
Sator Square - KhoomeiK
https://en.wikipedia.org/wiki/Sator_Square
======
Jun8
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...](https://www.amazon.com/Making-Alphabet-Dance-
Recreational-Wordplay/dp/0312155808)) one of the best references on
recreational wordplay (another good source to consult is the journal _Word
Ways_ ,
[https://digitalcommons.butler.edu/wordways/](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:

    
    
      CIRCLE
      ICARUS
      RAREST
      CREATE
      LUSTRE
      ESTEEM
    

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:

    
    
      RACISM
      EVINCE
      PERSON
      ASCENT
      STUCCO
      TASTER
    

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

    
    
      WORCESTER
      OVERLARGE
      RECOINAGE
      CROSSTIED
      ELISIONAL
      SANTONATE
      TRAINAGES
      EGGEATERS
      REEDLESSE
    

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](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.

~~~
KhoomeiK
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.

~~~
cipherboy
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...](https://github.com/cipherboy/sat/blob/master/sator-
square/square.py)

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](https://github.com/cipherboy/cmsh)

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

    
    
        개똥아
        똥쌌니
        아니오
    

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

Did you shit?

No I didn't."

~~~
KhoomeiK
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.

------
hprotagonist
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._

[https://en.wikipedia.org/wiki/Washington_Square_Park_(Chicag...](https://en.wikipedia.org/wiki/Washington_Square_Park_\(Chicago\))

[https://wiki.lspace.org/mediawiki/Sator_Square](https://wiki.lspace.org/mediawiki/Sator_Square)

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

[https://en.wikipedia.org/wiki/Speakers%27_Corner](https://en.wikipedia.org/wiki/Speakers%27_Corner)

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

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

------
greenglyph
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](https://github.com/greenglyph/SatorSquare)

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

~~~
LeoPanthera
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.

