Zeno's Paradox

let's say, you are standing at a point 'a' and want to move towards point 'b'; what if i told you that mathematically, you can't reach point 'b'.

image source : commons.wikimedia.com

this is the famous 'zeno's paradox', and it has been around for quite some time.
to get from 'a' to 'b', first you'll have to travel half the total distance; then the half of the remaining distance or a quarter of the total; then half of the remaining distance and so on. physically, you would reach your destination but mathematically, it should add infinite number of times; surely it would converge to the total distance but will never be exactly equal to it.
now, the solution of the paradox was found with the discovery of 'plank's length' which is the smallest separation between two objects (1.6 x 10^-35 m). once the distance between the person and the destination is close to plank's length, it would reach it's destination because travelling half the distance then would reduce the separation to less than the plank's distance which is physically impossible.
there are some other variations of this paradox too but the solution is same for all.

image source : google.com

in the above instance, as the person approaches the turtle, the turtle also move a little bit. 

let's say the man is at point 'a' and the turtle is at point 'b'.as the man reaches 'b' from 'a', the turtle moves to 'c'.as the man reaches 'c', the turtle moves to 'd' and so on.

when the distance between the person and the turtle is equal to plank's length he would overtake the turtle.

this was a fun little paradox and for it's considerable history, the solution was not known.

comment below to start any discussion or ask anything about it.

published by zain ul abideen.