Saturday, January 21, 2012

Numeracy fail

Side note- it's been a looong time since I wrote a blog post. Since then, I've had a second child, moved jobs (I'm now working at SparkFun- woot!), states (Colorado is state number six for me), and time zones. A lot of the more technical sort of blog post I'd write now goes up on the SparkFun website as tutorials, but I'm going to try to post more here.

Engineers and scientists (and other general nerd/geek types) like to talk about "numeracy", which is the ability of a person to grok math. It used to be that the primary "complaint" (if you will) was about people who play the lottery- "a tax on being bad at math". I'm not talking about valuation, here- being willing to pay five- to tenfold as much for a meal at a restaurant as it would cost to make at home, for instance. I'm talking about hard numbers- apples to apples.

Having a poor grasp on mathematics is getting to be a bigger handicap, though. I've notice recently when grocery shopping that the old principle of "buy more, save more" no longer applies- frequently, a bigger box of cereal, say, will cost MORE per ounce than a smaller box.

Or, containers will be cleverly redesigned to contain less but look the same, then the price is maintained. Next time you're at the store, check out the "half gallon" containers of orange juice. Many (most?) of them are 59 ounces, instead of 64. They don't look any different, of course, and there's no mention on them that 59 ounces is NOT a half gallon (and I'm not optimistic that many consumers know what a half gallon is, nor would be able to calculate price per ounce between a 59 ounce jug and a 64 ounce jug).

I noticed this BECAUSE I grok math. I do simple mental arithmetic many, many times a day as an electrical engineer- calculating expected currents, expected power consumption, approximate required resistance, etc etc. When I look at a package in the store, I can't help but calculate a price-per-ounce of the contents. It's usually right to within 5 percent or so- I round to make the math easier (metric would make it easier yet- is that why we haven't changed?). But I was noticing that there were discrepancies that could not be papered over by hurried mental math.

Keep an eye open- I've heard from a few others that they've noticed this but I'm curious how widespread this practice is.

One other place I've noticed crap numeracy is in science writing, and this is REALLY disturbing to me. Two variations on the same metric will be given in a book or article- say, the number of children who die of malaria every day and the number of people who die of malaria in a year. These values may be reported multiple times and usually won't be reported in close conjunction with one another (note that I don't think this is an attempt at dissembling by the author- it simply reflects the where and when in the work that each makes sense to be mentioned). The troubling thing is, the numbers reported are frequently mutually exclusive. For the above example, the number of deaths per year due to malaria may be reported as, say, 500,000. Quick mental math says that this implies slightly more than 1,000 people per day (remember, I'm an engineer- pi is "about 3" until I need a better answer). Elsewhere, a value of deaths of children will be given, and that number will be, say, 1,500 per day.

In my mind, alarm bells go off. I didn't calculate exactly how many people per day are claimed to be dying of malaria, nor exactly how many children per year are claimed to be dying, BUT my order-of-magnitude estimate tells me that the author is either not counting children as people or not paying attention to math. Frighteningly enough, neither was the editor nor anyone else who weighed in on the book. This kind of basic mathematical error casts doubts on everything else in the book- after all, someone who isn't capable of that kind of mental comparison is certainly unlikely to be able to judge the veracity of more complicated mathematics behind statistical predictions and observations that form the basis of most proposed solutions.

I'm not sure there's much we can do about this- I grok math because it's very much part of my daily life. I exercise those mental muscles constantly to a point where I apply them unconsciously to situations most people don't even relate to math. Maybe some kind of wide-scale gamification of mathematics? At any rate, I don't think it's something that can be addressed by education. Mathematics is fundamentally a foreign language to the human brain, and the only way to really learn a foreign language is to use it, over and over, until you are fluent.


  1. On the subject of obfuscated grocery pricing:
    Most places include information about "price per unit" on the price tag on the shelf. Unfortunately, they change units from one brand to the next. One brand will list cents per ounce and the next may be in dollars per pound.

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  3. When buying cereal in the larger box, keep in mind that the volume to surface ratio is important. The larger box has less packaging (r^2) per mass (r^3)of cereal. So the cereal will become stale at a slower rate. I stopped buying the smaller boxes because (I thought) they tasted bad and consumed more resources per unit cereal.