Beyond Quantum Computation: Constructor Theory | Chiara Marletto, Oxford University

i'm really really really really happy to have you here kiara chiara maleto is a researcher at the physics department of the university of oxford and she will speak to us today about constructive theory or she calls it the science of can and can't which is also the title of the book that is coming out i think in next spring if i'm correct and i contacted kiara after our previous faucet salon on quantum computing with scott aronson and while i don't pretend to fully understand your theory and i definitely won't attempt to and try to describe it to you in an introduction i'm really really looking forward to your talk i will post a description of both your talk and a little bit more intro about you in the chat here and then i would say we leave the questions for the discussions people can just mark them with a queue and i'll explain all of that again in the chat and yeah i would say take it away and i will moderate in the in the chat everything that i won't take much take much more space uh so but welcome i'm really really happy you made it and i can't wait for the presentation yeah thank you very much this is a great uh opportunity i i enjoy this the possibility of talking uh in this in this context is a great initiative and uh so i will um probably share my screen and um uh you know i'll try to um to to talk you through the basics of this new theory uh and of course this is a very short introduction so hopefully um you know because this should be a very interactive session i'm very happy to have more questions afterwards so i'll keep it short and then i'll open uh two questions and i'm hoping to have a nice conversation with you guys so the best way to understand uh i think constructive theory is to start with something that's possibly um well-known let's say at least the name is is now uh quite quite uh present in the news which is quantum computation or quantum computing and the the way i i like to start these kind of discussions is by um by reminding ourselves what can quantum computation really is and i think uh you know if scott was here scott irons was here at some point discussing about this you probably got the gist of it uh quite quite nicely from him um but i guess what i want to say here is that um the the quantum the theory quantum computation is a very interesting place from the conceptual point of view because it's a place where technology so applications and things that can have an impact on on the you know life of people uh in in everyday uh life um meet the the foundations of physics and this is very rare because usually you have these very abstract theories of physics that seem quite distant from what we do in our everyday lives and then we have we have applications that can come out of those for example gps coming out of general relativity but but this only happens after a long time uh since the proposal of the theory whereas in the case of quantum computing i think the theoretical ideas were proposed in the 80s and then it was immediately clear that this theory would on the one hand deliver lots of applications so things like quantum cryptography and quantum algorithms can run on this universal quantum computer but also um would allow us to understand quantum theory which is uh one of the most fundamental theories of physics we have at present much better than than we we did at the start so i think there are some issues that the basics of the foundations of quantum theory which are which were still on on um to be uncovered in the 80s and i think now we understand them much better thanks to quantum information now the interesting thing about quantum computing is that well on one hand there are lots of technological efforts going on at the moment to create this universal quantum computer which will replace the objects that we currently use as uh our personal computers um but but there is another interesting thing and this is the fact that uh conceptually uh quantum computation in itself if you look at it from the point of view of fundamental physics is an unfinished revolution so something is is is still to be done in order to complete this uh conceptual revolution was started in in the 80s um and this has uh impacts both on on theoretical physics but also on computer science and also on technology and constructed theory is is is um connected to to to the way in which i i imagine this revolution can be completed so let's see why i say that quantum computation is an unfinished revolution so um when you open a book about quantum computing i mean might happen uh if you if you're not a specialist it could be a bit of a an exotic experience but i think you can try and what you'll see is um a lot of equations that are based on the the the dynamical equations of quantum theory so the the themes that schroedinger and iraq and einstein and people like that came up with um at the start of the the past century are the very same equations rules that are being used in order to power the theory of quantum computation and this is a bit weird because um you would expect quantum computing being all about information and things that are more general than just a specific physical theory you would expect it to be expressed in more general terms um and it's not just an expectation that one has uh you know an intuition is is really this is actually um an expectation that comes from the fact that in physics we physicists know that our theories even our best here is like quantum theory nowadays or general relativity or newton's laws for example in the past are bound to be changed because they are let's say the current best guesses to understand the universe but they might be wrong and they might have to be modified so in fact most thesis expect quantum theory to be changed at some point in view of the fact that at present it doesn't quite um accommodate a very important phenomenon of our universe which is gravity and of course einstein there reminds us of the fact that gravity uh is well described within physics by a theory which is general relativity but that theory doesn't quite go uh together with with quantum theory so so that's why we actually expect both theories to be changed so from the point of view of quantum computing this is a bit worrying because if our understanding of quantum computing is really only based on on quantum theory's uh dynamical laws and if at some point these laws will be changed so then the question is is is quantum computing still going to survive then so one question through which we can try to go beyond quantum computing as we know it right now is can we find a way of formulating quantum information theory or quantum computation theory in a way that doesn't rely fully on on the operators of of this theory of physics as we call quantum theory so how do we go beyond the dynamical laws of quantum theory and still retain uh or improve actually on our understanding of quantum computation that's the first question there's also another sense in which quantum computing is not is not the whole story uh is not the you know the um that there's something beyond the universal quantum computer and and this is the title of this slide so it's the fact that despite the name when you think of a universal computer you're not referring to the most universal machine that one can conceive of and here we need to to have a little thought about this so um a universal computer is is a machine a computer that can um perform all computations that are physically allowed computations and this is something that turing and then uh deutsche and and also other pioneers um understood very well when they when they uh approached this concept within their own respective fields but there are some tasks some processes or transformations that the universal computer classical quantum cannot perform so there are things that go beyond the capabilities of of this machine and the most important one which is interesting for us for uh for various reasons is the task of creating a replica of um oneself so when you think of let's say the task of self reproducing a cell so you've got a cell the cell itself reproducing is creating a new instance of itself a new replica from raw materials that task is actually seems very straightforward from the point of view of biology but turns out that a machine like the universal computer although it can be programmed to simulate that behavior within its um workspace it cannot itself create a new instance of of itself so you know imagine you could program your mac or your pc to assemble a new computer out of raw materials that's not possible it's just not something that a computer is designed uh to to do and yet it's a physical process it's possible it's allowed by the laws of physics so this tells us that there is a more universal machine than a universal computer so that's why we need to to upgrade um quantum computing to include these machines as well and these machines are called universal constructors so this is an idea that john von neumann polymath uh great physicist mathematician um already understood in the in the 50s uh even before the discovery of dna so this was quite cool um so he he understood completely the logic of self-reproduction and in that context he defined this idea of a universal constructor which is a machine that can be programmed to perform any task or any physical transformation that is physically allowed so if you if you don't want to go into the details of this definition you can just think of it as um as a as a universal 3d printer uh in the sense that it's a it's an object that you you know you you load with a program describing what you want to be built and so longer that the thing you're writing in the program is allowed by the laws of physics whatever object you're considering um with the right program this machine will assemble it for you given enough raw materials and we don't have a theory for this machine so we know it we can define it you know in principle but we don't have a theory that explains to us what are the physical limitations of this machine under what conditions these machines can be built and so on and that's the second sense in which the the theory of quantum computing should be generalized because you would like to have a theory of quantum constructors of universal quantum constructors that are like the upgraded version of universal quantum computers and why is this exciting well it's exciting because we already know the universal quantum computer is bringing us very close to um possibilities that that we couldn't even imagine just with classical machines with classical computers and the theory of the universal constructor even though it could be very far in the future um could be bringing about um the next uh technological revolution which could be comparable to the iit revolution that we we've had uh just now so let me try to explain now the logic of how one could answer these two questions so we got two questions questions are good in physics because in fact in science in general or in in even in philosophy um the questions are actually problems and these problems are um interesting because they tell us that despite the success of quantum computing there is a lot more to be done and to be understood further than that and and so one can think of of ways of answering these two questions so how do we generalize quantum information so it becomes independent of quantum theory um and also it can include uh machines that are more general than quantum computers and the answer surprisingly comes from well maybe not so surprisingly um comes from taking a look at how physics uh formulates explanations and i think so this is the second part of the of this short presentation where i'm telling you where the um the gist of the answer to these questions comes from so as i said i think physics can can be considered as a collection of of guesses about how the universe works in its most fundamental ways and i think uh we really only have a handful of good guesses laws that work as rules that are good for making predictions and and also are not just rules for making predictions but they provide satisfactory unproblematic explanations of of physical reality and these laws are are written here in part so we've got newton's laws maxus equations and these are this is the classical part of physics um and then we have the recent theories general activity uh and quantum theory that as i said were discovered at the start of the last century um and and so together all of these laws are the best guesses we've had so far as far as um as far as the you know guessing how objects move in in space time is concerned and there is one trait so that all of these laws look very different but there is one specific thing that they have in common and that makes them um very similar to one another and it's the fact that they all rely on a specific uh way of formulating predictions which is that uh they a bit like in this little cartoon over here they are based on dynamical laws and dynamical law is like a um a description of the the the set of points in in space or in space-time that an object goes through given some initial conditions and i think even though in this case we're only looking at a football being kicked inside the goal um and of course you can use newton's laws to describe the football but you can also describe this uh through general relativity and quantum theory and you will get the same predictions at this scale um these laws are very general so you can do this for um this specific example but you could do it for the whole universe and in fact the goal of fundamental physics formulated in this way is to really give just the trajectory of all particles that constitute the universe and once you've given that in the initial conditions you've explained um well let's say most things that are to be explained so that's the kind of logic behind this way of looking at the world however there are other ways of of uh expressing physics and and i think you you you must know about these things because they are everywhere in in um let's say in the in in thermodynamics and in other branches of physics that we've all somehow met one way or another um and i've written here three examples of these other kinds of laws that i want to call physical principles uh the these three examples are um very famous in some sense so maybe the first two are more or more known so you see on the left uh this conservation of energy which uh says that that the the energy of the over of an isolated system can't uh change so if if energy changes somewhere in the universe there must be somewhere else in the universe where the energy uh is changing such a way that the first change is compensated so you know if there is uh there is a sense in which overall um the the total energy of the universe has to be conserved and this also implies that you can't build a perpetual motion machine of uh the first kind which is uh supposed to be uh i mean this is an example of a of an impossible motion uh the one that the thing i represented here on the left and so so the conventional energy basically says that certain transformations are impossible specifically it's impossible to build a perpetual motion machine of the first kind and the second law of thermodynamics which is the one in the middle here also says that some transformations are impossible so it says that that you can't turn um heat completely into useful work um with no other side effects if you could then you could use let's say the thermal energy or the sea in order to power a boat and make it um proceed uh you know through the waves and of course we know that can be done and and this is not just an accident it can't be done because the law that says this can't be done and that's the second law and the third law that i reported there which is actually not um a law about impossibility but it's about possibility is the computability of nature which says that a universal computer is possible and there's a question mark there because we we really don't know although the first so the first two laws are well established the third one is a bit um and well controversial or unsettled yet but i think um it it's interesting that it's formulated in terms of um a statement about what is what is possible and so this is a declaring that certain transformation can be done and there for your amusement i uh report you know i i put this nice cartoon um which comes from an illustrated um story about the first uh attempt to create a universal computer which um dates back to the victorian era and uh this is um uh charles babish this guy over here he was a scientist in the uk who who devised this machine called the analytical engine which uh the whole of it actually should have worked just like a computer does uh so it would have been the first programmable computer available to humanity and um and then here is uh ada lovelace who is uh who was the his collaborator and she um was the first to understand that this machine this universal computer could actually be used not just to make not just to compute um to churn out numbers but to uh to do many more general things and i think um she was even thinking of using it to produce music or poetry and so on so i think two of them really pioneered the idea of of the computability of nature the fact that the universal computer is possible it's a shame that they couldn't build the computer lack of funding you know these problems are present now as then um but i i think it's very remarkable that they that they had this uh this intuition so anyway to go back to our to our point um the gist of this slide is that the principles that are in physics um such as these ones are not about dynamics so there are no dynamical laws not like in the case of newton's laws but they are about so there are statements about possible and impossible transformation so they say some transformations can be um done and others can't and so here comes the intuition so is it possible in order to answer the questions that we started with about generalizing quantum computing is it possible to take inspiration from these kind of laws the principles about possible and impossible transformations that already exist in physics and generalize them and formulate the whole of physics in terms of these statements is that going to give us um as a byproduct also a generalization of the theory of computation it sounds like a crazy idea but that is what constructive theory is about and the idea is not so crazy if you look at it very carefully so um so here is how i introduced now constructed series program so this is a program for a it's a long-term program for for a scientific project that can be developed in the future so the the idea is that instead of defining physical laws um in terms of dynamics so like instead of using schrodinger's equation or newton's laws or einstein's equation and so on uh you take laws about um that are expressed as statements about tasks being possible uh or impossible and then generalizing these principles that i just mentioned and then you try to derive dynamics and initial conditions um from these statements as emerging consequences with the principles so you're somehow switching the standard way of looking at that's under way of formulating laws of physics which is in terms of dynamics um and you're trying to to put the statements about possible impossible transformations at the foundations and then you derive the the statements about dynamical laws as a consequence of those of those other statements um and this is so it's very interesting that if you do this you also solve the problem about um generalizing quantum computing because what you get out of this procedure is automatically a generalization of quantum computing to uh general tasks and this is actually what provides the tier of the universal constructor so following the constructor series program in this way also delivers um a potential answer to the questions that i presented at the start so let's see um to summarize let's say what the two roles the constructor theory is expected to play and i think um my work and and david's work in this field and the work of our collaborators shows that these two um that this this is actually um happening so this is quite quite exciting uh because it's it's something's happening right now um so so on the one hand you see that constructor theory is a candidate to expand on the zero computation uh in the in the two ways that i said so um because it doesn't rely on dynamical laws but only uses statements about possibly impossible tasks it automatically well doesn't rely on on quantum theory so it allows us to generalize the quantum zero computation to a domain where quantum theory may not hold anymore and we hope that this is going to be the basis for delivering the fear of the universal constructor and ultimately once you have a theory of the universal constructor you will also be able to um to construct a universal constructor so that's that's let's say the the very very long term goal that we that we have with this theory and at the same time uh the interesting thing for for let's say from the physics point of view is that the theory constructed theory has this novel physical principles that that generalize existing principles that we have in physics such as those that i mentioned to you earlier and and these nice principles of constructor theory have a very interesting feature so they are um they are general so they can apply to systems that don't necessarily obey the current dynamical laws that we know and the chief physical system that comes to mind when you talk to a physicist about this issue is quantum gravity so as i said earlier gravity is this uh weird entity that is very well described by the theory of um relativity but unfortunately it doesn't quite fit with quantum theory so if you have an object which is a hybrid object that involves both quantum effects and gravity you can't use either of the theories you can't use einstein's theory and you can't use quantum theory but you can use constructor theories principle and this is very promising and and let's say this is a second way in which constructor theory can deliver to us very interesting results because it allows us to to go and probe areas where current current dynamical laws are not are not directly applicable and so to end on a positive note this is a recent application of this of this logic which was very exciting to the physics community you can explain how to test non-classical effects in in gravity by using only constructor theoretic principles and this is very nice because it's i would say it's the first application of constructor theory that connects these general principles with experiment and so um i think on this on this note i'll just end this short presentation and i'm very happy to continue the discussion with you uh when i kind of stop the share thank you for listening thank you so much amazing um okay very understandable too well done on that um i i already see i i guess already five uh questions collected in the chat so this is for me an invitation to everyone who would like to join the queue and ask a question uh to just preface your question with a queue in the chat and i will start right off the bat with ted hawk and i'll meet you if you don't mind hi and edward okay yeah thank you um ted perhaps you can also say a few words just uh your background if it's sure so so my name is todd hogue i'm a physicist by background and done some work on quantum computing algorithms and have been involved with foresight and molecular machines for for many years uh so my my my question um is you at the very beginning you talked about the the conflict so to speak between quantum mechanics and general relativity and the need eventually for a better or more more complete theory um but also physics has this notion what's called an effective theory that the quantum mechanics works perfectly well it's sort of everyday scales and gravity's not so big and so not so strong and so on so in terms of a theory of computation isn't what we already have with quantum mechanics for sort of everyday earth-based computing likely to be perfectly sufficient in terms of what a computer that we could build on earth could ever do yes so this is an interesting question that um so the point so i think it's got two answers one is is more foundational and the other one is maybe more on the practical side so um i prefer the foundational one so i those are the more fun ones yeah yes so in a sense you are right that that one could have a pragmatic take on things and say well as you said if you know if quantum theory is um effective at least at the scales where we're expecting to be able to build uh computing machines then then why worrying about about other effects and incorporating more general theories and so on um so i think that the the foundational answer to this is that when you're thinking of as a purist um to a theory of information and you look at the at the classical theory of information that let's say uh on which shannon and and other things are i mean shannon's theory and and the classical theorem computations are based you see that the dynamical laws of uh classical physics feature very little and and it's the theorems and the the statements are made in in very general terms so it's they're made in terms of distinguishable states and and permutations of those states and then um you know there are some results about channel capacity and so on but when you switch to quantum computing on the other hand um as i said when you open a book about quantum computing it's really quantum theory uh dressed in in some computer science language and being a physicist i'm very happy about that you know i like that but on the other hand if i look at this from the information theoretic point of view um it would be much better to have a theory that's only expressed in terms of information theoretic concepts so for example when you talk about entanglement or when you talk about the the quantum advantage that comes with a certain algorithm it would be nice to be able to explain in in what sense this co just in terms of information theoretic concepts why these things are different from the classical counterparts and the only way in which you can do this at this stage i think is to just run certain dynamical processes with unified transformations or cp maps or whatever and then out of that you can distill uh some kind of comparison but it's very odd from the point of view of the foundations of information theory and so this is foundational answer it would be nice to have a unified way of treating classical and quantum information this general framework the other answer which is more practical is that there are very sensitive clocks that currently are being built which allow you to detect um effects like the gravitational redshift and and and related effects already with with very tiny masses and so in a sense uh quantum phases that could be used to perform quantum computations can be affected by gravity and there have been a number of experiments even though you know still much has to be done and so in a sense i think i'm not so sure if it's so true that quantum computers can't be built at the scales where gravity is important it's true that that you you want pro gravity uh where maybe gr is fully uh effective but there is still a point where you have to reconcile reconcile this fact that you've got a mass in a superposition of different locations it have been even tiny mass and then you've got to think what does the gravitational field do at that point and as we know einstein's theory suggests that the gravitational field is classical so it cannot be in quantum superpositions and so how do you how do you describe that from even from the point of view of quantum computing let's say you're using a tiny atom to perform a quantum computation that atom has a mass and it gravitates so so those are really interesting questions yeah thank you thanks for the question all right thank you okay next one up we have a list this question alyssa meet you hey can you hear me yes perhaps you could also say one or two words about your background just that kiara hasn't if you want to sure uh so my name is lisa vance um i'm a senior core technology engineer here at mcd tech labs where we are building a dialogue a conversational ai for the mcdonald's drive-through um so question uh when you talked about uh limitations on uh classical computers like classical computers that can't build uh copies of themselves um are you referring to like engineering limitations that we have like you know in the year 2020 or referring to like some sort of more general or more theoretical limitation um because we have one kind of limit where we like we know that computers will never be able to solve the halting problem or there's a generalization called rice's theorem where it's just like you know computers cannot do this ever and then we have things like oh you know it's the year in the year 2020 you know homo sapien sapiens has not yet figured out how to do this you know but it may still be possible in the future like you know right now you know you can't do more than like you know 10 to the 13th computations per second per chip or something like that that's not an inherent limitation that's just sort of like an engineering limit um so uh could you clarify what you meant by that yeah this is a great question and like you very much because i'm always well in theoretical physics you're very interested in the foundational limitations so not the one that's due to the lack of in you know creativity or lack of inventiveness or lack of money but but i think what we are interested in is really whether there is a fundamental limitation that really can't be overcome no matter how high you know how hard you try you can't do a certain thing and in this case i think women was really referring to this um logical impossibility so the so if you think of the architecture of a turing machine a theory machine just has like it's a workspace which is a tape and uh so all the all the outputs that the turing machine is supposed to to produce are confined to that tape so it's it's uh logically impossible for the turing machine to also construct um the rest of the of itself so it can only operate on this uh tape but in order to create a copy of itself should be able it should be able to operate on on you know on the other part it's not the tape because it should be able to copy uh in some way the full of its architecture into let's say a bunch of raw materials that are kind of floating about and that cannot logically happen it can it can simulate the self you know reproduction of a cell by suitable program of course cellular automata are all about that but here is the question of whether it can create a copy of itself uh given i mean with a suitable instruction and the phenomenal machine or more general the universal constructor has this feature so it's it it is um it is a programmable machine can that can perform any task that's physically possible and so if you assume that that thing that that machine is possible itself then it must be possible to create a new instance of the machine itself so so i think that's why the unit so the universal constructor is really a new class represents a new class of machines that go beyond turing machines because they can operate on other things than just bits confined to a tape so so in a way it's a fundamental limitation and i like your question very much and i think it's it's a great question here thank you thanks all right thank you so much next one up we have rowley and rowley i hope i'm not um i'm i'm not catching you off guard and i'm muting you and you right now really perhaps you could also say a word or two about your background and then your question hello hello cool hi yeah um so my background is i'm interested in philosophy and uh so i learned my studies in philosophy and that just kind of like because i don't know know about this constructive theory this new stuff for me and i just kind of like that comment caught my eye with the idea of uh nature being uh the computability of nature yes is that like so what to to what extent like is that to say that you know is that the question of is nature fundamentally mathematical somehow or is this like an ontological question or more like an uh i mean it's a huge like ontological question in philosophy in a way yes so yeah is there some is that the sort of strong sense in which you're suggesting that here now or yes i think i think this is a very nice question because it touches on a subtle issue that that sometimes causes um some confusion as well in different fields so the um so when when saying quantum computing or at least in physics we think of computations uh what we mean is a um is is some kind of function or uh permutation or uh transformation more generally of a bunch of input states uh in in in a bunch of output states and the the the additional thing that we want for this to be a computation acting on information degrees of freedom is that the input states are all somehow distinguishable from one another but what i'm just to answer your question i think the the computability of nature says something very specific once you have decided that this is your notion of computation it says this that if there exists um a computer a machine that when given specific inputs can perform one type of computation let's say addition and if physically i'm now thinking when i say it exists i mean it exists given the laws of physics that we know uh and if there is another machine if another machine is allowed which let's say perform another computation for example multiplication then there must exist also a more general machine that can perform either of those given a suitable program so you can think of a more general machine that when you say i want these two numbers to be multiplied perform performance multiplication and when you say i want them to be added it will do it will perform addition this means physically that you can compose these you know computing machines in very specific ways and it uh it's it's an accident of the philosophies that we know you can prove this through like with the theorem within quantum theory and within a discretized version of newton's laws that that they have this property but it need not be so there could be other models where where you know you've got uh you know lots of lots of tiny computing machines that can perform specific tasks but if you want a universal computer one like the one that we are using now uh you you can't build one so at some point you can't compose together further um you know all of these um special purpose computing machines so the computability of nature is kind of technical term i suppose that i was using to refer to this specific property and now the the then there are these other so there's a theory of computable functions in in mathematics and so on which refers to specific model computation which is turing's model and etc and that's that's a different thing so i was trying to be more general in the sense that this computability of nature can be really defined under any uh model so long as you have let's say some dynamical laws that tell you what are the processes that are allowed i hope that makes sense yes cool awesome thank you so much next one up we have mike hi this is mike my background's mechanical engineering design and also the computer i.t service so i just want to comment part of it sounds like the problem of the origins of life in a way that i would we know how to create the primordial soup and chemicals but we don't know how it actually starts as a self-replicating life so this constructor theory kind of reminds me of the same kind of situation just an observation but my question was if you've looked at all a category theory and applied that to this constructor theory as a way to deduce what principles and laws there might be based on your observations yeah that's a nice question i i think the so the category theory is this very powerful mathematical tool that that somehow powerfully generalizes set theory and kind of upgrades it in a dramatic way and and i think um although at the stage of the current stage so constructed theory is formulated more in the context of set theory but i think the so you know one of the students is working with me um he he is interested in translating the current results of constructive theory within category tier because that appears to be the most natural language so i i like your question because it's very is somewhat related to a current development in in my own research with with this collaborator of mine uh and and i think it's um it's very important to express uh the theory in more effective mathematical ways because of course once you do that then you can see even more uh connections that you maybe wouldn't otherwise be able to see um and about the origin of likequest i mean comment i think the um so the so the concept of a constructor is possibly i mean i think it is related with to to life in some sense in the sense that um i didn't go into these details but i think what phenomenon called the constructor is could be is generalizing in physics and in biology uh with anything that can effect the transformation on the physical system and stays unchanged in the ability in its ability to cause the this transformation again so it's it's something that works in a cycle and so obviously um cells and and organisms uh have this property but the so the the interesting thing about constructed theory is that we are trying to um so despite being called constructor theory it's a bit like with relativity the theory is not about constructors constructors are the things that you obstruct away from the description because all the laws are about possible and impossible tasks and ask is possible if you have um if that can be a constructor that performs it and it's impossible if there cannot be one and so by by restricting your statements to whether a task is possible or impossible you are avoiding the the issue of enumerating the constructors saying where they come from and and how they have to be constructed so in a way you you are obstructing away the issue of where do the constructors come from but i i think um you're right that that there is a strong connection with biology at least at the you know conceptual level when you're talking about constructors and for neumann was motivated by biology when he made these remarks about the universal constructor because he was trying to understand how life fits into the laws of physics which of course it does but i think at the time it wasn't quite clear because we didn't know about dna yet and and things like that so um yeah anyway thanks great yeah yeah polymerase and dna looks so much like a turing machine the way it operates yeah yes absolutely yeah well thanks a lot thank you lovely okay next one up we have logan hi i'm logan i'm a science writer hello so you said in your talk that you um hope to maybe deduce the boundary conditions uh from these constructor theoretic principles so i'm guessing that includes let's say the initial state of the universe hopefully but do you think constructor theory has anything to say about maybe the final state of the universe if people don't intervene between now and then for example yes i think i think the so the the program so that part of the program hasn't been so we we haven't uh realized it yet but i think the the expectation is exactly as you were saying to um once you once you lay out all of these statements about possible impossible transformations you can find ways of showing which laws which dynamical laws and which initial conditions or boundary conditions are compatible with with those uh statements um so in in a sense because of the well uh one would expect the dynamical laws that are compatible with the principles are of the form that we know already now so for instance general relativity and quantum theory uh should be compatible with constructed series principle and we know quantum theory is compatible in general activity also most likely is so because those laws are time reversal symmetric um what so that means that that um they are the same whether you know when you're evolving them from past to future uh they are the same as from future to past um once you make statements about the initial conditions the same statements should be possible to make about the final conditions so so because of the symmetry of the laws i would expect that once you know if you if you manage to say something about the initial conditions of the universe you should be able to say something about the final conditions um so hopefully yes the answer is yes to what you asked well of course we have we have to do it yeah yeah thanks for the question for the question thank you all right we are making progress on on the question so if if there's others that still want to collect theirs we may even get to them um so let's see next one up we have jessie jesse nichols i will i mute you now hey uh so i was wondering about the rationale or epistemology that this work comes from uh i ask because i know the context of this organization's a bit on the more beijing side so i wondered uh how does this theory deal with credences or probabilities yeah that's a great question uh the so i think the so in a way these these questions are uh more at the meta level in so you know it's a bit like uh the same question could be asked about uh current like current dynamical laws right so quantum theory or or newton's laws and so on and for all laws including i think constructor theory um for all those we know right now the deterministic structure comes first so if you think of all these laws that we have so there's newton laws marxist equations um quantum theory and general relativity and in all those cases you have a dynamical transformation which is deterministic so you know in newton's laws you you know what the dynamic laws are and then in quantum theory schrodinger's equation is also deterministic in the sense it evolves this quantum state deterministically from one time to another and so on um in quantum theory there is a bit of a complication because when you make a measurement on the quantum state then there is a probabilistic outcome but um if you describe everything uh from the point of view of the whole universe the and if you believe that quantum syria applies at the level of the whole universe which is what quantum theory seems to say then the whole universe is evolving really deterministically and the appearance of stochasticity is really only to do with the with the measurement events so um overall it's all deterministic and likewise i think you construct the theory the fundamental statements are deterministic so when we say a task is possible or impossible there is no probability involved in that statement however you can accommodate or derive probability within uh those from from those statements so you have like uh some axioms that are don't involve probabilities but you can derive derive the you know certain uh probabilistic statement out of those axioms just like in quantum theory and the so so this is as far as probability uh are concerned for credences this is even more abstract because this is refers let's let's say so to a certain theory of uh confirmation of of science of let's say uh theory conformation within scientific method and i think constructivity is agnostic about that in in a way so so if you know if you approach theory confirmation from the bayesian point of view uh you will be able to apply to construct the theory as much as you can with with other uh physical theory that we theories that we have at the moment and then you know i'm happy to discuss about basianism as well uh i mean my my inclination is that i you know i tend to i tend to think of things in in a more popular way uh so so i think basic news maybe is not so necessary uh but i don't think he would you know if you're a bayesian yeah exactly if you're a base and i think um you can still you know take uh the the whole constructors here and make sense of it just like you would with another physical theory but you know if you ask him about my own bias i think i i tend to think that basianism is um not completely adequate to explain theory confirmation and sometimes a bit misleading thank you i hope that answered the question yeah cool awesome thank you so much next one up we have dennis and us on hey can you hear me yeah great hi a great talk nice to meet you my name is dennis i'm a software engineer and i'm interested in the mind uh particularly within a papyrian and deutsche and epistemological framework um so i'm interested if you've learned anything from constructor theory about how the mind may work or if that's if you've had any insight on that so i think the the so the answer is yes i think the well so we haven't had an insight into that specific problem yet but i think what i i'm hoping is that and what i think david also is is interested in is that the conceptual tools that constructor theory provides will allow you to tackle this problem in a radically different way and and um so the stage is just a hope but i think there are reasons to to expect that and the main reason is that um when you discuss uh well the mind in a sense is is an entity that creates a particular kind of information which you can think of as a resilient kind of information that also has causal uh power on on the environment and this is some uh something that you can call knowledge that's the the term that i think david uh and i also use to refer to that and this particular kind of information in constructor theory can be characterized in a very in an objective way so you can talk about it as um a copyable set of states with other uh specific information theoretic properties that i can then list if you like but i think the uh important thing is that you can characterize what knowledge is in terms of possible tasks without ever referring to subjective um scale-dependent approximate concepts and this is nice because usually in the series of how knowledge is created you get a lot of these um well sometimes some stochastic um sort of approaches other times you have some subjective ways of this defining minds and and things like that and it's very hard to have an objective handle on these concepts and that's problematic because for uh well for scientists like me um you know it's it's important to have a way of objectively describing or handling concepts even before ever creating a theory about them so the hope is that once you have this concept available you can then make a theory of the kind of physical objects that can create knowledge like for example minds or even well i mean the other thing that creates knowledge is natural selection which creates it in a much less efficient way but these are the only two things that we know of in the universe that can create this kind of information and so the theory doesn't exist yet but i think it the the so the conceptual tools the constructor theory provides will be very useful to develop on and so there are also applications to i think ai and and agi so so and david is very interested in this kind of stuff i'm also quite interested and and you know because this is not my main focus because i'm a physicist i i i think this will i'm hoping that someone in the field of agi will notice these kind of comments and the concepts and they will use them and um i mean you already see that there are some people in that field who are trying to get away from the standard way of thinking about um stochastic so about about learning and and uh machine learning and things like that you know there's julia pal who has this nice theory about counterfactuals which is trying to get away with standard concepts away from the standard concepts so i think there is a need for these concepts and hopefully constructivity will provide some right on thank you yeah amazing hey kiara i'm realizing we're now one minute past the hour um i we have three more questions i'm not sure how you're doing on time i think i can take three more questions yeah it's fine absolutely okay lovely i know those folks will be very happy um okay then without further ado yasha your question is next and i'm gonna post a little more info on those salons here in the chat for those of you who have to jump off and for those who um for you whom it was the first time conjoining but for now we have joshua hi yasha hi i'm an agi researcher i'm quite interested in david's and your theories uh but i don't yet understand how constructive theory goes beyond constructive mathematics that is uh how can it compute things that uh finite state machine for instance cannot compute in principle i don't think that uh recreating yourself is an issue this uh a program that reproduces its own source code is uh basically it's called a client and it's a hobby that computer scientists have had successfully for quite some time and as i didn't understand your metaphor of a 3d printer uh for the constructor uh in this sense i do understand that uh you can take the constructor theory um as a methodological approach that um is basically puts computer science in a slightly different hierarchy but i don't see uh um an ontological difference and i don't understand the ontological statement that you and david are making when you say that you can compute things that uh other computers cannot right so the statement isn't so i think construct there was part of the motivation and in a way it's for norman's statement and i i'm just repeating what he said so i'm more or less pirating someone that was who was already ahead of um you know even biologists in a sense i think the point that phenomena made um which is somewhat motivating the whole idea of a constructor which should be a more general machine than a turing machine is that if you take a turing machine yes you can have programs inside the turing machine that can self-replicate or you can have uh well the turing machine simulating in within with the specific program the behavior of a cell that's self-reproducing but there is no instruction you can put in the turing machine that would get the turing machine to create a replica of itself out of elementary materials simply because the turing machine doesn't have but doesn't even have the the tools to do that in a sense right so you would need arms to like assemble the keyboard you know if you're thinking of a of a modern turing machine um you you would need your computer to be augmented with a number of of other uh well working arms that or or you know uh various tools that you would so this is about the substrate again it's about the substrate in other words so of course you uh if you are in a virtual world you can create another virtual world that has the same property virtual world but yes there's no space in the turing machine model the the only thing the turing machine can operate on is its tape and there's no way that the tier machine can create on its tape um a new instance of itself it doesn't even work so if you think of the turing machine physically it just doesn't look so it's not possible for this to occur well there is no space space is not computable what we observe is a set of locations and trajectories that information can take that is what physics is about and uh this space is something that exists in the limit when you look at too many of these locations to count and too many trajectories to count then you get to a space but uh you can see that there's singularities in this space um that are unavoidable so space itself is not mathematically consistent there can be space that exis works exactly like the space that you and me observe inside of a turing machine but i think i'm now thinking of the of just the discretized model that can support the turing machine so i'm not thinking of some exotic physical theory i'm just thinking of the the discretized model of classical physics that that within which you can define the model of the turing machine um so the program that said you know the client that this this program that can self-reproduce within the turing machine it's not really performing self-reproduction in the way that cells do because it's using the error correction mechanisms that's ready within the turing machine and it's using a lot of other bits of the environment in which it is self-reproducing which um don't uh exist let's say in the in the in the biosphere when you're trying to to look at what happens when the cell self reproduces so so it's conceptually different from from the self-reproduction that occurs in a cell and i think phenomenon was interested in that on top of it phenomenon was really to just talk about the turing machine as a whole so it wasn't interested in a specific subpart of it being able to say replicate um it was interested in the question i define a task which is self reproduction can the turing machine execute it and the answer is on itself so like um i mean there are different ways of self reproducing you can you can either have an entity look at its various details and then try to reassemble itself out of raw materials directly by inspection uh but that's very prone to errors and then of course there's the phenomenon logic which is the correct one for high accuracy self-reproduction which is that you have like a description of the whole architecture basically dna and then uh that thing gets copied uh bit by bit and then the the uh initial entity that self reproduction thing executes that program in order to create a new instance of itself and the turing machine doesn't have the space for this kind of stuff it just does not logically support this type of [Music] instruction at best it can do something on its tape and that won't include creating a new turing machine on its tape it's just that's not part of the turing machine architecture um i mean phenomenon has a nice article on this it's dated 1950 or something and and it's it's very nice so you know i can i can send it to you if you want um yes please thank you very much yeah it's not something that david and i claim in a sense constructed here is just taking the the motivation to go beyond quantum computing to have a theory about these machines that can act on more general transformations that are not just computations and this this is all what that reference to von neumann was intended to achieve i hope it didn't it didn't kind of confuse too much it didn't confuse but i'm not yet sure about the answer but thank you very much for your effort yeah no thanks for the question thank you all right well maybe we can find the paper and share it even in the chat yes you're very funny later that's amazing thank you next one up we have ted howard ted oh i need you hi ted thanks alison um look what is the role in constructing hi um what's the role in construction theory for fundamental uncertainty um like i heard you i was interested in jesse's response and joshua's question um they're both aspects of what i'm pointing at you seem to be coming from the idea that you can have something which is tightly constrained that can approximate causality but what if the universe we live in is constructed from infinities and if garrett lissy has something in the idea that what we see as order is something that falls out of the symmetries that are allowed in infinities when the symmetries are only like collector states where things tend to modulate but actually all infinities are allowed or any instance of an infinity is allowed then you're dealing with something that's fundamentally uncertain and the order that we have um is an approximation so it's we we're back to uncertainties does constructor theory allow for that sort of approach or is it where where the constructors are themselves fundamentally uncertain yes i think the so um well the way in which uncertainty can come into physics uh so there are several ways so one one is the one you mentioned uh the other one is of course through quantum theory um and i think the so the the key here is that uh let's take you know a theory with infinity um for example um you know quantum field theory or field theory in classical physics has uh lots of infinities there but you can still define uh within that theory um a set of possible transformations and so um so that doesn't mean that all the states of that theory when transforming to one another are free of uncertainty or free of infinities or free of whatever else but you can distill a subset of the properties of physical systems that obey that theory for which the statement a certain task is possible is valid and meaningful and consistent so i think constructivity is aiming to provide constraints on physical theories so that um they must be expressible at least in in in part uh through these statements about possible and impossible tasks if they cannot be expressed in terms of possible impossible tasks then they don't obey constructed theories so they would be somewhat ruled out from the constructor theoretic picture of the world it could be a constructor theory is wrong and those other theories are correct and in which case you know that's that's it would be nice to find an experiment that could tell those two things apart uh but i wouldn't you know in the specific case you were referring to i wouldn't know what experiment one could think of but what i'm trying to say is that we are still within you know the classical physics dialogue in a way because um constructive theory is just proposing a certain understanding or explanation of the of the world and it could be that it's just wrong in that case in which case you know it's it's you know we we should switch to something else at some point but we are not yet you can make a prediction and test it against something else it seems to me that our human brains are heavily biased by the fact that evolution most heavily selects for things that respond quickly under urgency so we're heavily biased to simplify things so we have this bias that likes to take us back to binaries and that's it and take us away from infinities and uncertainties um and that seems to be yes driving the direction that you're going in so it's possible still as then my first answer applies here because the first part of the answer in the sense that you can still reconcile a structure which is highly counterintuitive like let's say the structural field theory where you have infinities popping up everywhere with the presence of uh with the presence of the definition of an information variable which is a completely discrete and finite set of states so it's possible to construct a model that complies to this intuitive discrete type of structure within a theory that still allows for infinities and and continuum and so on such as field theory in other words what we are saying is compatible with certain kinds of infinities and and so i don't i don't see them in contradiction necessarily it's just that the statements i'm making at the level of the possible impossible tasks should be seen as the fundamental explanations for everything else and not the other way around yeah snacks of bias to me but yeah i can see why the bias is there well aspirationally biologists by yeah that's my background i suppose all all things are fired i mean it's impossible to approach any problem without a bias everyone has a background knowledge so in a sense um yeah i suppose you know the whole of quantum theory is biased or the whole of newtonian thank you all right thank you so much and then we have dan gershovich dang i'm gonna meet you now let's see harder to do than i thought sometimes it takes forever to go and meet someone oh now i muted him and now i'm going to determine that i mean thank you um for taking the time kiara really appreciate it uh i'm dan and for the last question i guess uh i'm really curious about what constructor theory has to say about observer independent facts there's a paper i think i just posted to the chat about the inability for uh modern physics to say certain things are objective and it seems from what we've been talking about with probabilities and what i know about how knowledge and constructor theory are tied together that in a sense it's a purely local or purely subjective approach and that would be fair to say you wouldn't be able to say uh you wouldn't be able to make purely objective claims using constructor theory right so so i think the as i was saying earlier in reply to another question the um so the the the take uh in constructed theory which is actually i would say the taking all other laws of physics we have is that um the most fundamental entities are actually objective and they are observed and independent so i know that there is let's say a you know even in quantum theory there is often a narrative about quantum theory that says that things are dependent on who is observing uh what for example you know there is this famous um title of a famous paper saying is the uh whatever flux there if nobody looks so so the this is referring to the fact that when you have a quantum superposition of various values um there comes a moment where someone is performing an observation of their superposition and then suddenly one of the various values become real for that observer or or something like that now i think that's not uh so this is an interpretational quantum theory which seems to me is not correct and and uh if you if you if you look at quantum theory properly you take it seriously and you're not adding other assumptions on top quantum theory just tells you that there is an objective reality made of the quantum wave functions and then the the measurement is just another quantum interaction and you can describe it all nicely and consistently and every statement you can make about entanglement superpositions outcomes probabilities all of these things are objective and they are observing dependent in the sense that having fixed the coordinate system um everyone and you know even people sitting in different coordinate systems will agree on what's happening module of course proper you know translating properly between their own way of predicting and the way of predicting of a different observer um but the the fact that let's say according to relativity there can be uh you know you can compute the probabilities of the outcomes of certain experiments in different coordinate systems doesn't invalidate the statement that the output that you get out of these calculations are referring to objective facts and there's just one truth one fact of you know truth of the matter uh that refers to the physical system that you are describing and i think this is true in all physical theories we have in one in constructor theory is the same and to convince you of this even if you don't want to go into construct constructor theory details you can just take the conservation of energy which is an example of a principle that has the same logic as constructed here is principle and it's well known because it's just already part of the structural physics when you say that energy is conserved in a certain physical theory that is an objective statement it doesn't depend on whether there are observers around or or um it doesn't depend on on the you know particular way of looking at the system in question it is just a fact and it just says that you know if you've got the system with a certain energy in order to change it you have to bring the energy from somewhere else or take it away into move it to to some other location in space time and that's it and i think the the spirit of the the logic behind all of the statements in constructed theory is very similar to to the to the logic of the conservation of energy so we are hoping that this approach is very much objective um and i would be very wary of statements about observable dependence because although it's true that there are some some quantities that you know in relativity you can express with different values in different reference frames or in different coordinate systems that's one fact but that isn't in contradiction with the fact that there are objective uh entities in the theory of relativity which are you know the symmetries of the laws and and there is other things that are actually the elements that we're using to describe physical reality so i very much support and i think i'm hoping constructor theory uh does the same i i i support the view that that let's say science should provide some objective view reality all right thank you so much even observers should be describable fully within the theory that's one lesson that we got from quantum theory even microscopic observers like us can be included in the laws of quantum theory let's say and i think constructed serials can can be applied in in a sense to to entities like like uh microscopic observers okay thank you so much i like i forgot one question by harrison from earlier maybe um you know he could if you don't mind he could ask the question and then you can decide either to take it or to do and and maybe you could read that into a few final remarks of a kind of like what's happening now is there a book coming out and i think i i said that in the introduction but you know so that we have like a a little uh a little roundup of how we can find out more about you and how i'll mute harrison and uh i i think the question is really worth it okay let's see harrison you are muted hi kiara uh thanks so much for coming on i've wanted to learn more about this uh stuff for a while and i think this idea um that you have in your program of taking uh the sort of like possibility statements and making them sort of the primaries and the dynamic laws and making them uh you know the epi phenomena of those primaries rather than the reverses we see today is really cool uh that being said the primary content of like dynamical theory isn't just like there's a dynamical law but like what the mathematical statement of those laws like is and so i guess this is a question about like where you are in your research program can you give us a sense of what the mathematical statement of a constructor theory or several different constructor theories would look like in the same way that like newtonian mechanics is an example of a compelling mathematical statement of this sort of like state and continuous transition function idea like what would the math of like you know what it is possible to construct look like that's a nice question i think the i started to mention something earlier into you know in reply to another question the and and i think it's nice that you're kind of asking this because the uh so the way in which the theory looks is very different from dynamical laws it doesn't have dynamic laws directly and the the basic formal objects are tasks and these tasks are basically if i can use some jargon they are sets of states input output states um and so being sets you can well you can think of them as being composable with one another so there's an algebra of these tasks and and um so the current way in which we're presenting our results is is based on set theory combined with algebraic tools that describe the properties of the algebra of tasks uh and and then there are there's a combination of uh of of well there are some rules that say how possible impossible tasks composed together so so there is a there is also a function which is this function that tells you whether a task is possible or impossible there is like a label that will you put on top of these uh sets and i think the these are very rudimentary mathematical tools if you like so you know if i've got as i said some collaborators who are trying to rephrase these statements and results that we have in terms of more sophisticated maths which is basically category theory so i think if you want to know what a constructor theory of you know fully fledged theory of constructors would look like um sorry i meant fully fledged constructivity will look like in the future it should be expressed with uh seems like the natural way of expressing it is category theory um having said that i think the current results are mathematically rich in themselves and i think it's possible to see this even with this set theory approach that that we currently have and in fact you know if if anyone has suggestions about you know different tools that one could use uh it would be welcomed you know because we we are really exploring something very different from the standard uh from the standard dynamical laws that you have in physics and although it would be these dynamic laws are compatible with we say the kind of statements and the proofs that we make are you know just follow a different formal structure so um happy to get suggestions and from from anyone in the audience i think you got one already in the chat um and is there a way in which people could follow up with your work specifically that i may have not mentioned yet or is there a way where we can i can well my email is on the internet and i'm very happy if well there are um there's constructortheory.org which is the platform where we kind of post our results but also as i said if anyone wants to ask more questions um you can google me and and there is an email address so i'm kind of very happy to reply to further questions and i will find the neumann article uh and maybe send it to you and you can is it possible to to send it back we have an email list yes um okay excellent fantastic hey kiara i can't thank you enough i think uh you know it was like a very very well enjoyed salon by everyone thank you so much for making the time so spontaneously i can't wait uh to to get the book maybe we can have you back on when the book is out and for now thank you so so much for making time i'm gonna follow up with you about the video and then i'll follow up with all of you guys to share the video relevant links for now i'm going to open up breakout rooms and if people want to continue the discussion informally i won't be there so please be nice to each other and you know maybe introduce yourselves in the chat and the breakout room should be open and i hope to see many of you again next thursday for andrew sandberg from the future of humanity institute at oxford uh for another salon thank you so much kiara from all of us it was really fantastic to have you thank you so much thank you everyone for the questions take care bye

Channel: Foresight Institute

Views: 90,417

Rating: 4.8769479 out of 5

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Id: B2SSJmE0TeM

Length: 83min 52sec (5032 seconds)

Published: Fri Aug 28 2020

Reddit Comments

[u/Peter_P-a-n]

I watched this video out of interest in the physics of Constructor Theory, also I find David Deutsch and Chiara Marletto to be very interesting. Then out of nowhere Joscha Bach pops up in the Q&A session asking exactly what I wondered as well. (Timestamp 58:30) *mind blown*

[u/AlrightyAlmighty]

green screen game over 9000