What is your favorite paradox?
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mParadox said:
Zenos paradox always puzzled me, until i learned calculus. A 'durationless moment' can be expressed as dt ( in the limit dt tends to 0), and the distance travelled in this time is not 0, but dx. From this we can get dx/dt which is of course velocity. Thank you Newton (or Leibniz, it doesn't really matter)
I always found the half full/empty thing stupid so I always respond with "That depends, are you filling the glass or emptying the glass?".
I like the good ol' grandfather paradox. My hypothesis is that time doesn't care that you killed your grandfather before you were born, sure history will be different but you'll be fine. I base this on assumption.
I like the good ol' grandfather paradox. My hypothesis is that time doesn't care that you killed your grandfather before you were born, sure history will be different but you'll be fine. I base this on assumption.
I like Russell's paradox.
Consider a set that contains all sets that do not contain themselves. Does this set then contain itself?
It's very similar to the barber paradox, but with more rigour. In a town, the barber shaves everyone who does not shave themselves. Who shaves the barber?
Consider a set that contains all sets that do not contain themselves. Does this set then contain itself?
It's very similar to the barber paradox, but with more rigour. In a town, the barber shaves everyone who does not shave themselves. Who shaves the barber?
I think i can solve those. Its a bit of a cheat though. You don't specify that they ONLY shave people who don't shave themselves, so they could also shave themselves without the statement being false. Similarly for the sets one.Redingold said:
Unfortunately as soon as you do specify the only bit, both problems become paradoxes again. Unless you just say that such parameter is impossible, like dividing by zero.
Hmm... though I don't know the mathematics behind it, the Banach-Tarski Paradox. It's a mathematical proof that a single object (typically a sphere) could be dismantled and rearranged in such a way as to create two object, both identical to the first in every regard. I don't know if it counts, but's it's famous in mathematical circles and it even says paradox in the name. 
The Paradox Machine wasn't exactly a paradox itself, but it allowed the presence of a paradox without the universe tearing in half:
I'm pretty sure that Zeno came up with 4 paradoxes, which were themselves a paradox, as they proved among themselves that neither space, nor time, could be either continuous (infinitely divisible) or discreet (one smallest possible unit), a concept that I love xDClockworkPenguin said:
Captcha: "you're not listening" slight irony.
The "A rock so heavy God himself cannot lift it" paradox.
1. God is omnipotent.
2.1 Therefore he can create anything.
2.2 Therefore he can lift everything.
3. A rock so heavy God himself cannot lift it is something, therefore God can create it (if he is truly omnipotent).
4. 2.2 states he can lift everything. If he can lift the rock, then it is not so heavy God cannot lift it.
5. This means God cannot create the rock, as he can lift it, meaning it is not a rock so heavy God himself cannot lift it.6
6. 4 and 5 together prove that either 2.2 or 2.1 is false respectively. 2.1 and 2.2 are both required for omnipotence, therefore if one is false then 1 is false.
2.1 Therefore he can create anything.
2.2 Therefore he can lift everything.
3. A rock so heavy God himself cannot lift it is something, therefore God can create it (if he is truly omnipotent).
4. 2.2 states he can lift everything. If he can lift the rock, then it is not so heavy God cannot lift it.
5. This means God cannot create the rock, as he can lift it, meaning it is not a rock so heavy God himself cannot lift it.6
6. 4 and 5 together prove that either 2.2 or 2.1 is false respectively. 2.1 and 2.2 are both required for omnipotence, therefore if one is false then 1 is false.