John Allen Paulos, A Mathematician Reads the Newspaper. Basic Books, 1995.
Author’s Conclusion:
Always be smart. Seldom be certain. Journalists should ask, in addition to Who, Where, What, etc., How Many? And How Likely? And no matter how detailed the explanation, sometimes things remain baffling because the *world* is baffling.
Brief Summary:
This is a book not so much requiring sophisticated math to understand, but to review many examples of items (of all kinds) in the newspaper with insights for understanding them from math but also from psychology, including the predisposition of humans to turn everything into stories. There are so many short chapters that it’s hard to identify broad themes (aside from those in the conclusion), but here I’ll cite some key points from each section.
Politics: about voting schemes, none perfect; about psychological biases (even back in 1995 people knew about the availability error, the halo effect, the anchoring effect); how newspaper stories are told; how equivocation can enable virtually any claim; beware finding significance in coincidences.
Local and Social issues: How newspapers are nodes of connectedness; why to beware use of SAT scores; how arguments about gun control and abortion can be challenged; why stock markets patterns are illusory; how selection of units or words like “many” and “uncommon” can be misleading; how lawsuits presume every problem has a definite answer; how advertising works; how humans are preoccupied with the short term at the expense of the long term.
Lifestyle and soft news: How to write celebrity profiles; how to perceive trends that don’t actually exist; how statistical factoids depend on definitions.
Science and Medicine: How in science news clarity and precision are not equally balanced; beware implausible precision, and the overemphasis of trivial risks; how reporting seldom debunks even claims about guardian angels, statues that bleed, etc.; how to easily generate a pseudoscience out of meaningless coincidences (this example also in Irreligion); how confidence intervals are often ignored; how some strategies don’t work when scaled up; how you can’t predict discoveries you haven’t made yet; beware category errors; about different reasons to study math and five misconceptions about math.
Food, Fashion, Sports: Beware precision of nutrition information; how team sports are different than individual ones; sports records are simple issues of probability; how advice columns are glib; how to spot obvious exaggerations; the superficiality of top 10 lists; how so few books are reviewed compared to the coverage of every sports game, every murder; how religious coverage avoids discussion of faith to avoid recognizing the absence of evidence for beliefs; how we read obituaries.
Detailed Description
Intro
Author recalls growing up, reading the Chicago Tribune, the Milwaukee Journal. As he grew up, he grew more sophisticated about newspapers, but reads a lot of them, and contributes occasionally. This book is arranged like a newspaper, and is intended to offer a mathematical perspective to enrich our understanding….
Section 1, Politics, Economics, and the Nation
Social choices are necessary because our two most basic political ideals, liberty and equality, are incompatible. Consider the algorithm for dividing a cake: one cuts, the other chooses.
Lani “Quota Queen” Guinier.. voting
The Banzhaf power index: the number of ways a group or party can change a losing coalition into a winning one, or vice versa. Examples apply to, e.g. stockholders’ percentages, in which a small percentage might be just as powerful as a large one, because coalitions can form between groups; or a relatively large one may have no power at all. (examples). Ms Guinier suggested an alternative, a cumulative voting procedure would grant each voter a number of votes equal to the number of contested seats, which votes could be distributed any way the voter wished, separately or cumulatively. This could be an alternative to the gerrymandering that results in geographically bizarre districts.
Many different voting schemes have been proposed. Another is the approval system–one candidate, one vote. Each voter either approves or disapproves of each candidate.
In fact, no voting system is perfect; every one has undesirable consequences. The issue isn’t whether to be democratic, it’s how.
Bosnia: Vietnam or World War II?.. psychological availability
The ‘availability error’ is the psychological tendency to make a judgment based on the first thing that comes to mind. Similarly, emotional news stories, or provocative wording of poll questions, have greater impacts than neutral ones. News stories invite particular interpretations depending on their resonances with other recent stories, or the similarity to other news stories that day. Things or people are judged (the ‘halo effect’) by one salient characteristic–a Harvard pedigree, etc. Or people make different estimates depending on the ‘anchoring effect’ of an initial suggestion. Uncritical newsgathering simply bolsters conventional wisdom.
Recession forecast if steps not taken.. unpredictability; chaos
There are surprising mathematical reasons why most political and economic commentary and forecasting is fatuous nonsense. One example is the Laffer curve, which purports to represent the relationship between tax rate and government revenue, but simplistically neglects the myriad historical and contingent factors which might affect the actual relationship. Like a billiard table set up, weather is a system sensitive to small changes in initial conditions (Lorenz, 1960); thus chaos theory, and the study of nonlinear systems. The trajectory through such a system is a fractal. The lesson is to beware glib interpretations of changes of such complex systems.
Headlines and the inverted pyramid
Newspaper stories are told in inverted pyramid format, from essentials to more details. Ironically this creates a shorter attention span more than does tv, which is usually blamed for it. The coincidence of rival tv news shows running the same stories simultaneously should not be surprising…
Pakistan’s Bhutto… dice and bluffing
Sometimes a conscious randomizing of choices is not irrational, but maximizes one’s effectiveness. Example: a pitcher and batter decide between fast balls and curve balls; it’s best to decide which to do randomly. This is game theory–or negotiation theory. On the other hand, sometimes knowing a probability makes it best to adopt an unvarying policy. A dial that lands on red 70% and green 30% of the time; it is better to always guess red, not to try to guess red 70% and green 30%, because then only the ‘overlaps’ will bring a correct guess.
Who’s News…
Most news is about a very few people who are deemed ‘newsworthy’; it is an inverted pyramid structure. Similarly with coverage of foreigners. 1 American = 5 Englishmen = 500 Ecuadorans = 5000 Rwandans. Similar structure for word frequency in English.
Iraqi death toll… benchmark figures
Figures of war dead are rattled off without any perspective or comparison. Or comparing American dead to Vietnamese dead; or MIA in that war vs previous wars. Such benchmark, or ballpark, figures would be useful to insure common ground in multicultural discussions. The claims of Farrakhan; numbers of aids cases; the national debt.
Hillary most honest.. ambiguity and nonstandard models
By carefully defining terms and equivocating, you can say almost anything. “Most honest person I know.” Mathematically, there is the difficulty of definitions intended to describe one entity that turn out to be satisfied by other unexpected things, thus ‘non-standard’ geometries. Such results also play a role in humor…
Voting fraud.. political and mathematical regression
In a contested race, both sides presented mathematical arguments about machine votes vs. absentee votes. Mathematical interpretations do not bound our actions; deciding between interpretations is a nonmathematical issue.
Cult plot… newspapers, coincidences, conspiracies
There are so many unrelated news stories available that it’s no surprise that odd coincidences should jump out. True believers have no trouble finding support for their theories. The famous coincidences between Kennedy and Lincoln are well known; similar links can be found between other presidents.
Section 2, Local, Business, and Social Issues
What is local? We tend to evaluate relevance of particular news stories by their relation to us, in some aspect or another–location, social type, profession. The multiplication effect reveals the ‘connectedness’ of society–the number of links between any two people, which both theoretically and empirically has been shown to be under 10. A group breakdown by sex contacts would consist of some number of celibate single-person groups, a larger number of two-person groups; a few groups having a few members; and a huge group, perhaps 100 million, connected by their connectedness more than by being promiscuous.
Newspapers, then, are about the nodes of connectedness.
Company charged.. test disparities
Stories about women and minorities often focus on small fluctuations that are magnified at the ends of bell curves. It’s easy to show that the differences between any two groups will always be greatly accentuated at the extremes. And differences between groups (which there must be, by definition) will likely show up on standardized tests. The issue should be whether any particular test is appropriate to its use.
Thus schemes of strict proportional representation are impossible to implement. E.g. hidden relationships between race and being homosexual will yield mixes that will look good or bad from different perspectives.
SAT
The Scholastic Assessment Test, it’s now called. Among many other issues is whether SAT scores are predictive of college achievement. The reason why not is that any one college takes only a particular slice of SAT scores, then this group is spread out by academic achievement (GPA) at that college. If everyone were accepted to the top colleges, then there would be a stronger correlation between SAT score and later achievement.
Guns will soon kill more than cars…
The problem with such a comparison is that deaths due to guns are almost always intentional. The reason stricter gun controls don’t pass, despite a sizeable number of people who would support them, is that those who disagree with them feel strongly about the issue and even though a minority, are more likely than the majority to let the issue be a determining factor in deciding their vote.
Abortion… prohibition and arithmetical arguments
Sometimes radical new arguments enable people to reexamine entrenched positions. Suppose something caused women to become pregnant with 30-50 fetuses at a time, and that some could be saved, or all could be lost. Abortion opponents would presumably opt to save them all, risking a population explosion. Or: if evidence was confirmed that smokeless tobacco drastically reduced tobacco-related deaths, why not encourage smokers to switch?
DNA finger murderer; life, death and conditional probability
The ‘prosecutor’s paradox’ is about conditional probability, e.g. a fingerprint match with an innocent person has a probability of one in a million, but an innocent person matching the fingerprint has a probability of 2 out of 3, which is the relevant issue. In logic, If A then B is not the same as If B then A.
Darts Trounce the Pros: luck and the market
Random selections of stocks do about as well as the pro’s, sometimes even better. This is partly due to statistical fluctuations. Also because of the way random processes work. In a sequence of 1000 random coin flips, most of the time the number of either heads or tails will be greater; it won’t flip back and forth. Even though statistically they come out about the same. Similar things happen with stocks, which become known as ‘winners’ and ‘losers’ without there being much difference between them.
There are also seeming patterns in random sequences, which compel ‘explanation’.
Despite such demonstrations, market analysts are always pronouncing explanations for every market swing.
Cellular Phones tied to Brain Cancer: multiplication, health, and business
Numerical quantities can be made to seem big or small depending on the units chosen, e.g. length vs. volume. This happens in discussing disease rates–minimize by discussing rates; maximize by discussing gross numbers, especially particular cases. Thus, an anecdote about a woman with brain cancer led to stock prices falling for companies manufacturing cellular phones. Similar hysteria applied to stories about silicone breast implants.
The media use words like ‘many’ and ‘uncommon’ which are essentially meaningless. Newspapers typically present only a single ‘credible’ figure, without indicating the range of figures depending on different classification criteria.
GM Trucks Explode on Side Collision: from pity to policy
There is an increase of 143% in the number of lawyers since 1971. We get the impression every daily activity is fraught with danger–lawsuits are everywhere, as if every problem has a definite answer, as if there is no room for uncertainty in the world. Court cases play up the victims. It is probable that the GM engineers made a rational decision in designing their trucks; but how many thousands whose lives were saved by that decision are aware of it? People tend to assign negligence when the consequences are significant, no matter what the element of chance.
The $32 billion Pepsi Challenge: advertising and numerical craftiness
Most everyone knows how advertising works; full of false inferences, omitting crucial information. Ads can even make dumb mistakes without hurting sales (it’s the impression that counts). An exception might be the Pepsi gaffe in which thousands of people had winning numbers in a lottery, and Pepsi couldn’t fulfill its jackpot promise.
Brief Fads Dominate Toy Industry: S-curves and novelty
The S-curve describes trends that rapidly increase and then level off, like bacteria growth in a petri dish. This happens because of a depletion of nutrients, say. But the curve also describes cultural patterns, like the popularity of new toys. Perhaps here what is being depleted is the sense of novelty.
Area Residents Respond to Story: repetition, repetition, repetition
Typical tv news strategy–interviewing men on the street about some breaking story; of course they all say the same thing, having been briefed the same way. (A man was unsure of a newspaper story, so bought dozens of copies of the paper to corroborate the story.)
Researchers Look to Local News for Trends: the present, the future, and ponzi schemes
Humans are preoccupied with the short term, at the expense of the long term; thus our attitudes involving aids, global warming, long-term debts, etc. They play out like ponzi schemes, in which early investors are paid off with later ones, but the even later ones lose everything. Trying to forecast such trends, by ‘adding up’ local short-term events, usually do not yield good results.
Section 3: Lifestyle, Spin, and Soft News
People are most interested in soft news with some pertinence to oneself. Note how often some essayists use the various ‘I’ words…
A Cyberpunk Woody Allen: how to write a profile of the fledgling celebrity
How to write it: pick someone not too well known, compare them to someone who is and gather testimonials, both of which are easy because of the interconnectedness of things…
Tsongkerclintkinbro Wins
(Written in Spring ‘92 when there were still 5 viable Democratic candidates for president.) A set of imaginary voting preferences that show that each candidate can declare himself the winner depending on which voting criteria is used.
Florida Dentist Accused to Intentionally Spreading AIDS: rumors, self-fulfilling prophecies…
Irrational fears can be understood as variations of the Dennett party game in which a dream is deduced through a series of yes no questions answered according to some arbitrary rule. The questioner deduces a dream that never occurred, one which has no author. Similarly dreams themselves may occur when the mind’s question-generating ability is intact, but is getting in effect a series of random answers by being unconscious. Whole societies can be victim of mounting fears when objective information is absent. (Guatemala peasants thought western women were stealing babies…)
Interlude: Selves, Heroes, and Dissociation
(missed a couple chapters here)
Newspaper Circulation Down: factoids on tabloids
Claims are 60,000 newspapers in the world, and 500 million readers… though of course these statistics depend on what one calls a newspaper, or how one counts readers…
Computers, Faxes, Copiers Still Rare in Russia: information and the commissars
It’s not preposterous to imagine that the failure of economies in the former Soviet Union is due to the control of information that suppressed information duplicating mechanisms…
Section 4: Science, Medicine, and the Environment
Usually clarity and precision are not equally balanced. Some scientists are happy with precision without a proper context; journalists often highlight the most alarming scenarios consistent with the story.
Ranking Health Risks: Experts and Laymen Differ
the Dyscalculia Syndrome
(article from Discover mg). The difficulties of ‘false positives’ and other misleading statistics. What’s critical about a random sample is its absolute size, not its percentage of the population. Similarly there’s a widespread confusion about correlation vs. causation. Often incorrect inferences are made due to lack of information (inadequate), e.g. data on condom failure rates, or disease incidence rates, which don’t take into consideration increased susceptibility due to longer lifespans. Implausibly precise statistics are often bogus — e.g. the normal body temperature is actually 98.2 (not 98.6) due to a rounding error from Celsius.
Asbestos Removal Closes NYC Schools: contaminated mountains out of mole spills
News stories of contaminations often overemphasize trivial risks; if everything is risky, nothing is. One pint of liquid dumped into the oceans becomes 6000 molecules per pint of ocean water. ! Virtually any such statistic can be manipulated into sounding alarming.
Super Collider a Waste of Money: science journalism and advocacy
Laypeople are often beset by dueling experts in the press; science journalists cannot assume the same level of audience background knowledge as can, say, a food critic. Example of Rudy Rucker story about mathematical proposals translated into musical performances for congress, “A New Golden Age”. Still, public face-offs and debates on scientific issues should be encouraged.
Harvard Psychiatrist Believes Patients Abducted by Aliens: mathematically creating one’s own pseudoscience
And science reporting should engage in gentle debunking, too. But seldom does, even when reporting on guardian angels, statues that bleed, or UFO abducting aliens. The ease of finding odd coincidences in life has already been discussed. Here’s how to create such coincidences– take four numbers about yourself and generate various combinations of them to different powers; some of them are bound to correspond to this or that physical constant. Virtually all such coincidences are not only not miraculous; they’re meaningless.
FDA Caught Between Opposing Protesters: statistical tests and confidence intervals
Other basic statistical principles to be aware of include Type I and Type II errors–making judgments based on small samples, either rejecting a true hypothesis, or accepting a false one. The FDA must balance these two risks when evaluating drugs.
Also, confidence intervals, as in “95% certain that such and such”; sort of like a margin of error. But these qualifications are often left out of reports.
Senators Eye Hawaii Health Care Plan: scaling up is so very hard to do
Strategies that work on a small scale often don’t work when scaled up…health plans, traffic patterns, size and weight. Compromises are needed, such as the prisoner’s dilemma, the tragedy of the commons. Arrow’s theorem describes ranking problems (nontransitive results).
Breakthrough Forecast by End of Decade: you can’t know more than you know
The Hay Theory of history was that the invention of hay made settlement of northern Europe possible, and thus the spread of civilization. Similar stories about other technologies can be told, and each one involves some contingency that precluded alternate technologies. Thus the qwerty keyboard; VHS over Beta; DOS. But really new paths are unpredictable. Despite the headline, you can’t predict discoveries you haven’t made yet.
Rodent Population Patterns Difficult to Fathom: ecology, chaos and the news
Stories on ecological issues frequently verge on category mistakes–ascribing human motives or agents to natural events. For instance, population trends of rodents may follow a certain formula that generates chaotic results. How much more complex are actual ecological systems! But news stories like facile analyses.
More Dismal Math Scores for US Students: x, y, and u
News stories about dismal scores–so what? There are three broad classes of reasons to study math. First is practical, for job skills, science, technology. Second is informed understanding; third is considerations of beauty, curiosity, wisdom. But politicians like innumerate people who can be easily swayed without recognizing quantitative arguments. Yet some types of mathematical subjects, puzzles and so on, are popular. Why isn’t studying math more popular?
Five misconceptions: Math is a matter of computation, not. Nor is it strictly hierarchical: algebra, then calculus, then etc etc. Storytelling is too infrequently used. The false distinction between ‘people person’ and ‘numbers person’, say. And that math is numbing of other sensibilities.
Section 5: Food, Book Reviews, Sports, Obituaries
761 Calories… : meaningless precision
Given how recipes are written, the precision of nutrition information is meaningless. It only takes one imprecise number to make any combination using it also imprecise.
Top Designs for the Busy Working Woman: fashion, unpredictability, and toast
To author the fashion pages make the astrology column look insightful. A toast and jam sandwich folded and stretch is analogous to reading a newspaper, which folds and stretches the mind to brings things once far apart closer together, in a complex way.
Agassi Wins Again: scoring and amplifying differences
Sports statistics suggest that often the best teams manage to lose, and the worst ones win, occasionally. In contrast, in individual sports the better player usually does win. But the rules of the game typically amplify the differences in skill between players; and who goes first often makes a big difference.
New Survey Reveals Changing Attitudes: societal gas laws
Has polling and measuring become a national pastime? The fascination with profiles counterbalances the fascination with celebrities and other individual stories. And statistical profiles are valid even when the data is erratic–example of sadistic nutritionist. The Central Limit theorem. Statistical averages apply routinely in physics–gases, for example. Or Lem’s one minute profile of sexual intercourse across the planet.
Near Perfect Game for Roger Clemens: how many runs in the long run
Sports records can be explained by the laws of probability, even amazing ‘streaks’, which occur with the same frequency as streaks of heads in coin tossing.
Bucks County and Environs: a note on maps and graphic games
Language includes knowing rules for various idiosyncratic uses and exchanges, which must be understood differently. So to graphs and pie charts and maps, which have peculiar emphases that must be understood in context.
Ask About Your Mother-in-Law’s Lladro: explanations, advice, and physics
Advice columns provide easy, glib explanations. These arise from making ‘intentional’ accounts of situations where only a physical explanation would do. It’s easy to invent numerous intentional explanations for every gesture and situation.
Garden Club Gala: incidence matricies on the society pages
Expressions such as “everybody was there” or “they’re all doing it” are annoying; they’re so clearly exaggerations. Showing incidence matrices with society stories would be revealing.
Ten Reasons We Hate Our Bosses: lists and linearity
The top 10 reasons that Top 10 lists are popular.
Stallone on Worst-Dressed List: traits and rates
Best and worst dressed lists, and the like, are the products not just of the measures of the traits involved, but also popularity or recognition.
New Biography Fills Much-Needed Gap: books and news
Books should be bigger news…50,000 are published each year, how many are reported on, especially compared to the attention lavished to every baseball game, every murder, every tv program listing. Instead, a relatively small number of books are reviewed, often with lavish amounts of attention.
Which way Mecca? Religion in the paper
Coverage is almost never about faith, but about peripheral issues (like the problems mosque builders in the US have in determining the direction to Mecca). But this is just as well. Discussion of the true issues would require explicit discussion of other beliefs, of the absence of evidence for beliefs, and so on. Better a tacit embargo that supports religious tolerance.
R. L. Vickler, 85, Aide to Truman: the length of obituaries
A nice vertical, historical contrast to the nowness of most news stories. Trends can be seen.
Conclusion
Always be smart. Seldom be certain.
Journalists should ask, in addition to Who, Where, What, etc., How Many? And How Likely?
And no matter how detailed the explanation, sometimes things remain baffling because the *world* is baffling.
