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.
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.
This is a dual Julia set done with a palette that changes color fairly quickly.
This is what happens when you use quadrant convergence on a Newton’s method fractal with a tiny rotation added into the iterator. This one is for z^6-1=0 with a rotation of about 0.2 radians.
This is a fourth-power Mandelbrot set view — the neon jungle.
This is a shot from the galactic cluster part of the Mandelbrot set using wedge convergence.
This week’s image is a deep zoom into the Mandelbrot set using a diamond-shaped convergence set. The positive and the negative space are interesting on this one.
The Mandelbrot set contains an infinite number of copies of itself – here is one of them. I’m using palleted quadrant convergence to get the leafiness.
This is a picture of Democratic Institutions Minister Maryam Monsef of the current Government of Canada from a CBC Story. Her job is empowering Canadians to have their say about our democracy. What she is doing in this picture is mocking a simple formula for measuring the fairness of an election. This formula appeared in a report on electoral reform in Canada. This is not her job. This is the opposite of her job. When an expert panel is convened to advise the citizens and government of their options to make elections more nearly fair, mocking the options (other than the one that let you win the last election) is malfeasance, fraud, and betrayal of duty. This is triply so in an official in charge of enhancing fairness.
No-one should mock an attempt to measure fairness. Mocking it by exploiting fear of math is especially vile.
Hot off the processor, a Newton’s method fractal with a complex array of small biomorphic shapes. Enjoy!