A Turing Test for Free Will by Seth Lloyd

so well thank you very much see the title of this talk is actually do um chemical reactions have free will and I'm actually not going to resolve real questions about whether things have free will or not because I learned from my supervisor for my MPhil and he'll history and philosophy of science Jeremy Butterfield who I see right over there that many of these questions are actually philosophical questions that have been debated for thousands of years and it's unlikely that physicists are going to resolve them however what I am going to argue today is it I will actually state the results of some other simple mathematical theorems and it show that if you were making a decision and chemical reactions do make decisions for instance the chemical reactions that govern the metabolism of a cell make decisions to raise or lower amounts of certain chemicals if certain other chemicals are coming in so if you are making a decision you have a some kind of systems making decision and if in addition that system is sufficiently complex to ask the question what decision will I make then it will in general not be able to answer that question by the way you don't have to have consciousness or anything like that to have the simple form of self reference if you're the operating system for a smartphone the operating system is a computer program that says it allocates time and space to other programs so it says what does program must number 17 want need and it gives it some time in space what does program number 743 need gives us some time in space what does program number 42 need gives us some time in space but it itself is programmed number 42 and if you have that amount of self-reference you will not be able to predict what you're going to do so the operating system your computer can ask the question what will I do and will not be able to answer it so I'm going to argue actually that the reason for let's where's my hockey stick the reason the reason for our the unpredictability of our actions at least so far as we're concerned is not have to do whether the universe is deterministic or probabilistic which is the way that the debate has largely been phrased over the last 2,500 years but in fact it has to do with the halting problem and uncomputable 'ti it's it's interesting by the way it's are interesting I don't know how many people know this but touring prior to coming up with his ideas about the halting problem and to address girdle's theorem he was actually studying quantum mechanics he was reading fun Norman's book and he was studying quantum mechanics because he actually was interested in the questions of consciousness and freewill all right so I'm you know the 2500 years ago Epicurus who was an Adam s he had adopted democritus's theory of atoms he he said very famously that the atoms move deterministically but occasionally perform a small swerve called the clinton we don't have Epicurus is writing on this but Lucretia's has him saying and Aaron iturra alluding he's quote way of a Bose Cognos Faraday Moscow clerk um they also rectum a banana ferret or pong goalie was Pro police and it basically says that the atoms fall under their own weights colliding with each other but every now and then they have to give a small swerve otherwise they just all fall to the ground that's one reason but the other reason which is quite interesting and this happens about ten lines later he says if they did not give this small swerve than the thing that we value most about our lives which is our freedom of will would not exist so epicurus and lucretius said we need indeterminacy in order probabilistic behavior in order to have free will now many two centuries to millennia later Newton came up with his laws of notion and he said that the laws of physics are deterministic this was very was so successful that for the subsequent three hundred years or so or 250 years people had a real problem with free will so um if you look at philosophers of the of the 18th century for instance people like Hume or or Locke they realized there was they said there's a real problem with free will Samuel Johnson said all theory is against the freedom of will all experience for it now there's some really if you dig through the history of this oh and by the this is if you want to really go into this in detail I have an article in the Proceedings of the Royal philosophical society a called at rowing test for free will it's on the archive as well you might want to take a look it has all kinds of more fun quotes and history about this but there's a lot of entertaining history about this a lot of interesting firsts like for instance the fact that Turing was actually studying quantum mechanics because he was interested in consciousness and freewill but there's a wonderful paper by Maxwell very little known but it's actually on freewill and what in which he actually he actually insensate that the motions of molecules are chaotic he says he wants to preserve freewill he says oh look when you I have hearts for your gas and they're bouncing off of each other then a little uncertainty will grow and grow and grow and grow this is a paper from the 1870s that that anticipates the notion of chaos at plonker ray analyzed 20 years later I'm now Eddington when when the advent of quantum mechanics which is intrinsically probabilistic people got excited because if you just think that the free will is all about whether things are probabilistic or deterministic then suddenly things are now probabilistic after have her having been deterministic for the previous 300 years then that's great and Eddington brought this up and he he actually said you know now that we have quantum mechanics and it's probabilistic nature and he said quote science withdraws its moral opposition to free well ok ok but does randomness actually save freewill um actually I I mean I I definitely think no but I actually have a whole bunch of other of other well-known philosophers and lotta mechanisms and people like that people like shorting or touring Hawking dammit people you know it's if you have a random mootness quantum randomness suppose you make a decision right you know should I have coffee caffeinated coffee or decaf a decision which I usually have to make around 3 p.m. right you know Catherine II is more excited but history means indicates I won't get as much sleep right so which do I do now I can think back and forth more exciting safer more exciting safer make a decision if I can't make a decision I could flip a coin right but adding randomness and flipping a coin is exactly for people who are abdicating their free will and so the real problem about freewill is not really whether its probabilistic or deterministic it's whether it's mechanistic can a mechanistic system possess freewill a mechanistic system such as the the set of chemical reactions that underlie the metabolism of a cell and I will actually show that this is not true this is just a mathematical theorems that I will argue by the way these serums have nothing to do with the so called free will theorems o'clock in Conway freewill theorems those theorems actually in my mind have nothing to do with free will not or at least have nothing to do with whether we can predict what we're going to do is questions about probable ism in probabilistic nature and quantum mechanics so I just in case somebody wants to ask if there's any connection between that what I'm talking about the answer is no so you don't actually have to get up and ask that now all right so actually right now there's an interesting time about freewill because you read all kinds of things actually in Stephen Hawking's most recent book he says he doesn't believe in free will because there's all this evidence from knurl from people putting you know electrodes into people's brains that they can predict the decisions are going to make beforehand here's my little scientist who's you know poking at your brain and you know the scientists poking at brain can look at the electrodes the outcomes the electrodes and predict the decision you're gonna make a split-second before you're aware of this and then Hawking says oh but this stuff means we don't have free will right okay that's fine if you don't want to say we have world that's okay you still will not be able to predict your own decision all right so what I'm actually gonna address is a smaller question but one up which I believe is the essence which is why we can't predict our own decisions now if you believe we have free will then this explains free will if you don't believe we have free will this explains why we have the illusion that we have free will okay so what's going on okay this is not what's going on what I'm gonna argue is it what's really going on is the halting problem so here's this is by my schematic of the halting problem this is the hand of a Turing machine it's moving along this Turing machine it's a universal Turing machine so it's capable of simulating any other Turing machine including itself so and so here it is it's simulate it's asking the question what am I gonna do so to ask the question what it's going to do it makes a little model of itself it starts simulating itself but the problem is it's simulating itself asking the question what am I gonna do so there's more of the model but simulating itself what am I gonna do it goes smaller and smaller and smaller until I ran out of resolution in my PowerPoint slide I hope you like my powerpoint technique here right and it's just this capacity for self reference which famously leads to the halting problem um if you have systems that have a capacity for self reference and they're computationally Universal then they cannot predict if they're going to halt they can't predict if anything's going to halt or not and in particular they also won't be able to predict what their decisions are going to be if their decision is made by some kind of logical process they won't even know they're going to make a decision or not ok so a computer which has a sense of self reference cannot predict what it's going to do indeed the halting problem as you know it so you can summarize it in this kind of way will ever be able to answer the question of whether I will be able to answer the question that I thought that thought and you know now you're in an infinite loop and now you don't know what's going to happen so this I claim is the essence of our inability to predict what we're going to do we're capable of self reference we can ask the question what will I do and then you can just prove you know if you have a decision-making process if you say what will I do the decision-making process is made in either a deterministic or probabilistic fashion you will not be able to predict what you're going to do and you don't have to be a human being to have this happen it's also true of the operating system of your smartphone so if if it's a now many people are the halting problem of course you know it really shows up if you have an infinite system with an input an infinitely extensible tape but there is a finite system version of it as well that applies to the kind of finite automata that Jim was talking about as well here is somebody it looks maybe a little bit like Lucille Ball's and I Love Lucy because she's got red hair she's trying to model what she's going to do what kind of decisions he was going to make so she makes a model of herself herself of course we have this recursive feature makes another model itself makes another model of herself if you're a finite system as opposed to an infinite system you cannot model yourself exactly for the simple reason that you're devoting fewer resources to model yourself than actually you have you have fewer degrees of pristine freedom in the model the new yourself possess so as you can see here the model is kind of more coarse-grained cartoonish and gets more and more cartoonish as it goes further down and the result is that now even for finance systems you cannot predict what you're going to do so if you actually want you can go and look at the details of how you prove this you you can prove that simulating oneself is either slower or less detailed or chancy er than just being yourself okay there's a bunch of different trade-offs but you there's always a trade-off you can't get away you cannot simulate yourself exactly in the Amandla same amount of time it takes for you to be yourself and the by the way the finite time finite system version of this is called the heart monitor in serum this is a theorem from the good old days of computational complexity before the polynomial hierarchy it basically says to predict with certainty what you will decide to do an hour from now takes more than an hour so there's two ways of actually deciding you can either just like go through the thought process you have to do to make the decision and make the decision I think what the hell I'll have caffeine you know right or you can try to make the decision in the following way you can ask what am I going to do what decision will I make well how will I make this decision here's the person trying to think of do it the second way how will I make this decision here's the person just making the decision heart Manas turns theorem says that if I have a system whose temporal resources are limited to T so it has to come up with an answer after time T so it's a finite automaton it's only gonna run for time T then indeed you can predict what it's going to do but to predict what it's going to do takes time T squared this is what the harm under stern theorem says it's rather nice it's just it's simply the finite system version of the Cantor diagonalization argument that goes into proving the halting problem it's the finite system version of the halting problem something that you're just gonna do it in time T if you're gonna ask yourself the question what how what am I going to do in time T answering that question takes in general time T squared okay it just takes longer that's just the way it is so um I invite you to think about this next time you're making a decision I understand that that there there's a very long thousands multiple millennia-old prejudice on part of many people and often particularly scientists it says oh it's just about free question of free will but whether we can predict what we're going to do is a question about whether the laws of fistic or physics are deterministic or whether they're probabilistic I claim that this actually just doesn't have anything to do with it our inability to ask to predict what we're going to do this this explanation this feature that you can't predict what you're going to do is nothing to do whether the universe is deterministic or probabilistic you could have a a Tommy Tom that's a deterministic automaton or probabilistic automaton it won't be able to answer the question of what it's going to do in general what decision that's going to make um it's true whether the universe is classical or whether it's quantum mechanical again it doesn't matter this is like you know the the quantum computers have the same problem as classical computers they also will not be able to predict what decision they're going to make um so indeed so is this the title the title the paper a Turing test for free will says I I suggested in this paper I suggest we this in a kind of whimsical fashion we should have a a self-administered Turing test for free will I mean it's self administered because unlike the ordinary Turing test where it's an adversarial thing it's like you know if you cheat on your self administered test about whether you are free will then you have only yourself to blame right there's no real point in cheating so so suppose you were sufficiently complicated as an information processing system to answer the following questions so am i a decider like George HW Bush famously saying I am the decider right he decided he was the decider so is there a decision to be made so like for example I think I encourage you to think of this decision that the operating system of a computer is going to make the operating system is going to allocate resources to other programs its deciding how to Alec those resources it's just an algorithm in your computer that's doing it but it is deciding how to do it nobody else is deciding how to allocate those resources can I model my behavior and that of others this is also true of the operating system of computer it has to have a model of the of the programs that it's allocating resources to and it has to have a model of itself in order to allocate those resources these models of course will always be incomplete and then you ask the question can I predict my own decisions and if you answered yes to equation question one and yes to question two truthfully then the only truthful answer to question three is no so if you answered yes to one yeste - and you answered yes to three then you're cheating and you only have yourself to blame because you're only just fooling yourself this is just not you know this has nothing to do with determinism or probability or chance eNOS it just has to do with processing information and with by systems that actually have a very rudimentary notion of self reference like the operating system the computer program number 42 that asks the question what will program number 42 do that's enough of the notion of self reference so you don't necessarily need to be conscious I don't believe the operating system my computer's conscious malevolent yes conscious No okay so who's gonna pass this a thermostat very simplest kind to finite automata with input output relations no it doesn't I can't compute it's way out of a paper bag it doesn't have enough computational power to ask the question you know what will I do or pets maybe people who have pets assign them superhuman consciousness and free will and all those other things we don't know the things like trees or bacteria probably not probably not once you get to human beings or systems that have immune systems whose job is actually to ask questions you know is this part of me or is this not part of me then you're starting to get in trouble in fact well this same argument I'm trying working on a paper to apply this to autoimmune diseases it's essentially says autoimmune diseases are inescapable because they involve this problem self-reference in a finite information processing system and that problem of self reference can never actually be answered correctly a hundred percent of the time for just the same reasons that you can't predict what you're going to do however if you look at your computer or your smartphone the answer is yes right they have the ability to model themselves they are deciders they have the ability to model themselves they can ask the question what do I need and what am I going to do and they will not be able to answer that question so you're operating a system of your computer cannot predict what it's going to do does it have free will I don't know I'm not you could even ask it if it's going to if it knows what it's going to do because that's it's a program you could ask it what are you gonna do we'll say I'm too busy allocating this memory resources to answer your stupid question go away I don't know the answer right so you could even ask it it would not be able to answer so uh yes so here's here's where we are somewhere out on the edge of the spiral galaxy there's a black hole going this is somebody falling into a black hole I just wanted to to play homage to everything that's going on here and actually the first time I gave this talk was the first time I had a smartphone actually and I asked Siri this is the first time I'd ever use Siri I asked said so Siri do you want to go out for a beer after this talk and you know what Siri said serious said this is about you Seth not about me thank you very much you

Channel: FQXi

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Keywords: Seth Lloyd, fqxi, turing test, free will

Id: 5wyJlUUEpSE

Length: 19min 30sec (1170 seconds)

Published: Sat Nov 26 2016