People use the word random pretty casually, but it is actually a big deal. What would it mean, for example, for a crowd in a movie to look “random”? Oddly, it seems to be one-sixth women and five-sixths men — this is a result found by the Geena Davis Foundation, which examines the issues of representation of women in media. Since there are slightly more women than men (women live slightly longer), a really “random” crowd would, logically, be about half women, probably slightly more. Asking audience members when a crowd looks balanced returns a positive response when the crowd is composed of about one-sixth women. When the crowd is one-third women, audience members think that the crowd is majority female. This is a simple, if startling, example of how human beings are terrible at determining if something is random.
In his awesome Discworld Series, Terry Pratchett often included twisted, hysterical versions of modern science and scientific myths. One of my favorites among these is the quantum weather butterfly. In this post we are going to talk about the famous butterfly effect and the odd notion of deterministic chaos as well as one of the biggest human misunderstandings of an obvious mathematical truth.
When people figure out how bad something is, they usually try and figure out how much changing one thing changes another and then use that to calculate the estimated impact. If you raise the price of a car model by $500 and sales drop 0.5% then you estimate a $1,000 dollar increase would drop sales about 1%. If several things are changing, you check the impact of each one individually and add up the results. In Occupy Math’s calculus+physics class we actually work out (as part of error analysis in physics) when this type of estimate works. The answer is when the factors either don’t interact or when the changes in all factors are very small. Most changes are pretty small so that means this “calculate them individually” approach works pretty well. In this week’s post we look at situations where this method of estimating impact fails catastrophically.
This post is the second on the game FRAX and spends some time explaining how the game works and where it came from. The first post was on Occupy Math’s sister blog Dan and Andrew’s Game Place. FRAX seems, based on our initial testing, to be a fun game in addition to giving the players practice with fraction arithmetic. To get the rules to FRAX (and if you’re interested in testing the game), click the link! We are giving away FRAX sets to people who will help us with the play testing. FRAX is a card game, not a computer game, though we have some thoughts in that direction.
Occupy Math has already written on the issue of thinking you’re not a math person and this week’s post examines the issue from another perspective: the value of hard work. If you want to be good at hockey or baseball, you go in knowing you’re going to have to practice. Contrast that with the way most people believe that either you can do math or you can’t. The academic tradition in Asia contains a strong belief that working on an academic subject makes you better at that subject. Americans — on average — only believe this about sports. This goes a long way to explaining why Chinese students are ranked top in math and Americans are in the bottom half.