I just finished Humble Pi (2019), by Matt Parker, and I absolutely loved it. Parker, a former high school maths teacher, now a maths popularizer, has an easy breezy style dotted with wry jokes and good humor. I read three-quarters of the book in one sitting because I couldn’t stop (just one more chapter, then I’ll go to bed).
It’s a book about mathematical mistakes, some funny, some literally deadly. It’s also about how we need to be better at numbers and careful how we use them. Most importantly, it’s about how mathematics is so deeply embedded in modern life.
It’s my third maths book in a month and the only one I thoroughly enjoyed.
I posted about one of the other two, Our Mathematical Universe, yesterday. If I were inclined to use the Good, Bad, Ugly, meme (I’m not, but if), that one would be the Bad. (Parker’s book obviously being the Good.)
The Ugly goes to the one I couldn’t finish, One, Two, Three: Absolutely Elementary Mathematics, by David Berlinski (who’s written many books). It’s a close look at what a number actually is, and I don’t disagree with or in any way fault the actual content.
It’s Berlinski’s style; it was too baroque and whimsical for me. And I thought many of his jokes required a deeper understanding of math theory than many readers were likely to have. It might be a book more for the cognoscenti.
Parker starts with an introduction (chapter zero, of course) in which he describes a contest run by the Pepsi company in 1995.
People collected Pepsi Points they could redeem for prizes, hats, sunglasses, etc. The highest prize was a leather jacket for 1,450 Pepsi Points. Pretty standard stuff.
The agency promoting the contest made a TV ad that included a bit of humor: a high school student, wearing the promotional gear, flies his Harrier Jet to school. The joke was you could win the jet for seven-million points.
The idea being that seven-million was a ridiculous figure far too high to be taken seriously. It seemed big enough to be clearly a joke.
Problem is they didn’t do the math. Pepsi sold Pepsi Points for 10 cents each. (In some contests, it’s not legal to force people to buy the product, so there has to be an alternate path to win.)
If Pepsi Points are worth 10 cents, then seven-million of them is a mere $700,000, which is peanuts compared to the price of a AV-8 Harrier II Jump Jet, usually valued around $20,000,000 dollars.
John Leonard did do the math, acquired the necessary points, fulfilled all the other obligations required by the contest, and demanded his jet. Pepsi refused, and the case ended up in the court, which found itself in the position of having to explain a joke.
Leonard didn’t get the jet, but it’s an object lesson: Always. Do. The. Math.
Still in the introduction (because I don’t want to spoil too much of the fun), Parker talks about the difference between a million, a billion, and a trillion.
He puts it this way:
“A million seconds from now is just shy of eleven days and fourteen hours. Not so bad. I could wait that long. It’s within two weeks. A billion seconds is over thirty-one years.
“A trillion seconds from now is after the year 33,700 CE.”
As he points out, if you think about it, it makes sense. A billion is a thousand times more than a million, and a trillion is a thousand times more than a billion. What’s a thousand times two weeks? What’s a thousand times thirty-one years?
This has to do with our intuitions, in this case our sense of the space between numbers. Various studies show that humans innately tend to think logarithmically (our senses are logarithmic), but modern culture teaches us to think of numbers as evenly spaced (because most of the numbers we meet in modern culture are linear). So we tend to think of million, billion, trillion as evenly spaced like one, two, three.
Parker repeatedly stresses the importance of basic math literacy (called numeracy) in a technological society. One can train one’s intuitions about math. (I personally know this to be true. I’m starting to “get” four-dimensional space.)
Oddly, that same society, despite depending on mathematics, often evinces pride at “not getting math.” Being “bad at math” is often seen as making one more human! (Ironically, our ability to count and do math is one of the things that defines us as human.)
Imagine being proud of being illiterate. It really is the same thing in a modern culture. Carl Sagan said something similar twenty-five years ago:
“We’ve arranged a global civilization in which the most crucial elements — transportation, communications, and all other industries; agriculture, medicine, education, entertainment, protecting the environment; and even the key democratic institution of voting, profoundly depend on science and technology. We have also arranged things so that almost no one understands science and technology. This is a prescription for disaster. We might get away with it for a while, but sooner or later this combustible mixture of ignorance and power is going to blow up in our faces.” (The Demon-Haunted World: Science as a Candle in the Dark, 1995)
It’s amazing to me how ignorant we allow ourselves to be about the vital underpinnings of what makes all this work. It makes one helpless and dependent.
Most of it is our fault for being so very bad at teaching it. We make it painful beyond reason. You can’t blame people for wanting nothing to do with it.
Something I think worthwhile to keep in mind is that, just because it’s not possible to learn all of it, that doesn’t mean you can learn some of it. All you need is enough for a basic understanding.
And maybe a good teacher.
[FWIW, there are a lot of great math education videos out there. Frequently in the comments of those videos, and I’ve experienced it myself, are people literally brought to tears by finally having a maths veil lifted from their eyes by a good video. (For me it was quaternions and tensors.)]
Parker (still in the introduction!) also mentions a National Lottery scratch card that had to be pulled off the market the same week it was released.
The card was called “Cool Cash” — it had a temperature printed on it. If the player scratched a window with a lower temperature, they won. The problem came from the negative temperatures.
A card might display the temperature -9 while the player scratched a -5. Because 5 is less than 9, many thought that should be a winning card. But, of course, minus five is not less than minus nine. Quite the opposite.
Parker goes on to explore calendars, time keeping, math in aviation and bridge building, randomness, big data, and many other topics. It’s an easy fun read.
Some of it will open your eyes to the fragility our dependence on mathematics introduces to our society. Some of it will make you laugh out loud.
Some of it may even terrify you. Airplanes have gone down due to bad math, bridges have collapsed, people have died from radiation treatments, and math errors in hospitals are almost routine.
All-in-all, it’s a book worth reading more than once to stick the lessons into your mind. I’d call it a must-read book for just about everyone.
I’ll leave you with a video of Matt Parker speaking at the Royal Institute on many of the same topics as the book. It’s a great video (about an hour long) I highly recommend it, too:
There’s another talk he gave at the RI about the fourth dimension. That one is from another book of his, Things to Make and Do in the Fourth Dimension: A Mathematician’s Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More (2015).
(That is a book I definitely need to track down!)
I’ll give you one more. Parker mentions this near the end of his book.
He wanted to create a Magic Square of squares, and he almost got it. He made the mistake of showing his almost got it effort in a video and the guy who made it (Brady Haran) turned it into a whole thing with tee-shirts and other merch. It’s now known as the Parker Square.
Matt Parker says fans show up at his talks wearing those tee-shirts and want a selfie. It’s ultimately (he hopes) become the “mascot for people who give it a go, but ultimately fall short.”
Math is beautiful, but more importantly it’s necessary in our world.
Navigation depends on math. Aviation depends on math. Engineering and construction depends on math. The Internet and all our computers depend on math. So much of this world is mathematical.
In such a world, not having some level of numeracy is much like being illiterate. One is forever at the mercy of numbers. One is forever not knowing about a vast sector of reality.
Stay mathematical, my friends!