Innumeracy: Mathematical Illiteracy and Its Consequences
By John Allen Paulos
No sense mincing words — this is the worst skeptical/debunking book that I’ve ever read. Period. How this book became a national bestseller at the end of the 1980s (and its author a mini-celebrity for awhile) is something I will never understand.
For one thing, the book is poorly written and difficult to follow. Although the title suggests that the book is primarily going to be about the abuse and misuse of statistics and other math-related issues, discussions of such things occupy only a small portion of Innumeracy. This is probably a good thing, because the math-heavy sections are confusing. If you do not already have a good handle on probability theory, for example, Paulos is likely to make you even more confused.
Innumeracy reads like it is nothing more than a few transcribed lectures that were never edited. Perhaps Paulos’ editors did not understand him, but did not want to look stupid by questioning him, and allowed the book to go straight to press. Either way, it is disconcerting to read such a disorganized book from someone arguing on behalf of organized thinking.
Aside from the poor writing, the biggest problem with Innumeracy is that it purports to advocate for sound, logical thinking only to make rash, unsubstantiated — and, in at least one case, erroneous — arguments itself.
For example, like some skeptics, Paulos argues that not only are reports of visitors from outer space almost certainly not true, but he also proceeds to argue that it is almost certain that there are no advanced civilizations capable of or interested in visiting our planet. I happen to agree with Paulos on this, but his argument is filled with unsubstantiated claims (there isn’t a single footnote or reference in the entire book).
According to Paulos,
The third reason we haven’t had any tourists is that even if life has developed on a number of planets within our galaxy, there’s probably little likelihood they’d be interested in us. The life forms could be large clouds, or self-directed magnetic fields, or large plains of potato-like beings, or giant plant-sized entities which spend their time singing complex symphonies, or more likely a sort of planetary scum adhering to the sides of rocks facing their sun. There’s little reason to suppose that any of the above would share our goals or psychology and try to reach us.
Potato people? Self-directed magnetic fields? These sort of fantastic creatures might be good fodder for a Star Trek episode, but, in the absence of evidence, Paulos here is simply making an unsubstantiated assertion. Paulos goes on throughout his book about the importance of careful thinking and then slips in meaningless phrases such as “there’s probably little likelihood” and “there’s little reason to suppose.” Similarly, Paulos ridicules psychics such as Jean Dixon and the people who believe such predictions, but concludes his book with a false prophecy of his own:
For example, when the recent decisions by a number of states to raise the speed limit on certain highways to 65 m.p.h. and not to impose stiffer penalties on drunk driving were challenged by safety groups, they were defended with the patently false assertion that there would be no increase in accident rates, instead of with a frank acknowledgment of economic and political factors which outweighed the likely extra deaths
Where I come from, if you are going to call something “patently false” you better be able to back it up — especially if you are going to put it in a book about how erroneous the thinking of other people is.
In 1995, the U.S. Congress abolished federally-mandated 55 mph speed limits and most states quickly raised highway speeds to 65 mph and higher in some places. Measured on deaths-per-mile traveled, deaths from automobile accidents in 1999 were the lowest ever recorded by the National Highway Traffic Safety Administration since that agency began keeping such statistics in 1966.
Highway deaths began declining almost immediately after the repeal. NHTSA had projected an additional 6,400 traffic deaths, but by 1997 all but one state (Hawaii) had raised its speed limits, and in 1997 highway traffic deaths were the lowest ever recorded by the NHTSA up until that point.
Why the decline in deaths when everybody knows (including Paulos) that speed kills? Because the 55 mph speed limit artificially raised the differential between cars obeying the law and driving 55 mph vs. those who broke the law and drove 65 or 70 mph. As Eric Peters wrote in the Wall Street Journal in 1998,
These higher speeds are safer because they reflect the normal flow of traffic — what highway engineers call the “85th percentile” speed. This is the speed most drivers will maintain on a given stretch of road under a given set of conditions. When speed limits are set arbitrarily low — as under the old system — tailgating, weaving and “speed variance” (the problem of some cars traveling significantly faster than others) make roads less safe.
As Peters notes, the interstate highway system was designed to be safe at speeds of 70 to 75 mph, and that is the speed that the majority of cars traveled before and after the speed limit was raised.
It is this sort of stuff that makes reading Innumeracy so irritating. There are plenty of excellent books that explain common misconceptions about probability, statistics and other mathematical subjects. Innumeracy is not one of them.