Architecture: When Constantinople was sacked by the Turks in 1453, scholars escaping (mainly to Italy) took away with them much of value in the way of ancient manuscripts, thus stimulating in the West the great Classical revival of the Renaissance; not only were Greek and Egyptian philosophy studied, but Greek and Roman architecture also provided models for Renaissance usage.

It is often wondered what real connection the modern 'speculative' Freemasons had with medieval stonemasons. One of the links is that the Hermetic Philosophers, who were among the predecessors of the Freemasons, rediscovered esoteric knowledge which, in its practical expressions, the architects and builders of the Middle Ages had never lost. Architecture was one of the many subjects which Cornelius Agrippa, John Dee and others studied and on which they wrote. The masons had kept their secrets of geometry and proportion for centuries. From the wealth of 'new' material which became available to them in the fifteenth century the Hermetic Philosophers discovered much the same knowledge; they also kept it, along with much else, secret - or at least, concealed.

The great Roman architectural writer of the first century BC was Vitruvius, who embodied philosophical ideas in his architecture. The Romans had absorbed Greek architectural ideas, though their slightly cruder approach to building shows they had lost some of the refinements.

Vitruvius's classic work De Architectura Libri Decem was certainly known in the twelfth century, but became lost for a while, being rediscovered in 1486. Both the medieval masons and the philosophers of the sixteenth and seventeenth centuries understood the symbolic truth of Vitruvius's architecture: proportion was all important. The proportion of buildings echoed the proportions of anatomy, for surely man was the pinnacle of God's design. The relation between the two can be found also in the preface to the notebook of the thirteenth-century French architect Villard de Honnecourt, which he hoped 'may be a great help in instructing the principles of masonry and carpentry. You will also find it contains methods of portraiture and line drawing as dictated by the laws of geometry.'

Much of the knowledge of the basic laws of geometry, known to the Greeks, had been lost by medieval times - at least to scholars. Medieval architects and builders (i.e. masons), however, still had this knowledge. Some was undoubtedly passed down from master masons to their journeymen and apprentices, as with the secrets of any craft guild. In addition, much was learned, however directly or indirectly, from the Muslims of southern Europe. It has already been seen that their level of scholarship and their love of learning were way above those of Christians of their day. Muslim scholars collected and preserved knowledge from all sources, including the Greek philosophers, and taught it to whoever wanted to learn; Arab universities were renowned seats of learning. All branches of mathematics, including algebra, geometry and trigonometry, were avidly studied. The route by which this knowledge came to Italian, French and English masons is no longer known, but those in contact with Muslims in the twelfth and thirteenth centuries certainly included both the Jewish Cabalists and the Knights Templar. From their geographical location and from their tolerance of others' beliefs, it is most likely that the Cathars had a similar contact.

It should be remembered that Gothic architecture was inspired by Arabic architecture.

According to the French historian Jean Gimpel, the secrecy associated with Masonic knowledge dates from the end of the thirteenth century. There is documentary evidence from a century later that apprentices were told to keep certain things secret; the Regius Manuscript of 1390 says,

He keeps and guards his master's teachings and those of his fellows. He tells no man what he learns in the privacy of his chamber, nor does he reveal anything which he sees or hears in the lodge or anything which happens there. Disclose to no man, no matter where you go, the discussions held in the hall or in the dormitory; keep them well, for your greatest honour, lest in being free with them you bring reproach upon yourself and great shame upon your profession.

Gimpel argues that, rather than any esoteric knowledge, this simply referred to tricks of the trade - trade secrets - which should be kept within the profession.

What was it that was so special about architectural knowledge? One thing, of course, was the skill of the trade. There was a vast difference between building a labourer's home - little more than a hut - and building a vast cathedral. The building trade, then as now, would have had its 'cowboys', and professional masons didn't want the incompetence of such workers ruining a cathedral. Masonic handgrips and other recognition signals seem to have originated in Scotland, to distinguish true masons from 'cowans', labourers capable of building, say, a dry-stone wall. Some of the mystique surrounding the secrets of masons may have been allowed to develop to emphasize the difference between architect-craftsmen - often known as magister, mattre or master of the works, and sometimes even as 'doctor of stonework' - and mere labourers.

It is likely that the new secrecy from the end of the thirteenth century in part simply reflected the increasing sophistication of society in the late Middle Ages. It is also quite possible that part of the reason for secrecy is that masons were worried about the Church's reaction if it discovered that they were acquiring architectural knowledge, directly or indirectly, from Muslims.

The mathematical knowledge itself needed to be protected. Pythagoras's right-angle theorem is known to every 14-year-old today, but seven hundred years ago few knew it, and fewer still knew its applications, such as how to construct a square with exactly half or twice the area of another square. Even how to measure an angle was unknown to most people. The Golden Section was even more esoteric, in the wider sense of the word. The complexity of mathematics - the 'magic' of mathematics, to ordinary people's eyes - led to it sometimes being referred to as a 'black art'.

Furthermore, buildings are constructed in three dimensions. Not Just a conceptual leap is required, but various specific principles, in order to go from a drawing on parchment to a finished building - taking an elevation from a plan. This particular knowledge, acquired through years as an apprentice and a Journeyman, would be Jealously guarded by master masons.

Finally, architecture involves geometry, and geometry (and this Gimpel misses) involves symbolism. The relationship of circles and squares and triangles, the superimposition of two triangles to form Solomon's Seal or the Star of David, the significance of the number of points, sides and angles in different geometric figures - all had meaning.

Medieval and Renaissance cathedrals across Europe are full of symbolism, not just in their paintings, statues and carvings, which people were used to interpreting on one level or another, but in their very design. The congregations worshipping in them, the priests taking the services, even the bishops officiating at the most solemn ceremonies, century after century, have in the main been entirely unaware that the very stones around them had a message built into them by those who planned and designed and supervised their construction: the architects and master masons.

The Golden Section mentioned above, was a specific proportion known to ancient Greek and Roman builders; its discovery is attributed to Pythagoras. A line A-B is divided at roughly a third of its length at point Q, so that the ratio between the shorter part, A-Q, and the longer part, Q-B, is the same as the ratio between the longer part Q-B and the whole line, A-B. The exact ratio is 1:1.618.

This is a fundamental proportion in geometry. It can be found in the relationship between the lines of a regular five-pointed star (a pentacle) and a regular five-sided polygon (a pentagon) inscribed within the same circle. It is crucial in the construction of the vesica piscis or mandoria, the pointed oval often seen in religious paintings and stained-glass windows. It is also found in the proportions of the 'ideal' human figure. And it is found everywhere in esoteric architecture.

Generations of schoolchildren tormented by 'the square on the hypotenuse' would probably have cursed Pythagoras for this further geometrical constant. Generations of worshippers in and visitors to cathedrals are awed by the majesty of the huge enclosed space towering heavenwards, testifying to the skill of the architects and builders; but they also feel a holy peace, a rightness, and this testifies to the art of the architects and builders - their knowledge and understanding of the use of proportion, developed over centuries, traceable back through the Muslims to the Romans and Greeks, and dependent on the esoteric significance of geometry and number. The Greek word for 'art', it should be recalled, gives the word 'magic'.

It is only fair to mention here that at least one historian of architecture sees the original link the other way around. Speaking of the ancient Greeks, Peter Kidson says, 'However they came by it, the architects' experience of applied geometry may well have supplied the philosophers with the raw material of their theorems.' This may or may not be so; in any case it makes no difference to the mutual interdependence of architectural and philosophical geometry.

What is clear, however, is that the medieval architects and builders had not lost this ancient knowledge, for it to be miraculously rediscovered in the fifteenth century. The architects kept designing and the builders building, long before Cornelius Agrippa and John Dee began studying the philosophy inherent in 'the queen of the sciences'.

At this point, a brief glance can be taken at the symbolism of geometry and architecture.

Churches built in the form of a cross are clearly symbolic, as is the placing of the altar at the East end, while spires direct the eye heavenward; so much is obvious. But there is much more to it than this. The mason takes lumps of raw stone (in Freemasonry, 'rough ashlar'), trims them into shape, polishes and carves them, and makes a glorious cathedral out of them to the glory of God; this is symbolic of the spiritual building, remaking or renewal of the shaped and polished soul from within the rough raw material of the physical body.

The Pythagorian idea of the spiritual qualities of numbers comes through clearly in the symbolism of the geometry underlying much of architectural design, from the smallest decorative carving to the structural layout of the largest cathedral.

Three is the number of God, both in the Christian Trinity and triple Gods in other religions, and in the idea of perpetuity or eternity, of past, present and future. In sexual symbolism, a triangle pointing upwards is male, a triangle pointing downwards is female. In terms of the elements, an upward triangle is fire, a downward triangle water. Four is the number of matter, and also of completion: the four elements, the four seasons, the four evangelists, the four cardinal points of the compass. The square, and hence the cube, is firm, solid, dependable, four-square authority. (The Emperor, in the Masonic Tarot, sits on a solid cube.) Five is the number of man: the head and four limbs in a five-pointed star, as in the well-known drawing of a human figure in a circle and a square. It also represents the five senses, and so the sensual world. It is also traditionally the number of esoteric spirituality, perhaps because (as in the dots on a die or a domino) the Unity of One (i.e. God) is within the Four of matter.

The numeral zero is not numerologically significant, but the shape of the circle is. The circle represents perfection, God's whole Creation, the entire cosmos. It also reminds us of the ever-rolling seasons, and of the continuance of life through death to life, and so eternity, and infinity - and, of course, the 'heresy' of reincarnation, believed in by many early Christians, and central to most esoteric beliefs. In astrology it represents the sun, but also the circle of the zodiac, the heavens in which the stars and planets move. The fifth-century BC Greek philosopher Empedocles wrote, 'God is a circle whose centre is everywhere and whose circumference is nowhere.'

The sphere is both the soul and the universe, and again the zodiac. It is the most perfect geometric figure.

The egg is something like the sphere, but also contains the mystery of birth, creation and fertility; it symbolizes life and latency.

The vesica piscis, the rounded lozenge or almond shape made from two overlapping circles, shows the meeting and joining of two forces or two worlds: male and female, matter and spirit, earth and heaven, man and God. It is often seen within stained-glass windows, sometimes enclosing the figure of Christ, the mediator between man and God. It also represents both virginity and female sexuality, because of its vulva shape. The almond symbolizes the sweet fruit within the husk, the hidden secret, and Christ's divine nature within his human form.

This is just a selection of shapes and numbers and their spiritual significance and symbolism. One further design, sometimes seen in continental cathedrals, will be mentioned: mazes and labyrinths symbolize the soul trapped and tangled in matter - a Gnostic idea - and its arduous journey to God. Few of these labyrinths remain undamaged and on open view; later Church authorities either didn't understand their symbolic message, and so built over them - or did, and so deliberately obscured them.

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