And then Weinberg moves without a break into metaphysics: “There is not much comfort in any of this,” he writes,
It is almost irresistible for humans to believe that we have some special relation to the universe, that human life is not just a more-or-less farcical outcome of a chain of accidents reaching back to the first three minutes. . . . The more the universe seems comprehensible, the more it also seems pointless.22
Moving from singularity to meaning is irresistible, and also nonscientific. Comfort and despair both are, entirely, non-Baconian.
Although The First Three Minutes begins by contrasting an ancient creation myth (from the Norse Edda) to the scientific tales that Weinberg is about to unfold, the two stories actually bear a striking resemblance to each other. Weinberg’s story of origins is complete with a projected apocalypse and (at the very end of the book), a moral, the goal of humanity:
But if there is no solace in the fruits of our research, there is at least some consolation in the research itself. Men and women are not content to comfort themselves with tales of gods and giants, or to confine their thoughts to the daily affairs of life; they also build telescopes and satellites and accelerators, and sit at their desks for endless hours working out the meaning of the data they gather. The effort to understand the universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy.23
Weinberg has moved deftly from physical questions, to the purpose of life: which is to glorify science, and to pursue it forever. The Baconian project has turned in on itself and swallowed its own tail; what began as the study of what could be verified by experiment has become a way to locate truths that can never be touched.
For the exceedingly persistent . . .
EDWIN HUBBLE
The Realm of the Nebulae
(1937)
The difficulty with Hubble’s text is summed up by the 1983 retrospective review in the New Scientist, which exclaims, “A serious systematic account written for the general reader,” and then concludes, “One suggests as a required first question in any PhD oral in astronomy, ‘Have you read The Realm of the Nebulae?’” These are not, exactly, the same audiences, and Hubble’s prose veers from the accessible to the impenetrable. However, the tenacious reader will find enough of interest to justify plowing through the Yale reprint version.
Edwin Hubble, The Realm of the Nebulae (Silliman Memorial Lectures Series), Yale University Press (paperback reprint edition, 2013, ISBN 978-0300187120).
For the rest of us . . .
FRED HOYLE
The Nature of the Universe
(1950)
Hoyle displays just how much authority an accessible, clear writing style lends to a scientific voice. The Nature of the Universe is out of print, but copies of the 1960 Harper hardcover are easily located secondhand. The most significant chapter of the text has been reproduced in the collection Theories of the Universe: From Babylonian Myth to Modern Science, edited by Milton K. Munitz (Free Press, 1965).
Fred Hoyle, The Nature of the Universe, HarperCollins (hardcover, 1960, ISBN 978-0060028206).
STEVEN WEINBERG
The First Three Minutes: A Modern View of the Origin of the Universe
(1977)
The classic text, which has never gone out of print, was published in a second updated edition with a new foreword and an even more recent afterword (1993) by Basic Books.
Steven Weinberg, The First Three Minutes: A Modern View of the Origin of the Universe, Basic Books (paperback and e-book, 1993, ISBN 978-0465024377).
* * *
* Over the next few years, his calculations were debated by other physicists but ultimately stood fast.
† See Chapter 25.
‡ Measuring the distance to any given star sounds easy but wasn’t. The historical steps in developing the ability to measure celestial objects are interesting but off topic; a more detailed but still nontechnical account can be found in Kitty Ferguson’s Measuring the Universe: Our Historic Quest to Chart the Horizons of Space and Time (Walker, 1999).
§ Einstein had saved the speed of light as a constant, so a light-year (the distance that light can travel over the course of a Julian year, 365.25 days) can be calculated as 9,460,730,472,580.8 kilometers.
¶ For a more detailed explanation, and the relevant equations, see the first two chapters of Helge Kragh, Cosmology and Controversy: The Historical Development of Two Theories of the Universe (Princeton University Press, 1996), 3ff.
# A more detailed and quite readable account is found in Gamow’s 1952 book The Creation of the Universe, intended for informed nonspecialists and reissued by Dover Publications in 2012 as an e-book.
TWENTY-EIGHT
The Butterfly Effect
Complex systems, and the (present) limits of our understanding
Where chaos begins, classical science ends.
—James Gleick, Chaos, 1987
The study of the universe, continually more rarefied, was now carried on at the highest levels mostly in equations. Cutting-edge theory was difficult even for readers with a firm grasp of calculus, essentially impenetrable to those who lacked it.
This inaccessibility gave great power to the popularizers, writers capable of translating academic shorthand into convincing narratives. Walter Alvarez was a geologist capable of turning a phrase; Dawkins, E. O. Wilson, and Gould were biologists who could write; Steven Weinberg, like Erwin Schrödinger, was both popularizer and physicist.
But in physics—particularly the branch of physics often labeled cosmology, the contemplation of the entire universe and its workings—the last major paradigm shift of the twentieth century was brought to light by an English major.
•
Even in the age of quantum mechanics and singularities, Newton’s principles persisted.
For one thing, Newton’s laws work so well in the everyday world. Drop your cookie on the floor, and Newton can tell you where it will land. Get on a train traveling 72 miles per hour, and Newton can tell you exactly when that train will intersect with the dump truck that’s speeding toward you at an angle. Take off from Washington, DC, in a 747, and Newton can tell you exactly when you’ll land in Paris (as long as the air traffic controllers cooperate).
In the nineteenth century, the French mathematician and astronomer Pierre-Simon Laplace* theorized that Newton’s laws, derived from present conditions, could predict anything that might happen in the future. This version of determinism—the current state of the universe “completely defines its future”—led Laplace to conclude that an all-knowing, all-seeing but time-bound being could predict the future with absolute accuracy.
An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.1
This theoretical intellect became known as “Laplace’s Demon” (demon, in this context, meaning “a hypothetical entity” rather than “an evil spirit”). Laplace’s Demon could not only see all forces in the natural universe and map where they were at any given time, but also had the ability to crunch the numbers and plot a future course from them. For Laplace’s Demon, time was irrelevant; the universe looked the same running backward as forward. Theoretically, the Demon could calculate into the past with just as much accuracy as into the future.
The first scientist to suggest that this might not be as straightforward as Laplace argued was another Frenchman, the mathematician and physicist Henri Poincaré, around 1910. Working with systems that appeared to be quite simple, Poincaré ran into unexpected results. He could not always predict the outcome, even when the forces in question seemed straightforward; and he believed that tin
y changes in the initial conditions, so slight that he could not easily detect them, were the cause. “Small differences in the initial conditions produce very great ones in the final phenomena,” he theorized. “A small error in the former will produce an enormous error in the latter. Prediction becomes impossible.”2
For half a century, no one followed up on this insight.
•
In the 1960s, Laplace’s Demon appeared on the scene, at least partially and in embryonic form: computers, which didn’t have the ability to comprehend the forces in nature but were potentially able to crunch all that data in a way that no human mind could.
In 1961 the American mathematician Edward Lorenz was working on weather. He had always been fascinated by weather patterns, which most mathematicians ignored as too quixotic to map. Using brand-new computer technology, he had written code that should have taken various factors (wind distance and speed, air pressure, temperature, and so on) and used them to predict weather patterns.
One particular evening, Lorenz entered the numbers that represented his factors, and his computer program, obediently, predicted a pattern. Lorenz decided to double-check the pattern. He reentered the factors, but to save time he punched them in to only the third decimal place, instead of the sixth (as he had done the first time).
This should have made no difference at all, since the change in wind speed, or temperature, from the fourth decimal place on was absolutely insignificant—in fact, almost nonexistent. But to Lorenz’s shock, the weather pattern that resulted began to diverge from the original . . . and then departed from it entirely. By the time it finished cycling, the program had produced an entirely different set of weather phenomena. In 1963 Lorenz published a paper chronicling these results: “Deterministic Nonperiodic Flow.” Perhaps, he wrote, the weather system was so sensitive to those tiny starting shifts that minuscule changes could actually produce massively different results.3
This sensitivity to infinitesimal conditions could hardly have been calculated before the advent of computers and their ability to run multiple scenarios very quickly. But now, Lorenz’s paper attracted a great deal of attention from other mathematicians, who also began using computers to solve these particular kinds of “nonlinear equations.”† In 1972, Lorenz followed up his original paper with another, called “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?” It was the first time that a butterfly’s wing was used as an analogy for one of those tiny starting changes: the first use of the phrase “butterfly effect.”4
In 1975, two other mathematicians, Tien-Yien Li and James A. Yorke, published a paper about nonlinear equations and their unpredictable results that, for the first time, gave this unpredictability a name. They called it chaos: an immensely powerful word for most English-speaking readers who, even in 1975, still knew something of its biblical use: utter formlessness, confusion, disorder.5
This was not exactly chaos in a mathematical sense. Chaos here means “unpredictability”—and not even ultimate, intrinsic unpredictability (as in, “No matter how much we know, we will not be able to predict the end result”) but, instead, a contingent, practical unpredictability (“This system is so sensitive to microscopic changes in initial conditions that we are not, at the moment, capable of analyzing those initial conditions with the accuracy necessary to predict all possible outcomes”).
A paper published the following year by the mathematically gifted biologist Robert May gave chaos theory a more realistic but less catchy name: “Simple Mathematical Models with Very Complicated Dynamics.” May’s paper extended these “chaotic” systems past weather into something a little more concrete: insect populations, with the proposal that apparently random fluctuations in the numbers of insects within a certain society could be understood as related to those initial conditions.
After May, studies in chaos theory and its application to various fields (physics, chemistry, biochemistry, biology) accelerated. But chaos theory was still in its early adolescence when the writer James Gleick—a New York Times Magazine columnist, freelance essayist, and science reporter—chose it as the subject of his first book.
Chaos: Making a New Science was (like T. rex and the Crater of Doom, like The Discovery of DNA and The Mismeasure of Man) snappily titled, beautifully written, and peppered with vivid metaphors. Like T. rex (which led directly, at least, to the movies Deep Impact and Armageddon, and indirectly to scores of others), like the Big Bang, chaos theory gripped the popular imagination. The “butterfly effect” became a household phrase, especially once Jeff Goldblum’s rock-star scientist character in Jurassic Park gave worldwide audiences the shorthand version: “It simply deals with predictability in complex systems. . . . A butterfly can flap its wings in Peking, and in Central Park, you get rain instead of sunshine. . . . Tiny variations . . . never repeat, and vastly affect the outcome. That’s unpredictability.”
The word “chaos” is deceptive, though; especially to readers who get the theory without the equations. “Where chaos begins, classical science ends,” Gleick writes, in his clear (and deservedly best-selling) account. But at its core, chaos theory turns out to be almost Newtonian. Laplace’s Demon, with its vast resources of knowledge and unlimited computational ability, could—theoretically—have tracked the air, moving from that butterfly wing all the way through to its ultimate end in rainy Central Park.
We cannot predict the outcome of complex systems, in the end, not because they are unpredictable, but because we cannot yet see deeply enough into the factors that shape them. But, buried deep in chaos theory is the promise—justified or not—that this may not always be the case.
JAMES GLEICK
Chaos: Making a New Science
(1987)
Gleick’s original 1987 text is still available secondhand; a slightly revised and updated second edition was published in 2008.
James Gleick, Chaos: Making a New Science, Viking (hardcover and paperback, 1987, ISBN 978-0670811786).
James Gleick, Chaos: Making a New Science, Penguin Books (paperback and e-book, 2008, ISBN 978-0143113454).
* * *
* See Chapter 25.
† Not all such equations have chaotic solutions; those that do are a subset of the larger category “nonlinear equations.”
Notes
ONE The First Science Texts
1. Albert Einstein and Leopold Infeld, The Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta (Cambridge University Press, 1938), 33.
2. Robert Parker, On Greek Religion (Cornell University Press, 2011), xi, 6.
3. Malcolm Williams, Science and Social Science: An Introduction (Taylor & Francis, 2002), 10.
4. Francesca Rochberg, The Heavenly Writing: Divination, Horoscopy, and Astronomy in Mesopotamian Culture (Cambridge University Press, 2004), 226.
5. Aristotle, Metaphysics 1.3, in Readings in Ancient Greek Philosophy: From Thales to Aristotle, 4th ed., ed. S. Marc Cohen, Patricia Curd, and C. D. C. Reeve (Hackett, 2011), 2.
6. Plato, Protagoras, trans. Benjamin Jowett (Serenity, 2009), 25.
7. Plinio Prioreschi, A History of Medicine, vol. 1, Primitive and Ancient Medicine, 2nd ed. (Horatius Press, 1996), 42.
8. Hippocrates, “On the Sacred Disease,” in The Corpus: Hippocratic Writings (Kaplan, 2008), 99.
9. Lawrence I. Conrad et al., The Western Medical Tradition: 800 B.C.–1800 A.D. (Cambridge University Press, 1995), 23–25; Pausanius, Pausanias’s Description of Greece, trans. J. G. Frazer (Macmillan, 1898), 3:250; Hippocrates, On Airs, Waters, and Places, in Corpus, 117.
TWO Beyond Man
1. Lawrence I. Conrad et al., The Western Medical Tradition: 800 B.C.–1800 A.D. (Cambridge University Press, 1995), 23; Hippocrates, On Ancient Medicine, trans. Mark J. Schiefsky (Brill, 2005), 32.
2. Gerard Naddaf, The Greek Concept of Nature (SUNY Press, 1995), 1–2.
3. Aristotle, Physics, trans. Robin Waterfield, Oxford World’s Classics (O
xford University Press, 1999), xi; Naddaf, Greek Concept of Nature, 7, 65–66; Aristotle, The Metaphysics, trans. William David Ross, in The Works of Aristotle (Franklin Library, 1982), 3:175.
4. Simplicius, Commentary on the Physics 28.4-15, quoted in Jonathan Barnes, Early Greek Philosophy, rev. ed (Penguin, 2002), 202; Aristotle, On Democritus, frag. 203, quoted in Barnes, Early Greek Philosophy, 206–7.
5. Steven Weinberg, Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature (Vintage, 1994), 7–8; see also Chapter 27, “The Triumph of the Big Bang.”
6. C. C. W. Taylor, The Atomists: Leucippus and Democritus, Fragments (University of Toronto Press, 1999), 214–15.
7. Naddaf, Greek Concept of Nature, 9.
8. George Sarton, A History of Science: Ancient Science through the Golden Age of Greece (Harvard University Press, 1964), 421–24; Benjamin Jowett, The Dialogues of Plato in Four Volumes (Charles Scribner’s Sons, 1892), 2:458–59.
9. Plato, The Dialogues of Plato, trans. Benjamin Jowett (Hearst’s International Library, 1914), 4:463.
10. Plato, Plato’s Timaeus: Translation, Glossary, Appendices, and Introductory Essay, trans. Peter Kalkavage (Focus, 2001), 60–61.
THREE Change
1. George Sarton, A History of Science: Ancient Science through the Golden Age of Greece (Harvard University Press, 1964), 423.
2. Jennifer Vonk and Todd K. Shackelford, eds., The Oxford Handbook of Comparative Evolutionary Psychology (Oxford University Press, 2012), 42.
3. Sarton, History of Science, 539; Jonathan Barnes, ed., The Cambridge Companion to Aristotle (Cambridge University Press, 1995), 123–26.
The Story of Western Science Page 26
