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You can impose a one-dimensional ordering on a finite state of any size. Drawing a parabola, for instance, yields a 2-D figure. But the process that draws it (o
by javajosh 11y ago
You can impose a one-dimensional ordering on a finite state of any size. Drawing a parabola, for instance, yields a 2-D figure. But the process that draws it (on a computer) is 1-D:
Start at the origin
Move right X
Move up X*X
Make a dot
If X = Screen.Width Stop
X=X+1
Repeat
There you go: a 2-D thing from a discrete sequence of 1-D steps. I hope you can see that it generalizes to N-D things.
- hyperion2010 11y agoI think the question here, which has been raised in other parts of the comments here, is what the complexity of the operation to serialize/deserialize is and how one might think about translating between computational complexity and dimensionality.
- javajosh 11y agoMy contention is that all things are understood one step at a time, and I believe this is influencing theoretical physics in a way that the theoreticians themselves are not fully aware of. Especially Wolfram's theory.