# The Noncombustive Property of Skulls

a weekly roundup of links and cartoons

Scott Alexander (a doctor and next-level blogger) wrote a tragicomic account of his skull-combusting experience trying to get a simple medical study through the ethical approval process. Mathematicians should read it, then doze through those “research with human subjects” university trainings with renewed gratitude.

It’s not really mathy, other than the number “3” in the title, but last week I read a gorgeous graphic novel titled 3 Story: The Secret History of the Giant Man, by Matt Kindt. It’s a modern fable, living on the borderland between realism and lyricism, which is exactly where I hope to buy a vacation home one day.

My sister (also a math teacher) meditates on the theme of coherence. It’s a funny thought for me to echo in the midst of roundup post – frenetic and unfocused by design – but I couldn’t agree with her more.

My fondest, most intense memories of my own education come from classes that cohered, that told a unified story, structured around clear themes. One of my greatest pleasures as a teacher is trying to craft classes that do the same.

This summer I saw a great math talk that had the blue-ribbon best title I’ve ever heard for an academic lecture: “Pools of Blood.” (It was about the mathematics of efficiently testing blood samples for rare diseases.) The speaker, Keith Ball, has a website that poses this nifty problem:

Show that if a square is cut by two lines (shown above in green) then there is an uncut square at least one third as large (shown in red) lying inside the original (and aligned with it). If this is too easy, try it with three lines and an uncut square at least one quarter as large as the original.

(Haven’t solved it yet; like everything else in my life, I haven’t given it enough time.)

Speaking of math talks, I really enjoyed this one by Patrick Honner, digging into some bad Regents Exam questions in New York, and revealing how they actually conceal some pretty cool math. One error by the examiners managed to pique the interest of a Fields Medalist, which is more than can be said for anything an exam has ever done on purpose.

This gyroscopic grill crested the Reddit frontpage last week, and hypnotized me for several hours until my computer battery died and the spell was broken.

https://gfycat.com/SelfassuredShorttermHoiho

But it loses the prize of “coolest mind-bending design-related Reddit thing” to these deliberately uncomfortable everyday objects by Greek architect Katerina Kamprani:

Yeah, sorry to violate the noncombustive property, but you had to know it was coming.

## 6 thoughts on “The Noncombustive Property of Skulls”

1. Dhanashree says:

Too difficult for me to comprehend! 🙁

2. Doug M says:

As this was left as an exercise for the reader.

Divide your square into a 3 by 3 grid (creating 9 squares). It is impossible for 2 lines to pass through all 9 squares. There is always one square that is uncut by the two lines.

1. Chester Draws says:

And how do we know that Doug?

3. Ummm…not an expert mathematician here, but isn’t that included square only 1/9th the size and not 1/3rd the size?

1. This is a weird “you’re both right!” situation. The included square has 1/3rd the side length, and thus 1/9th the area (because 1/3 x 1/3 = 1/9). So it depends what you mean by “size.”

4. drkottaway says:

Oh, my gosh. I am already ” living on the borderland between realism and lyricism, which is exactly where I hope to buy a vacation home one day.” You should definitely move in next door. And I read it as “noncombustive poetry” …. so if we postulate the existence of noncombustive poetry, then combustive poetry will soon make it’s mark…. possibly on a poet sized gyroscopic grill.