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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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http://people.csail.mit.edu/andyd/rec_method.pdf
A SCIENTIFICALLY-SUPPORTABLE
NOTION OF
FREE WILL
IN ONLY
6 CONTROVERSIAL STEPS
The Looniest Talk I’ve Ever Given In My Life
Scott Aaronson
Associate Professor Without Tenure (!), MIT
Introduction
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
Thanks
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
Hopelessly-Muddled?
Free will
Determinism
x := x + 5;
x := random(1…10);
x := input();
// Determinism
// Randomness
// “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!
Quantum Mechanics and the Brain:
A Bullshit-Strewn Interdisciplinary Field
Two obvious difficulties:
(1) 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)
(2) Even if QM were relevant to brain function, how would
that “help”? Again, randomness  free will
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?)
1. 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 different question:
“Are there imaginable digital computers
which would do well in the imitation 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”!
Discussion
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 the
in the
sense
relevantknows
for us,you,
they’d
bethey
In general,
better
someone
the also
better
perfectly
predictable!
can predict you … but
even people
who’ve been married
for decades
occasionally
surprise
each other!Game”
I’ll solvecan
that
problem using
a “Prediction
(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
It’s the year 3000.
You enter the brainscanning machine.
Hardest part of this
whole setup to
formalize!
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)
The Prediction Game: Testing Phase
Q #34: Which physicist would you least
want to be stranded at sea with: Paul
Davies,
Carroll,for
or or
Maxagainst?
Tegmark?
Q #35: Sean
Multiverse:
FEEDBACK
LOOP
“Max Tegmark”
0.8
0.6
0.4
0.2
0
Paul Sean Max
The Prediction Game: Scoring Phase
The Questions: Q1,…,Qn
Your Answers: A1,…,An
Predictor’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}
Justification
Beautiful Result from Theory of Algorithmic Randomness
(paraphrase): Assume you can’t compute anything that’s
Turing-uncomputatable.
Then the
inequality from the last
Crucial
Point
slide can be satisfied with non-negligible probability, in the
In retrospect,
on choosing
your entire
limit n,
if and only iflooking
you’reback
indeed
your
sequence
of answers
A1,…,A
predictor
could
n, the
answers
randomly
according
to the
predictor’s
claimed
always Ddecompose
the sequence into (1) a part
distributions
,…,D
.
1
n
that has a small Turing-machine description and
Note: B is(2)
itself
an uncomputable
quantity!
Can falsify a
a part
that’s “algorithmically
random.”
claimed Predictor by computing upper bounds on B, but
But when it’s forced to guess your answers one by
never prove absolutely that a Predictor works.
might
see a third,
(But the sameone,
issueitarises
for separate
reasons,“fundamentally
and even arises in QM itself!)
unpredictable” component.
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…
2.
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…
3.
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
BRIEFS
VANILLA
BOXERS
CHOCOLATE
But can
the No-Cloning
Theorem
used(e.g.,
to get
While
these proposals
raise actually
separatebe
issues
quantum
states that
are boththey’re
unclonable
and “functional”?
computational
complexity),
analogous
to what we
Recent
quantumrespect:
computing
theory
that
want inwork
one in
important
if you
don’tillustrates
know how
the
the
answer
is yes…
state
| or
|f was prepared, then you can copy it, but
only with exponentially-small
success probability
Putting
Teeth on the No-Cloning
Theorem
4.
(just like if you were trying to guess the outputs by chance!)
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
5.
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
Poetically,
we could
think oftheory)
this
SupposeKnightian
the Prediction
Game can’t beabout
won, even
by a being
uncertainty
initial
with unlimited
computational
power who
conditions
as “a place
forknows
freethe
will
dynamical
laws
of physics (but
is constrained
by QM).
(or
something
like
it) to hide
in a
Then such a being’s
knowledge mustworld”!
involve Knightian
law-governed
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!”
6.
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
MACROSCOPIC
MACROSCOPIC
“decisions”
about what the quantum state on the initial
AMPLIFICATION
AMPLIFICATION
hypersurface ought
to be.
|=|+ 
|=|1 
Alice
says
A decision
about
state
getsyes
made
Bob asks
Aliceparticle A’s initial
“before”on
a decision
a date 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
|0 |0 |
|1 |0 |1 |0 |0 |0 |
|+ |0
INITIAL HYPERSURFACE (AT THE BIG BANG?)
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
1. Evolution from initial to later states is
completely determined by the Hamiltonian:
there’s no room for free will to “hide” there
2. 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!
Conclusions
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