Susan Jacoby is the author of, among other books, “The Age of American Unreason.”

At a June rally in Richmond, Va., Republican presidential candidate Donald Trump lamented the “59 percent unemployment rate” of African American youth. Although I did not know the precise unemployment rate of young African Americans, I knew that Trump’s figure was wrong. I realized this not because I am a mathematical genius but because the statement was implausible, given that millions of young Americans — whatever their race — are full-time students who are not looking for jobs and therefore cannot be considered unemployed in the conventional sense.

As PolitiFact later reported, the May unemployment rate for blacks ages 16 to 24 was 18.7 percent — bad enough, but nowhere near the statistic trumpeted by Trump. You can look up that figure on the Labor Department’s website, but the key to spotting the bogus nature of the statistic is a logic-based awareness — not readily obtainable on Google — that it is as misleading to describe teenage students as unemployed as it would be to apply the term to retired octogenarians.

This stellar example of junk statistics came too late for the publication deadlines of two new books focused on the intertwined glut of real and false information, magnified by the Internet, that affects fields from politics to medical decision-making. In “A Field Guide to Lies,” Daniel J. Levitin, a neuroscientist and author of the fascinating 2006 bestseller “This Is Your Brain on Music,” observes that humans “have a tendency to apply critical thinking only to things we disagree with.”

"A Field Guide to Lies: Critical Thinking in the Information Age," by Daniel J. Levitin (Dutton)

Levitin’s book, which emphasizes fear of numbers as a general barrier to critical thought, is intended as a guide for those who wish to test the authenticity of information that inundates us from every corner, dark and light, of the Web.

Unfortunately, in examples on subjects ranging from medical tests to birth rates, the author emphasizes sophisticated probability theory that many readers are likely to find more intimidating than numbers.

You don’t have to know a thing about the 18th-century mathematician and theologian Thomas Bayses’s methods of calculating probability — which attempt to take into account changing and subjective conditions over time — to understand that if a drug is said to increase the life expectancy of cancer patients by 50 percent, the critical number is not the percentage increase but the typical life expectancy of the patient.

Fifty percent of what? If life expectancy without the drug is three months, that is the only figure needed to understand the negligible value of a 50 percent increase. Solving the problem requires only a working know­ledge of fractions, decimals and percentages — imparted in fourth grade when I was growing up in the 1950s.

In his zeal to apply Bayesian logic to such issues as assessing “false positive” and “false negative” results of mammograms (as well as treatment for his dying 13-year-old dog), Levitin complicates what is — or once was — essentially a grade-school math question. On the emotional plane, of course, such decisions are more complex. A mother might want an extra six weeks of life if she could see her child graduate from college during that period.

William Poundstone’s “Head in the Cloud” offers a different take on similar subjects, but he pays less attention to innumeracy and more to deficits in general cultural know­ledge. Poundstone is the author of 14 previous books, including a biography of the cosmologist Carl Sagan. He cites endless surveys demonstrating what the American public doesn’t know about subjects from religion to government.

Both authors rightly identify the inability of many Americans to distinguish between correlation (or coincidence) and causation as a major enemy of logic and reason.

"Head in the Cloud: Why Knowing Things Still Matters When Facts Are So Easy to Look Up," by William Poundstone (Little, Brown)

Poundstone, after discussing a survey of his own design (without really explaining his methodology) comes close to falling into a similar trap when he cites a number of factual questions that “have the power to predict income.”

Guess what? You are likely to have a higher income if you know that Emily Dickinson was a poet and not a chef, designer, philosopher or reality-show star. Even better if you also know that the Battle of Waterloo took place before the American Civil War.

The results undoubtedly mean (surprise) that the wealthy are better educated and more likely to have encountered certain facts in the course of their studies. “Predict,” in common English usage, is not a synonym for “correlate” — though it is often used that way, as Poundstone employs it, in the world of surveys and statistics.

I expected to like both of these books because of the thesis implied in their titles: that critical thinking and general knowledge still matter, and may even matter more, in a culture saturated with quack information. But, although Levitin’s grasp of the importance of numbers makes his book superior to Poundstone’s, neither author seems capable of full-throatedly praising cultural knowledge for its own sake. Does it really matter, whatever your income, if you know that Dickinson was a poet but have never read her poetry?

Levitin makes the important point that expertise tends to be narrow — that a physicist, for instance, is not necessarily an expert on social science. Then he proceeds to ignore his own admonition. To demonstrate that “even experts fail,” he cites a 1968 quote in which the historians Will and Ariel Durant predicted that the high birth rate of Catholic families would mean, no later than 2000, that “the Roman Catholic Church will be the dominant force in national as well as in municipal or state governments.” Levitin notes that the Durants failed to consider the possibility of change in Catholic attitudes toward birth control, but he follows up with the dubious observation that in 1968, alternative scenarios “were difficult to imagine.”

No, they weren’t. Neither 21st-century neuroscientists nor middlebrow cultural historians (as the Durants, born in the 19th century, were) are the best sources of information on American religious trends. The Second Vatican Council, with its long-term liberalizing influence, ended in 1965, and the size of middle-class Catholic families was already dropping (something the Durants clearly did not know). Alternative scenarios were being discussed at length in intellectual Catholic publications. Because Levitin is not an expert on religion, he picked the wrong sources of “expertise.”

Still, Levitin’s general point that some sources are more reliable than others is well taken. In the absence of gatekeepers, a broader and deeper level of general knowledge is the only real protection against bogus experts and theories of all kinds.

Yet Poundstone argues: “Canons are dissolving, and predictions of cultural doom have not come to pass. Cultivated taste is more diverse than it’s ever been. For the less cultivated, a superficial literacy cribbbed from the cloud is enough to get by in the world — and it’s time to stop pretending otherwise.”

If Poundstone believes this, it is difficult to understand why he wrote his book. Significantly, he offers no definition of “cultivated.” More than half of Americans, for instance, do not know that Genesis is the first book of the Bible (assuming that respected public opinion polls are right). Whatever the biblically illiterate are cultivating, in what is supposedly the most religious country in the developed world, it is certainly not the history of Western civilization. The real question is whether we want to settle for a world in which superficial knowledge, mixing half-digested facts and lies, is enough to get by.

A Field GUide to LIes
Critical Thinking in the Information Age

By Daniel J. Levitin

Dutton. 292 pp. $28

Head in the Cloud
Why Knowing Things Still Matters When Facts Are So Easy to Look Up

By William Poundstone

Little, Brown. 340 pp. $26