boat's communication
00:11:58.720 system, this property is trickier to express. Still, it can be elegantly and fully captured by
00:12:04.880 counterfactuals. It is the property of performing a copy-like operation. Remember that I already
00:12:10.720 mentioned replication in Chapter 1, which is a special case of copying. To see what copying is,
00:12:15.520 we can dramatize the communication between the bridge and the boat by adding further layers
00:12:20.080 of communication. Imagine that it is a foggy night and that even the strongest lamp can be seen
00:12:25.840 at no more than 500 meters from the bridge. But the requirement is that it can be seen by boats
00:12:30.960 that are at one kilometer from the bridge, along a particular straight path joining the bridge in
00:12:35.600 the entrance of the harbor. One way to deal with this problem is for another boat to anchor at about
00:12:40.560 500 meters from the bridge along that path. If that boat has another lamp, which can in turn be seen
00:12:46.240 from other boats approaching, then it can signal to them by setting its lamp to on or off.
00:12:52.160 In coordination with the lamp on the bridge, just like the old-fashioned telegraph or beacon
00:12:57.200 signaling. The communication is successful if, whenever the on-state appears on the bridge,
00:13:02.240 the boat sets its lamp to on to and if, whenever the state of the lamp is off on the bridge,
00:13:08.000 the lamp on the boat is also set to off. This process amounts to copying faithfully the state of
00:13:12.640 the lamp on the bridge onto the lamp on the boat. The state of the lamp on the bridge is perfectly
00:13:17.280 reproduced by the lamp on the boat, pausing that as my reflection. So here, what we're kind of saying
00:13:23.840 is that we have this concept of information being an entity which can be flipped so you can take a
00:13:30.640 zero turn into a one so you can negate it, as well as being copyable. Without ever saying precisely
00:13:38.000 what information is, so we're saying it has these qualities of being able to be negated and
00:13:45.360 being copied, flipped and copied. Now, I'm skipping a quite a large portion here where
00:13:51.040 Kiara goes through in more detail precisely what a copying operation is at the fundamental level.
00:13:57.520 And she also goes through the summary that I just gave you that a physical system is capable of
00:14:02.000 carrying information. If it has these two counterfactual properties, the first one being,
00:14:06.720 it can be set to at least two states, the flip operation is possible. And two, each of those states
00:14:13.360 can be copied, the copy operation is possible. And then she says, and I'll continue reading from this
00:14:18.480 point. So here is the reason why information is a physical property, whether or not some system
00:14:24.720 carries information depends on whether the laws of physics allow for these two transformations on
00:14:30.880 that system. If they don't, then the system cannot carry information. In a universe where no system
00:14:38.160 had both properties, information would not exist. So whether or not information is permitted
00:14:44.880 depends on whether the laws of physics permit certain kinds of counterfactuals,
00:14:51.600 but it is not a property like having a certain color or mass, factual properties of a system.
00:14:56.720 It is a counterfactual property, because whether a system contains information or not depends
00:15:03.760 on whether those two transformations can be realized on it. Through counterfactuals,
00:15:11.520 you have arrived at the elusive connection between information and physics, okay,
00:15:16.000 pausing the MRI reflection. Yeah, that isn't that brilliant. So physics here too has always been
00:15:21.120 about factual properties, as she says things there, like color or the frequency of light,
00:15:27.200 mass or the number of electrons in a particular atom. These are factual properties,
00:15:34.240 but information is a counterfactual property. It's something that could have been otherwise,
00:15:39.600 whether or not these particular transformations can actually occur given a particular system.
00:15:46.240 And as she goes on to say, quote, systems with those two properties are information media,
00:15:52.400 all information media, despite the differences, having common the fact that those two
00:15:57.760 transformations are possible on them. All the systems I mentioned in the Santoza example are
00:16:04.080 information media. They have those two counterfactual properties. The simplest information medium,
00:16:09.120 the fundamental unit of information is a bit. It is an information medium with two possible states,
00:16:14.320 zero and one. It's capacity is that it can signal at most two different messages.
00:16:19.520 You can think of countless ways in which our university and body a bit, the lamp of our previous
00:16:23.360 example, which can be on or off an arrow that can point up or down, a coin resting on a table,
00:16:27.440 which can show heads or tails, your answer to a yes or no question, and so on. Thinking in terms
00:16:31.840 of information allows one to forget about all the differences in the physical details of those
00:16:35.760 systems and consider them all is the same thing, a bit. The same holds for information media with
00:16:43.200 higher capacity. Those that can hold more messages, they too can be thought of as made of bits,
00:16:48.960 but not every system is an information medium. A good example is a memory and a computer that
00:16:53.680 is full but cannot be erased. It is possible to read information out, but not write new information
00:16:59.760 in because no more spaces available and reset is not possible. It was an information medium once,
00:17:06.320 but no longer. You could also have a case where information can be copied in, but not out.
00:17:11.760 Have you ever tried to write something on the phone on top of the Capacino or a beer? At first,
00:17:16.320 it looks possible, but the letters rapidly fade away to the point they can no longer be read.
00:17:21.280 Neither of these two types of systems would be capable of carrying information,
00:17:25.360 because they did not have enough counterfactual properties. They are not information media.
00:17:30.160 Pause their memory reflection. Yeah, they'd probably be information media for a very short
00:17:34.080 amount of time for so long as whatever is written on top of that phone, let's say, lasts, but
00:17:41.280 this does not fit Chiara's earlier description of a knowledge and information, for example,
00:17:47.040 as having a kind of resilience. So if the information media is something that quickly dissipates,
00:17:52.400 evaporates away, or as otherwise full, then we can't really talk about it as having the capacity
00:17:58.240 to copy information. It won't persist long enough to keep the message or to keep the information
00:18:05.120 such that someone can then take it away somewhere. Going back to the book, Chiara writes,
00:18:09.440 one of the most striking properties of information media is that in that regard, they are all
00:18:15.040 interchangeable, because information can be copied from one to the other irrespective of their
00:18:20.880 physical details. I shall call this property the possibility to copy information from one
00:18:26.320 information media to another into operability. For example, the information in a beer can be copied
00:18:33.760 into any other bit irrespective of what physical system it is. A transistor, an arrow, a coin,
00:18:42.000 or a switch. The music that has been recorded on old vinyl discs can be converted and copied
00:18:47.360 into digitally encoded music on a flash memory. The sound produced by a voice can be turned into
00:18:52.640 words stored in the transistors that compose the memory of our smartphone via voice recording.
00:18:58.000 The thoughts in my head can now be faithfully copied on this page. They will then be copied
00:19:03.040 into your brain and then possibly copied further into other brains or your notebook if you decide
00:19:08.240 to write them down. All these information media are interchangeable or interoperable
00:19:14.160 and information can travel among any of them without restriction pausing their hemline
00:19:18.720 reflection. This is also known as, and your ears should prick up when you hear some of those
00:19:26.160 examples there that she listed as the substrate independence of knowledge. So if I have some
00:19:34.720 knowledge in my brain and I want to get it to you, there could be all ways in which I might try to do
00:19:40.800 that. If you're on the other side of the world, one way in which I might do it is to speak,
00:19:45.680 so the knowledge that's in my mind then becomes sound waves. But if you're on the other side of
00:19:51.040 the world, me simply talking isn't going to get it there. But happily, the knowledge can be
00:19:55.600 transmitted relatively faithfully from my brain to my vocal chords. Vibrations are
00:20:01.280 folk chords and then to vibrations of molecules in the air. And then I can pick up the phone and
00:20:05.760 I can talk to you. Or perhaps I'm already on the phone to you. And then those vibrations of air
00:20:11.440 molecules get turned into vibrations of the diaphragm of a microphone that's in the phone,
00:20:16.880 which then get turned into electrical signals, which then get turned into electromagnetic
00:20:20.960 vibrations, which travel from here to the other side of the world, long story short. And then
00:20:26.400 that system all happens in reverse again, then into electrical signals in the aerial, then into
00:20:31.840 vibrations of the diaphragm of the speaker, and then into vibrations of air, and then into
00:20:37.520 actually vibrations of the tympanic membrane of your ear, and then into vibrations inside your
00:20:42.720 ear canal, and then eventually into your brain. And so this is how this copying type process works.
00:20:48.080 Of course, once it gets into a beyond, I should say, the ear canal, then we have an issue,
00:20:52.800 the okay, then the issue, therefore a preparing is that we are guessing what is meant, we are
00:20:58.560 interpreting what is going on there. So the process there becomes more complicated than
00:21:03.440 simply copying the message from one medium to another, because then we have the conscious
00:21:10.160 attempt to create the knowledge anew, which might be different to the way in which one person
00:21:15.920 was already thinking of it. So if I have a particular idea in my mind and I want to get it to you,
00:21:20.400 I can reasonably faithfully get it into the vibration of air molecules via the way in which I'm
00:21:26.560 talking, the way in which I'm talking right now. I'm trying to convey something to you.
00:21:30.480 And if I think I've made a mistake, if I think that the words coming out of my mouth
00:21:34.960 are not matching the thoughts I have in my head, I can quickly correct myself until I think there
00:21:40.240 is a, to my mind, to my standard, a perfect match as close as possible between what I'm thinking
00:21:47.520 and what I'm saying. And then the copying process happens very, very reliably between the
00:21:54.160 vibration of this microphone here. And what eventually happens at your end when you're watching
00:22:00.320 the screen or listening to my voice coming out through speakers or earphones, all of that is going
00:22:06.480 to be very reliable. But once those vibrations get into your ear canal, you then need to interpret
00:22:14.000 what is going on? What I'm actually really saying, what the knowledge is that Chiara had firstly,
00:22:20.960 and I'm sometimes I'm interpreting this, right? And so some of this copying process is a process
00:22:27.120 of interpretation, especially between minds, because when we have minds involved, we have memes involved,
00:22:33.760 and as we know from the beginning of infinity, meme replication is not as simple as copying.
00:22:41.120 It's a little bit deeper and more complicated than merely copying, which is what is going on
00:22:46.720 between the vibration of air molecules here and the vibration of air molecules that are happening at
00:22:53.600 your end, the replication of my voice. But the knowledge itself, which is encoded in that information
00:22:59.840 in some way, is more difficult to get from my mind to your mind than just copying, then just a chain
00:23:07.840 of copying. Or insofar as it is a chain of copying, it is an extremely imperfect chain of copying
00:23:14.000 between my mind and your mind, because there's layers of interpretation. Let's go back to the book,
00:23:19.440 Chiara writes. Interoperability is due to the fact that all information media
00:23:24.400 have in common properties the two counterfactuals I mentioned above that transcend most of their
00:23:29.280 specific details, i.e., whether they are photons, transistors, the spins of an electron, neurons,
00:23:33.920 or switches in a lamp. In all these cases, when interested in the information processing
00:23:39.760 abilities of these systems, we can abstract away their irrelevant details and simply talk about
00:23:44.800 them as information media, considering their information carrying attributes. Only, for example,
00:23:51.280 up and down for an arrow on or off for a lamp and so on. Now I'm skipping a bit here,
00:23:55.280 Chiara talks about the physics of interoperability and whether or not interoperability is possible
00:24:01.920 depends upon physical laws. So the extent to which we can actually have this ability of information
00:24:09.760 which is completely different in terms of its physical substrate is nonetheless able to
00:24:14.800 copy the same information. That is a property of our universe, which could have been otherwise.
00:24:20.400 And then that leads into a discussion about the kind of physical laws that allow computers to
00:24:26.960 exist at all. And so there needs to be a physics of computation, which we're also quite familiar
00:24:33.520 here in this podcast series with. And so I'm going to pick it up where Chiara writes quite.
00:24:39.840 Let me start with the link between computers and physics. Computers are embodied in physical
00:24:44.960 supports. They are made of information media, typically billions of switches or transistors,
00:24:50.640 therefore they are ruled by the laws of physics. In particular, which computations a computer can
00:24:56.240 or cannot perform depends on what the laws of physics permit. This connection between
00:25:01.280 computation and physics was not fully understood until the 1980s with some of the pioneers of
00:25:06.480 quantum computers. It was hinted at by imaginative thinkers such as Roth Landauer, Paul Benioff
00:25:12.880 and Richard Feynman. But it was fully expressed for the first time by David Deutsch and further
00:25:18.400 developed by the masterful computer scientist, Charles Bennett. A simple example of a computation
00:25:24.320 is the addition of two numbers which are encountered in chapter two. It's inputs other numbers
00:25:28.720 x and y, for example, 5 and 10. And the output is the number x plus y, for example, 15.
00:25:34.080 That a computer is capable of performing a computation such as addition means that every time it
00:25:40.160 is given the right input, the two numbers x and y, it is supposed to provide the design output,
00:25:45.360 the number x plus y, and it can do that over and over again. The set of all computations,
00:25:52.240 a computer is capable of performing is its repertoire. So, for example, a calculator as a computer
00:25:59.040 that has addition, multiplication, subtraction and division in its repertoire. What decides the
00:26:04.720 repertoire of the computer? The physical laws that rule its components under given laws of physics
00:26:09.360 for each computation that is physically possible, at least one kind of computer is capable of
00:26:13.920 performing it, pausing there just going back to consider that claim there. Under given laws of physics,
00:26:20.960 for each computation that is physically possible, at least one kind of computer is capable of
00:26:25.920 performing it, that indicates the universality of computation in a universe. If something is
00:26:32.400 physically possible to be computed, then there exists a computer in our universe that is capable
00:26:39.920 of performing that computation. But more than that, of course, for all the things that are
00:26:47.360 computable in our universe, there is a single device, the universal computer, which can compute
00:26:54.400 any possible, physically computable thing. By computer here, I am not necessarily referring
00:27:02.560 to something as sophisticated as your personal computer, I mean a special purpose computer,
00:27:07.040 which has only a few computations in its repertoire. For example, the adder mentioned above,
00:27:11.840 which can, as I said, output the number x plus y given to numbers x and y in input, or a multiplier
00:27:17.760 by that, when given x and y in input, provides x multiply by y in output. Then here goes on to explain
00:27:24.640 how we get from these special purpose computers to universal computers. All you need is,
00:27:30.640 if, for example, you have something that can do addition, something that can actually perform
00:27:35.680 that operation of x plus y, and something that can do multiplication, a different computer that
00:27:40.560 can do multiplication, x times y, that only need is a third computer that can talk to the first
00:27:46.400 two, and be able to send the operation off to the adder or send the operation off to the multiplying
00:27:53.280 computer, and so now you have a computer which can do essentially both of the operations,
00:27:58.080 because the other two computers that can do those single operations are part of its repertoire now.
00:28:03.040 And so, of course, that leads the idea as a universal computation, as Keira writes,
00:28:08.480 preceding in this fashion nothing stops you from imagining a computer that has all the physically
00:28:13.760 possible computations in its repertoire. It is a universal computer. It can be programmed to perform
00:28:19.520 any calculation that is physically allowed by certain physical laws. It so happens that the laws of
00:28:24.480 physics of our universe do not forbid a universal computer. Computers such as our laptops and
00:28:30.240 personal computers are universal in this sense. Another fundamental trait of computers in our
00:28:34.880 universe is that all the computations in their repertoire can be realized by combining a smaller number
00:28:40.880 of basic computations, which work like letters of an alphabet to compose words. This, too,
00:28:46.320 is a peculiar feature that holds in our universe, but need not hold in general. For example,
00:28:51.280 three is a number. Four is a number. If we juxtapose three and four, we find another number,
00:28:55.120 34. Any number can be represented in the decimal basis by juxtaposition of the numbers from
00:29:00.080 zero up to nine. Likewise, elementary computations can be composed with one another to realize
00:29:05.120 all the computations permitted by the laws of physics. For example, suppose you perform the flip
00:29:09.680 twice on a basis. You see that if the beat is initially zero, it is slipped to one,
00:29:13.680 and by applying the flip a second time, you obtain zero again. Likewise, if the beat is initially
00:29:18.880 one, after two flips, it gets back to the state one. So applying the flip twice to the same system
00:29:24.240 corresponds to performing a different operation in this case doing nothing or leaving the bit alone.
00:29:29.200 A set of computations that composed with one another permit one to recover the whole set of
00:29:34.960 possible computations in the repertoire of the universal computer is called a universal set.
00:29:40.720 When there is a universal set, any computation is reducible to a sequence of elementary computations
00:29:47.040 selected from the universal set. These elementary computations are in respect
00:29:51.520 a bit like Lego bricks. Anything that is allowed in a Lego world from cars to villas to pirate
00:29:57.600 ships can be decomposed into elementary Lego bricks of a few elementary different kinds.
00:30:03.520 Those basic composition rules are fixed. Likewise, when there is a universal set,
00:30:08.720 any physically allowed computation can be decomposed into a set of elementary computations
00:30:14.000 from the universal set, sometimes referred to as gates, which can be composed according to fixed laws.
00:30:20.800 When the laws of physics say that a universal set of computations is possible, we say that they
00:30:26.160 display universality. universality is a counterfactual property about what is possible,
00:30:31.920 and it has sweeping consequences. It is universality that permits the existence of a universal
00:30:37.440 computer like the ones we use nowadays. That property was first grasped in the Victorian era.
00:30:44.080 At that time, the inventor Charles Babbage proposed a scheme to build what he called
00:30:48.160 the analytical engine. This would have been, if realized, the first programmable computer,
00:30:54.800 the ancestor of our modern ones, only far larger and made of brass mechanical cogs and wheels,
00:30:59.520 made of lovelace, Babbage's collaborator and a brilliant mathematician, understood the universality
00:31:05.520 of this machine, conjecturing in her notes that the analytical engine could be used to produce
00:31:10.560 all sorts of information theoretic outputs, not just to compute functions. She even speculated
00:31:17.440 that it could be used to produce sophisticated music. Unfortunately, Babbage's idea was not
00:31:23.600 realising practice for a lack of funding, and the property of universality was not studied
00:31:29.920 until much later. It was Alan Turing, with his computing machine, who formalised the idea of
00:31:36.560 universality in the 1940s. This concept was then sharpened and connected to physics by David Deutsch,
00:31:44.240 who pioneered the universal quantum computer, which will encounter again in the next chapter.
00:31:49.520 Universal computers are capable of performing all the computations, permitted by the loss of
00:31:55.440 physics. Once a universal computer is constructed, all you need to do is to load it with the
00:31:59.200 right program, and it can simulate any other system that is physically allowed. This includes
00:32:03.760 the biosphere, with all its splendid richness of animals and plants and microorganisms,
00:32:08.080 and in principle, it even includes your brain together with thoughts and emotions.
00:32:12.160 Of course, they are my reflection. Yes, but we don't know what the program is, and this is the great
00:32:19.120 mystery of things, and is the central problem of artificial general intelligence,
00:32:24.800 despite what you hear elsewhere outside of the circles of people like David Deutsch,
00:32:30.640 where people think that what we need is faster, hardware, or more memory, that these systems,
00:32:37.840 like the internet, as they grow, eventually become self-aware in some way. That's all you need,
00:32:44.160 because isn't that what happened with us? Isn't what happened with our brains? Just the
00:32:49.520 slow accumulation of complexity, and by random chance we end up with, the capacity to create
00:32:56.000 explanatory knowledge. Perhaps. But in our case, as human beings trying to program AGIs,
00:33:04.800 if we want to do that, we need to know what the program is. Simply randomly putting together
00:33:09.920 components of hardware in a computer, it's not going to cause the thing to come alive,
00:33:14.800 again, despite what you might see in certain science fiction representations of what's going on here.
00:33:20.320 You need a program. You need an algorithm for how it is that creativity and knowledge creation
00:33:26.080 is actually done. I'm skipping another part here, and Kiara talks about a science fiction world.
00:33:33.520 But basically, I think that the comparison to dark matter that she makes here is probably just as
00:33:40.960 informative. The idea of dark matter is that perhaps there is this matter out there in
00:33:46.640 interstellar, intergalactic, otherwise almost empty space. And this matter is the thing that causes
00:33:52.720 galaxies to rotate faster than what they should, given the amount of luminous matter there.
00:33:56.320 So we assume there seems to be a matter that we cannot see there. It's very weakly interacting,
00:34:03.200 by which we mean we can't see it, so it doesn't interact with light, and it doesn't even appear to
00:34:07.920 interact with strong and weak nuclear forces. The only thing that it interacts with apparently
00:34:13.440 is gravity. Such a kind of matter doesn't appear to be able to store information. It appears to
00:34:19.440 violate interoperability with our universe. So if we have, when I say our universe, I mean the matter
00:34:25.200 that we're made out of, we can have information written on our matter, but we can't write that
00:34:30.160 information onto dark matter. I've speculated before it to be an interesting science fiction,
00:34:36.080 I guess some science fiction writers must have done this, to construct a story about beings that
00:34:41.280 live in this dark matter. It could be whole civilizations, and perhaps the way in which they interact
00:34:46.800 with one another. It's different to the way in which we interact with one another, but we can't
00:34:51.200 communicate with them and they can't communicate with us, precisely because the interaction,
00:34:55.520 the physical interaction that's going on operates via a different mechanism in some way
00:34:59.760 shape or form, which means that our matter and their matter is not interoperable. So I'm skipping
00:35:06.400 all of that and it's very, I think anyone who has the book should go and read that on
00:35:10.320 me, skipping a number of pages there about this science fiction world and an illustration of the
00:35:18.160 possibility of non interoperability and what that would mean in such a universe. I'm picking it up
00:35:24.800 where Kara has written, quote, you have transverse several pages in order to understand the
00:35:30.240 connection between physics and information. In what way are you now closer to understanding
00:35:35.280 physical reality? You have discovered by considering the two
00:35:39.040 counterfactual properties that characterize information media, a key feature of our universe,
00:35:44.000 interoperability, without which what we have been calling information and communication thereafter,
00:35:50.000 would not be possible, nor would computers, let alone universal computers that work the same way
00:35:55.200 as they do in our universe. What you have just seen is an example of the explanatory power
00:36:00.240 of interconnected counterfactual properties, this time all related to information. We can think
00:36:05.600 of them as a range in a pyramid structure at the base you find the counterfactual properties of
00:36:10.000 information media that the flip and the copy operations are both possible on some physical systems
00:36:16.160 information media. On top of this, there is the interoperability of information media,
00:36:21.520 information is copyable from any information media to another, no matter what type of physical
00:36:27.920 support embodies it. At the very top is universality, the possibility of universal computers,
00:36:34.400 each counterfactual is needed for the higher level counterfactual. In turn,
00:36:39.280 these counterfactuals enable a vast number of other transformations to be possible.
00:36:44.800 All our information related technology is based on the interoperability property,
00:36:49.840 so are the most fascinating properties of life and intelligent life, from the possibility of
00:36:54.880 self reproduction to the possibility of thinking. Remove some of these counterfactuals and you
00:37:00.960 wipe out all these properties too. What's more, by referring to information media and their
00:37:06.320 counterfactual properties only, without referring to specific irrelevant details about the
00:37:10.880 embodying systems, we're able to attain a greater degree of abstraction, going deeper than
00:37:16.720 all our existing physical theories. If you remember at the outset, I noted that the elements
00:37:20.880 in the Santoza landscape are described by very different theories in the traditional conception,
00:37:25.440 but with the view from counterfactuals, we understand the sense in which some of them are,
00:37:29.760 in fact, very similar, they are all information media. The traditional conception of physics cannot
00:37:34.720 express this fact, whereas the science of canon can't, can do so, elegantly and simply. The
00:37:41.120 approach with counterfactuals also frees information from subjectivity. When we say that some
00:37:47.280 set of states can be copied, we do not need to refer to any conscious subject or observer
00:37:52.960 performing the transformation. A simple chemical reaction where the structure of some crystal
00:37:57.280 is replicated over and over again, implements the copy operation, and it can do so in the absence
00:38:02.560 of a guiding entity. The objective, counterfactual properties necessary to explain information
00:38:08.000 are remarkably elementary, and yet they have far-reaching ramifications. Whether you are seeing
00:38:13.920 in a coffee shop drinking coffee while listening to your favourite music, sitting in your armchair
00:38:18.320 scrolling through your phone or reading a book or watching a beautiful sunset from your balcony,
00:38:22.960 all these phenomena can occur because those two operations, the flip and the copy,
00:38:27.840 are possible, and because of the interoperability of information media, both you and I are enjoying
00:38:34.240 the far-reaching power of those counterfactuals right now. I, while writing these lines and
00:38:39.920 putting a full stop here, you, while reading, these very lines and turning the page to discover
00:38:45.760 what's next. And that's the end of the chapter. So this brings information into the understanding
00:38:55.280 of physics at a fundamental level via the constructive theory of information. So rather than
00:39:01.840 it being merely a highly emergent phenomena that really is only prior to this understanding,
00:39:09.600 a property of some complicated emergent structure like computer, we now see that it is fundamental.
00:39:17.200 But as I like to say, lots of things that people think are emergent are actually also fundamental.
00:39:22.080 People are one such thing. If often to the infinite future as we expect, people are the thing
00:39:28.080 that go about transforming the universe in some way, then that will be fundamental. Now we
00:39:33.280 fundamentally do the evolution of the universe, their choices will be fundamental to the evolution
00:39:36.960 of the universe. But here we have this idea that in a more basic way, information is fundamental
00:39:43.760 to the way in which the universe operates. The possibility that certain matter can actually
00:39:50.640 hold on to information, information being the thing that can be flipped and can be copied
00:39:56.880 is something that means our universe has this special characteristic of allowing for information.
00:40:04.240 And because it can allow for information and it didn't have to be it allows a universe in which
00:40:08.800 computation is possible and universal computation is possible. And I would say, and therefore,
00:40:13.440 people are possible. Okay, so that's it for today. That's the end of chapter three. And next time
00:40:19.360 we will be on to chapter four, which is quantum information. So it will be very interesting.
