Anything moving from point A to pointB must first travel half of that distance. Before that it has to travel half of half of that distance and so on. It is possible to iterate this to infinity. Therefore, motion is impossible. — TheMadFool
Each step takes half the time of the previous step. There are an infinite number of steps, but they do not take forever. — Banno
I did conclude that Zeno started off with the wrong premise - that space is infinitely divisible.3. Zeno was wrong — Banno
So let's suppose it takes the runner one minute to run 1 km. That OK?
...
So after ½ a minute, she's traveled half the distance.
After ¾ minute she's traveled ¾ a kilometre.
And so on.
And, although there are in infinite number of steps in the process, it only takes a minute.
No paradox. — Banno
I don't get why this is a topic.
How do folk get through high school without being exposed to calculus? — Banno
There's no necessary reason to think that the mathematics of limits addresses the metaphysical problem. — Michael
SO, what is the metaphysical problem? My suspicion is that there is none, once the mathematics is understood.
If I am wrong, then set out the paradox for us, clearly. — Banno
The mathematics shows that despite there being an infinite number of steps, the result is finite. So the conclusion, that motion is impossible, is a non sequitur.
The paradox is that if distance is infinitely divisible and if instantaneous travel between one point and the next is impossible... — Michael
It seems to me that what you have written here is misguided - an inaccurate picture of the number line. — Banno
Since a number line is infinitely divisible, there is no "one point and the next"; between any two points there are an infinite number of points.
It follows that the notion of instantaneous travel between one point and the next is muddled.
I didn't say this earlier, but I did kind of think that there is a smallest point, and things do actually just teleport kinda, from one point to the next. That's a thing, right? — Wosret
I'm not talking about a number line. I'm talking about actual space. — Michael
However the paradox is framed precisely as a purported paradox of the infinite divisibility of a line — John
I agree with Banno; the realization that the finite time taken to traverse the line is infinitely divisible (in principle) just as the finite line is, dissolves the supposed paradox.
It takes a non-zero amount of time to travel any distance, and so given the infinite divisibility of space it should take an infinite amount of time to travel from any arbitrary point to the other. — Michael
No; and that's were the limits fit into the argument. There are an infinite number of steps between 0 and 1; it takes a specific time to travel between any two points; but the sum of those specific times is not infinite. Just as the sum of ½, ¼, ⅛... is not infinite. — Banno
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