|Plato, according to Raphael Sanzio|
Among Plato’s dialogues, Timaeus has always captured the attention of scholars, for it represents the first description in Greek philosophy of a coherent cosmological model, which reached great resonance by becoming part of the medieval model through the partial translation into Latin of this dialogue by the mysterious Roman philosopher Calcidius.
Very little is known about Calcidius. Although he lived in the fourth century, we do not know his date of birth or death, nor the place where he lived. It is not even known whether he was a Christian or a pagan (a Neo-Platonist). His book is dedicated to a certain Hosius, who may or may not be the bishop of Cordoba who participated in the Council of Nicaea.
It is often said that medieval philosophy in Western Europe was based initially on Plato, and from the twelfth century on Aristotle. This happened because, in the realm of the Western Roman Empire, the knowledge of the Greek language had been lost, therefore the Greek classics could no longer be read in their original language. There were no Latin translations, for the illustrated Romans of the imperial period could read the Greek language perfectly, so did not need them. What is not usually mentioned is that Plato’s works had also become inaccessible, with the sole exception of the Timaeus, which in the partial translation by Calcidius knew an unexpected boom during the Middle Ages, even stronger than Calcidius’s work during his life.
The Timaeus is a surprising dialogue for several reasons, among which I will mention the following:· According to the classic geocentric model, which centuries later would be formalized by Ptolemy, it presents a cosmos created by a demiurge and divided into two well-differentiated parts: the heavens, the dwelling of the gods (the stars and the planets), perfect in their structure and movements; and the Earth, located in the geometric center, but of inferior quality, where everything is made of mixtures of the four classic elements: earth, water, air and fire. Plato does not say what the heavens are made of. That is left for Aristotle.
· For the first time, a surprising theory, possibly of Pythagorean origin and based on geometry, is offered to explain the differences between the four elements. According to Plato, everything in the sublunary world (on the Earth) is based on right triangles, of which he distinguished two types: isosceles and scalene. The first are all similar to each other, so actually there is just one type. The scalene (those having three sides of different lengths) are of infinite possible types, but one of them is most perfect: that obtained by dividing in two equal parts an equilateral triangle. Plato defines it as follows: the scalene triangle where the square of the major cathetus is three times the square of the minor. Elsewhere he says that the lesser cathetus is equal to one half of the hypotenuse. Both definitions are equivalent. Now we join two by two each of these two basic triangles. With two isosceles triangles we get a square; with two scalene, an equilateral triangle. With these figures we can form the following four regular polyhedrons (three-dimensional bodies with all their faces equal, the so-called Platonic solids):
|The five Platonic solids|
1. With four triangles we have the tetrahedron, the sharpest of the polyhedrons, which therefore must be the base of the most incisive element: fire.
2. With eight triangles we can form the octahedron, less sharp than the tetrahedron, but more than the other solids, so this must be the basis of the second most incisive element: air.
3. With twenty triangles we can form the icosahedron, which is able to rotate around its twenty faces and move horizontally from place to place, so this would be the basis of water.
4. Finally, with six squares we can form the cube or hexahedron, most stable, because it can rest on one of its faces and does not move. This solid would be the basis of the earth.
5. Plato mentions that there is a fifth combination used by God to make the universe. He obviously means the pentagon-dodecahedron, the fifth and last regular polyhedron, which is not made by triangles or squares, but by pentagons. Although he does not say so, perhaps this simple allusion suggested to Aristotle the idea that there must be a quintessence, a fifth element that would be the fundamental basis of the world beyond the moon, the heavens.
· An interesting part of the Timaeus describes prophetic or divinatory dreams and tries to explain them. It says that, in order to receive them, reason must be hindered or impeded, for reason and inspiration are opposite. It is curious that Aristotle, in his treatise On divination in sleep, gave an explanation of dreams much more in accordance with our way of thinking. He says that prophetic dreams can arise for three reasons: a) simple coincidence; b) because a previous worry about an imminent and feared event has caused the dream; c) because once awake the dream has influenced the dreamer to act in the same way as he did in his dream.
- Finally the Timaeus is the first dialogue by Plato describing the myth of Atlantis, which had so much influence on later authors. He later wrote an entire dialogue, Critias, dealing with the same subject, but much of it has been lost, so the summary appearing at the beginning of Timaeus has become our only complete reference to the myth. But this is another story.