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Unicycle, the Book of Fictitious Symmetry and Non-Random Truth (Nature’s Democratic Pi)

A mathematical novel with a new proof unraveling some of the consequences of nature’s all-prevasive asymmetry: reasoning that all absolutes, from pure symmetries to would-be absolute monarchs, dictators and God Himself, must self-destruct in the asymmetric reality, ultimately preempting their own existence. The ethical consequences will delight advocates of secular democracy and the separation of church and state. And fiction gets curiously real, even to deductions in favor of immortality of soul.

Please scroll down for back cover transcription.


“Very scrupulously set out. It is extremely well written and beautifully literate.” —Dr. Diané Collinson, author of Plain English, Fifty Major Philosophers, Fifty Eastern Thinkers, coauthor of works including the Biographical Dictionary of Twentieth-Century Philosophers

“This book contains some serious mathematics—smart, thought-provoking, and engrossing.” —William H. Barker, PhD, Isaac Henry Wing Professor of Mathematics, Chair of the Mathematics Department, Bowdoin College, coauthor of Continuous Symmetry: From Euclid to Klein

“A provocative book by a serious thinker, well worth the reader’s time.” —William A. Haviland, PhD, Professor Emeritus, founder of the Department of Anthropology, University of Vermont, coauthor of textbooks including the bestselling Evolution and Prehistory: The Human Challenge, and Cultural Anthropology, author of At the Place of the Lobsters and Crabs: Indian People and Deer Isle, Maine, 1605–2005

“An eloquent explanation, with spare logic and excellent argument. In my critical thinking class, my students study the core ideals of the Enlightenment; this book’s world view gives me a position from which to triangulate between absolutism and relativism and illuminates all three.” —David S. Cook, MSc, author of Above the Gravel Bar: The Native Canoe Routes of Maine

“It’s an important book. I am very impressed. It covers a lot of territory, and it is very thoughtful and even charming. The math and logic are understandable to the interdisciplinary reader. I agreed with everything the book has to say.” —Esther Pasztory, PhD, Lisa and Bernard Selz Professor Emeritus in Pre-Columbian Art History and Archaeology, Columbia University, author of groundbreaking books including, Thinking with Things, Aztec Art, and Teotihuacan: An Experiment in Living

Author’s Note

At the end of his philosophical comedy, Religulous, Bill Maher says we must either “grow up or die.” In pursuit of a few basic answers I have been attempting, somewhat paradoxically, to take his advice most of my life. When we stop growing up we become the posturing “adults” I used to watch and wonder at as a teen. These adults seemed to think they had all the answers—and so many teens are pressured to look jaded, like they’ve seen it all. I didn’t want to grow up like that. But I loved fairy tales as a child, and later on I realized that this was also called “folklore” (a more grown-up expression) and “mythology,” which was religion when the human race was even younger than we are now. Isn’t there some way to grow up and still believe enough for the stories to be true enough, so we don’t have to leave it all behind and become “adults”? Adults who believe in fairy tales?

When I hear of a suicide bomber who murders men, women, and children with the idea that he or she will go to a paradise of ancient lore, it is like hearing something too horrible even for the Brothers Grimm or Lord of the Flies. When I hear a leader declare something like a crusade or jihad against another system of belief in folklore and mythology, I get that same feeling of children killing each other. In a sense, the terrorist, no matter how frightening, never got into growing up. While that may not be much of an excuse, lack of that particular excuse does not mean there is no shared responsibility. How many of our elders are responsible for the stories we tell?

But they are just stories, are they not? The power of what can seem nothing more than an idea or a fairy tale can be vast and projected over thousands of years by the force of human nature when it becomes religion. Without wishing to sound too responsible, I feel it’s a matter of citizenship to tell each other stories in ways that clarify and question where the fiction might be—and the truth—and that leave opportunities for the next storyteller to come along. As a publisher it has especially been my mission to contribute to the process of growth that keeps at bay the self-arrogation of “absolute truth” that confuses our grownups and children alike.

I have been fortunate in having some teachers who were so good that I began to get the sense that it might be possible continuously to advance the frontiers of the discovery of the truth in fiction and of the fiction in reason. Experiences in literary analysis encouraged me to wonder if it might not be possible truly to identify the greatest fictions of all in our most powerful mythologies—even to the logical uncovering of God Himself as a character in a long-standing story. The fact that God is regarded by many as so obviously a fictitious character does not, of course, make it so. Meanwhile my love of mythology would not be satisfied with an empty character. The problem was worse that I had thought.

Characters must be believable. This means there must be truth in them. Otherwise their credibility is only based on our gullibility. That’s not good enough for good fiction, let alone great works. I feared that to close the door on the credibility of the God of monotheism, for example, as mythology or otherwise, was to empty fiction in general of credible characters. Not because the character of God is so important to fiction, but any test that could be used to empty God of truth could be used on other characters as well. And what about us? Literature would become a paltry thing to be enjoyed only by the naïve or the cynical, who are in many ways closely related in decadence. How would the credibility of any individual survive? We can see these complicated interactions as we hear concerns about the infantilization of a proud American people dumbed down to a monoculture by cynical overachievers.

“King and country!” where God is king, is too often the result, with the rule of law in subservience. The problem has long been to find a reason for democracy, especially now to counter a culture of unreason. Violent revolution, though necessary in the Age of Reason, is no longer so rational an option with weapons of mass destruction.

But a logical reason for equal opportunity requires that elusive connection between nature and democracy alluded to in the Declaration of Independence as the “Laws of Nature and of Nature’s God,” where “we hold these truths to be self-evident,” though we had not been able to prove them intellectually. Quite the opposite; philosophers cleaning up the reasoning of their predecessors increasingly identified errors in the attempt to draw ethical conclusions from observations of nature.

After many spare moments untangling these conundrums, I have finally got the following results to present for your consideration. The questions involved are fundamental enough to require a varied exposition, where God may no longer seem so prominent in the maze.



Author’s Note    ix
Acknowledgments    xi
Of Myth and Reason    xv


Samuel’s Introduction    3
The Maze Tale    9
The Ancient Paradox    11
Definitions of Asymmetry    15

II    Changes

1.    I Revisit the Transformation Proof    19
2.    The Gnome and the Onion    28
3.    Salmon Barbecue    41
4.    Alice Disproves God and Deduces the Soul: Out of the Box of Everyday Awareness    46
5.    Alice Disproves God and Deduces the Soul: Nonrandom Multifarious Polarity    58
6.    Alice Disproves God and Deduces the Soul: Fundamentality    66
7.    Samuel Passes the Torch    71
8.    At the Pearly Gates, by Rolo    73

III    River of asymmetry

9.    Transition    79
10.    The Lady of the Lake or The Rings of Pi, by Rolo    81
11.    Context and Induction, by Lola    91
12.    Totalitarian Math, by Rolo    96
13.    Manitous    102
14.    Samuel’s Essay: Extremely Low Asymmetry    108
15.    Samuel’s Essay: Which Number Two Now?    114
16.    Samuel’s Essay: More About the Absence and Something About Set Theory    116
17.    Samuel’s Essay: The Largest Number Proof, Etc.    131
18.    The Jinniyah and the Greatest Number, by Rolo    159

IV    Aquilah and the Lamp, by Lola

19.    Awakening    169
20.    Genies in Bottles, by Rolo    172
21.    Quill Pen    178
22.    Aquilah’s Essay    183

V    The Tea-room Scenarios

23.    By the River    190
24.    Infinity and the Book of Changes, by Rolo    193
25.    Alice at Tea    202
26.    The Gingerbread Variable, by Rolo    216
27.    Molly    224
28.    Russell, Chapter 13    228
29.    Streams of Paradise    232
30.    Atlas Speaks    239

VI    Stirring the Pot

31.    The Asymmetric Economy, by anonymous economist    255
32.    Asymmetric Evolution, by extraterrestrial high school teacher    266
33.    Philosophical Habitat, by interplanetary inhabitant of no fixed abode    283

Notes        305
Bibliography    309
Author    310

Democracy — a force of nature (Back cover transcription)

The unicycle provides a singular image of balance and impending peril, lifted by whimsy for the weighty subject of this book. All the evidence of experimental science confirms that nature is asymmetric. No pure symmetry has ever been found. What does it mean to live in an asymmetric environment?

Unicycle introduces the logic of asymmetric change to interpret the evidence, while showing how our symmetry-based math has failed to grasp a vital ethical connection between humanity and the environment. The observation that nature is asymmetric allows us to introduce reasoning that is as organized as the logic of symmetries currently in use, by using symmetry as a foil in a proof by contradiction. One result is the discovery that nature, the universe, does indeed have a non-random sense of direction with vital ethical consequences.

Humans are drawn addictively to pure symmetry in the form of absolutes, like moths to the flame, or in this case — like fools to the unicycle. The more extreme the instability, the greater the requirement for balance. There is a Tao-like polarity where neither pure chaos nor absolute order can exist. The more monocultural we become, the more we need to reach out for balance, as though we are bound for chaos. We must learn to navigate the River of Asymmetry.

A key finding is that symmetry and asymmetry are mutually exclusive. That nature’s asymmetry is a creative continuum that cannot be stopped with absolute finality. That what connects us is more profound than the differences that divide us. Nature’s asymmetry is multifarious and fundamentally inclusive. This provides the ethical basis for a democratic society and a fresh understanding of natural law.

Economic value is nature-based — not confined to the prices of an easily distracted market. We are not to be valued by what we are paid. Business cycles can be balanced with cultural change.

The reasoning is elucidated with an interdisciplinary narrative fiction, including mythological tales. The stories gain a realism of their own through the deductions. Nature comes to life, along with the characters as they work on the book by a river in Maine — discovering Mother Nature’s moral compass.

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