Paradoxes

[Cannibal]

What's your favorite? Or are you stupid and don't know what that is (http://en.wikipedia.org/wiki/Paradox)? >:|

Mine would either be the Barber Paradox or the Grandfather Paradox.

Barber:

Suppose there is a town with just one male barber; and that every man in the town keeps himself clean-shaven: some by shaving themselves, some by attending the barber. It seems reasonable to imagine that the barber obeys the following rule: He shaves all and only those men in town who do not shave themselves.

Under this scenario, we can ask the following question: Does the barber shave himself?

Asking this, however, we discover that the situation presented is in fact impossible:

If the barber does not shave himself, he must abide by the rule and shave himself.
If he does shave himself, according to the rule he will not shave himself.


Grandfather:

The paradox is this: suppose a man travelled back in time and killed his biological grandfather before the latter met the traveller's grandmother. As a result, one of the traveller's parents (and by extension the traveller himself) would never have been conceived. This would imply that he could not have travelled back in time after all, which means the grandfather would still be alive, and the traveller would have been conceived allowing him to travel back in time and kill his grandfather. Thus each possibility seems to imply its own negation, a type of logical paradox.

[Chockeh]

Chrono Trigger made me a Grandfather Paradox lover.

[Justified]

The Barber Paradox isn't much of a paradox... it seems more like a false dichotomy to me.

[Cannibal]

The Barber Paradox isn't much of a paradox... it seems more like a false dichotomy to me.
I can see where you'd get that.

[Kyubey]

"snake, you can't do that"

i hope someone gets the reference :I

[Mrlucky77]

Er..

The Predestination Paradox, which is a very good example of what happens in Bender's Big Score (http://en.wikipedia.org/wiki/Bender%27s_Big_Score) and Roswell that ends well. (http://en.wikipedia.org/wiki/Roswell_That_Ends_Well)


In layman's terms, it means this: the time traveller is in the past, which means they were in the past before. Therefore, their presence is vital to the future, and they do something that causes the future to occur in the same way that their knowledge of the future has already happened. It is very closely related to the ontological paradox and usually occurs at the same time.


Also, the Temporal paradox, in which the time traveler goes in the past and prevents him from doing things that would make him travel through time in the first place.
Temporal Paradox. (http://en.wikipedia.org/wiki/Temporal_paradox)


Also, Zeno's paradoxes. One can never reach from point 1 to point 2, as they must go half of the walking distance, then half of the half, and half of the half of the half, and so on. Zeno's paradoxes (http://en.wikipedia.org/wiki/Zeno%27s_paradoxes)

[Melchinoir]

Also, Zeno's paradoxes. One can never reach from point 1 to point 2, as they must go half of the walking distance, then half of the half, and half of the half of the half, and so on. Zeno's paradoxes (http://en.wikipedia.org/wiki/Zeno%27s_paradoxes)

I dunno if you'd really count Zeno's paradoxes as paradoxes anymore, as they've been solved by calculus nowadays (infinite series, convergence and divergence, etc). Even then, before the advent of calculus, it was arguable (I'd say) whether or not the paradoxes were paradoxes, since they could still be solved depending on whether you interpreted time as discrete or continuous...it was just a matter of which of the two was the "true" way.

As for myself, I have several paradoxes that I'm a fan of.

Schrodinger's Cat:

A cat, along with a flask containing a poison and a radioactive source, is placed in a sealed box shielded against environmentally induced quantum decoherence. If an internal Geiger counter detects radiation, the flask is shattered, releasing the poison that kills the cat. The Copenhagen interpretation of quantum mechanics implies that after a while, the cat is simultaneously alive and dead. Yet, when we look in the box, we see the cat either alive or dead, not both alive and dead.

Maxwell's Demon:

Imagine a container divided into two parts, A and B. Both parts are filled with the same gas at equal temperatures and placed next to each other. Observing the molecules on both sides, an imaginary demon guards a trapdoor between the two parts. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics.

The Monty Hall Problem (my personal favorite, though it's technically not a paradox since it's a conditional probability problem with a solution, but thinking about the solution itself is counter-intuitive so it SEEMS like a paradox):

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Answer to above problem is that, statistically speaking, you should ALWAYS switch because your probability of winning increases from 1/3 to 2/3.

[Bankai231]

Thought of the Grandfather PAradox so many times its unbelievable.