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The Grandfather Paradox

Suppose a man traveled back in time and killed his biological grandfather before he met the time traveler's grandmother. As a result, one of the traveler's parents (and by extension, the traveler himself) would never have been conceived. This would imply that he could not have traveled back in time after all, which in turn implies the grandfather would still be alive, and the traveler would have been conceived, allowing him to travel back in time and kill his grandfather.

The Infinite Circle

The curvature of a circle's circumference decreases as the size of the circle increases. For example, the curvature of the earth's surface is so negligible that it appears flat. The limit of decrease in curvature is a straight line. An infinite circle is therefore a straight line.

Hotel Infinity

Suppose that, somewhere in New Jersey, there is a hotel with an infinite number of rooms. You arrive late one night and ask the front desk clerk if they have a vacancy. He replies that every room is occupied, however, he can arrange for you to get one. But how, you wonder, if there is no vacancy? The answer is simple: the clerk will simply ask the people in room 1 to move to room 2, those in room 2 to move to room 3, those in 3 to move to room 4, and so on. Since there is an infinite number of rooms, everyone will have a room to move into, and room 1 will be available for you.

The Thomson Lamp

Suppose you have a lamp with a simple on/off switch. Press the switch when it is off and the lamp will be turned on, press it again and it will be turned off. Now suppose you run the following experiment. You turn the lamp on at the start of a minute. Thirty seconds later, you turn it off. In another fifteen seconds, you turn it back on, then 7 1/2 seconds later back off again, and so on throughout the midpoints of whatever time remains. Now the question is this. At the end of the minute, will the lamp be on or off? Since the lamp has been turned on and off an infinite number of times, for every time it has been turned on, it has been turned off, and vice versa. At the end of the minute, therefore, it can be neither on nor off. But it must be one or the other.

The Paradox of the Spaceship

Suppose that a spaceship travels in a straight line for half a minute and then doubles its speed, then a quarter minute later doubles its speed again, and so on ad infinitum. Where will it be at the end of the minute? It must be infinitely far away. But does that make sense?

The Liar Paradox

This sentence is false.

The Unexpected Hanging

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day. Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that if the hanging were on Friday then it would not be a surprise, since he would know by Thursday night that he was to be hanged the following day, as it would be the only day left (in that week). Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday. He then reasons that the hanging cannot be on Thursday either, because that day would also not be a surprise. On Wednesday night he would know that, with two days left (one of which he already knows cannot be execution day), the hanging should be expected on the following day. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all. The next week, the executioner knocks on the prisoner's door at noon on Wednesday — an utter surprise to him. Everything the judge said has come true.

I'm confused. What is a Paradox? xD I only read the Grandfather One and i understood it

The last one was the best, they were dumb through

The space ship paradox and the lantern paradox both rely on the fact that the minute can never be reached if time repetedly duplicates, cutting itself in half thus creating an infitum in time.

i like the hanging one, but i don't really get how the hotel one is a paradox. nice post!

Haha nice one opec. Nice job elfmotat on two good posts in a row

every room is filled, but by moving everyone over one room it creates an empty room.

Dude these are trippy, especially the first and last ones.