The Clockwork Universe (41 page)

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

2
For convenience I will use the word
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.”

4
They cited passages 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.

5
Pepys
is pronounced “peeps.”

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

7
God 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 God'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.

9
Digby assured his audience that “there is great quantity 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.”

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
no
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 (
liberi
) rather than to
servants or slaves.

13
As 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.

14
The 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 passing 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 God it would fall into my lap as I pass 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.”

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

18
Glanvill provides yet another example of how seventeenth-century scien
tists 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 spir
its, Glanvill insisted, was to veer dangerously near to saying that only the
tangible was real, and
that
was tantamount to atheism. No witches, no God!

19
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.

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.-Rémy-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.”

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

24
Fontenelle's exuberance was characteristic, though consistency was not
his strength. In the next breath he professed, with equal verve, to be wor
ried 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 scholarship. 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
Astronomer
and his
Geographer
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.

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.

28
Augustine did not explain why God 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.

30
There are infinitely many choices of a, b, and c that satisfy a
²
+ b
²
= c
²
. But if you try
any
power higher than 2—if, for instance, you try to find whole numbers a, b, and c that satisfy a
³
+ b
³
= c
³
or a
⁴
+ b
⁴
= c
⁴
—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
.

31
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 space in Siberia and planting trees in an enormous diagram of the Pythagorean theorem.

33
Pluto 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. God 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.

36
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.

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.

39
“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
t
seconds a ball falls a distance
proportional
to
t
²
inches rather than precisely equal to
t
²
inches. (It falls, for instance, 3 ×
t
²
inches or 10 ×
t
²
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 illustration,
I chose the ramp that showed the pattern most clearly.