I dunno if you get intrigued by this paradox, but i was and did sone thiking over it(too obvious, after all thiking is what i love to do). However, surprisingly i also came up with some conclusion. i will share that but you opinions first.
Achilles and the Tortoise
Achilles and the tortoise is similar. Suppose that the swift Achilles is having a race with a tortoise. Since the tortoise is much slower, she gets a head start. When the tortoise has reached a given point a, Achilles starts. But by the time Achilles reaches a, the tortoise has already moved beyond point a, to point b. And by the time Achilles reaches b the tortoise has already moved a little bit farther along, to point c. Since this process goes on indefinitely, Achilles can never catch up with the tortoise.
4 comments:
Conclusion:
!I am Puzzled!
Well basically the conclusion is that Smooth movement can never be simulated or achieved.
We can come close to smooth movement but never perfectly smooth. It means that all motion that look smooth to us do have certain breaks in the motion.
The perfect example for this is a clock, a normal clock covers some distance and then stops. However , nowadays we also have some clocks which move smoothly,i.e., withouy breaks. Now all i'm saying is that even that smooth clock is like the classic clock but for a very very small distance and time, and our eyes cant make that out.
Now if 1 uses this concept one may be able to explain what is happening in the paradox.
Happy thinking
PS-- By the way i think i have made some sense this time, because unlike by previous post this doesnt happen to be completely foolish. And i hope intelligent people dont have a problem in understanding THIS ;) .
Yes, so i was slightly depressed after i made that conclusion, my approach to the paradoz was was .. very mechanical, and a lay man's.
So here is another better (looks more professional) approach.
Lets say that if the tortoise is at A and achilles reaches A in some time(t1). Now the tortoise has reached point B and achilles will reach that point in time t2.
Since Achilles is swifter this time will keep on decreasing,i.e, t1>t2>t3.......
Now since this time keeeps on decreasing after some time it will become very very small, and our time frame has then practically stopped,i.e,
This will go on happening till infinity, but when our time frame becomes infinitesimally small (and then even smaller), it has practically frozen and thats the time when they are at the same place.
So now we basically have to choose a new time - frame, defined by anything,say, 1 sec, or 2 sec. or twice the time till now, and we know that achilles will overtake the tortoise now.
Nice xplanation!
Post a Comment