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The U.S. military appears to be moving in the direction of eliminating pilots, albeit tentatively. The Pentagon and the C.I.A. have long operated unmanned drones, including the Predator, which are used for reconnaissance and bombing missions. In 2013, the U.S Air Force successfully tested the QF-16 fighter-bomber, which is practically identical to the F-16, except that it doesn’t have a pilot onboard. The plane is flown remotely. Earlier this year, Boeing, the manufacturer of the QF-16, delivered the first of what will be more than a hundred QF-16s to the Air Force. Initially, the planes will be used as flying targets for F-16 pilots to engage during training missions. But at least some military observers expect the QF-16 to end up being used in attack missions.

Blind to the mathematical odds, we fall to the marketing gods.

“People just aren’t able to grasp 1 in 175 million,” Williams says. “It’s just beyond our experience—we have nothing in our evolutionary history that prepares us or primes us, no intellectual architecture, to try and grasp the remoteness of those odds.” And so we continue to play. And play.

It may seem easy to understand why we keep playing. As one trademarked lottery slogan goes, “Hey, you never know.” Somebody has to win. But to really understand why hundreds of millions of people play a game they will never win, a game with serious social consequences, you have to suspend logic and consider it through an alternate set of rules—rules written by neuroscientists, social psychologists, and economists. When the odds are so small that they are difficult to conceptualize, the risk we perceive has less to do with outcomes than with how much fear or hope we are feeling when we make a decision, how we “frame” and organize sets of logical facts, and even how we perceive ourselves in relation to others. Once you know the alternate set of rules, plumb the literature, and speak to the experts, the popularity of the lottery suddenly makes a lot more sense. It’s a game where reason and logic are rendered obsolete, and hope and dreams are on sale.

People are often highly confident in their ability to see things as others do, but their attempts are typically barely better than chance. Other studies find that people who are instructed to take the perspectives of others tend to do worse, not better, at judging their thoughts and emotions.

Professor Pinker, in his superb book “The Better Angels of Our Nature,” explores whether the spread of affordable fiction and journalism beginning in the 18th century expanded empathy by making it easier for people to imagine themselves in the shoes of others. Researchers have found that reading literary fiction by the likes of Don DeLillo or Alice Munro — but not beach fiction or nonfiction — can promote empathy.

That question was the subject, two weekends ago, of an American Association for the Advancement of Science symposium at the San Jose Convention Center (which smelled, pleasantly but nonspecifically, of clean carpet). The preëminence of eye over nose was apparent even in the symposium abstract, which touted data that “shed new light” and opened up “yet new vistas.” (Reading it over during a phone interview, Jonathan Reinarz, a professor at the University of Birmingham, in England, and the author of “Past Scents: Historical Perspectives on Smell,” asked me, “What’s wrong with a little bit of inscent?”) Nevertheless, the people on the panel were decidedly pro-smell. “One thing that everyone at this symposium will agree on is that human olfactory discriminatory power is quite excellent, if you give it a chance,” Jay Gottfried, a Northwestern University neuroscientist, told me. Noam Sobel, of the Weizmann Institute of Science, used a stark hypothetical to drive home the ways in which smell can shape behavior: “If I offer you a beautiful mate, of the gender of your choice, who smells of sewage, versus a less attractive mate who smells of sweet spice, with whom would you mate?”