Paradoxes According to Websters College Dictionary a paradox

Paradoxes • According to Webster’s College Dictionary, a paradox is defined as “a seemingly contradictory or absurd statement that expresses a possible truth”.

Zeno • Lived during the 5 th century B. C. E. • Most well known for his paradox of Achilles and the Tortoise. – Achilles can never catch the tortoise as long as the tortoise is given a head start… • Argues that if something is divisible then it is infinitely divisible.

Divide……Infinitely The number 1 can be divided in half. ½ can be divided in ½ again which = ¼. ¼ ÷ 2 = 1/8 ÷ 2 = 1/16 ÷ 2 = 1/32 ÷ 2 = 1/64 ÷ 2 = 1/128… This process can be carried out an infinite number of times, which is the basis for Zeno’s paradox. In order to reach ½, you must reach ¼, but before ¼, you must reach 1/8, and because that can be done forever, reaching the number 1 is impossible.

Albert Einstein’s The Twins Paradox • We have 2 twins (with • This “paradox” / theory has been proven; obviously the same however, I believe it is age). called a paradox • One stays home, the because it is hard to other takes a trip on a comprehend with or spaceship capable of without mathematical traveling very near the data. speed of light. • Time passes slower for • Einstein's Demo the child in space, due • Hyperlink to the speed of travel.

Theseus’ Ship • Theseus is the man in Greek Mythology that killed the Minotaur – a half • • man half bull, that lived in the Labyrinth on the island of Crete. According to the story, the ship that Theseus sailed back to Athens in was preserved for years, and as the planks on the ship decayed, they were replaced. As the paradox goes, suppose that after hundreds of years, every board had to be replaced and there was not a single original board. Is it still Theseus’ ship? Or is it a copy? If it is considered a copy, at what point did it become a copy? Half way through replacement? Three quarters? It makes sense to think that if only one was replaced it’s still the same ship, and even if two were replaced it’s still the same; therefore, with this reasoning, it would still be Theseus’ even if all the boards were replaced. What if all of the old boards were stored somewhere? And what if, with all the original boards, intact, the ship was rebuilt, would there be, could there be, two of Theseus’ ships?

Irresistible Force vs. Immovable Object A classic paradox: What happens when an irresistible force meets an immovable object?

The Unexpected Hanging There was a man who had committed a serious murder. He was convicted, in spite of a high priced lawyer, and came before the judge for sentencing. Now the judge was known to be a man of his word, and when the convict came before him, he said, "You are hereby sentenced to death by hanging. You will be hung on one of the next seven days and on a day that you do not expect. " The sentence was given on a Saturday and the possible days for the execution were, therefore, Sunday through the following Saturday. The man returned to his cell in dismay. But his lawyer followed him with a big smile on his face. "What are you smiling about? ", asked the convict. "Relax, kid. ", said the lawyer, "The judge cannot possibly hang you. " "Why not? "

Other Classic Paradoxes The Barber ¢ The Heap ¢ Hotel Infinity ¢ The Liar ¢ The Paradox of the Stone ¢ The Two Envelopes ¢