MATH with Bad Drawings
I came across this book randomly at the book store while looking for Christmas presents for my nieces. I went back a week ago to buy it, after being bored on a weekend. It was a pretty quick read. I was not expecting anything in particular, and to be honest, I was a bit disappointed.
There are too many references to the USA: boring baseball, the country’s shitty implementation of elections, taxes. One section about taxes is quite relevant these days with Alexandria Ocasio-Cortez’s idea of a top marginal income tax rate as high as 70 percent:
As the income tax surged in 1942, the government commissioned Walt Disney to create a short film to inspire Americans to pay their taxes. The secretary of treasury demanded a fresh-faced custom-animated protagonist, but Walt Disney insisted on using the company’s biggest star at the time. Thus, more than 60 million Americans got to see on their movie screens a display of patriotic, tax-paying fervor (“Oh boy! Taxes to beat the Axis!”) from none other than Donald Duck.
The cartoon must have worked, because two years later, the top marginal tax rate achieved its historical high-water mark: 94%.
Here’s the mentioned Donald Duck video. The chapter is actually about people’s misunderstanding of tax brackets. People + money = interesting outcomes. For example:
Take this contrast:
I give you $1000. Which do you prefer? A: Another $500 guaranteed, B: 50% chance at another $1000.
I give you $2000. Which do you prefer? A: lose $500 of it, B: 50% chance of losing $1000 of it.
The questions offer identical choices: (a) you walk away with $1500, or (b) you flip a coin to determine whether you end with $1000 or $2000. But folks don’t give identical responses. In the first case, they prefer the $1500 guaranteed; in the second, they favor the risk. That’s because the questions create different reference points. When the $2000 is “already yours,” the thought of losing it stresses you out. You’re willing to take risks to avoid that fate.
When life is hard. we roll the dice.
I found the section of the book about geometry a bit more interesting than the ones about probabilities and statistics. Here is a bit from “An Oral History of the Death Star”:
There were about 2.1 million people on the Death Star; that’s counting droids. Meanwhile, with a radius of 70 kilometers, it had a surface area of almost 62,000 square kilometers. Now, assuming that you bring everybody to the surface level, you’ll have a population density of about 30 people per square kilometer. That’s five soccer fields per person.
[…]
Of course, it was even worse than that. Not everybody spent their time on the surface! The habitable zones of the station went 4 kilometers down. At 4 meters per level, that’s 1000 levels. […] On a given level, that’s a population density of one person per 40 square kilometers. The only comparable place on Earth? Greenland.
Given how America-centric the book is, I’m a bit surprised about the soccer field comparison. And thanks for using SI units! Anyways, the thought exercise was funny.
A final quote I noted is about the relation between surface and volume:
Ants have woes, too, and by “woes” I mean “a debilitating and wholly justified fear of water.”
The trick is surface tension. Water molecules love sticking together, and they’re willing to defy small amounts of gravity to do it. Thus, when any object emerges from a bath, it carries with it a thin layer of water, about half a millimeter thick, held in place by surface tension. For us, that’s a trifle: a pound or so, less than 1% of our body weight. We towel off and go on living.
Compare that to the ordeal of a bathing mouse. The water layer’s thickness remains the same, about half a millimeter, but our rodent friend finds this a far greater burden. The surface-heavy mouse steps out of the tub carrying bathwater that equals its own body weight.
And for an ant, the situation is dire. The clinging water outweighs its body by an order of magnitude; a single wetting can be fatal.