Math jokes (V)

Q. "What do you get when you cross an elephant with a banana?
A. Elephant banana sine theta in a direction mutually perpendicular to the two as determined by the right hand rule."

Q. "What do you get if you cross an elephant with a mountain climber?"
A. You can't do that. A mountain climber is a scalar.

Q. "Why did the cat fall off the roof?"
A. Because he lost his mu. (mew=sound cats make, mu=coeff of friction)

Q. "What do you call a teapot of boiling water on top of mount everest?"
A. A HIGH-POT-IN-USE

Q. "Why is it that the more accuracy you demand from an interpolation function, the more expensive it becomes to compute?"
A. That's the Law of Spline Demand.

Q. "How many seconds are there in a year?"
A. "Twelve; January second, February second, March second, ..."

Q. "What's the contour integral around Western Europe?"
A. Zero, because all the Poles are in Eastern Europe!
Addendum: Actually, there ARE some Poles in Western Europe, but they are removable.
Note: this is not a polish joke, so please, no Poles be offended. It is actually a mathematical joke--they are meant to be poles apart--oops, sorry about that.

Do you owe me something ... Mr. Nobel?

Six Nobel Prizes are awarded each year, one in each of the following categories: literature, physics, chemistry, peace, economics, and physiology & medicine. Notably absent from this list is an award for Mathematics. Let me check briefly some facts:

• Nobel prizes were created by the will of Alfred Nobel, a notable Swedish chemist.
• One of the most common -and unfounded- reasons as to why Nobel decided against a Nobel prize in math is that [a woman he proposed to/his wife/his mistress] [rejected him because of/cheated him with] a famous mathematician. Gosta Mittag-Leffler is often claimed to be the guilty party. There is no historical evidence to support the story.
• Gosta Mittag-Leffler was an important mathematician in Sweden in the late 19th-early 20th century. He was the founder of the journal Acta Mathematica, played an important role in helping the career of Sonya Kovalevskaya, and was eventually head of the Stockholm Hogskola, the precursor to Stockholms Universitet. However, it seems highly unlikely that he would have been a leading candidate for an early Nobel Prize in mathematics, had there been one - there were guys like Poincare and Hilbert around, after all.
• For one, Mr. Nobel was never married.
• There are more credible reasons as to why there is no Nobel prize in math. Chiefly among them is simply the fact he didn't care much for mathematics, and that it was not considered a practical science from which humanity could benefit (a chief purpose for creating the Nobel Foundation).
• Further, at the time there existed already a well known Scandinavian prize for mathematicians. If Nobel knew about this prize he may have felt less compelled to add a competing prize for mathematicians in his will.

In my opinion, Nobel, an inventor and industrialist, did not create a prize in mathematics simply because he was not particularly interested in mathematics or theoretical science. His will speaks of prizes for those ``inventions or discoveries'' of greatest practical benefit to mankind. (Probably as a result of this language, the physics prize has been awarded for experimental work much more often than for advances in theory.)

However, the story of some rivalry over a woman is obviously much more amusing, and that's why it will probably continue to be repeated.

Fractals and poems (VII)

Black Holes

As Poe said ... "A few words on secret writing"

Despite its long history, cryptography only became part of mathematics and information theory in the late 1940s, mainly as a result of the work of Claude Shannon (1916-2001) of Bell Laboratories in New Jersey.

Shannon showed that truly unbreakable ciphers do exist and, in fact, they had been known for over 30 years. They were devised in about 1918 by an American Telephone and Telegraph engineer Gilbert Vernam and Major Joseph Mauborgne of the US Army Signal Corps, and are called either one-time pads or Vernam ciphers.

Both the original design and the modern version of one-time pads are based on the binary alphabet. The message, or plaintext, is converted to a sequence of 0's and 1's, using some publicly known rule. The key is another sequence of 0's and 1's of the same length. Each bit of the message, or the plaintext, is then combined with the respective bit of the key, according to the rules of addition in base 2:

0 + 0 = 0
0 + 1 = 1 + 0 = 1
1 + 1 = 0

The key is a random sequence of 0's and 1's, and therefore the resulting cryptogram - the plaintext plus the key - is also random and completely scrambled unless one knows the key. The plaintext can be recovered by adding (in base 2 again) the cryptogram and the key.

As an example, suposse a sender, traditionally called Alice, adds each bit of the plaintext (01011100) to the corresponding bit of the key (11001010) obtaining the cryptogram (10010110), which is then transmitted to the receiver, traditionally called Bob. Both Alice and Bob must have exact copies of the key beforehand; Alice needs the key to encrypt the plaintext, Bob needs the key to recover the plaintext from the cryptogram. An eavesdropper, called Eve, who has intercepted the cryptogram and knows the general method of encryption but not the key, will not be able to infer anything useful about the original message. Indeed, Shannon proved that if the key is secret, the same length as the message, truly random, and never reused, then the one-time pad is unbreakable. Thus we do have unbreakable ciphers!