[QUOTE=nivlac]
This is called the dichotomy paradox. Essentially, it is resolved by the fact that the sum of an infinite series of numbers can be a finite number.
[/QUOTE]
Of course! Oi, my head hurts.
It’s simple.
The bullet doesn’t travel half the distance at a time. It travels the whole distance. When you’re counting chickens, do you count half at a time? And then half of that and that and that? Then how could you ever have 2 whole chickens? Or even 1 whole one for that matter.
When we count WHOLES, we are counting the SET. 1 is the set of all the infinite halves between 0 and 1.
[QUOTE=JohnT]
space isn’t infinitely divisible… IIRC, the smallest distance possible is 10^-33 centimeters.
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So space is quantized? What is the evidence for this?
[QUOTE=Bear_Nenno]
When we count WHOLES, we are counting the SET.
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I’m skeptical that summing an infinite series involves counting. And that chickens have much to do with the case.
[QUOTE=Xema]
So space is quantized? What is the evidence for this?
[/QUOTE]
Perhaps I’m wrong. That’s what reading popular science books will get ya! 
One of my first sigs:
"Tell Zeno I’m Willing to Meet him Halfway!"
This is stupid. It’s not even a paradox. Who aims a gun at a person’s chest anyway? You aim it at the spot directly behind the chest. Ergo, no paradox. 
[QUOTE=JohnT]
Perhaps I’m wrong. That’s what reading popular science books will get ya!
[/QUOTE]
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.
[QUOTE=Xema]
So space is quantized? What is the evidence for this?
[/QUOTE]
I’m guessing the 10^-33 number is the diameter of an electron or some such critter?
[QUOTE=Little Nemo]
We can give Zeno a pass because he lived 2500 years ago. But calculus has been around for three hundred years; even a French teacher should have gotten the word by now that an infinite series can add up to a finite total.
[/QUOTE]
In a country where possibly 50% of the people are so disconnected from science and reality that they believe in Young Earth?
[QUOTE=Xema]
I’m skeptical that summing an infinite series involves counting. And that chickens have much to do with the case.
[/QUOTE]
Starting with zero, what’s the very next number? It’s not 1. It’s 0.0000000000000000000000(infinity)1.
You have to count in sets or you can never reach the next number.
[QUOTE=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.
[/QUOTE]
Gotcha. Thanks for the clearing up.
(Though I think I got the “Planck Length solves Zeno paradox” idea from a book somewhere. However, since I recycle my books I likely don’t have the one that gave me the idea. I’ll just blame Timothy Ferris and be done with it. 
)
Did you consider quoting Anny Schrondinger: “Erwin, what have you done to that poor cat? It looks half dead!”
[QUOTE=Bear_Nenno]
You have to count in sets or you can never reach the next number.
[/QUOTE]
It seems to me that counting implies discrete entities: you can count chickens, sheep or atoms, but you can’t count distance, time* nor the elements of an infinite series.
- except perhaps in a musical context
I don’t know about any Anny, but I used a quote very much like that quite a while back. You musta missed it.
[QUOTE=Jayrot]
Yeah, it went from question to answer to snark in a matter of minutes.
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At this rate, we’ll get to the spanking well before dinnertime.
[QUOTE=Xema]
It seems to me that counting implies discrete entities:
[/quote]
Discrete finite entities which can be divided into an infinite number of pieces. Just like any measurement of distance, time, etc
[QUOTE=Q.E.D.]
So, it’s some sort of paradox, is it?
[/QUOTE]
It is and it isn’t.
[QUOTE=Bear_Nenno]
Discrete finite entities which can be divided into an infinite number of pieces.
[/QUOTE]
Well, my feeling is that once they’re divided into an infinite number of pieces, you can’t really count them (it’s kinda the nature of infinity). To be sure, there are techniques for computing the sum, but I’d say these lie outside the realm of counting.
It is fair to note that while, say, time can’t be counted, an effective way to measure it is to quantize it and count the quanta - for example, by making a cesium atom vibrate and counting the vibrations.
Ahh, you needs ta tread up on your infinities. “Countable infinity” is an actual term in mathematics. It’s the nature of some infinities.