3 ms·
True. Then I would counter with: We traveled 1/2 of the way, so we still have 1/2 to travel. Since we travel at constant speed the 2nd half of the entire way
by oifjsidjf 4y ago
True.
Then I would counter with:
We traveled 1/2 of the way, so we still have 1/2 to travel.
Since we travel at constant speed the 2nd half of the entire way cannot take longer to travel than the 1st half of the entire way.
So each subdivision can NOT ADD more time than the previous 1/2 interval.
So we have an upper bound on time, since time can never be larger.
So while we do have an infinite amount of time intervals, the sum will never grow, it's upwards limited.
But since each "parent interval" is upwards limited, it's irrelevant to how many "child" intervals you subdivide it as the parent time interval is always upwards limited.
So no matter how many times you subdivide, the TOTAL TIME never grows, thus time is not infinite.
- Calavar 4y agoI like this explanation. Every other argument I've seen against Zeno's paradox either takes as a given that an infinite series can converge to a finite sum (which I don't think is a self evident truth) or relies on theorems about infinite sums that weren't rigorously proven until well over 1000 years later. This is the only counterargument I've seen that seems like it would have held up in Zeno's time.
- Quekid5 4y agoI like this point, but I'm not sure exactly how well concepts such as velocity and time, etc. were understood. They were certainly thinking about it, but even the idea of no action meaning constant motion (without other forces) was about 1500+ years away. I think Zeno might have invented calculus if it weren't for the fact that math wasn't even nearly sophisticated[1] enough to admit any sensible formalization of the ideas. [1] Perhaps it was even just because the power of symbolic algebra hadn't been fully realized. Geometry and logic only takes you so far.