Imagine a distance of any length. How long does it take to cross an infinite number of that length? It takes an infinite amount of time.
Divide the length between A and B an infinite number of times. We now have an infinite number of lengths, which means it will take an infinite amount of time to cross them.
Which means nothing ever actually moves and movement itself is an illusion.
But that distance is also infinitesimally small, or put mathematically. If “any length” is L, it is L/inf. Cross that distance an infinite number of times, you get L/inf. * inf. By basic rules of fractions, these infinities cancel out.
I’m no maths wiz, but I’d say poof goes the paradox.
I think the issue is purely semantical and if we had a way to discriminate between the ultimate infinity from the subinfinities, the whole paradox would become completely irrelevant
It’s an interesting exploit of not having that distinction though
Imagine a distance of any length. How long does it take to cross an infinite number of that length? It takes an infinite amount of time.
Divide the length between A and B an infinite number of times. We now have an infinite number of lengths, which means it will take an infinite amount of time to cross them.
Which means nothing ever actually moves and movement itself is an illusion.
But that distance is also infinitesimally small, or put mathematically. If “any length” is L, it is L/inf. Cross that distance an infinite number of times, you get L/inf. * inf. By basic rules of fractions, these infinities cancel out.
I’m no maths wiz, but I’d say poof goes the paradox.
I think the issue is purely semantical and if we had a way to discriminate between the ultimate infinity from the subinfinities, the whole paradox would become completely irrelevant
It’s an interesting exploit of not having that distinction though
I was told by a philosophy professor that to understand the paradox, I should read Wittgenstein. I couldn’t figure out Wittgenstein.