The Man Who Mistook His Graph for a Hat

Equilateral triangles have been used as a graphical tool for presenting compositional data for at least 150 years, most prominently in geology, metallurgy, and related areas of physical chemistry; archeology and anthropology; and population studies, including genetics. According to Howarth (1996)[paywall], they were also used as early as the 18th century to show mixing of colors, including an example by physics pioneer James Clerk Maxwell.

I will write other posts about some of the numerical and mathematical aspects of these diagrams, but this one is focused on nomenclature, which varies by discipline or field of study, for example:
• physical sciences — ternary plot, triangle/triangular plot;
• math, especially geometry and topology — simplex; and
• genetics — de Finetti diagram.

Having worked extensively and intimately with these diagrams since my grad student days, I am firmly set with “ternary plot.” I still wax nostalgic over having derived the transformation equations and written my own code to generate plots for data on volcanic rocks to include in my dissertation. What can now be done with a few lines of R in even fewer minutes, took days back then.

Fast forward a lot of years to the early QED Insight era, when Laurie was telling me about sense-making and the Cynefin framework and Cognitive Edge and Dave Snowden. And there were these three-component triangular graphs called “triads.” Did I know anything about them? I had no idea what “Cynefin” was, let alone how to pronounce it, or who Dave was, but “triad”? I knew a ternary plot when I saw one, and yes, I could answer her questions about them. Purely by coincidence, I had recently come across the original sheet with my derivation of the transformation equations, so I could walk her through the math as well.

Very soon after that, I had learned about the Welsh origin of both Cynefin and Dave. I didn’t give much thought to “triad,” though, or its two-component cousin, the “dyad.” The obvious etymological mapping from the art world, diptych and triptych, was close enough. But, when the time came that I actually wanted to know, I looked up triad. There are more than 70 bulleted entries on that Wikipedia disambiguation page, in addition to the opening “group of three” definition. They cover biology and medicine, psychology and sociology, philosophy and religion, science and technology, organizations, entertainment, and more. But none of them is about a ternary plot.

The next-to-last heading, however, is Literature, and there I found a clue: “Welsh Triads, collections of medieval Welsh legend and history.” And if you click through on the link, you find this:

The Welsh Triads (Welsh Trioedd Ynys Prydein, literally “Triads of the Island of Britain”) are a group of related texts in medieval manuscripts which preserve fragments of Welsh folklore, mythology and traditional history in groups of three. The triad is a rhetorical form whereby objects are grouped together in threes, with a heading indicating the point of likeness. For example, “Three things not easily restrained, the flow of a torrent, the flight of an arrow, and the tongue of a fool”.

It has nothing to do with graphs, though it does sound a bit formulaic. (Haiku, anyone?) But at least there is a good mix of meaning and symbolism for data from storytelling and sensemaking. This is one of the hallmarks that I have come to admire in Dave’s adaptation or appropriation of terminology.

I also checked the Oxford English Dictionary, which says the first usage of “triad” was in 1611. Although it has literary and historical flavor going for it, I would have taken a slightly different tack.


I would have emphasized instead the three-cornered nature of the ternary plot itself by using the name for that symbol of 18th-century military and piratical dress, the tricorne. Or, if you’re into postmodern punctuation, you might prefer “tricorne(r).” Either way, and with apologies to Oliver Sacks, I could have lived with the risk of being labelled “The Man Who Mistook His Graph for a Hat.”

One thought on “The Man Who Mistook His Graph for a Hat

  1. It always helps to enrich a new idea with creative connections, to help it settle into the subconscious. This is good stuff.

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