Category Archives: Mathematics

Different ways to model a pandemic

Numberphile: The Coronavirus Curve. (YouTube, 22:17min) “Ben Sparks explains (and codes) the so-called SIR Model being used to predict the spread of coronavirus (COVID-19).”

I played along at home and created my own version with Geogebra, but you can also find Ben Sparks’s version here: SIR Model.

Be sure to also check out the links in the description of the video.

3Blue1Brown: Simulating an epidemic. (YouTube, 23:11min)

“While here we looked at what you might call an “agent-based” SIR model, if you want to see what it looks like as a set of differential equations, Ben Sparks just did a lovely video on the topic over at Numberphile [see above].

There are a few reasons I like the agent-based model here, for demo purposes at least. It’s a bit easier to understand for those who are not comfortable yet with ODEs, for one. It also conveys how things are not deterministic; no real-world curve will look as smooth as the differential equations. It also makes it way easier to ask questions and bake other assumptions into the model. Introducing things like travel or community centers into the differential equations would get very hairy very quickly. For those who want to go much more deeply into this, the Institute for Disease Modeling has a lot of models free for people to look at and play with.”

“They are indistinguishable”

NPR: Math Looks The Same In The Brains Of Boys And Girls, Study Finds.

“There’s new evidence that girls start out with the same math abilities as boys.

A study of 104 children from ages 3 to 10 found similar patterns of brain activity in boys and girls as they engaged in basic math tasks, researchers reported Friday in the journal Science of Learning.

“They are indistinguishable,” says Jessica Cantlon, an author of the study and professor of developmental neuroscience at Carnegie Mellon University.

The finding challenges the idea that more boys than girls end up in STEM fields (science, technology, engineering, and mathematics) because they are inherently better at the sort of thinking those fields require. It also backs other studies that found similar math abilities in males and females early in life.”

NPR: New Study Challenges The Assumption That Math Is Harder For Girls. “Research shows that when boys and girls as old as 10 do math, their patterns of brain activity are indistinguishable. The finding is the latest challenge to the idea that math is harder for girls.”

“Geary says differences seem to show up later and involve very high-level math tasks. His own research has found that in most countries, female students perform just as well as male students in science-related subjects. Yet paradoxically, Geary says, females are less likely to get degrees in fields like math and computer science if they live in wealthier countries with greater gender equality.”

“If the answer here doesn’t blow your mind, I don’t know what will.”

3Blue1Brown: The most unexpected answer to a counting puzzle and So why do colliding blocks compute pi? and How colliding blocks act like a beam of light…to compute pi. (YouTube, 5:12min and 15:15min and 14:40min)

The connection between the initial experiment and the calculation of π is surprising, and finding two different solutions in physics is even more astounding. The videos are extremely well done, and the presentation helps a lot with understanding the mathematical manipulations.

Mind. Blown.

Link via Futility Closet.