Deep Thoughts

[blueerica]

We're all really just props in each others' lives.

Or are we?

And I like the smell of tomatoes ripening on the vine, too. And that of fresh earth. Mmmm, it's rather intoxicating.

And yes, everything's going to be okay. It's all the way it's supposed to be. (Even if I don't like it. And I don't! hehehe )

[Ghoulish Delight]

If when you're sick, you're an invalid, when you get better have you been validated?

Can one be gruntled?

Why is the Jack Daniels distillery in a dry county?

A tortise challenges the great Achilles to a race. Achilles, knowing he can go exactly 10 times as fast as the tortise, generously gives the tortise a 1000 meter head start. The race begins. By the time Achilles has covered the first 1000 meters, the tortise, of course, remains in the lead, having moved 100 meters. By the time Achilles covers those 100 meters, the tortise has sprinted with all his tortisely might another 10 meters to retain the lead. Ten meters later for Achilles, and the tortise is still 1 meter ahead. 1 meter for Mr. Indestructable, 1/10 of a meter behind our hero the tortise. Will Achilles ever catch up?

[SzczerbiakManiac]

Originally Posted by Ghoulish Delight

Will Achilles ever catch up?

Catch up in time to win an x meter race or catch up ever? If the latter, yes.

[Ghoulish Delight]

Originally Posted by SzczerbiakManiac

Catch up in time to win an x meter race or catch up ever? If the latter, yes.

But how, asks Zeno? For every distance X Achilles covers, the tortise moves ahead by X/10 meters.

Consider this similar conundrum:

Consider a lamp, with a switch. Hit the switch once, it turns it on. Hit it again, it turns it off. Let us imagine there is a being with supernatural powers who likes to play with this lamp as follows. First, he turns it on. At the end of one minute, he turns it off. At the end of half a minute, he turns it on again. At the end of a quarter of a minute, he turns it off. In one eighth of a minute, he turns it on again. And so on, hitting the switch each time after waiting exactly one-half the time he waited before hitting it the last time. A simple series evaluation shows that if you add up all of the intervals on into infinity, this will actually continue for precisely two seconds.

So, at the end of 2 seconds, is the lamp on or off?

[Cadaverous Pallor]

Deep thought for the moment:

I've got to alter my view of the world.

[Kevy Baby]

Originally Posted by Ghoulish Delight

Will Achilles ever catch up?

Yes he will. At a hare* over 1,111.111 meters. I had to brush up on my algebra to do this. Okay, I cheated and found a web site to help me solve. But I DID come up with the formula on my own. Formula wasn't perfect, but it did help me find the correct answer (cuz I knew that Achilles would catch the tortoise).

My thinking was that x would equal the point where Achilles would catch the tortoise (the break-even point if you will). so I came up with the formula:

10x = x + 1000

And then I took this formula to an Algebra web site and plugged my formula in. It gave me this:

Simplifying
10x = x + 1000

Reorder the terms:
10x = 1000 + x

Solving
10x = 1000 + x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1x' to each side of the equation.
10x + -1x = 1000 + x + -1x

Combine like terms: 10x + -1x = 9x
9x = 1000 + x + -1x

Combine like terms: x + -1x = 0
9x = 1000 + 0
9x = 1000

Divide each side by '9'.
x = 111.1111111

Simplifying
x = 111.1111111

I knew that the answer was not 111.1111+ meters. (presumably the "1"s after the decimal point repeat ad infinitum, but I don't know how to put the bar over it like I could when I was handwriting, so just imagine it is there.) But logic dictated that it would be 1,111.1111 meters (or 111.1111 meters past the effective start point for the tortoise when Achilles started). Granted, I would still get a failing grade in algebra, but I knew the answer was correct.

Basic logic also dictates that Achilles would of course catch the tortoise. The relationship in their speeds is not exponential, it is linear. Both speeds are (presumably) constant, so of course Achilles would catch the tortoise.
_____________________

Well, there's a half hour of my life I'll never get back. :geek:

[MickeyLumbo]

I was standing in the park, wondering why frisbees got bigger as they came closer... then it hit me

[Not Afraid]

You don't always HAVE to respond.

[SzczerbiakManiac]

One hippopotami cannot get on a bus, because one hippopotami is too hippopotamus.

A paranoia is a bunch of mental blocks.

Has it ever occurred to you that the plural of "half" is "whole"?

What is half a pair of scissors... a single sciz?


Allan Sherman was too damn funny!

[Name]

Originally Posted by Ghoulish Delight

Consider a lamp, with a switch. Hit the switch once, it turns it on. Hit it again, it turns it off. Let us imagine there is a being with supernatural powers who likes to play with this lamp as follows. First, he turns it on. At the end of one minute, he turns it off. At the end of half a minute, he turns it on again. At the end of a quarter of a minute, he turns it off. In one eighth of a minute, he turns it on again. And so on, hitting the switch each time after waiting exactly one-half the time he waited before hitting it the last time. A simple series evaluation shows that if you add up all of the intervals on into infinity, this will actually continue for precisely two seconds.

So, at the end of 2 seconds, is the lamp on or off?

Yes