apophenia
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Incantations in English

The Sator Square — the cool S of antiquity — fascinated me the instant I saw it. I still repeat the motions of our first meeting whenever I see one: left to right, right to left, top to bottom, bottom to top, turning, reversing, and then, finally, the diagonals, where it breaks.

Word square: SATOR, AREPO, TENET, OPERA, ROTASSATORAREPOTENETOPERAROTAS
Scratched into wall plaster at Pompeii, before 79 AD.

Folks scratched those twenty-five letters into the walls at Pompeii, and on amulets, and in the marginalia of manuscripts for hundreds of years. Historians guess it is a meme, a religious graffiti, a ward against evil, it's never been clear. But it was popular and clearly meant something to the people invoking it.

Be it a diverting trick or powerful sigil, the square holds power for others too. Doug McIlroy — inventor of the Unix pipe — read about the square and described how he "...was instantly impelled to set my indefatigable machine seeking comparable incantations in English." His Bell Labs computer whirred to life and printed the following square:

Word square: LARES, ANELE, REFER, ELENA, SERALLLAARREESSAANNEELLEERREEFFEERREELLEENNAASSEERRAALL
McIlroy, 1976. Webster’s Collegiate, one machine, almost immediately.

To which McIlroy responded, "household gods anoint, witness unctuous Elena!" He was delighted, but after generating 350 more, declared them "mostly dull checkerboards of vowels and consonants" and moved on.

When I met the Sator square I had the same thought as McIlroy: how do I enumerate the possibilities for this in English?

In the years since Bell Labs, miraculous computation has become a commodity. I wrote a search against a 370k word dictionary that ran in under a second, performance that would make McIlroy weep.

When the search runs for 5-letter words, it finds 143 distinct squares. I ranked the results using word frequency and quickly found my square:

Word square: DAMON, ANIMO, MINIM, OMINA, NOMADDDAAMMOONNAANNIIMMOOMMIINNIIMMOOMMIINNAANNOOMMAADD
Found 2026. Not in McIlroy, Puder, or Gooch.

This square isn't in McIlroy or in Jim Puder's 2,029 palindromic squares or anywhere else that I can find. It seems like nobody has recorded this square until us. Maybe no one has read it before now.

But when I run my finger over the letters in the pattern I know so well, I can feel it. This puzzle is birthed by the same power that birthed Sator.

See also:

  • M. D. McIlroy, "5-by-5 Palindromic Word Squares," Word Ways 9:4 (1976), pp. 199–202. Butler University hosts a PDF.
  • Jim Puder, "Some Sentential Palindromic Five-Squares," Word Ways 37:1 (2004).
  • The NewSatorSquare project runs the same backtracking search over a 7.2-million-form Hunspell Latin list.