meditations on the tetraktys – 0 – what is the tetraktys
In the 5th century B.C. in the city of Siracuse (Italy) a man established the first philosophical school of the world. in fact he was also the inventor of the therm “philosopher” ; one time a man asked him “who are you?” he answered “i’m a wisdom lover” that in greek is translated with the words philos (lover) & sophos (of wisdom) : philosophos, in english philosopher.
the man was born in the island of Samo, during his life he was a scientist , a philosopher , a mathematical that discovered many theorems and for someone was also a prophet; his name was Pitagoras.
the school founded by Pitagoras put a strong stress on numbers , thinking that the number is the fundamental constituent of the reality or, in other words, that every aspect of reality can be quantified. in effect the pitagoreans scholars used to say “To pan einai arithmos” (everything is number). A particular importance between all the numbers was attributed to the first ten numbers especially if they was represented with a special figure. this figure was a triangular composition of ten points arranged in four rows: 1,2,3,4. It was called tetraktys or tetrad and to make it simple here it is :
* * *
* * * *
To exemplify the importance of this figure for Pitagoras, i will say that his school was also named tetraktys and the members had a prayer dedicated to it:
“Bless us, oh divine number, thou from whom gods and men derives. oh holy, holy Tetrad, thou that contain the root, the spring of the eternal flux of creation. the divine number begin with the pure and deep unity, and reach the sacred four; then he produces the matrix of all, the one that contain all, that join all; the first born, the one that never deviate, the sacred ten, that have in itself the key of all the things”.
The pitagorean thinking and the tetraktys in particular had great influence on occidental culture, even if today we don’t notice. for example, historically the tetrad was the first “scheme” associated with the structure of reality and seems (despite what some rabbi say) that this concept was one of the origin of the jewish cabalistic tree; also the classical representation of the “eye of god” (the eye in the triangle) is in fact a tetraktys with the center point transformed in an eye.
just for curiosity i will list some interesting properties of this figure.
if you count the dots in the four levels of the tetrad you will have:
1 representing the adimensional point
2 the points needed to define line ( one dimension)
3 the points needed to define a plane (two dimensions)
4 the points needed to define a solid (three dimensions)
using the points you can trace different figures : triangles, hexagons, 6 pointed star, triskel , the isometric projection of cubes and many other shapes.
the figure is constituted by 10 points, if you associate the points with the first ten numbers you will have:
5 even numbers (2,4,6,8,10) and 5 odd numbers (1,3,5,7,9)
5 prime numbers (1,2,3,5,7) and five composed (4,6,8,9,10)
if you use the points of a tetrad two by two you can obtain the following fractions: 1/1, 2/1, 3/2,4/3. applying this fractions to the length of the strings of a musical instruments you will obtain these intervals: tonic, octave, perfect fifth, perfect fourth. with these intervals you can compose blues music, most middle age music and traditional chinese and african music. with the same intervals you can tune most of the string instruments in a modern orchestra and most of the traditional chinese, indian and japanese string instruments.
In the next posts i will write some yarns and maybe stories using the tetraktys or tetrad as an inspiration, thinking to it as a representation of the nature of reality.
We think that the universe need an order because our mind need to be put in order. Universe is in order despite our idea of order.