Books of The Times: ‘Big Data,’ by Viktor Mayer-Schönberger and Kenneth Cukier

Does what? Uses “big data” analysis of the swelling flood of data that is being generated and stored about virtually every aspect of our lives to identify patterns of behavior and make correlations and predictive assessments.

Amazon uses customer data to give us recommendations based on our previous purchases. Google uses our search data and other information it collects to sell ads and to fuel a host of other services and products.

The National Security Agency, a news article in The Guardian revealed last week, is collecting the phone records of millions of American customers of Verizon — “indiscriminately and in bulk” and “regardless of whether they are suspected of any wrongdoing” — under a secret court order. Under another surveillance program called Prism, The Guardian and The Washington Post reported, the agency has been collecting data from e-mails, audio and video chats, photos, documents and logins, from leading Internet companies like Microsoft, Yahoo, Google, Facebook and Apple, to track foreign targets.

Why spread such a huge net in search of a handful of terrorist suspects? Why vacuum up data so indiscriminately? “If you’re looking for a needle in the haystack, you need a haystack,” Jeremy Bash, chief of staff to Leon E. Panetta, the former director of the Central Intelligence Agency and defense secretary, said on Friday.

In “Big Data,” their illuminating and very timely book, Viktor Mayer-Schönberger, a professor of Internet governance and regulation at the Oxford Internet Institute at Oxford University, and Kenneth Cukier, the data editor for The Economist, argue that the nature of surveillance has changed.

“In the spirit of Google or Facebook,” they write, “the new thinking is that people are the sum of their social relationships, online interactions and connections with content. In order to fully investigate an individual, analysts need to look at the widest possible penumbra of data that surrounds the person — not just whom they know, but whom those people know too, and so on.”

Mr. Cukier and Mr. Mayer-Schönberger argue that big data analytics are revolutionizing the way we see and process the world — they even compare its consequences to those of the Gutenberg printing press. And in this volume they give readers a fascinating — and sometimes alarming — survey of big data’s growing effect on just about everything: business, government, science and medicine, privacy and even on the way we think. Notions of causality, they say, will increasingly give way to correlation as we try to make sense of patterns.

Data is growing incredibly fast — by one account, it is more than doubling every two years — and the authors of this book argue that as storage costs plummet and algorithms improve, data-crunching techniques, once available only to spy agencies, research labs and gigantic companies, are becoming increasingly democratized.

Big data has given birth to an array of new companies and has helped existing companies boost customer service and find new synergies. Before a hurricane, Walmart learned, sales of Pop-Tarts increased, along with sales of flashlights, and so stores began stocking boxes of Pop-Tarts next to the hurricane supplies “to make life easier for customers” while boosting sales. UPS, the authors report, has fitted its trucks with sensors and GPS so that it can monitor employees, optimize route itineraries and know when to perform preventive vehicle maintenance.

Baseball teams like Billy Beane’s Oakland A’s (immortalized in Michael Lewis’s best-seller “Moneyball”) have embraced new number-crunching approaches to scouting players with remarkable success. The 2012 Obama campaign used sophisticated data analysis to build a formidable political machine for identifying supporters and getting out the vote. And New York City has used data analytics to find new efficiencies in everything from disaster response, to identifying stores selling bootleg cigarettes, to steering overburdened housing inspectors directly to buildings most in need of their attention. In the years to come, Mr. Mayer-Schönberger and Mr. Cukier contend, big data will increasingly become “part of the solution to pressing global problems like addressing climate change, eradicating disease and fostering good governance and economic development.”

There is, of course, a dark side to big data, and the authors provide an astute analysis of the dangers they foresee. Privacy has become much more difficult to protect, especially with old strategies — “individual notice and consent, opting out and anonymization” — losing effectiveness or becoming completely beside the point.

“The ability to capture personal data is often built deep into the tools we use every day, from Web sites to smartphone apps,” the authors write. And given the myriad ways data can be reused, repurposed and sold to other companies, it’s often impossible for users to give informed consent to “innovative secondary uses” that haven’t even been imagined when the data was first collected.

Kenneth I. Appel, Mathematician Who Harnessed Computer Power, Is Dead at 80

The cause was esophageal cancer, which was diagnosed in October, his son Andrew said.

Since the time of Euclid and Pythagoras, proofs of mathematical theorems had consisted of long strings of equations or geometric notations that any mathematician could read and quibble with, all marching logically, step by step, toward a conclusion. But the proof that Dr. Appel and a colleague, Wolfgang Haken, established in 1976 was of a different order.

Their conclusion, that four colors would suffice for any map, depended on 1,200 hours of computer time — the equivalent of 50 days — and 10 billion logical decisions all made automatically and out of sight by the innards of an I.B.M. computer at the University of Illinois in Urbana.

Hailed in some circles, including this newspaper, as “a major intellectual feat,” the proof shepherded computers toward a greater role in higher math. But it made many mathematicians uneasy; they worried about computer bugs and wondered how they could check or understand a “proof” they could not see. And it ignited a long-running debate about what constitutes a mathematical proof.

“Like a landmark Supreme Court case, the proof’s legacy is still felt and hotly debated,” said Edward Frenkel, a mathematician at the University of California, Berkeley.

Kevin Short, a mathematician at the University of New Hampshire, where Dr. Appel spent his later years, called the feat “a watershed for modern mathematics.”

“It has spawned whole fields of study,” he said.

Kenneth Ira Appel (pronounced ah-PEL) was born on Oct. 8, 1932, in Brooklyn and grew up in Queens, where he graduated from Queens College with a degree in mathematics in 1953. His father, Irwin, was an electrical engineer, and his mother, the former Lillian Sender, had been an office worker.

After a short stint as an actuary and two years in the Army, Kenneth Appel enrolled at the University of Michigan, where he earned a Ph.D. in math in 1959. During the summers, he programmed computers for Douglas Aircraft.

Dr. Appel soon went to work for the Institute for Defense Analyses in Princeton, N.J., doing research in cryptography and number theory for the federal government. He joined the University of Illinois as a professor in 1961. Long interested in Democratic politics, he also served a term on the Urbana City Council.

Some of the thorniest problems in math are simple to state but hideously complex under the surface. Such is the case with the four-color theorem, first enunciated by an English mapmaker, Francis Guthrie, in 1852. He asserted that to create a map in which no adjacent countries are the same color, only four colors are needed. Although everyone believed it was true, proof had eluded a century of mathematicians until Dr. Appel attended a lecture in 1972 by Dr. Haken.

Because of the bewildering variety of map configurations, Dr. Haken was contemplating using computers to solve the problem, but as he related in his lecture that evening, experts had convinced him that it was not possible.

Dr. Appel, familiar with computers from his defense and government work, was more optimistic.

“I don’t know of anything involving computers that can’t be done; some things just take longer than others,” he said to Dr. Haken afterward, according to an account in the journal Social Studies of Science by Donald MacKenzie of the University of Edinburgh. “Why don’t we take a shot at it?”

The two started off by showing that the universe of all possible maps must contain what mathematicians call an “unavoidable set” of 1,936 different configurations. One configuration might be a country surrounded by four neighbors, for example.

Their task, then, was to prove that each of these configurations could be rendered on a map using only four colors in such a way that no two adjacent land areas were of the same color. That was where the heaviest computation would come in. To help, they recruited a computer science graduate student, John Koch, and Dr. Appel persuaded the university to let them use its I.B.M. 370-168 computer, newly acquired for administrative services.

Those were the days when computers filled an entire room, although their memory capacities were minuscule compared with a modern smartphone. Dr. Short recounted an occasion, as described by Dr. Appel, when the computer gave an unexpected answer.

“Oh, that wire must have fallen out again,” Dr. Appel said.

Dr. Appel began to think of the computer as a partner, though with a different kind of brain, with almost “an artificial intelligence,” he told Dr. MacKenzie.

This article has been revised to reflect the following correction:

Correction: April 30, 2013

An obituary on Monday about the mathematician Kenneth I. Appel contained several errors. The author of an article in the journal Social Studies of Science that discussed Dr. Appel’s work was Donald MacKenzie, not Douglas MacKenzie. The agency in Princeton, N.J., for which Dr. Appel worked is the Institute for Defense Analyses, not Analysis. And Dr. Appel’s wife is Carole S. Appel, not Carole S. Stein. (Stein was her surname before she married, but she took her husband’s name.)