Oct 19

Predictability, Computability, and Free Will

I’ve been reading some philosophical discussion of the free-will/determism question recently. Quite a number of years ago I discovered a resolution of this question, but never did anything with it because I assumed I had simply reinvented a well-known position and could not really contribute anything to the debate. However, the research I’ve done recently suggests that my resolution of the question is actually a novel one.

Like a lot of philosophy, the discussion of free will and determinism I’ve seen founders on two errors. One of this is Aristotelianism, an attachment to observer-independent two-valued logic in a system of universal categories as the only sort of truth. The other is a tendency to get snarled up in meaningless categories that are artifacts of language rather than useful abstractions from observed reality.

In this essay, I hope to show that, if one can avoid these errors, the underlying question can be reduced to a non-problem. More generally, I hope to show how ideas from computability and complexity theory can be used to gain some purchase on problems in the philosophy of mind that have previously seemed intractable.

Formulating The Problem

The free-will question is classically put thus: do we really have choices, or are our actions and behavior at any given time entirely determined by previous states of the universe? Are we autonomous beings, who ourselves cause our future actions, or meat robots?

The second way of forming the question gets at the reason most philosophers have for finding it interesting. What they really want to know is whether we cause our own actions and are responsible for them, or whether praise, blame, and punishment are pointless because our choices are predestined.

Thus the free-will question, which is traditionally considered part of metaphysics or the philosophy of mind, is actually motivated by central issues in moral philosophy. At the end of this essay, we will consider the implications of my proposal for moral philosophy.

Classical Determinism And Its Problems

The ways philosophers have traditionally asked these questions conceal assumptions that are false in fact and logic. First, the evidence says we do not live in the kind of universe where classical determinism is an option. In almost all current versions of physical theory there is an irreducible randomness to the universe at the quantum level. Thus, even if we knew the entire state of the universe at any given moment, its future states would not be determined; we can at best predict the probability distribution of those states.

Another characteristic of quantum theory is that observation perturbs the system being observed. Let’s sidestep that for the moment and introduce the concept of a perfect observer, with infinite computational capacity and the ability to take infinitely precise measurements in zero time without perturbing the system under observation. In a universe with quantum randomness, even this perfect observer cannot know the future.

Matters are worse for imperfect observers, who have only finite computational capacity, can take only finitely accurate measurements, and perturb what they measure when they measure it. Even in theories that preserve physical determinism, imperfect observers have two additional problems. One is that they perturb what they observe; the other is sensitive dependence on initial conditions.

Two physical systems that are measurably identical to an imperfect observer and evolve by the same deterministic laws can have different futures because unmeasurably small differences between their present states are chaotically amplified over time — and some of those unmeasurable differences may be produced by the act of observation!

Even in the absence of sensitive dependence on initial conditions, though, an imperfect observer’s attempt to predict the future may fail without warning because his finite computer loses information to round-off errors (there are more subtle limits arising from finite storage capacity, but round-off errors will stand as a readily comprehensible representative of them). And like it or not, human beings are imperfect observers. So even without quantum indeterminacy, we cannot know the future with certainty.

For philosophical purposes, quantum indeterminacy and sensitive dependence on initial conditions in classical (non-quantum) systems have nearly indistinguishable effects. Together, they imply that classical determinism is not an option for imperfect observers, even in the unlikely case that quantum reality is not actually rolling dice.

Non-Classical Determinism and Irreducible Randomness

Philosophers have tended to make a fast leap from the above insight to the conclusion that humans do in fact have free will — but this conclusion is a logic error brought on by Aristotelian thinking. There is an unexcluded middle here: we may be meat robots in a universe that rolls dice, both non-determined and non-autonomous.

Most people (even most philosophers) find the idea that we are puppets on random strings even more repugnant than classical determinism. In classical determinism there is at least a perfect-observer view from which the story makes sense. The religiously inclined can believe in that perfect observer and identify it with God, and the rest of us can take some sort of fatalistic comfort in the face of our adversities that things could not after all have been any different.

In the indeterminate universe we seem to inhabit, the only way for even a god to know the future would be for it to intervene in every single collapse of a quantum state vector, and thereby to create that future by a continuous act of will. But if that were so, the behavior of all the matter in our bodies could be nothing but the god’s will. We’re back to determinism here, but it’s one in which a god is the sole causal agent of everything — good, evil, and apparent randomness. Some varieties of Hindu theology actually read like this; one rather lovely version has it that the entire universe is simply the vibration of the voice of the god Atman (or Brahman) chanting a giant “OM!” and will end untold eons in the future when He next draws breath. In the West this position has been called “occasionalism”.

The trouble with occasionalism is that it’s untestable. There is no observation we can make from within the universe to establish causal intervention from outside it. If we could do so, we would simply extend our conception of “the universe” to the larger domain within which causality operates — including the mind of Atman. The testability problem would immediately re-present itself. (This, of course, is a slightly subtler version of the standard rebuttal to the “First Cause” argument for the existence of a creator-God.)

For those of us unwilling to take occasionalism on pure faith, then, free will is about the only comfort an indeterminate universe can offer. Our experience of being human beings is that some of the time our behavior is forced by factors beyond our control (for example, if we fall off a cliff we will accelerate at a rate independent of our desire or will about the matter), but that at other times we make unforced choices that at least seem to causally originate within our own minds and not elsewhere.

To carry the discussion further, we need to decide what the term “free will” means. Our challenge is to interpret this term in a way that both consistent with its ordinary use and fits into a larger picture that is rationally consistent with physical theory. Try as I might, I can only see two possible ways to accomplish this. One has to do with autonomy, the other with unpredictability.

The Autonomy Interpretation of “Free Will”, And Its Problems

Most people, if pressed, would probably come up with some version of the autonomy interpretation. All the philosophical accounts of “free will” I’ve ever seen are based on it. We have no problem with the idea that our choices are caused, or even determined by, our previous thoughts, but the intuitive notion of free will is that our thoughts themselves are free. This implies that the measure of a human’s degree of “free will” is the degree to each human being’s history of mental states is autonomous from the rest of the universe — not caused by it, but capable of causing changes in it.

There are several problems with this account. The most obvious one is that we can often locate causal influences from the rest of the universe into our mental states. To anyone who doubts this, I recommend the experience of extreme hunger, or (better) of nearly drowning. These are quite enlightening, and philosophers would probably talk less nonsense if they retained a clearer grasp of what such experiences are like.

Less extremely, evidence from sensory-deprivation experiments suggests that a mind deprived of sensory input for too long disintegrates. Not only does the rest of the universe have causal power over our mental states, but we cannot maintain anything recognizable as a coherent mental state without that input. Which makes sense; evolutionary biology tells us that we are survival machines shaped by natural selection to cope with a reality exterior to our minds. Consciousness, reasoning, and introspection — the “higher” aspects of human mental activity that mostly concern philosophers — are recent add-ons.

None of this evidence outright excludes the possibility that there is some part or aspect of our normal mental activity that is autonomous, uncaused but causal. The real problem, the problem of logic and principle, is that we don’t know how the autonomously “free-willing” part of the mind (if it exists) can be isolated from the part that is causally driven by sensory stimuli and normal physical laws.

For materialists like myself who model the mind as a kind of software or information pattern that happens to run on an organic substrate, this is an impossible problem. We have no warrant to believe that any part of that system is causally autonomous from the rest of the universe. In fact, on functional grounds it seems quite unlikely such a part would ever evolve — what would it be good for?

But the problem is not really any simpler for dualists or mysterians, those who hold that minds have some “soul” attached that is non-physical or inaccessible to observation. That “soul” has to interact with the mind somehow. If the interaction is one-way (soul affects mind, but mind does not effect soul) then the soul is simply a sort of blind pattern- or noise-generator with no access to reality. On the other hand, if mind affects soul we are right back to the beginning of the problem — is there anything in “soul” that is neither random nor causally driven by “mind”, which we already understand to be either random or causally driven by the rest of the universe?

The basic problem here is the same as the basic problem with occasionalism. Define the “causal universe” as all phenomena with observable consequences, whether those phenomena are material or “soul” or the voice of Atman. Unless the occasionalists are right and it is all just Atman saying a trillion-year “OM!”, the concept of “soul” does not actually in itself make us any space between determinism and chance. The autonomy account of free will leaves us finally unable to locate anywhere autonomy can live.

The Predictability Account Of Free Will

I have invented a predictability account of free will which is quite different. Instead of struggling with the limits of imperfect observation, I consider them definitional. I say human beings (or any other entity to which we ascribe possession of a mind) have “free will” relative to any given observer if that observer cannot effectively predict their future mental states.

By “effectively predict” I mean that the observer, given a complete description of the mind’s state and a set of stimuli applied to that state, can predict the state of the mind after those stimuli.

Since we have access to mental states only by observing the behaviors they generate, this is arguably equivalent to saying that an entity with a mind has free will with respect to an observer if the observer cannot predict its behavior. However, I specify the term “mental state” because I think the natural-language use of the term “free will” requires that we limit the candidates for it to entities which we believe to have minds and to which we thus attribute mental states.

I am deliberately not proposing a definition or theory of “mind” in this essay, because I intend my arguments to be independent of such theory. All I require of the reader’s theory of mind is that it not exclude human beings from having one.

Can There Be Minds Without Free Will?

The first thing we need to do is establish that this definition is not vacuous. Are there any circumstances under which an entity to which we ascribe mental states can fail to have free will?

A psychologist friend of mine with whom I discussed the matter reports that the answer is “yes”. The example case she reported is a bot (software agent) named Julia designed to fool people in Internet Relay Chat rooms into believing it was a person. Julia could be convincing for a few minutes, but human beings would eventually notice mechanical patterns as they came to the edge of her functional envelope. Studies of humans interacting with Julia showed that they continued to ascribe intentions and mental states to the bot even after noticing the determinism of its behavior. The study evidence suggests that they went from modeling Julia as being like a normal adult human to being like a child or a retardate.

This was not even the first such result. The AI literature reports humans projecting personhood even on much cruder early bots such as the famous ELIZA simulation of a Rogerian psychotherapist — and not giving up that attachment even after the shallow and mechanical algorithms used to generate responses were explained to them.

The reader may object, based on some theory of “mind”, that Julia did not actually have one. But it is possible that we are all Julia. Suppose that the human mind is a deterministic machine with a very large but finite number of states; suppose further that the logic of the mind has no sensitive dependence on initial conditions (that is, its states are coarse enough for us to measure accurately). This simplest-possible model we’ll call the “clockwork mind”. If Julia has a mind, this is the kind of mind she has.

In principle, any clockwork mind can be perfectly simulated on a computer. The computer would have to be more complex than the clockwork mind itself. To predict the state of the clockwork mind, just run the simulation faster than the original. But — and this is an important point — a clockwork mind cannot be predicted by itself, or by any clockwork mind of comparable power to itself. Thus, whatever viewpoint a hypothetical perfect observer or god might have, human beings have free will with respect to each other.

It is also worth noting that human beings could have clockwork minds even in a universe of chaotic or quantum indeterminacy. If you put enough atoms together, the Law of Large Numbers will normally swamp quantum effects. If you make the states of a finite-state machine sufficiently coarse, there won’t be unmeasurable initial-condition differences to be amplified. After all, clockwork does tick!

The Indeterminate Mind

It is unlikely that humans have clockwork minds. The anatomy and physiology of the brain suggests strongly that it has chaotic indeterminacy. It may have quantum indeterminacy as well (the mathematician Roger Penrose suggested this in his book The Emperor’s New Mind, one of the favored texts of the new mysterians). It is possible that the mind cannot be modeled as a finite-state machine at all.

These distinctions make little difference, because what they all have in common is that that they make the prediction problem far less tractable than for a clockwork mind. Thus, they widen the class of observers with respect to which a non-clockwork mind would have free will.

At the extreme, if human minds have intrinsic quantum uncertainty then even a perfect observer could not predict their future mental states, unless it happens to be an occasionalist god and the only cause of everything.

The most likely intermediate case is that the mind is a finite-state machine with sensitive dependence on initial conditions and an intractably large state space. In that case it might fail to have free will with respect to a perfect observer, but will have free will with respect to any imperfect observer.

Implications for Moral Philosophy

The binding I have proposed for the term “free will” does not rely on any supposed autonomy of the mind or self from external causes. From the perspective of traditional moral philosophy, it combines the worst of both worlds — a non-autonomous mind in an indeterminate universe. How, then, can humans being be appropriate subjects of praise, blame, or punishment? In what sense, if any, can human beings be said to be responsible for their actions?

The first step towards solving this problem is to realize that these questions are separable. Because we ascribe intention and autonomy to human beings and believe their future behavior is controlled primarily by those intentions, we explain acts of praise, blame, and punishment directed at human beings in terms of the supposed effects on their mental states. But this is where remembering that we have no direct access to mental states is useful; what we are actually after when we praise, blame and punish is to change observable future behaviors.

Thus, we also praise and blame and punish animals without much regard to whether they have mental states or free will. When training a kitten it is of little interest to us in what sense it might be choosing to crap on the rug; what matters is getting it to use the litterbox. Humans, like animals, are appropriate subjects of praise and blame and punishment to the extent that those communications effectively alter their behavior. The attribution of “responsibility” is at best a sort of convenient shorthand, and at worst a red herring.

In any case the question of “responsibility” is simply the question of free will in another guise, and admits the same answer within a predictive account. An observer may hold a mind “responsible” for the actions it initiates to the extent that the observer is unable to identify external causes of those actions.

This accords well with the way people normally reason about responsibility. If all we know of a man is that he murdered someone in a fit of rage, our inclination is to hold him responsible. But if we then learn that he was unwittingly dosed with PCP, we have an external cause for the rage and can no longer consider him fully responsible.


The predictivist account of free will I have proposed here solves the classical problems with the autonomy account of free will, accords with natural-language use of the term “free will”, and is consilient with physical theory. It does so at the cost of making the ascription of free will dependent on the computational and measurement capacity of the observer.

The parallel with the way “space” and “time” are redefined in Relativity Theory is obvious. As in that theory, our intuitions about “free will” are largely valid in human-observable ranges but tend to break down at extremes. Relativity had to abandon the idea of absolute space/time; in our context, we need to abandon the ideal of the perfect observer and accept that finite computational capacity is yet another fundamental limit on theory-building.

I believe a similar change in stance is likely to prove essential to the solution of other outstanding problems in philosophy.

Oct 18

The Far Side of Irony

Having seen Team America: World Police last Friday on its
opening night, I’m amused by the mainstream-media spin that this movie
is an anti-right-wing satire too subtle for the yokels to get. In
fact, I think it’s it’s something much more peculiar and interesting
— a movie that hides a strong fundamental patriotism and appeal
to traditional values under a veneer of scatology and sexual crudity.

The MSM can’t see this, because in the MSM’s universe the kind of
patriotism for which the movie ultimately plumps is at best a joke to
be sneered at and at worst actually toxic. But the South Park guys
tip their hand early, during a sequence in which the the protagonist
Gary visits the Lincoln Memorial and other national monuments while
wrestling with a question of duty. The soundtrack is country music
of the most teeth-gritting, lachrymose awfulness — but the steel
guitars and schmaltzy vocals fail to obscure the fact that the song is
asking a serious moral question, and that the right answer (for Gary
and for the rest of us) is that he must accept his duty to defend
freedom. The entire rest of the plot follows from that decision.

This scene is a microcosm of the movie. In this satire, it’s the
satire you’re supposed to see through. Irony is enlisted to
anti-ironic purposes. In another early scene, Gary is cosmetically
morphed for infiltration purposes into a caricature of the generic
Islamo-terrorist so extreme that pained laughter is the only possible
response — and his teammates think it’s a perfect disguise. But
never once is this pointed jab at American parochialism allowed to
obscure the genuine evil of the type he is disguised as.

Throughout the film, Team America is clumsy, parochial,
hamfisted and inadvertently destructive. But this is emphasised mainly
in order to point up a continuing underlying message that it’s better
to be a dolt with traditional American intentions than a sophisticate
in the service of evil.

In this and other ways, this movie seems profoundly conservative to
me. I don’t often use the label ‘conservative’ as a compliment, but
such use is merited here. Team America knows it’s their job to defend
civilization, to conserve it. Part of the humor in this movie comes
from the contrast between that fundamental conservatism and the
profane, obscene, and jejunely disgusting moments that occupy much of
the film. These are not your father’s conservatives, a point the
South Park auteurs make early by showing two of the characters
sprinting a lust-a-thon through a marrionette kama sutra of sexual

And maybe that’s the most interesting message of this movie. We
watch it blowing up scenery in a parody of the Bruckheimerian action
flick, but what’s really being exploded is the fixed categories of the
post-1960s culture wars. The South Park guys are trying to divorce
the muscular self-confidence of a healthy civilization from the
cultural-conservative and religious fixations that confidence has
usually been married to. There is not one single reference to
Christianity in the entire movie. The good guys drink, swear, and
screw like frenzied minks, but they’re good guys just the same.

Ultimately, what matters about them most is that they never give
up and never compromise with evil. That’s what makes this vulgar
comedy ultimately a serious parable for our time.

Oct 17

Software vs. Art

Jamie Richards asks an intelligent question in response to my essay on
deadly genius in the arts:

I’m not programming-savvy at all, so maybe this is crap… what do you
think about the idea that computer programming is a cultural area
operating under the same conditions that set up the “Modernist

As I understand it, in the proprietary model of software building, a
company patron spends money to create products that are
“comprehensible to the patron’s peers.” In open-source software
building, programmers self-select, working on projects that are
interesting to them (art for art’s sake…). “The breakneck pace of
technological change” certainly applies to this chunk of human
history, as well.

Indeed it does, and your question is both subtle and astute.
However, you’ve missed a crucial difference between software projects
and fine art. Software has to work. Every piece of software
exists in order to achieve some instrumental goal, and can be
evaluated on how well it achieves that goal.

The vast con-game that most of modern art has become relies on a
definition of “art” that equates it with pure expressiveness. The
modern “artist” can say of some randomly ugly artifact “this is my artistic
statement, and if you don’t get it you are simply proving your own
lack of sensitivity and taste”.

Open-source hackers can’t get away with this sort of thing. If
their code is broken and crash-prone or doesn’t meet the functional
spec it claims to, nobody will take it seriously on any level at all
— much less as art. The requirement of engineering competence
has the kind of constraining and filtering effect on open-source
programming that the patronage system once did on pre-Modern art.

The really sharp reader is going to be asking, right about now,
“OK, so what about architecture?”

Architecture is like programming in that it’s a form of art that
operates within powerful functional constraints. Buildings have to
keep the rain off people, and not collapse on their heads. So why
haven’t those requirements prevented modern architecture from falling
into the back-to-zero trap, from blighting the landscape with
thousands of ugly brutalist cuboids?

We may cheerfully admit that some modern architecture is very
lovely; Santiago Calatrava’s or Eero Saarinen’s organiform buildings
come to mind. Nevertheless, to save the argument I’m making, we need
to show some relevant difference between architecture and software design.

One clue is that modern architects have not in fact forgotten how to
make buildings that fulfil the minimum functional requirements. It is only
in the aesthetic face those buildings present to the world that something
bad has happened. On this analogy, the place we should expect open-source
software to have regressed relative to the products of proprietary patronage
is in the specific area of user-interface design.

I have pointed out
that this is open source’s weakest area. But on closer
examination this analogy doesn’t work so well. Almost any software
user interface (UI) is more complicated and much more interactive than
a typical building’s interface — therefore, much more
constrained by the cognitive limitations of human beings; therefore,
designing software UIs is more like engineering and less like art than
designing building UIs. Thus, the idiom of software UIs is less subject
than is architecture to disruption by an expressive but deadly genius.

Oct 05

The Terror War Comes Home

For the first time in my life, I find that I am seriously considering
voting Republican in a presidential election. What has pushed me to it
is this report of shots being fired into a Bush-Cheney campaign HQ in Knoxville. TN.

It’s not the first shot fired at the Republicans. And it comes on top of a frenzy of anti-Republican hate speech that has been building even as Democrats have watched their electoral prospects sinking into a Vietnam-flavored quagmire brought on himself by the most incompetent and feckless candidate either party has fielded in thirty years.

We’ve seen three-year-old girls reduced to tears by Democratic thugs. We’ve seen swastikas burned into the front yards of those who dared to announce themselves Republicans. And all this from a Democratic left that poses as the champion of dissent.

This caps it. If Kerry is elected, the terrorists will have won.

UPDATE: As I was writing, Democratic protesters stormed and
Bush/Cheney headquarters in Orlando. Some now face
assault charges.

in West Allis, Wisconsin.

And these are the people who liken Bush to Hitler…