# 2021-01-19 - Fallible Animals - Constructor Theory of Information [Apple Podcasts](https://podcasts.apple.com/us/podcast/constructor-theory-of-information-with-david-deutsch/id1481994554?i=1000505745684) Duration: 00:36:09 ## Transcript ### Logan Chipkin 00:00:00 - 00:00:16 All right, I'm here with David Deutsch. David, thanks for joining me. ### David Deutsch 00:00:16 - 00:00:18 Thanks for having me. ### Logan Chipkin 00:00:18 - 00:00:43 Sure. So we live in a world of classical programmable computers that have been very successful in solving all sorts of problems in our civilization and researchers are also making strides in quantum computing. So given our civilization's success in employing concepts like information and computation, why was a constructor theory of information necessary in the first place? ### David Deutsch 00:00:43 - 00:02:21 It arose out of several motivations initially just from constructor theory itself because we needed to formulate rigorous concepts of things like measurement and possibility that didn't rely on existing, on particular physical theories like quantum theory. So we needed to know what it means in principle for say a theory of physics to support information because if you think of laws of physics, any old logically possible laws of physics, there wouldn't be information in the worlds that they describe. So what does it take to make information? Now, if you were confined to quantum theory, you'd say, well, an observable can store information if it has an observable with at least two distinct states which are measurable and something like that would do in quantum theory. But then quantum theory is a Hermitian operator and it has orthogonal states and all those things are rooted in just quantum theory and we want to think that it will apply to all theories including ones that haven't been invented yet, all reasonable theories. In fact, this will be usable as a criterion for whether a proposed theory is reasonable. ### Logan Chipkin 00:02:24 - 00:02:47 So what is it about information that makes the prevailing conception of physics, namely expressing laws of physics in terms of initial conditions and dynamical laws of motion, so difficult to capture whereas constructor theory, which is all about possible and impossible transformations or tasks, seems much more up to the task as it were of explaining and capturing the regularities of information. ### David Deutsch 00:02:47 - 00:04:57 Yes, that's exactly why. It's because constructor theory has counterfactual properties at its heart. So possible and impossible are both counterfactual concepts and information is inherently counterfactual. For example, if I say that, well, let's suppose somebody measures a constant of nature like pi or something. Now you can't use pi to send or store information because pi only ever has one value. Whereas whether, for example, a spin of an electron is pointing up or down, it can be used to store information and if you have more than one spin and they can interact in certain ways, then they can be used not only to store information but to process information. Using constructor theory, we can establish the minimum criteria for a physical system to be able to store information and to be able to process information, which is what makes computation classical and quantum possible. And then you can say, here's our defined class of conceivable laws of physics which allow information to exist and information processing, which means among other things, it allows measurement and computation and therefore growth of knowledge. And the rest would not allow that and we won't be looking there for potential laws of physics because those laws wouldn't allow physics to happen. ### Logan Chipkin 00:05:00 - 00:05:25 So following that argument, would you say that's a similar argument could be made for why it was important to establish concepts like measurement and distinguishing between outcomes of an experiment, which you've touched on in constructor-theoretic terms, because it makes it then easier to look for future object level laws of physics that must conform to the constructor theoretic definitions of these concepts? ### David Deutsch 00:05:25 - 00:07:00 Yes, of course it is possible that constructor theory, as we conceive of it, isn't true and that somebody invents a theory of physics which violates the principles of constructor theory. So there is no such thing under that theory as, for example, information or measurement or computation, but that nevertheless the theory is testable in some sense that transcends our present concepts. But even then that would be useful because if you had such a theory on the horizon and it looked as though, for example, it wasn't going to allow measurement, therefore it wasn't going to allow science as we know it to exist, then that would be an early indication either that the proposed theory isn't true or if it is true that it requires a conceptual revolution larger than one would at first thought think. Because such a theory might arise by just changing a few innocent looking parameters in quantum theory and you might then get a theory that didn't support science and then you'd have more than just technical difficulties in physics, you'd have profound philosophical difficulties in setting up that theory as well and constructor theory would have been an early indication of that. But I don't think that's going to happen. I think that future theories are going to conform to constructor theory, but that's just what I think. ### Logan Chipkin 00:07:00 - 00:07:20 Yeah, I guess time will tell. So let's talk about classical information in particular, which is the world of bits as most people are familiar with them. What is classical information in constructor theory and by expressing classical information in constructor-theoretic language, what problem or problems have you solved? ### David Deutsch 00:07:24 - 00:12:07 So the definition of classical information under constructor theory is that a system is an information medium if it can be in at least two different states, which can be, the states can be permuted by possible operations, that is the operations of arbitrarily permuting those states is physically possible. So then you can, if that defines an information medium, then you can define information as being present in a system if it is in one of those information states and could have been in the other or in one of the others. So there's your counterfactual definition of information. And we haven't had, apart from the fact that this works, the only concrete results that we can display at the moment is the fact that this is also enough to define quantum information. And quantum information, that is, it's not the same definition, but given that framework, you can define quantum information in a very simple way that you can say that an object can hold quantum information if it has some states that can hold information and if it has another set of states that can also hold information and if the union of those two sets of states cannot hold information. And that, when you have a system like that, it, we call it in constructor theory, we call it super information, but the only practical theory at the moment that has super information is quantum theory. So this, our result is that quantum information and all its important properties just follow from this small difference in the way that information appears in the theory. In classical physics, it appears in the way that every classical information medium has only one maximal set of states that can hold information. We can have another one, but it won't be compatible. And then quantum theory has two compatible sets of states where the union of the two is not a set of information states. That is because, by the way, because they can't be distinguished by any physical process. They can't be reliably distinguished by any physical process. So that's our main result in regard to information to date. But as I think Sam told you, the, what we're hoping for is that this notion of information and therefore of measurement and computation can tell us what information, can tell us a measurement theory in new proposed laws of physics, such as quantum field theory, where the existing concepts are not enough. We have in quantum field theory, we have separated systems where the observables do not commute with each other and yet causality is maintained. And that's conceptually very difficult. And so you have to build a new theory of measurement. We're not in Kansas anymore, as we keep saying. And to build a proper theory of measurement in quantum theory took like, depending on how you count it, 30, 40 years of head scratching and thinking that this is, this can't be right. ### David Deutsch 00:12:07 - 00:12:25 This is impossible. We think that constructor theory provides a very powerful tool for setting up a theory of measurement within a newly proposed theory of physics, even if it's very conceptually strange. ### Logan Chipkin 00:12:25 - 00:12:58 It kind of reminds me of the fact that you can ignore fundamental principles in a given domain, so long as you're far away from the limiting case. But by which I mean, it's easy to work in Newtonian physics if you're not approaching the speed of light. And it strikes me that measurement kind of feels similar, where you can rely on sort of your intuitions of how measurement ought to work. But as you said, once you start leaving Kansas, as it were, you really have to understand in physical terms what constitutes a measurement. Does that seem reasonable to you? ### David Deutsch 00:12:58 - 00:14:11 That's exactly right. And what you just said about measurements applies to information. I mean, it's really the same problem. Measurements and information are the same problem. And even in relativity, Einstein had this problem of defining what measurement is, essentially. And the concept of measurement had to be different because there's no such thing as simultaneity and so on. That problem was important, and he solved it, but it was minor compared with the analogous problem that arose in quantum theory. And I think that future theories are going to challenge our intuition more than previous ones. I mean, this has been the experience that new fundamental theories in physics challenge our intuitions in unpredictable ways. And with constructor theory, we hope to have a tool that helps us to formulate our intuitions properly, given the new theory, whatever it is. ### Logan Chipkin 00:14:13 - 00:14:25 So is it fair to say that with your and Chiara's work on constructor theory of information, you've effectively unified classical and quantum information, and it's only that they differ in one property? ### David Deutsch 00:14:25 - 00:16:06 Yes. I think that is a very good point. I think that's a very good point. Yes, I think that is what this work has done. And I would hold that out, as I just said, as being our one concrete result of the constructor theory of information so far. Maybe Chiara's results in constructor theory of thermodynamics also count as, because she uses the constructor theory of information there as well. So maybe her results in thermodynamics count as well. But the real fun is going to begin when we apply constructor theory to physical theories that go beyond quantum theory, that are incompatible with quantum theory. And that's what we mean by not being in Kansas anymore. And I think that is when constructor theory will come into its own. My guess is that it just won't be practically possible to make progress without an overarching framework like constructor theory. Now, as I said, constructor theory could be wrong, but in that case, trying to develop it will show us what is needed instead. I don't think we can make progress without such a framework. ### Logan Chipkin 00:16:06 - 00:16:21 Right. And even if constructor theory is wrong, as you say, every error will kind of show us maybe why it's wrong and we can progress in other ways. Either way, it seems like it's kind of a revolutionary conceptual revolution, as I think you mentioned earlier. ### David Deutsch 00:16:21 - 00:16:26 I think so. Yes, I think that's very much the case. ### Logan Chipkin 00:16:26 - 00:16:54 So much of constructor theory is about and is expressed in principles, which are laws that constrain other laws. And you've conjectured in your paper with Chiara several principles that explain or capture the regularities of information. So let's just go through a couple examples. So first of all, there's the interoperability principle. So what regularity of information does that capture? So we take for granted that ... ### David Deutsch 00:16:55 - 00:21:16 If we have information in one physical medium, let's say a book, even if it's an ancient book that was produced by a culture that we don't know about, we don't yet know what the symbols mean or what their language was and so on. We take for granted nowadays that the information content of this book and therefore the knowledge content as well can be faithfully copied into a different medium. For example, magnetic domains in a microchip or into sound waves when somebody reads it to somebody else, or indeed into our retinas and brains as well and so on. So all these are examples of information transcending the substrate in which it's instantiated. Information is this weird hybrid of a thing that information can only exist in physical form and yet it is independent of the specific physical form in which it is ever instantiated. So what I've just described now, although it's extremely familiar and taken for granted, is not logically necessary at all. It is conceivable that physics could be different and not satisfy this principle so that you could have some physical objects that have information and have science possible and observables and measurements and even civilization and so on. And that it simply wasn't translatable into another physical system which could also have science and so the whole edifice of knowledge and yet they weren't inter-translatable. So in theory, aliens from another planet could be based on different physics, not just different physical object, but different aspects of physical laws, could come and visit us and could be fundamentally unable to communicate with us. This is logically possible but the principle of constructor theory says that it is not so and all known physical theories have the property that wherever they instantiate information it is indeed interoperable with other information. So it can be information in electron spins, can be translated into information in microwave cavities which can be written down and published as ink on paper and you know the whole works and it all with arbitrarily reliable copying. So it seems to be a feature of our universe. It is as far as most people can conceive, as far as I can conceive, it is a necessary feature for knowledge and for science as we know it to exist at all. And although it is a feature of all known physical theories, there's no known physical law, or there had been before constructor theory, there is no known physical law that implies it. It happens to be a feature that laws, as far as we know, obey but unlike say the law of conservation of energy, no one has expressed this regularity as a law until constructor theory came along. So that's the principle of interoperability of information. ### Logan Chipkin 00:21:17 - 00:21:36 And you had mentioned the scientific method in your answer so I just want to talk about one more principle. First of all, it does seem like from your work in the constructor theory of information that you're actually integrating parts of the scientific method itself into fundamental physics. Tell me if I'm wrong but that's certainly what it seems like. ### David Deutsch 00:21:37 - 00:24:19 Yes, I would rather say that we're expressing parts of the scientific methodology in constructor theory. Specific principles like interoperability could be modified without making the rest of constructor theory fall. It's just that it could only be modified in a way that was compatible with the rest of the theory and if the theory has to be modified too much then it's a matter of degree whether you call it the same theory, you know, it might be some conceptually different framework from constructor theory. The interoperability of information is related to the comprehensibility of the universe in this way. If the universe isn't wholly comprehensible, which by the way philosophically I think that's ridiculous, but as a physicist I have to allow it as a possible property that a theory might have. Then in some ways constructor theory could be altered to reflect that but as I said earlier at least it would give us an early warning that something profound is happening when we postulate that, something which has profound implications for physics, for the laws of physics as we know them. The laws of physics have to be formulated not just differently but with different modes of explanation, not just with different explanations which have yet to be discovered. Constructor theory would give us an early warning of that and you know if these new theories had that property and made sense then they might be accommodatable in a modified version of constructor theory. But we're being very speculative now. I don't think any of that is going to happen. I think constructor theory will be a reliable guide not to what the next theory is but to what the next theory can't be or what the next theory can't be without a revolution bigger than it looks at first sight. ### Logan Chipkin 00:24:19 - 00:24:44 Right, right. So part of the one of the features of constructor theory is that because it's kind of in a way a theory about theories it forbids certain kinds of theories from being possible whereas in the prevailing conception the theories forbid just what physical phenomena are possible so it's kind of a level, it's a higher level theory in that sense. ### David Deutsch 00:24:44 - 00:24:51 Yes well the prevailing conception theories forbid what is possible under that particular theory ### Logan Chipkin 00:24:52 - 00:24:57 So the theories don't speak about each other so they don't say ### David Deutsch 00:24:59 - 00:26:02 Laws of dynamics don't say that a perpetual motion machine is impossible. They say a perpetual motion machine is impossible under Lagrangian dynamics let's say but physicists have conjectured for over a hundred years that there is a principle of physics the principle of conservation of energy that is a principle about other theories including ones we don't know yet and so we use the principle of conservation of energy as a guide to conjecturing new theories because we know that if a new theory violates the principle of conservation of energy then something either is false or something we have to reconceptualize the world under that theory it's not just a change of the type of changing the parameter or adding a new term in an equation. ### Logan Chipkin 00:26:05 - 00:26:18 Right, right and it speaks to the fact that merely falsifying theories is not quite as straightforward as sometimes it's made out to be there's you know there's always background knowledge and so forth. ### David Deutsch 00:26:18 - 00:28:20 That's right yes and with conservation of energy this has in fact happened for a start with neutrinos that's our favorite example neutrinos were discovered because people noticed that energy apparently wasn't being conserved and therefore some new process must be involved and this turned out to be weak interactions weak nuclear interactions but another example is relativity itself where the notion of the principle of the conservation of energy well principle of conservation of energy can be expressed in a number of different forms which in pre-relativistic physics were all equivalent to each other but with relativity it turned out that some of those formulations were incompatible with relativity and fortunately there are conceptions of the law of conservation of energy which are compatible with general theory of relativity. Now it could be that some modification of relativity like if there was a good theory of dark energy for example which violated the principle of conservation of energy some people have proposed then the principle of conservation of energy would have been refuted but this very fact guides our theorizing about dark energy because having a theory of dark energy that makes it incompatible with any kind of principle of conservation of energy would be a big revolution much bigger than it looks if you just look at an additional term in Einstein's equations. ### Logan Chipkin 00:28:23 - 00:28:50 So let's talk about one more principle so that listeners can get a taste of what the principles look like in constructor theory really but more specifically in constructor theory of information the principle of consistency of measurement you expressed in your paper with Chiara I wonder if you could elaborate on that principle and talk about what regularities you're capturing there that we all sort of take for granted already. ### David Deutsch 00:28:50 - 00:31:47 Yes so this is one of the principles that we use to make sense of information in the context of measurement which is the main context we originally wanted it in. Now we assume that this consistency of measurement has to do with information in the sense that when you measure something say a physical quantity like the speed of your car what you're doing is you're causing an information variable to go into a state that represents that physical property of in this case the car so that your speedometer for example that is showing that the needle is at a certain place that's an information observable with a certain sorry an information medium in a certain state and that according to the theory by which it was designed that represents a physical property of the car. Now the thing is you can also measure that physical property of the car by a physically very different process for example the policeman might be measuring your speed with a radar gun and the principle of consistency of measurement says that the speed on your speedometer and the speed indicated on the radar gun if both of those are working properly will be the same and that's really if that weren't true then there wouldn't really be such a thing as measurement in the way we normally conceptualize it and again conversely if it wasn't true the situation might be rescuable by a new conception of measurement but that would be a big thing a big thing it would be a change in our philosophical framework of what science is and so on that is much bigger than could be expressed by just saying that needles on speedometers and indicators on the display of a radar speed measuring device aren't necessarily equal that sounds like a very tame thing to say and it is a tame thing to say in terms of the object level theories involved but in terms of the principle involved it would be a huge change and again we think that that's not going to happen we think that the world in fact obeys the principle of consistency of measurement ### Logan Chipkin 00:31:47 - 00:32:18 So with these principles that you've conjectured again with Chiara and the results that you have from your initial constructor theory of information paper do you expect constructor theory to solve further problems down the road within information theory itself whether classical or quantum and I say that to contrast with what we've been talking about which is that you expect constructor theory of information to help physicists or scientists discover future theories ### David Deutsch 00:32:20 - 00:34:53 Uh yes um the um again Chiara has been working on this um the constructor theory of information does help with existing theories in situations where um although there is no new physics involved we don't know what physics is involved so for example in a situation where systems are interacting two systems are interacting via another system that is not understood or which is too complicated to analyze explicitly then constructor theory, because of the principles of constructor theory applying, can say something about that interaction we can make predictions about that interaction that are independent of the intervening process um provided that the intervening process obeys constructor theory you can do the same thing with energy you know you can you can say that regardless of the fuel that the rocket uses um uh if you have this amount of fuel you cannot reach if you have this amount of energy in the fuel you cannot reach more than a certain height so you can say that not knowing what form of energy is being used by the rocket and similarly when you have information being exchanged between systems like um gravitational field and electromagnetic field and the states of an electron and so on under quantum theory and the whole thing is uh only parts of the system are understood exactly and the rest are the medium that is um transferring the force or whatever it is from one well understood system to another well understood system isn't well understood you can still make predictions using constructor theory that the um uh Chiara and Vlatko have um several ideas where they have elaborated this into a useful form that may even be um usable in real experiments at some point ### Logan Chipkin 00:34:53 - 00:35:14 So since the constructor theory of information principles are expected to be universal you had mentioned I think uh dark matter earlier or maybe dark energy um but shouldn't those whatever they are would we expect them to also conform to the constructor-theoretic principles of information and the rest of constructor theory's principles ### David Deutsch 00:35:14 - 00:35:46 Yes I mean in my opinion um it's not on the cards it's not on the cards that they won't obey it and of course I could be wrong and as I said if I am wrong that there would still be useful things to be found from constructor theory but uh yes I think there is no sign in any of the problems arising from either dark matter or dark energy there is no sign that uh constructor-theoretic principles are being violated ### Logan Chipkin 00:35:49 - 00:35:54 All right David well this has been very interesting and very informative I really appreciate your time ### David Deutsch 00:35:54 - 00:36:02 Well thank you very much uh it was enjoyable answering these questions and I always learn something ### Logan Chipkin 00:36:02 - 00:36:07 Yeah well, you and me both. Have a good rest of your day ### David Deutsch 00:36:08 - 00:36:09 Same to you ...