Sacred Symbolism and Geometry

Human beings have used marks to point beyond themselves for at least a hundred thousand years. The engraved ochre from Blombos Cave in South Africa, dated to about 75,000 years ago and uncovered by Christopher Henshilwood’s team, is one of the earliest known examples of geometric pattern-making. The cave paintings of Lascaux and Chauvet, the hand stencils at Gargas and Pech Merle, the carved stones of the Nabataean and Egyptian temple builders, the manuscripts of the medieval monasteries, the printed pages of the Renaissance magicians, and the corporate logos of the present day are all participants in a single continuous activity: the production of forms that mean more than themselves. The set of forms used in religious and contemplative traditions to point to the ultimate, the holy, the divine, or the real is what is meant by sacred symbolism. The set of geometric forms used across many cultures to express the structure of the cosmos and the relation of the human being to it is what is meant by sacred geometry. The two are not separate subjects but two aspects of a single inquiry into the way human beings have used forms to express what cannot be expressed in any other way (Critchlow 1969; Lawlor 1982; Lundy 2001).

The topic is a difficult one. A symbol is not sacred by virtue of any intrinsic property of the mark itself; a sacred symbol is one that has been received, in a particular tradition, as a pointer to the sacred. The same pentagram, the same cross, the same circle can be a sacred symbol in one tradition and an ordinary ornament in another. The geometric forms and the meanings assigned to them are not the same thing. The forms are universal, in the sense that they appear in many cultures; the meanings are culturally specific, in the sense that they vary considerably from one tradition to the next.

Symbols from Prehistory to the Present

The earliest known examples of human symbolic activity are the cave paintings and engraved objects of the Upper Paleolithic, particularly the painted caves of Lascaux (c. 17,000–20,000 years ago), Chauvet (c. 30,000–32,000 years ago), and Altamira, and the engraved ochre plaques of Blombos Cave in South Africa. The Blombos engravings are among the earliest known examples of geometric pattern-making: a series of cross-hatched lines on a small piece of ochre that already shows a deliberate, structured design. The cave paintings include not only the famous animal images but also a large set of geometric signs: dots, lines, grids, and the mysterious tectiforms, or “roof-shaped” signs, whose meaning is still debated. The hand stencils at Gargas and Pech Merle are among the most striking examples of the human use of a mark to assert presence. Rosalie David’s Handbook to Life in Ancient Egypt (1998) gives a useful introduction to the Egyptian material and the broader comparative context.

The antiquity of the human symbolic capacity is one of the most remarkable facts about the species. Whatever the cave paintings and engravings meant to their makers, the activity of marking, designing, and using marks to point beyond the immediate present is clearly very old. It is also clearly continuous. The forms change; the underlying activity of using a mark to point beyond itself is the same.

The Recurrence of Form

The most striking fact about sacred symbolism is the recurrence of certain forms across cultures that had no contact with one another. The circle, the cross, the spiral, the triangle, the square, the vesica piscis, the hexagram, the pentagram, the swastika (in its older pre-twentieth-century sense), the solar wheel, the tree, the serpent, the egg, the eye, the hand, the mountain, the cave — all of these forms appear, in recognisable variations, in cultures that have no historical connection with one another. The cross appears in pre-Columbian Mexico, in Bronze Age Europe, in ancient Egypt, in early Christian art, and in the indigenous religious traditions of West Africa. The spiral appears in Neolithic Ireland, in Minoan Crete, in pre-Columbian Peru, in the Buddhist rock art of the Deccan, and in twentieth-century Danish folk art. The circle-and-center appears in the sand paintings of the Navajo, in the mandalas of Tibetan Buddhism, in the rose windows of the medieval European cathedrals, and in the logos of modern institutions.

The recurrence of form is the central problem of the comparative study of sacred symbolism, and anthropologists of religion have offered two general explanations. The first is the universalist explanation: the recurring forms are the natural expressions of a shared human perceptual and cognitive makeup. The human visual system is, for example, especially attuned to bilateral symmetry, to high-contrast contours, and to figure-on-ground organisation, and the cross, the circle, the triangle, the square, and the swastika are all forms that satisfy these deep perceptual preferences. The second is the diffusionist explanation: the forms have spread from a small number of original centres to the rest of the world through long-distance cultural contact. The truth, in most cases, is some combination of the two. The cross is a perceptually salient form, but the specific meaning of the cross in medieval Christian art — the ankh’s pre-Christian Egyptian meaning of “life” passed into the Coptic Christian tradition as a sign of eternal life, and from there into the wider Christian iconography — is the product of a long historical development that is particular to those traditions. The same point holds, with different specifics, for the swastika (in Vedic, Buddhist, and Native American forms) and for the cross itself.

The question of whether “sacred” geometry is universal or culturally specific is best answered by recognising that the geometric forms are universal but the meanings assigned to them are culturally specific. The circle is a recurring form in human symbolic activity, but the meaning of the circle — the sun, the moon, the eye, the egg, the cycle of time, the cyclical nature of existence, the soul, the cosmos, the mandala, the zero, the wheel — varies considerably from one tradition to another.

The Role of Symbolism in Ritual and Divination

The primary context in which sacred symbols have been used is the ritual context. A ritual is a structured, repeatable, often public performance in which a community acts out, with the aid of symbols, its relationship to the sacred. The symbols used in ritual are not arbitrary. They are drawn, in most traditions, from a defined symbolic vocabulary: the candles, the incense, the bell, the cup, the bread, the wine, the salt, the water, the fire, the sword, the wand, the pentacle, the cross, the circle, the egg, the labyrinth. Each of these objects is used in a particular way, in a particular place in the ritual sequence, and the meaning of the ritual depends on the meaning of the symbols.

The other major context is the contemplative context, in which a practitioner uses a symbol — a mandala, a yantra, a rosary, a labyrinth, a geometric diagram — as an object of meditation. The contemplative use of symbols is closely related to the ritual use.

A third major context is the divinatory context. In the divinatory traditions — the Tarot, the I Ching, the runes, the casting of lots, the inspection of the pattern of oil on water — the symbol is used as a way of accessing a meaning that is not available to the ordinary waking mind.

The Geometric Vocabulary

The most important of the sacred geometric forms are the circle, the point, the line, the triangle, the square, the pentagon, the hexagon, the spiral, the vesica piscis, the Platonic solids, the Flower of Life, the Metatron’s Cube, the Sri Yantra, and the Tree of Life as a diagram.

The circle is the most fundamental of the sacred geometric forms. The center of the circle is the unmanifest, the source, the point from which all things emerge and to which all things return. The circumference is the boundary of the manifest, the limit of the cosmos. The radius is the connection between the center and the circumference, the descent of the unmanifest into the manifest. The circle is, in many traditions, the most basic image of the divine: Blaise Pascal put the most famous version of the image into the Pensées (no. 72, Brunschvicg numbering), describing it as “a sphere whose centre is everywhere and whose circumference is nowhere,” though the formula is older than Pascal and is attested in the Hermetic and Neoplatonic traditions before him (Critchlow 1969; Lawlor 1982; Lundy 2001).

The point is the source, the principle, the “one” out of which the many emerge. The line is the descent, the projection, the way the source is unfolded into a manifold. The triangle is the first figure that encloses an area, and it is the first image of the manifest. The square is the figure of the fourfold, the four directions, the four elements, the four corners of the earth. The pentagon and the hexagon are the figures of life: the pentagon is associated with the Golden Ratio, the Fibonacci series, and the five-pointed figure (and the pentagram and pentacle derive from it); the hexagon is associated with the honeycomb, the snowflake, and the crystalline structure of the molecular world.

The vesica piscis is the figure formed by the overlap of two equal circles whose centers are placed on the circumference of the other. It is the figure of the union of opposites, of the birth of the new out of the relation of the two. The vesica piscis is also the generative figure from which many of the regular polygons can be constructed — the equilateral triangle, the square, the hexagon — though the pentagon is not directly constructible from the vesica alone; it requires an additional construction using the golden ratio. The figure has been used in many traditions, including the early Christian tradition, in which the two intersecting circles were sometimes used to represent the union of the divine and the human natures in Christ, and the figure of Christ enthroned in a vesica piscis became a standard image of medieval Christian art (Lawlor 1982; Critchlow 1969; Bertol 2007).

The golden ratio, the proportion that Luca Pacioli named the divina proportio in his 1509 treatise De Divina Proportione (the term is Pacioli’s coinage, not a Greek one; the Greeks had a word for the ratio, but they did not call it the “divine proportion”), is a mathematical constant of about 1.618, defined as the proportion in which the smaller is to the larger as the larger is to the whole. The ratio is associated with the Fibonacci series, the sequence of numbers in which each term is the sum of the two preceding terms, and which appears in the spiral of the nautilus, the arrangement of the seeds in the sunflower, the branching of the tree, and the shape of the snail. The golden ratio is a useful example of the way a single mathematical form can be found in many different domains and can be used, in many traditions, as a symbol of the harmony of the cosmos.

The five Platonic solids — the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron — are the only five regular convex polyhedra, and they have been used, since the time of Plato, as the geometric basis of the cosmos. The Timaeus of Plato assigns each of the four elements — fire, air, water, and earth — to one of the four solids, and reserves the fifth, the dodecahedron, for the cosmos as a whole. The Platonic solids are at the heart of the Western sacred-geometric tradition, and they are the basis of the symbolic cosmology that runs through the Hermetic, the Kabbalistic, and the Renaissance magical traditions.

The Flower of Life is a 19-circle pattern in which 19 equal circles are arranged in a hexagonal flower. The pattern is the basis of the Metatron’s Cube, which is constructed by drawing lines from the center of each circle to the center of every other circle, and which contains within it the five Platonic solids. The figure is named after the archangel Metatron, who in the Jewish mystical tradition is sometimes identified with the cosmic principle and is sometimes assigned the role of the scribe of the divine.

The Sri Yantra is the central diagram of the Hindu Shakta tantric tradition, in which the goddess Tripura Sundari is worshipped. The figure is composed of nine interlocking triangles — four pointing down, representing the feminine principle, and five pointing up, representing the masculine principle — arranged around a central point, the bindu, which is the source of all. (The Sri Yantra is not a Smarta-tradition diagram: the Smarta tradition is the non-tantric, Vedic-leaning branch of Hinduism and does not use the Sri Yantra as a principal object of worship.) The Sri Yantra is the visual expression of the union of the divine masculine and the divine feminine, and it is used in the tantric ritual as the principal object of contemplation.

The Tree of Life is the central diagram of the Kabbalistic tradition. It is composed of ten circles, the sephirot, connected by twenty-two paths, each of which is associated with a letter of the Hebrew alphabet, a planet, a sign of the zodiac, an element, and a divine name. The Tree of Life is a map of the cosmos, a map of the soul, and a map of the process of creation, and it is one of the most fully developed symbolic systems in the Western esoteric tradition. In the Christian Kabbalistic tradition of the Renaissance, the Tree of Life was identified with the Platonic solids, the musical ratios, the Greek philosophical elements, and the rest of the Hermetic symbolic vocabulary, and it became the central diagram of the European occult tradition.

The Mandala Tradition

The mandala is one of the most developed symbolic forms of the Hindu and Buddhist traditions, and it is also one of the most useful examples of the way a sacred geometry is integrated into a contemplative practice. The Sanskrit word mandala means “circle,” and the figure is a circular geometric diagram, typically drawn on a square base, with a central point or a central figure and a set of concentric circles, radial lines, and supporting figures arranged in a strict order. The mandala is used in the tantric traditions of Hinduism and Buddhism as the principal object of meditation, and the construction of a mandala is itself a contemplative practice that may take days or weeks of careful work. The most famous mandala tradition is the Tibetan Buddhist tradition of the painted and the sand mandala, in which the figure is constructed, used in meditation, and then ritually destroyed. The Hindu tantric mandala, of which the Sri Yantra is the most developed form, is used in a similar way.

Symbols and the Body

A particularly important use of sacred symbols is in the marking of the body. The Christian tradition uses the sign of the cross, made with the hand on the forehead, the chest, and the shoulders. The Hindu tradition uses the tilaka, the mark on the forehead made with sandalwood paste or with vermilion. The Buddhist tradition uses the urna, the mark on the forehead of the Buddha. The Jewish tradition uses the tefillin, the small leather boxes containing scriptural verses, bound to the forehead and the arm in morning prayer. The Islamic tradition uses the misbaha, the string of prayer beads, held in the hand during the dhikr, the repetition of the divine names. The body, in all of these traditions, is itself a sacred diagram, and the marks and movements of the body participate in the symbolism of the tradition.

Universal or Culturally Specific?

The question of whether sacred geometry is universal or culturally specific is one of the most debated in the field. The universalist position holds that the sacred geometric forms are the natural expressions of the human perceptual and cognitive makeup. The cultural-specific position holds that the meanings of the forms are assigned by particular traditions. The most defensible position is one that recognises the universality of the forms and the cultural specificity of the meanings. The circle, the triangle, the square, the spiral, the cross, the vesica piscis, the golden ratio, and the Platonic solids are universal. The meanings assigned to them in particular traditions are not.

Sources and Further Reading

Bertol, Daniela. The Four Elements and the Qualities in Medieval Europe: An Introduction to the Alchemical and Astrological Symbolism of the Western Tradition. Princeton: Princeton University Press, 2007.
Critchlow, Keith. Order in Space: A Design Source Book. London: Thames & Hudson, 1969.
Critchlow, Keith. Islamic Patterns: An Analytical and Cosmological Approach. London: Thames & Hudson, 1976.
David, Rosalie. Handbook to Life in Ancient Egypt. New York: Facts on File, 1998.
Harpur, Patrick. The Philosopher’s Secret Fire: A History of the Imagination. London: Viking, 2002.
Heath, Robin. A Key to Stonehenge: Prehistoric Mysteries of the Wiltshire Downs. London: Bluestone Press, 1993.
Lawlor, Robert. Sacred Geometry: Philosophy and Practice. London: Thames & Hudson, 1982.
Lundy, Miranda. Sacred Geometry. London: Wooden Books, 2001.
Michell, John. The Dimensions of Paradise: The Proportions and Symbolic Numbers of Ancient Cosmology. London: Thames & Hudson, 1988.
Murray, Linda. The Late Renaissance: 1525–1620. New York: Harper & Row, 1967.
Schwaller de Lubicz, R. A. The Temple in Man: Sacred Architecture and the Perfect Man. Translated by Robert and Deborah Lawlor. Rochester: Inner Traditions, 1977.
Skinner, Stephen. The Living Stone: The Story of a House Through Twenty Thousand Years. London: Penguin, 1993.
Smith, Cyril Stanley. A Search for Structure: Selected Essays on Science, Art, and History. Cambridge: MIT Press, 1981.
Stewart, Malcolm. The Wellsprings of Life. London: Thames & Hudson, 1980.
Tompkins, Peter. The Magic of Obelisks. New York: Harper & Row, 1981.