Saturday, January 17, 2009

Determinism

I wonder if the universe is deterministic.

Science shows tell me that even though virtually everything we see and experience is deterministic, on the atomic and subatomic levels, the universe instead operates probabilistically. I don't know nearly enough about QM to know if this is in any way true or if it's a result of an immense body of complex theory being distilled into a form suitable for the slightly-above-average TV viewer.

If the universe is deterministic, it has some interesting consequences.


"Fate" actually becomes correct, in a certain interpretation. Not in the "invisible people who decide what will happen in our lives" sense, but in the sense that because all interactions of matter and energy have only one possible outcome, if you know the state of the universe and all the laws that govern it, you can figure out what the state will be at an arbitary point in the future. The state of the universe is simply a function of time. Everything that happens was always "meant" to happen, although without the connotations of intent.


But even if the state of the universe is only a function of time, it is at the same time impossible to predict the future. Even if you had perfect knowledge of all the rules governing the universe, there is not enough matter and energy in the universe to simulate it (regardless of whether the universe is infinite or not). This is because simulation of a system is an inherently inefficient process. You will always need at least as much matter and energy to simulate a system as there is matter and energy in the system that you are simulating. (The most efficient simulator is the system itself, at which point you are no longer simulating!) Thus unless we are able to step outside the universe and somehow gain access to a separate quantity of matter and energy meeting or exceeding the sum of that which is in the universe, we cannot simulate the universe as a whole, and therefore cannot predict the future.

Another consequence is that there is no such thing as randomness. True randomness requires that at some point there has to be an event whose outcome cannot be known in advance, but since we are positing that all events have only one possible outcome, we cannot have a truly random event. Our concept of "randomness" really only refers to the fact that some sequence of events has no discernible pattern. The key word there is "discernible." The closest we can get to randomness in a deterministic universe is a process whose results depend on such a phenomenally large number of variables that we could not possibly comprehend the entire process involved in generating those results. We can't tell the difference between a truly random process and a process so complex that we can't find any patterns in it.

Blah, blah, blah.

2 comments:

  1. It is possible that you can simulate a portion of the universe without having to simulate the entire thing, as long as you can rule out certain interactions. Information is generally not transmitted instantly, so what is happening in the Andromeda galaxy right now is not likely to have any influence on my decisions. So if things like the human brain are deterministic, it should be possible to simulate it with a high degree of accuracy using significantly less than all the matter in the universe.

    Still way beyond our capacity, but not as clearly impossible as something which requires more matter than exists.

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  2. That's true. You would be able to simulate "islands" of the universe as long as the amount of information you're throwing out is negligible. Two galaxies on opposite sides of the universe (or at least, the sphere of it that we can see) would be obvious candidates.

    Although what's happening in Andromeda _now_ doesn't have any influence on your decisions, what happened in Andromeda 2.5 Mya might ;)

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