Wednesday, 4 February 2009

The new face of the possible

Warning: this is a change from our usual programming. If you are not interested in the theory of interacting systems, you might want to skip it.

One of the things that has really changed with the widespread use of computer models is the achievability of perfection. What do I mean? Well, one big difference between a computer model and reality is the ability to restore state. That is, to make the world just like it was earlier. The undo button. You really can, in a model (and by `model' I include programs like Word or Excel, computer games, and so on as well as more obviously model-like things) undo the result of some action as soon as it goes wrong. That is much much harder in the physical world, as anyone who cooks or does DIY will affirm. What this changes is the how hard it is to do some difficult things.

Suppose you have a 1 in 1000 chance of getting something right. What that thing is doesn't matter - think of making the perfect Bearnaise, or building a shed, or jumping just right so that Lara Croft navigates over a chasm. In the real world, it may take many many tries before you get it right. The amount of time required is considerable. In a computer model, though, if you save frequently, you can just restore from the last good point. So if that 1 in 1000 is the result of three separate 1 in 10 actions, then you can treat each separately. As soon as you get one of them right, you never have to do it again, as you can restore the state just after you succeeded. This dramatically changes the amount of time needed to do difficult tasks that rely on a sequence of smaller but still hard-to-do things. (It changes the hardness in particular from multiplicative time in the number of steps to additive time - as any complexity theorist will tell you, that is huge.) At least in a virtual world, perfection really is sometimes possible.

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