A circle-convergence view in the cubic Mandelbrot set.
A circle-convergence view in the cubic Mandelbrot set.
Right now covid-19 tests are going to important people more than others — because those important people are scared and we do not really have a strategy. When vaccines become available, if we do not have a science-based strategy, the strategy may well turn out to be “Vaccinate the rich!”. This post takes you through the initial stages of a research project on making plans for vaccine deployment, including some speed-bumps we hit. It may give you a sense of how computational research goes and why it has a good chance of success.
In an earlier post, Occupy Math talked about vaccine deployment strategies. Occupy Math is now part of a deployment strategy project, funded through St. Francis Xavier University in Nova Scotia. The project is led by Professor James Hughes at StFX University. Professor Sheridan Houghten at Brock University is also collaborating. We are old friends and have been collaborating for years. This post is about some of the results we have gotten so far and how the results changed the project. The picture at the top is a bit whimsical as the research we are doing is in three rooms in our houses with our computers. Six rooms if you include students currently in or joining the project.
A rotated Julia set that has spirals of spirals.
One of the funny lines in Back to the Future is when, after Marty says “Heavy …” one too many times, Doc. Brown asks him if there is a problem with the earth’s gravity in the future. Occupy Math has been running the gravity a bit high lately with many serious posts and (this is why we need editors) his editor has recommended a light-hearted post. Occupy Math will go through some hopefully amusing and possibly tragi-comic stories about things that did not go well during teaching. Two serious points are hiding in the comedy. First, many of these stories illustrate less than spiffy approaches toward passing a math class when you hit university. Second, if you are not enjoying your math class, neither is the instructor, and there is room to negotiate a better world for everyone.
A Glynn fractal with exponent 1.81.
Occupy Math has published a good deal of research on cooperation and conflict. Models of such behavior involve game theory and Occupy Math differs from the majority of researchers. Instead of assuming the agents are purely “rational” in the sense that economists use — that they are out for themselves — Occupy Math allows agents to evolve in such a way that their survival depends on how well they play the game in a group. This ends up generating a much more complicated strategy space than the economic optimization of each individual agent’s own gain. It also means that Occupy Math’s results are harder to understand and interpret.
As far as Occupy Math can tell, if they were purely rational economic actors — the sort of semi-human automatons that populate economic models — the black community would be reacting much more strongly than they are now. They are below the behavioral threshold that would be considered “self defence”, considering the amount of violence to which they are subjected. George Floyd ended up dead at the hands of the police because he was suspected –not proved — to have paid a corner store with a forged $20 bill; Rayshard Brooks ended up dead at the hands of the police because he fell asleep in his car in a drive-through lane at a fast food venue. This is utter madness. It is also all too common, suggesting the lack of self defence is itself powered by uneven penalties for black and white actors. There is hope in these tragedies. George Floyd’s murder was the proverbial last straw that triggered mass demonstrations around the world. Millions of people in a human rainbow of colors turned up in support of positive change.
This is a 232-Mandelbrot view with a sixty degree conjugation inserted about the cubic Mandelbrot. It’s another one of these river-delta looking areas in fractal space.
A common question in a first or second year university math class is “how do you remember all this stuff?” The answer is a little complicated, but the solution is simple — the students who ask this question need to change strategies. They are usually trying to memorize math rather than remember it..
Most students try to cram only the math they need to pass a test or quiz into their heads just before they need it. This may or may not work — depending on skill and aptitude — but it grants almost no ability to remember the math. This is often deadly because math is cumulative. It also absolutely maximizes the amount of work you need to do. When you memorize something — especially in a hurry and only for a particular purpose — you are putting a pile of individual facts into your head in a semi-organized fashion so that they are all available. This is difficult and the individual nuggets are often not durable. Remembering math, on the other hand, means that you have used the math enough that not only the individual parts, but the relationships between the parts, are familiar to you. Remembering math is actually easier that memorizing it, but you need to get to the state where you can remember it through practice. That is what this post is about.
A 323-Mandelbrot fractal from the river delta region with feathered hills.
This post is motivated by the phenomenon of Zoombombing, which should probably be called cyber assault. A dark actor will join an open meeting and share a video of something horrible, disgusting, and potentially traumatizing. Password protection can lessen the chances of such an attack on Zoom meetings, but the platform is fundamentally flawed. Account passwords for a huge number of Zoom accounts may be for sale on the dark web, which would allow dark actors to hijack meetings. For an account of an actual incident at a church, click here. If this happens to you, leave the meeting immediately and contact your host by e-mail or telephone. This post is going to discuss some of the issues and technologies in play in the problem of maintaining a safe society in the Wild West environment of the internet.