Innumeracy: Mathematical Illiteracy And Its Consequences
Innumeracy: Mathematical Illiteracy And Its Consequences by John Allen Paulos
Reviewed by Denise Noe
John Allen Paulos, a mathematics professor, is understandably dismayed at the widespread ignorance of his subject, an ignorance which he calls “innumeracy.†He is also dismayed by the fact that so many of his fellow Americans are math-anxious and math-averse and that this aversion is, as he writes, “often flaunted.†This is particularly appalling as our culture becomes ever more technologically advanced.
“Innumeracy†points out the consequences of mathematical ignorance and tries to offer some basic pointers to the innumerate. It is a book leavened with good humor partly because the author has a finely tuned sense of humor and partly because he knows all-too-well that for many people “(num)(ber) is automatically read as (numb)(er).â€
I’m definitely one of the people “Innumeracy†was written for. As a child and young adult, I was profoundly math-phobic. I thought it was the hardest and most boring subject around and approached it with an almost hopeless and hostile attitude. Paulos reminds readers of my type that they can skip the parts that have equations and still follow the basic thread of the book.
However, I would urge them not to do so. Readers like myself can profit from every word and mathematical symbol in “Innumeracy.†We do best if we remember that we’re not reading a novel and are not afraid to pause at length at the equations, reading and re-reading until we manage to make sense of them. We should also return to them. People can profit from several readings of this fact-packed and fascinating volume.
Paulos starts the book out by discussing how weak many people are in their grasp of large numbers. This is not a purely abstract failing. As Paulos points out, “Without some appreciation of common large numbers, it’s impossible to react with the proper skepticism to terrifying reports that more than a million American kids are kidnapped each year, or with the proper sobriety to a warhead carrying a megaton of explosive power – the equivalent of a million tons (or two billion pounds) of TNT.â€
Soon after this discussion, he introduces us to the “deceptively simple and very important†multiplication principle. That principle simply states that if something may be done in M different ways and something else in N different ways, there are M times N ways these things may be done. The author then shows that this principle has some surprising results: “A sportswriter once recommended in print that a baseball manager should play every possible combination of his twenty-five-member team for one game to find the nine that play best together. There are various ways to interpret this suggestion, but in all of them the number of games is so large that the players would be long dead before the games were completed.â€
In a chapter devoted to probability and how it figures into coincidence, Paulos shows how likely it is that seemingly unlikely events will occur. For example, there are 365 days in a year. Obviously, you would have to have a total of 366 people to be absolutely certain that two of them had the same birthday. But how many people would you need to have a 50% chance that two of them had the same birthday? Paulos states, “The surprising answer is that there need only be twenty-three.†I’ll leave the readers of this review to find the explanation in the book.
Paulos devotes a chapter to showing how rampant innumeracy is connected to the popularity of belief in pseudoscientific phenomena such as astrology, parapsychology, telephone psychics, and numerology. He writes, “Innumeracy and pseudoscience are often associated, in part because of the ease with which mathematical certainty can be invoked to bludgeon the innumerate into a dumb acquiescence.â€
Throughout “Innumeracy,†Paulos is crystal clear in his explanations as well as generous with wit and arresting examples. Early in the book he talks about a “fundamental property of numbers named after the Greek mathematician Archimedes which states that any number, no matter how huge, can be exceeded by adding together sufficiently many of any smaller number, no matter how tiny.†He continues that many innumerates have trouble with this principle and can’t seem to understand how “their little aerosol cans of hairspray could play any role in the depletion of the ozone layer of the atmosphere, or that their individual automobile contributes anything to the problem of acid rain.â€
I hope this little review contributes to increasing the popularity of “Innumeracy.â€
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April 26th, 2008 at 2:11 pm
perhaps the concept of “innumeracy” will die out once the government introduces new ways in which to level the playing fields in math, science and engineering, primarily to cater to feminists.
affirmative action laws always seek to apply numerical equality to outcomes by disregarding individuals’ natural tendencies, inherent strengths, obvious talents and the original principles and protections of law these same lawmakers swore to protect and preserve, as contained w/in documents such as the u.s. Constitution and Bill of Rights.
even more “innumerable” failed social engineering experiments followed by even more government handouts won’t turn a sow’s ear into a silk purse, madam. it will only slow our scientific development, and aid our enemies in overtaking us in the world marketplace, thereby making us all the poorer for the doing.
but that is like a gazillion years away, right?
April 26th, 2008 at 9:03 pm
I confess. I was a math illiterate at school. Well, maybe that’s an overstatement but just a little. Math was dull and hard and there were better things to occupy a boy’s mind. It was only when I did Stats in my Uni 4th year that I really got to grips and boy, did I have fun. I count myself now as adequate (or maybe I have a delusion of adequacy; who knows).
Our Minister of the Environment, a few weeks ago, made an astonishing maths statement/claim. Before being elected he was a rock and roll singer leading the ‘Midnight Oil’ group. That is a bit of a slur on good old rockers; he was a head-banging loon with gyrations on stage that insulted spastics with his parodies. Amazing who gets into Parliament here in Oz. His social ‘message’ speciality as a wailer/howler was just as jumbled and inarticulate then as now. Except now he had added innumerate too.
He is obsessed with plastic shopping bags and wants them banned. He rushed through signing the Kyoto Agreement ratification tout suite but that was just a side dish to his self-anticipated Main Course.
British MPs have more interesting fetishes, such as wearing stockings and suspenders (garter belts) and lacy knickers under their suits and visiting rude ladies for hire. American ones might focus on automatic weapons in home armouries, although some seem to be becoming more British in part by the day. French politicians all have mistresses, even the women ones. But Peter Garrett orgasms over plastic bags.
He stated that Australia gets through 4 billion plastic bags per annum with a combined weight of 220 million tons going eventually into our waste disposal sites. Every year. Whew, what a impact on the Environment! What a scandal.
It took a week before a newspaper critic was alerted to the maths by a reader; presumably one who paid attention in class. The rest of the media simply repeated the Minister’s claims as nauseam for the week.
Envision if you will the daily grind of housewives (oh, and house husbands, of course) doing the weekly shopping and lugging these immensly weighty plastic shopping bags each with a small packet of frozen peas. And each adult (approx 10 million) in Australia struggling with over twenty-two tons, just of the empty shopping bags each year. No wonder the food has all gone Lite and we all need friggin’ SUVs. It is small wonder we all don’t have Lorries in the driveway.
April 27th, 2008 at 4:10 am
amfortas: He is obsessed with plastic shopping bags and wants them banned.
(Denise) So he wants more of Australia’s trees cut down to supply the paper shopping bags?
April 27th, 2008 at 7:49 am
Amfortas: I envy you your Minister of the Environment. Here in the States, we grow them at least as incompetent, but far less entertaining. If they’re going to mess up the world and wreck our economies, at least they should give us a few laughs along the way.
April 27th, 2008 at 8:17 am
Competence in mathematics is sexist, racist, elitist, obsolete, and socially unacceptable.
It is not properly subjective, and does not respect the value of all diverse points of view, with added weight to those who have been completely wrong, thoroughly discredited, silenced or silent in the past.
Therefore it must be rejected, on the well-settled principle of disparate impact. The failure of women and “minorities” (ethnic groups present as a large percentage of the population, but dismal failures despite every conceivable advantage) to achieve Nobel stature in the sciences may not be attributed to lack of competence, but is, instead, proof positive that science is mis-construed as being derived from fact and logic.
Science, all science, is subjective, relative, personal, volatile, and interpretive. If we all say so, it has become true.
It’s not the future, it’s the present – just ask Larry Summers where his job went.