
Timaeos
The book Timaeus is one of the 34 preserved dialogues by the renowned ancient scholar Plato (428 BC - 348 BC). This concise work, with just under 60 pages, contains the earliest known mention of the legendary island of Atlantis.
The book is also of great significance for the history of geometry. In the concluding part of the work, Plato explains the metaphysical classification of a special group of geometric figures named after him: the Platonic solids—tetrahedron, cube, octahedron, dodecahedron, and icosahedron. From a mathematical perspective, only these five three-dimensional figures can exist when they are seamlessly bounded by regular two-dimensional surfaces.
Timaeus and the 5 Platonic Solids
The Platonic solids are named after the ancient scholar Plato. In the concluding part of his book Timaeus, he explores the connection between his theoretical mathematical knowledge and the tangible phenomena of nature. He concluded that every natural form could be represented as a combination of numerous Platonic solids. Plato's teachings were cited in textbooks for nearly 2,000 years and remained significant even in the late Renaissance, when the natural scientist Johannes Kepler (1571–1630) seemingly succeeded in explaining the planetary orbits based on the movement of nested Platonic solids.
The undoubtedly most beautiful representation of the Platonic solids comes from Leonardo da Vinci. Around 1498, he created 60 illustrations of geometric figures for a book by the mathematician Luca Pacioli (Divina Proportione, or The Divine Harmony in German). These included the five Platonic solids. What was novel about his depiction was the perspective-correct skeletal structure, which greatly enhanced their clarity and visual appeal.

A tetrahedron consists of 4 equilateral triangles

A cube consists of 6 squares

An octahedron consists of 8 equilateral triangles

A dodecahedron consists of 12 equilateral pentagons

An icosahedron consists of 20 equilateral triangles

John the Baptist was the patron saint of Florence, Leonardo's hometown
Timaeus and Raphael's The School of Athens
Plato's ideas, particularly the book Timaeus, were of great importance to Renaissance artists. This is evident, for instance, in Raphael's painting The School of Athens, located in the former private chambers of the Pope in the Vatican. The figure pointing upward represents Plato and holds the book Timaeus under his arm. The upward-pointing finger depicts Plato in a manner typical of representations of John the Baptist, the patron saint of Florence. Raphael spent several years in Florence, where he met Leonardo da Vinci, whom he deeply admired and often emulated. The central figure of Plato in Raphael's painting is therefore undoubtedly identified with Leonardo da Vinci. In addition to Leonardo, Raphael also portrayed prominent patrons, Michelangelo as Heraclitus, and even himself as an unnamed observer.

Leonardo da Vinci as Plato. The spine of the book features the inscription Timeo (Timaeus)

Michelangelo as Heraclitus

Presumed self-portrait of the approximately 27-year-old Raphael
Plato's Influence on Leonardo da Vinci
For Leonardo da Vinci's painting, Plato's Timaeus holds significance primarily because one of its characters, Critias, emphasizes that pre-ancient civilizations, such as the mentioned Atlantis, could be completely destroyed by a catastrophe—whether through a lost war, a devastating earthquake, or a massive flood. Subsequent generations would always have to rediscover the knowledge that had been lost.
This idea profoundly impressed Leonardo. On the one hand, he sought to make his paintings particularly durable in terms of the materials used. On the other hand, he aimed to create works of timeless content. His paintings were intended to be so beautiful that no being would wish to destroy them for their inherent beauty, and they would remain intact as a whole. This concern arose because the completeness of ancient texts, including Plato's works, is far from assured.
It is interesting that Plato, in the concluding part of Timaeus, employs metaphysical, almost spiritual models to demonstrate a geometric truth—namely, the mathematical interrelation of the Platonic solids. He likely hoped that the metaphysical connection would be more likely to survive the presumed collapse of his culture than the mathematical one. Since both were intertwined, the mathematical truth would also be preserved.
Leonardo da Vinci adopted a similar approach with his paintings: the idealized beauty of the depiction conceals the underlying geometric truths in his works, which are revealed only to those who view them with knowledge of geometry. The great flood that Plato's Critias cites as the cause of Atlantis's downfall is reflected in numerous drawings by Leonardo, particularly in his portrait of the Mona Lisa.

The head of the Mona Lisa divides the background into two distinct landscapes. Martin Kemp interprets this side as a future flood wave threatening to descend into an idyllic valley


The Flood in the Mona Lisa According to Martin Kemp
Martin Kemp, former Professor of Art History at the University of Oxford, with guest professorships at Harvard and Princeton, and widely recognized as the leading expert on Leonardo, writes about Leonardo's Mona Lisa:
"The dual-level landscape in the Mona Lisa—the elevated body of water on the right side [of the painting] is above its natural position—is the essence of what Leonardo learned through his reflections on high and low-lying areas in Tuscany. The instability of one of the mountains to the left of her head [i.e., to her left as seen in the painting], with its pronounced overhang and deep incision below, suggests that things will radically change at some unknown point in the future. A monumental transformation is imminent, in which the gently meandering rivers in the lowlands beneath the Mona Lisa’s balcony, with its neatly crafted bridge, will be overwhelmed and reshaped by a force majeure [a great force] against which any human engineer is powerless."
(Kemp, Martin [2005]: Leonardo. Munich: Verlag C.H. Beck oHG, pp. 176–177)
Kemp makes these remarks in the chapter "Master of Water," specifically in connection with Leonardo's attempts to harness the immense power of water.
Timaeus (Excerpt)
The following presents the monologue of Critias from Plato's Timaeus, referencing the fall of Atlantis. Before Critias begins the relatively brief legend of Atlantis, he builds anticipation with a much longer yet highly instructive prelude on the prerequisites and the formation of states.
Preface of Critias on the Sunken City of Atlantis
"[...] I will recount an ancient legend that I heard from the mouth of a man who was no longer young. For Critias, at that time, as he said, was almost ninety years old, and I was about ten years old. But it was the day of the Festival of Illusion. During this time, the traditional festival for us boys also took place. Our fathers offered us prizes for reciting songs. Many poems by various poets were recited, and as something new at the time, many of us boys also sang poems by Solon. Then one of the community's neighbors—whether this was his genuine opinion at the time or if he wanted to please Critias—said he believed Solon was not only the wisest but also the most intelligent among all poets. The old man, I remember well, was very pleased and, smiling, replied: If only, friend Amynandros, he had not treated writing as a side matter but, like others, pursued it with full seriousness and completed the story he brought from Egypt, rather than being forced to abandon it because of the unrest and other improper circumstances he encountered upon his return. If he had done so, I believe neither Hesiod nor Homer nor any other poet would have achieved greater poetic fame than he.
What was this story, Critias? he asked. "Certainly the greatest and justly celebrated heroic deed our city ever accomplished, of which no news has reached us due to the passage of time and the destruction of its perpetrators. Tell him, the other asked, from the beginning, what and how and from whom Solon heard it, which he narrated as a true event.
It is in Egypt, he replied, in the Delta, at the apex where the Nile divides, a province called Saitic, whose largest city is Sais, also the home of King Amasis. This city has a patron goddess called Neith in Egyptian, and in Greek, she is known as Athena, so they say. The inhabitants, however, claim they are great friends of the Athenians and, in a certain way, related to the natives. Solon said he traveled there, was received with great honor, and, when he questioned the priests most knowledgeable about ancient times, discovered that neither he nor any other Greek knew the slightest thing about such matters.
However, to prompt them to speak of ancient times, he began recounting the oldest stories of his homeland, about Phoroneus, who is called the First, and about Niobe, and, after the flood, the legend of Deucalion and Pyrrha, how they successfully survived. He listed their descendants and, reflecting on the years that had passed since the events of the legend, tried to calculate the dates. Then an elderly priest said: 'Ah, Solon, Solon! You Greeks are always children, and no Greek is truly old.' 'Why? What do you mean?' he asked upon hearing this. 'You are all young in spirit,' he replied, ‘because you have no ancient beliefs based on old traditions, nor any knowledge that has grown gray with time. And therein lies the reason.’
Many and various destructions of humanity have occurred and will occur, the greatest through fire and water, others, lesser ones, through a thousand other calamities. At least the story you tell among yourselves, that once Phaethon, the son of Helios, took his father's chariot and burned the surface of the earth because he could not follow his father's course, and then perished himself, struck by lightning—this is told as a myth. But its truth lies in the deviations of the celestial bodies circling the earth and the destruction on earth caused by mighty fires that occur at long intervals.
Those living in the mountains and in high, dry regions perish more quickly than those near rivers and the sea. But the Nile, which also brings us salvation, protects us from such disasters through its overflowing. When the gods, on the other hand, flood the earth with water to cleanse it, then the livestock and shepherds on the mountains survive, but those living in your cities are swept into the sea by the streams.
In this land, however, water never floods over the fields from above, but it rises naturally from below. Therefore, and for these reasons, it is said that what is preserved here has been kept as the oldest. But the truth is that everywhere, where excessive cold or heat does not forbid it, a larger or smaller number of people live. What happened among you or here or in other places reported to us—great and beautiful deeds or other remarkable events—all this is recorded and preserved here in the temples from ancient times.
Among you and other nations, however, they were just beginning to develop writing and all the other essentials for states when, after the usual interval, a flood from heaven descended upon them like a disease, leaving only those among you who were illiterate and uneducated, so you effectively returned to a youthful state, unaware of what had happened in ancient times both here and among yourselves. Thus, what you have just told about the ancient generations among you, O Solon, differs little from children's stories, for you remember only one flood, though there have been many.
Thus, you are also unaware that the finest and most outstanding race of men in your land, from which you and your present state originate, arose when a tiny seed of it remained. This was hidden from you because the survivors lacked the language of writing for many generations. For once, O Solon, before the greatest devastation caused by the flood, the state now called Athens was the bravest in war and distinguished itself most of all for its good governance. It is said to have accomplished the finest deeds and created the best institutions of any under the sun known to us.
Solon himself said he was astonished to hear this and urged the priests to recount everything about his ancestors in detail. 'This account,' said the priest, ‘I will not withhold from you, Solon, but I will share it with you for your sake and the sake of your city, and above all for the sake of the goddess to whom your land and ours were allotted by lot, and who caused both to flourish, yours a thousand years earlier, as she nurtured your people from Hephaestus and the earth, and later ours.’
But the number of years since the founding of our state here is given in the sacred writings as eight thousand years. Now I will briefly tell you about the laws and the greatest heroic deed accomplished by your fellow citizens nine thousand years ago. We will later discuss everything in more detail by consulting the writings. Conclude about their laws from those practiced here, for many similar ones that existed among you then can now be found here.
First, the class of priests, separate from the others; then the class of craftsmen, each of whom conducts their business separately from the others; and the classes of shepherds, hunters, and farmers. The class of warriors, who are legally devoted solely to war, is also separate from the others.
Moreover, the type of armor with shield and spear is the same as what we first used among the inhabitants of Asia, as the goddess taught us, just as she first did among you in that region.
As for intellectual cultivation, you can see how much care the legislation here has given it from the beginning, concerning both the order of the cosmos—deriving everything in general for human affairs from these divine matters—and acquiring all other related knowledge, including divination and the art of healing for health.
Thus, as the goddess first provided you with this entire organization and education, she also assigned you your dwelling place and chose the site of your origin, recognizing in the favorable alternation of seasons that it would produce the most intelligent inhabitants. Favoring war and wisdom, the goddess selected the site destined to produce the first people to come to her and founded a state there first. In this state, you lived under such laws and an even more perfect constitution, excelling in every virtue above all men, as could be expected from you as descendants and students of the gods.
The Fall of Atlantis
Accordingly, many great heroic deeds of your homeland, which have been recorded here, inspire admiration, but one stands out particularly for its significance and the heroism displayed. The recorded account tells of how, long ago, a great military force overwhelmed your state, coming from the Atlantic Ocean and arrogantly advancing to subjugate all of Europe and Asia. At that time, this sea was navigable, for in front of the entrance that, as you say, is called the Pillars of Heracles [Gibraltar], there was an island larger than Asia and Libya combined. From this island, access to other islands was open to travelers of that time, and from those islands to the entire opposite mainland, which borders this true sea. For what lies within the entrance we speak of appears as a harbor with a narrow passage, but that should rightly be called a sea, and the surrounding land, a true continent.
On this island of Atlantis, there was also a great and marvelous power of kings united, who ruled over the entire island, as well as many other islands and parts of the mainland. Moreover, they also held sway inland, in Libya as far as Egypt, and in Europe as far as Tyrrhenia.
This unified power once undertook to subjugate your land, our land, and all the territory within the entrance through a military campaign. Then, O Solon, the army of your ancestral city distinguished itself above all others by its courage and valor. Surpassing all in bravery and military skill, it faced the greatest dangers, at times leading the Greeks, and at times, after the defection of the others, standing alone. Yet it prevailed, erected victory monuments against the invaders, prevented them from enslaving those not yet conquered, and generously granted salvation to us, who dwell within the Pillars of Heracles.
But in later times, massive earthquakes and floods occurred, and your army was entirely and suddenly swallowed up by the earth. Similarly, the island of Atlantis, by sinking into the sea, disappeared from view. As a result, the sea in that region has become impassable and impenetrable because of the mud, which lies at a shallow depth and was left behind by the sinking island [...]".
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