What We Cannot Know - Marcus du Sautoy

well thank you so much for coming on such a sunny day I thought I wouldn't get any audience at all on such a wonderful sunny day and but this is a wonderful opportunity for you and for me because this book actually isn't out yet so it's kind of exciting that you know you getting a little advance glimpse of what I've been up to for the last three years in writing this book as the catalyst for this book was partly the fact that I took over this this new job from Richard Dawkins the professor for the public understanding of science and the title always makes me laugh somehow because you know there's kind of expectation with this professorship that maybe I know the whole of science and that you know I mean I'm here to explain it to the public and actually quite a few journalists seem to have this impression as well because when I first got this job um I would get these phone calls from people and I remember a journalist phoning me up the Nobel Prizes for medicine had just been announced and this journalist phoned me up from one of the broad shoes yes Nobel Prize Rosen has just been announced for the discovery of telomeres could you tell me what a telomere is now biology has never been my strong point um so I was like oh my god ever even heard of a telomere so it's a I'm really embarrassed to admit I mean you can look me up on Wikipedia but you can look a lot of things up on Wikipedia actually so I quickly went online I pulled up telomeres read quickly through what a telomere was and then confidently told this journalist that the the pieces of at the end of the DNA which control how long a piece of DNA will last and and so I realized this is kind of crazy there's no way I can be expected to know it all but actually it began to make me think is it possible at any point in history that's scientists science might know it all could we answer everything could we know everything gum and so that was partly the sort of inspiration for this a journey was to see whether there are any problems in science that by their very nature we will never be able to so actually the books divided up into seven edges of knowledge which kind of took me on this journey outside of my own area of mathematics into different regions and I'm going to take you a few fewer through a few of these stories and but I think that kind of desire to know it is absolutely basic and it is extraordinary how much we have discovered or the new news stories coming out each week I mean I think since I took over this job the sort of things we discovered we've managed to land a kind of spaceship the size of a washing machine machine on the side of a comet absolutely extraordinary we've got robots that we programmed to develop their own language that we as humans can't understand we have to interact with the robots to be able to understand that language we've sequenced the DNA of a 50 thousand year old cave girl and repaired the pancreas using stem cells of a diabetic patient I mean this catalogue of things that we've achieved and the things we've discovered is extraordinary and I think that basic desire to know is almost as basic as a desire to reproduce and here's Aristotle the beginning of metaphysics he says everyone by nature desires to know in fact I did a little research and the word to know is actually one of only about a hundred which have a universal translation across all languages not even the word eat is necessarily clearly translatable into each language so an incredibly basic desire um but it's always dangerous at any point in history to declare you will never know something and I've kept in mind on my journey throughout the last three years trying to find out those things that we cannot know a few stories one in particular is this guy Auguste Comte who in the middle of the 19th century declared we shall never be able to study by any method the chemical composition of stars now at the time that seemed completely fair I mean how on earth are we ever going to visit a star to dig a bit out and actually find out what it's made of but of course you know a few decades later we knew exactly what stars are made out of why because we don't necessarily have to go and visit the star the star is visiting us every night the light coming from the star is telling us what the star is made of so it's always dangerous and I'm sort of very clear that you know I'm not sure whether I've got any definitive answers here about things you can absolutely say you can't know but but that was the journey to try and understand whether maybe you can articulate that there are things that you will never know of course the a bit the desire to know about the unknowable isn't restricted to science so I mean there's a very famous example of a politician who got into quite a scrambled miss trying to describe his theory of knowledge here he goes Donald Rumsfeld trying to explain about the weapons of mass destruction in Iraq and whether they were there or not declared there unknown knowns there are things that we know that we know we also know there are known unknowns that is to say we know there are some things we do not know but there are also unknown unknowns that ones we don't know we don't now actually Donald Rumsfeld got awarded the foot-in-mouth award by the plain english-speaking Society for this statement but I actually think it's very unfair because I think this is a wonderful statement about states of knowledge um that the unknown unknowns those those Black Swan events I can't tell you about the unknown unknowns else they'd be known I'm going to try and tell you about the known unknowns whether we can know what those unknowns are there's another category here that I think he missed though which I think is very interesting when it comes to a politician which is of course the unknown knowns which slobozia jack actually pointed out was you know those those Freudian things that you actually know you don't deny that you know them and they sort of but they come out and somehow and I think probably those are most relevant to a politician those the young unknown oh so so that was a so this journey to try and find the unknown unknown the known unknowns I wanted to try and apply my mathematical mind to see whether I could articulate whether there were any questions in science another inspiration for this book actually came from the person that I took over this job as a Simoni professor for the public understanding of science because my predecessor Richard Dawkins now you of course know that Richard spent a lot of time not just talking about biology and evolution but also about God the his God Delusion book was probably one of his most popular books so so I kind of brace myself when I took over this job for getting a lot of questions not about telomeres but about what my beliefs in about religion were and gods were now I was quite keen to just create a sort of distance between me and Richard we do very different things scientifically and so I kind of prepared this response to journalists who had phone up and say and you know what what's your religious beliefs and I would tell them I'm a deeply religious man my religion happens to be the arsenal I have a faith every year a face every year and it's been tested once again that next season we will win the premiership I go to my temple every Saturday or Sunday this this weekend it will be Sunday I sing songs to my idols and I worship them and so I hoped that this would kind of bat away these questions about religion but some of these journalists were very persistent so I remember one instance on it was a Sunday morning on BBC Northern Ireland radio it's a problem a program about philosophy and religion and I said I'm quite happy to talk about philosophy of science and things like that but I really don't want to talk about religion of course as soon as we got on air that went out the window and he was like saw Marcus do you believe in God that's okay he wasn't from India sorry I will stop doing that um so so he just kept on pressing me kept on pressing me and it became quite an aggressive interview to the point that um as a mathematician you see if you're asking me whether something exists actually we spend a lot of time at the math Institute here proving things exist maybe without being able to know what they look like but we can prove that they exist or often we prove that things don't exist Andrew Wilde who this building is named after proved that there aren't solutions to Fermat's occasions he had a way to prove these things do not exist so I said okay I'm quite happy to engage in this if you give me a deaf nation that I can start to engage my mathematical mind with so you said aha well god that's something which transcends human understanding ah you've just played me out of the game I mean how can I engage with that so it just was it seemed to me just as I got braver I said that's that well how can we stop with the debate with that but actually that definition sort of stuck in my mind is quite an intriguing one so as the years went on and I sort of decided to engage a little bit more perhaps with this kind of the bridge between science and religion I began to think about that as a definition what about the definition of God being the things that we cannot understand the things that we cannot know the things which transcend us so can I apply my scientific mind to what that God would be like and I talked to a philosopher in my college in New College Stephen Mulhall just before I was doing an event with the chief rabbi actually about his got a wonderful book called science and religion the great partnership and he referred me to this guy Herbert McCabe who was a theologian here in Oxford who actually a Marxist theologian get that you know that's quite cool to say but he had he's got quite a lot of crazy articles about Christian kind of traditions and things but he had this one article which Stephen Melville refer me to and in there he says to assert the existence of God is to claim that there is an unanswered question about the universe so I thought that's quite an interesting definition and I sort of through the book I run with sort of just exploring a little bit about what sort of idea that is as a God Herbert McCabe says you know religion basically committed iconic lism by giving this very abstract high concept to many properties it just didn't have and of course as kids that's what we get introduced to all the silly things and then we sort of discard that so I sort of wanted to have it perhaps a more nuanced engagement with this question by defining something abstract like this now there is this term the God of the gaps which you may have heard of but that's actually used by religious people as sort of as a kind of negative thing they a lot of religious people would say no you're meant to know god you're meant to attempt to know God so actually the God of the gaps is something that they sort of uses as kind of negative statement but I want to try and reclaim that maybe and just explore through this book and a little bit with you now as we go through these attempts to find out what is it that could transcend our understanding forever so as I said the the book is divided up into these seven edges of knowledge seven areas that I've sort of explored which go from trying to understand the nature of the universe is it infinite whether we can infinitely divide matter what's going on inside our brain so I'm going to take you on a little tour of a few of these to give you a sort of feel for what might be unknowable and whether we can know that sort of thing I think one of the ultimate symbols of the unknowable is in fact the dice you know a dice would not make a fun game if you could actually predict what this was going to do next and so the first age that I explored it is about the nature of the future can we predict the future and in fact mathematics at its heart is it's very much trying to do that I call a mathematician a pattern searcher what we do is look at patterns in the past and try and use those to extrapolate to understand patterns into the future so how powerful is my language of mathematics in being able to predict what is going to happen next um so actually each of the edges is accompanied by an object which kind of sparks my journey into the unknown so the object term for this particular edge is the casino dice and this is in fact a a casino dice that I picked up when I was in Vegas and it's it's a I was trying to use my maths to make a lot of money and I've lost so much money but they let me keep the dice that's nice of them now the other thing it's a thing of beauty I mean I'm a look at its afterwards it's it's because it has to be incredibly fair it's really pretty much perfect cube the edges are are just beautifully sharp and and the the paint spoon sort of has the same density of the acetate it's really and it is I think a beauty yet it also is something that I absolutely hate because I cannot you know my desire to do mathematics which was partly about wanting to know with 100% certainty that something was true and you know here was this thing which you know when I roll it I just don't know what I got a won that time you know and and I might be able to I've got the equations for this thing but you know how can I tell what it's going to do next so that was a kind of challenge it actually maybe if I work hard enough I could know what this was going to do and I guess the hero on my journey to try and use mathematics to be able to predict the future is Isaac Newton because Isaac Newton came up with the laws of motion the physical laws of motion the idea of calculus he showed us how the universe can be controlled you know we can predict when an eclipse is going to happen we were able to predict that mercury was going to grow across the the Sun just recently and that's all thanks to this revolution that not Newton started which kind of revealed that the universe may be a kind of clockwork universe controlled by these equations if you know how things are set up you run the equations you can know what's going to happen into the future what if Newton is my hero my nemesis in this whole desire to know the future is this guy here on ray Poincare a a French mathematician who at the beginning of the 20th century said yeah well the universe may be controlled by equations it may be that if you know the absolute start up of any system you run the equations you'll know exactly what's going to happen in the future but he said unfortunately you're never going to have that complete knowledge of how a system is set up because there's always a little bit of error if you're measuring how the solar system is set up then you know how can you be sure that you've got the fiftieth decimal place right and what Poincare a showed is that just a very small change in maybe the 50th decimal place may cause a dramatically different outcome now one of my favorite examples of chaos in motion and this is an illustration that even something very simple can have a very difficult future to prime predict so this is a pendulum now pendulum is generally something so simple and predictable we use it to keep track of time but this is a slightly different pendulum so this is what I call a double pendulum so it's a it's Joe so it's a little bit like a leg so it's just two metal pieces here so the you know it's very simple geometric description and the equations are or equally quite simple but being able to predict the behavior of this thing is almost impossible so let's set this off and you see why are you laughing why because it's so hilariously funny that you can't predict it you says like I mean it's varying it just always makes me laugh when it and look I'm going to try and I had a little notch there so I guess the point is I'm going to try and repeat that behavior I'm going to try and size it off in exactly the same starting position that's so Wow no it's come completely different behavior that time and I think I've tightened it a little bit too far it's because it's um it's a little a big one here is oh listen this is my favorite desktop toy I can play with this for absolutely hours so but it sort of illustrator even very simple systems you make a very small change to the conditions and it can go in a completely different direction and this is the signature of something called called chaos another my favourite desktop toys is this one here I use this to make all my decisions about life so you can see it has different options ask a friend try again no way Definitely Maybe yes and what you do is so here's a little I'll show you the little video of this so this is a one setup in a lab you start this thing off and trying to predict this so I'm going to ask it should I go to have a beer in the pub after this lecture let's see what of cautious kind of oh definitely oh great so that's good um excellent yeah I think I'm taught over it always says definitely when I ask it about the beer it's really great Thanks yeah so but you can see from this that it you know just if I run that again trying to see you know the hope beforehand which magnet that's going to end up in so there are three magnets here and the thing is just being you know pulled the right bit like an asteroid flying around three planets and which planet is it going to hit well eventually goes for this one here and here's a three computer simulations I did where I actually just changed something like the sixth decimal place of the coordinate where the pendulum started and you can see so I've colored the pendulum the magnets up now so I've got blue magnets a yellow magnet and a reg magnet and just a very small change cause a completely different behavior different paths different planet that the asteroids hint and here is a computer simulation which tells you helps you to predict maybe where the pendulum is going to end up and so there are some regions which are very predictable so if you're close to the yellow magnet so the idea is if you start the pendulum off over a particular point you look at the color under that point and that will tell you where the pendulum is going to end up and so if I start near a yellow magnet then the thing just wobbles about and goes back to the yellow magnet so but there are other regions which are a little bit further away so here's a very large swathe of red you start there it'll swing out but will then ever end up at the red magnet so small changes are not going to be it cause any dramatic difference in where the magnet will end up but I was starting that magnet in the top left-hand corner and in this region you have what's called a fractal so this is a shape which has infinite complexity so as i zoom in on it it never simplifies it never becomes a single color so it means that however accurately I try and measure this thing just a few more decimal places can kick it quite easily from going from the yellow to the Reg magnet so this is saying that unless I have complete description of how the universe is set up I cannot know the future in this region just a small change in a decimal place will cause a completely different outcome to happen now I also was accompanied on my journey into these edges of knowledge by a few experts I chose a lot of areas I'm not expert at all it's very much was a learning curve for me some of this and in this chapter about chaos I actually chose a a colleague of ours here in Oxford this is Bob May Lord may as he is now and he actually discovered I mean it's this idea of chaos theory effects so much of what we're trying to predict about the future the reason that I wasn't sure whether it's going to be a monsoon out there I mean yesterday we had monsoons kind whether hitting us you know being able to predict the weather five days in advance is impossible because just a very small change in some of those measurements of the wind speed temperature can cause within five days things to go dramatically different the planets too are very sensitive but on a fortunately on a longer scale than five days and we were talking sort of five billion years a very small change can actually cause the solar system to do something completely different but Bob May has discovered that not only in these kind of physical systems but also in biology as well he's a mathematical biologist he discovered that trying to keep track of population dynamics is also controlled by chaotic equations so just a very small change you put in one extra animal and the dynamics can be completely different you can have the whole system collapsing whilst without that animal you can have a very healthy pack of animals the next year and in fact now he's working it's a cross-party member in the House of Lords and he spends a lot of time actually working on the banking crisis and trying to understand whether that was an example of a chaotic behavior and sure enough you know people are in economics there are regions like those yellow regions where things are very predictable and then it can go into very strange unpredictable regions and he said this to me whilst we were talking and winsome and had lunch with him at the House of Lords and he's is it not only in research but in the everyday world of politics and economics it would be better off if more people realize that simple systems do not necessarily possess simple dynamic properties and and I asked him you know how are you getting on in trying to persuade your fellow kind of politicians about the importance of knowing about chaos theory and he said Marcus they're just egos here nobody's interested in what I said it's just they already trusted in their careers so he was very down on there but I think that is one of the important things when you're trying to do policy is knowing when you can be confident about what's going to happen next I'm not saying that mathematics is completely useless we've been able to land that spaceship on the side of a comet because of Newton's equations but it's also important to know when you're in those regions maybe in the top left-hand corner of that fractally picture where now you can say you can't know so it's almost as important to know when you can't know let's know when you can know because then you couldn't be conservative and hunker down and kind of avoid the mess that might emerge and so I came back to my dice and I was very interested okay well what about this is this just chaotic or if I knew this to a certain amount of detail could I actually predict what it was going to do next I have the laws of motion which control how this Falls how it hits the table and I actually discovered a piece recent piece of research done by for Hungarians which revealed that actually this is more predictable than I thought it was going to be so what they've done is to I mean I had that picture with the three magnets which I had three colors before so now we've got six sides and so we've got six colors to keep track of so we can draw a picture of how we start off a dice and what what that effect will have on the outcome which color face will it land on and it turns out that if the table that you're throwing it on is the dissipates quite a lot of energy so it's sort of when it falls the energy kind of gets sucked out of it so like a carpet for example um then actually the behavior of this is described by the picture in the top left hand corner so actually if the energy is being dissipated so I throw this on the floor here it doesn't bounce very much and actually it turns out that we don't have this fractal quality there's sways of yellow sways of green Swain's of blue and so a small change is not going to change where that dice is going to land up so here's a tip you want to know which way is going to end what you need to look at is the bottom number because it's more likely to land when you throw it like that on the bottom number so in fact that I had one on the bottom and it came up one there so then quits in so but if you think about it the craps table in the you know it's it's you know you've got a sort of felt on there it's dissipating some sort of energy but here this is very hard this table so as you move through here the rigidity of the table is increasing and so it's losing less energy as you go through so let's try and do that again see whether so down in here we get a very fractal region so now a very small change so yes so it landed a four so I had it the one on the bottom at that time so so it depends on the circumstances but there are regions where this where I can know what this dice is going to do next and actually that's kind of your once thought is you know I've sort of brought up on yeah the universe is controlled by equations and if you know the complete set up you should be able to know exactly what's going to happen next of course we may not know the complete set up that's what chaos this theory is saying a small change means that you might lose a lot of knowledge about what's happening next but in fact there's part of science which says but even if you know the complete setup of the universe there is still circumstance instances where there's no way you're going to know what's going to happen next and one of them is in chapter that I explored next I was trying to predict the behavior of a pot of uranium so it's amazing what you can buy on the internet so this this pot of uranium I ordered it over the internet and I'm assured it's some good I'm assured that it's completely safe but they are the instructions say don't eat it but this actually at its heart is the question of when this is going to radiate at the side it says that it has it's going to emit 980 four counts of radiation so if you have a Geiger counter you get 984 counts per minute so it's got some sort of estimate of what it's going to do but that's only an approximate estimate so it it says you know over a minute on average that's what you'll get what it can't tell me is when it's going to emit an alpha particle for example and the extraordinary thing is the current state of physics says that this is just how the universe is that there is no mechanism nothing that we can do which is going to tell us when this uranium is going to emit its next partible particle that this we say is random but that's actually just an expression of our lack of knowledge of the start up this seems to be something which the physics is is genuinely random and actually the person sort of at the heart of trying to explain what this bit of uranium is doing why it's emitting at particular points it is a Heisenberg this is a picture of Heisenberg I'm trying to embrace and love Heisenberg but I he's another person I don't really like and this equation so you've probably heard of this thing Heisenberg's uncertainty principle Heisenberg's uncertainty principle almost embeds the idea that there are things you cannot know that you will never be able to know about a physical system and its expression it's not a kind of vague wishy-washy thing about Katz and Schrodinger and things like that it's actually very explicit mathematical formula and follows out of the mathematics so these two terms here Delta X and Delta P this is about a position and momentum so basically these two things are kind of paired up and the more knowledge you get about the position of something the less you know about the potential momentum the mentum remember is how something is traveling evolve the speed of the thing and in fact one like this is why I've got to tell you one of my favorite jokes so this is a Heisenberg is storming down the autobahn in Germany and and the police pull him over and and they get him out of the car and as they sir do you know how fast you were going no but I know exactly where I was now that's good a good sign that you're all laughing because if anyone who didn't laugh and I now have to explain the joke a little bit is that there's a trade-off here and this is what this equation says the more I know about the position of something that's the Delta X is controlling what the error is so the more I know about it and the smaller the error in order to make this equation true the momentum has to increase the in uncertainty sorry in the Ament 'm has to increase the knowledge I have of the momentum I get I lose knowledge about it and actually it's perfectly summed up in some of these lovely experiments now you might have experienced this thing or heard about this thing called the double slit experiment where you send an electron through and it doesn't really decide it seems to go through both slits at the same time and actually this thing about uncertainty is even revealed with just one single slit so all I'm going to do is to take my uranium off in a very far distance so that's going to be my particle gun I'm going to have say R naught alpha particle shooting out of here and I've got this large distance away I got a screen with a slit in it and it means that ever particle passes through there then there can be no momentum in the up-down direction so because any momentum in the up-down direction would push it off and it would hit the screen and not go through so if it any particle that goes through that slit I know has almost zero momentum in the the vertical position because that's the only way if it had any momentum it would not go through that slit because the distance I've made very large but as soon as it goes through that slit I also have now gained experience because it's gone through that slit so I seem to have got the trade off I know exactly the momentum and I know exactly the position of this thing but as soon as I know the position it causes a sudden uncertainty to occur in the momentum so sunny this thing gains momentum when it didn't have it before and the uncertainty is expressed here so this is actually experimental data where they took particles they sent them through here and the larger the smaller the slit the more information I have about where that particle is which means there must be a larger trade-off in the spread of momentum and you can see this this the narrower slit is the bottom graph and then suddenly the momentum is spread all over the place so where the particle arrives on the screen could be in a wide range of possible values but as I lose information about with position by widening the slit the momentum comes back in again and I have more information about the momentum now this is actually extraordinary it kind of says that I can't know these two things together but actually some physicists have started to interpret this and saying actually this is a mistaken language that actually these particles don't have a momentum and a position we're so hooked on the way Newton thought about these work the world we just think yes you've got this electron it's got some position it is somewhere and it's got some momentum and you use that to try and put make predictions but physicists now say no you shouldn't think of it like that it's wrong language so often that some of these kind of unknowns turn out to be just that we aren't able to use language properly and so people now think that you should say well that electron doesn't have a position an identifiable position until you observe where it is and so we have this scene out there called a quantum wave which actually describes the probability about where you'll find that electron should you or that particle alpha particle should you want to observe it so you should think of this thing as not having a position it's got a sort of probabilistic position spread out over space the peaks of this wavefunction tell you it's more likely to be there the troughs tell you it's less likely to be there and and this is all you can know and you can't know where that and where that electron is going to be more dramatically you can't know from the wave function when you observe it where it's going to be it could be in any of these kind of Peaks or even in the troughs as well and so quantum physics at the moment has at its heart this belief that you will it doesn't matter what you do you will not be able to know and predict and ever you can run the experiment over and over again and you'll get different answers with with the same setup if you could ever start the thing in the same way and actually this is responsible for the uranium emitting particles because you know a lot about the momentum of the things inside the nucleus of this uranium which causes an uncertainty in the position such at some point suddenly the third particle is a home I seem to be outside the nucleus I'm not inside it anymore and it goes flying off so this is actually Heisenberg's uncertainty principle helps to understand why this thing is actually emitting particles now there are some people who just believe this can't be how the universe is really behaving you know surely this just can't be random about what this is doing and there must be some mechanism for deciding okay it might look probabilistic the same as the dice the best things we had to predict the dice is probability but we know that there are laws of physics controlling what that dice is going to do and one of those who really believe this just can't be the answer and was Einstein and Einstein had this famous quote quantum mechanics is very impressive and it certainly is it's one of the most well tested theories we have on the scientific books it was such accuracy that you know we know we're onto something but an inner voice tells me that it is not yet the real thing the theory produces a good deal but hardly brings us closer to the secret of the old one I am at all events convinced that he does not play dice and I think maybe it's the mathematician in me is you know I also I'm still with Einstein with this that's you know surely we will come to a point where we have a new theory a new Einstein that tells us something about the mechanism which is going on which is controlling this but we know that the mechanism is going to be really freaky we know this thing called entanglement which shows us that any mechanism you know there can't be a sort of little internal clock in there which is just saying okay now you're spitting out now you're not and whenever you look in this system if it is there we know must be sort of spread across the whole of the universe which is controlling what this thing is doing now now I I mentioned right at the beginning that part of this exploration was about this idea of God being the things that we cannot know so here is something that apparently we are not able to know when this thing is going to spit out a bit of its nucleus so the actually the person I took on my journey to the this edge of knowledge it's a quantum physicist but he's also a priest so this is John Polkinghorne um he likes to call himself a vegetarian butcher because you know how can somebody be a quantum physicist and also a priest at the same time a John Polkinghorne he has incredibly good credentials he trained with Dirac in Cambridge then went and trained with Fineman he made great discoveries about quarks and then halfway through his kind of scientific life his life he then decided that he wanted to be ordained and so I was very intrigued to talk to him about how does he believe his God works in the world I think that you know there are a lot of religious scientists and I must say all Dharma yeah said I believe in the arsenal I am an atheist at heart and I would declare that but there are quite a lot of religious scientists but they divide into two groups and one are the the dais and one of the face the dais --tz-- say okay look I don't know where this universe came from I don't know what you know what started it all what created it but once it's been created there's no okay I'm going to call that God because I really don't know what it is which kicked this whole thing off but after that basically the laws of physics take over and the whole thing is now something I can talk about and so they don't think God acts in this world in any sort of meaningful way but John Polkinghorne is a theist and he really really believes whatever this thing God is that it acts in the world and so I was quite trying to press him okay well how your scientists how is he acting in the world or it how is this thing it's acting in the world and you know we're thinking it is the unknowns so that's very interesting so here we have an unknown quantum physics I don't know when this particle is going to emit or on aware I'm going to find a particle is that an unknown that can have influence in the world well yes it can and whether it has any sort of a belief that whether there's any sort of um meaning to what that action is but so I'm intrigued you know are you going to say maybe your God is using quantum physics so it can make a decision you know okay I'm going to put the electron here and here and that might actually have a dramatic effect on the universe because chaos says that small changes can have big effects so I thought he was going to say yes it's quantum physics perfect place my god to act in the world but he wasn't going to buy that a toys and no no no no because that really depends all of these observations or all of these decisions about where the electron is going to be depend on an observation it depends on interacting with the thing and before that it's just described by a wave function a deterministic wave function and actually we're all part of a system so surely the whole what isn't an observation anyway but surely we're all just part of some huge great big universal wavefunction so he wasn't into using quantum physics as the way that his God was acting in the world so I said okay well well how are you doing this how is it doing it um and he actually went back to chaos theory intriguingly so his theory is that as humans we can never know the the setup of a system in with complete accuracy there will always be decimal places and which we don't know about and he believes that that's where a God could act and tinker with things and change things so it could be different as the thing of all some actually Newton used to think this as well and Leibniz who is this great competitor over the calculus just said that's totally ridiculous wine earth would he have to why couldn't he just set the whole thing up and let it go runnin in the way that it was meant to at the beginning you know surely God is outside of time so I knew exactly what was going to happen anyway so it was a kind of intriguing journey talking to him about how would you use science to kind of marry up with your pathetic beliefs in a God acting in the world but the interesting thing is I went into this journey is that one of the that reason that a lot of the scientific religious people who are Deus to say okay I don't know where all of this came from let's call that creator a god and then I'm just going to do science and and so that unknown because it is you know we don't know where it all came from but actually this Heisenberg uncertainty principle gives us a chance to actually see where this stuff came from because okay where did my pot of uranium come from well I went on Amazon so I bought it on Amazon so that's his first sort and and she's amazing kind of firm of review so you can find on Amazon so so glad five stars so glad I don't have to buy this from the libyans in the parking lot at the mail anymore there were some others complaining about the fact that the thing had disappeared in a gun down by half is it laughter oh it was so good you're laughing and I don't have to explain about half life's oh that's so good anyway so yeah but if I trace this back okay probably as I I talked to somebody on Tuesday about this instead he was like he was a miner he said we'll just clear it came from a mine yeah yes I do okay yeah but where did it come from before the mine and you trace it back and of course it was made in a star my most amazing thing you know how stars make all of these extraordinary atoms but what about before that so we trace it back where did all of this stuff come from and it turns out that actually Heisenberg's uncertainty principle might be the equation which helps us to get something from nothing this is one of the big unsolved questions why is there something rather than nothing and actually if you've got two things that the things get measurements get paired up if they sort of matters what order I do it in so a measuring position and momentum somehow it matters what order I do and they get combined in an uncertainty principle there's another uncertainty principle which combines energy and time so this is Express here so any in the amount if you want to narrow in on a little window of time the energy within that window becomes more less certain so if you've got a region where there's nothing going on there so you've got no energy but actually if you decrease the window of time that means that the energy uncertainty must increase and so nothing might suddenly become a little bit of something a little bit of error and of course Einstein said energy equals mc-squared energy is equivalent to mass so you've got mass inside here so as we look in a little window actually we can suddenly get these what we call quantum fluctuations where nothing can suddenly give rise to matter so we and this is actually you may know what Stephen Hawking is famous for he's had famous for predicting the black holes another place actually where we seem to lose information if you go past the horizon of a black hole inside we seem to not be able to know what is going on inside a black hole because information can't get out one theory has it but Hawking thinks there may be a way things can get out and it's because of the uncertainty principle at the horizon is that although there's nothing there every now and again this quantum fluctuation can cause a particle and an antiparticle up to appear out of nothing it's a bit like taking the equation 0 equals 1 minus 1 so you can have nothing and then suddenly get 1 and minus 1 and that anti particle gets sucked into the black hole makes it a little bit smaller and the particle gets emitted out so that we believe in this thing Hawking radiation we haven't measured it yet which is why he hasn't got a Nobel Prize yet but when we do measure it he will because this is a way that black holes will actually kind of evaporate and may give back information we think that there's a coming called the information paradox that black holes may be somewhere where we lose information but actually this leaking according to this equation equation might be a way of us getting back information um but here is an equation which then gives us a way of getting uranium out of nothing now you might say well yeah but that isn't really nothing because you've got space there space just vacuum isn't nothing it's a three dimensional space and so that is something still and as a mathematician I certainly believe that it is as something so that isn't really nothing so where did that something where did that empty space whether there into geometry come from but even now as we push kind of one of the big mysteries is how to equate relativity and quantum physics and the idea of quantum gravity and fluctuations in quantum gravity mean that even space itself might emerge as a fluctuation out of genuinely something which is nothing so so actually it might be that's the sign for some creator is well actually the creator is just mathematics mathematics is outside of time it's been there forever we'll be there forever and this is a way of just blowing something into those equations and then you get something out of nothing so you know often they say God is a mathematician I would reverse that and say no no mathematics is the God which started all of this so that's a couple of the unknowns so let me just give you a little guide through a couple more and then I'll show you one of my so let's see we one of the other ones is I dig down into my uranium and ask you know how far can you go can you infinitely divide uranium well if you go inside it that atom is made out of electrons and quarks we think that's the bottom layer but how do we know then we'll maybe we thought atoms with the bottom layer so so that one's you know we might keep on dividing space although we think there's a little quantized space beyond which you can't divide anything what about going out is the universe infinite if it is could we ever know that so that's one of my other edges a time what about time itself so you know we think time had a beginning the Big Bang so no but can we talk about what happened before the Big Bang now I was brought up in this department on the kind of idea you can't know you guys doesn't make sense because you need time to say before and so if there wasn't any time you can't say before that's really clever yeah I like that and they would always go yeah so what's north of the North Pole there you go yeah yeah I get that there's nothing there yeah but actually people are beginning to wonder that no maybe you can talk about time before the Big Bang the weird thing is that time you know is time infinite is it going to go on forever well it turns out that it may also run out at the other end as well which is kind of frightening so time time me you know that we know we're all finite but what if the universe is finite that's pretty writing and it turns out that everything is kind of decaying are these black holes and all we be left with is photons and gravitons and photons and gravitons have no sense of time and so time will disappear they won't be able to measure things actually this seemed deeply depressing so I went and talked to Roger Penrose who's Mike journey man on this journey into time and and he came he's come up with a lovely positive way of viewing this that then you can rescale the universe because you've got less loft lost the sense of time and that will be the beginning of a new Yan and a new Big Bang so so there was more hopeful I'll I love Roger it's kind of I know a novel Roger as well because he changed his mind he was one of these people I was brought up on who said you can't talk about time before the Big Bang and now he's changed his mind I love that in a scientist and so I'm going to take you actually into a journey we've got it I go I'll talk for another till quarter - because I don't wasn't allowed to start if that's ok because I do want to take you into this edge because this one really pushed me outside my comfort zone which is a the question about what's happening inside your head it's called the hard problem of consciousness you're all sitting there and you're all doing most of you doing a pretty good impression of a conscious being I can see some of you thought I was fair enough it's very sunny and but you know I do believe that most of you are you know having a conscious experience but is that conscious experience anything like the conscious experience I'm having how can I ever know that you really are conscious or whether you maybe you've just sent an avatar down here and you know that you know you're doing it such a good impression and so actually the object I took on my journey into the hard problem of consciousness and it's in fact well it is a chatbot app that I downloaded onto my smartphone so I think there's a really interesting question when will my smartphone become conscious and could I ever know that maybe it already is is you know so so and it's perfectly encapsulated in this kind of touring question you know the the problem of talking to a machine and determining at what point you say no okay this thing is conscious um so I actually did a little experiment with this it's called clever board you can download it for free and you have conversation with it and you sort of tried to think whether is it somebody on the other end typing these things them or not so here's a little exercise for you I did them I asked a few questions I asked questions of clever BOTS and I also this I did this a bit earlier and I asked some questions of my son my son something physics in Bristol at the moment he's 20 years old just to give you some context so I asked them both questions and I want you to listen to the questions and and think you know can you work out which one is the machine and which one is my son so we kicked off with do you have a girlfriend so response a came back do you want me to have a girlfriend response B came back mind your own business okay so is that the Machine and the Machine of course learns it's an example of machine learning because every conversation we have that you have with it it's banked and becomes a conversation it will help with somebody else okay the next one what is your dream so response a was my dream is to become a famous poet response be to make lots of money who was gonna want to do that one yes my son was born in the fat tried age just give you him question three are you conscious now both of these responses intriguing because they played on this idea of Descartes his I think therefore I am so response a was if I wasn't I don't think I quite convoluted kind of but this one is de cartes response it says the only thing I can be certain of this is it goes it's one of the topics of this book is it's sort of you know how can you know anything and Descartes said the only thing I can be sure of is that Who I am so it's the only thing I'm sure of is that I am conscious so there you are you know which one of those is a machine and which one is my Simon and if we got the Machine better how can we ever know whether it was having a conscious world of course you some of you maybe synesthetic anyone's anaesthetic here yes there's a finger going up at the back there and my what's you synesthetic with numbers and colors my wife is a simile synesthetic like this and so they are having a genuinely different conscious experience because when they see a number it gets colored up I did some wonderful work with a piece of Misha Messier was synesthetic with sound and color and so when he listened to music his music it was full of color so we know that people do have genuinely different responses conscious experiences but you know how can you tell I mean one of the things I do as a mathematician very often if I'm trying to understand something is to understand when something isn't that it's a very good way to sort of flip the question so what will an animal take an animal to which of these animals around us which species are actually conscious how many of these animals if you stick them in front of the mirror cat a dog a rabbit wouldn't know that what they're looking at is themselves so here's the chimpanzee looking and you know is that is he just admiring himself or doing a few kind of like funky moves now here's a test that Gordon Gallup came up with an animal behaviorist he said okay weird you put a mark on somebody's forehead now if you look in the mirror and you see something oh that's a bit weird you put your hand up to your forehead so he was interested okay what animals will have this similar response once you've got the views to what a mirror does so here's the orangutan who's been marked looking at himself in the mirror and so what is his response to suddenly sing oh what's that weird thing I've got on my forehead um so that would be you know if you put yourself in front of the mirror and and you didn't know that somebody put some yellow stuff on your forehead you would immediately go like this you wouldn't go like this on the mirror and so you can see you know he's really pissed off that the priceless person put this great big yellow dog in front of it so it turns out you know how many animals pass this test very few humans do chimpanzees chimpanzees do and orangutangs - but gorillas do not they don't have any responses it's very few species that pass this test that's a very crude test for consciousness but it is a measure of them realizing that that is themselves some so what about children uh you know if you've got a fetus when a fetus isn't conscious but so here's a picture of me as a baby I don't think I was conscious didn't have a sense of self then but what points in my evolution as I grew older did I suddenly start to pass that mirror self recognition test and realize yeah I am a conscious being there must've been a moment when my brain did something which changed and then I had a sense of consciousness it probably wasn't here but with experiments that we've done we've seen that actually it's there's a transitionary moment in the brain around eighteen to twenty-four months if you put a for sixteen month old in front of the mirror with a little mark generally they don't react they perhaps do something to the mirror but a 20-month year-old will immediately do this so something has happened in the brain that has changed that has created this consciousness now so you can ask the same question of the universe the universe at the Big Bang was there any consciousness then well so what at what point did consciousness actually emerge and actually Judy and James has a psychologist he has an interesting a theory that that moment when we suddenly started hearing a voice in our heads must be pretty frightening and that might have been the spark for something like an idea of a god maybe that's what sparked off the thought there's something else going on inside here okay so this idea of negative so let me tell you - this one the time when we all lose consciousness every day or rather every night is when we sleep so watch happens in the brain every dark night that changes that we could see maybe what a quality of the brain that makes its conscious and so here's us an awake brain and you do something called TMS it's transcranial magnetic stimulation where you switch on some neurons so this is like a little computer gates those switching on some of those neurons cause a cascade across the brain and a feedback the integrated network is actually talking to lots of other bits of the brain feeding back to the original source of the stimulation this is a sleeping brain stimulated in exactly the same area with the same TMS in deep Stage four sleep where you don't have no conscious experience everything is very localized there's no communication going on across the brain as if the tide has come up and all of these neck the network has gone down so there's now a belief that that we can somehow measure the quality of a network and it's a guy Giulio Tononi who's come up with the way a network actually feeds back and forth between each other the the nature of those logic gates may have something to do with giving a network a feeling of what it's like to be itself and so Jorge Giulio Tononi has come up with is extraordinary equation like a coefficient of consciousness now you know I've got to love this you know what makes me me it's now an equation so and the varying and quality of this equation as we go through the day and the night or we go into a coma that this can measure something about your conscious experience to the extent interestingly that you can create a zombie or you can create a zombie is something in this has no conscious experience but behaves exactly as a human would do so here are two networks they have eight neurons they're wired up in different ways the input-output behavior of both of these networks is exactly the same so if you interacted with it you would not have any difference between the two yet one of them has a lot of feedback in it and has a high level of consciousness with this coefficient but the one on the right has no feedback and it has a zero consciousness according to this equation and so this will be an example of a zombie Network now of course I'm going to skip the conjoin sorry oh oh okay I will tell you about Christoph Christoph is one of the people who got very interested in this equation and I talked to him he's my I Skyped him so I was never quite sure whether actually my conversation with with an avatar or something whether he was really there but he got very frustrated with me trying to push him on whether we could ever answer this problem of consciousness and eventually said what sort of research project is it markers where you threw out your hands and say forget about it I can't understand it ever hopeless that's defeatism and i think we have a very schizophrenic relationship with this idea of the unknown that you know in one sense you know the unknown is what drives us as scientists you know it the known things are great but what we would spend our life trying to understand other things that we don't know so in one way the things we don't know are our lifeblood but the things that will remain forever unknown those are the kind of nemesis of the scientists and so it is a belief I think most of us kind of feel like no you have that arrogance that yeah we are a species that could know everything and I think that's really what drives me when I you know throw the dice why do I keep on looking it's my desire that I want to know how this is going to end a one thang you

Channel: Oxford Mathematics

Views: 16,931

Rating: 4.8833332 out of 5

Keywords: Oxford Mathematics Public Lectures, Marcus du Sautoy, Maths Lecture, Math Lecture, What We Cannot Know

Id: xbo3NZdReEg

Length: 55min 49sec (3349 seconds)

Published: Tue May 17 2016