Occupy Math is going to look at how math helps us design and play games.
Occupy Math has been writing articles for a new journal Game and Puzzle Design which seeks to bridge the gap between professional game designers and academic game researchers. You can order issues here. This is a unique niche and fills a real need. Professional game designers know how to make a game fun and interesting; the academic game designers can apply math and algorithms to solving problems that the professional game designers find during the design process. The academics also study the general space of all games and try and figure out how to classify games. A key point for Occupy Math is this.
Making better games helps us discover new math. Games can build interest in math.
With all the commotion in the news lately, a lot of people are saying “Oh, yeah? Prove it!” (often in an angry voice). This helped Occupy Math to select his topic for this week which is about proof and interpretation. In math, a proof is a series of connected logical statements that draw a line between some things that you assume are true and something else that you are trying to demonstrate is true. The Pythagorean theorem is a good example: “If you have a right triangle then the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longer side.” You are assuming that you have a right triangle and, if you do, the sometimes helpful fact about the side lengths holds.
This week we look at one of the big achievements in math, figuring out the minimum number of colors needed to permit adjacent countries to be shown in contrasting colors on any map, and connect it with a type of conflict resolution. Applications include efficient timetables for meetings, relatively peaceful assignments of students to cars for a field trip, and even putting as many types of fish as you can into the display window of a store that sells tropical fish. All of these applications have two steps: make a graph of the situation and then color that graph properly. We will explain the terms in italics in the rest of the post.
The fascinating mathematical fact here is that all these applications use exactly the same math.
Long ago, in Iowa, Occupy Math taught a course entitled “Introduction to Mathematical Concepts”. It was the course for people who might not have mastered arithmetic yet, but had a major that required a math course. During this course, there were only two days (other than examinations) with nearly complete attendance. The first day, because people wanted to know what was going to happen, and the day Occupy Math used a fair division algorithm to figure out the property division of Donald Trump’s (first) divorce. Short version: Ivana did not do well. In this post, Occupy Math examines two kinds of fair division. The simple one is dividing cake and the hard one is dividing property. We will also discuss why, with fair and equitable methods of dividing things, why we still spend piles of money on things like divorce lawyers.
Mathematical formulas exist to divide almost anything as close to fairly as possible — why then all the squabbles?
A perennial problem that people have is when the organization they work for, or with, makes a bad decision. A common refrain when this happens is “why didn’t they listen to me?” In today’s post we examine how to get them to listen to you using a mathematical tool called an influence map. The key mathematics that permits you to build and use influence maps is the directed graph, an example of which appears at the top of the post. The idea is this: objects in the directed graph are actors — people or organizations with power or influence — and the arrows show which way influence flows and, possibly, what type of influence it is.
Influence maps can be applied to an incredible number of different situations. These include your workplace and community.
Fifty is a big, round number and so Occupy Math decided to do something a little special — this is one of the images we’ve seen before, a cubic Mandelbrot set with quadrant convergence, but this time, instead of showing it a 56 iterations, Occupy Math has made an animation. This shows how the fractal develops, fits and starts and a final leafing out. Enjoy!