Paradoxes and such

[ultimategamer]

In light of the previous debate about time and space and all that (which i sadly missed yet still read) i figured i'd create a topic to spurr the minds of all you FFR'ers. Here are 3/4 of Zeno's paradoxes. Very interesting in discovering flaws of logic. I copied these off another website. Enjoy

Dichotomy paradox: Before a moving object can travel a certain distance, it must travel half that distance. Before it can travel half the distance it must travel 1/4 the distance, etc. This sequence goes on forever. Therefore, it seems that the original distance cannot be traveled, and motion is impossible.
Achilles and the tortoise paradox: Achilles gives the tortoise a head start, in a race. Before he can overtake the tortoise, he must run to the place where the tortoise began, and the tortoise has move on to some other point. From there, before he can overtake the tortoise, he must run to the place where the tortoise had move on to. This goes on forever, and Achilles can never pass the tortoise.
Arrow paradox: If you look at an arrow in flight, at an instant in time, it appears the same as a motionless arrow. Then how do we see motion?

[jewpinthethird]

Although it could be answered rather easy...I cannot put it into words...therefore, I do not know.

Prime example of "you have too much free time".

[Cenright]

The first one is calculus. You get there when the 1/(2^X) with the limit as X infinity.

The second one, although you tell him to pass, you negate that with telling him that he can onlly catch up and then wait, catch up and wait.

The third one looks like it is stopped in flight, but motion or speed is labeled as distance/TIME. Without any time, there is no distance.

[jewpinthethird]

Ah. It makes perfect sense.

[Cenright]

I like oxymorons also. They make sense from a certain standpoint only. That is what I like about them.

Such as:
Professional fools.
Lucky losers.
Good criminals.

[jewpinthethird]

Or Airline Food. And Military Intelligence.

[Brainmaster07]

oxymoron... like 'interesting textbook' :P.

[Cenright]

Surgical Mashing - Term used for FOTBB. I love it.

It can actually work also.

[Lupin_the_3rd]

The first one is calculus. You get there when the 1/(2^X) with the limit as X infinity.

The second one, although you tell him to pass, you negate that with telling him that he can onlly catch up and then wait, catch up and wait.

The third one looks like it is stopped in flight, but motion or speed is labeled as distance/TIME. Without any time, there is no distance.

holy crap, someone actually used that arrow

[makaveli121212]

The first one is calculus. You get there when the 1/(2^X) with the limit as X infinity.

The second one, although you tell him to pass, you negate that with telling him that he can onlly catch up and then wait, catch up and wait.

The third one looks like it is stopped in flight, but motion or speed is labeled as distance/TIME. Without any time, there is no distance.

i believe the first one is just 1/X...as the limit of x approaches infinty

[jpyb007]

makaveli...it is 1/(2^X)
1/X would be the entire distance, then half the distance, then a thrid of the distance...so on and so forth.
1/(2^X) would first be half the distance, then a quarter of the distance, then an eigth of the distance...so on and so forth.

[ultimategamer]

By my understanding, the same general equation can also be said about paradox #2, where the Limit as X infinity of 1/C^x, where C is the ratio of movement between the Achilles and the tortoise, which in this case is (Achilles speed)/(tortoise's speed).

[Cenright]

Ah. Don't you just love calculus?

[Anticrombie0909]

Here's one that'll rock your noodle.

A knight guards a path that goes over a hill and leads to a kingdom. This knight has the ability to distinguish who is telling a lie and who is being honest. If they lie, he kills them. If they are honest, he lets them pass. One day, a man walks up the hill and the knight says "Stop! Identify your reason for passing into this kingdom." The man says "I am here for you to kill me." What does the knight do? He can't kill him, because he was telling the truth. But if he lets him pass then the man will have been lying, so he should kill him, but he was telling the truth in the first place. See if you can figure it out.

Here's another one that isn't a paradox because it has an answer, but it took me a minute to figure out.

There is a fork in the road. One way leads to Truth Town, where everyone tells the truth, and one leads to Liar Town, where everybody lies. You come to the fork and stop to think. You want to get to Truth Town, but you don't know which way it is. You see a local and decide to ask for directions to truth town. But you can't tell which town they are from, and if they are from Liar Town, they will lie. What can you ask the local so that no matter what town he is from, he will always tell you where Truth Town is?

[jpyb007]

The second one's simple...you ask "Which way is the town you came from?"
I heard something similar to that somewhere else before.