Harmony of the Spheres

Pythagoras is mostly known for his contribution to mathematics and science but he was also a very religious and spiritual philosopher. Although none of his original writings have survived, what we do know about him comes from his disciples and his ideas went on to strongly influence other well-known philosophers, such as Plato and Aristotle. It was his belief that through mathematics, one can gain an insight in the workings of the mind of God so many of his mathematical and scientific discoveries, he attributed to his pursuit of finding God.

He believed that certain shapes made up the Universe, where the circle best represents God; singular, perfectly shaped, symmetrical and with no visible start or end. Any two objects, no matter where they are placed, can be connected to form a circle, where the distance between the two objects forms the diameter. To Pythagoras, this represented man's connection with God.

He also believed that on a more spiritual level, the Universe was made up of triangles, where even a triangle can form a circle. The most basic example of this is in trigonometry, when calculating the tangent, sin or cosine of a triangle.

Circles can also be used to create an equilateral triangle (a triangle with equal side lengths and equal angles of 60° each) by joining the two circles together so that one circle's centre touches the other circle's circumference and vice versa.

The "vesica pisces" was derived from these two circles by Pythagoras, to create the fish symbol that was later adopted by the Christians.

Pythagoras and the vesica pisces even make their way into the Bible. In the Gospel of John (21:11), Jesus is said to have caught 153 fish, which to many may have no significant meaning and almost seems like a random number. But Pythagoras had calculated the length and width ratio of the fish shape to be 265:153, which is also an approximation of the square root of 3.

Here's another interesting trick. If you take any number that is divisible by 3 (15, 18 ,21 etc) and add the cube of each digit, you will eventually get the number 153.

For example, the number 18:
(1x1x1) + (8x8x8) = 513, then
(5x5x5) + (1x1x1) + (3x3x3) = 153

Pythagoras believed that the Universe was made up of numbers using circles and triangles and that each number had its own spiritual and mystical meaning. These numbers can be found using the same circle technique.

The Monad - represents the number 1 and also God, the first being

The Dyad - represents the number 2 and the individual and diversity

The Triad - represents the number 3 and harmony, justice and perfection

The Tetrad - represents the number 4 and the four elements

The Pentrad - represents the number 5 and the soul

The Decad - represents the number 10 and the Universe, heaven and Earth and is the perfect number

All of these shapes can be formed to create the Tetractys, which represent different planes and also forms an equilateral triangle, and is the founding idea of the decimal system (1 + 2 + 3 + 4 = 10)

- The first line or plane contains just the one dot. This represents the Monad, or God.

- The second plane contains two dots. This represents the Dyad the man and the woman, harmony and diversity

- The third plane contains three dots. This represents the Triad (justice), the Pentad (life) and the Hexad (psyche)

- The fourth plane contains four dots. This represents the four elements.

Pythagoras attempted to apply this idea of "perfection" to explain the workings of the Universe. He even tried to apply it to the movement of the Sun, the Earth and the planets. Pythagoras was also a musician and he believed that the distance between the "heavenly bodies" and the Earth and themselves, corresponded with a particular harmonic lengths and intervals, which if could be heard, would create a musical harmony. This is known as the "Harmony of the Spheres"

Going back to trigonometry briefly, the sine and cosine of a triangle can be drawn graphically as a wave, much like the wave of light or sound.

So theoretically, all circles, and spheres for that matter, can be drawn graphically as shown above, where a larger sphere would have a larger amplitude and therefore would produce a much lower pitched sound, or note, whereas a smaller sphere would create a smaller amplitude and cycle and would have a much higher pitch.

It was Pythagoras' idea that when all the celestial bodies of the solar system would be able to produce their own unique tune depending on their size, together creating a sort of song, all in perfect harmony with each other. Of course, he never intended for this idea to be taken literally.

But what if the planets and stars could be heard? Have you ever wondered where the static noise of an untuned radio or television comes from? It comes from space. It's called Cosmic Microwave Background Radiation and is the remnants of the Big Bang. So, is what we're listening to when we hear this static just random chaos or is it the Universe's own unique song we are yet to fully understand?