The Innumeracy of Educators, or Mark Twain Was Right
Just for fun, here’s a selection of a few of the problems from the 2006 math test given to tenth graders, the one where Mr. Roach didn’t know how to answer any of them, and “Not a single one of [his friends] said that the math I described was necessary in their profession.” See if you’re smarter than a Florida school board member
US road accident casualties: every one mapped across America
369,629 people died on America’s roads between 2001 and 2009.
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You can zoom around the map using the controls on the left or search for your town using the box on the right – and the key is on the top left. Each dot represents a life
Of Mobius Strips and the Shape of Things
[E]ven though Earth is (roughly) spherical, the directions you travel can be broken down into two directions: North-South (longitude lines) and East-West (latitude lines). However, there are two places where the latitude-longitude coordinate system breaks down: the North and South Poles, where a single latitude corresponds to all the longitudes simultaneously. In fact, no coordinate system can describe the surface of a sphere without a breakdown at at least one point! It’s not for lack of trying, it’s just a mathematical fact. (There are coordinate systems that break down at only one point, but they’re less useful for cartography.)
Arguments about Möbius are always so one-sided.
Exposing a Climate Science Fraud
I’m shocked —shocked! — to find that someone is playing fast and loose with global warming analysis to support their position. Some aspects of this is the statistical significance game George Will played some time ago by looking at short sets of noisy data, only this time it’s a scientist — someone who should know better.
Quasicrystals as sums of waves in the plane
This is so cool, and artsy as well; like a very complicated moving moiré pattern (which is basically what it is, as far as I can tell). You can see lines emerging, similar to the effect of driving past an orchard with evenly-spaced trees, and glimpsing the far side when you hit a particular “order” of the structure, but there’s so much additional structure in the animation.
By golly, I wish I’d had this book as an undergrad.
As it was, I had to wait until this past January, at the ScienceOnline 2011 conference. These annual meetings in Durham, North Carolina feature scientists, journalists, teachers and students, all blurring the lines between one specialization and another, trying to figure out how the Internet can help us do and talk science. Lots of the attendees had books recently published or soon forthcoming, and the organizers arranged a drawing. We could each pick a book from the table, with all the books anonymized in brown paper wrapping. Greg “Dr. Skyskull” Gbur had brought fresh review copies of his textbook. Talking it over, we realized that if somebody who wasn’t a physics person got a mathematical methods textbook, they’d probably be sad. So, we went to the table and hefted the offerings until we found one which weighed enough to be full of equations, and everyone walked away happy.
The “we” includes me, because I scored a copy as well, and was in on the activity of sizing and weighing the anonymized books. There were probably more of these books than physicists (perhaps we can do better this year), though, so I imagine some species of biologist and/or journalist (statistically speaking) was disappointed.
By overthinking I mean spending a lot of time modeling the problem.
The Linear Theory of Battleship
I wrote a little code to generate random Battleship boards, and counted where each of the ships appeared. I did this billions of times to get good statistics, and what I ended up with is a little interesting. You can see the results for yourself over at my
results exploration page by changing the radio buttons for the ship you are interested in, but I have some screen caps below.…
This is an example of the failure of the linear model. All the linear model knows is that in the spots nearby misses there is a lower probability of the ship being there, but what it doesn’t know to do is look at the arrangement of misses and check to see whether there is any possible way the ship can fit. This is a nonlinear effect, involving information at more than one square at a time.
It is these kinds of effects that this theory will miss, but as you’ll notice, it still does pretty well.
I’m wondering if it does as well against human opponents, who would not place the targets randomly.