The Dangerous Bend Sign
Donald Knuth

Donald Knuth, in his series of books on the TeX typesetting system, introduced a whimsical symbol he called the "dangerous bend" sign. He marked the beginning of any parts of his books that were "more obscure than others" with a "special symbol ... to warn about esoterica" [The METAFONTbook, preface, 1986]. His purpose was to set off portions of the text that took a "dangerous bend" in the train of thought, and which could be skipped without missing the essential message. The symbol was also itself an exhibition of Knuth's wit and humor: To create the symbol, he used METAFONT, a system designed for mathematical "signs," not road "signs." The program for the dangerous bend symbol even becomes an example to illustrate custom-made characters [The METAFONTbook, pages 106--107]. And of course, the text of that example is itself preceded by the dangerous bend warning.

I was startled to find in 2005 that the estimable father of computer science, aided by his wife Jill, has taken to exploring and documenting every diamond-shaped traffic sign he can find, as exhibited in one of his Web pages, linked from his "what's new" link on his Stanford faculty page. Yes, exploring, as in driving around the continent in a car looking for them. With Knuthian rigor, MUTCD standardization numbers and GPS coordinates are part of this project. I am not so surprised to find this project underway, as it seems very characteristic of his accomplished mind, whether it is a manifestation of a rare and avuncular brilliance, madness from much learning, or the onset of an obsessive bird-watching type of dementia. My suspicion is that we are simply witnessing the ironic laughter of a leading intellect with the modern achievements of high-resolution digital photography and global positioning satellite navigation in hand, tooling about the country to research something trivial.


Knuth also used a double dangerous bend for his material that is "so far out" that the warnings are doubled.

The dangerous bend images on this page are a GIF file, which I created using a bitmap editor and my TrueType conversions of the Computer Modern fonts (including the "MANFNT" manual font used for Knuth's Computers & Typesetting series, which is where the dangerous bend symbol is to be found). I added a bit of color to the bilevel bitmap originals, in keeping with the iconic style of the Web versus the earlier print usage. The font metrics of Knuth's symbol are such that the baseline of the character runs across the widest part of the diamond, with the height of the character about twice the height of capital letters, such that the normal size will conveniently make the symbol a 2-line "drop-cap" for a paragraph. Drop-caps are a little tricky to achieve in HTML, but on this page I've attempted it in the first paragraph above, and at a smaller scaling in this paragraph; spy on the HTML code if you would like to try it yourself.

I don't know if anyone had much bothered with this GIF conversion before (Knuth actually has a small "dbend.gif" rendition appearing incidentally on his Web pages, but a Google search for that image on January 22, 2005 found no other uses), but I have lately (January, 2005) reached the point in my avocation of writing Web pages where I need the semantics of "stuff I'd like to publish for completeness, but which might not be of direct use to your application". So herewith I make this little contribution. I do not believe that Knuth claims any copyright on the symbol itself, and neither do I on this implementation as a GIF file. Feel free to copy db.gif (and do copy it, do not link to it here) and use it to set off your own dangerous ideas.

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Richard J. Kinch
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