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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). 9883603368  4288997768 42390752785149282624.

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ADVERTISEMENTFor 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)


 4288997768


free will




Scott Aaronson

Associate Professor Without Tenure (!), MIT

The Looniest Talk I’ve Ever Given In My Life



I’ll present a perspective about free will, quantum mechanics, and time that I’ve never seen before

I’ll place a much higher premium on being original and interesting than on being right


Compatibilist? Determinist? Automaton? No problem! You can listen to the talk too


This talk will assume what David Deutsch calls the “momentous dichotomy”:

Either a given technology is possible, or else there’s some principled reason why it’s not possible.

Example application: Quantum computing


Conventional wisdom: “Free will is a hopelessly muddled concept. If something isn’t deterministic, then logically, it must be random—but a radioactive nucleus obviously doesn’t 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



Free will


x := x + 5; // Determinism

x := random(1…10); // Randomness

x := input(); // “Free will”

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!


Cue a century of speculation

involving quantum mechanics…


Quantum Mechanics and the Brain:A Bullshit-Strewn Interdisciplinary Field

Two obvious difficulties:

  • The brain isn’t exactly the most hospitable place for large-scale quantum coherence (nor is there any clear reason for such coherence to have evolved)
  • Even if QM were relevant to brain function, how would that “help”? Again, randomness  free will

The Deterministic Path of This Talk

  • A proposed “empirical” notion of free will (based on algorithmic information theory)
  • A falsifiable hypothesis about brain function(Little or no exotic physics needed)
  • The No-Cloning Theorem
  • Recent applications of the No-Cloning Theorem(Quantum money and copy-protected quantum software)
  • “Knightian uncertainty” about the initial quantum state of the universe
  • A radical speculation about time(Independent motivations from quantum gravity?)

How can we define free will in a way that’s amenable to scientific investigation?


For inspiration, I turned to computer science’s Prophet

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 differentquestion:

“Are there imaginable digital computers which would do well in theimitation game?”


In this talk, I’ll 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) unpredictability—not 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”!



Obviously, many of your actions are predictable, and the fact that they’re predictable doesn’t make them “unfree”!

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, they’d also be perfectly predictable!

I’ll solve that problem using a “Prediction Game”

In general, the better someone knows you, the better they can predict you … but even people who’ve been married for decades can occasionally surprise each other! (Otherwise, they would’ve effectively “melded” into a single person)

If someone could predict ALL your actions, it seems to me that you’d be “unmasked as an automaton,” much more effectively than any philosophical argument could unmask you


The Prediction Game: Setup Phase

The machine outputs a self-contained “model” of you(running on a classical computer, a quantum computer, or whatever)

It’s the year 3000. You enter the brain-scanning machine.

The machine records all the neural data it can, without killing you

Hardest part of this whole setup to formalize!


The Prediction Game: Testing Phase

Q #34: Which physicist would you least want to be stranded at sea with: Paul Davies, Sean Carroll, or Max Tegmark?

Q #35: Multiverse: for or against?


“Max Tegmark”


The Prediction Game: Scoring Phase

The Questions: Q1,…,QnYour Answers: A1,…,AnPredictor’s Guessed Distributions: D1,…,Dn

We’ll say the predictor “succeeds” if:

where C = some small constant (like 0.01),B = the number of bits in the shortest computer program that outputs Ai given Q1,…,Qi and D1,…,Di as input, for all i{1,…,n}



Beautiful Result from Theory of Algorithmic Randomness (paraphrase): Assume you can’t compute anything that’s Turing-uncomputatable. Then the inequality from the last slide can be satisfied with non-negligible probability, in the limit n, if and only if you’re indeed choosing your answers randomly according to the predictor’s claimed distributions D1,…,Dn.

Crucial Point

In retrospect, looking back on your entire sequence of answers A1,…,An, the predictor could always decompose the sequence into (1) a part that has a small Turing-machine description and (2) a part that’s “algorithmically random.”

But when it’s forced to guess your answers one by one, it might see a third, “fundamentally unpredictable” component.

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 don’t like the uncomputable element, can replace B by the number of bits in the shortest efficient program


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



If you believe Hypothesis H, then there would appear to be a fundamental obstacle to winning the Prediction Game…

The No-Cloning Theorem


There’s no general procedure to copy an unknown quantum state, even approximately

“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!


Simple 1-Qubit Model Situation






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…

While these proposals raise separate issues (e.g., computational complexity), they’re analogous to what we want in one important respect: if you don’t 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!)

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 can’t 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 can’t use to create more states that also let f be computed


Knightian Uncertainty


In economics, Knightian uncertainty means uncertainty that one can’t 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”!

Suppose the Prediction Game can’t 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 being’s 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!


“Look, suppose I believed the Prediction Game was unwinnable. Even so, why would that have anything to do with free will? Even if I don’t 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


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


There’s a “dual description” of the whole spacetime history that lives on an initial hypersurface only, and that has no explicit time parameter—just a partially-ordered set of “decisions” about what the quantum state on the initial hypersurface ought to be.

A decision about particle A’s initial state gets made “before” a decision about particle B’s initial state, if and only if, in the spacetime history, A’s amplification to macroscopic scale occurs in the causal past of B’s amplification to macroscopic scale



|=|+ Alice says yes

|=|1  Bob asks Alice on a date

|0 |0 |0 |1 |0 |0 |0 |0







Are there independent reasons, arising from quantum gravity, to find such a picture attractive?(Now comes the speculative part of the talk!)

The account of free will I’m suggesting can not only accommodate a dual description living one dimension lower; in some sense, it demands such a description

“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, there’s 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?


Two Principles That I Held Inviolate

  • Evolution from initial to later states is completely determined by the Hamiltonian: there’s no room for free will to “hide” there
  • Classical memories and records, once written, can’t be “magically altered” by tinkering with the universe’s initial state

Without quantum mechanics (or some other source of unclonability), my account would have required abandoning at least one of the principles above!



I admit: the idea that the Prediction Game can’t be won (because of, e.g., quantum mechanics and Knightian uncertainty about the initial state) strikes me as science fiction

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?)

By Deutsch’s “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