I was just reading a calculus book and came across one of Zeno’s Paradoxes. It’s so friggin sweet - I can prove to you now that a fast (human) runner will never outrun a slow turtle.
Setup
- Man (general reference to the theoretically faster runner) starts at point 0.
- Turtle (general reference to any kind of slowpoke) starts at point 1.
- Both the man and the turtle start running.
The Race
- As the man takes a certain amount of time to get to point 1, where the turtle originally started, the turtle would have gone forward to another point (let’s say point A). Correct?
- As the man takes another period of time to get to point A, where the turtle was a moment ago, the turtle would have moved on (let’s say point B). Correct?
- Now, as the man takes more time to run to point B where the turtle was just a moment ago, the turtle would have moved on more. Correct?
- As this list continues, the man will never catch the turtle. Correct?
Isn’t that awesome? =D Even though the speed of the runner is greater than that of the turtle, the runner will not surpass the turtle.
I’ll tell ya the secrets tomorrow =;).
Haha, wish it would be like that :D
You could put the link just ‘gnu-’ :P that address is coming badly out of that box.
=)
Maybe in theory, but if you wanna get me a tutrtle, i can prove it wrong right now :P
There is a flaw in the theory goddamnit. The turtle takes more time to get a point than the man does. Thus, the man easily passes the turtle.
the man doesn’t stop everyime he reaches a spot!!!!! WHAT AN IDIOT.
The man doesn’t stop, and neither does the turtle. As the man takes time to reach where the turtle a second ago, the turtle would have moved on already. If this continues to happen, all the man will and can do is try to catch up, but not surpass the turtle.
If you can’t find a flaw in my theory, then my theory complies, and the runner is slower than the turtle :p
Negative. I may not be super mathematically smart, but common sense says that a god is much quicker than a freaking tortoise.
Who said this is common sense? haha. Prove me wrong using my logic and I’ll give you a dollar =p
You’re certainly not stupid, Oliver.
But I’m guessing this is a trick, one involving an asymptote. The problem is that you can’t create a slice of time small enough for the man to not pass the turtle in it. Even if it’s only 1/10,000 of a second, if the man is close enough, he’ll pass the turtle before that amount of time is up.
The problem basically works because you’re making the time elapsed between each point smaller and smaller:
10 sec
1 sec
0.1 sec
0.01 sec
0.001 sec
0.0001 sec
etc.
The man will never pass the turtle only if you keep slicing time into smaller and smaller bits - which, mathematically, you can do. But in the real world, our instruments max out when we get to, say, a few billionths of a second.
Pretty cool.
Yeah you got it! =D