'Tis delectable poetry, lifting up nature's chaste robe, seeking her forms, considering her measurements, fondling her figure. Penetrating the womb of truth. Behold; the voluptuousness of geometry!' (Multatuli, letter to Max Rooses, Aug. 1867)
In Plato's Timaeus, the divine craftsman, the demiurge observes an Eternal Model of the cosmos. From this 'paradigm' he creates a tangible imitation, 'a round, in the shape of a sphere, equidistant in all directions from the center to the extremities.' (33b) Platonists believe the sphere is the embodiment of perfection; Beauty, Truth and Virtue come together. The Model's (or Scheme's) perfect proportions are founded on a mathematical ratio. The demiurge is the ultimate architect and poet, but above all, a mathematician. All the elements; the motion of the stars; the recurring seasons; the shape of flowers; the state of the world; all are derived from the Model. Even in failure, creation gives a sense of order.
The four elements
The cosmos is made up of two right-angled triangles (an isosceles and a scalene) from which the demiurge can construct five regular polyhedrons: cubes, tetrahedrons, octahedrons, icosahedrons and dodecahedrons. These stereometric forms are known as 'Platonic solids.'
Using these Platonic solids, the demiurge then constructs from matter (mother substance–derived from mater, 'mother') the four elements out of which all sublunary phenomena are made: the cube constitutes earth, the tetrahedron constitutes fire, the octahedron constitutes air and the icosahedron constitutes water.
The twelve-faceted polyhedron: the dodecahedron
According to Aristotle, the dodecahedron corresponds with a translunary substance, the ether, of which the heavens and the stars are made. Plato called the dodecahedron a 'heavenly shape' because it approaches the sphere's perfection. The cosmos' scheme is inherent in the dodecahedron: just like the year and the zodiac, it consists of twelve parts which in turn are subdivided into thirty–the thirty days of the month and the 30 celestial longitudinal degrees of each sign. Due to the dodecahedron, the cosmos comes to life.
But the sphere's faceting leaves much to be desired because the cosmos is a feeble reflection of the Model and man's soul is trapped in a body whose senses can only offer an incomplete image of the material world.
In Phaedo, Socrates, while in jail, speculates about the appearance of earth from beyond the 'atmosphere.' Seen from heaven, earth would look like 'a ball made of twelve strips of leather and bright colors, of which our colors, the ones used by our painters, are only a reflection.' The uni-verse is literally that which revolves as a unit. The world is a soccer ball. (Phaedo 110b)
The World Soul
The demiurge transforms the ideal Model into a tangible body, the cosmos. He then develops the world soul, which mediates between the two worlds. This gives rise to the three levels of creation, which correlate to the cube: our world is enclosed in three dimensions, expressed by the Platonic lambda, 'a perfect model of the universe.' (Robert Fludd).
But the number three is not the only holy one; the number four is it too. The number 1 is a point, the number 2 is a line (the shortest distance between two points), the number 3 is a triangular plane and the number 4 is a pyramidal volume. Planimetry shapes the world. This argument plays a role in solving a second paradox, the reconciliation of opposites.
The four qualities: the tetrade
The four 'primary' elements were divided into two opposing pairs: earth opposite air, fire opposite water. How do you reconcile the opposites?
To temper the mutual tension and bond, the demiurge introduced four qualities: wet and dry, cold and hot.
The archgeometrician began creation with fire and earth: fire to make the world visible, earth to give it a tangible form. 'Thus it was that in the midst between fire and earth God set water and air. [...] air being to water as fire to air, and water being to earth as air to water.' (Timaeus 32b)
In their mutual contact, the qualities produce the elements: heat and moisture produce air, moisture and cold produce water, cold and dryness earth, heat and dryness fire. This also clarifies the transmutations on earth. Fire can exist in air due to heat; air can exist in water due to moisture. As such, each element can change into its opposite. But since the tetrade is a closed system each element's share remains constant despite the transformations.
Clashing of the elements leads to deterioration in nature. But since adjacent elements share a quality, reconciliation always transpires, a primordial love that leads to growth. 'The four elements move, as if they all had hands with which they hold each other, as in a round dance.' (Pierre de la Primaudaye (1546–1619)) The alternation of love and hate determines the cycle of life and death.
The Timaeus dialog was inspired by Pythagorean sect theories and laid the foundation of all Western cosmologies until Newton.
The quadrature of man
The tetrade is the Model for the macrocosm and for the many microcosms that are minute reproductions of the whole [i.e. the macrocosm]. Between the different levels of creation there is an elaborate network of correspondences. The universe is an enormous machine of interconnected tetrades repeating each other to scale.
The tetrade is situated in a series of concentric circles, with in its center, at the crossroads of all tensions, man, the conceiver of the scheme. Cosmic perfection is mirrored in man. Because Adam was formed to the image of a divine source, and because we are all his descendants, the microcosm of the human body reflects the diversity of creation: our flesh is like mud, our veins like rivers, our bones like stones, our hair like grass. As in the universe, our bodies' components are arranged in a system which is subordinate to a single will. We embody a small version of the divine principle of the universe as a whole.
The human body is positioned within circles and quadrants with the arms stretched to show the different principles of symmetry and harmony in God's masterpiece. All humans are mortal but as an element of divine creation we are eternal. In a sort of psychosomatic math, our temperaments, fluids and organs react to the four periods of the day, the four seasons and the four stages of life.
This idea was accepted until the seventeenth century.
The zodiac man
All the 'zodiac man's' body parts correspond to a planet in order to determine astrologically whether to revert to bleeding. The Sun controls the heart, Venus the ears, the Moon the head, Mercury the lungs, and so on. There is a jester at his feet who derides the body's mortality. The quadrature of the circle always leaves a residue, a flaw–the stupidity that keeps the system going.
The second Adam
According to the medieval humoral theory, God proportioned the four elements to perfection in Adam. However, the Fall caused the elements to be scattered among humans–an imbalance that explains the existence of choleric, sanguine, phlegmatic and melancholy dispositions, which, in turn, mean man is prone to sin. Microcosms and macrocosms are no longer in harmony.
The coming of Christ restored the 'elemental integrity.' The Second Adam was characterized by a perfectly balanced complexion, evidenced also in his perfectly proportioned body and behavior.
In time the quaternary division was complemented with four cardinal points, four evangelists, four winds that blow from the corners of the diagram, and so on.
According to Johann Peyligk's Philosophiae naturalis compendium (Leipzig 1499):
> Fire is the fruit of heat and dryness; it corresponds with cholera (yellow bile) in the microcosm of heavenly humors (which leads to a short temper and disease of the liver), with the summer in the microcosm of the seasons, with Aries, Leo and Sagittarius in astrology, with the planet Mars in astronomy, with youth in the microcosm of the stages of life, and with the east wind in the microcosm of the cardinal winds (Subsolanus is depicted as a skull because this hot, moist wind is thought to have spread the plague).
> Air is the fruit of heat and moisture; it corresponds with sanguinity (enthusiasm), blood, spring, Gemini, Libra and Aquarius, Jupiter, adolescence and the south wind (Auster).
> Earth is the fruit of cold and dryness; it corresponds with melancholy (black bile), depression, fall, Taurus, Virgo, Capricorn, Saturn, middle age and the north wind (Boreas).
> Water is the fruit of moisture and cold; it corresponds with phlegm (apathy), the brain, winter, Cancer, Scorpio, Pisces, Venus, old age and the west wind (Favonius).
From the edges of the cosmos up to the human being, the world is divided into four. The network of correspondences is a machine of metaphors that makes the transfer of meaning from one level to the next possible. Everything has to do with everything. The metaphors have no bearing on our sensual experience: summer is a metaphor for zodiac signs that are situated symmetrically around a circle, not for summer constellations. This is based on a network of ideal connections that are assumed to be active in our three-dimensional universe.
Note that the metaphors are not seen as literature or as components of a simple memory system, but as scientific facts based on which the world was created. In order to live in harmony and honor the creator, buildings, cities and social systems were designed that complied with the quadrant.
The theory of the four elements prevailed until the 18th century; the classification was, of course, arbitrary. Brahmanism distinguishes five elements: earth, fire, water, wind and void (akasa). The Chinese distinguish five elements: earth, fire, water, wood and metal. The periodic table has, by now, 118 elements.
Not only the elements within the cosmos, but also the greater cosmos, the macrocosm, was shaped after the ideal heavenly bodies. Saturn, Jupiter, Mars, the Sun, Venus, Mercury and the Moon are embedded in seven crystal orbs that rotate within the celestial sphere and its fixed stars. Earth is static and at the center of the cosmos.
In a sense, the theory of the harmony of the spheres was invalidated by one of its most fanatic adherents, Johannes Kepler (1571-1630), who strove to unify religion and science. Astronomy was a theology using other means. He expected to find perfect forms everywhere but was continuously disappointed with the results his instruments provided.
Kepler coupled the notion of a harmony of spheres with Copernicus' heliocentricism. According to his Mysterium Cosmographicum (1596), the planets orbit the sun in circles. In an endeavour to clarify this, he attempted to reconcile Plato with Genesis. He too believed that geometry was the archtype of the cosmos, that the mathematical form preceded the creation of heaven and earth. All heavenly bodies moved along the edges of an orb, and these orbs were enclosed within each other as in a Russian matroyshka. He believed that five spatial regions existed between the spheres of the then six known planets and that these were defined by the five Platonic bodies. He placed an octahedron between Mercury and Venus, an icosahedron between Venus and Earth, a dodecahedron between Earth and Mars, a tetrahedron between Mars and Jupiter, and a cube between Jupiter and Saturn.
By coincidence the gaps between the planets according to his model were almost identical to those according to his calculations. This led him to mistakenly conclude that he had discovered the key to the universe.
But, interestingly, these wild speculations about the blueprint of the cosmos paved the way to his formulation of the laws which to this day are still seen as the correct definitions of the planetary orbits. From a metaphysic he developed physics. But this occurred only after he had become acquainted with the empirical experiments of Tycho Brahe (who had designed the gardens around his observatory based on the cosmic model of the tetrade). Kepler suddenly understood that the planets do not obey Platonic law: their paths were not perfect circles but elliptical. It was, in fact, his search for the formal source of the universe that made it possible for him to recognize the true structures.
In so doing, Kepler manifests the transition from mystical mathematics to science. Keppler laid the foundations for the mechanization of the world-view: 'The heavenly machine does not resemble a divine, living entity but a clock (whoever thinks a clock can have a soul, pays tribute to the product instead of to its creator); just as practically every movement can be reduced in some way to one very basic, magnetic-material force, all movements in a clock are caused by a basic weight.'
For a period, Kepler made a living by making horoscopes. But he defined himself as a 'Lutheran astrologist': examine everything and retain the good, as the bible prescribes. He said of astrology: 'a foolish daughter, but Dear Lord, where would her mother, our highly ingenious astronomy, be without this foolish daughter.' All science is born of rectified superstition.
Fludd's cosmic viol
Saturn, Jupiter, Mars, the Sun, Venus, Mercury and the Moon are embedded in seven crystal orbs that rotate within the celestial sphere and its fixed stars. The friction between the orbs creates the harmony of the spheres, a loud chord inaudible to all humans barring a handful of gifted musicians. (Plato, The Republic, book X)
The Scottish Rosicrucian Robert Fludd (1574-1637), Kepler's archenemy, took the metaphor literally. He portrayed the universe as a monochord, a musical instrument of one string that stretches between the highest and lowest entities of creation, from the angelic choirs to the silent stones. Three worlds can be seen on the monochord: the angelic, the etheric and the elementary worlds. There is harmony in and between each of the worlds. Above, a divine hand reaches out of a cloud to a tuning peg in order to tune the cosmos. Fludd delineates the proportions, the consonances and the intervals of creation. The Sun is situated at the G between two octaves. At the bottom, from Earth to the Sun, we see first the elementary world that is composed of the four elements: fire, earth, water and wind. Stretching out above that is the ethereal world existing of the spheres of the seven planets, with the Sun in the middle. Above that, the hierarchy of angels.
This plan is based on Pythagorean Harmonics, dominant in music since antiquity.