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Sator Square (wikipedia.org)
38 points by KhoomeiK on Oct 30, 2019 | hide | past | favorite | 13 comments

Ahh, the topic of word squares! Let me start by saying this: If you find this sort of thing even remotely interesting, you owe it to yourself to immediately order Making The Alphabet Dance (https://www.amazon.com/Making-Alphabet-Dance-Recreational-Wo...) one of the best references on recreational wordplay (another good source to consult is the journal Word Ways, https://digitalcommons.butler.edu/wordways/). Ross Eckler has a whole chapter on this topic alone, the following tidbits are taken from there:

Eckler states that the modern history of word squares (following in the footsteps of the SATOR square) started with the following one, published in 1859:

This is called a single word square, same words appearing in both horizontal and vertical directions. When these are different it's called a double word square, which are much are harder to construct.

Here's a six-square:

Here's a nine-square, with all words from the OED, published in 1993:

Constructing a 10-square using all words from a single language's dictionary has not been successful so far (who knows, with the new word additions to the OED...) Wikipedia calls this " the Holy Grail of logology" (https://en.wikipedia.org/wiki/Word_square#Order_10_squares)

And then he goes on to discuss word cubes! An n-cube contains n words repeated three times each and n(n-1)/2 words used six times each, it has a total of 3n^2 words. And yes, people have extended the idea to hypercubes.

I don't intuitively see why a double word square would be harder to construct than a single word square. After all, if you allow the words to be different, surely there are more options / more degrees of freedom to complete the square?

Interesting. I feel like Sator is cooler though because it actually has a meaning (other than "Arepo") and is grammatically valid. It also seems to have some deeper philosophical connections with early ideas of time cycles.

They're a lot harder to find (especially for English) though.

Each word needs to be valid both forwards and backwards in a Sator, right? There's a number of 5x5 Sators, but no 6x6, 7x7s, or higher because the number of words which satisfy are much smaller.

There is probably a better SAT encoding but if you just want to play around: https://github.com/cipherboy/sat/blob/master/sator-square/sq...

It finds Sators and 6x6 and smaller word squares reasonably quickly, but larger takes a bit more work. :)

It does depend on your wordlist though (place words.txt in the directory with square.py).

cmsh from here: https://github.com/cipherboy/cmsh

I only know one such square in Korean, but that's funny enough that I'd like to share:

"Hey gaettong (literally "dog shit" - which was a popular affectionate name for kids a hundred years ago)

Did you shit?

No I didn't."

This is so cool. I wonder if there's more of a tradition of these types of squares in languages with syllabic/block scripts because they're easier, and probably way easier in logographies like Chinese, to construct.

see also the location in Ankh Morpork of the same name, which is probably also a reference to Bughouse (washington) square in chicago:

Sator Square is also a place where free speech is allowed, if not encouraged, and is a place for ranters, haranguers, and self-absorbed mumblers to say their piece. This all comes under the heading of street theatre, and no doubt the Patrician has somebody in the crowd to memorise names and faces and take notes, on the off-chance that what is said might actually be important, or lead to consequences.



Or Speaker’s Corner by Hyde Park. Pratchett was English, and likely more away of the London location.


I figured there was a london equivalent. CMOT would be at home in both, I think.

Word squares feel like something you could programmatically generate, although trying to imagine the algorithm to do so efficiently hurts my head.

I became interested in Sator Squares a while ago and wrote a Python script to generate them given an arbitrary list of words (it conveniently ignores words with an even number of letters, but still generates a large percentage of possible squares for a given list): https://github.com/greenglyph/SatorSquare

This isn’t that cool because Arepo is not a word.

Your comment is glib, but you're not wrong. It wasn't even a word at the time.

"AREPO unknown, likely a proper name, either invented or, perhaps, of Egyptian origin, e.g. coded form of the name Harpocrates or Hor-Hap (Serapis)."

However, I do think that the concept of word squares in general is still "cool", and this one is important because of its history.

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