This is a weird question that I wasn't sure where to ask. Say I have two points A and B. I roll a ball from A to B. Between A and B there are an infinite number of points right? Wouldn't it take an infinite amount of time to move across an infinite number of points? Why does it then only take a finite amount of time for the ball to get to B?
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1$\begingroup$ We observe the ball to do so, therefore any model which holds Zeno's paradox to be a true contradiction or antinomy is experimentally falsified. Look up Zeno's paradox, I'm sure this will help you reason this one through: philosophers have discussed this for two thousand years and in the meantime mathematicians have made the notions of limits rigorous. $\endgroup$– Selene RoutleyCommented Sep 10, 2015 at 2:55
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$\begingroup$ There is an infinite quantity of intervals too. $\endgroup$– ariveroCommented Sep 10, 2015 at 2:58
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$\begingroup$ Greek philosophers invented the atom, but it seems that they fell just short of inventing quantum mechanics. Had they just concluded that there can only be a finite number of states and applied their epicycles logic to how the states change over time (each eternal component gets multiplied by a phase factor), they might have succeeded. $\endgroup$– Count IblisCommented Sep 10, 2015 at 3:17
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$\begingroup$ those infinite points are packed infinitely close together to the point there is zero distance between each pair of points. add up all those zero distances and it is not surprising you can move from points A to B with ease. A and B are on top of each other $\endgroup$– scmCommented Sep 10, 2015 at 3:19
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$\begingroup$ @CountIblis: Quantum mechanics doesn't require that the number of states be finite. It doesn't even require that it be countable. The discovery of quantum mechanics was only possible because a great deal had been learned about atomic physics, nuclear physics and optics. The Greeks didn't even have the beginnings of either of these fields. $\endgroup$– CuriousOneCommented Sep 10, 2015 at 5:18
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``Wouldn't it take an infinite amount of time to move across an infinite number of points"
This is incorrect. The correct statement closest to yours is ``it takes an infinite amount of time to move across an infinite distance". Infinite number of points does not necessarily mean infinite distance.
In fact, to see whether a distance is infinite or not, you simply cannot use the count of the points it contains. You cannot measure the size of an 1D object (i.e. a distance) using the count of 0D objects (i.e. points), much like you cannot measure a weight using a ruler.
