Last night I attended the World Science Festival event, “The Illusion of Certainty: Risk, Probability, and Chance,” at the Tishman Auditorium. Entire courses are taught on these individual subjects, but the international panel managed to cover a lot of information in just 90 minutes.
Moderator Marcus du Sautoy, a mathematician, writer, and radio presenter from England, did a great job of eliciting meaningful remarks from the four participants: Amir Aczel, a mathematician and science writer from Israel; Gerd Gigerenzer, director of the Max Planck Institute for Human Development in Berlin; Leonard Mlodinow, physicist and author of several books including The Drunkard’s Walk; and Josh Tenenbaum, professor of Computational Cognitive Science at MIT.
The evening started with Tenenbaum flipping a coin five times while the audience wrote down their guesses and submitted them for tallying. This set the stage for a discussion that was filled with concrete, easily comprehensible examples about statistics and probability.
For example, when a weatherman says there is going to be a 30 percent chance of rain tomorrow, what does that mean? That it will rain for 30 percent of the day (about seven hours)? That 30 percent of that particular region will get rain? It means different things to different people, and that is often a problem with statistics, especially when they aren’t presented clearly.
The Monty Hall problem was also discussed. I lost a week of my life debating this problem with friends a couple of years ago, so I wouldn’t click that link unless you have a Tylenol ready for the inevitable headache it will cause.
Another audience experiment took place when the auditorium was divided in half for a geography quiz. Half the room covered their eyes while the other half was asked two questions: (1) Are there more or less than 180 countries in Africa? (2) How many countries are there in Africa? Then, the first group covered their eyes while the second was asked the same two questions, except 180 was substituted with five.
Later in the evening, after the results were tallied, we learned that the average guess for Group 1 was about 60, while the average guess for Group 2 was about a third of that. In other words, we were affected by the first number presented.
A major theme of the night was whether humans are inherently good or bad at interpreting numbers and statistics and probability. This audio clip reveals both sides, as a frustrated customer tries to teach a phone company’s employees the difference between .0002 dollars and .0002 cents.
Doctors and journalists are often, unfortunately, on the “bad” side. Some of the examples discussed last night were how doctors may misrepresent (or misinterpret) the probability of a positive breast cancer test or how the media may report a 100 percent increase in a disease, which sounds like a huge increase, when in fact the number of infected people rose from one to two in a population of one million.
“There is a systematic attempt [by editors of journals] to mislead the public,” Gigerenzer said, citing an U.K. newspaper story in which a particular birth control pill was reported to cause a significant increase in cancer—an extremely misleading representation of the numbers that led to an increase in unwanted pregnancies and abortions. Gigerenzer said we “need a risk-literate society” and it is up to our educations systems to provide that teaching.
Aczel added that it is “important to know how data was derived” and people should not make an “assumption of randomness.” In other words, look beyond the basic statistic provided to be sure the numbers represent a fair sample size.
The evening concluded with the release of the data from the coin flip experiment. My guess had been H-H-T-H-T, and it turns out that most people guess either this sequence or its exact opposite (T-T-H-T-H). When the flip sequence does follow this pattern (as it did last night), it would seem the audience is made up of mind readers. When it’s anything else (particularly three or four of one side in a row) the numbers would reflect the audience is comprised of terrible guessers.
Tenenbaum was perhaps a bit more optimistic about our ability to interpret data than the rest of the panelists. He gave the example of our response to a potential predator/prey. If we think we see something moving in a bush and suspect it might be, say, a leopard or a gazelle, our senses rarely fail us. Sometimes it is nothing but a strong breeze ruffling the leaves, but the consequences of missing a leopard/gazelle that does exist far outweighs the consequences of seeing an animal that isn’t actually there. While we may not always be good with raw numbers, our eyes and ears can be particularly good at analyzing stimuli.
In fact, despite all of my reading of mathematical formulas, it was not until this morning, when I watched a video explaining the Monty Hall problem that I finally understood it.
To give another statistic, “The Illusion of Certainty” was just one of 50 events taking place in New York this week as part of the World Science Festival. Please visit this space throughout next week for more coverage from our blog staff.
--Andrew Kahn
