Image of the week #46

This is another evolved, generalized Julia set — a paltry two complex parameters — but much to my surprise this fractal literally goes to infinity and beyond.  For symbolic values of infinity.


An Open Letter To “Non-Math People.”


You’ve probably been lied to. It might be a direct and intentional lie, as with high school students Occupy Math met at a girls math conference (not Occupy Math’s name for it). Teachers told these women that they couldn’t do math — often before grading any of their work. The lie might be implied, as when the person teaching you math in fourth grade was clearly scared of it herself. We also have a distressing cultural context which paints mathematical ability — or even just being smart — as being anti-feminine. Men are not immune to this sort of idiocy either. Occupy Math has encountered far too many students who, when faced with a difficult concept in math said “I can’t do math, I’m not smart!” With many of these students it turns out they could do the math and they were pretty smart. For some reason, however, running away was a much more comfortable proposition than, oh, saying “can you explain that again a different way?”

Occupy Math finds the term “math person” pretty frustrating. If you think you’re not a math person then you’re taking a whole hamper full of issues and putting a two-word sticky note on it. Do you mean you will never win a prize for mathematical research or do you mean you can never learn to add? “Not a math person” lumps together a huge spectrum of ability levels and training in one small place. Here’s the scoop: unless you meant the “not winning a prize for original research in math” extreme, you’re probably wrong about not being a math person. I don’t mean you’re good at math right now or that you’re not afraid of it. I mean that it is incredibly unlikely that you cannot do math at some basic (but useful) level and probably you can do more. In this week’s post we will look at both fear and the case for trying to overcome that fear.

At this point some of Occupy Math’s readers are thinking “But I don’t want to be a math person!”

Continue reading

Image of the Week #45

This week’s image is a generalized Julia set that uses six complex parameters.  As Occupy Math has noted before there are hard to find by hand so the parameters were evolved with an evolutionary algorithm.  Enjoy!IOTW

Serious Creativity can be a Goofy Process

One of Occupy Math’s claims is that academic research is too stodgy. This week’s post looks at a successful research idea that arose from a science fiction novel. This idea has supported more than ten peer-reviewed scientific publications and, in several of them, the reviewers made Occupy Math take the science fiction novel out of the references. One of the reviewers even said “No-one cares where you got the idea”, a notion with which Occupy Math disagrees. In fact, the most elusive quality Occupy Math tries to train into his students is having good ideas.

This post concentrates on one example application – generalizing a technology that makes pretty pictures. While more frivolous than trying to understand the wellsprings of creativity, it is another area of deep interest to Occupy Math. When looking at the pictures of cellular automata in this post, try to judge which ones look different and which ones look similar. A cellular automata is a simple model of calculating a new row of pixels from old rows of pixels — but the way the model works is not obvious, so Occupy Math uses tricky code to search for models that make interesting pictures.

If we want math and science to be appreciated, we cannot make the ivory tower too high or windowless!

Continue reading

Betsy DeVos and Equal Opportunity

devosThis week Occupy Math pays off on a promise to look at Trump administration appointee Betsy DeVos. Now confirmed — by the lowest margin possible and the lowest margin ever for a cabinet level post — Ms. Devos is in charge of the federal government’s education policies. While Secretary of Education is not as big a deal as Secretary of State or Attorney General, this is an important government post with a good deal of influence on education in the United States. Today’s post looks at her potential impact on education, including math education.

This post examines what we know about possible impacts of Ms. DeVos proposed programs, based on their partial implementation in her home state of Michigan.

Continue reading

Image of the week #43

This image is the result of alternating the cubic Mandelbrot and the cubic Julia with parameter 0,0.  It is an interesting type of structure I have not seen before — a four fold spiral whose elements are much higher order spirals.  Enjoy!


Digital Aikido


This week Occupy Math tries to give a sense of how big data, social media, and some simple machine learning techniques can be used to invade your privacy. If you know how some of these techniques work, you can be a little safer — Aikido is a defensive martial art, hence the title of this week’s post. Having said that, it is important to note that the greatest source of safety is that for the most part we are happy to live and let live. While you don’t need it, looking at an earlier blog, With Big Data comes Big Responsibility, may supply some useful context. In this post we will look at how machine learning lets people guess who you are and what you believe.

Continue reading

Image of the Week #42

This is a generalized Julia set with a contraction map.  Occupy Math looked for the answer to life, the universe, and everything, but this was what was available.  The appearance may merit the title “Truffula Forest”.  Enjoy!


Surviving math: avoid type errors!

The post was inspired by the grading of a recent midterm by Occupy Math. Consider the following matching test. It has an odd property: you can complete it with very little actual knowledge about Sally, Thomas, cars, or cooking. If you are not from an English speaking background, the useful tidbit that Thomas is a male name and Sally is a female one may evade you, but mostly everyday knowledge carries the day on this test.


What kind of thinking is this and is it useful in math?

Continue reading