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|Re: Okay Guys,The Final Train Crash. Re: Minimum Distance
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Posted by Larry Burford/">Larry Burford on February 22, 1999 11:51:52 UTC
As long as you insist on dividing the remaining distance in half, it is theoretically impossible to complete the journey. Even when also cutting the time interval in half along with the distance interval.
(from several of the previous posts)
>>1 second apart = 1 meters >>1/2 second apart = 1/2 meters >>1/4 second apart = 1/4 meters >>1/8 second apart = 1/8 meters >>etc. >>0 seconds apart = 0 meters
But that's not what happens in the real world. Since it *actually is* traveling at 1 meter per second, the train will travel a second half meter in the second half second and so on until it hits something or runs out of gas. End of problem.
Now you can think about something else.
? ? ! ! ?
Don't you guys get it? Zeno was a practical joker! He KNEW the answer, but posited this paradox anyway just to see who else really understood the limitations of logic. Apparantly many of us don't. (Geniuses seem especially vulnerable. Is that logical?)
Logic is very useful, but you have to think about your assumptions carefully. They need to be self-consistent, of course, but they also need to be consistent with the real world problem you are trying to solve.
Thought experiments (a form of logic) got the ancient Greeks into a lot of trouble, too. They thought heavy objects fall faster than less heavy objects. When you hold them, you can feel the extra force on the heavier one. To them it was so logical that they never asked the real world, i.e. performed the obvious experiments, if their logic made any sense. (It didn't.)
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