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ADVERTISEMENT For those who enjoyed the Memory session on Monday Multiplying 10-Digit Numbers Using Flickr: The Power of Recognition Memory by Andrew Drucker (my PhD student)

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FREE WILL Scott Aaronson Associate Professor Without Tenure (!), MIT The Looniest Talk Ive Ever Given In My Life A SCIENTIFICALLY-SUPPORTABLE NOTION OF IN ONLY 6 CONTROVERSIAL STEPS

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Introduction Ill present a perspective about free will, quantum mechanics, and time that Ive never seen before Compatibilist? Determinist? Automaton? No problem! You can listen to the talk too Ill place a much higher premium on being original and interesting than on being right Thanks

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This talk will assume what David Deutsch calls the momentous dichotomy: Example application: Quantum computing Either a given technology is possible, or else theres some principled reason why its not possible.

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Conventional wisdom: Free will is a hopelessly muddled concept. If something isnt deterministic, then logically, it must be randombut a radioactive nucleus obviously doesnt have free will! But the leap from indeterminism to randomness here is total nonsense! In computer science, we deal all the time with processes that are neither deterministic nor random… Nondeterministic Finite Automaton

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x := x + 5;// Determinism x := random(1…10);// Randomness x := input();// Free will Hopelessly-Muddled? Free will Determinism We can easily imagine external inputs to the giant video game we all live in: the problem is just where such inputs could fit into the actual laws of physics!

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Quantum Mechanics and the Brain: A Bullshit-Strewn Interdisciplinary Field Two obvious difficulties: (1)The brain isnt exactly the most hospitable place for large-scale quantum coherence (nor is there any clear reason for such coherence to have evolved) (2)Even if QM were relevant to brain function, how would that help? Again, randomness free will

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The Deterministic Path of This Talk 1.A proposed empirical notion of free will (based on algorithmic information theory) 2.A falsifiable hypothesis about brain function (Little or no exotic physics needed) 3.The No-Cloning Theorem 4.Recent applications of the No-Cloning Theorem (Quantum money and copy-protected quantum software) 5.Knightian uncertainty about the initial quantum state of the universe 6.A radical speculation about time (Independent motivations from quantum gravity?)

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How can we define free will in a way thats amenable to scientific investigation? I propose to consider the question, Can machines think? … The original question, Can machines think? I believe to be too meaningless to deserve discussion. A. M. Turing, Computing Machinery and Intelligence, Mind, 1950 So Turing immediately replaced it with a different question: Are there imaginable digital computers which would do well in the imitation game? 1. For inspiration, I turned to computer sciences Prophet

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In this talk, Ill propose a similar replacement for the problem of free will People mean many different things by free will: - Legal or moral responsibility - The feeling of being in control - Metaphysical freedom But arguably, one necessary condition for free will is (partial) unpredictabilitynot by a hypothetical Laplace demon, but by actual or conceivable technologies (DNA testing, brain scanning…) The Envelope Argument: If, after you said anything, you could open a sealed envelope and read what you just said, that would come pretty close to an empirical refutation of free will!

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Obviously, many of your actions are predictable, and the fact that theyre predictable doesnt make them unfree! Discussion In general, the better someone knows you, the better they can predict you … but even people whove been married for decades can occasionally surprise each other! (Otherwise, they wouldve effectively melded into a single person) If someone could predict ALL your actions, it seems to me that youd be unmasked as an automaton, much more effectively than any philosophical argument could unmask you But how do we formalize the notion of predicting your actions? After all, if your actions were perfectly random, then in the sense relevant for us, theyd also be perfectly predictable! Ill solve that problem using a Prediction Game

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Its the year You enter the brain- scanning machine. The Prediction Game: Setup Phase The machine records all the neural data it can, without killing you The machine outputs a self-contained model of you (running on a classical computer, a quantum computer, or whatever) Hardest part of this whole setup to formalize!

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Q #34: Which physicist would you least want to be stranded at sea with: Paul Davies, Sean Carroll, or Max Tegmark? The Prediction Game: Testing Phase Max Tegmark Q #35: Multiverse: for or against? FEEDBACK LOOP

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The Prediction Game: Scoring Phase The Questions: Q 1,…,Q n Your Answers: A 1,…,A n Predictors Guessed Distributions: D 1,…,D n where C = some small constant (like 0.01), B = the number of bits in the shortest computer program that outputs A i given Q 1,…,Q i and D 1,…,D i as input, for all i {1,…,n} Well say the predictor succeeds if:

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Justification Beautiful Result from Theory of Algorithmic Randomness (paraphrase): Assume you cant compute anything thats Turing-uncomputatable. Then the inequality from the last slide can be satisfied with non-negligible probability, in the limit n, if and only if youre indeed choosing your answers randomly according to the predictors claimed distributions D 1,…,D n. Note: B is itself an uncomputable quantity! Can falsify a claimed Predictor by computing upper bounds on B, but never prove absolutely that a Predictor works. (But the same issue arises for separate reasons, and even arises in QM itself!) If you dont like the uncomputable element, can replace B by the number of bits in the shortest efficient program Crucial Point In retrospect, looking back on your entire sequence of answers A 1,…,A n, the predictor could always decompose the sequence into (1) a part that has a small Turing-machine description and (2) a part thats algorithmically random. But when its forced to guess your answers one by one, it might see a third, fundamentally unpredictable component.

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So, can the Prediction Game be won? An aspirational question that could play a similar role for neuroscience as the Turing Test plays for AI! Argument for yes: All information relevant for cognition seems macroscopic and classical. Even if quantum effects are present, they should get washed out as noise But this is by no means obvious! Consider the following… Falsifiable Hypothesis (H): The behavior of (say) a mammalian brain, on a ~10s timescale, can be (and often is) sensitive to molecular-level events 2.

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If you believe Hypothesis H, then there would appear to be a fundamental obstacle to winning the Prediction Game… Penrose Lite: No speculations here about the brain as quantum computer, noncomputable QG effects in microtubules, objective state-vector reduction, etc … just the standard No-Cloning Theorem! 3. The No-Cloning Theorem Theres no general procedure to copy an unknown quantum state, even approximately

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Simple 1-Qubit Model Situation VANILLA CHOCOLATE BOXERS BRIEFS

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But can the No-Cloning Theorem actually be used to get quantum states that are both unclonable and functional? Recent work in quantum computing theory illustrates that the answer is yes… Putting Teeth on the No-Cloning Theorem Quantum Money (Wiesner 1969, A. 2009, Farhi et al. 2010, A.-Christiano 2011…): Quantum state | that a bank can prepare, people can verify as legitimate, but counterfeiters cant copy Quantum Copy-Protected Software (A. 2009) : Quantum state | f that a software company can prepare, a customer can use to compute some function f, but a pirate cant use to create more states that also let f be computed 4. While these proposals raise separate issues (e.g., computational complexity), theyre analogous to what we want in one important respect: if you dont know how the state | or | f was prepared, then you can copy it, but only with exponentially-small success probability (just like if you were trying to guess the outputs by chance!)

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Suppose the Prediction Game cant be won, even by a being with unlimited computational power who knows the dynamical laws of physics (but is constrained by QM). Then such a beings knowledge must involve Knightian uncertainty either about the initial state of the universe (say, at the big bang), or about indexical questions (e.g., our location within the universe or the Everett multiverse) For otherwise, the being could win the Prediction Game! Knightian Uncertainty 5. In economics, Knightian uncertainty means uncertainty that one cant even accurately quantify using probabilities. There are formal tools to manipulate such uncertainty (e.g., Dempster-Shafer theory) Poetically, we could think of this Knightian uncertainty about initial conditions as a place for free will (or something like it) to hide in a law-governed world!

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Look, suppose I believed the Prediction Game was unwinnable. Even so, why would that have anything to do with free will? Even if I dont know the initial state | 0, there still is such a state, and combined with the dynamical laws, it still probabilistically determines the future! A Radical Speculation About Time 6. If the Prediction Game was unwinnable, then it would seem just as logically coherent to speak about our decisions determining the initial state, as about the initial state determining our decisions! Backwards-in-time causation, but crucially, not of a sort that can lead to grandfather paradoxes

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|0 |0 |0 |1 |0 |0 |0 |0 INITIAL HYPERSURFACE (AT THE BIG BANG?) MACROSCOPIC AMPLIFICATION | =|1 Bob asks Alice on a date | =|+ Alice says yes MACROSCOPIC AMPLIFICATION | | |1 |+ Theres a dual description of the whole spacetime history that lives on an initial hypersurface only, and that has no explicit time parameterjust a partially-ordered set of decisions about what the quantum state on the initial hypersurface ought to be. A decision about particle As initial state gets made before a decision about particle Bs initial state, if and only if, in the spacetime history, As amplification to macroscopic scale occurs in the causal past of Bs amplification to macroscopic scale

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Are there independent reasons, arising from quantum gravity, to find such a picture attractive? (Now comes the speculative part of the talk!) The Black Hole Free Will Problem: You jump into a black hole. While falling toward the singularity, you decide to wave. According to black hole complementarity, theres a dual description living on the event horizon. But how does the event horizon know your decision? Could a superintelligent predictor, by collecting the Hawking radiation, reconstruct your decision without having ever seen either your past or your future? The account of free will Im suggesting can not only accommodate a dual description living one dimension lower; in some sense, it demands such a description

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Two Principles That I Held Inviolate 1.Evolution from initial to later states is completely determined by the Hamiltonian: theres no room for free will to hide there 2.Classical memories and records, once written, cant be magically altered by tinkering with the universes initial state Without quantum mechanics (or some other source of unclonability), my account would have required abandoning at least one of the principles above!

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Conclusions On the other hand, the idea that the Prediction Game can be won also strikes me as science fiction! (For then how could you ever know you were you, rather than one of countless simulations being run by various Predictors?) I admit: the idea that the Prediction Game cant be won (because of, e.g., quantum mechanics and Knightian uncertainty about the initial state) strikes me as science fiction By Deutschs Momentous Dichotomy, one of these two science-fiction scenarios has to be right! Crucially, which scenario is right is not just a metaphysical conundrum, but something that physics, CS, neurobiology, and other fields can very plausibly make progress on

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