Classic Paradoxes
The Crocodile Paradox: A crocodile has seized a child for his lunch, but the mother pleads with the crocodile to let the child go. The crocodile, fond of a wager, says that he will return the child if the mother correctly predicts whether or not the crocodile will return the child. The mother’s first instinct is to predict the child will be returned, but she reasons that this leaves the crocodile with a choice: he may return the child, saying that the mother guessed correctly, or eat the child, claiming that the mother guessed incorrectly. Either way, the crocodile could claim to be honoring the bet, and the mother suspects the child will be eaten.
The mother therefore predicts that the crocodile will eat the child. This freezes the crocodile with uncertainty. If he eats the child, then the mother predicted correctly, which means the child should have been returned. But if he returns the child, then the mother’s prediction was incorrect, and the crocodile should eat the child. While the crocodile is lost in thought, the mother grabs her child and escapes. This and other fun paradoxes can be found in aha! Gotcha.
Theseus’ Paradox: The Athenians were said to have preserved the ship of their mythical king, Theseus, replacing each rotting plank of wood as it decayed. The Greek historian Plutarch posed the question: When every piece of the ship has been replaced, is it still the same ship? Thomas Hobbes asked, If all of the original planks, after being removed, were used to build a separate ship, which, if any, would be the same ship?
Omnipotence Paradox: If an omnipotent being such as a god is truly all-powerful, it should be able to perform any action. Can an omnipotent being create a rock so heavy that the being itself cannot lift it? If so, then there is an action the being cannot perform: lifting the rock. If not, then there is an action the being cannot perform: creating the rock.
The Paradox of the Court: In ancient Greece, Protagoras is said to have taken on Euathlus as a pupil, with the understanding that Euathlus would pay Protagoras a fee for his education from the proceeds of his first court case. However, after receiving his education, Euathlus did not pay Protagoras, and did not practice law. Protagoras decided to sue Euathlus for the fee. Protagoras argued that he must be paid in any case: if he won the case, the court would find that he was owed the fee, and if Euathlus won the case, then the condition for Protagoras to be paid would be met. However, Euathlus argued that if Protagoras won, then Euathlus would not have won his first case and should therefore not have to pay, but if Euathlus won, then the court would decide that he did not have to pay.
Modern Paradoxes
Multiple Choice Paradox: If you choose an answer to this question at random, what are the chances that you will choose correctly?
A. 25%
B. 2/3
C. 1/4
D. 50%
Time Travel Paradoxes: There are two ways that time travel into the past could create paradoxes. The first is known as the grandfather paradox. If you went back in time to when your grandfather was a boy, and killed him, then what would happen to you? You could never have been born, but then who would have traveled back in time to kill your grandfather? The other paradox is a causal loop. What if you took one of Beethoven’s sonatas and traveled back in time to when Beethoven was a very young man and gave it to him, suggesting that he publish it as his own. If he did so, then Beethoven never would have composed the sonata, but merely taken it from you. But then how did you get it?
The Potato Paradox: A farmer has a sack of potatoes that weighs 100 kilograms. He takes note of the fact that these potatoes are 99 percent water. He decides to leave the sack outside until the potatoes are “just slightly” dehydrated, to the point where the potatoes are 98 percent water. To his surprise, when this is accomplished, the sack weighs only 50 kilograms.
Although the farmer was surprised, this result is correct. At the beginning, if 99 percent of the weight of the 100-kilogram sack was water, then the solid part of the potatoes must have weighed 1 kilogram. The weight of the solid part will not change. So to arrive at a result where water accounts for 98 percent of the total weight, we need for the 1-kilogram solid part to account for 2 percent, or 2/100 which can also be expressed as 1/50: 1 kilogram out of 50. The water therefore must account for 98/100, otherwise expressed as 49/50, or 49 kilograms out of 50.
Paradoxical One-Liners
Which came first, the chicken or the egg?
Everyone is unique, just like everyone else.
Promise me you’ll never promise me anything.
All things in moderation, including moderation.
The word “impossible” is not in my vocabulary.
Paradoxical Quotations
The only Golden Rule is that there are no golden rules.
-George Bernard Shaw
I don’t care to belong to any club that will have me as a member.
-Groucho Marx
Nobody goes there anymore; it’s too crowded.
-Yogi Berra
All generalizations are dangerous, even this one.
-Alexandre Dumas
There was only one catch and that was Catch-22, which specified that a concern for one’s own safety in the face of dangers that were real and immediate was the process of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn’t, but if he was sane, he had to fly them. If he flew them, he was crazy and didn’t have to; but if he didn’t want to, he was sane and had to. Yossarian was moved very deeply by the absolute simplicity of this clause of Catch-22 and let out a respectful whistle.
“That’s some catch, that Catch-22,” he observed.
“It’s the best there is,” Doc Daneeka agreed.
-Joseph Heller, Catch-22