The Shape of the Universe

By Howard Rheingold

Originally published in Whole Earth Review.

If you are fortunate enough to share a neighborhood with a leafy elm, a gnarly oak, a soaring redwood, take another look at its silhouette against the sky. That self-similar 4-D explosion of branching branches is a clue to a cosmic riddle or two and a key concept in fields as unrelated as vascular surgery and software design.

The Buddha knew this, and so do neurologists, database programmers, and mythologists.

Axis mundi, the axis of the world, is the tree at the center of everything sacred. Mythologist Joseph Campbell, referring to the Buddha's awakening, noted that: "This is the most important single moment in Oriental mythology, a counterpart of the Crucifixion of the West. The Buddha beneath the Tree of Enlightenment (the Bo tree) and Christ on Holy Rood (the tree of redemption) are analogous figures, incorporating an archetypal World Savior, World Tree motif, which is of immemorial antiquity."

To Hindu dream adepts, the question of how you know that you are awake is at once psychological and metaphysical. David Shulman, in Tamil Temple Myths, discussing a character in a myth who realizes that he is dreaming the tragedy of his life, notes: "The nature of his delusion is clear from the moment he first catches sight of the upside-down tree — a classic Indian symbol for the reality that underlies and is hidden by life in the world, with its false goals and misleading perceptions."

To say nothing of the Garden of Eden and its two special trees. Why do trees always happen to be on the set when God talks? It doesn't matter whether your cosmology is Hebrew, Christian, Hindu, Buddhist, Pagan, Shamanist or Animist: trees are always part of the scenery when a theophany happens.

Tradition has it that the Buddha's tree was the type known as "pipal" (ficus religiosa), and that it was precisely as old as the fellow who sat down in its shade to catch a case of satori. The legends linking "the one who awakened" and this particular variety of tree hold that Sakyamuni, as he was known pre-enlightenment, had a lifelong habit of sitting under pipal trees that were exactly his age. It was also written that Buddha's mother (aka Maya Devi) held onto the branches of a pipal when she gave birth to him. This tree-grasping birth pose is important enough to rate its own name: salabhanjka pose).

Why a tree? Why not a seashell, a lightning bolt, an old man with a beard? The iconography is not strictly Asian. Ygdrassil, the world-Ash, is Norse. The Druids were far from India and China. The theme surfaces in folk tales, holy books, cave paintings, tiled mosques, and frescoed chapels in every part of the globe. The Chinese saw it as a giant peach tree that bears the fruit of immortality. Every year, as the winter solstice approaches, hundreds of millions of Christians place a symbolic pine tree in their houses and cover it with ornaments. The Yule log dates back to Druid and Celtic customs of pre-Christian Britain, which at one time was covered in dense forests. In the nineteenth century, German scholars discovered that the word temple is derived from the Indo-European roots meaning "sacred grove."

The visual representation of a tree that branches at both ends is a model of the universe as a living organism, a metaphorical map that serves equally well for the cosmos external to the individual and the spectrum of consciousness deep within — with its highest branches in the heavens and its roots deep within the dark underrealm.

Are we also drawn to trees because our minds know that our brain structures are tree-shaped? Do these signatures of our internal informational systems keep emerging in symbols of our deepest religious impulses because they are what nineteenth-century anthropologist Adolf Bastian called Elementargedanken — "elementary ideas" that are hardwired into our brains? Our nervous systems are shaped like trees, and so are rivers, capillaries, data structures, probability worlds, solution-spaces, chess games, and chain reactions. Our ancestors lived in trees, not too long ago. It's no wonder that Sakyamuni sat under one when he was ready to awaken.

Trees are talismans of sanity and wholeness to Western psychotherapists as well as to Eastern mystics. According to Jungian psychoanalysts, the appearance of a tree in a dream can be fortuitous, in the sense that it often symbolizes, empowers, and heralds a movement toward wholeness of the personality. Marie-Louise von Franz notes that: "Since...psychic growth cannot be brought about by a conscious effort of will power, but happens involuntarily and naturally, it is in dreams frequently symbolized by the tree, whose slow, powerful involuntary growth fulfills a definite pattern."

One characteristic that doesn't vary much from one tree to another is the way components of the tree, the larger and smaller branches and twigs, reflect the shape of the entire tree; a computer programmer would recognize the tree as a "recursive structure" (because the same pattern "recurs" at both the top and bottom levels of organization). As the European alchemists of the middle ages would say: "As above, so below."

This shape that makes trees and other things look treelike brings a new perspective to several important questions about the way things work: How can you keep track of a billion units of anything and make sure you can find each unit as quickly as possible? How do you move things from one point to many other points most efficiently? A recursive, branching, tree shape is the visual analog of the answer for both questions.

A tree of the botanical variety is shaped that way because a branching plant efficiently collects moisture from the earth via ten thousand roots and distributes it rapidly to ten thousand leaves. (Kabbalism, the Jewish mystical tradition, depicts the path to God-consciousness as a tree-shape with the explanation that this is the way to distribute God-consciousness to numberless sentient beings.)

Examine an aerial photograph of a river delta next to an X-ray arteriogram of a human lung and you'll see that branches aren't limited to forests. Rivers branch as they run into their own sedimentary deposits because an arboreal shape is the most efficient way to distribute the river's flow when the main channel suddenly becomes shallow. Pulmonary arteries branch because this enables the lungs to distribute oxygen to the blood rapidly. The branching of nerves and blood vessels in the brain is known as "arborization."

Quantum physicists even dreamed up fourth-dimensional trees. Because of certain aspects of the equations describing the transformations of electromagnetic energy, it is possible to hypothesize that the universe is an infinitely branching entity. This formally permissible (if as-yet-unconfirmed) logical consequence of the equations describing the transformations of electromagnetic energy is known as "the many-worlds interpretation." Your lifeline and mine, called "worldlines" by quantum physicists, branch when we make decisions, take action, hesitate, move, or stand still. There are worlds in which you are the Buddha and worlds that are exactly the same as this one, except you part your hair on the opposite side. The abstract space of such a universe, filled with infinities of non-intersecting branch universes, is a fourth dimensional tree that grows at a rate incomprehensible to 3-D mindsets.

A tree can be a map of space or time or psyche, or it can be a map of information. Tree-shaped data structures are essential parts of all computer software systems because trees offer an effective and orderly way to store and retrieve large amounts of binary information. Trees in which each branchpoint leads to exactly two branches is the direct visual analog of a binary code, because you can get from the trunk to any one of the leaves by making either one of two decisions at each branchpoint.

You could assign a unique address to every leaf on a tree by specifying the binary decisions that a bug would have to make directly from the trunk to that leaf. You could specify the leaf on the first right branch after the first left branching of the right fork of the main trunk and call it "right-left-right," or, for that matter, "010" or "101" — which happens to be the fundamental alphabet of digital computers.

To programmers who are trying to write software to emulate human problem-solving, tree-shaped strategies are "a way to fan out quickly into a solution space." The first computer chess programs tried the "brute force" method of evaluating the consequences of every possible move at every step of the game, but the most powerful computers then and now bog down in the explosion of possibilities that happens if you try to look down too many branches in a recursively branching structure. It was Claude shannon, the father of information theory, who demonstrated that the explosively branching tree of possibilities is destined to destroy any brute-force approach after only a few steps. Among AI programmers, the creation of increasingly effective search-tree-pruning algorithms has become a grail.

Kids know about trees, and the easiest way to remember what the world like when you were a kid is to climb a tree. Kids climb them, lie down under them and look up at the dappled sunlight, hang swings from them, build houses in them, paint pictures of them, collect their leaves. Today's kids know that trees are disappearing because of human activity, and they know that trees are the lungs of the biosphere. Which means the act of planting a tree with a child has taken on ecological as well as psychological and spiritual significance. Years ago, I discovered a Bantu word that can teach us something valuable: mahamba.

A mahamba is a "spirit-tree" that is planted when a child is born. Can we make tree-planting both a part of family life and a sacred act again? We could start with a new meme — an idea deliberately designed to be infectious.

As soon as possible after birth, take the child and its parents to plant a mahamba. Make sure that the tree is native to the local environment and that it will be accessible in the future. Finding a proper place to plant and obtaining an appropriate seedling might not be easy; overcoming these obstacles is the spiritual offering of the child's sponsor. As soon as the child is able to walk, bring him or her out to meet the tree and to feed it. Encourage the child to take over the care and feeding, and seal the responsibilities with gifts. Continue reinforcing the merit to be gained from the act, in whatever terms the child understands: The legend of a tree that brings good fortune might be one of those harmless myths that can teach more than a hundred hard facts. And the simple act of nurturing a tree, distributed memetically, repeated recursively, might help our species get a grip on our planet's runaway throttle.


Martin Buber, I and Thou, Scribners, 1958.

Joseph Campbell, The Hero With a Thousand Faces, Princeton University Press, 1949.

V.S. Nararane, The Elephant and the Lotus, Asia Publishing House, 1965.

M.S. Randhawa, The Cult of Trees and Tree Worship in Buddhist-Hindu Sculpture, All India Fine Arts and Crafts Society, New Delhi, 1964.

David Shulman, Tamil Temple Myths, Princeton University Press, 1949.

Marie-Louise von Franz, "The Process of Individuation," in C.G. Jung, Man and His Symbols, Doubleday 1964.

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