Of the stacks of math and pop math and math & culture books now cluttering my table, I just opened one and laughed out loud. The book is Innumeracy, by John Allen Paulos, and and the discussion was about the relative danger of different threats. Which should we be more worried about?
- Choking to death on a piece of food.
- Getting killed by terrorists on a trip abroad
- Dying in a car accident
Well, circa 1985, the answers are that you have a 1 in 68,000 chance of choking to death; a 1 in 1,600,000 chance of getting killed by terrorists when traveling, and a stunning 1 in 5300 chance of dying in a car accident. Given these figures, my response is to say, “I’m never going to worry about getting killed by terrorists, I’m going to be an extremely conscientious driver, and I’ll try to remember to chew my food well.” Which is actually how I live my life, roughly (I know it’s 25 years later, but I doubt the statistics have changed much). If you’re familiar with the mathematics, it helps you assess risks, and not pay too much attention to those (like sharks attacks, terrorists) that aren’t likely to affect you.
Here’s what made me laugh:
Confronted with these large numbers and with the correspondingly small probabilities associated with them, the innumerate will inevitably respond with the non sequitur, “Yes, but what if you’re that one,” and then nod knowingly, as if they’ve demolished your argument with their penetrating insight.
Funny because it’s true!
Really big and really small numbers aren’t intuitive for lots of us. I love visualizations of them if you know any. A few of my favorites are:
and of course, the amazing classic Powers of 10, which I didn’t realize was available online! (I think it may be the older of two versions.)
There’s much more to the innumeracy that Paulos is talking about than not understanding orders of magnitude: not understanding chance is huge as well. These things are counterintuitive, of course, because we didn’t need them to live until quite recently in our species development. Now, cultural numeracy is vital.