October 01, 2006

Prediction, determinism, and free will

[Books_] Imagine standing around in a train station when you notice a TV monitor hanging on the wall. You recognize your own face looking back at you from the screen. You think no big deal, it must be one of those closed circuit security monitors with a camera hidden someplace. But then the you on the screen starts walking and gets on a train you know that is not due for another five minutes. The monitor is connected to a magic camera that shows what is going to happen five minutes in the future! Well, do you have the freedom not to get on that train now? Or will you somehow get compelled to get on the train against your will? If you do have the freedom to betray the monitor, does that mean a future showing monitor is impossible to build? Maybe quantum uncertainty or chaos make future prediction at that scale technically infeasible. Even for God? What if the universe was deterministic? Would that help things?

I thought about this problem on and off for a number of years until one day I ran into a paper by Gary L. Drescher. I had met Drescher once at the AI lab, enjoyed his book Made Up Minds like most fellow grad students, admired his explanation of quantum mechanics, and puzzled over his refusal to get any support from DARPA. And here he was again, with the solution to the puzzle.

To avoid the complications of the real universe Gary's trick is to think of made up universes with simple rules. This prevents confusion and eliminates prejudice. So going back to my train station, imagine a universe simulated on a computer that has completely deterministic rules. A bit like the Matrix movies. You program the simulation and let it run until sentient beings evolve and start building train stations. It is your program, and it is deterministic, so you know what is going to happen at any point in time. When in doubt, you can just load the program on a second computer and fast forward to see the future. Do YOU have the power to place a monitor that shows the future at the train station in your simulation? Well of course, you might say, you wrote the program, you own the computer, you can do anything. Not quite, it turns out...

You can certainly put a monitor in the train station and pump images of five minutes in the future to it. But trouble starts as soon as one of your simulated creatures actually looks at the monitor and decides what to do based on it. To decide what to put on the monitor at that moment, you need to fast forward. To fast forward you need to simulate what the creature is going to do. What the creature is going to do depends on what it sees on the monitor. Hmm, we have a circular impasse. Well, you might say, why not run a bunch of simulations putting various future movies on the monitor to see how the creature is going to react - one movie shows the creature getting on the train, another shows not getting on the train, for example. You fast forward in each case, then choose the movie that actually turns out to be correct. The trouble is none of the movies are going to turn out to be correct if you have a particularly stubborn creature that keeps doing the opposite of what it sees on the screen. And that brings us to the crux of the matter - the "creature" does not even have to be a sentient being. It can be a very simple automaton with the only talent of doing the opposite of whatever it observes on the monitor. And you are helpless.

So there is nothing in principle against an omniscient creator who knows the future. He just can't share the information with the inhabitants. Unless of course he forcibly compels them to obey his prophecies, but that would be lame, interfering with their free will. Determinism and (somebody else's) knowledge of the future are not inconsistent with your free will, being forced into a particular future is.

The real universe has the added problems of quantum uncertainty and chaotic behavior which may make future prediction physically impossible. But our story shows that knowledge of your own future is logically impossible - as far as impossibilities go, that one is hard to beat ;)

Any errors and misunderstandings in the discussion above belong to me, and I acknowledge Drescher for the rest. I am looking forward to his new book.

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