Friday words #271

By | June 4, 2021

Matt Parker is a “recreational mathematician,” or to use an alternative title, a “standup mathematician.” He writes about math in a way that makes it interesting for people who don’t really do much math.

Recently I was reading his book Humble Pi: When Math Goes Wrong in the Real World, which is where I got today’s new-to-me word. It takes a little bit of backstory, though.

The book recounts a series of stories about math disasters. These include state agencies that miscalculated the odds of lotteries they were running, a Y2K-type issue with air-controller software, and a building whose rounded, reflective windows acted as magnifying glasses, focusing sunlight on very small areas, whoops.

One of the mishaps that Parker talks about was a kind of self-own: the Parker square. Parker was interested in magic squares: a 3×3 matrix of unique numbers in which the rows, columns, and diagonals all add up to the same value. Here’s an example:

Magic square in which the numbers 1 through 9 are arranged in a 3 by 3 grid so that the rows, columns, and diagonals add up to 15.

Parker thought it would be cool to work on creating a magic square in which all the unique numbers were squares. (Get it?) This is what he came up with:

Parker's "semi-magic" square that contains square numbers (for example, 29 squared, 1 squared, and 47 squared across the top row).

Look carefully, though. First, the numbers are not all unique: 12, 292, and 412 are repeated. Second, the rows, columns, and diagonals don’t all add up to the same number:

Parker's "semi-magic square" showing that although the rows and columns and one of the diagonals add up to 3051, the other diagonal adds up to 4107.

As Parker explains in a video, although it technically doesn’t meet the definition of a magic square, he still quite likes his effort. He refers to it as a “semi-magic square.” Based on this near miss, so to speak, Parker and his fans have been promoting the term Parker square as (per Brady Haran) “a mascot for people who give it a go but ultimately fall short.”

People sometimes post pictures on Twitter to which they add the #ParkerSquare hashtag, pictures like these:

You pretty much have to know this story in order to appreciate how it applies to these examples. Still, it’s nice to know that there even is a term to describe a pretty good effort that nonetheless failed.

For origins today, a surprising etymology that was passed on to me by my daughter: the word vitamin. The interesting part is that it got its name kind of through a mistake.

The word goes back to 1912; it was coined by a biochemist who was investigating “micronutrients.” Medical people had known for a while that eating certain foods helped prevent various diseases. Most famously, perhaps, a Scottish doctor noted that eating citrus foods seemed to prevent scurvy. (As a result, limes for lime juice were issued to the Royal Navy, hence the term limeys for British sailors.) Someone else noted that a diet with fish oil helped prevent rickets. A Japanese doctor figured out that sailors who ate only white rice developed beriberi.

In 1912, the biochemist Casimir Funk isolated what we now know to be niacin (vitamin B3). He named the substance vitamine, which was a portmanteau of vital and amine.

This is where the mistake happens. The word amine refers to ammonia compounds that have organic (carbon) bits stuck on them. Funk imagined, incorrectly, that all of the micronutrients that people had been chasing were ammonia compounds like this. (“It is now known that all these diseases, with the exception of pellagra, can be prevented and cured by the addition of certain preventive substances; the deficient substances, which are of the nature of organic bases, we will call ‘vitamine’.”)

Funk’s mistake was recognized soon; it turned out that these essential micronutrients actually came in a variety of forms. In a journal article in 1916, some biochemists proposed more precise terms: “We would..suggest the desirability of discontinuing the use of the term vitamine, and the substitution of the term fat-soluble A and water-soluble B for the two classes of unknown substances concerned in inducing growth.”

Yeah, no. In 1920, someone said yes, the term vitamine is not technically correct. How about if we just drop the -e and go with Vitamin? The argument was that if they dropped the final -e, we get a “neutral” term that ends in -in. And bonus, this dispenses with the “somewhat cumbrous nomenclature” of calling these things “Fat-soluble A, Water-soluble B.”

And so we got Vitamin A, Vitamin B, Vitamin C, and so on. The way in which each vitamin was labeled (A, B, C, D, E) is beyond my ken. I did look into it enough to know that at various points there were Vitamins F, G, H, I, and J, but these were reclassified into variants of Vitamin B and whatnot.

There have to be other (many?) other examples of scientific-type names that have origins in mistaken notions. I can’t think of any offhand, but I’d sure like to hear about it if you know of some!

Like this? Read all the Friday words.