In a New York Times opinion piece, Steven Strogatz does a great job of articulating both the power and abstraction of numbers. It’s something I try to talk about in my classes — probably with less success than Strogatz. I often use the example of shepherds keeping track of how many sheep they have by creating piles of stones. The usefulness of carrying around a number, say “24,” rather than 24 stones, to express how many sheep one has is pretty self-evident. At the same time 24 applies equally well to sheep, bombs, dollars, stones, people, and more, which presents a potentially dangerous abstraction; that is, we don’t really want to treat 24 dollars the same as 24 people.
Strogatz writes about this issue and more in the article. His goal is to discuss “the elements of mathematics, from pre-school to grad school, for anyone out there who’d like to have a second chance at the subject — but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.”
If future installments are as well done as the first, the project will be useful for the math-interested and not.
(Thanks to Alisa for the heads up.)