Numbers and Shapes:
The Timeless Alphabet of Art and Life

Michael S. Schneider, author of "A Beginner’s Guide To Constructing The Universe" writes and teaches about the numbers 1 through 12 and their geometric and numerical expressions in nature, art and culture.

"Come into the light of things;
let nature be your teacher."

-- William Wordsworth





Microscopic radiolarian skeleton


Egyptian Eye of Horus, whose
parts were the hieroglyphs for
fractions totaling 63/64.
Where is the missing piece
which "restores" unity?



The Timeless Alphabet:



An introduction to the symbolic language
of numbers and shapes


My writings and classes introduce participants to the timeless, symbolic language of numbers, shapes, patterns and proportions which appear as the forms of nature, as symbols of religion and mythology, in the proportions of worldwide art and architecture, and in fairy tales and folk sayings.

Just a few numbers and their shapes compose this archetypal alphabet upon which the designs of the universe, from atoms, flowers, seashells to the human body and galaxies and are based. The forms of nature are forces made visible. Each number and shape conveys specific meaning, and everything in nature tells us its purpose if we know how to read the language in which it is written. Great spiritual art, crafts and architecture have always used this language of number, shape, pattern and proportion to manifest harmonious composition. Knowing nature's own language is a step towards our harmonious, respectful cooperation with a wonderworld of beauty, and a key to understanding the symbolic significance of numbers and shapes wherever they occur.

The symbolic significance of numbers and shapes is not arbitrary or cultural but comes from their timeless characteristics, their properties alone, and the ways they relate with others. It's best to let numbers and shapes themselves teach you directly, so bring a geometric compass, straightedge, colored pencils and blank paper for hands-on experiences.

We don’t need any math background to learn the gentle alphabet of nature’s design language.

The most important reason for these studies is their healing and uplifting property. With this in mind, Plato wrote ...

"'You amuse me,' I said, 'with your obvious fear that the public will disapprove if the subjects you prescribe don't seem useful. But it is in fact no easy matter, but very difficult for people to believe that there is a faculty in the mind of each of us which these studies purify and rekindle after it has been ruined and blinded by other pursuits, though it is more worth preserving than any eye since it is the only organ by which we perceive the truth. Those who agree with us about this will give your proposals unqualified approval, but those who are quite unaware of it will probably think you are talking nonsense, as they won't see what other benefit is to be expected from such studies."

These classes are informative and inspiring, and will rekindle and enhance your own investigations and understanding by means of the wisdom inherent in numbers and shapes.


Come learn the language of your native world!
The first twelve numbers are all that's necessary to understand the designs, patterns and proportions of this beautiful cosmos.
They naturally form four groups:

First Principles: 1 and 2
Numbers of Structure: 3, 4, 6, 8, 12
Numbers of Life: 5 and 10
Numbers of Mystery: 7, 9 and 11

This information is especially valuable to artists, craftspeople, architects, educators and students of symbolism in worldwide traditions.



God the Geometer,
Bible Moralisee, 1215


A star exhales



1&2 Unity & Polarity

This first session begins with an overall introduction to the language of numbers and shapes. It introduces participants to the ancient traditions of "philosophical mathematics" including symbolism of the geometer's tools, the spiritual allegory of geometric construction, and overview of the Timeless Alphabet. Through hands-on activities with the compass, straightedge and marker, we're guided to see geometric construction as a creation myth, a metaphor for the process by which all the forms of nature are created.

Unity is a fact of nature, and all numbers and shapes unfold from Unity, number 1, symbol of wholeness, completeness cycles and equality (all its points are equally distant from the center). It is represented by the point, circle and sphere which are most efficient forms and worldwide symbols of heavenly perfection. But Unity casts its own shadow pretending to be "two," thus "creating" polarity required for any creation. By this method 1 generates all the single digits and the Vesica Piscis, the almond opening through which other numbers and shapes are born:



 Notice that the Numbers of Mystery, 7, 9 and 11 are missing because they cannot be constructed with a compass and straightedge.


Notice the light triangle in the clover


  3 Trinity: Tri-Unity
The birth of the number 3 and triangle enables opposites to balance and transcend to a new wholeness they couldn't achieve by themselves. A third leg makes a tripod stable, and a third strand of hair allows a braid to knot as one whole, just as neutral judges balance opposing parties, neutrons balance the electrons and protons of atoms, as the Supreme Court plays the role of the balancing, transcendent third force between the Executive and Legislative branches. The triangle is the strongest and most stable of shapes and so appears in the constructions of humans and nature. Trinities appear in nature and as worldwide religious symbols and spiritual art which uses the unseen triangular frame to convey this archetypal power.

Tungsten atoms form a crystal



4: Fair And Square

This class examines the symbolism and appearances of the number four and its representative forms, the square, cube and tetrahedron. Fourness is the essence of volume, underlying the forms of crystals and creatures, and is a symbol of earth, manifestation and the four states of matter ("mater" or mother) shaping and clothing the designs of nature, arts, crafts and architecture. Thus it appears worldwide as a number of directions and sacred migrations, represented everywhere from goddess art to board games.

Slice of a Celery stalk



5: The Flag of Life

In starfish and flowers, corporate logos and flags, the number five and the amazing regenerative geometry of the pentagon and pentagram star appear in nature and human affairs as a sign of life (the flower of every edible fruit is five-petaled). It is a worldwide symbol of humanity, righteous authority, harmony, beauty and excellence. We can learn to recognize the five-ness of living forms, and see how artists from Egypt and Greece to Raphael and Dali have applied five-fold symmetry -- the flag of life -- to create harmony in their compositions.


Sensitive hairs within the human
ear's cochlea, arranged in hexagonal
pattern, transduce vibrations into
electric impulses and "sounds".



6: The Joy Of Six

The principle of sixness is that of structure, function and order, the efficient properties of space, power and time. It appears as the close-packed crystalline patterns of snowflakes, chicken wire and honeycombs, as well as the underlying pattern within much spiritual art including the Sphinx and Egyptian jewelry and painting, Chinese sculpture and the U.S. Great Seal.. Multiples of six (especially 12, 24, 30, 36, 60 and 360) provide the sacred measures of space, weight and time, from traditional rulers and protractors to clocks and calendars. The marvel of the sixfold pattern appears in many universal guises.

The Seven Pleiades



7: The Virgin Number

The number seven was considered "virgin" by the ancients because no number divides into it (without a remainder), and its geometric construction cannot be captured by compass and straightedge. Thus it appears to us as objects we cannot grasp like the colors of the rainbow and tones of the musical scale. The predominance of seven in religious and mythological symbolism reveals its role as the number of stages in a whole process, from the number of crystal systems and endocrine glands to chakras and "heavens" in the the stages of our spiritual journey. Participants will learn how to tune a musical instrument to the Pythagorean scale used in ancient musical healing therapy.

Aztec Sun Calendar


  8: Periodic Renewal: Between Heaven and Earth

What is it about the number eight and the geometry of the octagon which makes it so popular in the design of secular and sacred buildings around the world? As the shape between the circle and square (rotate a square to produce an octagram) it symbolizes "between Heaven and Earth." Eight reveals the principle of the musical octave, periodic renewal at work through the universe, from the mythology of Grandmother Spider and the Siberian Shaman’s eight-legged horse to the pattern of rhythmic flow symbolized in the I Ching, in computer's byte of eight bits, the Taoist "Eight Immortals" and Buddhist mandalas which make visible the "Eightfold Path". We'll look at sacred architecture from ancient temples to the U. S. Capitol Building to discover this principle of "periodic renewal" at work.

Dante and Beatrice gazing at the
thrice three rings of Heaven
aroundtheir divine center.


  9: The Horizon

In traditional worldwide number lore, nine, or thrice three, was referred to as “the horizon” symbolizing the ultimate, the maximum, “the whole nine yards”. This class will look at the ways people have revered the number nine and its principles through their arts, crafts, architecture, literature, mathematics, mythology, religion and folk-sayings, from "cloud nine" and a pagoda’s nine levels to a cat’s nine lives. Casual attire: no need to “dress to the nines”.

DNA molecule, seen from above


  10: New Unity

The number ten is a traditional symbol of fulfillment, a return to unity after having gone through the experience represented by single-digits. Tens, hundreds and thousands represent greater powers of Unity. A knowledge of the mathematical principles within “ten” help us to understand its appearances in nature, as well as the philosophical basis of many cultures’ religious scripture, architecture and arts. This is the traditional wisdom held in the Tetraktys, symbol of the Pythagoreans, as well as the hidden map of ourselves in the Kabbalah's "Tree of Life" diagram.


  11: The Passageway

The number eleven is quite a mystery. References in sacred literature, philosophy, art and architecture are rare and obscure, but they do exist. It was considered to tresspass beyond 10, but incomplete approaching 12. Resembling the principles of the number 2, of which it is a lower form, 11 represents a door, tunnel or passageway, not only between the great realms represented by numbers 10 and 12, but appears as the number of days of the Babylonian New Year's Festival (the door between years), as the link between the Chinese Magic Squares of Heaven and Earth, as Egyptian bread offerings, in many Islamic references. While it doesn't appear in music, nature or architecture, it's important in metrology as ratios (e.g., in the traditonal rationalization of pi 22/7). To where does this passage lead us?



12: Cosmic Dozens and
The Cosmological Circle

"The universe is simple if you use imagination.
Its pattern is the number Twelve which structures all Creation.
You need not study physics or be versed in numerology
To draw from Threes and Fours the duodecimal cosmology."

--"Twelve Fold Universe" by John Michell

To live in accord with the perceived cosmic order, countless societies mirrored upon Earth the patterns they saw in the sky and in mathematics, particularly around the wondrous properties of the number twelve. Twelve is the traditional "framework number" embracing and interrelating the numbers below and beyond it. From time immemorial the archetypal "twelve-around-one" pattern of the zodiac was mirrored in twelve-tribe societies, the mythologies of twelve heroic ordeals, twelve spiritual disciples, and the designs of monuments, temples and cultures mediating between Heaven and Earth, from Stonehenge to the U.S. Government. There are many worldwide traditions of the Duodecimal (twelvefold) Cosmology.

The "Cosmological Circle" refers to an ancient geometric diagram which appears throughout the world underlying the designs of temples, kivas, churches, mandalas and other expressions of sacred arts, crafts and architecture. Its secret is that it makes visible the harmony of all the numbers 1 through 12 and so represents a harmonious sacred microcosm. The Cosmological Circle's "squared-circle" design insures that such temples are properly oriented to the solstices and equinoxes, and symbolizes that the site occurs at the meeting of Heaven and Earth.


For further insight see

Volume 5
Constructing The Cosmological Circle Activity Book (more below)

Essay: "
Cosmic Dozens: Twelve-Fold Designs of Society and Art"

 More about each of these 12 numbers can be found here.

Do you want to learn more about the geometry of nature and art through hands-on experience?
Now it's possible, with


Constructing The Universe Activity Books


Create and Explore Geometric Patterns
of Nature and Art
720 pages of hands-on activities!
Michael S. Schneider




Ideal for Artists, Craftspeople, Architects, Designers, Home Schools
and anyone who wishes to be inspired
by the relationship of mathematics with nature and human creativity.
Filled with hands-on geometric constructions and activities.

Many Illustrations.
Easy To Understand.

Click here to learn more about these Activity Books
and see their Tables Of Contents.

 Also available: a four-hour DVD taking you on a journey through the landscape of the numbers 1 through 12:

Click on the disk for more information


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