Monday, April 11, 2011

Surfing PI

Never put random and infinite together. The results are just too weird.

The universe is a huge, random, unpredictable place with huge, random unpredictable things happening in it all the time. Many of them are meaningless. Most, actually. As a matter of fact, the vast majority of most are meaningless. Some, however, have meaning. Occasionally something happens that contains information that is intelligible and meaningful. These occasional anomalies have meaning even though they are still random events. This is what drives evolution: The fact that random is not the same as meaningless.

Take PI for instance. You know PI? The ratio of the circumference of a circle to its diameter? 3.1415somethingorotherforever? We were all taught that PI is an irrational number. That means that it cannot be expressed as the dividend of two whole numbers, a/b. In other words, the digits of PI go on forever and they are random.

Infinite and random. Here comes trouble.

Let’s take a look at the random part first, shall we? Random means that there is no reason for something to be. It is the product of chance. Chance can be expressed as a probability, as in, the probability of any given digit in PI being any single digit (0,1,2,3,4,5,6,7,8 or 9) is one in ten. The next digit in the sequence also has a one in ten chance of being any of those digits, regardless of what the digit before or after it is. In other words, the fact that the first digit to the right of the decimal point is a one does not mean that the chance of the second digit being also one is diminished. Every digit has an equal probability of being any number between zero and nine. After all, the digit “1” occurs twice in the first three digits. Coincidence? Yes, coincidence.

If the chance of any single digit appearing in any given position is one in ten, then the chance of two specific digits occurring together is one in 100. I.e., one in ten times one in ten. So, someplace in the digits of PI you will find two 1’s, two 2’s, two 3’s, etc. As a matter of fact, you will find repeating digits every 200 positions or so. How about the string 1234567890? What is the chance of that string appearing anywhere in PI? Well, the chance is one in 10x10x10x10x10x10x10x10x10x10. Or 1 in 1 followed by 10 zeros. 10,000,000,000. So every 100 Trillion digits on average you will find the string 1234567890. The same is true for any and every other string of ten digits. In every 100 trillion positions of PI you will find every possible combination of the digits 0 thru 9 in a string. Most are meaningless but some appear to have meaning. Or at least some kind of symmetry.

So what? Well, that’s where the infinite part comes in. Since PI is infinite the same logic can be applied to any arbitrarily long but finite string of numbers. For instance, somewhere in PI there exists a string of a billion zeros. Somewhere else is a string of a billion ones. These sudden strings of the same number are separated by vast light years of chaotic and meaningless numbers, but they exit none the less. They have to exist since the chance of them existing is greater than zero and the domain in which they can exist in infinite. In an infinite set of random things, anything that can exist must exist. They exist due to chance.

Take another example. What are the odds that, somewhere in PI, there are digits which, when evaluated as sets of three, never exceed 127? In other words, somewhere in PI is a string of digits that look like this: 067097108108032109101032073115104109097101108046. The odds of that specific string occurring anywhere in PI are one in one followed by 48 zeroes. This is highly improbable, but finite none the less. Again, in an infinite string of random numbers, a one in ten to the 48 power event is a certainty. Since these odds are finite, albeit huge, then in an infinite number of random digits, this string must occur. Not only that, but it must occur an infinite number of times.

What is the significant of these specific numbers? Well, if you treat them as ASCII characters and translate them into readable type, they read: “Call me Ishmael.” Somewhere in PI is the opening sentence of Moby Dick. And not only the opening sentence, the entire book, as well. Somewhere in PI is the complete works of William Shakespeare, Dante and Homer. The entire Bible plus all apologistic writings for and criticisms again it. All of the world’s great literature, past present and future, plus all variations therein. Anything that can be written, whether it makes sense or not, exists somewhere in PI.

In other places there are strings of just the digits zero and one. Some of these, if run through an MP3 player or a DVD player, will play all of the world’s music and every movie or play that ever was, is or could be. There will be different versions, as well. In one Tara burns and Rhett stays with Scarlet. Some will be completely absurd like War and Peace done with sock puppets or Macbeth on unicycles. Everything that could be, can be, may be or might be, must be encoded somewhere in the random digits of PI.

And this game doesn’t have to stop there. Somewhere in PI is a string of digits several billion long that are just the numbers 1, 2, 3 and 4. If you interpret these as amino acids, you will find the DNA of all living things. It seems that PI has something for everyone.

All of these things contain meaningful information yet are purely random. The universe in the arc of a circle.

Of course, these unexpected strings of meaning are rare. Extremely rare. For every string of meaning there are vast spaces of numbers that mean nothing whatsoever no matter how you interpret them or what encoding system you employ. These expanses are so vast that the meaningful bits are less than grains of sand in the ocean. Yet they must be there. This is the chaos from which worlds spring. Kind of. That is a nice, poetic way of making PI look like Plato’s world of pure forms. The reality is more like clouds which occasionally look like something real.

The universe is a huge, random, unpredictable place with huge, random unpredictable things happening in it all the time. Most of them are meaningless. Indeed, most of the universe is so meaningless that it is actually empty. Just void for unimaginable tracts of space. Every so often something happens. Galaxies, clusters of galaxies and super clusters of galaxies exist as sprinkles in the void. Within galaxies, between more vast empty spaces, are stars and clusters of stars. Some stars have planets. Some are habitable. Some are inhabited. Some have random structures called advanced brains that are capable of creating things like Shakespeare, the Bible and sock puppets. Meaning in the universe is about as scarce as it is in PI, which seems fitting.

And here we are. One small section of a mind numbing void with a clustering of random meaning. Just like PI.

Never mix random with infinity. You never know where it’ll get you.

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