Below is a message I sent to a mailing list I subscribe to and which you should too named CRUCIVERB-L.  Almost every subscriber is a crossword puzzle constructor, so keep that in mind as you read this really long post.

August 13, 2009

Hello, Cruniverse,

Is it worthwhile to debate the merits of abandoning the requirement of 180-degree rotational symmetry in every grid?

I'm not saying symmetry is bad, I'm just wondering whether it is always good.

Before I move on, let me say that I am a big fan of big, pretty grids, so it's not like I think symmetrical grid design for its own sake is bad.

Before I move on to specific pros and cons, let me explain the main reason I think asymmetrical grids can be good.  If the constructor is not hampered by the need to be symmetrical, MANY possibilities for even more excellenter puzzle-writing open up.  If you can put a black or a white wherever you want without worrying about what it does to the other diagonal of the grid, you can use MANY more answers that you couldn't have otherwise.

Before I move on I must mention two books of crosswords by the redoubtable constructor Frank Longo.  They are Cranium-Crushing Crosswords (ISBN 0-8069-8499-6, 2002) and Mensa Crosswords for the Super Smart (ISBN 1-4027-1387-8, 2005).  Both are collections of 72 themeless 15s of exceptionally high quality.  They are indisputably difficult -- past Saturday-level, I'd say -- which is why I bought them, but they are also so well crafted that I wonder whether I will ever see such a collection of 144 new puzzles again.  I've been forcing myself to wait a week before starting a new one just so I can spread out the pleasure.

Anyway, the point is that half of the grids in the second book are not symmetrical.  I will quote Mr. Longo in his introduction: "I did not undertake this course of action [abandoning symmetry] lightly, but ultimately decided to go ahead with it for a couple of reasons.  First, aesthetics is subjective anyway. . . . Second, doing so opens up avenues that otherwise simply would not be available, based on the mechanics of grid design" [emphasis mine].

For instance, one of the puzzles contains only 24 black squares and only 62 answers, and one corner thereof consists of a solid 9 by 6 chunk uninterrupted by a single black.  That's 20% more than a triple stack of 15s.  Another puzzle contains only 24 blacks, only 61 answers and -- get this -- a quadruple stack of 15s at the top.  That's a chunk of 60 whites without a single black.  Is it possible to achieve such density in a post-Maleska puzzle without abandoning symmetry?

If you're as impressed with open grids like this as I am, forgoing symmetry is a (relatively) easy way to accomplish it.  This also means, I think, that, for example, even a Monday puzzle could be more wide open and still be a Monday.

I just wonder whether it's worth the restriction the symmetry rule places on constructors.  How many time have you said, "I can't change that black to white because it messes up my other corner"?  How many times could you have improved the fill in some way or other if you didn't have to follow the rule?  How many times could you have improved the theme or even added a whole 'nother theme answer?

There can be no doubt that if asymmetry is permitted, even if not very often, that "opens up avenues that otherwise simply would not be available."

I think there are two such new avenues: content and grid art. Let me further address content first.

CONTENT

As I see it, there are three groups of people to be concerned about with regard to violating symmetry: constructors, solvers, and editors.

-- Constructors  I can't imagine why constructors would mind tossing out the rule from time to time.  As I say, that frees us up to do a lot more.  You can use a much wider variety of answer-lengths, and thus a wider variety of clues.  There surely would arise MANY more opportunities to be clever, to impress players with entertaining manipulation of the language, to improve the CONTENT at the expense of the FORM.  I suggest that the form is a purely artificial constraint on what matters most, which is the content.

Less work, more freedom. What's not to like?

Understand that I have not been wondering about prohibiting symmetry, just not requiring it.  Needless to say, a grid should be symmetrical if the constructor thinks it's better that way.

-- Solvers  Of course it's the solvers who matter.  If solvers would be less happy with asymmetrical grids for that reason alone, even if the content improved measurably, then I hereby declare this issue closed.  But I wonder how many solvers would care, and how much.

Remember with me back to 2006 when you watched "Wordplay" in a theater.  At one point the movie graphically demonstrates that when the grid is rotated 180 degrees it remains identical.  In the theater where I watched it, the reaction of many members of the audience was to make noises strongly suggesting they were surprised.  That reaction surprised me.  Now, granted, many of those people had probably only seen but never played a crossword, or had played so few -- perhaps spread out over so long a time -- they just didn't notice the symmetry.  But still it must be true that there are a lot of solvers out there -- mostly novices, no doubt -- happily filling in grid after grid in complete obliviosity of how pretty those grids can be and how symmetrical they always are.

It seems likely that many experienced solvers will notice that a grid is asymmetrical.  They might not notice for the first few, but eventually they will notice.  I don't know how to measure how unhappy they will be.  I do know that I, an experienced solver, have no problem whatsoever with Frank Longo's asymmetrical grids.

I recognize that violating symmetry made his job easier.  I also believe it made it easier for him to make better puzzles.  If, for example, asymmetry made his job 10% easier but improved the content of the puzzle by 5%, that's a trade-off I very much do want to make.  Speaking only as a solver, I don't care how, to be frank, long or difficult the process of construction was; I care about the answers and their clues.

(Sorry.  Also, do you think his buddies call him Franco?  Or even Frohnk?  Long O, get it?)

Let me now poll the list, because every subscriber here is surely a solver.  As a solver, if you opened next Friday's NYT and noticed it was asymmetrical, would you be less happy?  Let's assume even that the content was no better than what you expect from a symmetrical Friday.  Would you feel cheated or disappointed that the constructor didn't have to try as hard?  Would the puzzle be any less satisfying to play?

If so, would you be willing to forgive the constructor and the editor if the content -- the clues and answers -- turned out to be BETTER than you expected?  As a solver, how important is it to you that the grid be symmetrical compared to how entertaining or illuminating or otherwise worthwhile the clues and answers are?

By way of trying to quantify this, for me a visually pleasing or impressive grid's exact arrangement is worth maybe one extra-good clue.  Said another way, I'd certainly rather have an asymmetrical grid than give up the pleasure of as few as two extra-good clues.

(As a constructor, if you didn't have to follow symmetry would that extravagant freedom -- that removal of some serious shackles -- allow you to devise at least one more extra-good clue per puzzle?)

-- Editors  The third group to be considered is editors.  Needless to say, if all editors will always unthinkingly reject all asymmetrical grids then the incipient discussion is over.

What are the reasons an editor would reject out of hand any submitted grid that was asymmetrical?  I can think of three, but if there are others then I hope you'll introduce and discuss them.

1. Tradition.  It is traditional that American crosswords be symmetrical.  As for me, I understand the value of tradition but I never wish to be a slave to it.  I do understand that abandoning strict symmetry in a puzzle might be a disappointment to some of the players who notice it, and that's worth something.  Speaking for myself as a solver -- as I'm sure I've made clear by now -- it's not worth much.

2. Visual appeal.  Symmetrical grids, especially at the end of the week, can be satisfying to look at for a moment or two.  My guess is that only serious solvers know or even think to analyze the form for a moment before starting in on the content, and even they never look back again.  And I'm still guessing the visual appeal of a symmetrical, wide-open grid or even the patchy symmetry of a Monday is utterly lost on quite a significant portion of the playing population.

3. Harder.  Editors are aware that some players recognize a tough grid to fill and appreciate the extra effort exerted by the constructor.  I do suggest that the percentage of such players is small. I further suggest that many of that small group are so sophisticated that they will recognize and appreciate that the better content makes up for the asymmetry.  And I suggest yet further that that group is the one least likely to write angry letters to the editor threatening to cancel their subscriptions if symmetry is not re-instituted immediately, damnit!  Such solvers will, I think, be more happy, not less.  I know I am with Longo's asymmetrical crosswords.

All three of these reasons taken together are not enough for me, as a player, to wish to constrain constructors henceforth with the symmetry rule.

Of course there have been asymmetrical grids in, for example, the NYT.  But these exceptions usually arise only when the variance in form is necessary to the content, such as that cute crossword whose theme was to demonstrate a flawed crossword.

I do wish to point out at this point that according to the page at http://www.cruciverb.com/index.php/page=16, the NYT specifications make no mention whatsover of symmetry.

 
Now let me turn to some more specific topics, still with regard to the big topic of content.

-- Theme answers  The question of how to identify theme answers has probably already occurred to you.  They are usually identifiable by two characteristics: (1) They are the longest answers, and (2) they are symmetrically placed.

And sometimes shorter bonus theme answers are identified in the clue.  And sometimes they aren't identified at all; the player recognizes them or not.

First, it's important to remember that the asymmetrical grids used by Longo are all themelesses, so from Thursday or Friday to Saturday the question how to identify the theme answers need not arise.

(However, I think it's important to realize that by abandoning symmetry it is easier to create a wide-open grid that DOES have a theme.  Further, it's my guess that most Friday- and Saturday-level players wouldn't need the additional help of the theme answers' being symmetrically placed in order to spot them.  With asymmetry you could more easily lay out a wide-open grid and use Saturday-level clues and answers AND implement a theme.)

Second, I'm still not suggesting that symmetry be prohibited, just not required.  If you as a constructor think a symmetrical grid is better for a particular puzzle, you're right.  But I'm also saying if you placed three 12-letter theme answers at the very top and placed the fourth one, a 14-letterer, a few rows up from the bottom, players would still be able to identify the theme answers from the lengths alone.

-- Types of symmetry.  I think it's useful to categorize the degrees (ha ha) of symmetry.

(1) The most restrictive type of symmetry -- which, for good reason, few constructors attempt -- is a grid that exhibits not only 180-degree rotational symmetry but also 90-degree rotational symmetry, meaning if you rotate the grid 90 (or 270) degrees, the blacks and whites still correspond.  An example would be a centered square.  As far as keyboard examples go, I think the only two that qualify are the (round) letter "O" and the plus sign.

(2) The rest -- a good 98% of NYTs, I think -- exhibit 180-degree rotational symmetry, meaning that rotating the grid 180 degrees achieves correspondence.  Examples would be a centered circle with a "DO NOT" slash through it and the letters "Z" and "N."

(3) But there are also "mere" folding symmetries, which we rarely see except in specialty puzzles and which I think we should see more of either way.  Also, I will remind you that Will [Shortz] has specifically said he does not object to these folding symmetries.

In left-right folding symmetry if you fold the grid on its vertical axis the blacks and whites match.  Examples of left-right symmetry are the letters "A" and "V" and a smiley face and, for that matter, an upside-down smiley face (but not a winking smiley face).

(4) In top-bottom folding symmetry, if you fold the grid on its horizontal axis the blacks and whites match.  Examples of top-bottom symmetry are the letters "C" and "D."  Also, (ha) either parenthesis.

(5) In diagonal folding symmetry, if you fold the grid along one of its diagonals it is symmetrical but if you fold along the other it is not.  This is an extremely rare type of grid.  Indeed the only one I remember in NYTs, shown below, is Joe Krozel's of August 7, 2010.

In this grid the whites correspond with the whites and the blacks correspond with the blacks only if you fold it from its northwest corner to its southeast corner.  The long diagonal wall of blacks is placed above and to the left of the center of the grid.  Equally important, the 2-step diagonal of blacks in the northwest quadrant is matched by a four-step diagonal of blacks in the southeast quadrant.

(The grid above is significant for another reason.  If you count you will find that there are only 18 blacks.  No one has ever done better in the history of the NYT, and that's a big deal to constructors and fierce fans.)

(6) And you could also lay out a grid that, while not symmetrical per se, still achieves a pleasing geometrical balance.  An example would be a large plus sign in the upper left and a smaller one randomly in the lower right.

So for constructors desiring a degree of harmony in the grid itself, there are many options besides 180-degree rotational symmetry.

But remember that my point is that even these more relaxed rules (3 through 6) need not be followed in every puzzle.  I'm suggesting we dial it all the way up to 7 and consider abandoning any sort of format harmony whatsoever in order to have the freedom to improve the content generally.

-- Quotations and quips  Another benefit of an asymmetrical grid is the ability to introduce so many more quotations.  As one editor said, if I'm quoting (ha ha) him correctly, "If you change it, it isn't a quotation."  Think how many more terrific quotations -- ones that are clever or amusing or thought-provoking -- could be used as themes.  Finding a quotation that's worth repeating and that also fits in a symmetrical grid is so difficult, but without the symmetry rule the percentage of Bartlett's Quotations that opens up increases by -- and feel free to check my math here -- something like a budillion percent.

Same for quips.  You can write your own brilliant quip, or joke or riddle or whatever, phrased exactly as you want, without being hampered by symmetry.  You can improve the content of the puzzle, which I re-claim is more important to the end users than the format.  Players who spend 30 minutes on an average puzzle, beginning with a two-second assessment of the grid before plunging in, spend 99.9% of their time dealing with content, which is why I say the symmetry rule is needlessly hampering.

-- Fine-tuning  Without symmetry a puzzle's level of difficulty is easier to dial in on every clue.  Sometimes a Saturday-level answer or some crosswordese must be used in a Tuesday puzzle just to get it to work.  Sometimes a Monday's grid does require crossing answers whose intersection is more of a Friday degree of combined difficulty.  And sometimes you just have to use ERA.  [Note: ERA is the single most common answer in NYT crosswords.]

Surely many of these problems can be avoided if you don't have to match up answer lengths diagonally across the center cell.  If you can change a black to a white or vice versa without worrying what that does to two (and maybe more) other answers on the whole other side of the playground, you can make sure a Monday really is a Monday all the way through.  Or a Saturday.  I think both levels of player want that.

And if you're abandoning symmetry, you can (and probably should) change not just one black to white or vice versa but several.  As I say, it's an extravagant freedom.  In terms of chess it's the difference between a pawn and a queen.

(I also have to say that, with or without symmetry, I'm pretty sure I'm always going to expect a wide-open grid for late-week puzzles.  With symmetry, a black-square count under 25 is impressive, and the record for NYTs is, I think, 18.  Without symmetry surely even whiter grids can be filled, and I for one would like to see that.  Would a black-square count of 16 be possible?  Would a word count of 48 be possible?  I don't know but, as I say, I'd sure like to see it.)

-- Specialty puzzles  I am a big fan of specialty, or novelty, puzzles.  I admire the effort that went into the Clinton-Dole puzzle and the puzzles where the first letters of the clues spell out a sentence and all the other similar triumphs of the crosswording art.  As I figure it, without the symmetry rule the opportunities for creating such masterpieces increase by at least 2,384%, which is a lot.

If that's true, then I'm 99.83% sure the number of such masterpieces that get published would also increase by -- and please don't quote me here -- a bunch.  Surely that can only be good for the popularity of crosswords.

If you're a tyro at playing crosswords and you bump into such a masterpiece in the first few puzzles you try, you're much more likely to get hooked.  If solvers who normally give up on Thursdays stumble onto an especially brilliant Wednesday theme executed masterfully, they might well become more fanatic, more likely to complain if their puzzles are taken away or replaced by a computer-generated version that cranks out nothing but sub-Monday themelesses.

The likelihood a constructor can create such an extraordinary puzzle surely increases if the symmetry straitjacket is removed.  If you've had a brilliant theme idea but just couldn't quite get your answers to fit and eventually gave up and moved on, it might well fit in an asymmetrical grid.

And that even-better content will surely attract and keep more players, which I think all three groups want.  Constructors want it, solvers want it, and therefore, I assume, editors want it.
 

GRID ART

The first big topic was content.  Now I turn to the second big topic, which is what I will refer to as grid art.  By grid art I mean using the blacks and whites of a grid to draw a big picture that presumably relates to a theme.

Grid art -- using the blacks and whites of the grid itself to paint a highly pixellated image -- has been exploited several times over the years in the NYT, but almost always it has been symmetrical in at least one direction.  I admire the difficulty of confluing form and content, as many of you know from my page starting here.

But I claim that if symmetry may be abandoned, the number of opportunities to draw something in the grid rises by almost 7,352%.

I can imagine a permanent uptick in popular interest in crosswords because of such symbolic grids.  The grid paints a picture representing the theme of a winking face or a sailboat or the U.S. flag, and someone at a lunch counter or three rows back on the subway spots it and gets curious.

The possibilities for grid art open up even more when you consider a Sunday: They increase by 96% exactly for a 21 and 135% for a 23.  With that much extra room -- and that extra freedom to put blacks and whites wherever you want -- you can draw Utah or a basketball goal in one corner and a ball in the other or a working maze or . . . well, you get the idea.  Heck, you could even combine grid art with circled cells and greyed cells and starred clues and get really creative; I'm not imaginative enough to offer any examples, but I'll bet you are if symmetry isn't enforced.
 

I suspect there are some sophistications I have not considered here.  If so, what are they?

Is this just such a thoroughly closed subject that no debate can possibly be useful?

I think that if editors unapologetically publish asymmetrical grids whenever they benefit the player, then everyone who subscribes to this list will benefit as well.  What do you think?

--Johnny