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Acknowledgments
A lot of people in my life are partly responsible, in one way or another, for this book. My high school teachers instilled a love of science and of writing; my college professors showed me the beauty of mathematics. Jeremy Bernstein and Kenneth Goldstein started my career of science journalism. My friends and colleagues at New Scientist—well, they put up with me, which is no mean feat.
Special thanks go to my agent, Kerry Nugent-Wells; the illustrator, Matt Zimet; and my editor, Wendy Wolf. Thanks, too, to the people who helped me whip the text into shape—Dawn Drzal, Faye Flam, and, of course, my mom and dad. (They’re gentle parents, but harsh critics!)
Index
abacus, abacists
Absolom, Karl
absolute zero
acceleration
Achilles and the tortoise (Zeno’s paradox)
Alembert, Jean Le Rond d’
Alexander the Great
algebra
fundamental theorem of
Al-Ghazali, Abu Hamid
algorists
algorithms
Al-Khowarizmi, Mohammed ibn-Musa
American Revolution
Analyst, The(Berkeley)
“Anatomy of the World, An” (Donne)
Anti-Duhring (Engels)
Arabic numerals
Archimedes
axiom of
“Sand Reckoner” of
area and volume, measuring of
Aristotle, Aristotelian doctrine
God’s existence proven by
India and
rejection of
vacuum as viewed by
astronomers
Atman
atmospheric pressure
atomism
Augustine, Saint
Azrael of Gerona
Babylonians
Bacairi
banking
base-10 system
base-20 system
base-60 system
Bede
Berkeley, George
Bernoulli, Johann
Bhaskara
Bible
Book of John
big bang
big crunch
binary counting system
binary numbers
black holes
space-time curved by
string theory and
Boethius, Anicius
Book of Numbers, The (Conway and Guy)
Bororo
Boyle, Robert
Bradwardine, Thomas
Brahmagupta
branes
Brief History of Time, A (Hawking)
Brunelleschi, Filippo
Bruno, Giordano
calculus
calendars
Egyptian
Mayan
Cantor, Georg
cardinal numbers
Cartesian coordinates
Casimir, Hendrick B. G.
Casimir effect
Cavalieri, Bonaventura
century, arguments over start of
Cepheid variables
Chandogya Upanishad
Chandrasekhar, Subrahmanyan
Charles, Jacques-Alexandre
Christianity
see also God
Churchill, Winston, proof that he is a carrot
cipher
circle
Cohen, Paul
complex numbers
complex plane
computer programming
Confessions, The (Augustine)
conic sections
continuum hypothesis
“Convergence of the Twain, The” (Hardy)
Conway, John
Copernicus
cosmic background radiation
cosmological constant
C
ounter-Reformation
counting and numbers
Indian
starting with zero
counting boards
cubic polynomials
Danzig, Tobias
dates
decimal (base-10) system
derivative, modern definition of
Desargues, Gérard
Descartes, René
Dickens, Charles
differential equations
differentiation
dimensions
in painting and drawing
Dionysius Exiguus
Dirac, P.A.M.
Discourse on Method (Descartes)
distributive property
division
by zero
Donne, John
Doppler effect
drawing and painting, dimension in
duality:
in geometry
in religion
E = mc 2,
Earth, position of
Easter, date of
Eddington, Arthur
Egypt, Egyptians
Book of the Dead
calendar of
geometry invented by
numerals of
Einstein, Albert
n E = mc2 equation of
probability and
relativity theory of, see relativity
singularities and
universe as viewed by
Elder Edda
electrons
Eliot, T. S.
ellipses
elliptic curve
energy, in vacuum
Engels, Friedrich
Epic of Gilgamesh
epicycles
equations
beauty of
differential
linear
quadratic
escape velocity
Euler, Leonhard
event horizon
evil
exclusion principle
Feynman, Richard
Fibonacci
five-based (quinary) system
fluxions
fractions
free energy machines
French Revolution
galaxies
see also universe
Galileo Galilei
gases
plasma
Gauss, Carl Friedrich
gematria
geometry
Cartesian coordinates in
Egyptian invention of
projective
God
Aristotelian doctrine as proof of
complex numbers and
Pascal’s wager and
universe created by
golden ratio
Grandi, Guido
Graves, Robert
gravitational lenses
gravity
light bent by
Greeks
number-philosophy of
numerals of
guitar strings
Guy, Richard
Halley, Edmund
Hamlet (Shakespeare)
Hardy, Thomas
harmonic series
Hawking, Stephen
heat death
Hebrew creation myths
Hebrew numerals
Heisenberg, Werner
Hertz, Heinrich
Hilbert, David
Hinduism
Hippasus
“Hollow Men, The” (Eliot)
Hooke, Robert
Hubble, Edwin
imaginary numbers
India
infinitesimals
infinite vacuum
infinite zeros
infinity
Euler and
in Indian mathematics
limit and
and measuring area and volume
Pascal’s wager and
Renaissance and
of universe
vanishing point and
integers
integration
interference
irrationality
irrational numbers
irregular shapes, measuring of
Islam
Jansenists
Jesuits
Jesus
Jews
John I, Pope
Julian Date
kabbalism
Kelvin, William Thomson, Lord
Kepler, Johannes
Koran
Kronecker, Leopold
Lamoreaux, Steven
Laplace, Pierre-Simon
Leibniz, Gottfried Wilhelm
length
Leonardo da Vinci
L’Hôpital, Guillaume-François-Antoine de
Liber Abaci (Fibonacci)
light
bending of
interference in
speed of
ultraviolet
limit
line, slope of
linear equations
lottery
Lucretius
Luther, Martin
Maclaurin, Colin
Maimonides, Moses
Manichaean heresy
mass
inflation of
mathematics
beauty in
birth of
Indian
Mayans
calendar of
numerals of
Michelson, Albert
millennium, controversy over start of
Millis, Marc
Mohammed
Monge, Gaspard
monochord
Morley, Edward
motion
of planets
multiplication
by zero
musical scale
Muslims
myriads
mysticism, Jewish
NASA
nature
Nature
nautilus
negative numbers
square roots of
neutron star
Newton, Isaac
calculus of
Nicholas of Cusa
Number: The Language of Science (Danzig)
numbers and counting
Indian
starting with zero
numerals
Arabic
Babylonian
Mayan
omicron
“On Poetry: A Rhapsody” (Swift)
orders
ordinal numbers
Oresme, Nicholas
origin of zero
painting and drawing, dimension in
parabola
Parmenides
Parthenon
particle accelerators
particles
string theory and
virtual
Pascal, Blaise
experiments of
wager of
Pascal, Étienne
Pauli, Wolfgang
Pensées (Pascal)
pentagram
perpetual-motion machines
perspective, in painting and drawing
photoelectric effect
photons
physics
Planck, Max
plane, complex
planets:
motion of
Pythagorean model of
see also universe
plasma
point
vanishing
Polder, Dik
pole
polynomials
Poncelet, Jean-Victor
probability
projective geometry
Ptolemy
Puthoff, Harold
Pythagoras, Pythagoreans
planetary model of
quadratic polynomials and equations
quanta
quantum leap
quantum mechanics
string theory and
quantum sail
quarks
quartic polynomials
quinary system
quintic polynomials
rate times time equals di
stance
rationality, rational numbers
ratios
golden
Rayleigh-Jeans law
real numbers
Rees, Martin
Reformation
relativity
string theory and
Renaissance
renormalization
retrograde motion
Riemann, Georg Friedrich Bernhard
Rig Veda
Romans
numerals of
Scaliger, Joseph
Schrödinger equation
scientific revolution
sets
Seven Years’ War
sexagesimal system
Shakespeare, William
Shiva
Sierpinski, Waclaw
singularities
essential
naked
slope
of tangent
space-time
space travel
speed of light
sphere
square
diagonal of
square numbers
square roots of negative numbers
stain, measuring of
standard candles
stars
Cepheid
collapsing of
light bent around
movement of
statistical mechanics
steady-state theory
Stefan-Boltzmann equation
Stone Age
string theory
Suiseth, Richard
supernovas
Swift, Jonathan
Sylvester II, Pope
tachyons
tally sticks
tangent
Taylor, Brook
Tempier, Étienne
Thales
theories, beauty in
Theory of Everything
thermodynamics
Thomas Aquinas, Saint
time:
relativity of
space-time
travel in
timekeeping
see also calendars
time machine, making
Times (London)
Torricelli, Evangelista
transfinite numbers
triangle, estimating size of
triangular numbers
trigonometry
two-based (binary) system
ultraviolet catastrophe
ultraviolet light
uncertainty principle
universe:
Aristotelian model of, see Aristotle, Aristotelian doctrine
big bang theory of origin of
Earth’s position in
as eternal
expansion of
fate of
God as creator of
Hindu model of
as infinite
lumpiness of
size of
steady-state theory of
vacuum and
vacuum
energy in
infinite
and lumpiness of universe
see also void
vanishing point
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