On October 10, 2026, our group of five continued exploring Neil deGrasse Tyson’s Starry Messenger. We were fascinated by his discussion of the Gaussian or normal (bell-shaped) distribution—a statistical tool used to determine whether sets of measurements differ significantly. Gauss originally developed this method to separate signal from noise to determine the orbit of the asteroid Ceres.
We can calculate the significance or certainty for sets of astronomical measurements or data to compare the effects of one drug with another. In a normal distribution, 95% of the points for a set of measurements fall within ±2 standard deviations from the mean. If a point is more than two standard deviations from the mean, it is unlikely to be part of the main distribution and is considered noise. This echoes Plato’s Allegory of the Cave, which suggests we see reality as a shadow projected on the cave’s wall. Is reality found in a set of data points collected by instruments that cluster around their mean, or do we still see only the shadow of reality when we infer it from approximations? Yet, by using instruments and the Gaussian distribution, we glimpse beyond the cave, seeing much evidence for reality’s nature—a reality greater than what can be imagined.
Probability and statistics also explain evolution. Tyson shares an allegory of the African savannah: if you see tall grass swaying, you face a matrix of four possible outcomes. Walking toward it when a lion is present removes you from the gene pool. Even if it is just a breeze, continuing this reckless behavior means you will eventually become a lion’s dinner. Running away—whether a lion lurks behind the grass or the breeze moves it—costs you nothing. Caution ensures survival, as evolutionary pressures weed out careless boldness. While this shapes modern human behavior, it also suppresses the curiosity needed for innovation. We need a way to hone our prudence and evaluate risk better.
Can education counter these hardwired biases and reduce the dangerous consequences of learning the hard way? In 1986, the American Physical Society moved its conference to Las Vegas, resulting in a famous local headline: “Physicists in Town, Lowest Casino Take Ever!” Knowing how to calculate the odds, the physicists declined to gamble. Tyson also observed that airport bookstores in Las Vegas notoriously lack science and math sections, since casinos prefer customers who cannot calculate the odds stacked against them. Yet even when they know the odds, gamblers still flock to the casino tables, suggesting a different, primitive brain circuit is at play.
B.F. Skinner revealed this circuit by using hungry rats in a lever-equipped chamber. A food pellet dropped each time they pressed the lever, and the rats quickly learned the behavior. This activity stopped when no pellets dropped. But when Skinner switched to an unpredictable, intermittent reward schedule, the rats pressed the lever obsessively. Unable to predict the next payout, they pounded the lever thousands of times an hour, neglecting sleep and grooming, and finally succumbed to exhaustion. This dopamine-driven neural loop also blinds gamblers to the odds of winning, driving them relentlessly to pull slot machine levers. Can education help us to hone prudence to manage risk better and counter these hardwired biases?
Beyond casinos, cognitive bias causes us to miscalculate other risks. Consider the public outcry against GMO corn engineered to resist the weed killer glyphosate. To objectively evaluate this risk, Tyson introduces the LD50 metric (the lethal dose required to kill 50% of test animals). Glyphosate’s LD50 is 5 g/kg, whereas table sugar is 30 g/kg. Because refined corn syrup, used to make ice cream, contains only trace amounts of glyphosate, Tyson calculates that you would have to consume 400 million pints of ice cream to die of the contaminating weed killer—but you would die from the sugar content after just 20 pints. Could cost-benefit ratios be used to find the appropriate response to 9/11, ways to reduce firearm fatalities, the best measures to strengthen the economy, and methods to improve security in communities?
Finally, we see this same failure of risk assessment with self-driving cars. Even if autonomous vehicles drop annual U.S. traffic fatalities from 35,000 to 1,000, the overwhelming public reluctance reflects their pervasive sense of foreboding. As essayist Walter Bagehot suggested, humans naturally avoid the pain of a new idea. Are we biologically prone to fear change, or are we simply resistant to the education needed to become more prudent in evaluating risk?
Join us for our next meeting as we continue exploring *Starry Messenger* (Library of Congress call number: CB478.T96 2022) and discuss how to turn divisive arguments into objective, informative dialogues.
