Why does the bullet reach me?

[Xema]

@CalMeacham

“Countable infinity” is an actual term in mathematics. It’s the nature of some infinities.

Good point - the integers are an example.

But I continue to maintain that summing an infinite series (as in the OP) is something different from counting.

[Little_Nemo]

I don’t know about any Anny, but I used a quote very much like that quite a while back. You musta missed it.

Obviously not.

[Bear_Nenno]

@Xema

Good point - the integers are an example.

But I continue to maintain that summing an infinite series (as in the OP) is something different from counting.

Sure, I can go along with that. All I’m saying is that the idea that a flying arrow is so complicated and somehow a paradox because you can divide the whole distance into infinite stationary moments is about as assinine as saying you can’t count chickens because they can be divided into infinite numbers of pieces. In the real world we count whole objects and measure whole distances. If something travels a meter per second, then in one second it will travel one meter. There’s nothing mysterious in the fact that the meter and the second can be divided into infinite parts.
If I’m counting 2 chickens every minute, how can I ever count a whole chicken…

[Der_Trihs]

@Q.E.D.

Yes, you were thinking of the Planck length, about 1.6 × 10[sup]-35[/sup] m. It’s not the smallest possible length, it’s the smallest meaningfully measurable length. There may indeed be structures smaller than the Planck length, but we can never measure them. Motion is not quantized, and we can meaningfully examine any arbitrarily small distance mathematically, even if we can’t actually measure it.

I’m not sure of that ( but I’m no physicist ). From your own link :

Hence in any theory of quantum gravity combining general relativity and quantum mechanics, traditional notions of space and time will break down at distances shorter than the Planck length or times shorter than the Planck time.

Bolding mine. In other words, there are no structures smaller - or at least not much smaller - than the Planck length, because size is one of those “traditional notions”. As I’m always understood it, the usual ( Copenhagen ) interpetation of quantum mechanics is that the the “uncertainty” in quantum uncertainty is real; that the reason they can’t measure various quantities is because those quatities are undefined, not just unmeasurable.

Or in other words, motion is quantized, along with everything else.

[Xema]

@Bear_Nenno

In the real world we count whole objects and measure whole distances. If something travels a meter per second, then in one second it will travel one meter. There’s nothing mysterious in the fact that the meter and the second can be divided into infinite parts.

This makes sense, but as a way of dealing with the paradox it seems to be much the same as saying “Hey, don’t think about the problem that way - here’s a simpler way to analyse it.” True, but not a very satisfactory resolution of the thought problem.