Truth or Beauty: Science and the Quest for Order


In this sweeping book, applied mathematician and popular author David Orrell questions the promises and pitfalls of associating beauty with truth, showing how ideas of mathematical elegance have inspired—and have sometimes misled—scientists attempting to understand nature.

Orrell shows how the ancient Greeks constructed a concept of the world based on musical harmony; later thinkers replaced this model with a program, based on Newton’s “rational mechanics,” to reduce the ...

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In this sweeping book, applied mathematician and popular author David Orrell questions the promises and pitfalls of associating beauty with truth, showing how ideas of mathematical elegance have inspired—and have sometimes misled—scientists attempting to understand nature.

Orrell shows how the ancient Greeks constructed a concept of the world based on musical harmony; later thinkers replaced this model with a program, based on Newton’s “rational mechanics,” to reduce the universe to a few simple equations. He then turns to current physical theories, such as supersymmetric string theory—again influenced by deep aesthetic principles. The book sheds new light on historical investigations and also recent research, including the examinations ongoing at the Large Hadron Collider. Finally, broadening his discussion to other fields of research, including economics, architecture, and health, Orrell questions whether these aesthetic principles reflect an accurate way to explain and understand the structure of our world.

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Editorial Reviews


"Orrell swings from the ancient preoccupation with musical harmony and numerical ratios to Renaissance nature studies, the mechanistic approach and the physical sciences of today. Imperfect as it is, ‘messy’ science, he argues, has a novel beauty of its own."—Nature
Peter Woit

"Truth or Beauty gives a well-written, historically informed argument that science has gone off the rails....The question Orrell is addressing is an important and topical one."—Peter Woit, author of Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law
Margaret Wertheim

"A graceful and insightful history of the Pythagorean impulse to model the world in mathematical terms. Orrell analyses Western scientific culture's quest for order and links it to an essentially religious conception of beauty."—Margaret Wertheim, author of Pythagoras Trousers and Physics on the Fringe
Marcelo Gleiser

“If science is the search for truth, we’d better understand what is this truth that we seek. As David Orrell pointedly argues in this well-written and accessible book, modern science runs the danger of being blinded by an overarching aesthetic prejudice—traceable back to Ancient Greece—that truth is necessarily wedded to beauty. Quite the opposite, the more we learn about the natural world, the more we are forced to accept a different kind of aesthetic based on the imperfect and the asymmetric, and no less beautiful for it.”—Marcelo Gleiser, author of A Tear at the Edge of Creation, Appleton Prof. of Natural Philosophy, Dartmouth College 
Robert Smith

"A lively and engaging work....The range of topics Orrell brings to bear is impressive, and I always wanted to keep turning the pages.”—Robert Smith, University of Alberta
The Sunday Times - Ian Critchley

"Fascinating . . . Orrell is an engaging and witty writer, adept at explaining often complicated theories in clear language . . . he argues persuasively that scientists need to let go of outmoded aesthetic notions and embrace complexity."--Ian Critchley, The Sunday Times
Canadian Science Writers' Association - General Audience Award

Shortlisted for the Canadian Science Writers' Association Outstanding Adult Book Awards.

"Orrell swings from the ancient preoccupation with musical harmony and numerical ratios to Renaissance nature studies, the mechanistic approach and the physical sciences of today. Imperfect as it is, ‘messy’ science, he argues, has a novel beauty of its own."—Nature
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Product Details

  • ISBN-13: 9780300186611
  • Publisher: Yale University Press
  • Publication date: 11/13/2012
  • Pages: 356
  • Product dimensions: 6.10 (w) x 9.10 (h) x 1.20 (d)

Meet the Author

David Orrell is an applied mathematician and popular author. In early 2012, he completed an honorary visiting research fellowship at the Oxford University Smith School of Enterprise and the Environment.

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Read an Excerpt


Science and the Quest for Order


Copyright © 2012 David Orrell
All right reserved.

ISBN: 978-0-300-18661-1

Chapter One


From harmony, from heavenly harmony, This universal frame began: When nature underneath a heap Of jarring atoms lay. And could not heave her head, The tuneful voice we heard from high: Arise, ye more than dead.

John Dryden, "A Song for St. Cecilia's Day"

Many people think that modern science is far removed from God ... in our knowledge of physical nature we have penetrated so far that we can obtain a vision of the flawless harmony which is in conformity with sublime reason.

Stephen M. Barr, Modern Physics and Ancient Faith

After a while, another voice said: One, two, three, four—And the universe came into being. It was wrong to call it a big bang. That would just be noise, and all that noise could create is more noise and a cosmos full of random particles. Matter exploded into being, apparently as chaos, but in fact as a chord. The ultimate power chord.

Terry Pratchett, Soul Music

For centuries, sages, mystics, priests, and more recently scientists have sought an explanation or model for the universe. A common component in many of these descriptions is a fascination with harmony. The Greeks thought that the cosmos was based on musical harmony, and this belief has persisted, in modified form, over the ages. Scientists ranging from Johannes Kepler in the seventeenth century to modern string theorists have used harmony to describe the universe. In this chapter, we put our ear to the ground and to the skies to pick up the timeless melodies that have entranced, inspired, and sometimes confused us since the dawn of science.

* * *

The Buddha observed that the question of how the universe was formed would only "bring madness and vexation to anyone who conjectured about it." Nonetheless, most civilizations have given it a try and produced some kind of creation story, an overarching theory that attempts to explain why things are the way they are.

In a Chinese version, for example, the universe began with the opposing powers of Yin and Yang, who produced an offspring called Pan Gu that grew for 18,000 years inside a great egg. When it finally hatched, the dark part (Yin) sank down to form the Earth while the light part (Yang) rose up to form the sky. After another 18,000 years Pan Gu died, and its dismembered body parts formed the Sun, the Moon, the stars, and all the rest of the universe.

In classical Greek mythology, everything began with Chaos, who gave birth to five progeny including Gaia, the Earth goddess. She in turn spawned Uranus, the sky, and Pontus, the sea; and then coupled with her own child, Uranus, to create more gods and goddesses.

Our current version of the creation story reconciles astronomical observations with studies of matter carried out at physics laboratories. According to this, the universe was produced from an infinitesimally small dot in an event known as the big bang. It happened about 13.7 billion years ago and we are still feeling the effects. The universe hasn't stopped expanding. In fact, rather mysteriously, the expansion is accelerating. We can hear the birth pangs of the early universe in the so-called cosmic microwave background, whose detection in 1964 provided tangible support for the big bang theory.

Scientists can only hypothesize about what happened in the earliest moments, but the story goes that all the fundamental forces that make up the universe and hold it together—gravity, electromagnetism, and the weak and strong nuclear forces—were united in perfect symmetry so that all things were one, in a kind of pulse of pure energy. As the universe expanded and cooled, the forces separated and distinguished themselves according to patterns that were programmed by mathematical laws. Recognizable particles such as electrons, protons, and neutrons emerged into being, all colliding together chaotically with tremendous energies. At this point, the universe was about a second old.

After a minute or so, protons and neutrons combined to form atomic nuclei, but the temperature was still some 3 trillion degrees centigrade. It would take hundreds of thousands of years more for the universe to cool sufficiently for nuclei to be able to join with electrons and form complete atoms. It took longer still for complex molecules such as water to appear; and it took about 9 billion years for the planet Earth to form itself from a swirling mass of vapor around the Sun.

Today, the universe has cooled to an average temperature of about -270°C. Most places on Earth are of course considerably warmer, thanks to radiation from the Sun. And then there is the Large Hadron Collider, where scientists—with the occasional break for complicated and time-consuming repairs—have been risking "madness and vexation" since 2008 to recreate, in a controlled way, the ultra-hot conditions that existed shortly after the big bang.

The technology is cutting edge, but its aim is ancient: to hear the flawless, heavenly harmonies that were present at the dawn of time.

Number Is All

The Greek philosopher Pythagoras didn't have a particle accelerator, but he too was preoccupied with the questions of where we came from, what we're made of, and where we are going. He also had a creation myth. According to the Pythagoreans—the quasi-religious cult he established in the sixth century BC—in the beginning there was Unity. It then divided into two components, the Limited and the Unlimited. These two, which were opposite, came together to form numbers, which the Pythagoreans believed formed the structure of the cosmos (a word coined by Pythagoras).

To the Pythagoreans, each number had its own meaning. One, the monad, represented the initial unified state which marked the creation of the universe—in today's terms, the state at the start of the big bang. Two, the dyad, represented the polarization of unity into duality, and was associated with change, mutability, and the feminine. Three signified all things with a beginning, middle, and end; while four represented completion, as in the four seasons that make up a year. The greatest and most perfect of all numbers was ten, the sum of the first four numbers, which symbolized the universe.

Pythagoras is best known today for his theory concerning right triangles, but his most profound achievement was the discovery that musical notes are governed by mathematical ratios. The story goes that Pythagoras was outside a blacksmith's shop when he noticed that the sounds produced by different hammers were in some cases consonant with one another, and in other cases inconsonant. Intrigued, he entered the shop to investigate and discovered that the hammers which harmonized well together had weights which were related by simple ratios, such as 1:2, 2:3, or 3:4.

As with much of what has been passed down about Pythagoras, this story was clearly made up; in fact the tones produced by hammers do not vary in proportion with weight. The story probably reflects an ancient tradition that associated wizardry and magic with blacksmithing. The idea does work perfectly, however, for the strings of a musical instrument. As the Pythagoreans also showed, a string plucked on an instrument such as a lyre will produce a certain note. Fret the string exactly halfway up (ratio 1:2) and the note raises an octave. Fretting 2/3 of the way up produces a musical fifth, and 3/4 up a fourth. Playing the three notes together on different strings gives a major chord.

These musical ratios of 1:2, 2:3, and 3:4 were represented by the four rows of the tetractys, shown in Figure 1.1. The Pythagoreans considered the tetractys to be a sacred symbol and associated it with both harmony and the Delphic oracle (see Box 1.1). A Pythagorean aphorism read, "What is the oracle at Delphi? The tetractys."

Since music was considered to be the most expressive and mysterious of art forms, the discovery that harmony was ruled by mathematical laws was powerful evidence that the universe could similarly be reduced to numbers. "Greek philosophy," noted the scholar John Burnet, "was henceforward to be dominated by the notion of the perfectly tuned string."

The Harmony of the Spheres

For the Greeks, the word "cosmos" did more than represent the observed universe; as scholar W.K.C. Guthrie notes, it united "the notion of order, arrangement or structural perfection with that of beauty." Central to this was the idea that the universe is based on mathematical harmony. In the same way that musical harmony imposes a kind of limit and order on the unlimited continuum of possible tones, so harmony was the organizing principle that brought together the Limited and the Unlimited when the universe was formed. Its tune was the score for the choreographed movements of the heavenly bodies.

Because ten was the perfect number, it followed to the Pythagoreans that there should be ten heavenly bodies. According to the Pythagorean philosopher Philolaus, these consisted of the Earth, the Moon, the Sun, the five planets that were known at the time, the stars (which were considered a single outer layer of fire), and something called the counter-earth. The Pythagoreans believed that all of these rotated around a "central fire" which, like the counter-earth, was always opposite to us and out of sight.

The Pythagoreans were well ahead of their time in believing that the Earth could be in motion. Their invention of the counter-earth, on the other hand, was an early example of scientists inventing a phenomenon—in this case a planet—in order to meet the requirements of an elegant theory. As Aristotle drily observed, "And all the properties of numbers and scales which they could show to agree with the attributes and parts and the whole arrangement of the heavens, they collected and fitted into their scheme; and if there was a gap anywhere, they readily made additions so as to make their whole theory coherent. E.g. as the number 10 is thought to be perfect and to comprise the whole nature of numbers, they say that the bodies which move through the heavens are ten, but as the visible bodies are only nine, to meet this they invent a tenth—the 'counter-earth.'"

The movement of each of these ten bodies was thought to produce a musical tone, with the pitch depending on the speed of rotation: the fast-moving Sun had a higher pitch than the laggard Moon, for example. Together the tones produced a beautiful music known as the Harmony of the Spheres. As his biographer Iamblichus wrote, only Pythagoras was capable of "hearing and understanding the universal harmony and consonance of the spheres and the stars that are moved through them, which produce a fuller and more intense melody than anything effected by mortal sounds." To the rest of us this celestial concert went unnoticed; having been exposed to it since birth we had become unaware of it, like people who live next to a railway track and have learned to tune out the sound of trains.

The Pythagorean assertion that the universe was ordered and rational and based on mathematical harmony had far-reaching and radical consequences, for it implied that there was a kind of sympathy between our faculty of reason and the cosmos. As the philosopher Sextus Empiricus wrote, "The Pythagoreans say that reason is the criterion of truth—not reason in general, but mathematical reason." Einstein later identified this belief in rationality as akin to religion: "I have no better expression than 'religious' for confidence in the rational nature of reality insofar as it is accessible to human reason." By exercising reason, we should therefore be able to understand the universe—and, as physicist Stephen Hawking put it, "If you understand how the universe operates, you control it in a way." Instead of being at the whim of random events, or of squabbling and recalcitrant gods, we could be masters of our own destiny.

The Standard Model

If the cosmos was based on number, it followed that the movements of the heavenly bodies could be modeled and predicted using mathematics. In a time when events in the human sphere were believed to be strongly influenced by astrology, this was of no small practical interest. The Greeks therefore set about building sophisticated geometric constructions which could be used to chart the skies.

These early versions of mathematical models were based on two main assumptions: that everything moved around the Earth (the notions of the central fire and counter-earth did not survive); and that everything moved in circles, since circles and spheres were the most symmetric—and therefore the most pure—of forms. In his Republic, for example, Plato described (from inner to outer) the Moon, Sun, Venus, Mercury, Mars, Jupiter, Saturn, and stars as rotating in concentric circles: "on the upper surface of each circle is a siren, who goes round with them, hymning a single tone or note. The eight together form one harmony."

The assumption of circular motion around the Earth worked well enough for the Moon, Sun, and stars. The planets, however, followed a more complicated path. Mars, for example, would complete a full revolution in about 780 days, but partway round it would perform a retrogradation lasting about ten weeks in which it slowed down and backtracked a bit before proceeding—like an unruly soloist in a jazz orchestra.

In the third century BC, Plato's associate Eudoxus came up with a way to reconcile this motion with Pythagorean spheres. Each body was imagined to be located on a sphere, rotating around an axis whose center was the Earth. To account for effects such as retrograde motion, the endpoints of the axes of rotation were fixed on other spheres that themselves rotated. This allowed for highly complex motion. The complete model of twenty-seven spheres was a remarkable achievement in mathematical modeling, and it captured the overall motions of the cosmos even if it could not give a perfect fit to the observed data.

Other astronomers, including Plato's former student Aristotle, later improved on the model by adding more spheres, which allowed for better reproduction of planetary motion. It was again believed that the spheres produced musical tones as they rotated. "It seems that bodies so great must inevitably produce a sound by their movement," wrote Aristotle. "Even bodies on Earth do that, although they are not so great in bulk or moving at so high a speed."

In Aristotle's system, matter was made up of five elements: earth, water, fire, air, and ether. Each had its own natural level—earth tended to sink down towards the center with water floating on top, air above that, and fire pushing upwards. The celestial bodies were made of the fifth element, ether. His version of the geocentric model featured some fifty-five concentric spheres. While Eudoxus may only have used the spheres as a mathematical construct (his position is not clear one way or the other), Aristotle thought they were actual crystalline objects made of ether, all rotating around the Earth like an elaborate mobile constructed by an ingenious sculptor. The innermost body was the Moon, which he considered imperfect because it did not produce its own light. It therefore marked the transition between the corporeal world and the heavens.

Around 150 AD, Ptolemy of Alexandria came up with a new version of the model which provided an even better fit to the available data. It was known that the brightness of the planets, and the size of the Moon, varied slightly over the course of their orbits, suggesting that their distance from the Earth changed with time. Rather than ditch the circle hypothesis—as Ptolemy noted, circular motions alone are perfectly regular and therefore "strangers to disparities and disorders"—he just arranged them in a different way. Each planet moved in an epicycle, which was a small circle with its center on another larger circle. The circles rolled around in such a way that the planet would produce the correct retrogradations, to an accuracy of about the size of a full moon.


Excerpted from TRUTH OR BEAUTY by DAVID ORRELL Copyright © 2012 by David Orrell. Excerpted by permission of Yale UNIVERSITY PRESS. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

Acknowledgments vii

Introduction 1

I Infatuation

1 Harmony 15

2 Integrity 37

3 Radiance 59

II Complication

4 The Crooked Universe 85

5 The Masculine Philosophy 115

6 Unity 138

7 Broken Mirrors 167

III Maturation

8 The Shadow World 199

9 The Virtual Universe 239

10 The Left-Hander's Guide to the Cosmos 260

Notes 289

Bibliography 316

Index 338

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