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Book Notes: “Millions, Billions, Zillions” by Brian Kernighan

I recently finished this book and, in an effort to try remember what I actually read, I’m making some more #bookNotes.

This book is about teaching “numeric self defense” (14). Numbers are everywhere in our lives (especially as tech workers). It’s so easy to take numbers at face value as proof. As Kernigham says:

At best we take away a vague impression that something is important and should be believed because it has numbers attached to it.

[however remember that many numbers] are intended to convince us of something.

Just because there are numbers attached to a presentation of fact doesn’t mean it’s true. Or even based in reality. But we too easily become “number numb”:

there are too many numbers to assess, to the point where we ignore them or take them at face value, rather than thinking about them (21)

Having a kind of numeric literacy can help you do rough, approximate math in your head to determine whether any given numerical fact is even close to being based in reality.

The internet is invaluable but it may not always be available, and even if it is, it may not be accurate.

The author gives a number of examples in the book of numerical errors he has encountered in even the best of reporting, which is quite fascinating to read.

For example: lots of reporting can confuse “millions” and “billions”. To many, those words just mean “big”. Kernighan cites examples where a news article said “800 billion gallon reserves of oil” when really it was 727 million gallons. Close in the rounding, but off by a factor of a thousand in saying “billion” not “million”. This happens all the time.

Million and billion are confused surprisingly often: surprising because a billion is a thousand times bigger than a million, that is, a factor of 1,000. Let me try to make that factor more meaningful. Suppose you think you have $100 in your pocket right now. If that’s too small by a factor of a thousand, then you really have $100,000, which is enough to buy a fancy car or even a modest condo in some part of the country. On the other hand, if the amount is too big by a factor of a thousand, then you only have ten cents, and that’s not enough to buy anything. (12)

Once you get to large numbers beyond “billion” to numbers like “zeta” — which is better expressed as 10^21 — the brain just refuses to cooperate with that many zeroes. At that point, those kinds of large numbers “convey nothing at all to most people”. (33)

But it’s not just large numbers we gloss over and unquestionably take at face value when presented with factual assertions. It’s the shaky assumptions baked into those numbers when they’re presented in a form like rankings. Speaking specifically of college rankings, which present themselves as objective assessments, the author says:

We’ve collected data that is often flaky...converted non-numeric data into numbers...and combined them with arbitrary weights...Flaky data plus arbitrary weights is a recipe for shaky results.

However much we’d like to believe it, you can’t boil everything down to a ranking, i.e. “how many stars does it have?”

If you combine approximate data, sometimes not even numerical, with arbitrary weighting factors, you can produce rankings that are good for starting spirited discussions but nearly useless for drawing meaningful conclusion. Treat all ranking schemes with a grain of salt.

Besides presenting what can be a facade of objectivity, numbers can also paint a shiny but misleading veneer of precision.

When a number is expressed with high precision, that suggests that it is in some way more accurate than if it were written with lower precision, and thus that the number is more important or significant. It has subliminally acquired an unwarranted authority.

Kernighan presents a rather comedic example of this in the form of a comic from Hilary Price. You know the old saying, “an ounce of prevention is worth a pound of cure”? What happens when you translate that for an international audience? A literal translation would result in something like: “28.35 grams of prevention is worth .45 kilograms of cure”.

A cartoon by Hillary Price depicting one man saying to another man “You know what they say son—28.35 grams of prevention is worth .45 kilograms of cure.”

You have to watch out for numbers which undergo literal translations without taking into account “the spirit” of what is being conveyed. “A result should not be presented with more precision than the input values warrant.”

This particular kind of metric-English conversion is common in the US. For instance, a story in the New York Times in March 2008 quoted the editor of The Yacth Report […] as saying “When a yacht is over 328 feet, it’s so big that you lose the intimacy.” […] Where did 328 come from? Of course, it’s 100 meters, a nice round number of the sort we use in everyday speech…Spotting multiples of 328 can easily become a kind of nerdy party game.

Lastly, it couldn’t be a book about scrutinizing numbers if there wasn’t an entire chapter devoted graphs and charts.

A picture is worth a thousand words, so presumably a misleading picture is worth a thousand misleading words.

Also: a misleading graph is worth a thousand misleading words.

The chapter is really good, not solely as a reminder for people reading at graphs, but for people designing graphs.

One-dimensional pictures are often used to suggest more impact than is warranted, though they are sometimes merely a misguided attempt to make mundane numbers look interesting (103)

Overall, I enjoyed the book. It’s a short read. My impression is that it almost reads more like a personal scrapbook of snippets the author has picked up over the years of the misuse of numbers—and lessons we can draw from them.

Nonetheless, it was a good reminder to try and hone a skill of “numerical self defense” in a world drowning with numbers asserting factual proof (however misguided or malicious).

People can come up with statistics to prove anything. 14% of people know that. — Homer Simpson