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Let's Build a New School

Thoughts on Radical Education

The following essay by Lawrence Dobson is a beginning attempt to voice the dream of establishing
a radically new learning environment on South Whidbey Island, Washington. {written 1974}


I. The Present System

America has evolved into the most materialistic country in the world. We are in love with the material world. We consume more of it than any other culture by far. We have conquered and subdue it. Having been seduced by transient material desires, we now awake to find we have raped, almost killed, our priceless natural heritage. Now we repent and vow to establish a new harmony with nature, for reverence for nature runs deep in marrow; our deepest gratitude and joy is released through working with her forms and energies, discovering her laws, and dancing to the pulse of her seasons.

Physical involvement with the material world, "wading in and getting our hands dirty", has been a typically American trait, yet in our schools we learn to talk about, rather than do. This country was built by a pragmatic "do it now" approach, working with what was there and needed to be done. Without blind tradition to aide us, we developed a simple, direct "horse sense". Yet an overly intellectual approach to learning in our schools has usurped control from common sense. Concerns for following prescribed forms and assuming legal responsibility has made it easiest to intellectualize on a subject, rather than get physically involved with it.

Public education has developed along one general pattern of growth, which graduates a citizen adapted to survive in a specialized environment -- the institutional, status-quo, paperwork- oriented, conservative American bureaucracy. The institution is so highly developed that it can no more evolve into a radically different system than the dinosaur could evolve into the monkey. Yet, just as nature must evolve new life forms to express her dynamic purpose, so must public education take on new life forms that we may realize our true destiny.

In our schools the practice of damming the natural flow of childish enthusiasm by abruptly changing focus every 55 minutes with the ring of a bell, or, on the other hand, demanding mental concentration on a subject foreign to the spirit of the moment, may have created the analytical detachment necessary to focus critically on our present dilemma, but it leaves us without the practical skills to resolve it. If we now have the vision, we seem powerless to act on it. Having evolved from a nation of pragmatic doers into a society of servile sitters, we are ruled by regulations that quickly exhaust the energy released for active involvement .

The public school system is self-perpetuating and non-corrective. As it becomes larger, it becomes top-heavy, so that often less than half of the employees are teachers. The desire by those out of contact with the students to know what is happening creates time-consuming accounting, regulations that are unreal to the students, classes of unruly mobs, and impersonal distance between authority and subject.

Learning must proceed from the students and flow along their channels of interest. The teacher's job is to strengthen the flow, remove obstacles from the path, and entice enthusiasm to branch out into the many fields of human delight. Excessive control from above sucks energy from the system, which can only be captured by damming the natural flow of bubbling enthusiasm to create a quiet, passive, artificial mind that is slowly silting up. What happens when the dam breaks? Authorities shudder at the thought, and quickly add another regulation.

The school system cannot change from within; it lacks the integral vision. It may produce well-disciplined, law-abiding citizens, but what treachery to turn them loose into a society ruled by leaders without vision and laws that have lost their meaning in the maze.


We must begin a radically new orientation to education, even if it is not appropriate yet for the majority. Radical is defined as, "arising from or going to a root or source; fundamental; basic." In mathematics, a radical number can he approached by a fraction or decimal, but it can never be exactly pinned down; it is an irrational number.  (The circumference of a circle, pi, the diagonal of the square, the square root of 2, he diagonal of the cube, the square root of 3 are all radical numbers, quite real to our perception but unmeasurable.) This is the problem we face in trying to define fundamental, basic education, and, how totally different it is from the preprogrammed education we are used to. Fortunately, just as an irrational radical number can he seen to be as real as a rational number, radical education can be seen to be a real alternative to our present system, which reason might convince us can be modified to fulfill our needs. The path of warring duality in denial can never lead to integrated, harmonious self-discovery.

CUBE_MERKABA202An analogy may clarify this point. Let the institutional view of basic education be represented by the square, the shape we are most familiar with, each side measuring one unit. (diagram above) This is the right shape to begin with, we reason, since one is the most elementary number, and all the angles are "right", 90į, the angle we make with the surface of the earth when balancing against gravity. We measure our world with this angle; front-back, left-right, up-down; length, width, height; all at right angles to each other. If we slice space with three planes at right angles to each other, assuming that any slice parallel to another is the same slice, since they never intersect and must be therefore be connected at infinity. This means we can define every point in our three-dimensional world by the cubeic matrix in space.  Therefore, we think, this must be the proper shape to build our institutions of learning. But when we try to construct our square environment in the real world, we discover that our framework collapses unless we add at least one diagonal brace on each side, which length is ÷ 2, a radical, irrational number, so defined because we cannot measure it exactly with our square ruler. But we can measure it accurately enough to build with, so we finish building our school, write into our building codes that all buildings must have diagonal braces, and proceed to educate our pupils with knowledge assembled from the four corners of the world.

But we have overlooked a fundamental fact that is now outside the knowledge of our system. The six diagonals of the six sides of our unstable cube form a simpler structure, which stands rigid by itself. It has four sides instead of six, four corners instead of eight, and six edges instead of twelve! But alas, from corner to corner it measures 1.4142135......etc., etc., an irrational, impossible number to work with!  Besides, who can even pronounce its name, tetrahedron, and how confusing to think of it in terms of length, width, and height! So we can approach an understanding of the tetrahedron, but never clearly see it, for to do so would necessitate enthroning the tetrahedron as our one ruler (which would make the square world irrational, measuring ÷ 2/2), and thinking in four dimensions, rather than three. We would have to develop a whole new way of thinking, based on this new conceptual framework and "irrational" system of logic. The world would look as different as it does through the eyes of an Indian astronomer compared to an American psychiatrist. But it would be as real a world as the square, three-dimensional one, perhaps even more so, since when we account for the two possible diagonals of the cubic sides, we get a dual tetrahedron, which is the foundation of the energy matrix which determines the structure of our crystal world of atoms! Just as admitting irrational numbers into the world of real numbers has opened new vistas of mathematical discovery; so there is now the need of an "irrational" approach to education to give our nation a balanced vision and direction.

An individual with a predilection toward seeing from as fundamentally different a perspective as our example would find the public school environment alien to his nature, for public education in America has long had the job of homogenizing diverse cultural elements into a cultural identity. The emphasis has been, consciously or unconsciously, on developing a standardized American perspective, discouraging radical diversity of thought. Now we are so thoroughly Americanized that a wave of discontent and disillusionment is sweeping over the land. We open our eyes to see that unity has come to mean stifling uniformity, and justice has become the slave of mediocrity, for all the ruling elite. What has happened to the invigorating delight of diversity, the freedom to be different, for which we have shed the blood of countless thousands?  It lies dormant in all of us, crying for release from the cultural, institutional mold .

Deep within all of us we feel a uniqueness, that if we could but fully express it, would make us so different from anyone else that there would be no competition, no jealousy, no hatred; only a harmonious play of such vitality and strength of diversity that it would truly be heaven on earth. To nurture this divine personality should be the aspiration of our school.

We need an alternative fundamentally different and divorced from the present system. Otherwise we will never be able to see the forest from the trees. It must be deeply rooted in the noblest aspirations of all our ancestors, back before our blood was joined on this soil. It must be universal in scope, uniquely American, but exclusively designed for this particular community. To the extent it is founded on the principles that built this nation, it must to the same degree be free from the constrictions that are strangling it. This requires the good will of the community, which can best be acquired by focusing on positive concrete proposals, not reacting against the present school system. If it is radically different, it will present fewer territorial challenges to the present system and trigger fewer built-in reaction patterns, provided it is founded on principles revered by the majority of us.

Education is a process of bringing out from within an awareness of the forces, forms and laws of being that exist in this universe of ours. Before a mental consciousness can evolve, there must proceed a physical and vital involvement. Otherwise a blind knowledge, without personal verification, develops, and this leads to distortions of all kinds. So our approach to education must be experientially based, both with the physical senses and with the vital emotions. For example, the experience of swinging through the air at a tempo determined by the length of a trapeze rope, the force of gravity, the arch of the body, to intercept the connecting rhythm of another swinging trapeze rope of different Lengths, provides a familiarity with the law of motion of a pendulum such that the truth of the equation t = ÷2*pi*1/g is immediately recognized, rather than memorized when formal study of such laws has progressed to that degree of abstraction.

Simply stated, the richness and fullness of life can only be fully appreciated by living it with every nerve and fiber of our body, not just in the cool elegance of our thoughts. Alan Holden, a renowned physicist-mathematician, stresses this in the preface to his book, Shapes, Space, and Symmetry, "Space provides no three-dimensional blackboard. We learn about space only by living in it. A child climbing in his jungle gym may learn more about it than he will ever learn again, for his books will be made of 2-dimensional sheets of paper."

First and foremost our school must be a living experience, involving the whole being in a rich interaction of interests from sports to academics; social, sexual, cultural, creative, artistic, spiritual pursuits. This sounds like the ideal description of our preferred life. Why the need for a special school environment? The following discussion will focus on one answer to this multifaceted question: the need to isolate and simplify in order to focus upon the basic laws of life's overwhelmingly complex expressions. Our school should be an archetypal setting, where teacher and pupil can establish basic rhythms, play with the elementary laws of the universe, pursue their emotions and energies with guidance, build insulated cocoons when the urge takes them inward, and pursue in concrete form their most treasured fantasies.

Let us pursue a fantasy now, and picture a possible form of "elementary" school environment, from the perspective of mathematics and physics. Our universe is composed of energy in definite patterns of space and time. Let our school structures express these archetypal contours. We are not familiar with the shape of atoms in crystal array, the harmonious pattern of their interactions, yet most of the world around us is built upon these few fundamental relationships. These forms would make elegant buildings, providing the potential for an integrated modular building complex of infinite variety, and moving within their patterns would awaken a sense of the universal rhythms of life in mater.

We are quite familiar with the cube, so exclusively familiar, in fact, that its three dimensions we consider to be at "right" angles to each other. All other angles are felt to be less perfect, not "right", despite the fact that the "right" angle for the atomic structure of the majority of the earth is 109į 27' 16....", a radical, unfamiliar angle. Gravity forces us to relate to the earth at right angles, thus it seems appropriate that the ancients should have seen the cube as the elemental form of the earth. But they knew other elements and other elementary forms: Earth, Air, Fire, Water, and Ether are expressed in pure form as the Cube, Octahedron, Tetrahedron, Icosahedron, and Pentagonal Dodecahedron, respectively.

          the All Five Puzzle02 

These elementary shapes, with every edge and angle identical, are truly archetypal, for they are the five simplest (regular) vibrations of space. Plato was so fascinated with this truth that they are commonly referred to as the Platonic Solids.

What difference does the shape or orientation of a structure have on the consciousness that develops within it? Acoustically, the cube has the greatest echo, because there are two opposite walls to reverberate in each of its three dimensions. The cube has the greatest reflective symmetry, expressing duality in the highest degree. No wonder it is so familiar to us! The tetrahedron, fire, simplest of all form, has no reflective symmetry. Who is familiar with tetrahedral space? Surely we would feel different in a bare room that was as 'live' as a cubic handball court, but with no direct echo. Shouldn't we be experimenting with these elemental forms?

We have learned to focus, filter and direct light through physical matter in the shape of lenses, prisms, mirrors, crystals. Other frequencies of vibration close to light we are learning to control, such as heat, radio waves, x-rays, microwaves, etc.. But existence expresses itself as an infinite variation of vibrations, and we must have the potential for awareness and control on levels undreamed of by most of us blind souls. If we can put together materials of a particular atomic shape into a certain relationship, and focus our familiar vibrations, why not likewise for these other octaves of awareness? Research into the Great Pyramid of Cheops and many deliberately shaped and oriented structures and lines of communication throughout the world overwhelmingly suggest that the ancients knew how to control fields of energy unfamiliar to us outside of our fables.

Let us pursue this quest for ever-expanding sensitivity and control by organizing our school environment based on these teachings, from the Great Pyramids and Chinese geomancers to Theodore Reich, Victor Shauberger, Buckminster Fuller, and a host of great teachers of all persuasions. History has placed in our hands the collected knowledge of all the peoples of the world. Our task is to thoroughly enjoy the diversity and the unity. We know not how, until we have experimented with it. We know not when, beyond our creative presence, where it arrives in perfect step.  The physical school environment is a logical place to begin.

There are simple mathematical curves that represent fundamental flow patterns of energy in our world. Let us build our playground from such patterns. Gravity, for example, flows most elegantly along certain curves. A ball rolling down a track in the shape of a catenary curve will reach the bottom quicker and be going faster than on any other shaped track; the tractrix curve changes direction smoothest of any curve; and the parabola is the path taken naturally by a projectile under the influence of gravity. Let us combine these curves to make a "roller coaster" where children can experience these 'truths totally, integrally, The supporting framework could graphically demonstrate how these curves are generated mathematically.

If the student is to develop a balanced sense of the flows of energy within his/her environment, the school should be as self-sufficient as possible. How much energy is used to heat the buildings? If this energy comes from outside, from an oil truck or power pole, the student never really learns that reality. If part of his/her education is dealing directly with this concern, she/he will learn the balances of ecology, learn conservation of energy and establish the basis for a simpler, more direct life-style. Let us incorporate into the school solar heating and lighting, windmills, wind turbines and water pumps, rainwater collection and storage systems, various methods of power storage, such as batteries, electro-gyroscope, elevated water reservoir, rock-, water-, earth- heat storage systems, electrolysis of water and use of the hydrogen/oxygen for welding, lighting, etc. Students could have numerous jobs monitoring the equipment, where they would become aware of the cycles of the sun and wind, and the translations of energy forms one into another. With such a familiarity with energy systems, the laws of physics and chemistry should appear much more obvious and practical.

Wood is an important materials in our life, yet we are blindly consuming our forests with little awareness of forestry management and the many properties of wood. Let a tree farm be part of our school, with students actively involved in cutting firewood, logging, replanting new species, developing park areas, and keeping track of the life of the tree farm. They could graft alder archways for blackberry farms, grow ornate furniture and all sorts of trained tree creations. Lumber for new buildings and furniture could be milled and seasoned by the students. They would develop a greater reverence for wood and the objects made with it, as well as a greater knowledge of the material and how best to use it.

Food is one of our most basic needs and should certainly be a primary focus of an enlightened education. It would seem appropriate to have a school farm, where all the foodstuffs of a balanced diet could be cultivated. Here, knowledge of local weather, soil, natives, particularly well-adapted species of plants and animals, and the collected experience of local farmers could be assembled, further experimented on, and that accumulated knowledge made available to the larger community.

In a traditional school environment, where everything closes down at 4 o'clock, such a farm, especially where animals are involved, is impractical. Yet, if our school is to offer a real education for life in its unpredictable fullness, we cannot turn it off and on like a TV set, so we must expand our vision. The radical picture that comes to mind is a community of boys, girls, men, women, babies, pets and barnyard animals, many living "on campus" for periods of time, pursuing numerous ongoing projects for internal development, economic venture, "pure research" and pure fun. Various trades and skills would be practiced, with emphasis on perfection of the art of living by the harmonious integration of the necessities and fascinations of life.

All actions would be guided by the goal of establishing a radically new and universal Earth Consciousness of loving grace, and creating the fertile environment for its growth.

FUNdamental Geometry ~ the Geometry of Natural Form

Preliminary Course Description

Discover the elegantly simple and magically interrelated geometries underlying nature. Learn the language of Form fundamental to Science, Art, Engineering, biology, etc..  Explore the interrelationships of crystal structures, life forms, space grids, the Platonic Solids, the Great Pyramid, bridges, bubbles, honeycombs, sunflowers, sound reflectors, the Divine proportion, curves & curved space, etc. Play with geometric blocks, puzzles, construction sets, marbles, soap bubbles and films. Build a new world of archetypal forms with straws & cardboard, etc.

Geometry of Natural Form has been a passion of mine for 35 years.  I have come to realize how elegantly simple and aesthetically beautiful are the underlying forms and principles upon which nature builds to create everything from atoms to honeycombs.  I have constructed many models, blocks, puzzles and construction sets to illustrate the magical interrelationships of elementary forms, and when I show them to people, they too get excited and often comment that they wished mathematics had been as fascinating and understandable in school. I feel that this subject should be part of basic education and could be introduced in elementary school with blocks and construction sets. 

The geometry of natural form is fundamental to many fields of interest.  The engineer will find the strongest, most modular and most easily analyzed structures in the crystal world.  The chemist, electronics engineer, geometrician, biologist, botanist, etc. will see their fields magically intertwined at their roots.  The artist and metaphysician will delight in the infinite simplicity of archetypal forms that interpenetrate, transform, and reappear continually in nature's intricate dance.

A sense of order is essential to everyone's stability and sanity.  An awesomely simple order underlies our complex physical world, and in its recognition lies the potential for liberation from our flat superficial world-view. The student should leave this course with an elementary mastery of an archetypal design language from which to understand the universe and evolve his/her own unique forms of expression.

Students will be continually challenged to see the myriad interrelationships between elementary forms. They will make models of straws and paper and play with construction sets, geometric blocks and puzzles. students will need pencil, note paper, ruler, compass, protractor, and colored markers.  They will also be asked to bring to class examples of flowers, honeycombs, crystals, etc. that they have ready access to without cost.

 I have taught classes on this subject at Tomanhaus School and Community School on South Whidbey Island; at Evergreen School for the Gifted, and at The Northwest School in Seattle. I have built scores of geometric models, puzzles and construction sets, geometric playground equipment (featured on television), and houses and domes based on crystal facets.

8. Describe your teaching/training background.   I taught 4 years in Peace Corps, India, and Peace Corps training programs in the U.S.; 3 years mathematics, film making, and tumbling at Tomanhaus School on Whidbey Island; and Geometry of natural form at 4 other  public & private schools. I have further communications experience in acting.

The following is a course outline for my teachings in FUNdamental Geometry:


    Session one

  • Our 3-dimensional world: how we perceive it.
    • an etymological perspective
    • normal, right, real, orthodox, radical, dimension, etc.
  • The Cube as the foundation for 2-dimensional thinking
    • the cube inside-out: the rhombic dodecahedron
    • the face-centered-cubic crystal structure: different ways of perceiving space
  • The tetrahedron within the cube - a more fundamental form
    • The diamond bond and the true diamond shape: the building blocks of both organic and inorganic world
    • a class shape-preference pole

    Session two

  • The diamond as the foundation for 3-dimensional thinking
  • seeing cubes in the diamond matrix
  • garnet
  • honeycomb
  • stellated rhombic dodecahedron
  • moving from one space grid to another
  • ÷2,÷3 as primary proportions
  • atomic refraction photos
  • Class construction project
  • Session three

  • Space-filling shapes
  • tessellations in 3-D
  • cube
  • rhombic dodecahedron
  • tetrahedron with octahedron
    • Buckminster Fullerís Tensegrity structure, Vector Equilibrium
  • Why there are only 92 natural elements
  • playing with blocks & puzzles
  • discover the body-centered-cubic crystal structure
  • discover the diamond crystal atomic shape
  • class project---building a space grid
  • Session four

  • Atoms as spheres
  • playing with marbles, building crystal arrays
  • seeing space as interfacing energy waves or as interpenetrating energy grids
  • dual forms and dual grids
  • playing with soap bubbles and soap films
  • the diamond bond angle as a universal relationship of balanced proportion
  • soap film curves
  • hyperboloids, hyperbolic paraboloids, curves of all straight lines, and curves of zero curvature
    • interconnecting curved planes in elementary space grids to form interpenetrating space volumes
  • make your own unique curved space matrix
  • Session five

  • The five Platonic Solids
  • their mathematical and mystical significance
  • Volume ratios based on the tetrahedron
  • The three geometries of the world of matter
  • The two geometries of Life forms
  • viruses, pollen, spores, radiolaria, flowers, etc.
  • fundamental reproductive differences of the two geometry classes
  • Playing with blocks and construction sets
  • Session six
  • The Divine Proportion:
  • The Fibonacci series and the five-pointed star
  • ÷5 as the basis of  magical interrelationships of branching patterns in nature
  • class show and tell
  • Session seven

  • The Great Pyramid of Cheops as a synthesis of  and
  • The magical number 25,920
  • The procession of the equinoxes
  • rhythms of the human organism
  • earth's size and gravity
  • The concept of "Universal Energy Matrix"
  • The Earth is a giant crystal
  • The Russian hypothesis
  • power spots, weather fronts, natural energy grids on Earth
  • Session eight

  • Fundamental curves and their properties
  • The conic sections, circle, ellipse, parabola, hyperbola
    • elliptical, parabolic & hyperbolic reflectors
  • the catenary curve and its relationship to the parabola
  • bridges and spinning buckets
  • the tractrix
  • freeways and bearings and grinding stones
  • how they all interrelate
  • curves for windmills & gears
  • Session nine

  • Putting it all together
  • architectural applications
  • class project: building a campus of the future with geometric blocks, construction sets, and student-designed structures.
  • Session ten

  • Class project, continued
  • student and teacher reports on relevant topics of general interest

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