As I keep saying, you are trying to map Euclidean objects onto discrete space. That's a mistake. If space is discrete, lines are composed of points.
In this example, the "lines" are somehow magically between the points in continuous space.
Post by twetch#1832
Second, the Pythagorean theorem gives you a number that's relevant in Euclidean space. In discrete space, it doesn't work. There isn't enough information (i.e. there are changes in two dimensions that cannot be capture by a single number)
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Mapping from euclidian to discrete space worked reasonably fine for quite a while now, and a few people used pythagorean theorem in this seemingly discrete world - no pi, no squares, no negatives, maybe it's fun, maybe it's true, don't think it's useful
Mapping from euclidian to discrete space worked reasonably fine for quite a while now, and a few people used pythagorean theorem in this seemingly discrete world - no pi, no squares, no negatives, maybe it's fun, maybe it's true, don't think it's useful
Right - Euclidean geometry is arguably the most practical mathematical theory of all time.
But like the Ptolemaic model of the solar system, "practicality" often does not translate into "truth," and I'm interested in truth.
Geocentricism worked just fine for a long time. But eventually, it needed to give way to superior theories.
Discrete space will be the same. Already useful in physics, and it will become more important as micro-microtech improves.