Your Brain’s “Law of Large Numbers”

Those educated in statistics are familiar with the law of large numbers: the larger the sample size (or the greater the number of trials run), the closer the sample’s mean gets to that of the overall population.

In brain science there’s a completely unrelated law of large numbers, and it’s this: the larger the number, the worse the human brain’s ability to comprehend it.

A general rule of thumb is that the brain counts like this: one, two, three, four, many. (Research varies at exactly what point the brain loses its ability to comprehend numbers.)

This presents a problem for communicators: what to do if your argument’s success rests upon the audience understanding the impact or meaning of a large number?

Here are three strategies:

I.
Subitize. Break down larger numbers into groups of recognizable numbers, notably into 2s, 3s and 4s. For example, instead of showing 20 items in a mass show five groups of four items. This will make comprehension easier for your audience’s brains.

II.
Create “perspectives”. Dan Goldstein and Jake Hofman, with Microsoft Research, ran experiments to see what kinds of contextual clues – what they call “perspectives” – can enable people to comprehend large quantities like distances, dollar amounts, population sizes, etc. For example: 1 million seconds is nearly 12 days, whereas 1 billion seconds is almost 32 years.

Another, more arcane example comes from David Letterman’s career as a TV weatherman. (You didn’t know about this earlier career, did you?) On air he once described hailstones “the size of canned hams.”

Why do perspectives work? They show context. (Imagine the terror of canned hams falling in the multitudes from the skies.) Share the “hard numbers” first, of course (we don’t want to abandon large numbers), but then provide context that enables your audience to make sense of those numbers. For example, suppose a new air conditioning system will reduce energy consumption by $7,500 annually, a reduction of 50 percent. Share those figures, then contextualize it by stating something like, “That’s like getting free air conditioning every other month.”

III.
Show causality. This is related to perspectives (context) and could be the most-important strategy of the three. It’s not enough to simply throw the number out there, for example one showing a cost or a benefit. You’ve got to connect the number to the “so what,” to export the insight: to the conclusion you want them to draw, to the action you want them to take, etc. Share the number, then tell your audience what it means for them.

Showing causality via graphs and graphics is one of Edward Tufte’s big ideas. His Challenger space shuttle analysis is a legendary case study in what can happen when data are not presented to show causality.

 

Additional Reading

Wikipedia entry for subitizing: https://en.wikipedia.org/wiki/Subitizing

“Visualizing Vastness,” by Steven Strogatz, https://opinionator.blogs.nytimes.com/2012/10/15/visualizing-vastness/

“Improving Comprehension of Numbers in the News,” by Pablo J. Barrio, Daniel G. Goldstein, and Jake M. Hofman, accessed at https://dl.acm.org/citation.cfm?doid=2858036.2858510

“How to Understand Extreme Numbers,” by Elizabeth Landau, https://getpocket.com/explore/item/how-to-understand-extreme-numbers?utm_source=pocket-newtab

“Visual Explanations: Images and Quantities, Evidence and Narrative,” by Edward Tufte, Graphics Press, 1997. See pp 38-53 for discussion of Challenger disaster.


Written by

Mark Bourgeois