Sunday, September 16, 2007

Book Club: Innumeracy

Mathematical illiteracy and its consequences
John Allen Paulos, 1988
Hill & Wang, New York

I read an entire book this weekend, further contributing to the enormous variance in my reading pace. I'll write a book club about the other book I just finished, S. J. Gould's The Lying Stones of Marrakech, when I get a chance to go over it in detail.

Anyway, I think I picked this book up a while ago at one of SFU's annual United Way booksales, probably for $1.00 or less. Innumeracy is a short book, and a quick read, at only 180 pages. Reading this book (today, a nice lazy Sunday), I wanted it to be longer. Specifically, the first two chapters, covering a third of the book, feels like an introduction to a much larger and more comprehensive discussion about innumeracy, its occurrence in society, and specific case studies of innumeracy as a problem to be solved. All of that discussion does happen in the rest of the book, and in a remarkably well-written and consise fashion, but there is certainly room for much more.

Innumeracy is defined in this book as an analog to illiteracy - the inability to work with numbers and basic mathematics. In 1988, this was apparently very common. I doubt its much less common today, but I have no evidence to support that hypothesis of "no change". More on that in a second.

As I mentioned above, the first two chapters are essentially introductory. The first chapter is a quick guide to what innumeracy is, how widespread it is, and most importantly an attempt to instill some of the joy of mathematics to the reader - the author is a professor of mathematics at Temple University (or at least he was in 1990, when my edition was printed). The second chapter is a review of basic mathematics, particularly probability and statistics. Most of the examples throughout the book involve probabilities and statistics, so it's nice to have this refresher. Despite the claims throughout the first half of the book that this is a book for innumerate people, examples and arguments in later chapters seem to assume the reader has acquired the high level of mathematical familiarity that the author possesses. For example, a description of averages and means on pages 169 to 170 includes a joke (for lack of a better term) that the reader would only 'get' right away if they were highly familiar with cubes (3 cubed is not equal to 63). Yes, this is an easy bit of math, but for people who do not deal with exponents, volumes, or scientific notation on a daily basis, I do not think they'd see the disconnect in the example in time to get it.

That's a pretty minor quibble, really. There are a couple of other little things in this book that struck me as sub-optimal, like the statement that many problems involving more components than the number of particles in the universe (a popular computer engineering definition of "practical infinity") are of practical importance, but without any hint of an example of such a problem. The author also describes the Drake equation without crediting professor Drake, and is too eager to insult the social sciences in broad terms. All of these I could probably live with, but the author makes one major mathematical mistake.

This mistake is something I'll probably rant repeatedly about: trends. More than once in this book, despite a later section devoted to describing polls, opinions, confirmation bias, and standard error (in the statistical sense), the author casually declares a trend to exist without providing a scap of evidence in support of these hypotheses. Apparently, he feels it unnecessary to back up statements about the rise of lazy, unmotivated students (nostalgia?) or increasingly poorly-educated soldiers. Lots of people misuse observational data about such putative trends, but I expect better from a mathematician.

There are some other interesting things going on in this book, some good, some not so good. One widespread phenomenon that came up peripherally here is what I'll call, for the sake of the current argument, "unbiology": a general ignorance of biological sciences and the knowledge therein, combined with a failure to consider basic biological phenomena such as broad scale biodiversity or the unifying fact of evolution and common descent. This is not a failing of this book so much as it is an opportunity to tie a phenomenon that I see often and that bothers me to a phenomenon this author sees often and is bothered by.

Overall, I actually really enjoyed this book. It's just that the negative bits are much easier to describe and complain about than the good bits, which make up the vast majority of this book. A quick look at reveals that a newer edition (perhaps without chronic reference to President Ronald Reagan) is available, as well as several other books by the author. I expect I would enjoy reading his other works, based on his writing style and the interesting topics of many of the examples.


Carlo said...




I'm sorry, but this was the only way that I could actually provide some semblance of what fanboyism is actually like.

In terms of the book, it actually sounds pretty interesting. It's like when people have to close down a small community store because the cash register is broken (I'm obviously talking about something like a small Tim Horton's here where all the prices with taxes are already known by heart). I'm no mathemagician, but some people are BAD at maths.

TheBrummell said...

There's a line in the book about a recent experience of the author's, at a local fast food restaurant. This was probably written in 1987 or 1988, to explain the $2.01 total for his burger+fries+drink. Anyway, the cashier had a little table to look at for calculating sales tax (6% = $0.12), which took some time. Apparently, this was just before the wide-spread adoption of machines that automatically add sales tax. Then he says something about some places putting little pictures of the order on the cash-register buttons, for employees who are both functionally innumerate and functionally illiterate. Forget about bad at maths, these people are bad at life. How do functionally illiterate people survive?

Necator said...

How do functionally illiterate people survive?

Welcome to my estimation about 1/3 of all grade nines are illiterate (though functinally literate). And don't pull any of your "well it's beter in BC or NS or whatever" - speaking to teachers from across the country, it's pretty much the same. We don't see it becaue of the bias inherent to our environment.

Necator said...

Awesome typos Nktor...jeez.

TheBrummell said...

And don't pull any of your "well, it's better in BC or NS or whatever"

Having little-to-no experience of children and their reading skills (or lack thereof) in any province, I'm in no position to argue. I agree that grad. school insulates one from such individuals.

Necator said...

...sorry...sensitive...I overreacted. But I hear it often. I bring the reality of the situation to a group of people and it's either, "well not my kid", or "well in Manitoba we beat the literacy into them," or whatever.

So, sorry for the freak out. But it is disheartening.

TheBrummell said...

sorry for the freak out. But it is disheartening.

Don't apologise - RANT! You have a blog, use it for your frustrations! I hear regional bullshit like that pretty often, too.

And don't apologise for apologising, either.

Anonymous said...

I'm feeling pretty innumerate myself but I don't get the 3 cubed is 63 joke. Is there some funny reason the author picked 63 or is it just some random number?