Gothic Cathedrals: A Guide to the History, Places, Art, and Symbolism (2015)

CHAPTER 6

WONDERS OF LIGHT:

Cathedrals and Solar Observation

Agrowing amount of research in recent years—both scientific and archaeological—has been devoted to exploring various theories about how earlier megalithic stone circles and sites may have been orientated to the annual solstices and equinoxes, the sun, moon, or other planetary bodies. Some have asked how—or if—such knowledge and conscious awareness may have been understood and deliberately assimilated into certain medieval Church buildings—including the Gothic cathedrals. Researchers all over the world are delving into these and related themes from many disciplines, so the debate will undoubtedly continue for some time to come. (1)

At many early sites, from neolithic, megalithic, and other past eras, it has been observed that sunlight often enters, or strikes upon, a particular place at the solstice: for example, in the Orkneys at the Maeshowe chamber at sunset on the winter solstice. (2) At Callanish in the Outer Hebrides on the Isle of Lewis, the double stone avenues are aligned upon the ur-monument, a natural outcrop known locally as the Cnoc an Tursa. (3) Newgrange, in Ireland, has its annual sacred event involving light striking a specific point in its innermost chamber every winter solstice, as do other early sites in Europe and around the world.

Other medieval Gothic cathedrals are aligned so that the center line down the cathedral is oriented directly with the place on the horizon that the sun rises on the feast day of its patron saint. “With the light piercing those east-facing windows and going down the central aisle, cathedrals were seen as being re-enlivened or reborn or rekindled on that day when there was that particular alignment,” as architect Anthony Lawlor observes, adding that even today, “people want to extend the search for sacredness to their homes and workplaces. They ask how buildings can be perceived and designed to reflect the transformations in consciousness they are experiencing.”(4) People hope their own homes may evolve into true temples of the spirit.

The ancient knowledge “centers on a study of number, harmony, geometry, and cosmology that stretches back through the mists of time into the Egyptian, Babylonian, Indian and Chinese cultures. It is evident in the layout and relationships of the stone circles and underground chambers of ancient Europe...and the Gothic masons embedded it in their cathedral designs.” (5)

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Callanish stone circle, Isle of Lewis, Western Isles, Scotland (Karen Ralls)

Lux Lucet In Tenebris: “Light shines in darkness”

Gothic cathedrals often have certain features that align and relate to the sun and the cycles of the day or year, reflecting an interest in and knowledge of astronomy and the heavens, as well as man's relationship with the earth. To the medieval mind, cathedrals were microcosms, or little models, of the entire cosmos—geometrical buildings, in which the classical proportions of the cube, double cube, circle, and conic section were all brought together to form a spectacular aesthetic whole, stunning visitors even today.

We might be surprised to learn that the first mechanical clocks in western Europe were housed in medieval Gothic cathedrals and abbeys. The clergy and others would have needed to have sufficient astronomical knowledge to calculate the dates of holidays such as Easter. The Church's affiliated schools (i.e., the School of Chartres, York Minster school, et al) taught the use of the astrolabe, the principles of Ptolemy's epicycles, and elements of Pythagorean and Platonic philosophy. And the gardens around cathedrals often featured a sundial, maze, or other geometric designs. So the widespread idea that “the medieval Church attempted to suppress astronomical knowledge is proved to be ridiculous by the sheer weight of evidence to the contrary.” (6) Clearly, some of the clergy knew more about such matters than others. Monastic environments could vary greatly; if the overall situation was not supportive, then openly speaking of or studying such matters may not have been prudent.

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Newgrange passage tomb. (Dr. Gordon Strachan)

Medieval Europe created the experimental science of optics. Philosophers held stimulating discussions in cosmology. In addition to theology, medieval universities began the systematic teaching of the ancient philosophy of Aristotle, Pythagoras, and Plato, and taught the science of astronomy to undergraduates. It is interesting for us today to contemplate that Chaucer's Treatise on the Astrolabe produced what we would now call a classic student textbook in that science—and all with the full knowledge of the Church. (7)

It is more than plausible that the medieval stonemasons who built and designed the cathedrals would consider the sun, moon, and other astronomical factors when designing a Gothic building. Chartres, for instance, has a rather unusual annual event that some visitors claim to have witnessed: a direct beam of light is said to emanate from its large Rose Window (high above) that precisely hits a specific nail in a flagstone on the floor below—but this event is said to occur only on the summer solstice each year. Some maintain that medieval stonemasons at such sites would likely have made an effort to incorporate such natural phenomena into their designs, deliberately enhancing the incoming light at certain times.

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Medieval mechanical clock at Rouen in northern France, erected in 1389.

Many books have been written on Chartres, some of which include direct mention of a key solar and/or geometric aspect to the cathedral that was included into the medieval design of the building. It has also been observed that medieval French churches have their apse turned towards the southeast, their front towards the northwest, while the transepts—forming the “arms of the cross” in the overall layout of the design of the building—are directed to the northeast and the southwest. The idea was that the visitor or pilgrim would be symbolically walking from darkness to experience the light: “That is the invariable orientation, intended in such a fashion that the faithful and profane, entering the church by the west, walk straight to the sanctuary facing the direction in which the sun rises, i.e., the Orient, Palestine, the cradle of Christianity. They leave the shadows and walk towards the light.” (8) The pilgrim's journey to perfection was reflected in the overall design of the entire building itself. The architects of these Gothic cathedrals consciously situated or oriented their buildings to embrace the light. (9)

At Chartres, a major consequence of this arrangement is that one of the three rose windows which adorn the transepts and the main porch is never lighted by the sun at all. One researcher comments:

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Wells cathedral, clock.

This is the north rose, which glows on the facade of the left transept. The second one blazes in the midday sun; this is the southern rose, open at the end of the right transept. The last window is lit by the colored rays of the setting sun. This is the great rose, the porch window, which surpasses its side sisters in size and brilliance. Thus on the facade of a Gothic cathedral, the colors of the Work unfold in a circular progression, going from the shadows—represented by the absence of light and the color black—to the perfection of ruddy light, passing through the color white, considered as being the mean between black and red. (10)

When you visit Chartres and other spiritual sites around the world, you will often notice throughout the course of a day, there is a daily circular progression of the sunlight that emphasizes different parts of the cathedral or ancient site. At various times of the day, you can much more easily see the stunning blue colors of the stained glass windows; the sun's angle tends to emphasize them in the mornings. By late afternoon, the bright reds often come out in “full color.” The angle of the light hits on different places in and around the building, highlighting different sculptures and windows through the course of a day. We mentioned that Abbot Suger of St-Denis—the artistic patron and supervisor of the first Gothic building—built his entire theory around the concept of continuous light, “Lux continua.”

Seeing these changes in the light as you walk around the building you discover another type of journey in the experience of the Gothic cathedral—the natural journey of the Light itself around the site or building. And you will be aware as you contemplate this beauty that this is a principle which our early ancestors already knew many ages ago.

“Light out of darkness,” such places seem to be proclaiming. Ironically, this is a sentiment rather similar to what one British agnostic visitor to Chartres for the first time told me upon returning home. I asked him what he thought of his first visit to a Gothic cathedral. “Well, there are no words, really; but I cannot believe how dark it all seemed when I first walked into it, a bit spooky, really. As I walked around, however, the effect of the sunlight coming in was quite extraordinary.... reflecting the beauty and awe of the place.” He then commented that after three days in the town of Chartres—extensively exploring the cathedral, town, and surrounding landscape—upon coming back home, he felt he had left there changed in some way. He came back with new insights, and felt transformed in an inexplicable way. But it was his comment about the initial impression of how “dark” the building seemed that I also found interesting, and especially, his comment about how extraordinary the effects of the incoming light were for him. Many others have made similar comments about Chartres in particular, and I myself recall my own impression of how initially “dark” Chartres seemed when I first walked in years ago.

There are other medieval cathedrals and chapels where similar types of solar phenomena exist, suggesting what some scholars believe to have been a hidden “science of the Church” of some type. As to many of its details, we may never know. Those pursuing such knowledge had to operate clandestinely to avoid the increasing powers of the Inquisition. Possibly, as some believe, in the process they may have helped preserve a variation of Christian hermeticism—the ancient knowledge of solar and lunar patterns; as well as Pythagorean and Platonic principles of geometry, number, music, and light; and, in their Christian view, the Christ principle envisioned as the “solar Logos.” After all, the ancient religious world “was a fluid as well as an open one. Ironically, one of the implications of this openness is that in considering the survival of Pythagoreanism we must not just restrict ourselves to the so-called ‘Neopythagorean’ movement, but must also take Hermeticism into account as well.” (11) This is also true for the works of Aristotle and earlier key thinkers like Heraclitus. Discussion and debate on these and related points continues.

Within the Church itself, discussion about this type of symbolism has been an ideological conflict that went back to its earliest days, especially the often fervent arguments at various Synods involving what was called “Christology” and the doctrine of the Trinity, i.e., what to do about the concept of the “light of Christ.” Chancellor Thierry of Chartres wrote in one of his major works that he associated “the regular triangle with the Holy Trinity.” (12) What if, as some progressive theologians would add, the “light of Christ,” and “the light of the world,” and so on, were also inclusive of—if not based upon—some earlier ideas gleaned from ancient philosophy, including those which involved direct knowledge of geometry, number, philosophy and harmony?

Pythagorean philosophy and medieval cathedral design

What were the underlying strains of the ancient Pythagorean and Platonic philosophy that eventually became part of Christian teachings in the late medieval period? What may have been possible major streams of philosophical thought that involved a concept of an ancient system of correspondences, which some believe integrated aspects of the earlier Pythagorean philosophy with the newly re-worked Christian philosophy, resulting in its new “hybridized” form? And, as always, what, then, was the “price” paid for such decisions for posterity?

In the eyes of theorists from differing perspectives, this unique system would appear to be a philosophy of the ancient world that especially valued mathematics, number and geometry, as well as key elements of music and harmonic theory, the seven liberal arts, and astronomy/astrology. Unfortunately, until fairly recently, for various reasons, the connection between the Pythagorean and other philosophical traditions and Christian studies had been frequently ignored by modern Christian theologians and scholars.

Currently, professional scholars, theologians, historians, and philosphers are investigating the Christian side of Pythagoreanism, geometry and number. These include, for example, the work of Dr. David Fideler. His book entitled Jesus Christ: Sun of God: Ancient Cosmology and Early Christian Symbolism; makes clear that the Pythagorean tradition has a long and distinguished history in the West in various forms—from the first century CE lasting into the late Renaissance. In his view, it has roots going back to Alexandria, and was only “marginalized” in the West during the seventeenth and eighteenth centuries, when science, rationalism, and an encroaching ideology of the materialistic industrial age became more predominant. The overall situation regarding what one modern-day professor described as the “historical enigma” of the rise of modern science is a multi-threaded tapestry with many strands, as “modern science emerges from an interaction of very complex ideological forces ...” (13)

We mentioned earlier that medieval churchmen studied Greek language and philosophy, geometry, as well as theology—subjects required in the twelfth century curriculum. The debate in twelfth century Paris as to “what to do with” the works or theory of Greek philosopher A or B, came to a head many times—with fierce arguments, some nearly coming to blows over this or that theological position, or, whether or not number, geometry, the works of Aristotle, and Pythagorean theory should still be studied and to what extent. (14) But whose works were ignored?

One aspect of this conflict is rather aptly summed up by the twelfth century scholar, optics expert, and theologian Roger Bacon, who wrote in his Opus maius that “philosophy is nothing except the unfolding of divine wisdom by teaching and writing.” (15) The word “philosophy” essentially means the love of wisdom, a topic as much debated in the High Middle Ages as it often was in the ancient world. Unfortunately, Bacon and others attempting more progressive research and teachings were at times vociferously attacked by the Church later in the mid-thirteenth century.

The end result of such conflicts was that the medieval Church largely “picked and chose” what it wanted to assimilate from antiquity. They either re-worked old ideas in new ways to entirely suit themselves, or simply ignored and threw out much else, including the great wisdom from the earlier tradition of Greek philosophers such as Heraclitus, for example. In this manner of “picking and choosing,” much material about number and geometry was lost—ironically, the very subjects that Bernard of Clairvaux, Abbot Suger of St-Denis, and other prominent medieval churchmen involved in the rise and exponential growth of Gothic design were known to highly revere and sought to explore. As we recall, initially the new Gothic style was certainly not welcomed by everyone at the time.

Western civilization has often paid a high price for its overemphasis on the mechanism of logical thought. Earlier philosophies from the ancient world, including, among them, Pythagoreanism, attempted to incorporate geometry, number, and mysticism into a unified philosophy and way of seeing the world. Losing such an integrated world view, as Dr. Richard Smoley has pointed out, has had consequences for Western culture:

Since that time, mainstream Western philosophy and theology have hardly known what to do with mystical insight—or indeed with any state of consciousness apart from the totally ordinary. Usually they have found it easier to act as if such things did not exist. And this has brought terrible suffering upon us who are the heirs of European civilization. Our mastery of the physical world has not cured us of the wish for another one; our deft handling of materiality has not taken away our longing for the spirit. (16)

Also lost was the earlier integral view of spirit within matter and the earth; the immanence vs. transcendence debate continued well into medieval times. With such an eventual overemphasis on logical thought, at the near-total expense of the intuitive, the quest for ultimate meaning and understanding of the universe and humankind's place in it continues unabated. Our modern-day world is greatly out of balance, as many from all sides of the spectrum have noted. An additional part of the problem is that modern Western culture has largely cast aside awareness of an inherent spirituality *in* Nature, and much else.

Who was Pythagoras and what did he teach?

Who, then, was Pythagoras and what does this philosophical tradition represent? How, or why, are many of his geometric principles enshrined in so many medieval designs and carvings? While certainly not everyone in medieval times revered Pythagorean thought per se, for the purposes of our study of Gothic cathedrals and the supreme focus of their designers on geometry, let us try to understand the medieval fascination with the father of Western esotericism and his teachings.

We know that the importance Pythagoras placed on number symbolism was matched by a fervent dedication to geometry in the Gothic cathedrals. To medieval man as well, geometry was considered to be a divine activity. Number and shape were believed to have a sacred dimension. God was ultimately envisaged as a “geometer”—the Great Architect—and churches had been built on various geometric principles since early Christian times. Geometry was the basis for all Gothic cathedral design. The ground plan was nearly always cruciform; the baptismal font and the baptistry often octagonal; and the circle was everywhere. A common motif and picture seen in medieval times was that of God holding a pair of compasses. The eminent art historian Ernst Gombrich believes that an Old Testament verse may be responsible for this portrayal. In Proverbs 8:27, the female figure of Wisdom puts forth her voice: “When he established the heavens, I was there when he set a compass upon the face of the deep....”

Again, let us recall that the word “philosophy” meant a love of Wisdom (Sophia).

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Image of Pythagoras on a coin made under the emperor Decius, from Baumeister, Denkmäler des klassischen Altertums, 1888, Band III, Seite 1429. (WMC)

Pythagoras (570–500 BCE) was a highly regarded Greek philosopher and teacher. He has been called the first pure mathematician, instructing not only about geometry and spiritual matters, but topics relating to music and harmony. (17) He is known to every school child for his Pythagorean theorem. He was born at Samos, Ionia, where he lived until his late thirties. Samos is a Greek island in the eastern Aegean sea, a powerful city-state in ancient times; it has been named a UNESCO World Heritage Site today. The island has been associated with a stream of other brilliant philosophers, astronomers, and writers in the ancient world, including Aesop.

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Pythagoras depicted conducting harmonics experiments with stretched vibrating strings on a monochord. From Franchino Gafori, Theorica Musice, Milan, 1492, (WMC)

Pythagoras traveled widely and then, in about 532 BCE, he migrated to Crotona, the Achaean city in Magna Graecia in southern Italy, where he taught his philosophy to his circle of students. In around 500 BCE, there appears to have been a major uprising at Metapontum against the power of the Pythagoreans; Pythagoras fled and is thought to have then been killed or died shortly afterwards. His death is still shrouded in mystery, as little is known about his life due in part to the secrecy of his philosophical school.

There is little that can be said without qualification about Pythagoras' life and philosophy. He taught orally and never wrote his teachings down. But his contemporaries far and wide revered him; he was a renowned teacher during his life; and was immortalized after his death. But as Porphyry said in his Life, “What Pythagoras said to his associates, there is no-one who can tell for certain, since they observed a quite unusual silence.” In fact, on acceptance to his school, the novice underwent a five-year period of silence. It is well known, however, that Pythagoras taught music, meditation, and vegetarianism to his spiritual community.

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A progression of numbers that can be fitted into triangles

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The “square” numbers, 4, 9, and 16, can be laid out in a similar way

Many ancient philosophers based their ideas upon the concepts of Pythagoras. The Pythagorean school of thought is still studied today. While the Greek geometers produced works which remain astounding for their brilliance and clarity, “it is known that the study of geometry and mathematics was vigorously pursued in remote antiquity by other civilizations, such as the Babylonians and the Egyptians... The Pythagorean theorem was known to both the Babylonians and megalithic builders of prehistoric England.” (18)

A central teaching of Pythagoras and his spiritual brotherhood was that all things are numbers. Ultimately, in this view, everything comes down to number. Geometry was seen as “number in space.” Aristotle says: “the Pythagoreans, as they are called, devoted themselves to mathematics, they were the first to advance this study, and having been brought up in it they thought its principles were the principles of all things.” (19) One of the more popular examples of Pythagoreanism would be the illustrations here how numbers are closely linked to various geometrical shapes.

Such concepts were taught in the early medieval universities, too—in or near where some of the major Gothic cathedrals were built.

Pythagoras and his followers developed the geometrical concept of numbers. When we call numbers “figures” today, we are thinking like Pythagoreans. For them, the number one was a point, two points gave extension to a line, and three points gave the triangle, a two-dimensional plane. This led Plato to believe that the triangle must be the basis of all objects perceptible to the senses, and that surfaces are composes of triangles (Timaeus 55–6). The Timaeus and other works of Plato were immensely influential among later medieval Christian theologians. The number four was the first solid, the pyramid or tetrahedron, the extension of the Spirit into three dimensions.

The Pythagorean and Platonic emphasis on mathematics and numbers introduced an important concept for both Hebrew and Christian philosophy and theology. From Philo (a 1st century BCE. Jewish philosopher) through the early Church theologians, and later to scientists like Johannes Kepler, God is conceived of as creating by geometrical principles.

Pythagoras was also credited with having been the first to discover the connection between simple whole numbers, ratios, and musical consonances, especially the octave, the fifth, and the fourth, i.e., 2:1, 3:2, and 4:3. There are many legends about how Pythagoras made these discoveries, but it may well have been on his experimental musical instrument, the Monochord, also called the Kanon. “Pythagoras initiated the conception of incalculable importance for later science, that qualitative differences in sense perception may be dependent on mathematics.” (20)

The tradition of an allegorical number symbolism has unfortunately often been sidelined by religious scholars right up to the twentieth century and from nearly all sides of the spectrum. This is ironic because, as we have seen, geometry and number symbolism were taught in relation to spirituality in many ancient academies and in the medieval university curriculum itself as studied by twelfth century Church philosophers in Paris and included in the medieval curriculum of the School of Chartres.

In more recent years, however, a greater number of scholars in the scientific, religious, esoteric, and mathematical fields are examining such links again, retrieving and translating earlier sources on number symbolism. For instance, British researcher Keith Critch-low, commenting on his extensive research at Chartres, shares his own thoughts about the geometry of the labyrinth at the center of the cathedral. He addresses the complex issue of sacred geometry in relation to time. Critchlow states that one explanation for the negative associations of the number “thirteen in Christian superstition is due to the suppression of the thirteen-month lunar calendar when the Christian era brought in the twelve-month solar calendar.” There are thirteen “darks” of the Moon, or new Moons, each year, in contrast to the twelve-month solar calendar. (21) Thus, the number thirteen had imporant, longstanding female and lunar connotations. Critchlow further points out that a plan of the six-petalled Center of the Chartres labyrinth—as it has survived the ravages of time—shows a thirteen-pointed star in the geometry on which it is proportioned. (22)

In truth, the Pythagorean system is so ancient that it is not known ultimately from where it came. Even if those ideas existed before the time of Pythagoras, as some scholars maintain, it is Pythagoras who popularized and developed this particular system. In Pythagorean teaching, number was the overall synthesizer of cosmological knowledge, an underlying truth. Rightly or wrongly, this philosophy remained of central importance for a period in the West spanning over two thousand years: from the time of Pythagoras through to the High Middle Ages and the late Renaissance.

Numbers for the Pythagorean-Platonic tradition were not merely quantitative, they were also qualitative. Each number was associated with certain universal principles. Aetius said that the Pythagoreans proclaimed that the numbers were archai, meaning that they were first principles which had been there from the beginning of time (arche), and as such, were divine.

Pythagoras and his disciples concentrated upon number as the principle of the cosmos; they believed that numbers followed their own intrinsic, logical law. Through this perspective came the belief that the Gods themselves were numbers, and through this came the realization that all things soever were ultimately numbers. “Thus, the number one was symbolic of the One, the Monad, God, the potentiality of all number, a point, or a circle within which the attributes of all the other numbers could be geometrically ascribed.” Two was the Dyad, associated with division and strife, but also with the potentiality of harmony. Three was harmony, what the Pythagoreans called the wondrous “third term.” Four, the first square number, was associated with justice because justice involved reciprocal personal relationships and that reciprocity was symbolized by square number. Five was viewed as symbolizing marriage, as it was the product of two, the first feminine number, and three, the first masculine number. (23) And so on.

In the understanding of the early Christians, that which in ancient times had been known as the Limited, the Unlimited, and the Potentiality of the Logos, came to represent “Christ as the Logos”—the symbolic Mediator between heaven and earth, light and darkness. Christ, then, was to the early and medieval Christian mind often viewed as the ultimate “solar Logos,” the highest Truth of all, i.e. a “sun” of God.

Medieval thinkers understood the mathematical aspects of number to be of divine origin. The reaction against the wisdom of earlier Pagan philosophy may well have been key among the major reasons some books were deliberately excluded from the Biblical canon. Umberto Eco has suggested, for example, that the focus on the triad—measure, number and weight—in the Apocryphal Book of Wisdom of Solomon may have been offensive to established Church canon centuries ago. The book states “But thou hast arranged all things by measure and number and weight.”

On the other hand, numbers and numerical symbolism were used to interpret the meanings of biblical phrases from time immemorial. For example, as one modern theologian commented: “on every page, from Genesis to Revelation, numbers are obviously being used for symbolic purposes.” (24) Ironically, it was largely through Augustine that much of Pythagorean and Platonic teaching ended up being transmitted to the Christian Church throughout Europe. Augustine, of course, is considered to be one of the most important Western theologians. He wrote:

We must not despise the science of numbers, which, in many passages of Holy Scripture, is found to be of eminent service to the careful interpreter. Neither has it been without reason numbered among God's praises “thou Hast ordered all things in number and measure and weight.” (25)

The Neo-Platonic and Neo-Pythagorean revival in the third and fourth centuries—associated with Plotinus, Proclus, Macrobius, Porphyry, Iamblichus, and Diogenese Laertius—had already had a great impact on early Christianity by the time of Augustine. Although it was, to a considerable extent, the expression of a revival of ancient world Pagan philosophy and beliefs—as in the case of Plotinus, Iamblichus and Porphyry—to others, it resulted in the reinterpretation of Platonic and Pythagorean thought in ways more compatible with Christianity. This was so much the case with regard to the whole debate about the doctrine of the Trinity, which was especially fierce in the fourth century. In fact, it has been argued by some scholars that the influence of the ancient Pythagorean number symbolism may have been a decisive factor in ensuring that the Christian God of the Western Church would finally end up being defined as “Three in One.”

The number two, the Dyad, was associated with strife and division and the breaking away from Unity, while the number three—the Triad—was associated with all things good. As Proclus said, “Every divine order has a unity of threefold origin from its highest, its mean and its last term.” (26) So, the philosophic thought behind what eventually became the doctrine of the Trinity was hotly debated, but was finally ratified at the Council of Constantinople in the year 381 BCE. Later in history, as we now know, it would cause great rifts between Eastern and Western Church thinkers, resulting in the Great Schism of the eleventh century in 1054.

Leading philosophers throughout the Middle Ages, such as Boethius, carried on this Pythagorean-Platonic philosophical tradition. Far from dying out, it actually gathered strength through the centuries; by the time of the early Renaissance, philosophers, theologians, and others could consistently draw from the wellspring of Pythagorean philosophy and other ancient systems.

Ancient and Medieval Mechanical Instruments

A major archeological find has had far-reaching effects in our understanding of the level of sophistication of the ancient world. The Antikythera Mechanism has been dubbed the “most complex scientific object preserved from antiquity” in the Greek National Archaeological Museum in Athens. It is 2,000 year old and was found by divers working off the isle of Antikythera in 1901. It is a corroded bronze object which consists of a box with sophisticated dials on the outside, and a very complex assembly of gear wheels mounted within. Scientific researchers have marveled at its fine workmanship, commenting that it must have resembled a well-made 18th century clock, so intricate is its overall design.

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LEFT: The design of the Antikythera Mechanism appears to follow the tradition of Archimedes' planetarium. The mechanism consists of a complex system of 30 wheels and plates with inscriptions relating to signs of the zodiac, months, eclipses and panHellenic games. It dates to around 89 BCE. (Marsyas, WMC)

RIGHT: Schematic of the Antikythera Mechanism. (Lead holder, WMC))

A new paper from the Antikythera Mechanism Research Project (AMRP) was published in the prestigious science journal Nature on July 31, 2008. It reveals surprising findings concerning the dials on the back of the Antikythera Mechanism. For example, one dial measured the four-year Olympiad Cycle of athletic games in ancient Greece. The Antikythera Mechanism reveals a much higher level of geometric principles, number, and engineering capacity among the ancients then has previously been known to scholars. More recently, reports have emerged that a chant to what appears to be a reference to a mother goddess has been deciphered, but further research is to be done on this particular inscription and others on this controversial artifact.

While such an understanding has been sidelined or ignored in the past, scientists, philosophers, and astronomers are now delving into such matters more thoroughly than ever before. (27) Historians of philosophical studies, mathematics, and science, and curators at science museums have probed further into this area. They have incorporated discussions of the contributions of earlier measurement systems known in the ancient world, as well as the impact on medieval Europe of Jewish, Muslim, and other distant lands regarding specific scientific knowledge, “gadgets,” devices, and so on:

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A planispheric astrolabe from the workshop of Jean Fusoris in Paris circa 1400, on display at the Putnam Gallery in the Harvard Science Center. (Sage Ross, WMC)

Mathematics thus became an international instrument of calculation long before the advent of Islam. It took the Greeks of the last few centuries before the Christian era to turn this instrument into a profoundly disciplined and resourceful language—a set of laws and terms that could be used to measure and reveal, with a subtlety never before possible ... From the time of Pythagoras, numbers and their relationships mesmerized the Greeks and, along with geometric shapes, allowed them to perceive a whole universe and, in a sense, to comprehend its structure and function. (28)

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Astrolabe. A modern-day computer generated planispheric astrolabe, to further illustrate for the modern reader what the basic design of a medieval astrolable would look like. (WMC)

While we know that the Hermetic and Neo-Platonic scholars fled Europe to the Mideast in the 6th century, and that their writings and archives were reintroduced to Europe in the High Middle Ages, less has been writtenon the migration of European natural philosophy back to the Islamic world in the early modern period. More research is being done by historians and curators, and we know there was more travel and exchange going “both ways” between European and Islamic cultures than has previously been thought to be the case. Early scientific ideas and knowledge of mechanical instruments were part of this interaction. (29)

One medieval scientific instrument of interest today is the astrolabe. Perfected by scientists and master craftsmen working in the East, “this instrument, probably invented by Greeks in the second century BCE, displays a mathematical model of the heavens. It can be manipulated to provide year-round celestial and timekeeping data, terrestrial measurements, and astrological information.” (30) Most astrolabes are quite compact, ranging between five and ten inches. They have four parts with key pointers representing the prominent stars, and a circle representing the ecliptic, the sun's apparent path against the stars. Other markings show the horizon for a specific latitude, the meridian, altitude, and azimuth circles. Most astrolabes have several plates for different latitudes—something very handy for a medieval traveler. Many fine examples of astrolabes exist in the world's museums today.

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Chartres cathedral carving, dubbed the “angel of Chartres,” is holding a sundial; the original is now placed in its crypt, as shown by this portrayal. (Christian Kyriacou)

Ancient Symbols: the Vesica Piscis

Certain geometric shapes were used more frequently than others in Gothic cathedrals. One of these is a vertical, almond-shaped geometric figure called the vesica piscis. Technically speaking, in geometry, the Vesica piscis is a geometric shape arrived at by the intersection of two circles with the same radius; the center of each one lies on the circumference of the other. It is the property of the overlapping geometric almond shape in the middle (vesica piscis) that the ratio between its short axis AB and its long axis CD, is 1 to the square root of 3.

The vesica piscis was known to the Pythagoreans as the “Potential Logos,” because it symbolized the Dyad (twoness), becoming the Triad (threeness), harmony, or the Logos. Later, it became incorporated into the vertical, almond-like halos of light portrayed around saints in certain paintings. Known as the mandorla, this image has been called the “Christianized vesica piscis” by some art historians. It is often seen around images of saints, heraldic designs, and other visual representations today. The vesica piscis design is incorporated throughout the Gothic cathedrals as well.

The Vesica Piscis as a universal “form generator”

Like the Fibonacci number series that mathematicians study today, in geometry, the vesica piscis has universal connotations in the world of geometric forms. It also has a most unique characteristic to geometers—it is considered a universal geometrical “form generator,” as a number of other geometric forms can be created by initially starting out with the vesica piscis, and then, step by step, gradually creating another shape geometrically from it. Here is one poignant example of this principle, where a pentagon can be geometrically created by initially starting out with the vesica piscis and ending up with a pentagon, as outlined by Keith Crichlow in Time Stands Still:

Geometrically, all of the regular polygons can be constructed in a similar way from the succession of this geometric form, the vesica piscis. Symbolically, the reference to the Vesica piscis as a highly productive characteristic may not be all that surprising. In other words, geometrically speaking, this shape is the “mother lode” of all regular geometric polygons—it is the root of them all, according to geometers.

As we recall, the construction of a cathedral involved extensive knowledge of many types of geometric forms and the necessary practical skills in executing building plans. The vesica piscis, equilateral triangles, and the major polygons were key. The geometric form known as the rhombus was also important:

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A method illustrating how to construct a Pentagram using the Vesica Piscis. (Keith Crichlow in Time Stands Still)

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Rhombus figure. (James Wasserman)

“If we look again at the plan of a Gothic cathedral, we can see that the two equilateral triangles lying base to base and thus forming a rhombus, have the same ratio of axes as the vesica which encloses them, that is, 1 to the square root of 3. For the purposes of architecture the rhombus, being angular, is an easier figure to work with than the vesica and so came to represent it for practical purposes. It was this rhombic figure which formed the basis of the building principle ad triangulum, which, together with the principle ad quadratum, lay at the heart of medieval ecclesiastical architecture.” (31)

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A Mandorla-shaped image depicting Christ within the geometric Vesica Piscis surrounded by the four animal symbols representing the four evangelists in Christian art iconography. (Evangelistar von Speyer, 1220, Codex Bruchsalin, Badischel, WMC)

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Vitruvian Man by Leonardo DaVinci.

Knowledge of the relationship between Pagan sacred geometry and Christian philosophy was often suppressed because of political and ecclesiastical pressure. Ironically, there is a great deal of ancient philosophy underlying the overall concept of what the Christians eventually called “Christ as the solar Light” of which many people in the West today seem to remain largely unaware. It will be interesting to see what scholars and researchers from interdisciplinary and non-religious perspectives learn or conclude about these matters in the future.

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Sacred Geometry. Medieval depiction of Christ as Pantocrator creating with a compass. (Bodleian Library)

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Grail envisaged as the Elements, number(s), Platonic philosophy.

Underground “scientists of the church”?

Of course, the often bitterly polarized arguments of the Church “vs.” Science may, in fact, not be quite as simple or black-and-white as it may seem—vitriolic as they often were. In fact, the sacred and the secular (which included scientists in both camps) historically intermeshed far more than we realize. It is quite obvious that an enormous amount of science and mathematics went into the construction of these huge stone cathedrals. On the other hand, the spiritual and artistic goal of the Gothic cathedrals is as an expression of cosmic harmony, geometric proportion, and, above all, Light. As some theorists maintain, bringing in elements of ancient, neglected philosophical knowledge undoubtedly enhanced the overall acceptance of the Gothic cathedral at the time by re-integrating geometric elements into the design.

Medieval philosophy shows the decisive influence of the two main systems of ancient thought—Neo-Platonism (especially in what has been called its Augustinian and Pseudo-Dionysian form)—and Aristotelianism. This debate caused some rather enduring rifts through the centuries, East and West. Proponents of each nearly came to blows in the twelfth century, in particular, as differing factions of theologians and philosophers insisted on their position.

Neo-Platonism

Many wonder today what Neo-Platonism was all about. Basically, it was Plato's philosophy as it got passed down to—and further re-worked and transformed by the Pagan philosophical writings of Iamblichus, Proclus, and Plotinus—and Christian scholars like Augustine and Boethius.

Neo-Platonism perceives love itself as the cosmic bond of order that holds everything—from the elements to human society—all together in the mind of God. However, when it was assimilated in and re-worked by Christianity in the medieval period, it tended to further exacerbate an existing dualism already present in early Church asceticism. Theologians pitted body against soul, flesh against spirit and mind—resulting in a rigid split from which Western culture has never healed.

Nature, the feminine, the body, and other aspects of ancient world belief and philosophy had long been sidelined, feared, discounted, or eliminated in some streams of Christian thought and theology as they had in Jewish thought before them. However, over time, there were a number of strongly differing opinions about many of these matters, both within and without the Church itself, East and West. Lives were often at stake. Like any large organization spread out over a large geographical area, it may be useful to recall that there really never was any “one” unified religious belief system about any of this—then or now. There was a lot of debate. Not everyone agreed. Some of our more contentious modern-day issues are the same, or similar, to those debated centuries ago.

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Chalice Well cover at Glastonbury. Its design also incorporates Vesica Piscis geometry, horizontally, in the center. (Simon Brighton)

Human behavior, too, is a factor to consider. Add superstition and intolerance to the “skullduggery” of power politics, and Church philosophy and theology became quite a brew. Overall, while the conflict between Church and State (religion and politics) has often been viewed as an “us” vs. “them” situation, it is not ultimately so black and white. It is, rather, a highly complex web of varying influences affecting each other both ways. In the High Middle Ages, theological and religious spheres joined town, civic, and state policies to influence the identity of the Church in any given locale.

The twelfth century was a most exciting time for the philosophers and theologians of Paris. Many new translations and philosophical streams of thought were then being discovered, re-read, studied and/or re-worked. Nothing like that type of stimulation had occurred for some time. What came to be dubbed Augustinian Neo-Platonism began to slowly become available to readers of Latin, creating a revolution in the newly developing universities of Paris and Oxford. The School of Chartres was a highly influential group of humanists, men of letters, who were associated with Chartres and the flowering of the twelfth century. Among them were Bernard of Chartres, Thierry of Chartres and William of Conches. This influential group of humanist philosophers shared not only a return to the ancient philosophical texts of Plato's Timaeus, and Ovid's Art of Love, but were interested in further exploring topics such as history, politics, the art of governance, science, and nature—all within a Christianized framework. It was a new and exciting development, one that changed Western thought. Umberto Eco describes its essence: “The School of Chartres remained faithful to the Platonic heritage of the Timaeus, and developed a kind of ‘Timaeic’ cosmology. For the School of Chartres, the word of God was order, opposite of the primeval chaos.” (32)

Neo-Platonism shaped the medieval mind with quite a vigor and persistence from the time of the Church Fathers, right up until the Renaissance period and the philosophy of Marsilio Ficino (1433–1499). Ficino founded the Platonic Academy in Florence, translated from Greek into Latin Plato's Dialogues and Letters, the Corpus Hermeticum, the Enneads of Plotinus, among many other stupendous achievements. Before Ficino, medieval philosophers had practically no real firsthand acquaintance with the sources of either Platonism or Neo-Platonism. Although Aristotelianism triumphed in the scholastic age of the thirteenth and fourteenth centuries, in order for a truly new era in philosophy to flourish, both systems had to mingle in the minds of many at the time.

But medieval philosophy was not just an echo of ancient thought. Rather, it was a voice attempting to speak its own mind—despite the backlash, criticisms, and gridlock of others within the Church. The stakes were high. Lives could be at risk. Various factions battled for dominance. Opinions were both vociferously attacked and defended

By the twelfth century in particular, Arabic science and mathematics had found their way to Oxford and Padua (Italy), and from the early twelfth century onward, there existed in Europe a continuous tradition of scientific endeavor. One of the key examples of this burgeoning new trend of courageous experimentation is Roger Bacon, whose remarkable story is indicative of the age.

A case in point: Roger Bacon, “Doctor Mirabilis”

Roger Bacon, dubbed “Doctor Mirabilis” in his day, was born in 1220 at Ilchester, Somerset (or, some claim, Bisley, Gloucester) in England and died 1292. An English philosopher and educational reformer, he was a major proponent of experimental science, Bacon was a renowned lecturer on Aristotle at Oxford, and had extensive knowledge of a number of fields: including mathematics, optics, astronomy, alchemy, and languages. He read many Latin, Greek, and Arabic works and was the first European to describe in extensive detail the process of making gunpowder, the steamship, the motor car, the airplane, the submarine, and the cantilever bridge—all this in the 13th century. He described eyeglasses, observed lenses and mirrors, studied reflection, refraction, and spherical aberration, and used a camera obscura to observe eclipses of the sun.

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Roger Bacon, medieval philosopher, scientist, alchemist, astronomer.

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Copernicus, Heliocentric diagram of the Universe 1543.

Not one to be merely hunched over a desk in a dusty library or archives, he lectured in Paris, greatly impressing his colleagues and students alike. A contemporary of leading Paris churchmen and philosophers like Albertus Magnus and Thomas Aquinas, Bacon's interests included the serious study of alchemy and a broader knowledge of Arabic and other Eastern sources. Albertus Magnus's astrological work, The Mirror of Astronomy, contains a solemn warning that its teaching should be kept secret. Bacon quoted this text, and others against the breaking of secrets, and “then suggested a series of ways to preserve the more hidden character of nature's own knowledge.” (33)

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Kepler's model to explain the relative distances of the planets from the Sun in the Copernican System, ca. 1610.

Bacon produced his three major works, the Opus Major, Opus Minor, and Opus Tertium, which outlined a scheme for further research in languages, optics, mathematics, and so on; his dream was to introduce the natural sciences to the universities of Europe. We know he had became a Franciscan in Oxford in 1251. He was a Christian who genuinely believed that his scientific work would contribute to greater knowledge of the world, and so of God through understanding His divine creation. Perhaps not unsurprisingly, he eventually ran into serious trouble with the Church.

Clearly a lodestar of his time, in 1277 and 1279, Bacon was condemned to prison by his fellow Franciscans because of alleged “novelties” and “irregularities” in his teaching. The condemnation was probably issued because of his strong attacks on some of the theologians of his day, or because of his serious interests in alchemy, astronomy, and astrology. Exactly how long he was imprisoned is unknown, but some believe it may have been for a period of fourteen years. Sadly, little is known about his life from the time of his imprisonment. His last work was completed in 1292, the year of his death. A commemorative plaque exists in Oxford in his memory today, and there is a statue of him outside the University of Oxford's Museum of Natural History. (34)

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A medieval astronomer at work (WMC)

It is worth noting that the scientific revolution of the sixteenth and seventeenth centuries did not take place in a vacuum, nor did the Renaissance suddenly spring “out of the blue.” Elements of their roots were planted in earlier times—including during the late Middle Ages. The scientists of the seventeenth century—mathematicians, astronomers and philosophers—had an awareness that they also owed a great debt to the past. Isaac Newton famously remarked that “If I have seen further it is because I have stood on the shoulders of giants.” (35)

To simply “blame the Church” for all lack of scientific progress in days gone by may seem entirely logical to some in our secular era today, yet it would appear that, there was a dedicated group, however small, within the Church itself, that actually did welcome new ideas and change. But, not without significant risks to their own “life or limb.” An example is the tragic case of the brilliant Giordano Bruno. All thinkers knew they had to be ever-careful due to the vigilant eyes and ears of the Inquisition. (36)

It may appear counterintuitive to contemplate the many scientists, alchemists, and mystics within the Church hierarchy and monastic orders. Certainly the Church was guilty of the repression of scientists and new ideas. Yet those few courageous progressives within the Church did make the effort to continue to operate, although they were forced to remain underground lest they be branded as “heretics”—even during the Renaissance, one of the most active periods of the Inquisition. Copernicus (1473–1543), for example, got into real trouble with his theory that the earth revolved around the sun—a concept he had read in the works of Plutarch, who recorded the Pythagorean opinion that “the earth revolves about a central fire and also spins like a wheel.” (37)

Cathedrals, solar observation and the post-medieval Church

What, then, did these underground philosophers and scientists of the Church actually do? Perhaps, as some scholars believe, they ingenuously “coded” knowledge into certain buildings, utilizing geometric principles and elements of ancient philosophy—a number of such buildings would appear to be Gothic cathedrals.

Lest all of this sound either fanciful or unscientific, please note that a particularly influential book in this field is written by Professor J. L. Heilbron, Professor of History and Vice Chancellor Emeritus, University of California (Berkeley), and a Senior Research Fellow at Worcester College, Oxford. His The Sun in the Church, is published by Harvard University Press. A New York Times Book Review called it a “notable book of the year” upon its release, and it was also reviewed in the prestigious science journal Nature. The Sun in the Church explains how even after late medieval times (after the time of the Gothic cathedrals), between 1650 and 1750, four Catholic churches in particular were the best solar observatories in the world—and this, remarkably, was after the Church had burned Galileo, and others. (38) Built to determine an unquestionable date for Easter, these four churches housed instruments that threw light on the disputed geometry of the solar system. Thus, within sight of the altar, Church doctrine about the order of the universe was subverted. This seminal book also describes how Rome supported astronomical studies, and accepted the Copernican hypothesis as a fiction convenient for calculation. A supreme irony of history is thus that the Catholic Church was perhaps the largest patron of sophisticated astronomical research throughout the whole period of the debate with Copernicus; obviously, it has always been deeply interested in cosmology, planets, and the sun.

The poet Dante, in his II Convito (xiv 13), displays a strong and clear support of astrology. Extolling its virtues, he comments at one point that “the science (of astrology) more than any (other) is high and noble on account of its high and noble subject (measurement)...” (39)

The potential for inner Light: an “immense present” for all?

In a groundbreaking article on “Botticelli's Mythologies,” the eminent art historian Ernst Gombrich quoted a letter from the Renaissance philosopher and translator of the Corpus Hermeticum, Marsilio Ficino to Lorenzo de Medici. Ficino tells the young Lorenzo that he is giving him an “immense present”—but reminds him there is a great price, too:

For anyone who contemplates the heavens, nothing he sets his eyes upon seems immense, but the heavens themselves. If, therefore, I make you a present of the heavens themselves what would be its price? (40)

Ficino then goes on to advise Lorenzo about the inner spiritual Work required, i.e., the price of such an immense gift, Knowledge ... the vast wisdom of the hermetic writings from ages past, a “light” all its own. (41)

Light, of course, has always had a powerful effect on humans—the light of the cosmos, the light of a beautiful early morning sunrise or evening sunset, and the inner light within each of us.

But among the most potent examples of this principle in a Gothic cathedral are the huge Rose windows in cathedrals like Chartres. We will now walk into the cathedrals with new eyes, exploring more about the stained glass windows, bejeweled gems of Light.