Pujjle yagain
There is a very famous puzzle known as Zeno's paradox. It has remained one of my favourites thru the last few years - specially because of its simplicity. This is how it goes.
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Suppose there is a guy, X, who is 10 metres in front of another guy Y. Further suppose that X and Y are running in the same direction; Y running 10 times as fast as X. Then,
when Y covers 10 metres, X will have covered one metre (so, he is one metre in front of Y). When Y covers that 1 metre, X would have moved a further 0.1 metres. When Y covers the 0.1 metres, X would have moved 0.01 metres ahead... till infinity.
If this goes on till infinity, how will Y ever catch up with X? Yet, we know thru common sense, that given the above initial conditions, Y will definitely overtake X. That too, pretty quickly!
That is the paradox:). Now, obviously, Zeno's reasoning was faulty. Where and what is the error?
*****
Suppose there is a guy, X, who is 10 metres in front of another guy Y. Further suppose that X and Y are running in the same direction; Y running 10 times as fast as X. Then,
when Y covers 10 metres, X will have covered one metre (so, he is one metre in front of Y). When Y covers that 1 metre, X would have moved a further 0.1 metres. When Y covers the 0.1 metres, X would have moved 0.01 metres ahead... till infinity.
If this goes on till infinity, how will Y ever catch up with X? Yet, we know thru common sense, that given the above initial conditions, Y will definitely overtake X. That too, pretty quickly!
That is the paradox:). Now, obviously, Zeno's reasoning was faulty. Where and what is the error?
posted by karthik durvasula | 1:50 AM
1 Comments:
perfect, manka.
What Zeno didn't know was that an infinite (geometric) series can have a finite sum. He assumed it would be unbounded.
as we know now, an infinite gemoetric series is unbounded only if the multiplication factor is more-than-or-equal-to one.
This paradox was solved only after there was a proper understanding of infinite geometric series (which was in the second half of this millennium - i still believe that we are in the 20th century;))
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