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.
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.
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.
Suppose that you have a friend helping you rake the yard. If you take three hours to finish the job by yourself, and your friend takes two hours by himself, then, if you work together efficiently, how long does it take for you to finish the job working together? The answer is one hour and twelve minutes. This post is about a tool called the harmonic mean that lets you do calculations like that. The harmonic mean also shows up in some of the laws of physics, which is interesting. You may remember that “mean” is the highfalutin’ mathematical term for average. We will also talk about the sense in which the harmonic mean is an average, even though it does not act like the averaging you are used to.
A number carries a certain authority. We are bombarded with statistics about what people want, what they need, and what they will tolerate. Mathematical models are used to decide what to build, what to build first, and whether to build anything at all. Most of these planning results are summarized as a cost. There is a problem with this: the context and meaning of the numbers are often missing. The cost of a new subway line is not accompanied by a careful statement of the cost of not building it — partly because the cost of not building something is usually not a number. In fact the cost usually has dozens of components. These include reduced traffic, improved commute times, change in property values near stations, changes in both car and pedestrian traffic patterns, impact on local businesses, and on and on.
Diversity is often lauded as a virtue. Biodiversity is the presence of a broad range of plants and animals in an ecosystem. Societal diversity is the presence of people of many colors and cultures, both male and female, in positions of power and authority. Intellectual diversity is the situation when a group possesses a wealth of different viewpoints from different fields. All of these sorts of diversity pay benefits and — this is where this becomes a mathematical topic — for very similar reasons. The same mathematical thought governs the fact that diversity is helpful in all three domains. Diversity grants strength in adversity. Intrigued? Read on!
When you make a law that is supposed to help people who badly need help, it is important to write the law so that it continues to help over time. A problem with democracy — a very visible problem at the current point in history — is that an elected government has an awful time thinking farther into the future than the next election. Long-term planning is critical to combat poverty, climate change, ignorance and also to promote fairness, justice, and knowledge. In this post we will look at several examples where too-simple mathematics has sent the train of state so far off the rails that it’s in the lake with many of the passengers drowning.
A person might have an ethical right to damage themselves. Long settled custom and law make it clear that people do not have a right to damage others. The concept of herd immunity demonstrates that your self-care decisions have an impact on others. In the year 2000 measles was declared eliminated from the United States. It is now back and in danger of becoming widespread, with outbreaks in 22 states. If an infected individual walks through a room, infectious virus particles hang in the air for up to two hours: measles is highly contagious. This post is about a mathematical concept called herd immunity which is an important part of the current debate about the vaccination of children. The World Health Organization has “reluctance to vaccinate” as one of its top ten global health threats of 2019.
Occupy Math had a difficult year this time around. He taught first, second, and forth semester calculus and four instances of a research capstone course, which is a one-on-one research project to let seniors figure out if they like doing research. These student research projects will show up next week on Occupy Math. This week’s news is this: Occupy Math took of more points from his calculus students for not being able to do arithmetic and basic algebra than he did for not learning the calculus. Overall it was a good year, but there are some disturbing trends that Occupy Math would like to talk about including collapsing instructional resources from high school through university and absolute sabotage of the educational system by deeply confused parents.
Occupy Math is delighted to report that Professor Karen Uhlenbeck will, on May 21st, 2019, be awarded the Abel Prize for her work in geometric analysis and gauge theory by the King of Norway in a ceremony in Oslo. The prize is awarded at the discretion of the Norwegian Academy of Science and Letters and was established to serve as the “Nobel Prize” of Mathematics. Professor Uhlenbeck is currently at the Institute for Advanced Study in Princeton, New Jersey. She holds a permanent faculty position at the University of Texas at Austin. Dr. Uhlenbeck is the first woman to be awarded the Abel Prize, which Occupy Math takes as evidence that the world is continuing to become a more reasonable place, in some ways.