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"The real voyage of discovery
consists not in seeking new lands,
but seeing with new eyes"

Marcel Proust

If the word mathematics brings discomfort to your ears there is hope on the horizon. Michael S. Schneider has written a wonderful book that can dispel mathaphobia forever. After reading A Beginner's Guide to Constructing the Universe, your appreciation for the world of numbers will be elevated and inspired. The title itself speaks volumes.

In Schneider's own words, "A vision of mathematics different from that which we were taught in school holds an accessible key to a nearby world of wonder and beauty." The very essence of form and life as we know it is built on numbers and their inter-relationships. The creative archetype of nature is number.

Creative Mathematics


Schneider does an excellent job of bringing the art and science of numbers to a level anyone can assimilate and grasp. The subtitle of the book is The Mathematical Archetypes of Nature, Art and Science. This book will permeate your psyche and spark creative ideas. As you look around your world and everyday life you will be illuminated by the simplicity and perfection of the natural world and understand its mathematical relationships. Once you grasp the essence of each number from one to ten the beauty of mathematics will become clear.

The Beginner's Guide takes you on a journey from the numbers one through ten. In Part One of this review we will briefly delve into the numbers one through five. In Part Two we will explore the numbers six through ten. I will only give the barest hint here of what this book contains. To get a full appreciation you need to purchase and savor the book. It will be a book you treasure. Your children should read it, and if they are too young to read, read it to them.

What Michael does that sets this book apart from other writings on mathematics is that he shows you how to create all geometric forms with the three simple tools of a straight edge, a compass and a writing stylus. All forms can be created with these three simple instruments. As you take this journey you begin to get a feel for how nature has constructed its myriad of structures from the simplest of tools. This is only a brief example of what treasures of knowledge this book holds. Let's begin.


Number ONE

"You cannot conceive the many without the one..
The study of the unit is among those that lead the mind on
and turn it to the vision of reality."

The book begins with a study of the initial Monad, the One, the source of all things. Schneider points out, "The ancient philosophers conceived that the Monad breathes in the void and creates all subsequent numbers (111111111 x 111111111 = 12345678987654321). Numbers only express different qualities of the Monad." If you stop and contemplate the above equation something very profound will reveal itself. The Monad expressed nine times, multiplied by itself, produces all the subsequent numbers progressively and then inversely.

Studying the number One you also come to understand cycles. Circular rotary motion is a principle of the Monad. All nature embodies these orbital circuits, from the stars and galaxies to the atomic elements. Seasonal periodicities, cyclic rhythms and spiraling vibrations permeate the universe and touch our lives every day in every way. Learn why the simplest most basic articles you use every day are based on circular principles for their strength and resiliency.



"Everything that originated from the tree of knowledge carries in it duality."

The circle is the womb of creation. Yet the circle regenerated by creating a mirror of itself. In this mirror is the first Dyad. It is said that the void contemplated itself, reflected it's own light and cast its own shadow. This was the beginning of all form and duality. Contrast is absolutely necessary for the recognition of form. The light defines the dark and vice versa. Magnetic fields are the purest expression of the Dyad. Polar opposites attract and repel and the world is woven between them.

The vesica pisces or intersection of two circles is the opening of the womb from which all five Platonic solids and volumes are created. Duality creates polarities and we can feel this principle in everything we engage. Many corporate logos utilize the vesica Pisces, TWA, CBS, MasterCard and others.



Creative Mathematics
But every tension of opposites culminates in a release, out of which comes the "third."
In the third, the tension is resolved and
the lost unity is restored."

Carl G. Jung

The triad is most obvious to us as the beginning, middle and end; birth, life and death; past present and future; thesis, antithesis and synthesis. According to Greek philosopher Iamblichus, "The triad has a special beauty and fairness beyond all numbers, primarily because it is the very first to make actual the potentialities of the Monad. Schneider reveals to us that "A triangle is a statement about relationship and balance. As the centers of the two circle repel and tug at each other, a reconciling third point occurs naturally above the place were the circles cross and agree.We see this balanced path between extremes in periodic phenomena such as a swinging pendulum and a heartbeat."

When designing a universe you need triangles to create self-supporting structures. Carpenters stabilize structures by bracing it with triangles. Triangles provide strength, balance and efficiency of energy space and materials. Many knots and braids utilize the principle of the triad for strength and self-reinforcement. All color photography is the blending of three basic colors, yellow, magenta and cyan. Nature uses triads fluently. Notice how the triad is the basic design in the butterfly above.


"The right thing is to proceed from second dimension to third, which brings us,
I suppose, to cubes and other three dimensional figures."


The tetrahedron is the simplest four sided solid composed of perfect triads. The number four is the beginning of depth in space. The number four is the mother of three-dimensional form. The number four permeates our lives. We have the Four Corners of the globe; the four elements, fire, air, water and earth; and four seasons.

A pyramid is four triads poised upon a square. This is the strongest structure known. The butterfly also utilizes four stages of life to complete its life cycle. Beginning as a silent egg, is becomes a hungry green caterpillar, rests in a cocooned pupa to emerge as a winged creature at last. Human maturation is measured in childhood, adolescence, adulthood, and old age.



"If you would understand the invisible,
look carefully at the visible."


Five is the number of regeneration. Form is ripe and ready in three-dimensional space, and now it is time for this form to recreate itself. The Pentad is present everywhere. The human body expresses the Pentad's symmetry in its five senses, five extensions from the torso with each limb ending in five fingers or toes. Pentagrams are stars we see fluently in advertising and corporate logos. Most flags embody a five-pointed star somewhere in their symbolism. Cut open an apple and you will notice that the core is in the shape of a star.

Creative Mathematics

The Pentad is also the key to the self-generating number series knows as the Fibonacci sequence. The Fibonacci series is created by zero and one (nothing and everything) adding to itself successively. For example, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89... The series is a self-accumulating sequence that grows from within itself, it's immediate past and takes nothing from outside the sequence for additional growth. This is the essence to the Pentad's principle of regeneration, self-replicating growth, which began from nothing and became everything.

Sacred geometry is the study of how the universe was constructed through number and form. After reading this book you will have an immense appreciation and greater understanding of the world you live in. We will continue this review in Part II and learn briefly about the numbers six through ten. Michael Schneider also gives workshops with hands on approach to creating all two and three-dimensional forms with the simple tools of a compass and straight edge. The following link is a brief synopsis of one of these Seminars. To contact Michael for more information on when and where his next workshop is you can email him at Michael Schneider.

Everyone desiring to increase their creative potential and creative mind should read this book and absorb its message. Life is truly an elegantly ordered creative system. Once this order is gleaned, even briefly, the interconnectedness of all that exists is appreciated. The integrity of nature once grasped has an elegance of its own. To see this unity and appreciate it will enhance your own creative aspirations.

© J.L. Read, 1997. All Rights Reserved.
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This site is dedicated in loving memory
to its creator, Janet L. Read
1949 — 2000


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