"If a rabbit runs a distance of one mile, then it must first run half the distance or half a mile, then it must then it must run half of what remains or a quarter mile, run half of what remains or an eighth of a mile, and so on ad infinitum. The rabbit must run through an infinite series of finite distances. Since an infinite series, by definition, can never come to an end, the rabbit should never arrive at the end of the mile."
One of Zeno's (Xeno's?) paradoxes. Or really, a false paradox, see: http://www.jimloy.com/physics/zeno.htm ps, check out that guy's homepage after viewing that one, there's all kinds of cool shit to read.
I've heard something like that before, only simpler: "If there is an infinite amount of numbers between 1 and 2, then how do we ever get to 2?" It kind of bothers me though because when we're counting we normally just state the full integers, or round numbers or whatever, but if we were to try to count every single number between 1 and 2 it would be impossible.
The mind cannot really fanthom infinitity. It is all a mind game, a waste of time and mental energy, a rut. http://www.discussanything.com/forums/showthread.php?p=917075#post917075 The mind, being finite, cannot fanthom the infinite - so it has to rely on mathematical constructs, ideas, theories, conjectures. The mind is then fed what it most desires - mental energy.
Yeah, we count in intervals of whole numbers. we never usually count EVERYTHING. Even in money, banks sometimes count fractions of a cent, but for evryday money, we never even worry about anything less than a penny. I can fathom Infinity. I understand it perfectly. It never stops. That means forever. The only thing is I cant EXPERIENCE it.
I've experienced it once (I think it felt like I did), it was a door, I had a grand mal seizure, it sucked. Pushed my trip to the jelly belly factory back a year and three days.
this is only true if the rabbit runs half the remaining distance everytime. but it's not. you said "if the rabbit runs a distance ofone mile.." that's it. it ran a distance of one mile. if you said "if the rabbit walks half the remaining distance blah blah blah" then you'd be correct. it is almost like the concept of going form 1 to 2. sure tehre are an infinite amount of possibilities on the way, but you just want to go from 1 to 2, just like the rabbit travels the whole mile, not one half at a time.
I don't see any paradox there, it's just a regular calculus limit. If the distances the rabbit runs constantly shrink, the rabbit will never reach the ened of the mile. Nothing surprising there. Open a first year calculus textbook, and the first chapter will be full of such "paradoxes".
