The capital of Indonesia, Jakarta is sinking beneath the sea and a new capital is being planned on the mountainous island of Bali. In Italy, a regional government council voted against measures to combat climate change and then, within minutes, their council chamber flooded with sea water. These are dramatic examples, and the underlying fact is that sea levels are rising much faster than predicted — except that they are not — which is the topic of today’s post. The apparent contradiction arises from the multiplicity of models.
A view from the quintic Mandelbrot set.
In this post we look at several ways traditional textbook publishers are poisoning math instruction — charging insane prices for books, writing lectures for professors (bad ones), and doing a bad job of generating problems for practice, homework, and examinations. We begin with the price issue. A while back, Occupy Math announced he had written a calculus book, Fast Start Calculus for Integrated Physics. The material from the book is being republished as the three books pictured at the top of the post. This is part of Occupy Math’s war on outrageous textbook prices. These books are distributed at low cost to a university and zero cost to students at participating universities.
A conjugate quintic Julia set. Reticulation rules!
Today Occupy Math takes on some of the basics of capitalism and looks at some serious problems with the current economy. The picture at the top of the post is an objection to capitalism. It is a common argument to make that capitalism is better than socialism because capitalist countries have better levels of wealth and comfort than socialist countries. A common technique is to compare socialist North Korea with capitalist America. If you look at the underlying mathematics and how it can suggest manipulations of both systems, this comparison comes up as sort of ridiculous. One might as well compare socialist Sweden with capitalist Detroit. Occupy Math should state here at the beginning of the post that he favors neither capitalism or socialism because both of them can create excellent or horrible outcomes. Occupy Math’s motto is that “Math is the Right of All Free People”. Even a basic understanding of the forces at work in an economy, which are mathematical in nature, can reveal that the keys to the general welfare lie in having an aware and involved citizenry, not in the straw man debate about which system is better.
A deep zoom into the cubic Mandelbrot with color and more color.
In this week’s post we look at a game for practicing recognition of multiples of a number. It can be used in class by a teacher or it might be a good game to play with your kid by way of some math practice. The game prepares a student for multiplication by practicing how to recognize which numbers are multiples of five. The numbers 5, 10, 15, and so on generate scores when they come up in the course of the game. There are multiple versions of the game (for other numbers besides five), but the demonstrations are based on recognizing multiples of five. The game is a little like dominos and it’s a little like a crossword puzzle.
A Julia set with an added spin component. Whee!
Michel Mayor was one of two scientists awarded the Nobel prize in physics for finding the first earth-like planet outside of our solar system. This is one of the more exciting parts of discovering thousands of new planets, including the seven-planet Trappist system, forty light years away, diagrammed above. He gave an interview which has been widely distributed in which he said we will not colonize another planet as a way to deal with Earth becoming uninhabitable. The reason to write a blog about it is that what he is saying is both critically important and almost certainly wrong. The problem, as it often is, is a lack of nuance that can be restored by looking at the basic math. In this case the key phrase is “we will colonize” — the idea is problematic.
Lurking deep in the Mandelbrot set…