Zero (32 page)

Neugebauer, O.
The Exact Sciences in Antiquity.
New York: Dover Publications, 1969.

Newman, James R.
The World of Mathematics.
Vols. 1–4. New York: Simon and Schuster, 1956.

Oldach, David, et al. “A Mysterious Death.”
The New England Journal of Medicine.
338 (11 June 1998): 1764.

Ovid.
Metamorphoses.
Trans. Rolfe Humphries. Bloomington, Ind.: Indiana University Press, 1955.

Oxtoby, David, and Norman Nachtrieb.
Principles of Modern Chemistry.
Philadelphia: Saunders College Publishing, 1986.

Pais, Abraham.
Subtle Is the Lord.
Oxford: Oxford University Press, 1982.

Pappas, Theoni.
Mathematical Scandals.
San Carlos, Calif.: Wide World Publishing/Tetra, 1997.

Pascal, Blaise.
Pensées and Other Writings.
Trans. Honor Levi. Oxford: Oxford University Press, 1995.

Pausanius.
Guide to Greece.
Vol. 2,
Description of Greece.
Trans. Peter Levi. London: Penguin Books, 1971.

Perricone, Mike. “The Universe Lives On.”
FermiNews
, 19 June 1998: 5.

Pickover, Clifford.
The Loom of God.
New York: Plenum Press, 1997.

Plato.
Parmenides.
From
Plato in Twelve Volumes,
Vol. 1 translated by Harold North Fowler; introduction by W. R. M. Lamb (1966); Vol. 3 translated by W. R. M. Lamb (1967); Vol. 4 translated by Harold North Fowler (1977); Vol. 9 translated by Harold N. Fowler (1925). Cambridge, Mass.: Harvard University Press; London: William Heinemann, Ltd., 1966, 1967, 1977. (Machine readable text.)

Plaut, Gunther.
The Torah: A Modern Commentary.
New York: The Union of American Hebrew Congregations, 1981.

Plutarch.
Makers of Rome.
Trans. Ian Scott-Kilvert. London: Penguin Books, 1965.

Plutarch on Sparta.
Trans. Richard J. A. Talbert. London: Penguin Books, 1988.

The Poetic Edda.
Trans. Lee Hollander. Austin, Tex.: University of Texas Press, 1962.

Polchinski, Joseph. “String Duality.”
Reviews of Modern Physics,
October 1996: 1245.

Pullman, Bernard, ed.
The Emergence of Complexity in Mathematics, Physics, Chemistry, and Biology.
Vatican City: Pontificia Academia Scientarum, 1996.

Randel, Don, ed.
The New Harvard Dictionary of Music.
Cambridge, Mass.: Belknap Press, 1986.

“Random Samples.”
Science,
23 January 1998: 487.

Rensberger, Boyce. “2001: A Calendar Odyssey.”
Washington Post,
11 December 1996: H01.

Resnikoff, H. L. and R. O. Wells.
Mathematics in Civilization.
New York: Dover Publications, 1973.

The Rig Veda. Trans. Wendy O'Flaherty. London: Penguin Books, 1981.

Rigatelli, Laura Toti.
Evariste Galois.
Trans. John Denton. Basel: Birkhauser Verlag, 1996.

Rothstein, Edward.
Emblems of Mind.
New York: Times Books, 1995.

Rotman, Brian.
Signifying Nothing.
Stanford, Calif.: Stanford University Press, 1987.

Royden, H. L.
Real Analysis.
New York: Macmillan, 1988.

Rudin, Walter.
Principles of Mathematical Analysis.
New York: McGraw-Hill, 1964.

———.
Real and Complex Analysis.
New York: McGraw-Hill, 1987.

Russell, Bertrand.
The Philosophy of Leibniz.
London: Routledge, 1992.

———.
The Philosophy of Logical Atomism.
Chicago: Open Court Publishing, 1985.

Schecter, Bruce.
My Brain Is Open.
New York: Simon and Schuster, 1998.

Scholem, Gershom.
Kabbalah.
New York: Meridian, 1974.

Seife, Charles. “Ever Outward.”
New Scientist,
3 January 1998: 19.

———. “Final Summer.”
New Scientist,
25 July 1998: 40.

———. “Magic Roundabout.”
New Scientist,
8 November 1997: 5.

———. “Mathemagician.”
The Sciences,
May/June 1994: 12.

———. “Music and mathematics and their surprisingly harmonious relationship.”
The Philadelphia Inquirer,
21 May 1995: H3.

———. “No Way Out.”
New Scientist,
5 September 1998: 20.

———. “Running on Empty.”
New Scientist,
25 April 1998: 36.

———. “The Subtle Pull of Emptiness.”
Science,
10 January 1997: 158.

———. “Too Damned Hot.”
New Scientist,
1 August 1998: 21.

———. “Unlucky for Some.”
New Scientist,
4 July 1998: 23.

Singh, Simon.
Fermat's Enigma.
New York: Walker and Company, 1997.

Slakey, Francis. “Something Out of Nothing.”
New Scientist,
23 August 1997: 45.

Smith, David Eugene.
A Source Book in Mathematics.
New York: Dover Publications, 1959.

Sturluson, Snorri.
The Prose Edda.
Trans. Jean I. Young. Berkeley, Calif.: University of California Press, 1954.

Swetz, Frank.
From Five Fingers to Infinity.
Chicago: Open Court Publishing, 1994.

Teresi, Dick. “Zero.”
The Atlantic Monthly,
July 1997: 88.

Thompson, Damian.
The End of Time.
Hanover, N.H.: University Press of New England, 1996.

Thorne, Kip.
Black Holes and Time Warps.
New York: W. W. Norton, 1994.

Thorpe, J. A.
Elementary Topics in Differential Geometry.
New York: Springer-Verlag, 1979.

Thucydides.
History of the Peloponnesian War.
Trans. Rex Warner. London: Penguin Books, 1954.

Turok, Neil, and S. W. Hawking. “Open Inflation, the Four Form and the Cosmological Constant.” Los Alamos National Labs Archive: hep-th/9803156 v4.

The Upanishads. Trans. Juan Mascaro. London: Penguin Books, 1965.

Urmson, J. O., and Jonathan Ree, eds.
The Concise Encyclopedia of Western Philosophy and Philosophers.
London: Routledge, 1996.

Valenkin, Naum Yakovlevich.
In Search of Infinity.
Trans. Abe Shenitzer. Boston: Birkhauser, 1995.

Vilenkin, Alexander. “The Quantum Cosmology Debate.” Los Alamos National Labs Archive: gr-qc/9812027.

Voltaire.
Candide.
London: Penguin Books, 1947.

Wang, Hao.
Reflections on Kurt Gödel.
Cambridge, Mass.: The MIT Press, 1987.

White, Michael.
The Last Sorcerer.
Reading, Mass.: Addison-Wesley, 1997.

Xenophon.
Hellenica.
Trans. Carleton L. Brownson. Vols. 1–2,
Xenophon in Seven Volumes.
Cambridge, Mass.: Harvard University Press; London: William Heinemann, Ltd.; Vol. 1, 1985; Vol. 2, 1986. (Machine readable text.)

Web Sites

Papyrus of Ani; Egyptian Book of the Dead. Trans. E. A. Wallis Budge. http://www.sas.upenn.edu/African_Studies/Books/Papyrus_Ani.html

Clement of Alexandria.
The Stromata.
http://www.webcom.com/~gnosis/library/strom4.htm

“The Life of Hypatia.” http://www.cosmopolis.com/alexandria/

“Frequently Asked Questions in Mathematics.” http://www.cs.unb.ca/~alopez-o/math-faq/

Odenwald, Sten. “Beyond the Big Bang.” http://www2.ari.net/home/odenwald/anthol/beyondbb.html

———. “The Decay of the False Vacuum.” http://www2.ari.net/home/odenwald/anthol/decay.html

Perseus Project. http://hydra.perseus.tufts.edu/

Slabodkin, Gregory. “Software glitches leave Navy Smart Ship dead in the water.”
Government Computer News,
13 July 1998. http://www.gcn. com/gcn/1998/July13/cov2.htm

The MacTutor History of Mathematics archive. http://history.math.csusb.edu/

Weisstein, Eric. Eric's Treasure Trove of Astronomy. http://www.treasuretroves.com/astro/astro0.html

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!)

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

Counter-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 = mc
²
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