This past Sunday I made my (now routine) road trip from D.C. to Nashville, where I will be working for the summer. Having made this trip at least 10 times in the past 2 years, I’ve learned to stock my iPod with plenty of good podcasts to keep me entertained on the 11 hour drive. On Sunday I was listening to this particular episode of Radiolab, entitled “Numbers.”
There were so many good mathy things covered in this episode, some that I was familiar with (Erdos numbers, Steve Strogatz and The Calculus of Friendship) and some that I hadn’t encountered before (Benford’s law, the development of number sense in babies.) It’s that last one I want to talk about a little bit.
While I’d recommend you just listen to the segment (“Innate Numbers”), I’ll take a stab at recapping it: there’s a big difference between the way babies perceive numbers and the way adults are taught to understand them. To a grown-up-type-person, the difference in (or, really, “space between”) 8 and 9 is the same as the difference in 1 and 2. Our number line is linear, and in each case, the numbers are equally far apart. (“1” apart, to be exact.) But to babies, the jump from 1 to 2 is huuuuuuge, while 8 and 9 don’t really seem different at all… the “space between” them is much tinier.
Basically, we have this innate number sense that has us perceiving numbers logarithmically – where the distance between two numbers represents their ratio (division) rather than their difference (subtraction.) A baby number line, if they could draw it for us, would be all spaced out on the left and bunched up on the right – with the numbers closer together the larger they get.
This innate, logarithmic understanding of numbers gets schooled out of us at some point, as we learn to count and attach a new, different, abstract kind of meaning to each increasing integer. But when I think about my life lately, I can’t help but feel like I’m trapped in the baby math.
When I was little, the space between my 8th birthday and 9th birthday was huuuuge. Christmases are so far apart! Summer takes forever to get here! But then time started “speeding up” and the space between each milestone was compressed on the number line of my life. I’m going to college? Too soon! College is half over? Junio-senio-grad school… and then I barely blinked and year one and two of teaching have already disappeared. I can hardly believe it.
Driving back to Nashville (and aren’t road trips a time-distorting wormhole in and of themselves?) I realized that If I’m not careful, these next 3, 9, 27 years of teaching will rush past me at increasing velocity. Maybe that will happen even if I’m careful. But I decided that the most logical way for me to react, in the face of this “baby math,” is to make my best attempt at filling up the space between those closer-and-closer points on the number line.
Writing is not one of my strengths, but I have this sneaking suspicion that documenting my teaching successes, struggles, and assorted mathemusical interests/insights will help me to strrrretch out that number line. Just a little bit. So here is bloggy me.