Tuesday, August 5, 2008

How our brains deal with large numbers

Via Andrew Gelman, a recent Science article claims that humans innately use a logarithmic scale.
When asked to point toward the correct location for a spoken number word onto a line segment labeled with 0 at left and 100 at right, even kindergarteners understand the task and behave nonrandomly, systematically placing smaller numbers at left and larger numbers at right. They do not distribute the numbers evenly, however, and instead devote more space to small numbers, imposing a compressed logarithmic mapping. For instance, they might place number 10 near the middle of the 0-to-100 segment.
(Full text here, SciAm report here)

When I was a little kid my dad helped me "count to a million" using log scale (1,2,3...10,20,...100,200,...). Even then it seemed intuitive. I knew that there were increasingly more numbers in between counts as it got higher, and I felt I was "cheating" by skipping them, but I did not understand how long it truly would have taken if we'd counted all the numbers in between (I probably would have guessed it'd have taken hours, rather than days).

It's not that people cannot grasp large numbers-- they just have trouble converting back to a linear scale. :-)

1 comment:

Twyla said...

Interesting to know.