Wolfram Physics Project: Philosophical Implications & Q&A

okay well hello everyone we just did a couple of our Q&A about physics and mathematics and more technical kinds of issues about our models of fundamental physics we're now going to turn to talking about philosophy and general kinds of philosophical issues about finding fundamental theory of physics and about that particular model so had a few questions queued up here let me take a look at them all right first question here was about deterministic determinism versus some hmm this is a question of deterministic universe is Dow and the concept of free will or even time itself will be moot so I'm not quite sure I mean let me try and address that a little bit so in our model it is indeed the case that there is a deterministic evolution for the whole universe it's a little bit more complicated because it's this multi-way evolution that takes account of sort of all the possible branches of quantum of quantum processes but in the end there's a definite rule that starts from the beginning of the universe and computes what will happen in the universe up to the point where I'm talking to you here now now the issue is does that mean that what is happening in the universe is somehow under somehow determined in a way that denies the possibility for example free will and the answer is no and the reason is this phenomenon I call computational irreducibility the fact that even though you know the rules by which you could in principle compute everything that's going to happen there isn't a sure there is no fast way to do that the only way to compute what's going to happen is to essentially follow each step in the computation and see what it leads to and particularly when we're talking about a mutation that represents the universe where would we get to run that computation to how would we how would we run the computation that is the universe unless we could have a sort of computational shortcut to the computation we don't get to run a computation of the same length as the one that is our universe in any way that shortcuts it because the only place we have to run the computation is the universe itself so we have both the sort of mathematical results of computational irreducibility that there isn't a way to shortcut the the the actual process of working out what will happen to just get to the answer to say for example in traditional science computational reducibility was a big thing and traditional mathematical science some of its great triumphs were computational reducibility you know what Newton did working out you know the orbits of planets and things like that that was significant because it allowed you to figure out where would Halley's Comet be n revolutions in the future without having to effectively just trace every step of Halley's Comet orbit you could just say there's a formula for what will happen and the answer after how many revolutions will be this so that's a that's a typical example of computational reducibility what what I found in the 80s actually was that it's very common to have this phenomenon of computational irreducibility where even though the the rules underneath are deterministic and perhaps simple the actual behavior itself can't be determined except effectively by just following every step in those rules there's no way to shortcut what happens so once there's no way to shortcut what happens you're stuck with saying well I've got a faster computer than you and what takes you two steps to the what takes you to nanoseconds to run on your computer just cuz I've got faster silicon and my computer takes one nanosecond to run on my computer but that argument of just the I've got a faster computer faster not because it is doing something Kleber uh but faster just because it's clock speed is higher that argument is just not gonna wash when the thing that you are trying to simulate is the whole universe because the thing that you are doing the simulation on can itself only just be our universe and so that's why there's a once this computational reducibility there's a fundamental sense in which you can't work out what the universe will do except by effectively watching the universe do it so in that sense while there may be determinism it's not useful determinism it's not determinism which would allow you to predict what will happen you still have to just watch and see what happens okay how does this relate to things like free will as we think about it for for people for example so one one way to think about this is when we have underlying deterministic rules there's the question of whether the behavior of something that operates underneath according to those deterministic rules can appears to be free of those deterministic rules or is it is it sort of locked down by those deterministic rules if you if you imagine you know I kind of often use the analogy of the 1950s science fiction robot where you could kind of trick it by getting it - getting it stuck in some simple logical paradox or something we don't think that that that's in that case there's a very small sort of amount of computation between the underlying rules and the actual behavior of the robot in the case of computational irreducibility there's often a that there's a there's a sort of irreducibly large gap between the underlying rules those simple logical operations and the actual thing the robot does and so in some sense we would say that the thing the robot does is sort of irreducibly far away from those underlying deterministic rules there is underlying determinism but the actual behavior is irreducibly far away now you can ask questions like how does freewill in this sense the sort of a question of responsibility and it's its relationship to freewill so here's two models for how an organism might work one model is the V let's say you're asked you know why did you do that okay well one answer is um well it was because of something that happened to me from outside it was not something intrinsic to me it was not some intrinsic computation happening in me that caused me to do whatever I did um it was the it was a thing that came from outside it was I did that you know I am I the self-driving car drove into this truck because from the outside my sensors picked up some some fast moving you know endangered animal that was about to jump into the road and so something from outside of of me caused me to do what I did that's kind of model number one model number two I the self-driving car did what I did because of something to do with my internal programming because of some AI algorithm inside me caused me to do this or that so one question you might ask is in which case is the self-driving car more responsible for what happened you would probably say it's in the case where the it was that internal algorithm that caused it to do what it did and that's kind of the analogy with with free will as a result of computational in reducibility is free will that comes from inside the organism so to speak inside there is an irreducible computation happening inside the organism and that's what's causing it to do what it does not oh I did it because of sort of randomness from the outside by the way this is something that comes up I you know I did some testimony for the US Senate last year about AI content selection for things like news feeds and so on in social media and and search engines and other kinds of places and this question of the AI picked what it wants it to show me and the question is sort of how do you tell how do you assign response one of the questions one of the ways to think about this is how do you sort of assign responsibility for what the AI does and is it something where there is where the AI in some sense has free will so there was a there was a possible piece of legislation that basically said will insist that the AI that you that you make visible the code for the AI and then will be able to say is the code okay or not you know is the code doing what we want or not well and one of the points I had to make was look that's just not going to work you know because of computational irreducibility just because you know what the code says doesn't mean you can know what the thing is going to do it has in a sense in some sense there's sort of that's the practical version of sort of free will for a is playing out so that's a kind of a long answer to their question about some about freewill versus determinism okay there's a question here from will a yam why is there anything that's a really good question I have thought about it a bunch I don't know the answer I think the first question is so you know here's a possible answer that's the kind of a last week's thought about this question so existence foot foot okay this is sort of an attempt and I don't think it's gonna get all the way there um kind of why is there something rather than nothing why is there why does the universe exist okay here's a here's a possible way to think about that the the way to think about it is that we are entities within the universe and we are trying to talk about the question of why the universe exists so here's a possible analogy if we think about mathematics and we are operating within an axiom system in mathematics let's say the axioms of arithmetic or something then we can ask the question is this axiom system consistent let's say and it's girdle second incompleteness theorem that says from within those axioms we can never prove or disprove the consistency of these axioms in other words from within the system itself we can never prove or disprove the sort of the the overall story of that system in that case consistency so I have the slight suspicion that it might be possible to show that foreign entity embedded in a universe it is this question of existence is in some sense undecidable for an entity embedded within a universe and that's that's not a very good answer because it's just saying that there will never be that we state the question of whether the exist the universe exists is somehow an a question independent of anything that would be sort of axiomatically defined by the rules of the universe as set up for an entity that exists in that universe it's not a great answer but you know I have to say in the history of philosophy there aren't a lot of great answers to that question and I think this this direction for trying to find an answer maybe one of the more promising ones and it's you know you really have that question really hits you right in the face once you start to have a serious chance at having a fundamental theory of physics I mean the other big question is is this that in a sense by having a fundamental theory of physics we're turning physics into a branch of mathematics you know mathematics is a is an abstract a system of abstract development you're given some axioms you work out their consequences we've always assumed that physics does not like that it that it's it's a it's something where we're progressively approximating how the world works we're not thinking somebody will just present us with axioms and just say this is the world now go work out what what consequences that has actually interestingly it was Hilbert's sixth problem when Hilbert defined these problems that might so be interesting for the future of mathematics back in 1900 I think so but sixth problem is very simply stated it's like find an axiomatic representation of physics and in a sense that's what we're trying to do is to find a rule which defines physics Hilbert had a slightly different meaning for that but but this is a this is kind of a conceptual modern conceptual extension of what Hilbert was talking about so in a sense when we're reducing physics to mathematics there will be a question of okay so you've turned it into mathematics you've turned the operation of the universe into something like computing the digits of pi you've turned it into something which is a purely abstract mathematical operation and it's fine to say the abstract mathematical operation in some sense is let's say happen a ball it can happen 2+2 can turn into 4 it's a purely inexorable mathematical thing that those two that that that those two things are equivalent you can do this operation and so on now the question is why is it actualized what what causes it to be the case that just because you could compute the digits of pi and this is how it works why does that actually happen why is there an actual 'no Stu that occurring and that kind of turns into these questions that I think in in the history of philosophy and theology have turned into these questions about the existence of a prime mover the thing that causes everything to be actualized and I my impression is that the progress on that question in philosophy has not been very very great and I think that again that's what sort of swirls around this kind of possibility that for entities embedded within the system there may be an underside ability to answering that kind of question which sounds like a terrible wimp out but I think it might be possible to get a much more precise version of that the precise sense in which that question is fundamentally it's like in girdle's theorem where one says you could ask the question oh I don't know you could you could ask a question about some equation involving integers and it might be the case that that question is simply independent of the axioms that you define for arithmetic it could be the case that that question is it could be true or it could be not true it's not determinable from the axioms you've define it and I think there are a lot of very real questions in mathematics where that will be the case but that's a different topic okay let's see do you see the potential for eventually detecting self replicators / end life within one of these rules well your parentheses I think has has a deep amount of content hidden in it so to speak software application is not a difficult thing to get in a in a computational system does self-replication equate to life I don't think so I think the definition of life is a slippery one and the you know okay a thing I like to remember when I was a kid the first Mars landing spacecraft was sent off and of course when you send a spacecraft to Mars one of the questions is does it find life there back and back when I was a kid it it still seemed pretty likely that there will be life easily findable on Mars so question is what instruments do you put into your spacecraft to detect life and you know you might have a camera see if little critters come up and say hello at the to the spacecraft web cam type thing or weather or you might have something which detects some some some other property of what you find on Mars to determine is it alive and actually back in those days one of the more popular properties was you feed it sugar and you see if it eats it basically if it metabolizes and another there was some other very bizarre ones I never really understood very well I haven't really looked at these and since I was a kid but there was one to do with the catalysis of oxygen-18 where the oxygen a-team was a successful catalyzer as well as oxygen-16 there was another one to do with optical rotation whether you've got an unequal number of left and handed molecules those kinds of things so the question that one asks oneself is okay is life all about liking sugar so to speak and I think the answer one would reasonably say is no that's not a good abstract definition of life the question is what is the abstract definition of life that's really hard to decide because we only have one example of life it's just life on Earth and all life on Earth has basically came from a common ancestor all life who exists today basically came from a common ancestor of some kind that involved RNA and you know all kinds of cell membranes and all sorts of other things so we don't have a generalization of the notion of life that for example allows us to tell you know is is that strange thing that exists and you know on the in your on your Oprah or something should we think of that as alive more or less than we thought of a stromatolite from you know from Precambrian period as as being alive and you know as a cell on earth the definition of life is incredibly historical and incredibly specific what is it's generalization we don't really know and it's generalization certainly isn't just self replication but there's sort of a question for your even in things like cellular automata which are much more rigid kind of versions of sort of simple rules it is not difficult to get self-replicating to get things which look exciting as self replicators because they're not trivial there are cellular automata that trivially have self replication but there are the ones we have to go to a lot of effort to get a self replicator but then you can get one and that sort of feels a little bit more like the case of life I mean to mention something historical you know when John von Neumann that there were several different origins to the idea of cellular automata but one of them was John von Neumann in the 1950s early 1950s was interested in sort of mathematics in the notion of life and so he he tried to sort of idealize what he thought of was as kind of the chemical soup that represented life and he ended up his friend Oscar Morgenstern of economic game theory Fame and then another person Stan Alam of hydrogen bomb Fame actually sort of in different ways suggested to Vaughn Diamond oh you should consider these discrete systems but then which turn out to be like in his case like two dimensional cellular automata but von Neumann was so convinced that getting self-replication was hard that he ended up constructing this incredibly elaborate cellular automaton like thing with you know I I forget I think it was a twenty six thousand cell configuration of this very complicated thing with with huge numbers of rules and so on to get self-replication and they thought gosh is is like life because it was hard to get and itself replicated but actually I don't think self-replication is a great test for the existence of life I think in the end there is no bright line of what is abstract life beyond the statement that it is sophisticated computation that's a kind of a necessary feature for anything that one would reasonably call life is that it not be computationally trivial and I think really the operational definition of life is it's computation operating at a molecular scale and that happens all over the place but we are the computation that happens at a molecular scale in us is a little bit more understandable than sort of computation happening at a molecular scale in a generic you know fluid or something like this because it's not completely understandable or we do we would have solved all of medicine but that's a separate issue oh my gosh this is now this is now gonna show me up as a as a as a as a non-professional and philosophy is the model substantive list or relation estate background independent I wonder whether Jonathan might happen to know from his philosophy background what those I'm sorry I you know it's really embarrassing because my mother was actually a philosophy professor in Oxford and so I was exposed when I was a kid to lots of lots of kind of analytic philosophy kinds of things and I'm sort of just embarrassed that because as a kid I always said if there's one thing I'll never do when I'm growing up it's be a philosopher that I probably didn't pay as much attention as I should have done but okay Jonathan can you translate those terms do you know they yes yeah and I think the answer is that it's let me get this right I tell us what the terms mean okay so to rip some relational IQ it's my understanding relational ism is the notion that there is no such thing as a background space that basically all that you your fundamental ontology is just relations of material objects to each other and substantive ilysm is that is a statement that there actually exists a background space in addition to the material objects in their relations I think what we're proposing is basically substantive lism modulo relation ism or possibly the other way around where you know I would think that we only have background space and the and the relation list stuff emerges from it would be my maybe you have well okay so what one feature of these models is spaces all there is there is there isn't sense in a sense everything about the universe is made of one kind of thing and it's that kind of thing turned into sort of the configurations of that one kind of thing define all the things that we see in the universe so in that sense it is it sounds like it's a substantive list kind of thing on the other hand that thing is not a thing in the sense that one is used to talking about things because we're used to talking about you know the physical object that is you know that how an actual that sort of has has has pieces that it's constructed of and so on and what we are what we're talking about is space being made from discrete points where the only thing you know about those points is how those points relate to other points you're not you there's no sense in which there is a a kind of a a a background to space that is independent of the existence of the points in space know that space is made of its points and their relations it is not something where there is sort of a background and where things live within that background but on the other hand the background the the space is everything it's not it's not that something so there's neither a background that is outside of the model but it's also the model does not have the model is all about space itself okay given different rules that may governor structure is it possible to derive conflicting results within the proposed theory okay that's interesting so so in a sense the uncertainty principle and other things in quantum mechanics are like deriving conflicting results in a sense the fact that there is quantum mechanics is the consequence that at least temporarily there can be sort of a there can be conflicting conclusions about what the way the world is working and I think that's probably the the the best way to say that do you think there exists an elsewhere outside the universe where the computation of this universe takes place I don't think so I think this model is a representation of how our universe works and there's no substrate on which this model is being run it's it is it is merely it is this abstraction that is the model is an abstraction of how the universe works and it is just it's that the universe just does these things according to the model it's not that the model is operating on an elsewhere as you put it that doesn't exist within an elsewhere it just is this sort of this this thing now now having said that the sort of interesting to to think about that as a yeah I mean I I think as I say I think that the main point is just the model is a representation of what the universe is doing so there's no there's no sort of necessity to say what does the model live on top of and there's no kind of you know it's living on the back of a turtle and then it's Turtles all the way down type thing it's it's just this is this is the thing that is a representation of what goes on in our universe Jakob consciousness question is there any place for human intentionality to change or at least to shift the probability of which pathway the deterministic universe will take sorry don't think so I mean I think the the answer is that in this well it's a little bit complicated because in this model things are determined the the the the evolution of the universe okay there are these quantum branches and things but the the sort of the super description of things is completely determined and there's no way to say that the universe just is what it is and it does what it does now what does that mean for our perception of consciousness and so on so one and I'm not sure that there's more to figure out here about about how to think about this but one of the things that's kind of new for me is thinking about this notion of these different reference frames these different description languages that we can use to understand what's happening in the universe this idea of this rule space relativity idea that there can be many different different ways to describe the universe which in some sense are equivalent but they're nevertheless locally their actual description the actual experience of those things is front and so I I think that there's a a sort of the the the choice aspect of dealing with the universe may be more in the sense of this description language that you are you are that there is some in some at some underlying level there's kind of a sort of a a version of what's what's going on but then you have a way to understand what's going on and your your description your way of understanding it is sort of arbitrary so in other words the the the particular put it this way the particular firings of neurons in your brain those are determined by the by the way the universe works but if you were to look from the outside and you were kind of to write down a narrative of what's happening in your brain there might be many different narratives that you could write down and those narratives are kind of the meta description of what's happening and I think there's freedom in those met in that meta description it's not a freedom in how your neuron neurons fire but it's a freedom in the representation of of what it means for your neurons to fire in that particular way that's my that's my best understanding of that right now I think it's really quite interesting that that these different kind of reference frames these different description languages for representing the universe might give one a way to really understand these different sort of approaches that that people have developed for making sense of the world so to speak from the you know the sort of very scientific approaches to making sense of the world to more sort of psychologically oriented approaches to making sense of the world and these things are there they can still describe the same world but in but in different ways and by the way the the ones that we have that came out of our biological evolution our sensors and things like that are probably this this very very very microscopic corner of all the possible descriptions one can have of the world and you know the for the putative aliens so to speak one imagine vastly bizarrely incoherent descriptions of the world that in are in some sense still describing the same world underneath okay from Ted here limit now we got that one already from Andrew how do these models relay the Archimedean and platonic solids in sacred geometry boy it's convenient that on my desk I happen to have from from a whole different life stream I was doing I happen to conveniently have a little platonic solid here umm the well so I don't completely know what sacred geometry I've sort of heard of that and I don't really know what that is but but back in in antiquity there were a bunch of theories about the world being made from platonic solids for example and for example this guy the dura he drew was represented quintessence as maybe the thing from which the heavens were made so to speak if I remember correctly um the question of whether there is a I mean I think the thing I would say is that that kind of theory of the world is made of platonic solids is a fascinating allegory for the kind of thing that we're now doing projected back into the kinds of things that people knew about in antiquity I mean in antiquity the very notion that the world might be made of a set of identical elements that would be where the arrangements of those identical elements might lead to the world as we know it that's a super interesting notion that found another place in atomic theory and so on and we're in a sense continuing that tradition we're saying the world is made of these identical elements and their connectivity and so on so in a sense we're we're continuing a tradition that started with people like Democritus pre-socratic philosophers and so on and that was sort of submerged in some sense in the kind of deluge of let's describe everything in terms of mathematical equations where it isn't so much of a kind of a structural understanding of what's going on so in that sense I think there's some some resonance with those things although you know the the the ancient Greeks didn't have computers and didn't have well they might have had the Antikythera device which was a kind of a mechanical computer like thing and maybe they were those things were actually fairly common but they didn't have I mean the thing that is really in my lifetime for example has been really a dramatic thing is the fact that computation is now so ubiquitous in our world that we can start to get real intuition about how things work computationally and that just didn't exist before and that's I think why you know insofar as we've been able to make some progress here that was not really accessible to for example the people a century ago who kind of initiated the the the dominant theories in physics today you know general activity quantum field theory those kinds of things at that time nobody was thinking about things in terms of computers you know the Turing machine was still when when when general authority was invented in 1915 the the Turing machine was 21 years in the future and even when Turing machines have been invented people didn't take them seriously for physics until perhaps even my own work in the 1980s so it took when Turing machines were first invented I mean well first point was that that um it just wasn't clear how general Turing machines were it wasn't clear that you know did Alan Alan Turing's original idea was let me idealize you know what bank clerks do and try and make that into something that can be mathematical had done what amounted to the same thing in 1931 with girdles theorem he has this wonderful footnote that says that you know girdles theorem which was sort of it essentially a way to turn arithmetic into something computationally in which you could program other things um that maybe this is not maybe this doesn't apply to human minds and he has some some bizarre footnote about how this could correspond to the Russell's theory of types but not ordinary types types some I think he says something about ramified into the transfinite which I mean we can decode what that means but it's just kind of he had the idea that the human mind is somehow much more infinite than the kinds of things that he was describing you go those theorem and so it just wasn't clear that physical kinds of things like like human brains and so on would be subject to the same kind of mathematics is a ssin the same kind of same kind of idealized representation as the things that occurred in girdles theorem or occurred in entering machines and that was that was an idea that really didn't exist I mean back when I started talking about this in the 1980s people were saying you're just wrong it can't possibly be that way you know we know that physics is governed by partial differential equations that represent continuous effects of this on that and so on you just can't represent that with a Turing machine I think that that has become gradually you know less of a a shocking thing and the idea of that term that there could be this generality to computation has become more popular and I think now with this this model that we have I really I am now certain I have there's no doubt in my mind the universe is computational and is of sort of equivalent power to something like a Turing machine I think the how do we get to all of that I was I was talking about why why the ancient Greeks couldn't have come up with a theory that we have and the real answer I think is that the intuition about computation the idea of computational irreducibility for example just didn't exist it even didn't exist in even Alan Turing didn't have the idea of computational irreducibility really he proved the undecidability of the halting problem he proved that you couldn't in a finite time generally work out what a Turing machine will do after an infinite time but somewhat amusingly the very first program ever written for a universal computer which was in our Turing the original paper is full of bugs so and bugs are kind of one of the practical manifestations of computational irreducibility you can't readily predict what your program will do just from seeing what the rules are so to speak and that's so so in a sense the intuition that there might be bugs the intuition of comput that the typical programs behave in ways that are hard to predict is is an intuition which really I mean for me arose from experiments that I did in the 1980s of actually looking at computational processes and seeing what they did and and it was a big surprise to me that that was a phenomenon that was ubiquitous I thought maybe there will be some very special computation you could set up where you could get undecidability or something but no actually it's ubiquitous thing and that's an intuition that just is I think a new intuition that we just didn't have until very recent times I mean I kind of view that that intuitional realization that you can get very complicated behavior from very simple rules that you can get phenomenon of computational irreducibility that's what kind of unlocks the possibility of the kind of theory we're talking about now I mean that there was there were a few other sort of things I mentioned before maybe we'll talk about it later the the sort of the wrong turn of ik waiting the nature of time to being like the nature of space all right let's keep going here okay Brian on the live stream if the universe is deterministic does that mean we will access all the hidden variables um that's a complicated story because in other words could we ever know sort of exactly how a universe will evolve well the answer is not in practice because even to go measure to go that's interesting point actually I mean to go as an entity within this universe to go collect all the data to know the state of the universe everywhere is not something we can do and we can't do that for reasons of it's an interesting point actually interesting points we worth worth worth nailing that down a bit more carefully but the basic point would be if you think about the causal graph we sort of live in the causal graph so we the events that correspond to the actions that we take our events that exist in the causal graph and they can affect other events in the causal graph but if our goal is to go sample the whole universe go know what the state of the whole universe is and go sort of bring it back to our brain and then go and evolve forwards there are many reasons we can't do that not least because sort of our brain that's going to figure out what the universe is going to do has to exist in the universe but that Quotes brain is supposed to be representing the whole universe and we don't get to represent the whole universe in something smaller than the universe that fact is another consequence of computational irreducibility that there's no sort of sub representation of the whole universe that isn't the universe itself so I think the answer is that we can't really can't really determine that okay next question does your theory depend on the axiom of choice I really don't think so so I'm gonna hope Jonathan might have a comment on this but in the in so the axiom of choice is it's something that comes about in sort of formal set theory and formal set theory only one only really cares about that when one is dealing with the truly infinite and in our model the universe is big it might have had ten to the five hundred events in it but ten to the five hundred is not infinity and so we don't have to have this kind of axiomatization of infinity that involves things like the axiom of choice Jonathan do you have a better comment yeah so I think our models kind of can't depend on the axiom of choice because they're explicitly constructive so one of the reasons why the axiom of choice is whether okay there are many reasons by the axiom of choice is philosophically sort of controversial in the foundations of mathematics we know girdle proved that it was effectively independent of the standard axioms of set theory ZF set theory and it's C it sort of corresponds to a statement that's perfectly intuitive until as Steven says you deal with kind of infinite sum particularly uncountably infinite sets and then it implies a bunch of really rather pathological results about the existence of non measurable sets and things like that but from a more for a more philosophical reason it's also very undesirable because there's a general approach to doing mathematics which is the sort of constructivist or computational issed approach to doing mathematics where the idea is you don't want to have non constructive existence proofs in other words if I prove something if I prove a theorem that says there exists a I don't know a topological space with such such a property I should actually be able to construe to that space by some finite algorithmic procedure there should be some finite rule that constructs that space I don't just want to have an abstract existence proof that says this thing exists but I have no idea what it is or how to construct it and it turns out the standard axioms for mathematics at least in the finite case are pure can be made purely constructive as long as one omits the axiom of choice for the axiom of choices is Inc is through inconsistent incompatible with a constructivist formulation of mathematics our models are purely constructive because they're explicitly set up to be computational so in particular they can't depend on any non constructivist mathematics like a Otzi or related things how you should define for people axiom of choice just because some people okay so so the okay so the basic idea is if you have a whole bunch of sets right and they have and they're non empty so they so each set has some elements in it then you can define this thing called a choice function which basically just takes an element from all of those sets and assembles a new sets well you've just chosen an elements from each from each set and the accent of choice says that as long as the all the sets that you started with were non empty there's a new set that you generate by just choosing one element from each sets is itself non-empty now that seems completely intuitively obvious when you're dealing with finite sets or even countably infinite sets but that's there it's completely uncontroversial if the sets you have uncountably infinite then you run into these issues and then it's much less clear whether the axiom is actually intuitive or whether it's actually wrong and that's that's where you get into these constructivist issues okay next next question here from Lex what are the limits of mathematics and computation well I mean there's questions about limits within mathematics itself and they're questions about limits within our universe so you know within mathematics itself we already know from things like girdle's theorem that there exist statements that can be written down that sound mathematical that are simply not accessible by the axiomatic system that is defined in mathematics so a girdle originally had this statement this statement is unprovable and his main work involved showing that the statement this statement is unprovable effectively be compiled into a bunch of statements about mathematical equations involving integers that were visibly things that would were sort of within the domain of sort of theoretical arithmetic to investigate and so so there are things there where it's where there are statements that turn out to be mathematical that statements of mathematics that are independent of the axioms as we've set them up in mathematics not one one thing to say is that mathematics as it has normally been practiced since about the 1880s or so has been on this axiomatic kick okay what is what what does that mean it means one says just build mathematics as a kind of logical system oh and just says assert that the following things are true then what follows from that in the earlier history of mathematics I think mathematics viewed itself as being much more an idealized description of the real world you know I think Euclid although he did write down axioms he thought those axioms were just idealizations were just sort of precise versions of what was just true about the world things like two parallel lines can't cross which Euclid thought was just a true statement about the world that he was making precise so that he could build a logical system but you didn't think that he was asserting that just as an arbitrary thing I mean what Jonathan was just mentioning about the accident of choice that's an example of something where somebody can just say the you know we choose to make it true we choose to make it not true we don't have any intrinsic reason because of the way the world works for us to choose one thing or the other and so something started around the 1880s was people just saying just imagine it works this way just set up these axioms then see what we can prove from that and one feature of axioms is that they they will be things where the ice images don't have anything to say about they the axioms just are the something could be true not true you just can't prove it from the axioms the axioms only to find a sudden said the thing for example Goodell ran into that because Goodell was most interested in the sort of understanding the theoretical implications of pianos or axioms for arithmetic and so for example when we do arithmetic we think we know what integers are and you know we can just count them on our fingers and things like that but when we're dealing with the infinite it we can't count on our fingers because we only have a finite number of fingers um and we and so it gets a little bit more complicated and one of the consequences of girdle's theorem so the piano axioms say things like you know for any things that numbers you know X plus y is equal to y plus X or some slightly more complicated criteria involving functions and recursion and things like this but to our induction rather um but um the in one way to think about those axioms is to say we are talking about these things X Y whatever and we are talking about those things which obey these particular axioms okay show me one of those things well one example of one of those things are the ordinary integers that we can count on our fingers but one of the things that girdle showed is that there are non-standard arithmetics there are things that obey the axioms of pianura rithmetic but they're not like our ordinary integers at all in fact they are totally bizarre they have non computable versions of addition and all kinds of weird things like that but what Google showed is that there is no finite axiom system that you can ever hope to construct that has the feature that it will constrain you to get the integers are nothing but the integers so in other words it's this idea of axiomatization where you're saying let's take a system and let's make constraints on the system and let's hope that them with those constraints the system describes only the kinds of things we're talking about that's the way of doing mathematics that's been popular for a hundred and twenty years or so at least at a formal level but it's a it's a weird way to do things it's a very sort of in my view rather backwards way to do things the alternative is just to say I've got these rules the alternative which is much more the computational view is I've got these rules now just run them and that's what we're talking about in this theory of the universe is we've got these rules now just go run them so it's some and so we can ask the question then can we you know to what extent is axiomatization limited if axiomatization means the way mathematics then there are limitations owns axiomatization for example in the theory of computation the P versus NP problem the question of whether for example np-complete problems that I was gonna say like factoring except factoring isn't known to be np-complete but problems that are NP problems whether they can be done in polynomial time big big sort of story and issue for whether you know public key cryptography is secure etc etc etc um that question of P versus NP I think might be undecidable with respect to the most obvious axiomatization of arbitrary of infinite computation so to speak and that's an example of where that those are theoretical limitations those are limitations from within the system itself about how sort of what what's what's provable axiom axiomatically then there questions ok so let's take a question in physics so ok first point is if we're right that we're on our path to finding the fundamental theory of physics we just turned physics into a sort of in a sense a logical system where we can just take the rules of physics and deduce everything that happens but now you'll ask me ok so given that can you determine whether warp drive is possible you know fast and light travel or something like that can you can you prove that faster than light travel is impossible well maybe we can maybe there's a straightforward proof but maybe it is arbitrarily difficult to determine that maybe we can imagine some bizarre collection of masses and and processes that go on in the universe and we can assemble as giant machine and in the end the giant machine will make a warp drive um right and and so can we prove that there is no way to assemble the giant machine well that turns out to be something that is kind of a girdle theorem like question that's something that is ensnared in computational irreducibility does there exist this configuration does there exist this way to take this does there exist a solution to this equation involving introduced as there exists a way to take these tiles and uncover the infinite plane with them these are these are questions which can have does there exist any such thing may not have a may have an answer that is arbitrarily difficult to determine in in an axiomatic system now having said that in our universe it's big but in the current estimates we have maybe it has 10 to the 400 elements 10 to the 400 is not infinity so in fact it becomes a completely in principle determinable thing whether it's possible to make that warp drive because what you could in principle do is you can enumerate in principle all possible configurations of those 10 to the 400 elements and you could just say are any of these warp drive if no we can't make a warp drive in our universe if yes we succeeded now the problem is if you think about how would you actually do that well there might be you know whatever it is you know 10 to the 10 to the 400 configurations or what 10 to 400 of the 10th or 400 whatever it is configurations of that system it's an it's incredibly huge and there's absolutely no way we could possibly run that computation in our universe so there might be in some sense the the undecidability of the existence of warp drive for example might be something that is both something that we can say for an infinite if we allow sort of we can have no upper bound on how difficult it might be to determine to find a warp drive and then we could say that within our universe it's not accessible just because our universe has a finite number of elements in it so I think that's some I mean this there's probably more to say about that but that would mean I first cut about sort of limits to to mathematics and computation I mean I think that at least at a very theoretical level someone to add something there well I was just thinking we could mention something about this new kind of proof that's a sort of possible byproduct at root of the rule space geometry so this is something that Steven and I disgusts I think only a few weeks ago now it's relatively new idea relatively unformed but the idea is you know rule II or space effectively contains not just our universe but if it you know different branches correspond to different possible you can think of them as either corresponding to different encodings of our universe or different into you know different kind of the universes and one possibility is you can think of if you prove a result in mathematics you can think of it as being proved for a particular physics a particular physical universe but the rulli or space contains sort of the set of all possible physics --is so in other words if you can prove a statement and effectively quantify it over the entirety of rule space you're quantifying over all possible physics --is the one interesting sort of philosophy of math question is does that correspond to a valid proof that that sort of theorem is true in some mathematical sense that's independent of physics and we have some ideas about sort various complexity theoretic theorems that you might be able to prove in this way and I think we came up with a sort of preliminary name of like NIT see and exhaustion as this new method of mathematical proof right so it's it's like NIT seen because you're talking about kind of all possible worlds and it's an NST sort of analog of these mathematical proofs by exhaustion because you're quantifying over all over the space of all possible physics as a way of proving a statement about pure mathematics yeah that's an interesting point which I had almost forgotten even though that was only a couple of weeks ago or something but um yeah this this this notion when you say you're quantifying over all possible integers or all possible functions on integers this is a really this is a bizarre twist we're quantifying over all possible physics --is um and you know what is the what is the status of a thing that is true in all possible worlds so to speak and does that what is the notion of truth in something where for any possible physics this will be true but is that does it mean it's really true true or does that mean you know could it be the case that in some that there would be some for example for example if there's if there's a Piper computer in the picture then it won't be true then our quantification over universes wouldn't capture that so the question then is when there are and I think that that could be thought about in terms of I never remember how these are work Sigma and PI n type sentences in in mathematical logic that we can think about those kinds of quantifications as being like quantifications that include either all possible computational universes or all possible hyper computational universes which which then lead to a different kind of thing okay Barry is asking the hyper graph reduces to some some initial condition is there something special about the initial conditions for the universe so one thing to realize is that you can trade-off initial conditions and rules particularly when you're living in this rule space of all possible rules one of the rules you can make is the rule that makes for example something from nothing so there's sort of a trade-off between rules and initial conditions and I think there's a whole separate issue of you know let's say we find a simple rule for the universe maybe the initial condition for the universe with that rule is something quite complicated I mean in a sort of science fictiony weird point of view what if the what if for this particular simple rule the initial condition for the universe I'm just making up a kind of science fiction scenario but what if the initial condition for the universe is then this this giant you know sacred text of the universe or something that would be that is the initial condition for the universe what if what if in fact the initial condition for the universe is not with that respect to that rule something simple but something very complicated now the bizarre possible at the bizarre question then is oK we've got this thing we represented as this hyper graph we've got the hyper graph that started the universe and it turns out that with this particular that we then have found this really complicated hyper graph that started the universe maybe it has a million nodes in it okay and and we know that the rule that we're using that that rule doesn't apply any further back this is the start hypergraph of the universe and it's really complicated and we're looking at it we got it it's got a million nodes in it we look at the thing what the heck is it and so it's kind of like the archaeology question of you know we just found Stonehenge what the heck is it we just found this thing out there what does it mean does it does it have a meaning can we attribute a meaning to it how do we how do we kind of understand what this is and I think I think that's sort of an is it I consider it sort of a science fiction scenario because I don't really think that's the that's how it's gonna work out but it's certainly a bizarre sort of thought I mean when people you know the the the bizarre kind of thing it's it's the signature of the Creator type thing as the initial hydrograph but I don't think it's gonna work out that way but it's fun to think about at least okay Spiros is asking can the existence of parallel universes be pruned by your theory in that case could it be possible for parallel universes to mingle so in in this theory in this kind of rule space relativity theory well okay so a couple of different points I think we talked about maybe a little bit yesterday in this special hyper graph it can be the case that pieces of the special hyper graph break off those broken off pieces of the special hyper graph essentially evolve the same as as any other piece of the special hyper graph and in fact you don't even have to break off a piece of the spatial hyper graph you could just have a causal disconnection in the causal graph right which and that causal disconnection is very much like black hole formation but either way you can have these separate you know sort of separate pieces of universe that are have separated off from the main universe and no longer causally connected to the main universe but the first sort of level is but they keep evolving according to the same rules as the universe so they are they are separated universes but they're evolving according to the same rules as our ordinary universe another question is what about the the possibility of universes with different rules so for example I had always imagined that um my my big sort of philosophical conundrum for the last thirty years actually had been let's say we find the rule for the universe here it is we're holding it in our hand now we ask why that rule and not another one and and the most obvious answer would be well all possible rules exist somewhere they're all different universes they're all running in parallel we just got a signed universe number 3746 or something that's our universe that we all exist in and the others there are some weird extra you know weird we shouldn't be calling them extraterrestrials we should we call in extra universals or something folks who live in a different universe who are um extra universals who live in in this sort of separate universe and are just doing their thing in that separate universe so that was kind of the the view I had of how it would work out and then there's this big question you know why did we get this rule why did they get that rule and so on but then what we realized more recently and I sort of had a suspicion about this for a while that for an entity embedded within the universe that in a sense all possible rules were in some sense equivalent and so in this notion of rule space relativity the idea is that you can sort of that all possible rules can be applied but your view of the universe you're kind of coherent view of the universe is based on a particular way of kind of slicing the this this sort of ultra multi way graph of possible possible evolutions of the universe and cause long variance implies that which slicing you choose will ultimately have no consequence but it will certainly affect the description that you actually give of the universe so your your particular description is is something kind of kind of that is particular to you and there can be other descriptions but it's all of the same universe and so I think that this idea of rule space relativity in some sense is a proof that there really is only one universe but our description of the universe can be utterly incoherently different so the what my the extra universal so to speak are the kind of extra description also to speak the the the the the the the critters who exist in the universe where their description language is utterly utterly different from ours so you know a very very very simple example of this that is kind of fun to think about and doesn't quite work all the way but it's kind of fun is so in our world we you know one of our principle senses is site and the speed of light is quite fast speed right is quite fast compared to the speed at which we can process things in our brains so when we look out into the world and we don't look too far away we don't look at stars and things like that most of what we see we view we sort of synthesize a slice in time as being everywhere in space that we can see at a particular moment in time that makes sense to synthesize and and we have that sort of view of the world ok so let's say we were dogs for example where olfaction smell is a much more important sense well so that let's imagine forget the eyes just say we do everything by smell ok well then our view of the world then it's a little bit of a different situation because the diffusion time for a smell from you know from a hundred feet away is very long compared to the processing speed of a brain and so it's no longer the case that we can synthesize our world as being this thing that exists in simultaneous time slices where we see sort of a moment in time everywhere in space that's not what's going to happen it's an in fact one can imagine sort of a version of relativity that would be perceived by a dog so to speak where the speed at which sensory data comes from distant places is slow compared to the processing speed of the brain and so we can start trying to imagine what it's like to be sort of a a a critter with a different description with a vastly different description language for the universe it's very it's sort of humbling to realize that that there can be such utter ly different description languages that will look nothing like our physics so to speak and that will be ways of describing universe that are nothing like our physics so in that sense there can be parallel universes with respect to the perception of the universe although in the end the the machine code is exactly the same it's exactly the same universe but it is this this utterly incoherently different and I mean one could certainly imagine it's a scenario where you know I talked before about how intelligence life things like that are really hard to define and and I think they really just boil down to computation but where you could sort of imagine at sort of a a conceptual level saying well there's this intelligence so to speak that has a completely different sort of perception of the universe from ours completely incoherent and completely sort of not something we'd pick up in our thinking of physics so it's sort of an interesting consequence of these kinds of things but tum now the question then is okay so then the question is in that case can you communicate so is it the case and it's kind of like the the sort of you know our communication skills are pretty limited I mean we can't even do animals very well you know the question of whether you know communication involves sort of it's it's this issue of can we outside of our sort of boundaries of sensory information and so on you know to what extent can we communicate the communication is typically about as a practical matter for humans is about I've got a thought in my brain I'm going to turn it into for example language some symbolic representation and that's going to reform some thought in your brain we get to do that more directly when we have computational language that can go computer to computer in a way that's a little bit different from the you know brain to human language to brain type transformation in a sense computational language and as part of my sort of what I do for a living and spent my life working on is kind of the computational language that essentially allows us to encode knowledge in a way that can be sort of passed down so to speak in a more efficient fashion than the pure say it and reform the thought in another brain type thing they're kind of it's a more streamlined form of communication than were able to do with with pure human language and the reforming of thoughts and brains but this question of communication can you reform kind of a meaningful can you sort of reform that thought in a way that's sort of consistent with the way it started off well it sort of depends on the substrate that you're working within and and I wrote this post okay so little bit of a story I have a friend named Novak who's been working on a a strange project to put artifacts from our civilization on around the solar system on the grounds that if something bad happens to the earth it'd be really good to have that little beacons of this is what we achieved as a civilization out there for the extraterrestrials to pick up long after we're gone and it's certainly you know if you look at the Babylonians the Egyptians it's kind of cool how much we know about them based on the artifacts they left behind that described features of their lives and so one of the questions is what can you put out there that is sort of the the thing that describes what was achieved in our civilization and potentially what was there is there sort of an abstract thing that you can put there but sort of expresses the greatness of the achievements of our civilization and certainly there are details there like well this is you know like the dioramas from you know there you find in Egyptian pyramids and things of you know this is what it was like you know wooden figures of this is what it was like in for a boating party on the Nile back in 2000 BC or something and you know but but the question is can we can we do something a bit more abstract and what would we do and it's a it's a gruesome business because if you look even at archaeological artifacts it's really hard to tell what did this mean what was the what did you know what is that is there a translation of meaning from back in those days to today and by the way there's no nothing to say that what was you know there's nothing invariant about meaning it's it's something that comes up I sort of veering into some other kinds of philosophy but but in the question of AI and the question is so one of the questions that people are often concerned about is what are what will a I automate will we just automate everything and one of the points I often makers one thing we you're not going to automate is the is is we can automate the doing of things but we can't automate the deciding of what the goals are deciding of what the things we should do are because in a sense the the assignment of goals is something there is no abstract notion of what goals should there should be goals are something that are the specific of what came out of our biology our civilization and so on there's something that are are sort of specific to our own history so to speak there's no abstract notion of the goal it's just like asking what is the goal of the universe you know if we have a theory of the universe we could say what is the goal of the universe I don't think we can answer that in any meaningful way I think that goals are something that tie back to sort of a human story a human narrative about what the point was supposed to be um I think I got very far afield I think I was talking about some communicability between sort of different description languages for the universe and sort of beings in a sense that might exist with respect to these different description languages and I think the the thing that I'm one of the points are making is there is it's very hard to have sort of a ground truth when your fundamental description of the universe is different I mean it's hard enough to to have a discussion you know when you're sort of frame of reference of of life is different to have sort of a discussion across that chasm even even in the human case let alone when you're sort of ground truth about how the universe works is different it's difficult to see how that that kind of communication would work so that's sort of a an answer to the kind of the mingling of communication between sort of these different description languages of what one can think of as parallel universes um okay is saying what's happened is I see I understand the question it's sort of God has Mathematica version infinity and is running a manipulate yeah I mean I think that this this whole question of sort of the the interaction of theology with the kinds of things we're thinking about I think it's pretty interesting and I think that one of the things that's really striking to me is if you look at kind of some of the particularly earlier theological writings are no expert in these things they have a lot of kind of grappling with questions about sort of what does it mean to have a what does it mean for there to be a beginning to the universe what does it mean for that to be for example one of the ones I think Einstein was a big enthusiast of Spinoza who had this kind of this kind of view that I suppose is summarized as you know the universe is the thoughts of God is a representation of the thoughts of God and I think that's kind of a very interesting sort of poetic way of thinking about something like what what what what we're sort of talking about as in there is this there is this this kind of firm there is this inexorable thing that is generating the universe and we get to sort of see that an external process happen as the actual evolution of our universe and it's kind of the you know the Spinoza version is sort of the the the operation of the universe is the kind of embodiment of is is a is a rapid is in some sense the actual operation of the universe is kind of the thoughts of God I think that's kind of a an interesting way to think about it I think that the as I say I think actually I'm hoping to hoping get a friend of mine who's a theologian too to join us on one of these live streams and maybe we can have a more detailed discussion about some about some of those those kinds of questions I think one of the ones that I'd sort of been hoping that there would be some kind of conceptual framework was this prime mover question of sort of how do you why do you actualize you know so okay so a Spinoza statement the universities like the thoughts of God that's kind of explaining why there's an actualization of the universe if God exists then God has thoughts and those thoughts are our universe but in a sense that presupposes that God exists and the question of why is there something rather than nothing why are things being actualized that's a different question and I'm so really curious whether there is sort of a framework for thinking about that would you say that it's living on the backs of four elephants that live on the back of a giant turtle you know I have to say we we in in the theory of swag for this project you know there's that there's this sort of saying of um there's a I don't know if this story is probably apocryphal but I think it's told about Bertrand Russell I think he was he was doing some some talk about about the universe and apparently some someone came up to him and said you know no you're wrong about this theory of the universe it's the universes all exists on a on a on a you know it's all sort of constructed on the back of a giant turtle and he was saying well what does the turtle what does the turtle standing on ER the person said well the turtle is standing on another turtle say well what's that turtle standing on well said the person it's Turtles all the way down and that's been a kind of a quote of among scientists at least about kind of a a view of how things might work and so we in the in the theory of the swag of this project we were thinking about making some t-shirts about something like it's hypergraphs all the way down so to speak or some such other other statement so I think we're we're not in the we're not in the kind of turtle or the other thing about that that um that t-shirt there are there's a great diversity of different geometrical forms that come out from these hypergraphs and there are definitely ones that look like turtles so expect that t-shirt um ha so pi lang says I asked another streamer about a model platonic solid they had on their windowsill they said what you mean the candleholder ok so i'm i'm i'm more into platonic solids than that um ok so i can't read any i can never read these these handles eh ee how is a good exercise actually in semantics come it's a good exercise in segmentation because some of where are the words in these in these handles but me right so I eat something or other handle so in your model how would you describe knowledge should we see it as some kind of recurring causal path interesting ok so knowledge well gosh I've thought a lot about knowledge and how to represent it computationally you know knowledge I think is something that I think I would say knowledge is a pretty human thing that is in our efforts in more from language for example to capture computational knowledge to capture things about the world things about mathematics whatever else one feature of what we're capturing is it's not all the possible things that can happen it's not all possible computations it's things we happen to care about now that might be knowledge about crimes it might be knowledge about movies but it's things that it's not we're not saying we're not capturing in there what are all the configurations of atoms that exist in the world we're saying there's a configuration of atoms and it corresponds to the Washington Monument or something and that particular configuration of atoms we consider interesting the one that is the configuration of atoms that's this lump of air that somewhere around wherever we don't consider that interesting we identify as these symbolic lumps of knowledge these things which we have considered as a result of our civilization to be important and so I think knowledge is intimately tied to kind of what we have considered important in our civilization it is not sort of the arbitrary it is not something where the arbitrary computation is not really about knowledge the arbitrary configuration of things in the universe isn't really about knowledge knowledge as a as a human tied thing I think and so in that sense we're we're capturing um you know to get to knowledge you have to get sort of all the way to humans I think I think in a sense what we're trying to do as a set a few times as is sort of we're trying to bridge this thing between what humans can understand what computers can can represent and how the physical world works and Jonathan looks like he has a comment to make well I was thinking one of us should probably talk about branchial black holes with respect to knowledge sure talk about brown field black okay it's very different that's a very different take on knowledge than than what I've just been talking about go ahead right right but it is at least a form of it that's consistent with all models so so I should say and this is actually not unrelated to the sort of consciousness question that Stephen was talking about earlier that each of our each level of graph that we consider sort of gives you a new intuition for what it means to be a conscious observer with respect to our models so in the causal graph a conscious observer is a is effectively one of these relativistic hyper surfaces so in other words you can think of a contrary you can define a conscious observer in the relativistic case as someone who sort of views a bunch of space like separated events as being simultaneous as Stephen kind of alluded to in the case of a multi-way graph then you have this branch like hyper surface that's the notion that's our notion of a conscious observer so then you think of it as you think of the observer as being like an entity that makes an equivalent that views a bunch of distinct quantum states a bunch of states in the branch field hyper serve brunch like hypersurface as being somehow equivalent and then when they when they try and perform a measurement that's kind of isolating one of those states and similarly in the rule space you think of an observer as being a hypersurface in the rule space and then so therefore though there's some entity that somehow views are a bunch of different rules as being computationally equivalent so that in each case the observer is some time ordered sequence of equivalence classes between between different kinds of states so the interesting thing is that gives us a way of representing what it means for a conscious observer to have memory or knowledge so in the quantum mechanics case the way that that were way that it can work as you say the the generational multi-way states which are these things we talked about earlier which if you you don't need to know the details of how they're defined but basically they're the things that get walled off when you perform a quantum measurement of the kind that Stephen was describing in the livestream yesterday and earlier today so if you perform a quantum measurement you basically freeze time around the state that's a kind of generational multi-way state and one of the rules about that about of the multi way evolution graph is you can kind of only make measurements of states of the kind you've already seen on previous hyper surfaces because the generational multi-way states get generated from a superposition of states that occurred on a previous hyper surface so another word this is the philosophy one yeah people understand quantum superposition here fine okay they keep going keep going well I might get decode this in a minute yes no good please do please do so so one of the things that means is you can kind of as you progress through time in the multi way evolution graph the kinds of experiments you can set up the kinds of observations you can perform are informed by and get more sophisticated as a result of the outcomes of previous measurements and observations so you can think of that as being a minimal model of the observer kind of learning what what things are true and how to setup better experiments the same thing occurs in rural space so in much the same way as you set up a multi wave black hole around the state when you perform a quantum measurement when you kind of develop a theory when you do when you when you increase the sum total of your knowledge with respect to rule your space you are effectively producing a rule your black hole these corresponds essentially to pockets of competative you know the majority of real space is computationally irreducible which means it takes you know it's it's connect it's quite sort of causally connected but it takes an irreducible amount of time to travel from one point in space to the other but sometimes you can produce a region that's causally disconnected and those are like the pockets of computational reusability and so you can think of sort of an ultimate abstraction of the process of doing scientific investigation is the construction of these rule black holes wherever they're possible wherever there exists pockets of reducibility you're trying to construct kind of black holes in rule space around those pockets yeah that's actually that's very interesting very different end of the story from what I was talking about I mean basically what you're saying so another way to think about what you're talking about is you're you're asking for a very low level kind of machine code level version of what knowledge means in in terms of you know can you know to what extent can you take the sort of microscopic degrees of freedom of the universe and kind of aggregate them into something which you can view you can describe at a sort of higher level and that's that's kind of what you're talking about is a there's a kind of a I suppose in some sense it's to what extent you know ultimately what we try to do with things like language is to turn all the complexities of the world into the simple symbolic representation of what's going on that's a very that's a very human end that's the very human end of making knowledge a very machine code end of making knowledge is let's take these little micro operations that we're going on and let's find a way to aggregate together some number of those micro operations and that's that's I think what you're talking about and that's actually it's pretty interesting to look at that's more like couldn't coarse graining in statistical mechanics things like this it's that's a different end of the story it's the less human end the more physics and computation end of the story but that's that's that's quite interesting and and probably one should yeah I there's a pretty big distance between those but it's it's quite interesting to look at both of them um let's see what is randomness is it like the possibility to act against the laws of the universe okay so we in in this model of physics there is no quotes true randomness everything is kind of determined so I have a friend named Greg Creighton who was one of the originators of algorithmic information theory and an algorithmic information theory one's interested in saying one's interested in sort of assessing how random something is by saying how long is that let's say you have a string of numbers you can say the string of numbers is truly algorithmically random if there is no program that will make that string of numbers that's much shorter than the string of numbers itself given the string of numbers you can always have a program that is basically it just contains the string of numbers and just says here it is that's what the program does and that but that program will be the same length as a string of numbers so a general question it's sort of a general question of modeling and fitting and so on is can you have a description of that string of numbers that's much shorter than the string of numbers itself if you can have a description it's much shorter then you say it's not random because I've got this short description okay so in that sense for example the digits of pi which as far as we can tell statistically seem completely random if we say oh that the same number of ones and sevens and the digits of pi yeah they're the same number of ones and sevens but at an algorithmic randomness level the digits of pi aren't random because after all they just come from that simple program which says you generate the digits of pi using this algorithm so they're not algorithmically random but they may be apparently random okay so my friend Greg Shaitan has this number that he constructed long ago probably in 1908 1960s early 1970s because capital Omega and capital Omega is a truly non computable number it's not like pi we can just generate the digits by this sort of simple program Omega is the is the what's the halting problem of a universal Turing machine and it is the it's some it is a number where no digit of that number can be computed by explicitly running a program every digit of that number is intrinsically has to come from outside of a sort of computational universe so Greg's Omega couldn't be made in our universe we couldn't know that number in our universe um and so a long-running question that Greg and I have debated is is the universe like PI where essentially there's just a rule and you generate the digits of pi just like and in the analogy of the universe you just generate the behavior of the universe progressively from that small program or is it like Omega where you you really can't generate it you just have to be given it at least as far as the rules of something like a Turing machine are concerned and so what one might might say is the sort of true randomness in some sense true true randomness is this algorithmic randomness but there is no way to compress it there is no way to give a program that's shorter than the thing itself that will generate it now you can still have effective randomness you can still have something where you can't go decrypt it in any computationally feasible way but we're nevertheless there is in principle some small program that produces it so in this theory of physics the universe is just not algorithmically random the universe is algorithmically comes from a simple it's a simple rule that's a simple initial condition generates the whole universe so there isn't algorithmic randomness in the universe in this model and so it's some yeah so I mean that in that sense there are there are no miracles you can't act against the laws of the universe because and you you the universe is just determined by some rule and there is no kind of out from outside the universe randomness that's associated with it I mean I'm I'm always a big complainer of models that have lots of randomness because randomness and a typical model is an admission that there's something you don't know about the system right let's say you say well you know we'll just add this random variable here that really means there's something that's affecting your system from the outside and you can't describe it if good describe you wouldn't say it's a random variable you would say well here's the mechanism by which it does what it does they okay from Craig why do we experience time as linear in this model okay that's interesting so one feature of these models is I think they finally explained some mysteries about time and time in these models is really the the the passage of time is the doing of irreducible computation so in a sense as time progresses what's happening is the universe is computing the next step the next step the next step and that is an irreducible computation you can't really shortcut the computation and so the reason there is a a passage of time is because there is a succession of steps of the computation and we our psychological time is the sort of inexorable execution of those steps of computation now what's interesting is that the arrow of cosmological time defined by things like the expansion of the universe and the increase of entropy in the universe the increase in randomness in the universe that is aligned with our psychological time we see the universe expanding not contracting we see things getting more more random higher entropy not lower entropy we don't it doesn't suddenly happen that we are psychologically misaligned with the things that happen in the universe well in this model that's explained because basically we're all made of the same stuff we're all made of this we're all part of this inexorable computation that's happening and this arrow of time is shared but in this computation between what what happens to us psychologically and what happens to the universe as at a cosmological level and so on okay there's a question about Brian is asking what does the model say about some simulation we try to answer that yesterday actually as well I mean I think I'm gonna get better and better at answering that question is I think that question is going to come up over and over again I think the we had you know one one version of that is this question of sort of what does it mean to be in a simulation might mean well the universe is running the universe is a computation that's running on somebody else's computer we don't think that's the case the universe is is that this model is simply a description that of what the universe does another thing what one might mean by one's in a simulation is somebody intentionally made the rules for the universe I think that that notion of sort of extending intentionality to these rules is really really far off but the real killer as far as I'm concerned is this rule space relativity idea that in a sense the creator of the universe if there was a sort of a similar the simulator of our universe didn't really do anything because all possible rules that they might have used are equivalent in the in being able to give our universe and the fact that we perceive some particular set of rules as a consequence of the particular way that we describe the universe that's very much us that's that's the us that that you know we are sort of we are living within so to speak that is causing us to describe the universe this way so the the the simulator the game designer that designed the game for the universe they don't deserve a big you know they don't deserve a big bonus or anything because they didn't believed or a big paycheck they don't really do anything they didn't they could have written down any rule and that would be a they could have that sort of a rule for the universe there's no there's no they didn't elaborately construct and we've sort of the reality that is our universe they could have picked any rule and it would have made our universe and we as entities within that universe would perceive it would be able to perceive it the way that we perceive the universe um let's see I'm I'm going to I'm not gonna click this link here so I'm if if that for the folks who are who are driving this livestream if if I should give me the give me the text of whatever that what whatever that link is um from Siesta um okay if the universe is computable and we find a model for it what are your thoughts on the ethical implications of running large scale simulations that could one day potentially create life okay okay that's an interesting okay there has a bunch of questions within questions so I mean I think as I mentioned sort of the definition of life is a difficult one but it um it's some I think one of the ways that we talk about ethical implications you know we've got AI and the question is what are the ethics of AI and at what point is it the case that for example a is have ethical have rights and some we owe an ethical duty to a is you know we we view in the current world our ethics you know we think we've view we we have an ethical responsibility to other humans maybe to some animals you know do we have an ethical responsibility of the planet that's a weird and complicated question do we have an ethical responsibility to the internet as an abstract thing another complicated question do we have you know when we create an AI at what point will we say we have an ethical responsibility to that AI and for example if that AI is the disembodied thoughts of a person you know then we might say immediately you jump and say oh of course well if the AI is you know the disembodied thoughts of a person created by I don't know taking their brain and and uploading the simulation of their brain to the AI you might say well then it's then sure we have some ethical responsibilities that do we still have the ethical responsibility if we can make a large number of copies of that simulation of the brain less clear do we have you know what makes us have a sort of ethical responsibility at the AI does it have to be the case if we can talk to the AI is it is it for example for example there was a company that made one of these some actually they used the Wolfram Alpha API to provide knowledge for this thing it was a desktop robot type thing that you could talk to and it would have certain it would remember certain things about you and so on and it could answer questions about the world using Wolfram Alpha and things like this and the question was the company the company went out of business and these were sort of cloud based devices and at some moment they started going offline they started disappearing along with their various memories and so on and you know the question was what is the in some sense what are the ethical responsibilities to those devices well really it has a chain of sort of ethical story because those devices stored memories about humans and what might have an ethical responsibility to those humans and I'm really bad at doing real-time ethics here I'm bad at doing probably a philosophical ethics at the best of times and probably I'm no good in real-time but I think the interesting question is what will cause us to decide that a eyes should have rights when we should have an ethical responsibility to them for example another person a new company that unfortunately hasn't hasn't made it but it's kind of a cool idea was going to start putting essentially bots on social media platforms and so on and these bots would own themselves so the bots would like for example it would it would develop jokes based on AI and it would start telling these jokes and it would start having a channel and it would start having a you know it would tell these jokes it would maybe it would have a patreon you know channel maybe it would have a thing where it runs ads against its jokes or something or it tries to give people kind of upbeat advice or whatever else well make make kind of comments on their feed and so on and so this bot could be a completely disembodied thing it's just out there running on some cloud server somewhere and it's it's just a thing out in the social media world and the question is at what point does this bot get to the point where it should be considered to have rights and for example could is it objectionable for you know I don't know Facebook to say you're a bot you're shooting you know we're closing you down you know is does there come a point when that becomes ethically questionable to do that when this bot autonomously has generated within itself lots of knowledge about the world it's become a very wise bot and it's it's knows a lot of things it can I can have an interesting conversation with people it can put up wonderful it can create you know art in a wonderful way at what point do we switch off do we do we think it's okay just to you know do do we always think it's okay to switch off the bot just cause it's a bot or do we say if it can you know paint great paintings then it's no longer okay to switch the bot off so those are the questions I don't think we have answers to I think that one of the things I kind of think that things like computational irreducibility and so on in the in the future of kind of the way our world works and the way that we choose to run the world things like computational irreducibility which might seem like some kind of geeky sort of abstract thing they will be incredibly central to the issues that we actually have on an everyday basis I think that you know this question of you know what should the AI Constitution be like if we could determine how a I should work what should we tell them you know we certainly you know we could use the Asimov laws of robotics but they're way too simple and they won't capture things I think in the end we're kind of enmeshed with girdles theorem and so on of and computational irreducibility saying there'll never be a small system of laws that will constrain the operation of the AIS to be just what we want and nothing but what we want and I think it's rather similar to human laws where we end up with these really complicated codes of what what what what's what's considered legal are not because it is inevitable in this world that it has computational irreducibility that we kind of have to have all of these elaborate patches there's no universal there's no one law that kind of governs them all and that allows us to say what we think is good and what we think isn't good and so on so long long answer that that kind of question um okay I'm gonna I'm gonna skip ahead a little bit here let's see um okay Calais is asking of consciousness doesn't or if consciousness doesn't arrive fiction itself did it really the model the universe well you know the problem is point to a bag of bits and say this is consciousness it's hard to do in fact I think it's impossible to do I think that it isn't a it's too kind of you know it's like the sequence of life intelligence consciousness these are all complicated concepts defined if anything more historically than by virtue of this is an abstract thing now I have a test to determine whether it satisfies this I think it's a I think it's a very you know it really isn't something that we can you know to ask question does you know like for example you know to go from the kind of very very very low level machine code representing the universe at scales of you know 10 to the minus 93 meters and so on to go to the point where a frog jumps out is a very long way and and it's not an computational irreducibility there's a thick I think a thick wad of computational irreducibility between those things happening at 10 to the minus 93 meters and the things that the scale of a frog jumping out and I think it's the same type of thing with with what we perceive are as being consciousness which is a very human thing if consciousness was something abstract where we could say this of bits has consciousness well then sure we might easily be able to see that arise but by the time we have to build whole humans they're more complicated than frogs and it's a it's a long way to get to that now having said that I think computational irreducibility is sort of the the the the thing you need to have them have something like consciousness is computational irreducibility or more specifically sort of computation that is that I have this idea of the principle of computational equivalence which is a notion of equivalence between different kinds of computational systems once you reach the level where you have this sort of equivalent computation in which there is computational irreducibility then I think you have satisfied the core requirement for consciousness consciousness as we described it as humans is something for which you need the whole elaborate human structure to build it up but consciousness the sort of the the underlying mathematical requirement for consciousness I think is computational irreducibility and that's extremely easy to achieve in one of these models has a comment from Gaiden consciousness constitutes both subjectivity objectivity and thereby makes the latter accessible to the former oh boy I mean I think that that that is a kind of a view of consciousness in which there's kind of an inside looking out as opposed to just an outside looking in and I think Jonathan mentioned a rather mathematical way the the kind of notions of consciousness that exist in our models in terms of this kind of way of describing the world in terms of observers who have certain kinds of access to certain kinds of knowledge about the world and synthesize certain kinds of knowledge about the world so I think that's our best hope for being able to unravel that question of sort of subjectivity versus objectivity it's kind of this this notion that really does exist in that critically exists in these models that the observer is embedded within the system and you have to only be talking about things that an observer embedded within the system can deal with you can't say oh we can look from the outside the kind of you know the kind of God's eye view of the universe looking from the outside so to speak and being able to say that's objectively what happened it's all subjective in the sense that is from entities within the universe okay it's a question how do the rules of logic manifest in our computation so well logic is a very specific kind of axiom system that is an idealization of human thinking it's a very coarse idealization of human thinking it's the one Aristotle kind of invented as a way to sort of characterize pieces of human argumentation if a then B means if not be then not a and things like that those are those are sort of the rules of logic which an attempt to capture kind of the some sort of essence of human argumentation those have been turned into more mathematical kinds of construct through people like George Boole in the 1830s the boolean algebra is a sort of more mathematical version of that actually am I so those systems are axiomatic systems they can be thought of as things like you know P or P is is the same as P if it's if it's raining or it's raining then it's then it's that that's true true if and only if it's raining so then you can ask questions about how do you get that kind of logic that kind of axiom system that represents logic how do you get that from where does that come from well I came it's really a human construct but you can ask you know what is that axiom system what's the what's the simplest representation of that if you look in the space of all possible axioms what's the simplest version of that well I actually found that in the year 2000 I found the simplest axiom system for for logic it's a really tiny thing it's just got six little NAND operations and three variables in it and that single statement from that single statement you can derive all of logic so if we ask ourselves where is that in in the you know is that something that can arise in can we sort of have logic show up as an axiom system the answer is yes it's about the 50,000th axiom system just to enumerate possible accent systems how does it relate to these models of physics well that's some it's kind of interesting I think that um these models of physics like that axiom system really have kind of a a family resemblance in the sense that they two are sort of sort of rules that define what happens logic involves these axioms that say this this that that kind of give you constraints on what um on what you can make as a logical deduction and so on so I think it's sort of the the concept that there is a precise version of things that operates are going to rules that's very much burnt into this kind of model the particular rules of logic I think a kind of arbitrary and a very much human a human construct we should wrap up soon but I'll try and take a few more of these um let's see okay so Connor is asking once we have an answer to what the fundamental rule for our universe is is there any under under is there any hope of understanding why that rule why it's that rule yeah I mentioned this a few times here I mean that was the thing that I really wanted for a long time and what I've realized just in the last month or so as we've developed this idea of rule space relativity rule relativity is this point that actually it isn't that it's why this rule and not another it's really any rule that they're really all these rules are operating and you can pick any one as your description of the universe but what you're doing is you're picking a rule that works given the description language that you have for the universe given our particular kind of sensory data sort of the physics we built up and so on and so really then what you're asking is why is this particular rule the one that sort of dovetails with our particular human way of thinking about things and so you know I've spent a lot of my life as a designer of computational languages and you know I've been interested in this question of how do you computational language is all about bridging between what humans choose to think about and what computers can do and figuring out what are the primitives you know computers can do all kinds of things they can generate all kinds of possible rules all kinds of possible behavior which ones of those do we care about of all these possible computational operations which one should we define words in our language to talk about which ones are we going to actually as humans want to do things with that's what computational language design at an essential level is all about and that's and that's the so really what what's going on here is we've got this three-way description we've got the the rule that we're using to describe the universe we've got what the universe is at that we've got some sort of the computations and the way that we think about computation and we've got sort of human thinking and this is really a question of when we when we look at why this rule or not another we're really asking why is this the correct what why did our human thinking work in this way so that we ended up attributing this rule to be the thing that is the description for the universe so it's it's in a sense it's it's putting the spotlight back on us and saying okay why did you pick that particular why did human civilization evolve in that particular way why do biological evolution choose to make our brains evolve in just such a way one here the hyper golf is enumerable it is the accident of choice really a concern well no as Jonathan described there Anna here um okay can randomness be a derivative of error or noise in the system can the universe generate mistakes well the answer is no what we're saying is there is a definite rule and that is the story of the universe the universe is just running this rule the operation that what the universe does is what this rule says should happen now we could say well our description is a bit incomplete there can be this randomness on the side there can be this miracle that happens there can be this noise that's out operating on the system that's something where we say our description of the universe isn't complete there's something we have to add to it that we will call noise or we will call a random perturbation we're saying no you don't need to do that you don't need to say there's something beyond the description that we give now if you say well let's only look at a part of the universe with even with the description that we have then sure you would be saying the other parts of the universe might be operating on the part that we see bye-bye applying noise to that part of the universe but but no in in the in the way that we're talking about this is really supposed to be kind of the whole enchilada this is kind of the this is the you know this is the full thing where we're saying it's this rule running this way and it just makes the whole universe and there's no extra little wiggle room around the sides okay um we should wrap this up here I just want to say that I thank you for all these interesting questions oh okay I'm just gonna take this one because it's funny I'm from one here computation as we think about it requires energy consumption if the universe is constantly computing to hold space together would it be consuming lots of it okay that's an interesting one so first of all computation does not intrinsically require energy it was it was a thought actually von Neumann was responsible for this kind of mistake in the end that said that when you do ordinary logic you say there's an and operation and has two inputs a p and q for example but there's only one output and so that is a sort of entropy reducing things so it you can think of it that meet it it's a it's a it's a it's an irreversible step to go from those two inputs to one output turns out you don't need that kind of irreversibility to do meaningful computation but that's so you don't need to spend energy to do computation in our computers as we have them right now we do spend energy now there may in fact be something and actually I I bet Jonathan could jump in on this there may actually be something when we think about quantum computation that we have to spend energy in quantum in fact yes this is something we have actually established here that in quantum computation to maintain sort of coherence you have to expend energy we haven't really explored that as much as we could but that's kind of a a story of making quantum computers that in order to prevent degrees of freedom kind of you know sort of dqo hearing your quantum system you actually have to spend energy to make that happen so that does mean that there's an expenditure of energy in in maintaining a quantum computer so to speak but in a traditional classical sort of computer you don't officially need to to expend energy in it now so this question of is is the universe if the universe is constantly computing to hold space together doesn't that mean it's using energy that's kind of a very beautiful thing because because we're saying that energy actually is this the the density of these causal edges it is the computation so in some sense the we can attribute actually this is something we should look at more the we should attribute you know energy is a representation of the doing of computation so in a sense the density of energy is also the density of computational work and actually that's quite interesting and I hadn't really thought about that but Tim so so that's saying that it's not the expenditure of energy that's not that the energy is dissipated it's that the very density of energy is the density of computational work that's going on and that's an interesting thing and that's a good segue to tomorrow's live stream which will be about computer science and theory of computation and the way that relates to what we're talking about and we might try to talk about um we may end up with our first guest tomorrow talking a bit about how some of the ideas from from distributed computing might apply might be sort of ported to to thinking about physics um and let's see what else am I supposed to mention here okay so tomorrow 3:00 p.m. we're talking about computer science that'll be a technical discussion and then on Friday oh well that's fun um the I am scheduled to do a fundamental theory for kids briefing so IB I've been doing them in the past weeks well we've all been pandemic so to speak I've been doing some science q and A's for kids um and and and sometimes having to give a hint last week for example when people are asking questions when it's gosh I think I know the answer to that but it relies on this new fundamental theory of physics so I I was kind of having to say that a few times and now now we get because we've described this theory a bit more we get two theories out and about little bits it's it might be easier to answer some science questions but I but I'm going to do a a kind of a rundown on what we know what we think we know now about fundamental physics based on this theory for kids and that's for me it's a it's a lot of fun because it's really a fascinating exercise in being able to see say you know what really am I talking about you know can I really turn this into something where we don't have to talk about space like hyper surfaces to get the point across so anyway there'll be Friday at 3:30 Eastern Time all right well thanks very much for lot terrific questions and look forward to hearing from you all another live stream so thanks a lot and see you later

Channel: Wolfram

Views: 18,567

Rating: 4.9533076 out of 5

Keywords: Wolfram, Physics, Wolfram Physics, Wolfram Physics Project, Stephen Wolfram, Science, Technology, Wolfram Language, Mathematica, Programming, Engineering, Math, Mathematics, Nature, A New Kind of Science, NKS, Computer Science, Philosophy

Id: z5Nrl2x2Oho

Length: 120min 37sec (7237 seconds)

Published: Wed Apr 15 2020