The Philosophical Tradition of Classical Architecture, Part II, The Roots of the Tradition

Ancient Egypt

The beginnings of art, architecture, and philosophy are lost in the mists of time; but to be human is to do these things. Everywhere in the world and in every era we can find objects of art, buildings, and writings of some sort, but in this course of study we limit our examination to the Western tradition as has been passed down to us through the ages. Although the roots of this tradition are lost, we do know that the Western tradition comes most directly from the Greeks, who wrote things down, and whose many writings exist to this day. And the Greeks studied in Egypt, so we should look there for roots of the tradition.

According to the fifth century B.C. Greek hisotorian Herodotus, refering to Egypt, "there is no country that possesses so many wonders, nor any that has such a number of works which defy description". And,"Of all the nations in the world, the Egyptians are the happiest, healthiest, and most religious". These are strong words of praise. To Herodotus, Egypt was a civilization that was as ancient to him as Herodotus is to us today. Egypt was the admired and civilized center of the ancient Mediterranean world, a model and a prize to the Romans, and remains to this day the cultural center of the Middle East.

When we study history, there are perhaps three ways we can go about this. A modern cynic can approach the subject in a highly critical manner, rejecting anything that cannot be rigorously proved using the scientific method, with a philosophy that "the past is dead" and can have no relevance to contemporary man. On the contrary, a modern mystic may study the past in order to seek out ancient, arcane lore, and Gnostic or occult knowledge. Both of these historical viewpoints ultimately derive from the subjective philosophical theories developed since the Renaissance. However, we will take a third, and more traditional, approach to history. Our method is to find the true, the good, and the beautiful in the past, in the Western tradition.

According to what is found on their monuments, the ancient Egyptians praised good workmanship, quality materials, sturdy construction, and flowers. It isn't much of a general theory of aesthetics, but we don't really need words much, since we know what they built and why. We do know that all of the arts were highly developed, and were vibrantly practiced by all levels of society. But the Egyptians did not have the modern concept of "fine arts": being practical, they simply assumed that all things should be made well.

We can actually develop a good theory of arts and aesthetics based on what the Egyptians praised. Good workmanship is just doing what you set out to do: if a workman needs to cut a rectangular block of stone, then if he is good, he will make sure that the stone is cut with right angles and that the surfaces are smooth and have the correct dimensions. Good workmanship is therefore conforming the object made to the intellect. Likewise, quality materials are those that do the job properly: some stones are better for carving or take a better polish than others, some woods are better for making ship hulls than others, and some materials please the eye more than others. Quality materials do the job as intended. Sturdy construction ought to be self-explanatory, but someone with a purely fine-arts outlook may neglect this as irrelevant, or only as a requirement of a contract or a building code. The practical Egyptians wanted buildings that would last, and which would need minimal maintenance, this is all the more important due to the relative lack of changes in style and fashion. The Egyptian praise of flowers is praise for the natural world (much depicted in Egyptian art), whose designs far exceed those of man.

Egypt is essentially the Nile River. This rich river draining the African interior was fairly predictable in its annual flooding and left behind thick deposits of soil excellent in its fertility. The Nile was protected on all sides: by the Mediterranean Sea to the north, the cataracts to the south, and vast deserts to the east and west. The Nile flows to the north, while the prevailing winds blow south, allowing easy navigation along the river. This relative protection, along with predictable, excellent agriculture, and ease of transportation is what perhaps led to the great stability of Egyptian civilization. Egypt was not isolated, due to extensive trade, but was able to experience an organic, internal development, leading it to be the "happiest, healthiest, and most religious" nation in the West.

The natural predictability of the Nile led to stable traditions in government and in daily life. Everyone from peasant to King knew his place in society, and what was expected from him. While this may be a great restriction on individual freedom, it was also a freedom from mob rule and princely tyranny. The kings were usually as bound to tradition as were the people, leading to an organic unity of society. Revolution, civil war, and unjust oppression were rare in Egypt compared to other western nations. Egypt was wealthy, and had enough riches to care for the sick, elderly, and even foreigners. Even the Israelites, at one time enslaved by the Egyptians, often found themselves dependent on Egypt for their survival.

Recognizably Egyptian art existed for three thousand years and has an easily identifiable iconography, even to those who are not very familiar with the style. The symbolism of their painting and writing were conventional and overlapped considerably. Instead of representing specific people and places in just a single point in time, this art instead attempted to symbolize greater truth. Typically, images of kings were not clear representations of a specific individual, but instead were symbols of kingliness in general. The same goes for images of everyday workers.

The lessons of Egypt were not lost on the latter Greeks and Romans; these nations were not blessed with the natural stability of the Nile, but instead hoped to duplicate the success of Egypt by art instead of by nature. How can a society ensure happiness and stability? Obtaining the good of both individuals and of society is the great project of the Western tradition, and this goal is embodied in the Western arts tradition.

Western geometery got its start in ancient Egypt, as a means of surveying property along the banks of the Nile after its yearly flood. This flooding would obliterate all but the most sturdy and massive of boundary-markers. The ancient Egyptians developed geometric methods to accurately determine property boundaries via triangulation. 'Geometry' is of course the Greek word meaning 'Earth measurement', and the Greeks learned it from the Egyptians. The Egyptians also elevated astronomy to a precise science, in order to predict the date of the annual flooding. They developed a good calendar using carefully-recorded astronomical measurements, and kept a vast historical archive of these measurements. Our current calendar was initially developed by Julius Caesar, based on the advice of Egyptian astronomers.

Greek building design also comes from Egypt. While the symbolism and detailed form of Egyptian buildings is quite different from the Greeks, the basic structural design and modular elements are quite similar, and we can use the same architectural terms to describe them. The Egyptians, through long experience, knew what materials, proportions, and scales worked best.

The Western tradition also has roots to the East, in Babylon and Persia, although the links are not very clear. We do owe our measurement of time and angle, both derived from astronomy, from the east. Their base-60 numbering system is still found in our definition of minutes and seconds, with 60 seconds in a minute, and 60 minutes in a degree and an hour.

The West benefited greatly from the ancient, stable, and traditional culture of Egypt. It was able to copy what the Egyptians had to learn via thousands of years of trial and error. If Egypt had published its learning, then she would be the starting point for the Western tradition instead of Greece.

The Beginnings of the Greek Liberal Arts Tradition

Viturvius tells us about the education of an architect, which is the standard Greek and Roman course in Liberal Arts—Liberal coming from the Latin libre, or free. So this education is specificially for a free man, not a slave. In is interesting that this Classical Education, based on the liberal arts, was the standard for American schools until quite recently in history—perhaps we are no longer free! This curriculum has its roots in Greece, particularly the school of Pythagoras, and also in the later educational tradition started by Socrates.

According to Aristotle:

"Contemporaneously with these philosophers and before them, the so-called Pythagoreans, who were the first to take up mathematics, not only advanced this study, but also having been brought up in it they thought its principles were the principles of all things. Since of these principles numbers are by nature the first, and in numbers they seemed to see many resemblances to the things that exist and come into being-more than in fire and earth and water (such and such a modification of numbers being justice, another being soul and reason, another being opportunity-and similarly almost all other things being numerically expressible); since, again, they saw that the modifications and the ratios of the musical scales were expressible in numbers;-since, then, all other things seemed in their whole nature to be modelled on numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number. And all the properties of numbers and scales which they could show to agree with the attributes and parts and the whole arrangement of the heavens, they collected and fitted into their scheme; and if there was a gap anywhere, they readily made additions so as to make their whole theory coherent. E.g. as the number 10 is thought to be perfect and to comprise the whole nature of numbers, they say that the bodies which move through the heavens are ten, but as the visible bodies are only nine, to meet this they invent a tenth--the 'counter-earth'. We have discussed these matters more exactly elsewhere.

- Aristotle, Metaphysics, Book 1, Part 5

The idea that mathematics are an ultimate truth goes back to the Pythagoreans; while this was neglected somewhat for the next two thousand years, it was never forgotten, and mathematics remained a core part of the classical, liberal education. During the Enlightenment, the idea of "mathematics as truth" became stronger, and this idea remains to our very day, especially in our theories of physics and computer science.

Earlier Greek philosophers were materialistic and tried to explain the cosmos in terms of the elements: earth, air, fire, and water. But Pythagoras was on to something new and more demonstrably true. His notion that nature was governed by numbers seems almost obvious now, especially to someone trained in the sciences or engineering. His studies of the musical scales and astronomy led him to believe that much of the cosmos could be described in terms of ratios of small numbers, and that certain ratios predominate: particularly those that have pleasing musical sounds. He thought that phenomena could be described by rhythm and cycles. While a stringed musical instrument can have an infinite number of possible lengths of strings, only certain ratios of lengths between strings sound harmonious; likewise, the orbits of the planets are not arbitrary, but have a simple harmonic ratio between them, and these, remarkably, are the same ratios that make harmonious music.

This is not a wild or mystical idea, nor is it just a coincidence; for modern engineers and scientists often use linear mathematics and harmonic analysis to approximate real-life systems. Systems that operate linearly will be stable and predictable; and nonlinear systems will often settle down into linear systems via frictional losses. Harmonious physical systems are indeed 'pleasing', like music. Galileo Galilei re-introduced mathematics into the study of physics, and he may have been strongly influenced by his father, who was a maker of fine musical instruments and would have been familar with these harmonious mathematical ratios.

The idea that musical harmony is analogous to harmony in nature and society is also present in Confucianism.

The Pythagorean school, founded in the late 6th century B.C., emphasized music and mathematics, as well as mysticism. Pythagoras, a Greek, set up his school in a southern Italian colony, and is said to have studied either in Egypt, or with the Magi in Babylon, or even in India. He gathered together both male and female students, who lived together in a community with common meals; he had a strict code of discipline, and he wanted his followers to pursue virtue and to always speak the truth.

Music was an essential part of his school; students would regularly sing hymns to Apollo (these were considered "uplifting"), recite poetry, and would use music to relieve stress and illness. A mystical aspect of the school involved purification rituals, the goal of which was to hear the 'music of the spheres', which was a sound supposedly made by the heavenly spheres of the planetary orbits.

The course of study in the Pythagorean school later became known as the Quadrivium (Latin for 'the place where the four roads meet') and was the second and final phase of the Liberal Arts curriculum. Upon completing the liberal arts, a student could go on to specific professional studies such as law, medicine, or architecture. A student would be ready for the Quadrivium at about the age of 16 or 17.

The subject taught in the Quadrivium or Pythagorean traditon was 'Mathematics' divided up into two categories, discrete and continuous. Discrete mathematics was absolute—arithmetic—and relative—music. Music is relative, because although it deals with fixed ratios, the starting point is arbitrary. Continuous mathematics was static—geometry—and dynamic—astronomy. While mathematics was the core subject studied in the Quadrivium, other subjects were also taught: although by this time a student was assumed to be proficient in reading and writing skills.

According to the story, Pythagoras experimented with a simple plucked-string musical instrument, and discovered that the intervals that pleased people's ears were:

• octave 1 : 2
• fifth 2 : 3
• fourth 3 : 4
• octave plus fifth 1 : 2 : 3
• double octave 1 : 2 : 4

Note that these are simple ratios of small numbers. It was soon noticed that the ratios that are pleasing to the ear are also pleasing to the eye in art and architecture.

But the Pythagoreans were not simply interested in ratios of whole numbers. As geometers, they knew about the irrationality of the diagonal of a square; an irrational number is one that is not the ratio of any two whole numbers. The Pythagorean Theorem, "the square of a hypoteneuse of a right triangle is equal to the sum of the square of its sides" is indeed the most famous result to come from that school, and often it involves irrational numbers. There are hundreds of proofs for the Pythagorean Theorem, and it appears in various forms in all branches of mathematics. Due to the universiality of the theorem, any type of art or architecture that incorporates right angles will necessarily end up with Pythagorean irrational numbers in its diagonals.

Pythagoras and his school are also famous for the investigation of the "Golden Mean", a ratio where "the whole is to the larger part as the larger part is to the smaller part". Called "the most irrational of irrational numbers", this ratio appears frequently in geometry, and there are a vast number of ways to generate this number. It appears frequently in architecture, art, and even in musical compostions, especially among the Classical composers. Tuning musical instruments is problematical, especially if you want to play the instrument in various keys, and it happens that the Golden Mean appears often in tuning. The Golden Mean has been called 'pleasing to the eye' due to its being on the cusp between symmetry and asymmetry, although this is certainly not a satisfying theory. Some think that a room with a length and width ratio of the Golden Mean will have superior acoustics. The Golden Mean does appear in numerous circumstances, but its appearance is probably due to complex mathematical factors. Some theorists state that artists should not put too much emphasis on the Golden Mean, except in cases where it is specifically needed by geometry.

An occultist may think that all of these ratios make up a kind of 'Sacred Geometry' appropriate only for mystical structures, while a skeptic may think that these ratios are merely changeable social convention, and that a modern artist should not be bound to them. I take the traditional view: there seems to be some geometric or mathematical necessity behind these ratios, pointing to the truth; we may not now understand why they are important, but we should take them very seriously.

The ancients did not know why certain ratios were desirable, but they certainly found evidence in nature and in mathematics that these ratios had a basic truth. The reason that certain musical chords sound harmonious is probably due to the specific anatomy of the ear: and those organs are also constrained by geometery and mathematics in the exact same way as the musical instrument! But we must not slavishly restrict ourselves to pure ratios: perhaps there are certain compromises in the design of the ear, which will make certain chords sound better if they are slightly out of tune. There is plenty of evidence for this in musical practice: the pure ratios are almost, but not quite, perfect. The same goes with ratios in architecture: the eye does not see things perfectly, for there are also compromises in the structure of the eye. Vitruvius tells us that we have to make specific modifications from pure ratios to make a building look right.

Fortunately, a major part of the Western Tradition, and in all the great world traditions, is the principle of successive refinement. You take an existing design, and you make slight changes in order to improve it, and then do the same to the new design until you are satisfied. Creating something completely from scratch is likely to end in failure or be an ugly monstrosity, but the pure ratios of Pythagoras' geometry are most likely a good starting point for refinement.

Copyright (C) 2006 by Mark Scott Abeln, ALL RIGHTS RESERVED
Saint Louis, Missouri
http://saint-louis.blogspot.com
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