THE PYTHAGOREANS AND THE NUMBERS.
The oldest known cult based on the rule of numbers was that of the Pythagoreans.
They focused mainly on the importance of number in the cosmos: for them all things were countable, and many could be expressed numerically. Thus, the relationship between two things can be expressed by a numerical ratio; the order existing in a number of ordered subjects can be expressed by numbers.
But what seems to have impressed them more than anything else was the discovery that the musical intervals between the notes of the lyre can be expressed numerically.
They discovered this by experimenting with the length of the lyre's strings, which produced a certain sound at a certain length, for example: a string half as long produces an extremely harmonious note, and is called an octave. A string two-thirds the length of the first string produces the next most harmonious note, now called the fifth. And a three-quarter length produces the fourth, which also has a very harmonious sound.
It could be concluded that the pitch of a sound depends on the number, insofar as it depends on the lengths of the strings, and it is possible to represent the intervals of the scale with numerical proportions.
Today these harmonies can be traced back to the physics of vibrating strings, which move in wave patterns. The number of waves that can fit on a given length of string is a whole number, and these whole numbers determine the simple numerical ratios. When the numbers do not form a simple ratio, the corresponding notes interfere with each other and form discordant “thumps” that are unpleasant to the ear.
This later led the German astronomer Johannes Kepler to the concept of the "music of the spheres".
Since the Pythagoreans noted that musical harmony depends on number, they concluded that the harmony of the universe also depends on number.
“As they saw that the attributes and relationships of musical scales could be expressed in numbers, from then on it seemed to them that all other things were modeled in their whole nature after numbers, and they judged that numbers were the first in the world, the whole nature and that the whole sky was a musical scale and a number” (Aristotle).
Translating these observations to the world in general, the Pythagoreans spoke of cosmic harmony. They emphasized the importance of numbers in the universe, and went further, declaring that things are numbers.
“The Pythagoreans held that the elements of number are even and odd, and that, of these elements, the first is unlimited and the second limited; the unit, the one, comes from both (since it is both even and odd), and the number comes from the one; and all heaven, as has been said, are numbers.” (Aristotle).
To say, then, that all things are numbers would mean that "All bodies consist of points or units in space, which, taken together, constitute a number."
That the Pythagoreans considered numbers in this way is reflected in the tetraktys, a figure they considered sacred.
The tetraktys represents the number 10, which results from adding: 1 + 2 + 3 + 4, that is, it is the sum of the first four integers.
Therefore, for the Pythagoreans, the most perfect number was 10.
They realized that the juxtaposition of a few points engenders a line, not only in the mathematician's imagination, but also in external reality; in the same way, the surface is generated by the juxtaposition of several lines and, finally, the body by the combination of several surfaces. Points, lines and surfaces are therefore the real units that make up all the bodies in nature and, in this sense, all bodies must be considered as numbers. In short, each material body is an expression of the number four (τετραϰτύς), since it results, as a fourth term, from three classes of constitutive elements (points, lines and surfaces).
For the Pythagoreans, the limited cosmos, or world, was surrounded by the immense or unlimited cosmos (the air), and it "inhales" it.
The objects of the limited cosmos are therefore not pure limitation, but have a mixture of the unlimited. Now, the Pythagoreans, when considering numbers geometrically, also conceived them as products of the limited and the unlimited (because they were made up of even and odd.)
They also linked specific numbers with mystical properties. The number 1 symbolized the unity and origin of all things, since all other numbers can be created from 1 by adding enough copies of it. For example, 7 = 1 + 1 + 1 + 1 + 1 + 1 + 1.
For the Pythagoreans, the earth was not only spherical, but it did not occupy the center of the universe. The earth and the planets revolved —at the same time as the sun— around the central fire or “heart of the Cosmos”.
(identified with the number One).
Pythagoras believed that the monad was God and good. The monad is the origin of the One. The monad is the seed of a tree for which numbers are to the monad what the branches of a tree are to the sight of a tree. The monad in relation to other numbers retains the identity of any other number or anything it encounters. Any number multiplied by one is itself, and any number divided by one is itself.
“The Pythagoreans believed that nothing exists without a center around which it revolves. The center is the source and it is beyond comprehension, it is unknowable, but like a seed the center will expand and realize itself as a circle” (Hemenway 51).
From here, they gave meaning to the rest of the numbers, for example, the dyad implies the principles of "two" or "otherness". They referred to the dyad as "audacity" because of the audacity of separation from the one, and "anguish" because it has a sense of tension in the desire to return to unity. They believed that the dyad divides and unites, repels and attracts, separates and returns. “Pythagoras held that one of the first principles, the monad, is God and the good, which is the origin of the One, and is itself intelligence; but the indefinite dyad is a deity and the evil that surrounds it is the mass of matter”
The number three, represented by the triad, is the only number equal to the sum of the previous numbers. For example, one plus two equals three. And three is also the only number whose sum is also equal to its product. Or, one plus two plus three equals one times two times three. The triad means prudence, wisdom, mercy, friendship, peace and harmony. The triangle represents balance and is a polygon of stability and strength.
They built the tetrad, drew a horizontal and vertical line connecting the centers and intersection points of two circles (The Vesica Piscis). When a circle is drawn along a line connecting the two centers, the perfect shape of a square within the circle is created.
The form of the pentad represented for them the symbol of life itself. For it consists of all the preceding numerical symbols: the point of the monad, the line of the dyad, the surface of the triad, and the three-dimensional volume of the tetrad.
The pentad also refers to the well-known five-pointed star. We can see it reflected in our five fingers, in the union of the head with the four members, that is, the symbol of man, it is also referred to as the symbol that protects from evil and power and immunity.
The pentad was used as a secret sign among the Pythagoreans to distinguish themselves and recognize other members.
The symbolism of the pentad can be directly related to the Divine Proportion. And the regeneration of the pentad is related to the value of phi (Ф).
The image of the pentad is found in nature in leaves and flowers. And it was also believed that each point of the pentad represented an element: water, earth, air, fire and idea.
The decade represents the number ten. Instead of simple numerical and geometric interpretations, the decade further extends to the idea of a new beginning of the limitless.
Symbolizing both the world and the sky, the decade helps us understand the creation of the universe. The monad multiplied by the dyad multiplied by the pentad (one times two times five) gives us the decade. Since any number times ten is similar to any number times one, it is similar to the monad.
The Pythagoreans also considered that the number 2 symbolizes the feminine, 3 the masculine; and when joined in 2 + 3 = 5 they result in marriage. For them, all even numbers were feminine, and all odd numbers were masculine.
They also recognized the existence of nine celestial bodies: Sun, Moon, Mercury, Venus, Earth, Mars, Jupiter, Saturn and the so-called Central Fire. For them the number ten was so important that in their vision of cosmology they had a tenth body, called the Counter-Earth, which is perpetually hidden from us by the Sun.
- Pythagoras and the Mystery of Numbers. Kate Hobgood. [http://jwilson.coe.uga.edu/EMAT6680Fa06/Hobgood/Pythagoras.html](http://jwilson.coe.uga.edu/EMAT6680Fa06/Hobgood/Pythagoras.html)
- Number symbolism. Pythagoreanism. Britannica. [https://www.britannica.com/topic/number-symbolism/Pythagoreanism](https://www.britannica.com/topic/number-symbolism/Pythagoreanism)
History of Philosophy / Vol. 1. From Ancient Greece to the Christian World. Frederick Copleston.
