Institute For The Future

Do We Have Mathematical Instincts?

At our Health Horizons conference earlier this week, we spent some time discussing the challenges of communicating future risks to every day people and noted that one of the key challenges in the coming decade will be to understand how to explain fuzzy genetic probabilities to people in ways that help improve their health. Underlying this challenge is a question of how instinctively we grasp mathematical concepts, something two prominent science writers--Jonah Lehrer and Carl Zimmer--recently tried to answer, with seemingly different conclusions. Either we have an evolved trait, stretching back 30 million years to intuitively grasp numbers, as Zimmer suggests, or as Lehrer suggests, our emotions frequently color any attempt at arriving at rational mathematical understandings.

 

Let's look at Zimmer's argument. Citing research from childhood development as well as evolutionary biology, Zimmer argues that:

 

Children enter the world with a head for numbers... Newborns consistently looked longer at the screen when the number of shapes matched the number of sounds they had just heard. For example, a baby who heard “tuuu, tuuu, tuuu, tuuu” would look the longest at four shapes, less at eight, and still less at twelve. Izard’s study suggests that newborns already have a basic understanding of numbers. Moreover, their concept of numbers is abstract; they can transfer it across the senses from sounds to pictures...

 

Indeed, recent research indicates that our forebears possessed such an intuition long before they could walk upright. Scientists have found that many primates, including rhesus monkeys, can solve some of the same mathematical problems we can. Since monkeys and humans diverged 30 million years ago, mathematical intuition presumably is at least that old.

 

Zimmer explains that this "mathematical intuition" involves two key principles: We grasp small numbers more effectively than large numbers, and the greater the difference between two numbers, the more easily we can distinguish between them.

 

The distinction between how we understand small and large numbers is critical to Lehrer's piece, which aims to make sense of why football fans are so angry that Patriots coach Bill Belichick made a statistically justifiable but controversial play call at the end of a high-profile game this past week.

 

The reason I bring up this analysis is to demonstrate that even defensible decisions can have wrenching emotional consequences. Belichick's call might have been statistically correct, but it felt horribly wrong...

The point is that there's often an indefatigable gap between the rigors of cost-benefit analyses and the emotional hunches that drive our decisions. We say we want to follow the evidence, but then the evidence rubs against a bias like loss aversion, and so we make an exception. We'll follow the evidence next time.

 

 

In other words, Lehrer and Zimmer are analyzing fairly distinct things: Zimmer is suggesting that people have an innate ability to grasp the difference between five and 10, while Lehrer is suggesting that when numbers get larger and more complex, we lack instinctive understandings of numbers. We have to hope our cognitive abilities to think through numbers will override our other instincts, and for that matter, our past experiences and the experiences of friends and family.

 

As Lehrer notes, the distinction between small and large numbers has implications that stretch beyond football.

 

Just consider health care: the only way we're ever going to reduce medical costs is to restrict procedures that haven't passed evidence-based efficacy tests. Maybe that means 40 year old women don't get mammograms, or that we treat prostrate cancer less aggressively, or that we stop performing spinal fusion surgeries. Although there's solid evidence to question all of these medical options, such changes provoke intense debate. Why? Because our emotions don't understand statistics.