If you want to go 10 miles by traveling halfway every day, you will never get there, but after a month you'll be so close it hardly matters.
can you explain that to me please because thats never made sense to me.
i remember being told about achilles and the tortoise, a tortoise sets off then achilles chases it but can never catch it as its always moving. never made sense to me as something moving will always catch something moving slower than it.
It is supposely a paradox but it's really a play on words to me.
The idea is playing on the idea that you can only cover half the distance at each stage. So for example, if I were to cross a room but only go half the distance it takes to get across the room it would reduce infinitely.
So for example....in my first stage I go half way across the room....yeah I'm 1/2 way there! BUt the next distance is only half the room....thus I can only go 1/4 of the distance i originally took. Now 1/2 + 1/4 = 3/4.....75% there! WOO HOO....but now I can only go 1/8 of the distance I originally went....then 1/16....then 1/32....then 1/64 and so on and so on....and the amount of distance I would have to travel is getting smaller and smaller every time but I never quite get there because there is just a infinitely small fraction between me and the goal. The person gets stuck in perptual stillness as the distances get smaller and smaller.
So the idea is that as Achilles moves forward the tortoise is also moving forward and as such the tortoise is adding a bit of distance in increasingly smaller bits but just enough that Achilles can never quite make that distance all the way up.
The whole thing is based on motion....not amount of distance over an amount of time at a particular speed.