![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
Imagine, for a moment, that we're in ancient Greece. A man sits by the lakeside. On the water, he sees two birds. They are both male, and it is mating season. Naturally, they immediately begin flying towards each other at top speed.
The two birds fly at the same speed, so they'll meet in the middle. Given the original distance between them and the speed at which they fly, it should be simple enough to calculate when they will reach the meeting point.
Look at it from another perspective, though: Consider just one bird and the meeting point. At some point before it gets to the meeting place, it must pass through a point that's halfway there. Once it reaches that halfway point, there will be a new halfway point - a quarter of the original distance. And so it goes. Every time it reaches the halfway point, there will be a new point halfway between where it is and where it will end up. Although the distance obviously gets smaller, there are an infinite number of halfway points it must cross before it actually arrives. The same is, of course, true for the other bird. Taken this way, it appears that the two birds can never actually meet.
This, my friends, is Zeno's pair o' ducks.
The two birds fly at the same speed, so they'll meet in the middle. Given the original distance between them and the speed at which they fly, it should be simple enough to calculate when they will reach the meeting point.
Look at it from another perspective, though: Consider just one bird and the meeting point. At some point before it gets to the meeting place, it must pass through a point that's halfway there. Once it reaches that halfway point, there will be a new halfway point - a quarter of the original distance. And so it goes. Every time it reaches the halfway point, there will be a new point halfway between where it is and where it will end up. Although the distance obviously gets smaller, there are an infinite number of halfway points it must cross before it actually arrives. The same is, of course, true for the other bird. Taken this way, it appears that the two birds can never actually meet.
This, my friends, is Zeno's pair o' ducks.
![[identity profile]](https://www.dreamwidth.org/img/silk/identity/openid.png){kind=small}
From:
no subject