There is a crisis in the price of textbooks. Occupy Math paid eighteen dollars for the calculus book he used for his first two courses in calculus. The calculus book used for the first-year for-majors calculus course at Occupy Math’s institution costs more than ten times that, though the price varies from year to year. Worse, after you buy many textbooks, you have to cough up a hundred dollars for access codes to let you get to the on-line material that comes with the book. The professor may well assign parts of the on-line material, from exercises to pre-generated homework problems, so access to the on-line material is not optional. With a book, roommates or study-buddies might buy one copy and share. The on-line materials track one person’s progress and grades, so sharing is impractical. This post is about the mechanisms behind insane pricing and some resistance strategies.
A conjugate Mandelbrot set, rich in spirals.
Occupy Math works with digital evolution on a number of projects including evolving parameters that generate interesting fractals. The advantage to doing this with a computer, assuming you can come up with an automatic function that at least sort of measures “this looks good”, is that you can sort through billions of fractals per hour. One of these is shown at the top of the page. The disadvantage is that people are much better than any of the automatic functions we have found so far at spotting cool fractals. If we use people, though, they burn out way before looking a even a paltry million fractals. This is the phenomenon of user fatigue. This post is about a way to let computers and people collaborate on a project, drawing on the strengths of each. Computers can evaluate huge numbers of fractals to find ones that might look good. Humans have a much better ability to judge which fractals are actually beautiful.
A really elegant conjugated Julia set, with lots of apparent self-similarity.
This post is an activity post with activities for grades four and above. It uses a kind of math that Occupy Math has talked about before in A Wonder of Mathematics, but the post is structured to help a teacher or parent present this material as a discovery activity. The core of the exercise is a simple three-part rule:
- If a number is a multiple of three, divide it by three.
- If a number is one more than a multiple of three, multiply it by five.
- If a number is two more than a multiple of three, add one to it.
So, for example, 4 equals 3+1 and so gets multiplied by five, yielding 4×5=20. It is a little startling how many odd properties this three-part rule has.
A conjugated Julia set (30 degree rotation) with a structure like a minerals section.
This post is about a mathematical notion called self-organized criticality and its relationship to a recent strike by Amazon workers. As we will see, this strike, on Amazon Prime day, was a small “avalanche” (in a sense defined later in the post) that is probably a harbinger of worse problems at Amazon warehouses. Amazon has created a digital work supervision system that tries to maximize productivity by automatically tracking the workers and telling them when they are not working hard enough. The theory of self-organized criticality suggests that, initially, using this system will permit them to find the most productive workers. It will also cause a workplace that is very stressful with high turnover. This is the claim that Amazon workers are now making to explain why they are striking. This situation forces workers to achieve “high productivity”, but also stresses them to breaking point. In the rest of the post we explain self-organized criticality — which actually appears in many systems. Hopefully this will let you recognize it and perhaps avoid doing it to other people.
A complex spiral in a 30-degree conjugated quadratic Julia set.
If you want to be a doctor you need to earn a university degree with good grades in hard classes and then go to medical school after which you do an apprenticeship (residency). In addition to the four years of university, medical school and the residency take about eight years –making it about twelve years of post-secondary education. Given this remarkable level of preparation, why are a large number of the diagnostic protocols used by medical doctors way too simple, ineffective, and generally something a high-school drop-out could probably run? In this week’s post we look at the problems with threshold-based medical protocols.
Occupy Math’s image of the week is a triple cubic Julia set: copper dawn!