John Allen Paulos is a mathematics professor at Temple University and the author of many books, including Innumeracy, A Mathematician Reads the Newspaper, and, most recently, A Numerate Life.
by John Allen Paulos Election Day is just a week or so away and we can be sure that there will be many bogus claims that elections in this or that state or district were rigged. Of course, these claims generally depend on outright lies, not on the counterintuitive subtleties of probability theory, one of…
by John Allen Paulos Here is a very simple notion that is astonishingly powerful. It’s called the multiplication principle and states that if some action can be accomplished in M ways and another action can be accomplished in N ways, then these two actions can be performed in succession in MxN ways. Hence the word…
by John Allen Paulos The director of the National Science Foundation, appointed by newly elected President Robert F. Kennedy, Jr., just announced a number of heretofore largely secret findings. At a hastily organized press conference, Ed Cayce, the rather pugnacious man at the helm of the agency, stated that his staff had convincingly verified a…
by John Allen Paulos Donald Trump has famously called climate change and global warming a hoax. Ignorant and benighted as he is, he is far from alone. Skepticism about global warming and its causes is widespread. One overly kind reading of this skepticism is that it is, to an extent, a consequence of the general…
by John Allen Paulos What do you call someone who is not religious? There are a lot of choices, but is there a need for a new name for such people? And, whatever they’re called, should not politicians more fully acknowledge them? The philosopher Daniel Dennett and others years ago pushed for the adoption of…
by John Allen Paulos Oy. Where to start? Let me begin with a recent abuse involving percentages. Trump’s absurd claims about price declines of more than 100% have elicited a lot of well-deserved derision. How could someone with an undergraduate degree in business from Wharton make these mathematically impossible claims? And why would the billionaire…
by John Allen Paulos A bit of information is common knowledge among a group of people if all parties know it, know that the others know it, know that the others know they know it, and so on. It is much more than “mutual knowledge,” which requires only that the parties know a particular bit…
by John Allen Paulos The stock market, social media, award contests, product reviews, beauty contests, social media, fashion styles, job applications, award contests, product reviews, and even elections, don’t seem to belong in the same crowded sentence. What do they have in common? Before I get there, a couple of abstract analogues to pave the way.…
by John Allen Paulos As atrocious, appalling, and abhorrent as Trump’s countless spirit-sapping outrages are, I’d like to move a little beyond adumbrating them and instead suggest a few ideas that make them even more pernicious than they first seem. Underlying the outrages are his cruelty, narcissism and ignorance, made worse by the fact that…
by John Allen Paulos Voters are lazy and often pay little or no attention to numbers and facts presumably relevant to their concerns. I remember initiating a discussion of the housing crisis in the US. I mentioned a headline I claimed to have just read, which stated “Experts Fear Annual Housing Costs in the U.S. –…
by John Allen Paulos Despite the fact that Newcomb’s paradox was discovered in 1960, I’ve been prompted to discuss it now for three reasons, the first being its inherent interest and counterintuitive conclusions. The two other factors are topical. One is a scheme put forth by Elon Musk in which he offered a small prize…
by John Allen Paulos When studying a technical field there is a strong temptation, especially among those without a scientific background, to apply its findings in areas where they may not make sense or are merely metaphors. (“Merely” is perhaps unnecessarily dismissive since much of our understanding of these fields is metaphorical.) Quantum mechanics and…
by John Allen Paulos Every time I read or watch anything about the election I hear some variant of the phrase “margin of error.” My mathematically attuned ears perk up, but usually it’s just a slightly pretentious way of saying the election is very close or else that it’s not very close. Schmargin of error…
by John Allen Paulos Election season has put an increased focus on the stock market, but little attention is ever paid to the Efficient Market Hypothesis (the EMH, for short). As I’ve written in A Mathematician Plays the Stock Market, it is a fundamental and important notion, but it is also a little weird. Its…
by John Allen Paulos Several years ago the Nobel committee selected two economists, Thomas Schelling of the University of Maryland and Robert Aumann of Hebrew University, to receive the prize for their stellar work on game theory. Aumann has contributed many seminal ideas with real-world applications, one in particular that is especially relevant today. It…
by John Allen Paulos With apologies to Charles Dickens, it will be the best of times, it will be the worst of times. In his recent book, Deep Utopia: Life and Meaning in a Solved World, philosopher Nick Bostrom, the author of Superintelligence, speculates about human and trans-human lives after AI has developed to a kind of…
by John Allen Paulos An abstract paradox discussed by Yale economist Martin Shubik has a logical skeleton that can, perhaps surprisingly, be shrouded in human flesh in various ways. First Shubik’s seductive theoretical game: We imagine an auctioneer with plans to auction off a dollar bill subject to a rule that bidders must adhere to.…
by John Allen Paulos Bertrand Russell’s advice for aging gracefully is rather simple: Broaden your horizons. He recommends that we should try to expand our interests and concerns. Doing so will help us become less focused on ourselves and more open to the world around us. He adds metaphorically, “An individual human existence should be…
by John Allen Paulos Philosopher Daniel Dennett’s new book, I’ve Been Thinking, just came out, and I was reminded of a party game he’s written about. A variant of the child’s game of twenty questions, it is relevant to an increasingly pressing question: How do different social bubbles, media subcultures, or cults develop. Let me…
by John Allen Paulos Over the years I’ve been teaching, many people have asked me about the content of an elementary course I teach. I’m interested in the syllabi and exams of courses in other fields, so this I hope may be of interest to others as well. The survey course on which this exam…