The Clockwork Universe Part 22

Also by Edward Dolnick The Forger's Spell The Rescue Artist Down the Great Unknown Madness on the Couch

Copyright THE CLOCKWORK UNIVERSE. Copyright 2011 by Edward Dolnick. All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this e-book on-screen. No part of this text may be reproduced, transmitted, down-loaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of HarperCollins e-books. Copyright 2011 by Edward Dolnick. All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this e-book on-screen. No part of this text may be reproduced, transmitted, down-loaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of HarperCollins e-books.

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1 The historian Jules Michelet described the Middle Ages as "a thousand years without a bath." The historian Jules Michelet described the Middle Ages as "a thousand years without a bath."

2 For convenience I will use the word For convenience I will use the word scientist scientist, though the word only came into use in the 1800s. The seventeenth century had not settled on a convenient term for these investigators. Sometimes they were called "natural philosophers" or "virtuosos."

3 Christopher Wren's father, a prominent cleric who also had a deep interest in mathematics, calculated the apocalypse in a different way. A list of the Roman numerals, in order from biggest to smallest-MDCLXVI-corresponded to the date 1666, which "may bode some ominous Matter, and perhaps the last End." Christopher Wren's father, a prominent cleric who also had a deep interest in mathematics, calculated the apocalypse in a different way. A list of the Roman numerals, in order from biggest to smallest-MDCLXVI-corresponded to the date 1666, which "may bode some ominous Matter, and perhaps the last End."

4 They cited pa.s.sages such as Revelation 11:3: "I will give power unto my two witnesses, and they shall prophesy a thousand two hundred and threescore days, clothed in sackcloth." Scholars took each day to represent a year. They cited pa.s.sages such as Revelation 11:3: "I will give power unto my two witnesses, and they shall prophesy a thousand two hundred and threescore days, clothed in sackcloth." Scholars took each day to represent a year.

5Pepys is p.r.o.nounced "peeps." is p.r.o.nounced "peeps."

6 The The ye ye we are all familiar with ("Ye Fox and Hounds Tavern") was p.r.o.nounced "the we are all familiar with ("Ye Fox and Hounds Tavern") was p.r.o.nounced "the." The use of the letter y y was a typographical convention, like was a typographical convention, like f f for for s. s.

7 G.o.d watched over the highest and the humblest. In Queen Elizabeth's reign the bishops of Canterbury, London, and Ely declared "this continued sterility in your Highness' person to be a token of G.o.d's displeasure towards us." G.o.d watched over the highest and the humblest. In Queen Elizabeth's reign the bishops of Canterbury, London, and Ely declared "this continued sterility in your Highness' person to be a token of G.o.d's displeasure towards us."

8 In 1823 a twenty-one-year-old Hungarian named Johann Bolyai conceived the inconceivable: a universe in which parallel lines meet and straight lines curve. In 1919 Einstein proved that we live in such a universe. In 1823 a twenty-one-year-old Hungarian named Johann Bolyai conceived the inconceivable: a universe in which parallel lines meet and straight lines curve. In 1919 Einstein proved that we live in such a universe.

9 Digby a.s.sured his audience that "there is great quant.i.ty of it in Ireland." Digby a.s.sured his audience that "there is great quant.i.ty of it in Ireland."

10 Bacon's zeal for experimentation may have done him in. On a winter's day when he happened to be in the company of the royal physician, Bacon suddenly had the bright idea that perhaps snow could preserve meat. "They alighted out of the coach and went into a poor woman's house at the bottom of Highgate hill, and bought a fowl," wrote the memoirist John Aubrey, and Bacon stuffed the bird with snow. Bacon came down with what proved to be a fatal case of pneumonia. He blamed the snow but noted on his deathbed that the story had a bright side. "As for the experiment itself, it succeeded excellently well." Bacon's zeal for experimentation may have done him in. On a winter's day when he happened to be in the company of the royal physician, Bacon suddenly had the bright idea that perhaps snow could preserve meat. "They alighted out of the coach and went into a poor woman's house at the bottom of Highgate hill, and bought a fowl," wrote the memoirist John Aubrey, and Bacon stuffed the bird with snow. Bacon came down with what proved to be a fatal case of pneumonia. He blamed the snow but noted on his deathbed that the story had a bright side. "As for the experiment itself, it succeeded excellently well."

11 The ancient world had clung just as fiercely to the code of secrecy. Legend has it that Pythagoras banished one of his followers (or in some accounts threw him off a boat, drowning him) for "telling men who were not worthy" a dreadful mathematical secret. Hippasus's sin was revealing to outsiders the discovery that certain numbers (in this case, the square root of 2) cannot be written down precisely (14/10 is close, for instance, but The ancient world had clung just as fiercely to the code of secrecy. Legend has it that Pythagoras banished one of his followers (or in some accounts threw him off a boat, drowning him) for "telling men who were not worthy" a dreadful mathematical secret. Hippasus's sin was revealing to outsiders the discovery that certain numbers (in this case, the square root of 2) cannot be written down precisely (14/10 is close, for instance, but no no fraction is exact). The Greeks found this numerical truth horrifying, a rip in the cosmic fabric. fraction is exact). The Greeks found this numerical truth horrifying, a rip in the cosmic fabric.

12 We still see relics of that prejudice against "applied" knowledge today. The historian Paolo Rossi notes that the term "liberal arts" originally came into use to mark off those areas of study deemed proper for a gentleman's education. These were the fields suited to free men ( We still see relics of that prejudice against "applied" knowledge today. The historian Paolo Rossi notes that the term "liberal arts" originally came into use to mark off those areas of study deemed proper for a gentleman's education. These were the fields suited to free men (liberi) rather than to servants or slaves.

13As a thirteen-year-old, Hooke briefly apprenticed with the famous portrait painter Peter Lely. (It was Lely whom Oliver Cromwell instructed to "paint my picture truly like me," warts and all.) Hooke's artistic career came to an early end when he found he was allergic to the paints and oils in Lely's studio.

14The esteemed eighteenth-century mathematician Laplace, for example, inspired despair even in his admirers. "I never came across one of Laplace's 'Thus it plainly appears,' " wrote one, "without feeling sure that I have hours of hard work before me to fill up the chasm and find out and show how it plainly appears."

15 "As one of [Thomas More's] daughters was pa.s.sing under the bridge," according to John Aubrey, "looking on her father's head, said she, 'That head has lain many a time in my lap, would to G.o.d it would fall into my lap as I pa.s.s under.' She had her wish, and it did fall into her lap, and is now preserved in a vault in the cathedral church at Canterbury." "As one of [Thomas More's] daughters was pa.s.sing under the bridge," according to John Aubrey, "looking on her father's head, said she, 'That head has lain many a time in my lap, would to G.o.d it would fall into my lap as I pa.s.s under.' She had her wish, and it did fall into her lap, and is now preserved in a vault in the cathedral church at Canterbury."

16The word disease disease is a relic of this theory. When the humors fell out of balance, the patient's is a relic of this theory. When the humors fell out of balance, the patient's ease ease gave way to gave way to dis-ease. dis-ease.

17 Like James Thurber, who never managed to see anything through a microscope but a reflection of his own eye, Pepys had trouble getting the hang of his microscope. "My wife and I with great pleasure," he wrote in his diary in August 1664, "but with great difficulty before we could come to find the manner of seeing anything." Like James Thurber, who never managed to see anything through a microscope but a reflection of his own eye, Pepys had trouble getting the hang of his microscope. "My wife and I with great pleasure," he wrote in his diary in August 1664, "but with great difficulty before we could come to find the manner of seeing anything."

18 Glanvill provides yet another example of how seventeenth-century scientists simultaneously endorsed new beliefs and clung to old ones. He argued strenuously in favor of science's new findings and at the same time insisted that spirits, demons, and witches were real. To deny the existence of evil spirits, Glanvill insisted, was to veer dangerously near to saying that only the tangible was real, and Glanvill provides yet another example of how seventeenth-century scientists simultaneously endorsed new beliefs and clung to old ones. He argued strenuously in favor of science's new findings and at the same time insisted that spirits, demons, and witches were real. To deny the existence of evil spirits, Glanvill insisted, was to veer dangerously near to saying that only the tangible was real, and that that was tantamount to atheism. No witches, no G.o.d! was tantamount to atheism. No witches, no G.o.d!

19 The mystery would only be unraveled around 1800. The mystery would only be unraveled around 1800.

20 The moon gave the Greeks problems. It was a heavenly body, which meant it had to be perfect and unblemished, but no one could miss its patches of light and dark. One attempted explanation: the moon was a perfect mirror and its dark spots were the reflections of oceans on Earth. The moon gave the Greeks problems. It was a heavenly body, which meant it had to be perfect and unblemished, but no one could miss its patches of light and dark. One attempted explanation: the moon was a perfect mirror and its dark spots were the reflections of oceans on Earth.

21 The stars will not look exactly the same, mostly because the earth wobbles a bit on its axis, like a spinning top. But the changes are so small that art historians and astronomers, working together, have answered such questions as what the sky over St.-Remy-de-Provence looked like on June 19, 1889, the night Van Gogh painted "Starry Night." (Van Gogh stuck remarkably close to reality.) The stars will not look exactly the same, mostly because the earth wobbles a bit on its axis, like a spinning top. But the changes are so small that art historians and astronomers, working together, have answered such questions as what the sky over St.-Remy-de-Provence looked like on June 19, 1889, the night Van Gogh painted "Starry Night." (Van Gogh stuck remarkably close to reality.)

22 Galileo's intellectual offspring espouse the same view today, in virtually identical words. "To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature," wrote the physicist Richard Feynman. "If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in." Galileo's intellectual offspring espouse the same view today, in virtually identical words. "To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature," wrote the physicist Richard Feynman. "If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in."

23Modern-day astronomers have shown that Tycho's star was a supernova, an exploding star, rather than a new one.

24Fontenelle's exuberance was characteristic, though consistency was not his strength. In the next breath he professed, with equal verve, to be worried that the immensity of the universe made his own efforts seem tiny and irrelevant. Like Carl Sagan in our day, he was known as much for enthusiasm as scholars.h.i.+p. Fontenelle lived to be one hundred and scarcely slowed down along the way. Near the end, he met one famous beauty and remarked, "Ah madame, if I were only eighty again!"

25 Leeuwenhoek was a contemporary of Vermeer. Both men lived in Delft, the two shared a fascination with light and lenses, and Leeuwenhoek served as executor of Vermeer's will. Some art historians believe that Vermeer's Leeuwenhoek was a contemporary of Vermeer. Both men lived in Delft, the two shared a fascination with light and lenses, and Leeuwenhoek served as executor of Vermeer's will. Some art historians believe that Vermeer's Astronomer Astronomer and his and his Geographer Geographer both depict Leeuwenhoek, but no one has been able to prove that Leeuwenhoek and Vermeer ever met. both depict Leeuwenhoek, but no one has been able to prove that Leeuwenhoek and Vermeer ever met.

26 The microscope that Leeuwenhoek used on that fateful night was put up for auction in April 2009. The winning bidder paid $480,000. The microscope that Leeuwenhoek used on that fateful night was put up for auction in April 2009. The winning bidder paid $480,000.

27 As one of Pythagoras's followers told the tale, the story began when Pythagoras listened to the sound of hammering as he walked by a blacksmith's shop. As the blacksmith struck the same piece of iron with different hammers, some sounds were harmonious, others not. The key, Pythagoras found, was whether the weights of the hammers happened to be in simple proportion. A twelve-pound hammer and a six-pound hammer, for instance, produced notes an octave apart. As one of Pythagoras's followers told the tale, the story began when Pythagoras listened to the sound of hammering as he walked by a blacksmith's shop. As the blacksmith struck the same piece of iron with different hammers, some sounds were harmonious, others not. The key, Pythagoras found, was whether the weights of the hammers happened to be in simple proportion. A twelve-pound hammer and a six-pound hammer, for instance, produced notes an octave apart.

28 Augustine did not explain why G.o.d did not make the world in 28 days (1 + 2 + 4 + 7 + 14) or 496 days or various other possibilities. Augustine did not explain why G.o.d did not make the world in 28 days (1 + 2 + 4 + 7 + 14) or 496 days or various other possibilities.

29 A prime number is one that can't be broken down into smaller pieces. For example, 2 is prime, and so are 3, 5, and 7; 10 is not prime (because 10 = 2 5). Prime numbers get rarer as you count higher and higher, but no matter how big a prime you name, there is always a bigger one. A prime number is one that can't be broken down into smaller pieces. For example, 2 is prime, and so are 3, 5, and 7; 10 is not prime (because 10 = 2 5). Prime numbers get rarer as you count higher and higher, but no matter how big a prime you name, there is always a bigger one.

30 There are infinitely many choices of a, b, and c that satisfy a There are infinitely many choices of a, b, and c that satisfy a2 + b + b2 = c = c2. But if you try any any power higher than 2-if, for instance, you try to find whole numbers a, b, and c that satisfy a power higher than 2-if, for instance, you try to find whole numbers a, b, and c that satisfy a3 + b + b3 = c = c3 or a or a4 + b + b4 = c = c4-you will never find a single example that works (discounting the trivial case where a, b, and c are all set equal to 0). The statement that no such example exists is one of the most famous in mathematics. It is known as Fermat's last theorem, after the mathematician Pierre de Fermat, who jotted it down in the margin of a book in 1637. He had found "a truly marvelous proof," he scribbled, but "the margin is not large enough" to fit it. No one ever found his proof-presumably he'd made a mistake in his reasoning-and for more than three hundred years countless mathematicians tried and failed to find proofs of their own. Success finally came in 1995, as detailed in Amir Aczel's Fermat's Last Theorem Fermat's Last Theorem.

31 At the half-moon, for instance, sun, moon, and Earth form a right triangle. At the half-moon, for instance, sun, moon, and Earth form a right triangle.

32 The nineteenth-century German mathematician Carl Gauss, a towering figure in the history of mathematics, believed in the possibility of life on other worlds. Gauss supposedly proposed-the story may well be apocryphal-that since all intelligent beings would eventually discover the same mathematical truths, we could communicate with moon creatures by choosing a vast, empty s.p.a.ce in Siberia and planting trees in an enormous diagram of the Pythagorean theorem. The nineteenth-century German mathematician Carl Gauss, a towering figure in the history of mathematics, believed in the possibility of life on other worlds. Gauss supposedly proposed-the story may well be apocryphal-that since all intelligent beings would eventually discover the same mathematical truths, we could communicate with moon creatures by choosing a vast, empty s.p.a.ce in Siberia and planting trees in an enormous diagram of the Pythagorean theorem.

33Pluto is considerably smaller than the moon, and in 2006 astronomers decided to downgrade it to "minor planet" status.

34 Not by the human ear, at any rate. G.o.d could hear these cosmic harmonies, as dogs can detect whistles pitched too high for human hearing. Not by the human ear, at any rate. G.o.d could hear these cosmic harmonies, as dogs can detect whistles pitched too high for human hearing.

35 The first person to refer to Kepler's "laws" was Voltaire, in 1738. Scientists eventually followed his lead. The first person to refer to Kepler's "laws" was Voltaire, in 1738. Scientists eventually followed his lead.

36 Tycho, like Galileo, is generally referred to by his first name. Tycho, like Galileo, is generally referred to by his first name.

37 A circle can be thought of as a special ellipse, one in which the two focuses are in the same place. A circle can be thought of as a special ellipse, one in which the two focuses are in the same place.

38 Ballet dancers and basketball players seem to hang in midair, but that is an illusion. The trick for both dancer and athlete is to throw in a few moves midflight. The eye reads the extra motions as taking extra time. Ballet dancers and basketball players seem to hang in midair, but that is an illusion. The trick for both dancer and athlete is to throw in a few moves midflight. The eye reads the extra motions as taking extra time.

39 "Music," Leibniz wrote, "is the pleasure the human soul experiences from counting without being aware that it is counting." "Music," Leibniz wrote, "is the pleasure the human soul experiences from counting without being aware that it is counting."

40 To be more accurate, in To be more accurate, in t t seconds a ball falls a distance seconds a ball falls a distance proportional proportional to to t t2 inches rather than precisely equal to inches rather than precisely equal to t t2 inches. (It falls, for instance, 3 inches. (It falls, for instance, 3 t t2 inches or 10 inches or 10 t t2 inches or some other multiple, depending on the steepness of the ramp.) Everything I've said here carries over to the more general case, but the numbers would be off-putting. For purposes of ill.u.s.tration, I chose the ramp that showed the pattern most clearly. inches or some other multiple, depending on the steepness of the ramp.) Everything I've said here carries over to the more general case, but the numbers would be off-putting. For purposes of ill.u.s.tration, I chose the ramp that showed the pattern most clearly.

41 One prominent historian calls it "incomprehensible" that Greek mathematicians never conceived of graphs. But neither did their intellectual descendants for well over a thousand years. Even an enormous hint went unnoticed. Monks in the Middle Ages invented musical notation, which meant they no longer had to commit countless chants to memory. "The musical staff was Europe's first graph," noted the historian Alfred Crosby, but several more One prominent historian calls it "incomprehensible" that Greek mathematicians never conceived of graphs. But neither did their intellectual descendants for well over a thousand years. Even an enormous hint went unnoticed. Monks in the Middle Ages invented musical notation, which meant they no longer had to commit countless chants to memory. "The musical staff was Europe's first graph," noted the historian Alfred Crosby, but several more centuries centuries would pa.s.s before scientists saw that they, too, could use graphs to depict changes in time. would pa.s.s before scientists saw that they, too, could use graphs to depict changes in time.