Addition Is Useless, Multiplication Is King: Channeling Our Inner Logarithm

TIME magazine has been running a series called "Brilliant: The science of smart" by Annie Murphy Paul. The latest column, "Why Guessing Is Undervalued," quoted several results from research on learning estimation, a topic near to my heart. One result surprised me particularly:

…good estimators possess a clear mental number line — one in which numbers are evenly spaced, or linear, rather than a logarithmic one in which numbers crowd closer together as they get bigger. Most schoolchildren start out with the latter understanding, shedding it as they grow more experienced with numbers.

I do agree that children start out with a logarithmic understanding. I first learned this idea from a wonderful episode of WNYC’s Radio Lab on "Innate numbers" (Nov. 30, 2009). The producers had asked Stanislas Dehaene to discuss his research on innate number perception.

One of his studies involved an Indian tribe in the Amazon. This tribe does not have words for numbers beyond five, and does not have formal teaching of arithmetic.

Tying With Your Hands

Economists have long recognized the potential value of artificially restricting one’s choices. Tying your hands can be useful in strategic situations. The old idea of burning bridges behind an army so they can’t retreat is a classic example. Strategic situations usually involve you and some adversary, like an opposing army, a competing bidder, or maybe […]