The Ancient Sacred Basis for Today's Ordinary Numbers
Word count: 915
In today's culture, numbers and math in general are taken for granted. Children are taught the basic "1+1=2" in elementary school while older kids and adults wonder what possible use algebra and geometry will be to them once they are out of class. What most people don't realize is math was once considered to be a philosophical and sacred practice. Since I have a limited amount of time, I will only hit a few of the very basic ideas.
Many ancient cultures had various forms of math but no civilization took it as seriously as the Greeks. Perhaps one of the best known today for his contributions to modern math is Pythagoras.
We know almost nothing about Pythagoras since none of his writings have survived. All we do know have come down through his students' and contemporaries' writings. Through them, it has been said that he studied with the priests in Egypt as well as Babylon.
After returning to his homeland, he soon began to have the reputation of being something of a crackpot. Although they were serious about math, the Greeks did not see it as a religion. Greek society largely worshipped a pantheon of deities, with one of the most popular at the time being Bacchus, in whose honor orgiastic festivals were held. Pythagoras' teaching of a universe whose deepest reality was based in mathematics was definitely out of kilter with the times.
Pythagoras traveled to the south of Italy where he established a school in the town of Croton. Today, this would be called a 'mystery school,' since it was considered to be something of a religious order. It has been said that the school was called the 'The Temple of the Muses,' although it is better known as "The Order of the Pythagoreans" or simply "the Pythagoreans." We also know that they chose the pentagram to be their symbol, which, along with symbolizing the golden section, meant well-being, completeness and health.
There were two levels of students in Pythagoras' school, sometimes called circles. The outer circle contained the majority of students and was called the askousmatics. Those in the inner circle, whose members lived permanently in the Order, where they lived a largely monastic life, were called the Mathematikoi. All members were sworn to keep the teachings of the school secret and believed that the universe was built on orderly numerical ratios. Subjects that all students studied in the school were arithmetica (number theory), harmonica (music theory), geometria (geometry) and astrologia (astronomy.)
Although much of their teachings have been lost, we do know a few things about how Pythagoras and his students saw numbers. Through numbers, the Pythagoreans thought that the important mysteries of nature could be revealed but this could only be done through whole numbers, or integers. The Pythagoreans thought that each number had a definite shape - one of which is still recognizable today. The four most important shapes to the Pythagoreans were triangle, square, oblong and gnomon. Gnomons were thought to be the shape of a carpenter's square. It is easier to think of it this way: if the number three is written as a gnomon, visualize it as three dots drawn as a ninety-degree angle: . : Square numbers are still in use today however, where we say 'the square root of, ' they would have said 'the side of a square of.' Numbers were said to have gender as well. Odd numbers were considered to be masculine while even numbers were considered to be feminine. Using this logic, the number five was said to represent marriage, since it was the union of the number two - a feminine number - with the number three, which is male. However, other numbers were considered to be special.
The number one is such a number. It was considered to be the 'source' or 'generator' of all other numbers. For example, in order to get the number two, all you have to do is add one to itself. To get three, you add one more. The number one was also considered to be a triangular number and square, as well as both odd and even. It was thought to be indivisible and harmonious - unity itself.
These are just a few of the Pythagoreans' very basic ideas. While we no longer see mathematics as being sacred, it appears that Pythagoras and his students may have been on the right track after all. His ideas about the shape of numbers led to modern number theory as well as some modes of thought in quantum physics, where the reality of the world is seen as being composed of progressively smaller and smaller units. Before I end, I want to leave you with something Pythagoras thought was a secret of the universe: 1+3+5+7+9+11+13+15=82. He thought that something this simple had to reflect an aspect of the basic design of the universe. 2,000 years later, it was proved that he might have been on to something. This particular series of numbers is typical of the distance that an object will move with constant acceleration. Say that you drop a lead ball from a certain height. The ball will fall about 16 feet during the first second, not accounting for air resistance. If you are able to measure the distance traveled in each quarter second during the next two seconds, you will find that the distance traveled will approximate the numbers in this series, with the total distance equaling sixty four. Perhaps Pythagoras wasn't a crackpot after all.
Sources:
Valens, Evans G. The Number of Things: Pythagoras, Geometry and Humming Strings. New York: E.P. Dutton & Co., Inc. 1964.