Nine Algorithms That Changed the Future: The Ingenious Ideas That Drive Today's Computers

224 Pages·2011·3.25 MB·English

by  John MacCormick

Nine Algorithms That
Changed the Future THE
INGENIOUS IDEAS THAT
DRIVE TODAY'S COMPUTERS
John MacCormick
P R I N C E T O N U N I V E R S I T Y P R E S S
P R I N C E T O N A N D O X F O R D
Copyright © 2012 by Princeton University Press Published by Princeton University Press,
41 William Street, Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press,
6 Oxford Street, Woodstock, Oxfordshire OX20 1TW
All Rights Reserved
Library of Congress Cataloging-in-Publication Data MacCormick, John, 1972–
Nine algorithms that changed the future : the ingenious ideas that drive
today's computers / John MacCormick.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-691-14714-7 (hardcover : alk. paper)
1. Computer science. 2. Computer algorithms.
3. Artificial intelligence. I. Title.
QA76M21453 2012
006.3-dc22 2011008867
A catalogue record for this book is available from the British Library This book has been composed in
Lucida using TEX
Typeset by T&T Productions Ltd, London
Printed on acid-free paper
press.princeton.edu
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
The world has arrived at an age of cheap complex devices of
great reliability; and something is bound to come of it.
—Vannevar Bush, “As We May Think,” 1945
CONTENTS
Foreword
1. Introduction: What Are the Extraordinary Ideas Computers Use Every Day?
2. Search Engine Indexing: Finding Needles in the World's Biggest Haystack
3. PageRank: The Technology That Launched Google
4. Public Key Cryptography: Sending Secrets on a Postcard
5. Error-Correcting Codes: Mistakes That Fix Themselves
6. Pattern Recognition: Learning from Experience
7. Data Compression: Something for Nothing
8. Databases: The Quest for Consistency
9. Digital Signatures: Who Really Wrote This Software?
10. What Is Computable?
11. Conclusion: More Genius at Your Fingertips?
Acknowledgments
Sources and Further Reading
Index
FOREWORD
Computing is transforming our society in ways that are as profound as the
changes wrought by physics and chemistry in the previous two centuries. Indeed,
there is hardly an aspect of our lives that hasn't already been influenced, or even
revolutionized, by digital technology. Given the importance of computing to
modern society, it is therefore somewhat paradoxical that there is so little
awareness of the fundamental concepts that make it all possible. The study of
these concepts lies at the heart of computer science, and this new book by
MacCormick is one of the relatively few to present them to a general audience.
One reason for the relative lack of appreciation of computer science as a
discipline is that it is rarely taught in high school. While an introduction to
subjects such as physics and chemistry is generally considered mandatory, it is
often only at the college or university level that computer science can be studied
in its own right. Furthermore, what is often taught in schools as “computing” or
“ICT” (information and communication technology) is generally little more than
skills training in the use of software packages. Unsurprisingly, pupils find this
tedious, and their natural enthusiasm for the use of computer technology in
entertainment and communication is tempered by the impression that the
creation of such technology is lacking in intellectual depth. These issues are
thought to be at the heart of the 50 percent decline in the number of students
studying computer science at university over the last decade. In light of the
crucial importance of digital technology to modern society, there has never been
a more important time to re-engage our population with the fascination of
computer science.
In 2008 I was fortunate in being selected to present the 180th series of Royal
Institution Christmas Lectures, which were initiated by Michael Faraday in
1826. The 2008 lectures were the first time they had been given on the theme of
computer science. When preparing these lectures I spent much time thinking
about how to explain computer science to a general audience, and realized that
there are very few resources, and almost no popular books, that address this
need. This new book by MacCormick is therefore particularly welcome.
MacCormick has done a superb job of bringing complex ideas from computer
science to a general audience. Many of these ideas have an extraordinary beauty
and elegance which alone makes them worthy of attention. To give just one
example: the explosive growth of web-based commerce is only possible because
of the ability to send confidential information (such as credit card numbers, for
example) secretly and securely across the Internet. The fact that secure
communication can be established over “open” channels was for decades
thought to be an intractable problem. When a solution was found, it turned out to
be remarkably elegant, and is explained by MacCormick using precise analogies
that require no prior knowledge of computer science. Such gems make this book
an invaluable contribution to the popular science bookshelf, and I highly
commend it.
Chris Bishop
Distinguished Scientist, Microsoft Research Cambridge
Vice President, The Royal Institution of Great Britain
Professor of Computer Science, University of Edinburgh
1
Introduction: What Are the Extraordinary Ideas
Computers Use Every Day?
This is a gift that I have…a foolish extravagant spirit, full of forms, figures, shapes, objects, ideas,
apprehensions, motions, revolutions.
—WILLIAM SHAKESPEARE, Love's Labour's Lost
How were the great ideas of computer science born? Here's a selection:
• In the 1930s, before the first digital computer has even been built, a British
genius founds the field of computer science, then goes on to prove that
certain problems cannot be solved by any computer to be built in the future,
no matter how fast, powerful, or cleverly designed.
• In 1948, a scientist working at a telephone company publishes a paper that
founds the field of information theory. His work will allow computers to
transmit a message with perfect accuracy even when most of the data is
corrupted by interference.
• In 1956, a group of academics attend a conference at Dartmouth with the
explicit and audacious goal of founding the field of artificial intelligence.
After many spectacular successes and numerous great disappointments, we
are still waiting for a truly intelligent computer program to emerge.
• In 1969, a researcher at IBM discovers an elegant new way to structure the
information in a database. The technique is now used to store and retrieve
the information underlying most online transactions.
• In 1974, researchers in the British government's lab for secret
communications discover a way for computers to communicate securely
even when another computer can observe everything that passes between
them. The researchers are bound by government secrecy—but fortunately,
three American professors independently discover and extend this
astonishing invention that underlies all secure communication on the
internet.
• In 1996, two Ph.D. students at Stanford University decide to collaborate on
building a web search engine. A few years later, they have created Google,
the first digital giant of the internet era.
As we enjoy the astonishing growth of technology in the 21st century, it has
become impossible to use a computing device—whether it be a cluster of the
most powerful machines available or the latest, most fashionable handheld
device—without relying on the fundamental ideas of computer science, all born
in the 20th century. Think about it: have you done anything impressive today?
Well, the answer depends on your point of view. Have you, perhaps, searched a
corpus of billions of documents, picking out the two or three that are most
relevant to your needs? Have you stored or transmitted many millions of pieces
of information, without making a single mistake—despite the electromagnetic
interference that affects all electronic devices? Did you successfully complete an
online transaction, even though many thousands of other customers were
simultaneously hammering the same server? Did you communicate some
confidential information (for example, your credit card number) securely over
wires that can be snooped by dozens of other computers? Did you use the magic
of compression to reduce a multimegabyte photo down to a more manageable
size for sending in an e-mail? Or did you, without even thinking about it, exploit
the artificial intelligence in a handheld device that self-corrects your typing on
its tiny keyboard?
Each of these impressive feats relies on the profound discoveries listed earlier.
Thus, most computer users employ these ingenious ideas many times every day,
often without even realizing it! It is the objective of this book to explain these
concepts—the great ideas of computer science that we use every day—to the
widest possible audience. Each concept is explained without assuming any
knowledge of computer science.
ALGORITHMS: THE BUILDING BLOCKS OF
THE GENIUS AT YOUR FINGERTIPS
So far, I've been talking about great “ideas” of computer science, but computer
scientists describe many of their important ideas as “algorithms.” So what's the
difference between an idea and an algorithm? What, indeed, is an algorithm?
The simplest answer to this question is to say that an algorithm is a precise
recipe that specifies the exact sequence of steps required to solve a problem. A
great example of this is an algorithm we all learn as children in school: the
algorithm for adding two large numbers together. An example is shown above.
The algorithm involves a sequence of steps that starts off something like this:
“First, add the final digits of the two numbers together, write down the final digit