Saturday, June 19, 2010

How Can You Tell if There's an Elephant in Your Math Club?

By the pi on it's breath? 

I don't understand it. Whenever I casually remark that pi contains an infinite number of elephant jokes, I get pitying looks. Since the prospect of endless elephant jokes would surely delight anyone, I can only suppose that I am not believed. Let me explain: 


Those three dots at the end of this expansion of pi, the "ellipsis" aka "marks of elision" aka "naughty bits" (I suppose, since they are customarily left off) are what I'm talking about. That's where the elephant jokes are. In there, the "and so-on, ad infitum" of pi. 

“And so on” what

You know. Forever. Not lover's vows forever, but the real thing, the big lazy eight, infinity. Out of which, absolutely anything that can happen must happen, infinitely many times. 

Moreover, if you try to guess the next digit hiding in that ellipsis, you have exactly one chance in ten of being right. and that's not just because you're guessing. Humans are good at recognizing patterns, if any exist. Almost as good as elephants. 

Statisticians say we are right; there is no pattern. No, the elephants did not intimidate them. (OK, a little) They counted. Any digit 0-9 has an equal chance of being the next to pop out of the ellipses. It's as if there was a random digit generator in there. 

Except there isn't. It's pi. The unpredictability disappears as soon as you know that and where you are in the sequence. But you have to know where you are, or no dice—I mean, yes, dice. Die. One ten sided die. But not—I want to emphasize this—made out of ivory. 

I understand that among mathematicians it is good form to say “pi is normal,”(meaning the digits in pi are normally distributed) because if you say “pi is random” it's apt to start a food fight. On the other hand, one time I said “pi is random” and got laid.

Since pi is random and endless, we can very easily answer such questions as, “Does 0123456789 appear anywhere in pi?” The answer is yes, infinitely many times. “Oh yeah? Well, what about a hundred zeros in a row?” Same answer. And, before you ask, 314195265… is there, too, in sufficient length to have mathematicians biting their nails until some digit finally strays and there is a great sigh of relief. Infinity is like the old joke about a totalitarian country: anything that is not forbidden is mandatory. None of the above is forbidden, just highly improbable.

To go from digits to the all-important elephant jokes, we could make up a substitution cipher. But we don't need to make up our own. Let's use the one you're looking at now. We can easily expand pi in binary and, voila! Gibberish…and some of it not printable. OK, let's expand pi to the base of the computer's unicode character set. Still gibberish. But printable.

An infinite string of printable pi, and somewhere in that gibberish will be the treasure we seek: elephant jokes! Not just one or two, nor thousands nor millions, but an infinite number of elephant jokes! Elephant jokes in every language on earth, living, dead, and yet to be. Elephant jokes in Klingon. (The Federation could avert tragedies…or possibly cause one) And since we have them in a form computers can work with, we can seek them out efficiently. World—nay, universal—peace would ensue. 

Would it surprise you to learn that I have already written a program that does this? Of course, by the time an ordinary supercomputer—or even a game box—could find even one elephant joke in pi, politicians would have stopped lying, so I had to build a quantum computer. Off to the hardware store.

Writing the software was the worst part  I don't recommend quantum debugging at all. Still, one night last week, the reward for my all my hard work was nigh. The program produced its first output:

I just flew in from Nairobi, and boy are my ears tired.

This wasn't even the correct form, but the algorithm is heuristic. It learns. I pressed the punishment key and it tried again. 

Take my wife's fleas.


Knock, knock…

Punish! Punish! Punish!

How can you tell if there's a fruit bat in the bath with you? They hog the soap.

Classic, as to form, but fruit bat? Still, I pushed the reward key.

How does a fruit bat hide in the jello? Are you kidding? It's a fruit bat!

This "fruit bat" fixation might be leading it astray. Reward, punish.

What did the elephant say to the fruit bat? Nothing. Fruit bats can't talk.

Hm. Reward, reward, punish.

How does an elephant get in touch with its higher power? By ringing it up. 

Weak. But a real elephant joke. Success at last! Reward, reward, reward! I celebrated appropriately. The next day, appropriately hung over, I looked at what the program had been churning out.

How can you find an elephant in pi? Follow its tracks.

Can elephants calculate the millionth digit of pi? They don't have to. They'd just remember it.

Wow. How many digits of pi can an elephant remember? About 314,159,265.

OK. But could an elephant calculate pi? Sure. It would just use circular reasoning.

I could see a judicious application of the punishment key might improve the output, but a pattern was beginning to emerge…

Are elephants good at math? Weren't you paying attention just now?

How can you tell if there's an elephant in your math club? Ask it to recite pi. If it's still talking at the end of the meeting, its an elephant. If it says nothing, it's a fruit bat.

So, are elephants good at math? To a degree.

Then I suppose they must be educated? To a degree. Quite a few, actually. It's why they're good at circular reasoning.

How do you keep an elephant from walking in circles? Move the decimal.

How do you keep two elephants from walking in circles? Move it two places.

Can you tell if there's an elephant in your house? Yes. There will be one elephant circling your house. Unless you moved the decimal, then no.

Where do elephants go when they die? To the elision fields.

How do you know if an elephant is saintly? By the radians.

Do all of the elephant jokes in pi reference it in some way? You should ask an elephant. They're good at math, you know.

You see the pattern. It led me to an unexpected and exciting result, mcwbr's first, last and only  theorem:  

All of the elephant jokes in pi allude to pi.

Theorem, I say, because I have found a simple and elegant proof of it, which, however, is too large to fit in the margins of this blog.