portegys (08/09/82)
I think that it is not possible for a being contained in a system to ever know the system completely. Because, to know the system completely would be to also understand itself within the system completely, which would be a model of itself contained within a model of itself contained within a model of itself ... an infinite regress. This bears on determinism vs free will in that I think in order to show one vs the other, it is necessary to have a perfect knowledge of the world, which cannot be done. So, if you can't choose conclusively between them, why not just use the one that fits the situation best? For science, determinism seems to be most appropriate. For accounting for a person's responsibilities within society, I think a free will model works better. Tom Portegys
davidson (08/23/82)
Interestingly, it does not necessarily involve an infinite regress to have part of a system completely model the whole system. It does, however, require that the system be describable with less information than it contains (and there are other requirements too). An analogous situation is with the common programming exercise of writing a program which prints itself out. Indeed, a deterministic universe with simple physical laws and a simple initial state is easily modelled completely from within. A non-deterministic universe, on the other hand, can not be completely modeled at all. This brings up one of my favorite speculations about the universe: assuming that the universe is finite in extent, or taking a finite subset of it, does the universe or that subset contain a finite or an infinite amount of information? That is, could one completely specify an instantaneous time slice with a finite amount of information? The answer to this question depends, I think, on whether space, as well as everything else, is quantized.