Sunday, September 19, 2010

Determinism and Retro-Determinism

I was watching another one of those History Channel specials where they have futurists (including that guy with the increasingly crazy hair, I can't remember his name) talking about the technology to come (I know, I need to stop doing that, but it's entertaining.  And how does one become a "futurist" and get on TV talking about things that don't exist?  That sounds like a great job.) and one of the subjects that came up was how, with distant future technology, a civilization would be able to "model the universe" such that, having unlocked "the equation of the universe," they could theoretically construct a model of the universe and rewind/fast-forward to any point in order to study the past or predict the future.

You know "the equation of the universe" we're talking about here.  It's the idea that there is somehow one complete mathematical model that describes the interaction of all things which exist (matter, energy, various forces such as gravity, things we haven't even discovered yet, maybe a Higgs-Boson for good measure, etc.).  It's sort of an unofficial goal of the entire physics community, some are just a little more realistic about it than others.

This idea didn't sit right with me, and I've determined two main reasons why that's the case.  It's not so much that "the equation of the universe" isn't possible, or isn't worth at least in part pursuing, but rather it's the idea of "rewinding and fast-forwarding" that doesn't seem to add up in my own reasoning.

Let's start with fast-forwarding.  Seems simple enough, right?  You construct a complete model, you have the equation, you just move it forward faster than time itself is moving forward.  Computers are fast, future computers will be even faster, so it should work, right?  No.  See, there's a problem of infinite recursion.

The model of the universe needs to contain everything within the universe, right?  Otherwise you're not modeling the universe, you're modeling a pretend universe.  Hardly a useful model, because then you're just predicting a pretend future based on non-existant circumstances.  So you need the whole thing.  Well, the universe includes the computer you're using to model it.  Which means the computer needs to also be calculating its own act of calculating, which is part of the overall interaction of matter/energy/forces/etc. in the universe.  And it needs to do this in fast-forward.  Essentially, the computer needs to be able to calculate what its own calculations will determine faster than it itself would have determined them.

Yes, in the future we'll have really fast computers.  But this particular application of the technology would require a computer that's faster than itself.  Maybe someone can throw together a lot of quantum mechanics terminology and theory and begin to imagine a computer of unbounded processing speed, where it can calculate without being limited by the passage of time and therefore be infinitely fast.  Sounds cool, sure.  But isn't all of that still within the scope of "the equation of the universe" and therefore still needing to be calculated?

All you've done by removing time from the equation is demonstrated that any single "step" in the model being calculated can contain an infinite amount of interactions.  It's not entirely dissimilar to Zeno's Paradox of Achilles and the Tortoise.  That particular example was a little silly, of course, related rates being what they are.  But that age-old philosophical exercise would actually become real under this model.  In order to calculate "the next step" (that is, predict the state of the universe a moment before it happens) you first must calculate an infinite number of interactions taking place within that step.  In this case that includes your own act of calculating the calculations.

The second thing that didn't sit well with me, of course, was the act of "rewinding."  This doesn't fall into the same trap at fast-forwarding because when looking backward time is finite.  The act of calculating takes place after the base state of the model and therefore doesn't need to be calculated.  So it makes more sense and seems more plausible, right?

But what would this mean about the model of the universe and the equation of the universe?  If any state of the universe, given a finite set of previous states, can be calculated backward to any of those previous states, and if there are an infinite number of states moving forward, then that would mean that the state of the universe can contain an infinite amount of information (considering also previously where I discussed that there can be an infinite number of interactions in any infinitesimal amount of time).  It would also mean that the equation of the universe is an algorithm of infinite decompression of information (and, by extension, infinite compression of information).

Could such a thing even be considered plausible?  That somehow, in some way, the current state of the universe contains within it all of the information about all of its previous states.  And that this collection of information continues to grow within the confines of a finite model which does not grow.  That somehow a finite amount of matter, energy, forces, etc. can contain an infinite amount of information.  And that this is possible because at the very core of the nature of existence exists a single equation that, essentially, does nothing more than compress and decompress information between finite and infinite sizes.

You can see where that wouldn't sit right with me.  It's great to sit around and think about the boundless possibilities of future technology.  (And it would be awesome to have that job.)  And things like the technological singularity present deeply fascinating thought exercises regarding all facets of human nature.  But I just haven't been able to reconcile these particular gaps in the speculation.

Granted, there are probably aspects of this I don't fully understand.  I do understand that time itself is not a constant line forward (or backward) and that it is a variable part of that whole equation.  I understand that "in the beginning" (that is, in the immediate moments following the big bang) time was a very different thing than it is now, and that it will continue to change, well, over time.  (I've often pointed out when asked "what was before the big bang?" that, given the nature of time and the universe, "before the big bang" isn't part of the coordinate system.  It's akin to asking "what's north of the north pole?"  Time isn't constant, and it itself began when the universe began.)  But, simply as a matter of exercising what I consider to be reason, these seem to be significant holes in the theory.