So wait did anyone ever fix the whole "to cross a distance I must cross half the distance etc" all distance contain an infinite sum thing? Is the answer just that infinite sums can have finite results?
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in the mathematical model, yes, infinite sums (over either distance or time) can have finite results. in âthe real worldâ (slightly less idealized model) itâs not at all clear that itâs possible ro infinitely subdivide space or time, or perform infinitely many actions
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a thing that i think mathematicians and physicists donât do a good job of conveying is that most of our use of large infinite objects like the real numbers is a matter of convenience. the infinite is a convenient approximation of the merely unimaginably large finite
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at infinity all the error terms disappear so you only have to work with the asymptotic behavior. when we do something like model heat diffusion with the heat equation we are *approximating* the behavior of ~avogadroâs # of particles by the solution to a differential equation
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it would seem to be more fair to say that it's clear that it isn't
or y'know why would we keep using this word "quantum"
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also we have changed our concept of time.
for zeno, i don't think there is any paradox in an object having a non-zero spatial extent, even though for the wall to extend from one side of the room to the other it (")first(") has to extend half-way, and so on.
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we are now more accustomed to thinking of time as akin to a spatial dimension.
then motion is conceptually just like spatial extension.
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