Review of John Allen Paulos’ Innumeracy

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.

Fur Farms Banned in Britain

The bill to ban fur farming the Great Britain is essentially a done deal. The 13 fur farms left in Great Britain will have to shut down by 2003; though the bill provides ample compensation for the remaining few fur farms. Ironically the ban on fur farming comes at a time when fur is making a comeback on the world fashion stage including in the United Kingdom.

In fact, the thing that comes through loud and clear about the use of fur is that animal rights activists have had almost no impact on the world fur market. Take mink, for example. In 1980, 22 million mink pelts were produced worldwide. After a boom in the 1980s that saw almost 42 million pelts produced in 1988, mink production crashed to an all-time low of 20.4 million in 1993 — due in large measure to the world-wide recession of the late 1980s. By 1997, however, world mink production had climbed back to 26.3 million pelts (although economic downturns in Russia likely lowered world production in 1998-1999).

As Richard North points out, the reality is that fur and fur farming is important only to a relatively small portion of the public. In large measure that is because the animal rights activists in their campaign against fur are inevitably forced into what Adrian Morrison calls the “muddled middle.” An editorial in the Daily Telegraph put this problem succinctly.

In singling out fur-farming for destruction, Miss [Maria] Eagle [the sponsor of the anti-fur farm bill] is trying to distinguish mink from cows, sheep, pigs and all the other animals that are farmed and slaughtered in this country. There is no real distinction: we eat or wear body parts from all these animals. … By all means let animal rights activists search out extreme brutalities in any farming process — and fur farming is no more brutal than other livestock farming — but it is wrong to demonise a particular process because of some perceived wrong in the people who wear the product.

As their noble lordships put on their cowhide shoes today, tied the cocoons of a thousand silkworms around their necks and arrange the fur of that norther stoat — the ermine — above their collars, they might do well to consider why the mink gets off so lightly.


Fur should fly. The Daily Telegraph (London), November 13, 2000

The question for all dedicated followers of fashion: can they stomach the rage for fur? Mary Braid, the Independent (London), November 4, 2000.

Fur and Freedom: in defence of the fur trade. Richard North, Institute for Economic Affairs, January 2000.

Interesting Computer Game Promotional Page

The other day I bought Shiny’s amazing RTS game, “Sacrifice,” and spent too many hours playing it over the weekend (review coming soon). Anyway I was visiting the game’s web site to see if there was a patch out yet.

There isn’t yet but they did have another interesting feature — a sort of mini-Pricewatch specifically for the game. At the bottom of the main Sacrifice web site is a link that reads Sacrifice4Less. Click on it and you go here where the Shiny folks keep you up to date with the cheapest place to buy the game in several different parts of the world.

This is an obvious idea that for some reason I’ve never seen anyone do before. I’m always visiting manufacturer’s web sites, and it would be excellent if they all included a link on a product page so I could immediately find the cheapest place to buy the product.

Can Computers Detect Internet Cheating?

Duncan Smeed, who is an educator, worries enough about traditional plagiarism and notes that, “of course, the situation is further complicated by the ready availability of vast resources over the Internet.” He points to a group that is evaluating iParadigms’ electronic system that claims it can detect papers copied off the Internet.

Several comments. First, I don’t know about the situation in the UK, but in the United States cheating is endemic. A professor I once had held up a newspaper story reporting a poll in which 60 percent of American college students said they had cheated. “What about the other 40 percent?” he asked rhetorically and then quickly answered his own question, “They’re liars” which elicited knowing laughter from the class.

Although I’m not to proud of it now, I have to admit that when I was in college I helped numerous people who had more money than brains by “helping” them write term papers that I’m sure their professors would have probably thought crossed the line into outright writing their papers for them. IParadigms claims that, “Students themselves report that unchecked cheating and plagiarism by others undermines their own efforts and educational enthusiasm,” but most of the good students I knew were more cynical about the overall lack of academic rigor and didn’t feel that much guilt in helping people bend the rules in their classes (to put it another way, what does it matter if I help someone get a B when they’re going to get a C just by showing up and breathing?)

Anyway, leaving my bit of true confessions behind, the problem with the iParadigms approach is that as the amount of published works on the Internet keeps expanding, the usefulness of the sort of brute force comparison iParadigms is doing is going to lose its usefulness.

Consider a college freshman writing his first paper on Shakespeare’s MacBeth. How many tens of thousands of articles and papers are there going to be about MacBeth available on the Internet? Sure if somebody is dumb enough to just cut and paste wholesale you’re going to catch them, but most of the people I knew who were chronic cheaters were far more sophisticated than that and were perfectly capable of taking a paper written by someone else and modifying it and rearranging it to more closely mimic how they would write the paper if they could be bothered.

Using something like statistical sampling to test for originality is a great idea when you’ve got a relatively small number of documents to deal with, but when you start comparing a very small body of work, such as a single paper, with a huge document base of 1.4 billion and rising documents on the Internet (using Google as a measure for the moment), the risk of a false positive will likely be unacceptably high. Imagine what it will be in 5 or 10 years when we could very well be measure the number of discreet documents indexed by search engines in the tens of billions.

The More Freedom You Have, the Less Privacy You Need

The United States and the European Union recently published a draft version of an international cyber crime agreement with an interesting proviso — the less political freedom users have, the more privacy they will be granted. Conversely, the more political freedom users have, the less privacy the states of the world will cede them. Make sense to you? Me neither.

The proposed agreement is designed to allow police to easily track cyber criminals across national borders. Among other things the agreement would ban the mere possession of “hacking devices,” allow police from member countries access to computer data worldwide, and broaden that access to include close monitoring by Internet service providers which the agreement would now require of member countries.

Ironically, people living in an authoritarian state such as China would have far more privacy protection under this treaty than people living in relatively less authoritarian countries such as the United States and United Kingdom. This is based on the hypothesis that citizens of repressive governments need greater privacy protections than citizens of less repressive governments. Of course this completely reverses cause and effect — the reason countries like China are more repressive is precisely because they don’t constantly invent justification, as this treaty does, to abrogate the rights of their citizens for short term gains.

Besides which, although it is undeniable that European nations aren’t as repressive as China, they (along with the United States) are not perfect and do have backwards-looking laws as evidenced by recent demands from France that Yahoo! block auctions of Nazi memorabilia to citizens of that country. France is especially egregious, as people have been thrown into jail for denying that the Holocaust ever happened. While Holocaust deniers are absolutely wrong about their claims, and are in large measure motivated by racism rather than any genuine concern over historical accuracy, France like China is not above jailing people simply for the words they speak and write.

In both the United States and Great Britain, meanwhile, there is a long history of state law enforcement agencies being used to carry out political repression. Great Britain has often cut human rights corners in pursing IRA terrorists, while in the United States the state has often looked the other way at law enforcement violations of human rights in pursuit of left-wing and right-wing extremists, not to mention the prosecution of the drug war. In fact the United States has decided to emulate France by making it illegal to publish on the Internet instructions on making certain drug compounds.

Rabbi Abraham Cooper, of the Simon Weisenthal Center, advised the Council of Europe on the treaty, and confirms by his words that the treaty will allow Western governments to go after web sites and individuals for what amounts to pure speech. According to Cooper, the treaty will allow prosecution of “violent” web sites. “We’re talking about web sites that teach people how to build bombs, claiming it’s for educational purposes.” I hate to burst Cooper’s bubble, but however noxious it might be, the right to publish instructions on how to make bombs — so long as such instructions are not accompanied by incitements to commit crimes — is protected by a long line of Constitutional law. In fact the First Amendment is so liberal in this area, that the U.S. government was unable to prevent a leftist magazine (The Progressive if I remember correctly), from publishing an article explicitly describing how to build a nuclear bomb — something that the United States asserted was a state secret.

Besides, does the world really need this treaty to pursue cyber criminals? Advocates of the agreement site numerous examples of criminals in one country using the Internet to commit crimes in other countries. But for the most part, international authorities had little problem identifying and punishing those troublemakers — usually extremely quickly. Look how fast, for example, the author of the “Love Bug” virus was identified last year. Most other high-profile Internet-related crimes have been solved without recourse to the sweeping police powers called for in the international cyber crime treaty.