Stochastic Bookmark

abstruse unfinished commentary

about correspondence


back up some more

Once again, a curiosity fished from comments at thevalve (and re-dressed here); in a response to a question regarding overlaps between chess and poetry, rather than taking the route of chess problems as the poetry of chess (or bringing up Nabokov as is my wont), I went the other way round and posted a conundrum poem I'd concocted long before:

magic won the tourney’s quintain
the knight’s sheer determination too
detouring only when facing six
completing the circuit though outnumbered
and skewering the anchored ring

I'll get to its solution below, in due course (for those who would rather ponder). Meanwhile, notes on form: the traditional conundrum / riddle poem / charade is typically of the "What am I?" variety, with an unknown object given voice to list its properties or attributes, often from its own perspective (to further defamiliarize). Popular in England over 200 years back (farther if one counts kenning), the form never really went away, not just in current constructions as a minor form anyone can play, but also contributing along the way to the sensibilities of such as Emily Dickinson & Sylvia Plath, the latter f'rinstance in "Metaphors":
I'm a riddle in nine syllables,
An elephant, a ponderous house,
A melon strolling on two tendrils.
O red fruit, ivory, fine timbers!
This loaf's big with its yeasty rising.
Money's new-minted in this fat purse.
I'm a means, a stage, a cow in calf.
I've eaten a bag of green apples,
Boarded the train there's no getting off.

Nine syllables in nine lines ... pregnant with meaning, one might say (via, more). The form doesn't require the first person, though, so long as the context of a hidden meaning is clear.

In the example I pose, the explicit description is of a jousting tournament at which one event is a quintain, attempting to run a lance into a fixed target. I've complicated it a bit by adding opposition to overcome along the way. But, not being satisfied with mere correspondence to the implicit meaning, I've tried to embed an algorithm for unveiling it within the wording. The reader may be the judge as to how well this succeeds. I'll repeat it so as to obviate scrolling:
magic won the tourney’s quintain
the knight’s sheer determination too
detouring only when facing six
completing the circuit though outnumbered
and skewering the anchored ring

So, consider this as an instruction set operating upon itself. Without excessive parsing, then ... quintain, defined as a jousting contest, tilting at fixed target (or the target itself), alternatively denotes a 5-line poem. This particular 5-liner has 5 words per line; a square (skewer?) matrix, if you will.
outnumbering suggests numbers are relevant, though only six appears explicitly, unless one counts homophones, in which case the matrix has these entries:
xx 01 xx xx xx
xx xx xx xx 02
xx xx xx xx 06
xx xx xx xx xx
xx xx xx xx xx
I'll bring in the chess aspect now, as the knight's tour, in which the piece visits every square in succession, is signalled by tourney, detouring and by sheer determination (determinism), circuit, and outnumbered (since the representation is shown by which move number occurs on which square). 5x5 is the smallest square board on which a knight can complete the tour, but in this instance 01 and 02 do not appear to be a knight's move apart.
This can be resolved, though, by attaching the left and right edges, top and bottom likewise, to form a torus (aka anchor ring). Then 01 and 02 are a knight's move apart, and continuing in that direction one can add 03, 04, 05, before hitting the starting square 01, but the square labelled 06 is a knight's move away in a different direction (detouring only when facing six):
xx 01 xx xx xx
xx xx xx xx 02
xx xx 03 xx 06
04 xx xx xx xx
xx xx xx 05 xx
With this pattern established, resume the prior direction (with diversion on hitting 6 modulo 5) to fill in the rest of the grid:
12 01 20 09 23
16 10 24 13 02
25 14 03 17 06
04 18 07 21 15
08 22 11 05 19
Result is a knight’s tour on a torus that resolves into a magic square (same sum in adding rows, columns, or diagonals) by cutting the joined edges, squaring (skewering) it, as it were.

In 25 words or less, a fair bit of complexity/abstraction, but hardly a lasting cultural artifact. It was brought back to mind by The Guardian on magic square stamps, which in turn made me aware that I had unknowingly employed a known variation of De la Loubère's (or, the Siamese) method (cf Wolfram's MathWorld). Also, this was constructed before I'd encountered the writings of Georges Perec (yes, I was geek enough to work out the knight's tour in Life: A User's Manual, but blanched at the Graeco-Latin square for being unable to identify its constituents), but I offer it in homage.

(as noted, a much-stripped down version of the above appeared at thevalve)


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