Free Will

Who says a computer is deterministic? I'm writing this on my friend's Windows machine; within the week, it will probably crash in some horrible way while he is trying to perform an important task. He'll reboot it, do the exact same thing, and watch it work perfectly.

Perhaps, as Laplace suggested, if we knew the exact state of every atom in the Universe we could "run the machine in fast-forward" and figure out, by equations and/or simulations, how the Universe will be tomorrow before tomorrow arrives. But it's worth remembering that Laplace advanced this idea in a paper on probability theory, the branch of mathematics we use to reason when we have incomplete knowledge.

It's not obvious that we can represent the full, complete Universe by a simulation simpler than the Universe itself. In fact, I'd argue that it's impossible. Consider the old, folksy version of chaos theory: "for the want of a nail, the kingdom was lost," etc. (Most babble in philosophy or management supposedly based on "chaos theory" has no more backing than this folk wisdom.) To know the fate of the kingdom, we need to know the state of every nail. If we don't have total knowledge, then we can only give probabilities.

To all human observers, the state of this computer is the same at ten o'clock and at eleven o'clock, but the web browser crashed at ten and did not at eleven. The machine has free will!

(You can also solve the "problem of evil" this way. God wants a Universe full of shiny happy people, but it's impossible to tell how such a complicated problem will turn out — even God needs complete knowledge of the System in order to predict in advance its outcome. God, we presume, isn't willing to trust in probabilities. So, in order to find which set of starting conditions will lead to a perpetually free-from-evil Cosmos, God has to imagine or simulate the whole shebang. This requires simulating the atoms inside the brains of all the Universe's sentient beings, and thus those beings are sentient, even in God's imagination. . . You can fill in the rest. The upshot is, even if God cares, if evil is here now then it isn't going away — not in this Universe's lifetime.)

Listen to the Feynman.

We have already made a few remarks about the indeterminacy of quantum mechanics. That is, that we are unable now to predict what will happen in physics in a given physical circumstance which is arranged as clearly as possible. If we have an atom that is in a excited state and so is going to emit a photon, we cannot say when it will emit the photon. It has a certain amplitude to emit the photon at any time, and we can predict only a probability for emission; we cannot predict the future exactly. This has given rise to all kinds of nonsense and questions on the meaning of freedom and will, and of the idea that the world is uncertain.

Of course we must emphasize that classical physics is also indeterminate, in a sense. It is usually thought that this indeterminacy, that we cannot predict the future, is an important quantum-mechanical thing, and this is said to explain the behavior of the mind, feelings of free will, etc. But if the world were classical — if the laws of mechanics were classical — it is not quite obvious that the mind would not feel more or less the same. It is true classically that if we knew the position and the velocity of every particle in the world, or in a box of gas, we could predict exactly what would happen. And therefore the classical world is deterministic. Suppose, however, that we have finite accuracy and do not know exactly where just one atom is, say to one part in a billion. Then as it goes along it hits another atom, and because we did not know the position better than to one part in a billion, we find an even larger error in the position after the collision. And that is amplified, of course, in the next collision, so that if we start with only a tiny error it rapidly magnifies to a very great uncertainty. To give an example: if water falls over a dam, it splashes. If we stand nearby, every now and then a drop will land on our nose. This appears to be completely random, yet such a behavior would be predicted by purely classical laws. The exact position of all the drops depends upon the precise wigglings of the water before it goes over the dam. How? The iniest irregularities are magnified in falling, so that we get complete randomness. Obviously, we cannot really predict the position of the drops unless we know the motion of the water absolutely exactly.

Speaking more precisely, given an arbitrary accuracy, no matter how precise, one can find a time long enough that we cannot make predictions valid for that long a time. Now the point is that this length of time is not very large. It is not that the time is millions of years if the accuracy is one part in a billion. The time goes, in fact, only logarithmically with the error, and it turns out that in only a very, very tiny time we lose all our information. IF the accuracy is taken to be one part in billions and billions and billions — no matter how many billions we wish, provided we do stop somewhere — then we can find a time less than the time it took to stat ethe accuracy — after which we can no longer predict what is going to happen! It is therefore not fair to say that from the apparent freedom and indeterminacy of the human mind, we should have realized that classical "deterministic" physics could not ever hope to understand it, and to welcome quantum mechanics as a release from a "completely mechanistic" universe. For already in classical mechanics there was indeterminability from a practical point of view.

Chaos theory is largely the formalization of Feynman's insight, as recorded in chapter 38 of the Lectures on Physics (1963).

Short version: free will/determinism and human/computer are false dichotomies.

Infophile has mentioned the M-word, so I figure I should pull an earlier rant of mine from Bad Astronomy. Here goes:

For various reasons, I am extremely skeptical of the notion that consciousness could be rooted in quantum phenomena. Of course, the entire world is quantum, in a sense: it’s the principles of quantum mechanics which determine the properties of materials out of which the world is made. Like Democritus of Abdera said twenty-five hundred years ago, “Nothing exists save atoms and the void”, and quantum physics constitutes the rules by which atoms play.

The challenge, then, is not to say “all is quantum” (a statement with no more content, by itself, than saying “all is love”). In what way do the strange and esoteric mathematical descriptions of the atomic and sub-atomic world build up the everyday stuff with which we are so familiar? This is a deep problem, one with many mysteries left to resolve, and physicists spend lots of time worrying about it. One thing which we do know is that when you put a lot of quantum particles together, at a certain point they stop acting in the quantum way and become better approximated by Newton’s laws of classical mechanics. This is odd, because if you put a pile of classical pieces together, you get a bigger classical object! Newton’s laws reproduce themselves at higher scales, but the quantum laws do not.

It’s a bit like discovering that all the ordinary houses on your ordinary street are made of bricks from Faerie.

So, in order to test the idea that consciousness, Mind, Spirit or any such vaguely defined phenomenon has a quantum flavor, we need to know if essential aspects of Mind depend upon objects which are small enough for quantum oddities to apply. Lengths, time scales and temperatures need to be sufficiently small to avoid the problem of decoherence, the tendency of quantum objects to collapse into classical behavior.

On the one hand, we have fairly specific models of how brain cells might contain tiny switching elements to which quantum mechanics might apply. The most notable by far is Penrose and Hameroff’s proposal that “microtubules” — protein rods which form a kind of cellular skeleton, used for transporting molecules around and giving the cell mechanical rigidity — can transmit quantum pulses. Unfortunately, this model doesn’t stand up to close scrutiny very well: decoherence steps in and ruins everything. Hameroff, an anaesthesiologist, came up with a (moderately wacky) way in which this “model” explained the action of anaesthetics. Supporters made a big fooferaw about how scientists had no other model to explain aneasthetics, but oops, never tell a scientist that something can’t be explained; we now have biochemical theories which handle anaesthetics without needing to invoke quantum consciousness.

The neuroscientists have also done a very good job finding places in brains where neurons can be probed directly. In the barn owl, for example, there is a brain part called the inferior colliculus, which the owl uses to process sound. We can identify places in the inferior colliculus where neurons act like AND gates: they have two inputs and only produce an output when both inputs fire simultaneously. Models exist to explain this in terms of ion fluxes through the neuron’s cell membrane (”dendritic computation” is one term, referring to the dendrites which carry the input signals). These models do not invoke quantum mechanics.

One of the better general resources I have found on this subject is a paper by Litt et al., in the journal Cognitive Science (2006). They lay out the evidence that

explaining brain function by appeal to quantum mechanics is akin to explaining bird flight by appeal to atomic bonding characteristics. The structures of all bird wings do involve atomic bonding properties that are correlated with the kinds of materials in bird wings: most wing feathers are made of keratin, which has specific bonding properties. Nevertheless, everything we might want to explain about wing function can be stated independently of this atomic structure. Geometry, stiffness, and strength are much more relevant to the explanatory target of flight, even though atomic bonding properties may give rise to specific geometric and tensile properties. Explaining how birds fly simply does not require specifying how atoms bond in feathers.

In essence, we can enclose all the quantum weirdness within “black boxes” and discuss the interaction of the boxes using classical science. There’s legitimate science in figuring out what goes on inside those black boxes, but it’s equally legitimate (and perhaps more useful) to understand what happens when they hook up together.

Indisputably, phenomena requiring quantum mechanical explanation exist throughout the brain, and are fundamental to any complete understanding of its structure and physical mechanics. […] However, none of these effects contribute essentially to explaining the overall functionality of the associated system, which can be fully described without explicit appeal to quantum-level phenomena. In our wing analogy, it is unnecessary to refer to atomic bonding properties to explain flight. We contend that information processing in the brain can similarly be described without reference to quantum theory. Mechanisms for brain function need not appeal to quantum theory for a full account of the higher level explanatory targets.

Penrose has also argued that classical computers cannot perform some of the tasks which humans do quite readily. This argument from computational complexity, however, also falls flat. Solomon Feferman dissected it fairly neatly in a review entitled “Penrose’s Gödelian Argument”; more recently, Mark C. Chu-Carroll has written relevant posts about “quantum complexity classes” at his blog Good Math, Bad Math. The physicist Scott Aaronson has advanced plausible arguments that a quantum computer can't solve NP-complete problems in polynomial time. Et cetera.

Then we have the people who claim that quantum entanglement can explain telepathy or telekinesis. Using esoteric jargon and vague pseudo-math to lend credence to a phenomenon which nobody has experimentally observed, and which experiments have quite frequently ruled out — it’s a bit like a ghost leading a blind man.

This is the realm of Deepak Chopra and the charlatans who made What the Bleep Do We Know!? To them, quantum is just a handy term, on a par with “energy field” or “Good Side of the Force”. None of the specifics of modern physics relate in any way to their specious psychobabble. There’s more good science in the Beach Boys’ song “Good Vibrations” than in Chopra’s whole catalog. They want the credibility of modern science, the trust people place in the competence of white-coated Einsteins, but they’re not willing to pay the price. They want to provide the appearance of reconciling science and faith, but what they have truly reconciled is jargon with gullibility.

Beren,

You've really made my point for me!

When we're dealing with computers, it is just barely possible for people with hefty amounts of experience and training to figure out what caused a system crash. . . most of the time. Believe me, I've grown up with computers, and I've hunted down an awful lot of causes, but on particularly rough days, I've found myself stumped. So have all of my computer-expert friends, many of whom have degrees and paying jobs in the field.

Increase the complexity by a factor of ten to the umpty-ump, and the difficulty of predicting a human brain's next move becomes clear. We need perfect information to predict with perfect accuracy, but in real systems, small uncertainties are often rapidly magnified. This is why, for all practical purposes, deterministic physical laws can coexist with unpredictability at the human scale. Is it a troubling problem? Yeah, sure, maybe in a philosophical sense, but I can think of about six billion more pressing concerns which should be addressed first.

There is a pretty puzzle here, which is deeply connected to the reason why my laptop is making my legs warm right now. The following is quoted from the physicist John Baez's column, This Week's Finds in Mathematical Physics, week 235 (15 July 2006).

You see, to make any physical system keep acting "digital" for a long time, one needs a method to keep its time evolution from drifting off course. It's easiest to think about this issue for an old-fashioned, purely classical digital computer. It's already an interesting problem.

What does it mean for a physical system to act "digital"? Well, we like to idealize our computers as having a finite set of states; with each tick of the clock it jumps from one state to another in a deterministic way. That's how we imagine a digital computer.

But if our computer is actually a machine following the laws of classical mechanics, its space of states is actually continuous — and time evolution is continuous too! Physicists call the space of states of a classical system its "phase space", and they describe time evolution by a "flow" on this phase space: states move continuously around as time passes, following Hamilton's equations.

So, what we like to idealize as a single state of our classical computer is actually a big bunch of states: a blob in phase space, or "macrostate" in physics jargon.

For example, in our idealized description, we might say a wire represents either a 0 or 1 depending on whether current is flowing through it or not. But in reality, there's a blob of states where only a little current is flowing through, and another blob of states where a lot is flowing through. All the former states count as the "0" macrostate in our idealized description; all the latter count as the "1" macrostate.

Unfortunately, there are also states right on the brink, where a medium amount of current is flowing through! If our machine gets into one of these states, it won't act like the perfect digital computer it's trying to mimic. This is bad!

So, you should imagine the phase space of our computer as having a finite set of blobs in it — macrostates where it's doing something good — separated by a no-man's land of states where it's not doing anything good. For a simple 2-bit computer, you can imagine 4 blobs [see the original for a picture]. Now, as time evolves for one tick of our computer's clock, we'd like these nice macrostates to flow into each other. Unfortunately, as they evolve, they sort of spread out. Their volume doesn't change — this was shown by Liouville back in the 1800s:

5) Wikipedia, Liouville's theorem (Hamiltonian), http://en.wikipedia.org/wiki/Liouville's_the…

But, they get stretched in some directions and squashed in others. So, it seems hard for each one to get mapped completely into another, without their edges falling into the dangerous no-man's-land [in between].

We want to keep our macrostates from getting hopelessly smeared out. It's a bit like herding a bunch of sheep that are drifting apart, getting them back into a tightly packed flock. Unfortunately, Liouville's theorem says you can't really "squeeze down" a flock of states! Volume in phase space is conserved. . . .

So, the trick is to squeeze our flock of states in some directions while letting them spread out in other, irrelevant directions.

The relevant directions say whether some bit in memory is a zero or one — or more generally, anything that affects our computation. The irrelevant ones say how the molecules in our computer are wiggling around. . . or the molecules of air around the computer — or anything that doesn't affect our computation.

So, for our computer to keep acting digital, it should pump out heat!

Here's a simpler example. Take a ball bearing and drop it into a wine glass. Regardless of its initial position and velocity — within reason — the ball winds up motionless at the bottom of the glass. Lots of different states seem to be converging to one state!

But this isn't really true. In fact, information about the ball's position and velocity has been converted into heat: irrelevant information about the motion of atoms.

In short: for a fundamentally analogue physical system to keep acting digital, it must dispose of irrelevant information, which amounts to pumping out waste heat.

In other words, we get away with calling our computers nicely deterministic, even though they're actually full of jiggling atoms and surging electrons, only because we've built a higher level of organization which lets us not care about individual atoms and electrons. Each of those atoms is, in principle, a random number generator, but because we are so terribly clever we can sidestep that fact! As long as our transistors, each of which are made of many atoms, keep acting like our idealized concept of a transistor, we can put their component atoms inside "black boxes" and worry only about how the transistors are connected. Similarly, by assuming that the processor, memory and so forth always act like our idealizations of processors and memory devices, we can create software and not worry about what the hardware is doing. I don't need to know the quantum physics of semiconductors to code a program!

Of course, we pay a price for erecting these abstraction barriers. . . . but I'll leave it to others to play with that.

It's interesting how rapidly discussions like this, about free will and such, always come down to hope. Why, I wonder, do we want so badly for our brains to be different than computers, or than our caricature of computers? The answer seems to be tied up with our desire to have an immaterial soul, some essential part of us which is forever preserved against dissection.

For my own part, I find the premise that we have immaterial souls quite troubling. The chaotic nature of physical phenomena, as Feynman described in the passage I quoted earlier, seems adequate to satisfy whatever appetite for "free will" I happen to have. I am, in principle, unpredictable, although my friends will testify that I have many buttons they know how to push. Why, then, postulate anything else in order to save a concept of "free will" which doesn't really need saving?

This topic came up after dinner a few nights ago, and my friends and I spent hours hashing out the ramifications, long into the night. Ben said he liked the idea of a part of consciousness which was insulated against the vicissitudes of life, firewalled away from drunkenness or brainwashing, a part of the identity which only accepts the changes it is willing to accept. Of course, we have no demonstration that such a part actually exists, and in order for the "firewall" to be an effective guard, it has to be a complicated device. We can actually make this assertion with some degree of rigor: the cybernetics people have a rule called Ashby's Law of Requisite Variety, which says that in order to be effective, a control system has to have as many different states as the system it is trying to control. Insufficient flexibility leads to breakdown. To shield against the troubles of a complicated life, the soul's firewall must have many states of being, indicating that the soul cannot be the featureless point of light we so often imagine.

The evidence for the existence of matter and energy is, quite literally, all around us. Why, to paraphrase Sagan's Demon-Haunted World, should we presume that something quite different from matter and energy is necessary to explain thought, memory, feeling or self-awareness? The problem becomes particularly acute when no phenomenon claimed to have its basis in the non-physical soul — telepathy, telekinesis, precognition, et cetera — has been observed in anything like reliable circumstances. Furthermore, we face the troubling issue that chemical substances, from alcohol to LSD and Prozac, can alter our mental state. The exact nature of the change is not predictable, but the fact that a change will occur can be asserted with high confidence, and the qualities of the change can often be stated with some reliability.

For thousands of years, we've been accumulating evidence that emotion, thought and all other activities of the mind are material in nature. Beer is as old as civilization, and so too without doubt are children conceived in drunkenness. Psychedelic mushrooms also have a pedigree stretching back into dim antiquity. We are now giving pills to children in order to modify their behavior and stamp out phenomena which we aren't even quite sure are diseases. Yes, all our pills have side effects, and yes, we don't know the details of how they work, but our culture is now replete with the components of a very big idea: that which we call the soul is an arrangement of matter.

That awestruck memory of the night sky, that warmth from a lover's smile, that fear for the species' future — they're all yesterday's chocolate bar. Nothing exists, save atoms and the void. We take in atoms and make them part of us, each bit of the molecular dance remembering what the steps were when the dance was performed by the previous set of partners.

I have the strong suspicion that we will learn more about cognition and consciousness before we're done. Our drugs will change our souls in ever more involved ways, and our computers will execute many more of the functions once believed to be humankind's sole property. You don't have to go all the way to the Singulatarian, upload-your-mind-into-software view; even a "weak AI" scenario is theologically troubling. Just as we've imperiled traditional religions by shrinking the margins of physics back to the first instants of time, though not all the way, so too are we imperiling mysticism by advancing towards our own consciousness. We have already encountered the God of the Gaps. I have little doubt that in coming years, we will move into a worrisome presence, a growing awareness of the Ghost of the Gaps.

Yes, that's me.

I can think of a few more things to say, but I should probably try submitting this comment now.