Review by Choice Review
Does the world need a book that documents the process of writing a book? Devlin (Stanford Univ.) says "yes" and presents documentation of his decade-long expedition for information about Leonardo of Pisa, better known as Fibonacci. Throughout this new book, which complements his The Man of Numbers: Fibonacci's Arithmetic Revolution (2011), the author justifies sharing his journey because Fibonacci had "more influence on the course of the world than almost any other mathematician in history." Devlin rightly recognizes the efforts of four individuals who aided him in his journey to uncover further information about the influential medieval mathematician. Though these stories are interesting and well-documented, readers must muddle through a significant amount of fluff and self-aggrandizement on Devlin's part, who has the temerity to compare his work as an "expository" author to that of Fibonacci. All the book's important content could have been reduced into an explanatory journal article. Summing Up: Recommended. General readers only. --Jerry Johnson, Western Washington University
Copyright American Library Association, used with permission.
Review by New York Times Review
WITH THEIR STRANGE AND PUZZLING RELATIONSHIP to numbers, the Pirahä, a small group of hunter-gatherers who live deep in the Amazon rain forest, seem like some fantastical creation of Jorge Luis Borges. Their relationship to numbers is: They don't have one. The language they speak has no precise number words, not even "one" or "two." It also lacks what linguists call grammatical number - terms like "both," from which you can tell the speaker is referring to two of something. While the Pirahä do have some number-like phrases, they are ballpark expressions, like "a few" in English. More curious still, these linguistic limitations track behavioral limitations. The Pirahä cannot, with any consistency, precisely differentiate quantities larger than 3. If you show them a lineup of seven spools of thread and ask them to replicate it, they struggle, creating lineups of five or six or eight. They can tell that a large group of spools is bigger than a much smaller group - psychologists call that an approximate number sense - but their exact number sense conks out after 3. Were there four Beatles or five? The Pirahä couldn't rightly say. One of the lessons of numbers andthe making of us: Counting and the Course of Human Cultures (Harvard University, $27.95), a fascinating book by the anthropologist Caleb Everett, is that to exoticize the Pirahä (say, by likening them to Borges characters) is to misunderstand the insight they represent. The Pirahä are not fundamentally unlike other human beings. On the contrary, they show us what human beings are like in isolation from a cultural innovation we take for granted: the written and spoken symbols of quantities known as numbers. Everett stresses that numbers are not concepts we arrive at "naturally and natively." Like a flint arrowhead or the wheel, they are tools people invented a long time ago, and we know how to use them only because we find ourselves in a society in which that knowledge has been preserved and transmitted. Without these symbols, we, like the Pirahä, could not "see" divisions between most quantities. With them, as Everett tells it, our ancestors learned to count, and thereby "radically transformed the human condition," making possible such number-dependent developments as complex agriculture. You needn't venture into the wild to find illustrations of our crude inborn number sense. Perhaps the most convincing evidence, Everett notes, comes from cognitive research on children. Even shortly after birth, prelinguistic infants are capable of identifying discrepancies between the quantities 1, 2 and 3, as well as recognizing disparities between large and small groups of things. But well after they start walking and talking, children still find it hard to learn what 4 and 5 are, and how they are related. This rudimentary feel for quantities - precision with small ones, blurry approximation thereafter - can be observed not only in young children and isolated peoples like the Pirahä but also in nonhuman primates like chimps and some nonprimate animals like rats. It appears to be our genetic endowment, an apparatus good enough to have helped us survive the rigors of natural selection. It may also underlie certain widespread features of the world's languages, such as the fact that they permit distinctions between one thing and many ("car" versus "cars") and allow for the identification of two things ("both") or three (though not in English), but in no known cases do they give you the means to refer to precise quantities of 4 or more - unless, of course, you use a number. If numbers don't come to us naturally, where do they come from? When children learn numbers, Everett emphasizes, it can't be a process of learning names for concepts they already have. It must be a process of "concepting" those names: Words like "four" and "five" and "six" function as place holders for ideas children eventually grasp. With instruction and practice, they start with concepts they know intuitively (such as that 2 is one more than 1) and learn to construct others by analogy (such as that 8 is one more than 7). Much as a fishing rod is a tool we use to acquire fish, number words are tools we use to acquire number concepts. This account seems to present a paradox: How did we ever manage to create names for quantities if we weren't able to recognize quantities without names for them? This consideration has led many scholars to conclude, contrary to Everett, that we must be biologically "wired" for numbers. Everett's response is speculative: While human beings typically cannot discriminate an exact quantity such as 4 without number words, he suggests that some people - people we might call inventors - must have occasionally hit upon the idea that the quantity of 4 could be referred to precisely. Many thousands of years ago, by giving names to these otherwise fleeting ideas, such inventors made their insights available to others, creating tools to be borrowed, shared and developed further. Sharing mathematics is consequential business. Just as the transmission of numbers made possible the development of agriculture, so too the transmission of more sophisticated mathematics, many thousands of years later, made possible the scientific revolution, industrialization and modern medicine. In his jaunty book FINDING FIBONACCI: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World (Princeton University, $29.95), Keith Devlin sets out to tell the elusive story of the 13th-century mathematician Leonardo of Pisa. As the author of the first extensive text on modern practical arithmetic in the West, Leonardo has some claim to being the pre-eminent sharer of mathematical tools of his age - and thus, in Devlin's estimation, "one of the most influential men of all time." In 1202, Leonardo, also known as Leonardo Fibonacci, published "The Book of Calculation." While the book didn't contain any original mathematical discoveries, it did offer elegant methods for solving arithmetical problems, often using examples involving money - investing, converting or otherwise allocating it. The impact of these examples, which underscored the application of arithmetical methods to business and trade, was considerable. In the early 2000s, a historian of mathematics demonstrated that "The Book of Calculation" was a main driver of the financial revolution that arose in medieval Ttiscany soon after its publication. Around the same time, a professor of finance showed that the book's innovative treatment of financial decision making facilitated the development of complex financial tools over the next few hundred years. Devlin, a mathematician who has proved a few "largely unremarkable theorems" while distinguishing himself as a popular expositor of mathematics, has more than a little sympathy for Fibonacci. No doubt he was also relieved to learn that although Leonardo's name is attached to the famous set of numbers known as the Fibonacci sequence, Leonardo did not discover them, but merely included a brief discussion of them in his book. The Fibonacci sequence - a progression of numbers whose first two terms are 1 and 1, and each subsequent term of which is the sum of the two preceding terms (1,1,2, 3,5,8 and so on) - seems to have first appeared more than a millennium earlier in a book by a Sanskrit grammarian. Another popular myth about the Fibonacci sequence of which Devlin disabuses his reader is that it has "deep connections to human aesthetics." So what is interesting and true about the Fibonacci sequence? For an answer to that question, you can consult the mathematics lover's companion: Masterpieces for Everyone (Yale University, $28), by the mathematician Edward Scheinerman. It includes the Fibonacci sequence as one of 23 masterworks whose analysis Scheinerman presents with rigor and accessibility (assuming you have some taste for formal systems) for nonmathematicians. Are you interested in the properties of the sums of the terms of the Fibonacci sequence? Of their ratios? Of their relation to the so-called golden mean? Or perhaps you'd rather learn a bit more about that weird tribe in the Amazon? ? JAMES RYERSON is a senior staff editor for The Times's Op-Ed page. His column appears every eight weeks.
Copyright (c) The New York Times Company [May 5, 2017]
Review by Publisher's Weekly Review
Stanford mathematician Devlin (The Unfinished Game) leads a cheerful pursuit to rediscover the hero of 13th-century European mathematics, taking readers across centuries and through the back streets of medieval and modern Italy in this entertaining and surprising history. Devlin's target is Leonardo of Pisa (later known as Leonardo Fibonacci), a mathematician whose book Liber abbaci played a key role in the making of the modern world. Leonardo was the son of a prosperous merchant in Pisa, a major trade hub between Europe and the Arab world, and he would have had plenty of hands-on experience with practical math and algebra in the marketplace. His book, filled with "recreational" math problems, was well known in its time, Devlin says, and it spawned an entire popular genre of abbacus books, only to be forgotten until the 1960s, some 800 years later. From the busy streets of Pisa's Piazza dei Miracoli and Leaning Tower to the ornate buildings of the University of Siena and the mysterious chambers of the Biblioteca Riccardiana, Devlin relates Leonardo's adventures with brio and charm. Readers will enjoy this deft and engaging mix of history, mathematics, and personal travelogue. Agent: Ted Weinstein Literary Management. (Apr.) © Copyright PWxyz, LLC. All rights reserved.
(c) Copyright PWxyz, LLC. All rights reserved
Review by Library Journal Review
Devlin (cofounder, executive director, Human-Sciences & Technologies Advanced Research Inst., Stanford Univ.) follows up The Man of Numbers: Fibonacci's Arithmetic Revolution, a biography of 13th-century mathematician Leonardo of Pisa (otherwise known as Fibonacci) and examination of his enduring influence on math education, with this story of how that book was researched and written. Over the course of a decade, Devlin took research side trips to Pisa and other cities while in Italy for conferences and talks leading to the publication of Numbers. Luckily for his readers, he also wrote this engaging and entertaining account of his experiences. Even math neophytes will appreciate this title, although they may have difficulty understanding some of the concepts sprinkled throughout. The anecdotes touch upon many of the joys and frustrations of conducting historical research when there are few primary sources and everything is in another language. VERDICT An excellent read for those who enjoyed the author's previous volume, are interested in the history of math, and/or would like to learn more about the sticky research process.-Holly Boyer, -Reston, VA © Copyright 2017. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
(c) Copyright Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
