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the Complete Review
the complete review - mathematics


John Allen Paulos

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To purchase Innumeracy

Title: Innumeracy
Author: John Allen Paulos
Genre: Non-fiction
Written: 1988
Length: 186 pages
Availability: Innumeracy - US
Innumeracy - UK
Innumeracy - Canada
  • Mathematical Illiteracy and its Consequences
  • The new US edition appeared in 2001. It is a very slightly revised edition, and includes a new preface.
  • The new UK edition appeared in 2000

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Our Assessment:

B- : fun facts and examples, but less than ideally presented

See our review for fuller assessment.

Review Summaries
Source Rating Date Reviewer
American Math. Monthly . 1/1990 Lisa J. Evered
American Scientist . 3/1990 Alan H. Schoenfeld
Christian Science Monitor . 14/2/1989 R. Langdon Wales
The Guardian . 21/12/1989 Walter Gratzer
The LA Times . 14/2/1989 Lee Dembart
New Scientist . 1/12/1990 Ros Herman
The New York Times . 23/1/1989 C. Lehmann-Haupt
The NY Times Book Rev. . 15/1/1989 Morris Kline
Partisan Review . Winter/1991 Margarita Levin
San Francisco Chronicle . 22/10/1989 Lee Dembart

  From the Reviews:
  • "Paulos is very good at explaining all of this, though sometimes with a hectoring, bitter tone, for which he apologizes at the very end. He notes correctly that the public's failure to understand chance phenomena, statistics, probability and the nature of many numerical assertions opens the way for all manner of belief in nonsense. Perhaps more important, it leads to distortions in the making of public policy." - Lee Dembart, The Los Angeles Times

  • "On the whole he succeeds in avoiding what he deplores as "the overly earnest and scolding tone" common to endeavors "concerned with various inadequacies." But his pervading wit occasionally shades over into hostility. (...) But what makes his book most worthwhile is the playfulness of Mr. Paulos's mind" - Christopher Lehmann-Haupt, The New York Times

Please note that these ratings solely represent the complete review's biased interpretation and subjective opinion of the actual reviews and do not claim to accurately reflect or represent the views of the reviewers. Similarly the illustrative quotes chosen here are merely those the complete review subjectively believes represent the tenor and judgment of the review as a whole. We acknowledge (and remind and warn you) that they may, in fact, be entirely unrepresentative of the actual reviews by any other measure.

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The complete review's Review:

       John Allen Paulos' 1988 book Innumeracy stands up quite well even more than a dozen years after its initial publication. He defines "innumeracy" as "an inability to deal comfortably with the fundamental notions of number and chance", and it seems as popular as ever. As he mentions in his new preface to the (American) 2001 edition, examples of widespread innumeracy still abound -- as the "infamous presidential election of 2000" demonstrated so well. Paulos correctly states that, for example: "An examination of the tiny difference between Gore and Bush in the official vote totals, especially given the crude Florida election apparatus, would have shown it to be statistically meaningless."
       This is part of the strength of the book -- stating the obvious that too frequently remains overlooked, ignored, or misunderstood. But he already shows part of the weakness of the book here as well. Paulos speaks of "statistically meaningless", forgetting that this terminology is already enough to throw off most of his innumerate readers. He doesn't bother to state what is perhaps obvious to him and should be obvious to all: "statistically meaningless" means not only that it is meaningless in some obscure, abstract "statistical" way, but that it is really and truly and in the simplest and most down to earth manner meaningless.
       Paulos heaps on many marvelous examples of how we misapprehend risk and misinterpret data and generally make a muddle of many things having to do with numbers. Politicians, the press, and advertisers are shown -- surprise, surprise -- as manipulators of numbers in entirely inappropriate ways (intentionally and not). And Paulos shows how the largely innumerate population so readily allows itself to be duped, to its own detriment.
       Paulos is right in his outrage: innumeracy -- like illiteracy -- is unacceptable, and the cost to society (in bad decisions made on the basis of bad and misunderstood maths) far too great. Individual decisions and broader policy decisions are far too often made on the basis of badly understood statistics, data, and mathematical principles.
       But Paulos' book is also an uneasy compromise between primer and exposé. He offers real and current (or at least recent) examples, as well as explaining the maths behind many of the examples more generally, so in places it is a straightforward (well, a less than straightforward ...) maths textbook while elsewhere it focusses on real-life examples. The real-life examples are generally more useful: Paulos gets the maths right in his general examples, but many of these are ... a bit boring. Worse is that the general examples often seem entirely arbitrary -- chosen, the innumerate might suspect, merely to prove a point and not necessarily relevant in (or applicable to) other situations. (One difficulty the innumerate often have is translating principle into practice, and though Paulos does his best to show the principles in practice it often isn't enough.)
       The maths are fun for those that can follow Paulos, but in his mad rush (he covers a great deal of ground) one imagines the innumerate might have some difficulty in keeping up. There are asides galore, from scientific notation ("not nearly as arcane as many topics discussed in the media") to his idea of a "logarithmic safety index". The latter is a quite fascinating and useful idea -- and relevant to much that he writes about -- but some of the many asides and tangents, and the fast pace, make even numerate heads spin.
       There is also some charming naïveté:

I think the establishment of statistical ombudsmen by television networks, news magazines, and major newspapers would be a welcome and effective step in combating innumeracy in the media.
       "Effective" -- quite possibly; "welcome" -- perhaps by consumers. But the media isn't much interested in combatting innumeracy (think of how many people got fired after all the networks prematurely declared first Gore then Bush the winner in Florida in the 2000 American presidential election -- none: incompetence on even this spectacular scale is apparently deemed perfectly acceptable, since people -- even supposed professionals -- apparently can't be expected to deal with such complex things as numbers). Look at the popularity of polls on TV, in newspapers and magazines, and now on the Internet, and look how feeble the presentation of these usually is (almost none would stand up to much Paulos-scrutiny, for example). Paulos did get himself a gig at ABCNews.com clearing things up, and there are a few watchdogs and debunkers out there (generally ranting and raving very much at the periphery), but a more realistic solution lies in decreasing mass-innumeracy itself.
       Paulos does consider both the causes and the possible ways to decrease the prevalence of innumeracy, but his discussion and suggestions are necessarily barely elaborated on (he has a lot to get to in this short book).
       Innumeracy is a fairly fun, fairly quick read, addressing an important issue. It isn't quite as much fun as it could be, and the mathematics is probably largely too familiar (and the theoretical examples unnecessary) to the numerate and too daunting for the innumerate. Paulos is aware of some of the problems ("I have a difficult time writing at extended length about anything") and he is probably right when he writes: "mathematics is too important to be left to the mathematicians"
       By raising the issue of innumeracy and reaching such a large audience (Innumeracy spent a couple of weeks on the bestseller list) Paulos certainly achieved something with this book. One imagines that it could have been done much (much !) better, but it was good enough for a lot of people, and it did serve a valuable purpose. And since innumeracy still plagues the nation (more than ever, it often seems) the lesson has apparently not been learnt and it may still be a necessary book.

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Innumeracy: Reviews: John Allen Paulos: Innumeracy: Other books by John Allen Paulos under review: Other books of interest under review:

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About the Author:

       John Allen Paulos teaches mathematics at Temple University. He has written numerous books about mathematics.

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© 2001-2010 the complete review

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