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Even if the world is fundamentally discrete, that does not mean that continuous models are not valuable. They are. We are used to doing discrete approximations
by mtzet 9y ago
Even if the world is fundamentally discrete, that does not mean that continuous models are not valuable. They are.
We are used to doing discrete approximations to continuous problems, but the other way around works too. For example, evaluating the sum
1 + 1/4 + ... + 1/n^2
is quite hard. On the other hand, we may approximate by the integral over x^2, which remarkably has an easy formula.
Continuous and discrete models complements each other, they are not mutually exlusive.
- hvidgaard 9y agoI wasn't trying to say that continues models are not valuable, only that the question "is the world continues?" does not make sense if we can only interact with it in a discrete way.
- tome 9y agoWe don't interact with complex numbers but "Are quantum 'probabilities' complexL" is still a meaningful question.
- hardlianotion 9y agoThat is simply a rewording of the question: is it useful to use continuity to model the world.
- hvidgaard 9y agoThis is getting quite philosophical now. It depends on the intrepetation of "world". If we mean the universe then no, it is to our current understanding of it, not useful to model it's entirety using continuity, if we can only messure it discretely. If by world we mean a subset of the universe, then it makes perfect sense, because the world might be on the macro level where this "discretness" is far smaller than we ever want to go.
- hardlianotion 9y agoI think you should concentrate on the world model in my sentence rather than world. I have something I want to analyse. How is it useful to think about it and what techniques do I want to use?