From time to time an academic makes an argument about how math isn’t all that important. Like this one in the NYTimes:
A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.
The article is a series of randomly thrown out and disconnected statements about how math might not be so important. The kind of non logical arguments you might expect from someone without a good grasp on math and logic. 🙂
It is true that I rarely use my math in my job as a software engineer. Where I use the math I learned in high school most often is on one of my hobbies, wood working. The moment you get beyond 90 degree angles on things, all that algebra and trig comes into play. A few years ago I created a set of built in shelves that had to deal with a 73 degree corner in my house, and have a sheet of pencil scribbles and trig functions to figure out all the cuts and sizes of pieces I’d need. I’ve got a host of custom built furniture in my house, all of which required algebra and trig to get right. And don’t even get me started on my deck.
The math you learn in high school is actually the math of carpenters and farmers. It’s a foundation for high math, but it’s real use is in much more concrete things. And that’s the reason why “Our civilization would collapse without mathematics.”
So the next time someone starts going on about how math is unimportant, look them in the eye and say: you’ve never built anything with your hands, have you?
Kevin Drum has a good post on what he calls Statistical Zombies, 10 of the top mistakes people make when using statistics. I particularly love #2:
What’s the survey error? Statistical sampling error in opinion polls is trivial compared to the error from other sources. Things such as question wording, question order, interviewer bias, and non-response rates, not to mention Bayesian reasons for suspecting that even the standard mathematical confidence interval is misleading, give most polls an accuracy of probably no more than ±15%. Example: a couple of years ago a poll asked respondents if they had voted in the last election. 72% said yes, even though the reality was that voter turnout in that election had been only 51%. Most polls and studies are careful to document the statistical sampling error, but who cares about a 3% sampling error when there might be 21 points of error from other causes?
After nearly a month of tinkering with code, nearly giving up twice, and realizing that I was going to actually need to relearn my linear algebra to get a real solution, I managed to create this graph. It is the position of the moons of Jupiter relative to the planet as seen from earth.
Thanks to Thor for helping me get to the realization that straight up geometry wasn’t going to be good enough, and help boot strap my relearning of vector math. Once I started using real linear algebra I didn’t even have to cheat on generating the sign. Next step… JNI.
Robert Wright provides a nice analysis on the current Toyota recall:
Let’s do the math.
My back-of-the-envelope calculations (explained in a footnote below) suggest that if you drive one of the Toyotas recalled for acceleration problems and don’t bother to comply with the recall, your chances of being involved in a fatal accident over the next two years because of the unfixed problem are a bit worse than one in a million — 2.8 in a million, to be more exact. Meanwhile, your chances of being killed in a car accident during the next two years just by virtue of being an American are one in 5,244.
So driving one of these suspect Toyotas raises your chances of dying in a car crash over the next two years from .01907 percent (that’s 19 one-thousandths of 1 percent, when rounded off) to .01935 percent (also 19 one-thousandths of one percent).
The rest of the op ed fills out some more of the details, and talks about the dangers of fearing something that is such low risk. It echos back to Tom Engelhardt’s thoughts from last week.