Dialogue Text

Timaios (Continued) The generative substance, being moistened and heated by fire, receives the forms of earth and air, and undergoes all sorts of other changes that accompany them, presenting a truly varied appearance to the eye. However, because it is filled with forces that are dissimilar yet unbalanced, it itself remains out of equilibrium in every respect, and is shaken irregularly in all directions. While being shaken by these things, it also shakes them as it moves.

Timaios (Continued): The things that are set in motion, while being divided, always move in separate directions. Just as grain is sifted with a sieve and shaken, the dense and heavy ones go to one side, while the sparse and light ones are carried to another place and settle in different locations. At that time, the four kinds also undergo this process, being shaken by the receiver. The receiver itself moves and initiates a shaking motion like a tool. As a result, the most dissimilar things are separated as far apart as possible, while the most similar things are brought together as closely as possible. Thus, each occupies a different place. This is before the whole is ordered and arises from it. Before that, all of this existed without reason or measure.

Timaios (Continued) When the God arranged the entire cosmos, He first formed fire, water, earth, and air. These elements, like everything else that exists without a divine order, were initially in an indeterminate state, possessing only faint traces of their true forms. We must always assume that the God meticulously assembled these unordered elements into the most beautiful and best possible arrangement. Now, I will explain to you how each of these elements was arranged and generated.

Timaios (Continued) I must explain this to you in unfamiliar terms. However, since you are on the path of education necessary to understand what is being explained, you will follow along. First, it is clear to everyone that fire, earth, water, and air are substances. Any substance has form and depth. And depth always includes the property of a plane. Plane figures with right angles consist of triangles. Every triangle begins with two fundamental triangles.

Timaios (Continued). The two triangles each have one right angle and two acute angles. In one triangle, the equal sides divide the right angle into two equal angles. In the other, the unequal sides divide the right angle into different-sized angles. We assume this configuration as the principle of fire and other objects, and proceed according to a plausible explanation that follows necessity. Knowing the principles even further back is reserved for the gods, and those among humans who are close to them. Now, what must be said is...

Timaios (Continued): What are the four kinds of objects that can be made most beautifully? These should be distinct from each other, yet some of them may arise by being separated from others. If this can be achieved, we will grasp the truth about the generation of earth and fire, and things proportional to both. Because no one will concede that there exist any more beautiful objects than these, in their respective categories. Therefore, we must strive to harmonize four kinds of objects with different qualities of beauty, so that they fully capture the essence of what is being described.

Timaios (Continued): Of the two triangles, one with equal sides can be defined as a single shape, but the other, with unequal sides, has countless forms. Therefore, if you intend to begin in the correct order, you must choose the most beautiful form from among those that are infinite. If someone can select a more suitable triangle for these constructions and explain their reasoning, consider them not an enemy, but a friend. We will then choose the most beautiful of many triangles, by which we will construct three equilateral triangles.

Timaios (Continued) To explain the reasons in detail would make the story too long. However, there is a reward of friendship for anyone who can prove this and discover its true nature. Let us choose two triangles as examples: one that is isosceles, and another where the square of the longer side is three times the square of the shorter side. We must now define more clearly what I mentioned vaguely before. It appeared that all four kinds of objects were transformed into each other through a process, but this was not the correct way to view it.

Timaios (Continued): In this way, four types are derived from the selected triangle. Three types are produced from triangles with unequal sides, and only one type can be constructed from isosceles triangles. Therefore, not all types decompose into each other, nor do they proceed from many small ones to a few large ones, or vice versa. Only three types can do this. This is because these three types are all composed of the same triangle, so when a larger one decomposes, it creates many smaller ones that are assembled from the same triangle and receive appropriate forms.

Timaios (Continued). Furthermore, even small elements can be divided into many triangles and scattered; when these combine as a single number to form a single volume, they create another large shape. Regarding how these elements transform each other, the above is sufficient. Next, let us describe what shapes are formed and how many of them combine to make up the whole. Therefore, we will begin with the first and smallest shape that can be assembled. Its constituent element is a triangle whose hypotenuse is twice the length of its short side. Combining two such triangles along their diagonals, and repeating this three times,

Timaios (Continued) By bringing the diagonal and the shorter side together to a common point, six triangles are combined to form one equilateral triangle.

Timaios (Continued) Four equilateral triangles combine to form a solid angle, where three of them create the solid angle. This solid angle follows the largest obtuse angle among the planar angles. When four such solid angles are formed, the initial solid is assembled. It divides the entire sphere into mutually equal and similar parts. The next solid is also made from the same triangle, but this time eight equilateral triangles combine to form a solid angle using four planes. With six such solid angles, the second solid is completed in this way.

Timaios (Continued) The third solid is constructed by combining one hundred and twenty elements, which is twice sixty. It has twelve vertices, each surrounded by five triangular faces, and it possesses twenty triangular bases. One part of this solid was separated from the elements that created it. Isosceles triangles give rise to a fourth type of property. When four are combined, they gather around a right angle to form one square. Six such squares combine to create eight vertices. Each vertex is formed by three right angles joined together on a plane.

Timaios (Continued) Thus, the resulting three-dimensional shape became a cube, and it has six square faces with equal sides as its base. Furthermore, there was a fifth element. The god used it to color and depict the whole thing.

Timaios (Continued) If someone carefully considers all of this and is uncertain whether to say that the universe is infinite or finite, then the assertion that there are countless universes should be understood as a view concerning something truly infinite, and it is a matter for those who have knowledge of such things.

Timaios (Continued) As for when it is appropriate to discuss whether the universe originated as one or as five, it seems more reasonable to pause and hesitate on that point. Regarding what we are saying, the god will reveal that the universe originated as one, following a plausible explanation. Others may focus on different things and hold different opinions. For now, let us set aside this point, and instead, let us divide the kinds of things that have come into being by name: fire, earth, water, air. Let us give the earth a cubic shape.

Timaios (Continued). This is because earth, of the four elements, is the least mobile and most suitable for forming shapes. And what has the most stable base must necessarily arise as such. In the triangle we initially considered, the base of a triangle with equal sides is inherently more stable than that of a triangle with unequal sides. Furthermore, the planar figure of a quadrilateral formed from either type of triangle will be inherently and inevitably more stable, both in its parts and as a whole, compared to an equilateral triangle.

Timaios (Continued). From this, let us assign earth to what remains, and maintain a plausible explanation. Of the remaining things, we will assign the shape that is least prone to movement to water, the shape that is most prone to movement to fire, and the intermediate shape to air. Furthermore, we will assign the smallest objects to fire, the largest objects to water, and those of intermediate size to air. We will also assign the sharpest objects to fire, the second-sharpest objects to air, and the third-sharpest objects to water. Regarding all these things, that which has the fewest fundamental components is inevitably most prone to movement, most acute in every direction, possesses the greatest cutting power, and furthermore, exhibits the lightest properties.

Timaios (Continued). This is because it consists of a very small number of fundamental components. Let the second element possess these qualities in the second degree, and the third element in the third degree. Therefore, following the correct explanation and what seems plausible, let us consider the pyramidal shape as fire, which serves as the seed. Following the order of generation, we will call the second element "air," and the third element "water."

Timaios (Continued): All of these things must be considered as being extremely small. Each individual type is so small that we cannot see it at all, but when many of them gather together, the mass becomes visible. Furthermore, regarding numbers related to ratios, movement, and other forces, God has meticulously finished every point in a way that the inherent nature itself willingly submits and yields, harmonizing everything according to proportion.