Making intelligible sense of the pi

By Lim Tri Santosa

BANDUNG (JP): Welcome to the world of mathematics. Believe it or not, you have been living in a world synchronized by numbers your entire life. Everything has a shape and in order to get to that shape, numbers are needed. Unfortunately, there aren't very many things in nature that are lines, squares or cubes. In nature, you see curves, circles and spheres. If only we could measure circles as easily as we can measure squares.

You might say that anything round is "pied" because in order to get the area of it, you need a special ratio, namely pi. In order for us to make the first step in determining pi, however, we have to understand the concept of magnitude. For example, the bigger a stone is, the heavier it is. The smaller the stone, the lighter it is. From these simple observations, the person must then realize that some things have direct proportional relationships. The next step is to look at a circle and observe that the wider a circle is 'across', the longer it is 'around'.

From this, a very profound statement would be, no matter how long or wide a circle is, the relationship between the circumferential length of circle and the diameter is always the same. Pi is the number of times a circle's diameter will fit around its circumference. In other words, the circumference of a circle equals to its diameter multiplied by pi, where the diameter equals to two times the radius length.

What do people know about pi? It isn't rational, it isn't normal. It's transcendental. Can you even call something like that a number? Numbers are things that you can count, but you can't count pi. You can't measure pi either. The best you can get is an estimate. Okay, so 3.14 is a pretty rough estimate. How about 3.1415927? That's what my calculator says. You want to be on the safe side because you're calculating the rocket trajectory of a nuke? Try 3.1415926535897932384626434.

Pi occurs in hundreds of equations in many sciences including geometric problems, waves equations and even Einstein's gravitational field equation. Calculating pi with that much precision is like measuring the distance that I put my foot in each step that I make to the nearest picometer and then taking the average of it, hoping that if I do so, I won't ever trip again. Maybe that's a bad analogy, but I think you get my point.

As humans, we estimate everything. For instance, as you walk, you have to estimate where you put your foot. Sometimes you make a mistake and trip, but most of the time things work out. Computers need exact numbers instead of estimates, so they are much more limited than we are. If you could teach a computer to estimate like we do and make judgments, you would have artificial intelligence.

Statistically, the decimal expansion of pi is about as random as it can get. The distribution of the digits is nearly perfectly even. In other words, any method for trying to find intelligence in pi is as likely to be as successful as trying to find intelligence in a random stream of numbers. There is an interesting idea: take the decimal expansion of pi and using whatever dubious methods we can come up with, convert the digits into a stream of letters and try to make some sense of the letters.

Also you can even search millions of digits of pi for a number string using The Pi-Search Page (www.angio.net/pi/piquery). Exchange the letter a for 1, b for 2, and so on. Pick the word 'GOD' (= 7154), the string 7154 was found at position 9429, counting from the first digit after the decimal point. It also tells you where in pi your birthday first occurs, e.g. If you were born on February 20th 1973 search for 200273. The original pi searcher featured up to 50 million digits. However, this also means that with enough digits, almost any message will appear eventually.

I'm immensely curious about pi. How can we know that it is infinite? We know that pi is an infinite decimal because of the work of many fine mathematicians over the course of several centuries. In 1767 a mathematician named Johann Heinrich Lambert proved that pi was an irrational number. Irrational numbers are numbers that do not terminate or repeat when written out as a decimal.

The digits look random, with about the same number of zeros and ones and twos and threes and so on, spread throughout. Some modern mathematicians suspect that this pattern continues "out to infinity" which would mean that it will never become a sequence of just ones and zeros or any other digits.

Recently, with the help of powerful digital computers, the most accurate version of pi was from Professor Yasumasa Kanada and Dr. Daisuke Takahashi of the University of Tokyo (www.guinnessworldrecords.com/record_categories/recordhome.asp?RecordID=4705 5). Pi has been computed to 206,158,430,000 decimal places in September 1999 (that's over 206 billion places), an astonishing feat!

Here is another simple theory to ponder. A rational number is any number that can be written as a ratio of two integers. An integer is in the set: {...-3, -2, -1, 0, 1, 2, 3, ...). It is just a positive or negative whole number. Thus 354564 is an integer, but 1/2 isn't. In other words, a number is rational if we can write it as a fraction where the numerator and denominator are both integers. Now then, every integer is a rational number, since each integer n can be written in the form n/1.

An irrational number is any real number that is not rational. For example, the square root of 2 is an irrational number because it can't be written as a ratio of two integers, hence similar to pi. You would find that while there are infinitely many of each kind of number, still there are more irrational numbers than rational numbers. The sizes of the infinities involved are somehow a little different. Another property is that between any two rational numbers on the number line, there is an irrational number. Also, between any two irrational numbers there is a rational number.

Confused? That's why being a mathematical genius will make a person more rational in irrationality. Well, if you've come to this ending sentence, then you must be a mathematician; in which case, I really admire you. Perhaps you were looking for something interesting; in which case I really thank you. Maybe you are on the wrong link; in which case I wonder why you have read until the last part. Whatever. Anyway, this is the article devoted to the above subject

Pi is a discovery, not an invention. Finding a message in pi would be a profound discovery beyond comprehension. By the way, Satan does not appear in pi too quickly: The first time '666' appears is at position 2440.