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It surprises some to know that the following famous people where outstanding mathematicians.

CHARLES LUTWIDGE DODGSON (1832-1898), who wrote under the pseudonym LEWIS CARROLL

JAMES ABRAM GARFIELD (1831-1881, 20th President of the United States)

IMMANUEL KANT (1724-1804, philosopher)

NAPOLEON BONAPARTE (1769-1821)

HENRY WADSWORTH LONGFELLOW (1807-1882)

You probably realize that Dodgson (Lewis Carroll)
is best known for famous children's classics such as *Alice's Adventures in Wonderland * and *Through the Looking
Glass.* He also wrote books and pamphlets
on mathematical subjects. In his fantasy
tales and even in his regular life, Carroll loved to invert things.
For instance...

* He wrote letters to friends that had to be read from the last word to the first word.

Let's look at Carroll's classic, *Alice*. One could easily argue
that this is an amazing mathematical document, since Carroll
"inverts" many mathematical and scientific concepts the we use to
describe the world of reality as we know it. Here are just a few
examples.

* After running very fast for a period of time, Alice and the Red Queen get absolutely nowhere. They are exhausted, but they are at the point where they started. Alice is obviously confused, but the Red Queen says "Now here, you see, it takes all the running you can do to keep in the same place." In the real world, speed = distance/time. In Carroll's world, speed = time/distance. Carroll has inverted reality. The higher the speed, the smaller the distance covered. One has to run very fast just to remain at the same place.

* When Alice says "I am so hot and thirsty," the Queen says "I know what you'd like. Have a biscuit." (Would you offer a biscuit to a thirsty person?)

* Then there is the famous exchange between Alice and the Cheshire Cat:

"But I don't want to go among mad people," Alice remarked.

"Oh, you can't help that," said the Cat: "We're all mad here. I'm mad. You're mad."

"How do you know I'm mad?" said Alice.

"You must be," said the Cat, "or you wouldn't have come here."

Now, the book clearly states that "Alice didn't think he proved it at all." The Cat justifies a statement equivalent to "If you're here, you must be mad" by merely reversing the premise and the conclusion, saying "If you're mad, you must be here." Alice doesn't buy the Cat's argument. Smart girl! If the Cat's inversion technique represented a valid argument process, then, in geometry, one could prove the statement "If a quadrilateral is a rectangle, then it is a square" (a false statement) by merely stating "If a quadrilateral is a square, then it is a rectangle" (a true statement). Alice would probably have been a good geometry student.

Our world and universe are mathematically designed. Lewis Carroll, an excellent mathematican, inverted the mathematical laws of reality and created a classic about a fantasy universe that delighted humanity. Carroll was truly a master of the art of nonsense... and he fascinated the literary world with his inverted sense of reality.

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