(February 13, 2018 at 7:47 pm)Grandizer Wrote: About Zeno's paradox and infinite divisibility, a general question for all: would it be reasonable to argue that what works on paper does not necessarily translate effectively to the real because mathematics doesn't suffer the constraints reality (or at least this local universe) tends to haveMath has it;s limits..but in this context that isn;t ne of them.
Consider the following; I place you in a rubber room with a piece of granite. You can't actually break it in half.but that doesn't mean it doesn't have two halves, hemispheres, if you will. Further, your practical inability to break a piece of granite in two in a rubber room does't mean that each of those hemispheres can't be divided into quadrants. So on and so forth. Whereas once it was thought that an atom was indivisible, it was always similar to a piece of granite in this regard..and in truth we learned that we could split them practically as well. Now we're down to the subatomic..and while at some point we have no practical ability to split x..this doesn't make the concept of the hemispheres and quadrants (ad infinitum) of x any less intelligible or valid.
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