Wednesday, July 21, 2010

The Greatest Dispute in Science, Part 1: A Perfect Circle

Today, I am going to start writing a series on what has become the largest battle in science history. This battle started brewing shortly after Einstein published his work on General Relativity and exists to this day. It is a battle that means everything for the human race, how we view ourselves in the Universe and in the end, who we actually are. You can see this battle occur everywhere, both within the world of science and between you and your friends and family. It exists at all levels of the human conscience:

Order vs. Chaos

I do not pretend for to know the answer, nor will I claim one. What I will do is discuss the fascinating battles and theories that have taken place over the years. The battles won and lost on both sides. While most of us make our arguments with books, religions, history and anecdotes; we'll be focusing on how science has waged these battles, the only place where solid evidence and the scientific method serve as referee to constrain the participants’ arguments.

We are going to start with something simple:

Humanity's search for perfection in the form of a circle.

If you ask the average person on the street what they know of π, you might get an answer of 3.14 from someone who either studied math or has a good memory. If you are really lucky, you might hear 3.1415 from an engineer or scientist. Many however, have lost sight of what π actually means: the illusiveness of perfection.

First of all, π is a number, pure and simple. It is not a formula and it means nothing more than the number it represents (3.1415…etc). Its simply much easier to refer to this inconveniently long number as an old Greek letter (anybody with a very long name can sympathize with early mathematicians).

Obviously, there has to be something special about this number, since its one of the oldest numbers in human history. Ancient Egypt and Babylon knew it was a little bigger than 3, but they couldn’t figure out the exact decimal representation. Over 2000 years ago Archimedes of Cyrus was able to figure out the best approximation of π which lasted until the 1800’s, when William Shank calculated it to 527 decimal places (in a time long before computers and calculators no less).

Why all this devotion to a seemingly random number?


You see, in order for a circle to truly be a circle, its MUST have the exact number of π describing the ratio between the circle’s diameter and circumference. My favorite graphical illustration of π is below:


You see, we can easily measure a circle's diameter. With the advent of flexible or clothe rulers (like the ones tailors use), we are also able to accurately measure the diameter of the same circle. However, unlike other basic shapes (squares, rectangles, triangles), these measurements do not easily provide us the area of the circle. For this calculation, we need π.

Area of a circle = π multiplied by the circle’s radius, squared.

Without knowing π, we can never know the true area of a circle. So it was important for mathematicians to discover this number so people could know things like land area for early circular shapes (coliseums…etc). Unfortunately, finding this number precisely, has taking the smartest human brains thousands and thousands of years to determine.

The end of this story is not a very satisfying one for many people: the exact number of π does not exist. In fact, the true amount of decimal places extends to infinite. Which in turn means humans can never make a perfect circle. We can never know the exact amount of area within a circle. Therefore, early mathematicians learned that in the case of geometry, the ultimate and most advanced mathematical tool of the day, perfection does not, cannot, and will never exist.

This ultimately makes sense in one crucial way: a perfect circle is not provided to us, anywhere, in the known Universe. No planet is perfectly circular. No orbit is perfectly circular. Nature, it turns out, might be a chaotic and haphazard place, the idea's of perfection and order were disappearing; A frightening idea indeed to most people in the ancient world.

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