Saw a really interesting question on my brother's tutorial a few
days back, and thought I should perhaps share it. I still don't
have the answers to the questions though...
The following paradoxes are thought up by some thinker from ancient
time. I think I can find the answer easily simply my googling his
name, except that I forgot his name, and the name of the paradoxes
thought up by him. In fact, I've forgotten the question in it's
exact words...so I'll just try writting them down in my own
words.
Paradox 1: Suppose two competitor, A and B, are getting ready for a
race with each other. Competitor B's starting point is 100m ahead
of competitor A. However, competitor A runs 10 times faster than
competitor. Going by the logic of that thinker, it is theoretically
impossible for competitor A to overtake competitor B. Why so?
Suppose the race starts. When competitor A has ran 100m (i.e.
competitor B's starting point), competitor B would had ran 10m,
since competitor B runs 10 times slower than competitor A (in
another word, competitor B is 10m ahead of A). When competitor A
runs a further 10m, competitor B would be 1m ahead of competitor A.
When competitor A runs another 1m, competitor B would be 10cm ahead
of competitor A.
As this goes on, we can see that while the distance between
competitor B and competitor A shortens as time goes by, it's
impossible for competitor A to catch up with and overtake
competitor B, for theoretically, competitor B is always ahead of
competitor A. However, we know from our practical experiences that
this is not so.
How do you explain this?
Paradox 2: According to that thinker's logic, motion is
impossible.
For us to move 100m, we must have moved 50m. For us to move 50m, we
must have moved 25m. For us to move even 1cm, we must have moved at
0.5cm.
In another words, for us to move, we must have moved a shorter
distance. Yet, moving even the shortest distance should be
impossible without moving an even shorter distance. Hence, motion
is impossible.
My answer for this would be that nothing is ever stationary. For us
to make sense of this logic, we must deduce another logic: that
every partical or physical substances that makes up this world is
in constant motion. Since we are always in motion, we are never
stationary. Since we are never stationary, there's no need for us
to start a motion. Hence, motion is possible (for it is always
happening).
Still, I believe there's a simpler answer for this. I await those
who can come out with a satisfactory answer...by themself!
