Free Will and Turing-completeness of the Brain
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.]]