This year, Occupy Math is presenting ornaments made with a recursive fractal method. As this is the seventh collection, we provide links for the earlier sets as well, below the fold. This holiday season is coming as we try to wind down the pandemic and endure the climate emergency. Do what you can about these planetary disasters, but also remember that the duties of charity and kindness lie on you as strongly as they ever have.
Image of the Week #282
A complex part of the conjugated 9th order Mandelbrot set.
Data Science: what is it?
Occupy Math’s employer has launched a Masters Program in Data Science. The pyramid picture at the top of the post shows a major process goal of data science, which is more aspirational than real, as data science often achieves knowledge but seldom gets to wisdom. In graduate school, Occupy Math knew a professor of computer science who was fond of saying “Anything that calls itself a science probably is not one.” Data science is not even close to being a science, though it applied many of the results of science to the problem of understanding and reducing data. The word “reducing” in this definition can mean “concentrating into a useful form”, not “getting rid of”. Occupy Math is simultaneously developing and teaching a course entitled Data Manipulation and Visualization and so there may be several posts that arise from the experience. Another troublesome word: in this case “manipulation” means “transformation into a useful or tractable form”, not “deceptive modification.” Aren’t words fun?
Image of the Week #281
A recursive fractal, adjusted to have bright colors.
Announcing a book on problem factories
Writing a book is a big project and Occupy Math is very pleased to announce the first book arising from, well, Occupy Math. This book started at a conference for math educators that Occupy Math was invited to by his former student Andrew McEachern, now a professor at York University. Something that happens when you get math educators together is they tell you their favorite motivating problems, the problems that get students excited and interested. Andrew and I noticed that many of these problems fit into large families of problems. We coined the term Problem Factory for one of these store-houses of problems. Later in the post we have a list of the problem factories that have appeared in Occupy Math posts, to give you the flavor of things and tempt you to purchase the book. The book is Mathematical Problem Factories Almost Endless Problem Generation and it gives a number of problem factories, each illustrated by collections of problems drawn from the factory.
Some readers may find the subtitle “Almost Endless Problem Generation” to sound like what has been happening to all of us during the pandemic. Occupy Math’s editor laughed for several minutes after reading it. Do not worry, in a math book, “problems” mean “exercises” and having lots of exercises is a good thing. At least for math teachers. Never mind.
Image of the Week #280
A conjugate Newton’s method fractal — a rain of flowers.
Luck — a mathematical discussion
Luck is something a lot of people care about and they often go to great lengths to call up or control luck. Mathematically, luck can be explained by random chance — which is beyond control and which is very even-handed in how it bestows good or bad luck. Superstitions are pervasive in human societies. Different societies — and different people — have firmly held beliefs about what is lucky or unlucky. The mathematical science of statistics has, at its core, the quantification of chance. Statistics takes us part of the way to replacing the notion of luck with the notion of chance.
There is an important point to this. Chance is even-handed and brutally fair. Luck is often seen as being the result of virtue. People whom chance favors are often called lucky (especially by themselves) and people who experience bad outcomes by chance are called unlucky. The search for ways to summon up, invoke, and control luck is a huge human preoccupation, from a refusal to wear clean socks in major league baseball teams to the belief in auspicious and inauspicious numbers like seven and thirteen in European cultures. A revealing fact is that the “good” and “bad” numbers vary from culture to culture.
Image of the Week #279
Something bright and cheerful from the Newton’s method catalog, to counteract the rainy October weather.
What do mathematicians do all day? Part VI
Today’s post is another exposition of research, this time on a game that my colleague Joseph Alexander Brown created for teaching artificial intelligence. The game is about the foraging behavior of moose, very much simplified, and is a good example for demonstrating how to make a strategically interesting game. The basic idea is simple. We have two moose that can choose between three different fields where they might forage. The fields have plants in them that grow back after being eaten, fast at first and then slower as the plants get back to full size. Each morning, the moose each choose a field. If they choose different fields, then they get a score equal to the forage in that field. If they choose the same field, they trumpet and threaten and tear up the field a bit but get no forage. Sounds simple, but there are some subtleties.
Image of the Week #278
A rainbow palette cubic Mandelbrot view, in case you were color-deficient!
Occupy Math 