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Free Will and Turing-completeness of the Brain

In this essay, I’m going to explore the question "If the human brain is Turing complete, what does that imply about the existence of free will?"  And moreover, what does that mean about the ability to upload our consciousness into computers?

First, a little computer science background.  Turing completeness is the idea that a computing system has the same capabilities as a universal Turing machine.  This theoretical machine moves along a long tape which has various symbols on it that the machine can read and write.  The machine itself is always in one internal state, but will change to different states based on its programming and input.  It is programmed by a huge state transition table which says "if you’re in state X, and you’re reading symbol Y, then write symbol Z, move left n spaces, and switch to state W" for all possible states and symbols.  It turns out that with a long enough tape and enough states this device can do just about anything you think of a computer being able to do.  In fact, computer scientists have shown that every modern computer system is functionally equivalent to a Turing machine.  That is to say all modern computers are Turing complete.  It’s useful because it’s simple enough to prove theorems about.  Some important things we know about Turing machines and anything which is functionally equivalent to one:

  • Turing machines are deterministic — given a set of inputs they’ll always reach the same output.
  • It’s impossible to reliably predict whether or not a program on a Turing machine will ever finish.

I see two ways to interpret the question of whether or not a human brain is Turing complete.  The first one is "Can a human brain perform the same functions as a Turing machine?"  I think that given a pen, paper, and enough patience the answer is clearly yes.  But that’s not the question that interests me.

As a transhumanist, the interesting question for me is "Can a Turing-complete computer perform the same functions as a human brain?"  This question is important to me because if the answer is yes, then it is possible for a computer to simulate a human personality.  That is to say uploading of a human consciousness into a computer is possible.  I’m going to dodge the detailed analysis of this question today, and get back to it in a later article.  For now, let’s assume the answer is "Yes" and see what that implies about free will.

Remember that theorem that says Turing machines are deterministic?  That is, once you start it going with a given set of inputs, that it’s always going to reach the same answer?  If this were true for us as humans, then we would have no free will — our actions would be entirely determined by our current state and our surroundings.  We might think we are making choices, but in fact a fast computer could run the same calculation and tell us what our answer would be before we thought we had decided.  So by this logic if uploading is possible, then humans have no free will.  Troubling, eh?

Fortunately, I think the above analysis has a flaw.  Let’s dive down a little deeper into neurochemistry.  Neurons fire as a result of electro-chemical processes.  Basic chemistry tells us that the rates of chemical reactions are deterministic based on concentrations of the relevant input chemicals.  But if you took stat-mech then you learned that these predicted rates are actually just statistical averages and that they’re only accurate if the brazillions of molecules involved happen to collide with each other at a constant frequency as they randomly bounce around in solution.  And quantum mechanics tells us that this apparently random bouncing around is in fact, to Einstein’s chagrin, truly random — god does play dice with the universe.  (I’m not sure I completely buy this, but I’ll have to save that for another article too.  Yes, I know that the Bell inequalities were experimentally observed in the 1980’s but it still sits funny with me.  Sorry grandpa.  More on this later.)  Because of this randomness, the instantaneous rate of any chemical reaction will vary randomly, while still averaging around the classically predicted rate.  So the upshot is that neurons don’t behave completely deterministically, but that the exact timing of neurons firing has a truly (quantum) random component to it.

Now this implies quite firmly that our brains cannot be simulated by a Turing machine since Turing machines can’t act randomly, and thus wouldn’t be able to properly simulate the randomness of neurons firing.  But if we modify a Turing machine slightly so that a spot on its tape read a different random symbol each time you check, I think we’re good.  Given this, it seems reasonable that a modern computer that has a source of truly random data could simulate a brain.  Some have argued that we need quantum computers to simulate consciousness, but I don’t think so.  (Again, more on this later.)

Computers are pretty good at generating psuedo-random data internally, and by listening to the outside world (hard drive vibration, microphones, etc) can generate what is probably actually random data.  If true randomness is really important, we can build small accessory cards that sample thermal noise on
a resistor and produce large volumes of truly (quantum) random data.  Some advanced cryptographic systems do this today.  So it’s totally possible today to build this modified Turing machine that also incorporates random input.

Now our transhuman dilemma is solved.  The essence of free will lies in the quantum randomness of electro-chemical processes in our brain.  Moreover, it will be possible to upload our personalities into computers, complete with our free wills in tact, by incorporating random processes into the hardware that simulates our brains.  If the computers we upload into are only psuedo-random (as almost all software is today), we will appear to have free will, in fact we will believe that we have it, but we will in fact be total robots.  Now, who can come up with a Turing test for free will?

[[Thanks to Barry Brummit.  This article is a rehash of a couple good conversations we had over New Year’s and this morning after yoga practice.]]

  1. Tomek says:

    Very interesting topic. I think the randomness of a brain (if exists, thus free will) is hugely influenced by a body that acts as a main sensory device and parametrizes its functions. The discussion involves talking about the brain as separate organ, completely disconnected from a body, totally separate entity. I believe a brain’s “decisions” are mostly influenced by information coming from body cells (I heard this saying once – “happiness on the cellular level”).

    So even if we get the brain simulator running (as two software hemispheres or one, that’s another question), there still be a lot of work to feed it with the information in order to simulate the human behaviour. Although this seems simple (as we just could use working sensory devices like thermometers and touch sensors) we’d need to multiply them by millions in order to make this simulation truly work.

    It might be only an illusion but sometimes it seems I can feel my body as balanced wholeness, it seems like there is another consciousness (of physical existence).

    Just a few thoughts.

  2. Nikunj Raghuvanshi says:

    I’d also like to throw in another piece of information that very few people seem to be aware of. David Bohm’s book “The Undivided Universe” describes a consistent explanation for quantum randomness in terms of purely deterministic, objective events. J.S.Bell (Bell inequality fame) was a big proponent of his theory and mentioned it in his book “Speakable and Unspeakable in Quantum Mechanics”. Bohm’s theory makes explicit use of non-locality at the quantum level, as verified by EPR-inspired experiments by Aspect etc. and very recently too:
    Bohm shows that you can really state quite consistently that electrons _are_ particles which have _trajectories_ that are governed by quantum wave functions in a non-linear fashion. This non-linearity generates the apparent randomness, while ensuring that all statistics are reproduced exactly as in the classical (Copenhagen) interpretation of quantum mechanics.

    All the weirdness of quantum mechanics lies in the non-linearity of what he calls the “Quantum Potential” that influences a particle not in the standard multiplicative way, but in a weird non-linear fashion that is required for agreement with experimental results. In addition to unpredictability, this quantum potential also captures non-locality because the strength of interaction between two particles does not depend on the strength of the wave function, being of the form $\frac{\nabla^2\psi}{\psi}$.

    In the context of your article, Bohm explicitly mentions that one very important fact that physicists have learned in the past few decades which was not known in the early twentieth century when quantum mechanics was conceived, is the distinction between Determinism and Predictability. Navier-Stokes equations have taught this to us very well, and Bohm’s theory just takes it many leaps ahead — in both cases the non-linearity generates highly unpredictable results, without making Einstein unhappy (at least as far as determinism in a philosophical sense is concerned). So, a way of thinking might be, God doesn’t play dice, but boy, can he do non-linear math with infinite precision.

    Either way, it seems that we need a better understanding of the dynamics of non-linear systems and come up with a useful vocabulary for talking about determinism and predictability.

  3. My personal take on free will is that it’s an illusion, as is consciousness.

    The impression of free-will is very believable though as the brain probably exhibits chaotic dynamics (or at least I’d expect it to, I don’t have references on hand). From any given state of the brain, a slight change, however minute, could give rise to a very different outcome later on. This means that for any external system to an individual brain, it is impossible to completely predict the behaviour of that brain… eventually the brain’s state will diverge from your model/simulation. In addition, I believe that consciousness is due to a recursive model that represents ourselves, because it’s a model of our of the epiphenomenon of our “selves”, it also has incompletely knowledge of the rest of the brain – this gives our conscious minds the illusion of free will.

    (That is, assuming we exclude the almost impossible ideal of having perfect knowledge of the brain’s state which would include all neurochemistry as well as structure)

  4. mauszozo says:

    The christian biblical story of the Garden of Eden shows a Turing test for free will.

    God: "Hmm, I made humans, but how do I know if they're ready to leave the test environment? I know, I'll give them a fruit tree, and tell them they'll die if they eat from it. Then I'll have some animal tell them I lied. If they choose to go against their creator's warning and risk death, they must have free will."

  5. leodirac says:

    Thanks for the feedback. You make some good points. I'll address the easy parts first.

    As to whether or not randomness is important to the useful parts of consciousness, I agree with you completely. I think the silicon computer analogy is very apt — randomness exists in computers and generally doesn't effect the behavior, and when it does, the effect is negative. I wouldn't be surprised to learn that the brain contains many error-correcting features which try to average out the effects of randomness. Clustering axons into nerves is an example of this — the law of large numbers says that the random variances get averaged out.

    I hear you addressing a related issue that I side-stepped which is a definition of free will. It's a tough one. I agree with you that it might not be a very useful concept, because I think entities without free will can do just about everything we want conscious entities to do. Theologians have debated for centuries how people could have free will in the presence of a good-natured omnipotent god — it's paradoxical. If our decisions were being made for us, how would we know? And to the point I think you're making, what would it matter? IMHO not much.

    Intentionality is perhaps a more interesting & meaningful metric by which to analyze consciousness, but I don't think it's useful to equate it to free will. I don't believe that an intentional system which is deterministic can be said to have free will. If intentionality only requires reaction to surroundings based on internal rules and a model of the world outside, then a vending machine qualifies. (Especially the ones that make clunking noises whenever a person walks by!) I don't think vending machines have free will, except perhaps when they violate their programming and choose to leave that bag of gummy bears hanging by a corner. When vending machines behave, they act deterministically, and I argue that this determinism precludes them from having free will.

    I'm really not sure I know what free will entails, but I can demonstrate cases where it does not exist. For example, if my choices could be reliably predicted by an outside agent before I make them then I would not have free will. If my brain were deterministic, a sufficiently advanced model could do this. Due to the error-correcting features we've both discussed, I think my brain might be effectively determinsitic — I'm not sure I really have free will. I think many intelligent, even conscious entities might believe they have free will when they don't. But the fact that they don't actually have free will doesn't detract from their value. All this is an argument for why free will requires something non-deterministic, which in our understanding of the world means randomness.

  6. mez says:

    Whoa there, tex.

    I usually agree with what you put on your blog so I have no reason to comment. :)

    But I disagree with this post on a couple deep levels!

    The first is the association of randomness with free will. What about a random process implies free will? If you a shroedinger box, and the behavior inside is the result of a random process, does that entail free will?

    I don't think so. To me "free will" is kind of a weak concept, to be honest. But if we have to find it anywhere, let's look for it in terms of "intentionallity". A system is intentional to the extent that it can choose its course of action. To choose its course of action it needs some some degree of awareness of the universe around it, potentially a way to model that universe (and the results of actions it takes), and a way to take action.

    The human brain/mind constitutes such a system. So what if all the component operations going on are (or might be) deterministic? If you break the system up into sufficiently small components, you'll find that free will disappears. So does intelligence. So does sensation. So does (that cursed word) 'consciousness'.

    Free will is something that only shows up at the right level of abstraction. Put another way, intentionallity is an emergent property of the system, not a property of its components.

    There's a far better treatment of this than my short comments in Dan Dennet's "Freedom Evolves".

    The second area I don't agree with (or at least question) is whether quantum processes or slight random fluctuations in neural signalling are important in cognition. Honestly what I'd say is that we just don't know. But there's no reason a priori to believe that those fluctuations are actually important.

    Put another way – an electronic computer also has apparently random fluctuations in behavior, due to quantum tunneling of electrons, the effects of nearby electric and magnetic fields, imperfections in the chip itself, etc… It doesn't behave 100% consistently. But those inconsistencies are not important to its successful information processing. If anything, they detract from it.

    So before we get into saying that quantum fluctuations in chemical reactions that underly neural signaling are important to free will, I'd ask for evidence that those quantum fluctuations are important to cognition, or to the biological function of the brain. Maybe there's evidence for that, but I don't know of any.


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