You get very little credit for being wrong. This post is going to look at a couple of situations where being wrong was incredibly important and useful. This usefulness arises from the different way that mathematics treats being wrong, in one special way. Two claims that are supported by mathematical reasoning are these: there are no trees on earth, there is no multi-cellular life on earth. The post looks at why these claims are worth considering, since they are obviously false, and then ends showing an example of how being wrong is actually a core technique in math.
This post begins Occupy Math’s fifth year of publication and it’s on a serious topic: support for gifted kids. The post is motivated by a confrontation at a school board meeting in which the parent of a child with severe learning disabilities took the parent of a gifted child to task. The parent of the disabled student was obscenely and profanely certain that money spent on the gifted student ensured that her child would not get the help they needed. They also felt that being gifted was a privileged state and so support for the gifted was robbing the needy to help those who were already ahead. There are a number of problems with that argument, and that is the subject of this post. Occupy Math has been an advocate for gifted children for decades and so this matter is near to his heart.
In the first post Occupy Math did on dodgy statistics, Occupy Math talked about the problem of using statistics without understanding them. This leads to the publication of results that are simply wrong. In this post we will look at some other issues –particularly effect size — which lead to the publication of results that are almost worthless. Further, we will find that this lack of interest in the mechanisms of evidence creates a situation where more than half of all treatments prescribed by doctors lack any evidentiary support and a few are actively harmful.
There are two different issues at stake in reporting that a scientific or medical finding is real. The first is to ask what the chance it that the result happened by accident, instead of because some treatment was used. The second is to ask how much difference the effect made — and that is effect size.
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.
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.
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.
This post is inspired by an excellent blog post on why algebra is an awful experience for many students. This problem with dry, boring algebra has led to a call to stop teaching algebra to many students. This seems to Occupy Math to place the cart before the horse. If students are having trouble succeeding because of math, the math should be taught in a more effective fashion. Getting rid of it is like saying “horses are too much trouble — everybody walk and carry heavy loads on your back!” Beyond this, Occupy Math finds the idea that people should only study algebra if it enhances their economic well-being, and that for many students it will not, to be racist, classist, and contrary to having a democratic society. The students that are designated to “succeed” by not having to study math are disproportionately inner city, brown, and from the bottom end of the economy. The whole idea of making math the property of the privileged few is the opposite of what the coming complex, perilous world needs. This post discusses some ideas for making algebra less of a pain and more of a routine mental tool.
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.