Data Science: what is it?

Occupy Math’s employer has launched a Masters Program in Data Science. The pyramid picture at the top of the post shows a major process goal of data science, which is more aspirational than real, as data science often achieves knowledge but seldom gets to wisdom. In graduate school, Occupy Math knew a professor of computer science who was fond of saying “Anything that calls itself a science probably is not one.” Data science is not even close to being a science, though it applied many of the results of science to the problem of understanding and reducing data. The word “reducing” in this definition can mean “concentrating into a useful form”, not “getting rid of”. Occupy Math is simultaneously developing and teaching a course entitled Data Manipulation and Visualization and so there may be several posts that arise from the experience. Another troublesome word: in this case “manipulation” means “transformation into a useful or tractable form”, not “deceptive modification.” Aren’t words fun?

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Luck — a mathematical discussion

Luck is something a lot of people care about and they often go to great lengths to call up or control luck. Mathematically, luck can be explained by random chance — which is beyond control and which is very even-handed in how it bestows good or bad luck. Superstitions are pervasive in human societies. Different societies — and different people — have firmly held beliefs about what is lucky or unlucky. The mathematical science of statistics has, at its core, the quantification of chance. Statistics takes us part of the way to replacing the notion of luck with the notion of chance.

There is an important point to this. Chance is even-handed and brutally fair. Luck is often seen as being the result of virtue. People whom chance favors are often called lucky (especially by themselves) and people who experience bad outcomes by chance are called unlucky. The search for ways to summon up, invoke, and control luck is a huge human preoccupation, from a refusal to wear clean socks in major league baseball teams to the belief in auspicious and inauspicious numbers like seven and thirteen in European cultures. A revealing fact is that the “good” and “bad” numbers vary from culture to culture.

Is your child behind in math due to the pandemic? Here’s how to help.

Occupy Math has recently become the chair of his department. Getting more mail is one of the side effects of this. Recently he received a rather tense letter from the mother of an eleventh-grader; she pointed out that her son was not getting as much math instruction as he should and wanted to know what the university was going to do about it. Occupy Math regretfully told her that we were going to do nothing about it, because we were losing resources, and thus had no people to assign to remedial education for incoming students. This is somewhat tempered by the fact that we already have some measures in place, a help center and a packet of summer review questions that at least serve as a warning about what a student is supposed to know. Occupy Math looked into the matter: a tense letter from a parent can fall anywhere between prophetic warning and arrant nonsense. This one was spot on. The rest of this post looks at what happened to math education during the pandemic, discusses why the pandemic adaptations of math education are very bad for learning math, and suggests some things a parent might do to compensate.

Never say “I’m not a math person”!

Today’s post was inspired by a story in the Washington Post entitled Want kids to learn math? Level with them that it’s hard. The post will discuss how math can be perceived as hard or easy, depending on who you are; it will also deal with the myth that one is or is not a “math person” by nature. There is a widespread notion that some people are just naturally good at math and others are just naturally hopeless at it. This is untrue. Like any other learned skill, you get better at math with practice. While there is some degree of natural talent, anyone who does not have one of a very few rare disabilities can master basic mathematics.

One fairly large problem is that most people teaching math are usually pretty good at it themselves. To them math really is easy, at least at the level they are currently teaching it. If too few of the people charged with explaining math to the rest of us are sufficiently self-aware to realize how difficult and strange math can be to those encountering it for the first or second time, there’s a problem. Worse, many students who are supposed to be learning math are instead actively avoiding learning math while looking frantically for a way to tunnel under the actual work. This leads to the tragicomic sight of people doing huge amounts of work to avoid moderate amounts of work — largely based on a terrifically inaccurate estimate of the amount of work required to achieve basic competence.

Are Bitcoin and cryptocurrencies Ponzi schemes?

Fair warning, this post has several moving parts. The gentleman depicted at the left is Charles Ponzi who, in the earlier part of the 20th century, invented a type of swindle that is named after him, the Ponzi Scheme. You offer a low-risk, high-return investment with a lot of ballyhoo and enthusiasm. As money comes in, you pay generous dividends to the earlier investors with the money of more recent investors, skimming a healthy chunk for yourself. If people get suspicious or if you saturate the market, you run for it or create a plausible reason for the whole scheme to have collapsed. This is the basic Ponzi scheme and it comes under the sensible rule if it seems too good to be true, it probably is. Occupy Math has already written with enthusiasm about the potential of block chains, which are, among many other things, the enabling technology for Bitcoin. Today’s post discusses the question “is Bitcoin a Ponzi scheme?“, which turns out to be a bit complicated.

The sickle cell condition and covering up police brutality

Today’s post takes up another difficult issue, use of a usually benign medical condition to excuse or cover up murder under color of authority by police. The sickle cell trait, used in this fashion, is also a biologically interesting condition in its own right. This post will go through the biology and then move on to evidence that the sickle cell trait was used as an excuse — in the form of a falsehood by a medical examiner — to justify the death of a Black man in police custody. This is structural racism at its worst. Rather than investigating honestly for the medical cause of a death, someone whose job is to do exactly that is instead searching for the reason that the cause of death was not police brutality or negligence.

Rediet Abebe: A Rising Star in AI

This is Rediet Abebe, an AI researcher and new faculty member at the University of California at Berkeley (picture by Anoushnajarian). Berkeley seems very proud of their new assistant professor, and with good reason. Her insights about the way inputs to artificial intelligence are chosen have huge implications for social justice and discrimination, and are foundational to progress in the application of AI. Occupy Math has chronicled a number of people from under-represented groups that made huge contributions in math, but most of those posts were obituaries. Professor Abebe is a current phenom. She is a co-founder of Black in AI, an organization that is trying to increase the number of black people working in artificial intelligence. The post will look at how this remarkable woman got where she is today and discuss some of the reasons why increasing the representation of underrepresented groups in AI is both important and a really good idea.

Math is being used to institutionalize racism in medicine!

Usually, a correction is an additional term added to a formula to make it more accurate. If you are using a ballistic equation to model the behavior of a golf ball, there is a simple formula that would work well on the moon. There is a fairly complex correction for air resistance that make the formula’s ability to predict the behavior of the golf ball much better on Earth. The “usually” at the beginning of the post is because there are correction factors which are just plain wrong. Today’s post is about race corrections in medicine. There is medical software that requires the race of the patient as an input. This software includes programs that compute kidney function, try to determine if a person is having a heart attack, assess the need for pain medication, and on and on. Biologically “race” is an almost meaningless term, medically, and the software makes it pretty clear that race is not actually the issue. The only races available are “black” and “other”. If racial differences were actually important (for that, they would need to exist), then the patient’s race would matter well beyond a yes/no question about blackness. Outraged? Please read on.

Another Hidden Figure: Raye Montague

Occupy Math sometimes chronicles the trials and tribulations of women in mathematics. Katherine Johnson, Margret Hamilton, and Elizabeth Williams are examples from earlier posts. Today’s post is the next in this sequence, concerning naval architect Raye Montague, pictured on the left working at someone else’s desk. In addition to having a huge talent for mathematics and computer science, Raye Montague was a black woman from the American south, born in Arkansas in 1935, quite a load to carry while revolutionizing ship design and winning awards. Ms. Montague was clearly a genius level talent, and while this is wonderful, genius is too rare to carry civilization. The system that Ms. Montague bucked to become the remarkable person she was must have turned back many excellent and many competent persons simply for being women or having the wrong color of skin.

Symmetry in Math, Nature, and Society

Symmetry is one of the mainstays of mathematics; it is also one of the points where math intersects with art and architecture. In nature, symmetry is common and beautiful, as in the plant at the top of the page. For physical objects, symmetry is built out of three basic types of transformations: rotation, reflection, and translation. A flower often exhibits rotational symmetry, the wings of a butterfly exhibit reflective symmetry, and the repeating units of a crystal exhibit translational symmetry. In mathematics, with access to abstract spaces and higher dimensions, far more types of symmetry are possible. We will look at all of this in this post, as well as looking at the ability to use lack of symmetry as a warning or sentinel in both nature and society.