Pythagoras. Unless your daily work requires a lot of calculations, you probably don’t give much thought to Pythagoras. In fact, you may not have given him any thought at all since high school geometry. Since most people remember him solely in the field of mathematics, if you are like most, you might just as soon forget him all together, intentionally. However, Pythagoras’ thoughts and work have had a huge impact not only on the world of mathematics, but also science and philosophy.
Pythagoras devoted himself to questions serving the purposes of wisdom itself. He wanted to know the truth of things. He is most well known for his theorem a2 + b2 = c2 and for the discovery of the mathematics behind musical scales and harmony. He saw that reality was created out of something that, in and of itself, was not material, but that was instead the architectural structure for all that is material. He maintained that the ultimate reality was abstract and relational and dependent on numbers.
The “New Age” concept of the harmony of the cosmos is not new at all. Pythagoras described this numerically more than 2500 years ago. He taught that the harmonies of music are nothing more than sensible, audible manifestations of the relationships between and among numbers. He believed creation itself is harmonic and expressive of a rational plan. Pythagorean medicine included music therapy much like today’s medicine, because the body, which might manifest disorders, is still, ultimately, the manifestation of something else that is fundamentally relational and not just material. We humans too then, according to Pythagoras, resonate to the harmony of the universe – a universe which again is not material, but relational. These relationships determine which combinations will be heard as concordant or discordant. Those that resonate in a way consistent with the laws of numbers are heard as concordant. Those that do not are heard as “off”, offensive or discordant. This is because the soul itself can naturally perceive the same harmonic relationships that keep the planets in their orbits.
Pythagoras held the numbers 1, 2, 3, and 4 in particularly high esteem. To him, in the physical world, the number “1” represented a “point”. A line was a representation of “2” or the connection of two points. The number “3” brought a plane to reality and “4” made solids accessible to the senses. The connections between these numbers and the physical, material world are relatively simple and easy to visualize. However, this concept is applicable and true from the simple to the very complex. The periodic table and all the resultant chemicals can ultimately be described in terms of mathematical equations or relationships. The same could be said of quarks and gluons. So the abstract can correspond with and describe or influence the material world.
This has not always been evident. Sometimes, and in fact often, mathematical abstractions predate by decades or even centuries the physical discoveries that the mathematics describes with precision. This fact is even more intriguing when you consider that some things in our material world can only be calculated or described through the use of irrational or imaginary numbers. How, you ask, can the irrational or imaginary explain the physical? The number pi is necessary for the calculation of the circumference of a simple circle. Imaginary numbers, such as the square root of negative one, were conceived long before they were useful to science. How is it that mathematical equations describe everything physicists know about our physical world? How is it that the cosmos operates in an orderly manner according to mathematical equations that when conceived had nothing to do with the cosmos?
For Pythagoreans, coincidence does not explain this. Statistically, the odds against a mathematician coming up with a complex equation that would perfectly explain some hard physical fact some 200 or 300 years in the future would be astronomical. From the perspective of Pythagoras then, such occurrences must express some plan. He saw that the ultimate plan must be abstract but at the same time capable of generating the physical reality and that it must also be a plan of relationships.