# Crossword Errors

Okay, I know there are a certain number of mathematicians who enjoy crosswords. There were a few of us at Yale who’d collaborate, or compare notes if we preferred working them ourselves (holla if ya hear me). Occasionally there’d be a “math” hint, which would throw us off because we’d have to come up with the non-technical answer.

But this one I can’t explain at all:

“Mathematical subgroup”.. Well, they probably mean “group” as “collection”, rather than group. But what is the layman’s meaning for “coset”? They can’t possibly mean the technical sense, because a coset isn’t a subgroup, unless it’s the trivial coset. A coset is an element of the *quotient* group, and usually isn’t even a group at all!

So what was Mark Milhet thinking? Does anybody know the guy? If so, point him here so he can explain hisself!

Write either a snail mail or an email; I bet you get a response. Crossword editors tend to be obsess.

And here I thought you were going to be talking about EULER appearing in a crossword. (He’s been showing up a lot lately, or maybe I just started noticing it.)

For what it’s worth, lots of the time crossword clues are altered by the editors, so it may not be Milhet’s fault.

(Also, if Milhet’s a self-googler you may get a response soon — this post is on the first page of the google results for his name.)

Well, technically the coset containing the identity is a subgroup, so it’s sort of not completely wrong.

My guess is that he has a girlfriend named Cosette, as in Cosette and Valjean…

“unless it’s the trivial coset”

Thanks for the clarification, Greg.

It could be as Isabel suggests. Otherwise, think of it from the standpoint of the compiler: after fiddling around with the grid construction, he backs into “coset” as a plausible-sounding word, which he then looks up and verifies to be a word, but with an unwieldy definition (if the dictionary is all he has to go by). So he trims the definition down a little, not realizing he’s going to send mathematicians off on a rant for getting it technically wrong. What does he know?

As a sometimes crossword compiler myself, I can easily see this happen.

So why not change the hint? Or call a mathematician?

Probably neither he nor the editor have the background to know how to change the hint into something snappy and correct. I guess they *could* have called a mathematician, but maybe that would have been an unusual step for them to take — I don’t know. Or, maybe they were pressed for time, or didn’t think it worth the bother (“ehh, good enough”), or didn’t think they were doing anything wrong in the first place, or just didn’t think to do anything like that.

Yes, they fell down on the job! Shame on them! :-)

Okay, if we interpret “coset = “Mathematical subgroup” in the vernacular sense of a bunch of mathematicians, should it be:

“Coset of mathematicians” is dual to a “set of comathematicians”?

Hi all. Mark Milhet here.

While it is true that editors change clues at times, this is not the case here. The clue you saw is the clue I submitted.

As for calling a mathematician, I’d say it is very unlikely any constructor would actually consult with a professional about a clue unless the clue was directly related to the theme of the puzzle. I (obviously) did not.

However, I did consult a couple of reference sources. We cruciverbalists (yes, that’s what we’re called) have a website to which I subscribe (www.cruciverb.com). The website has a database to which we subscribers have access. The database tracks every word used in several major crossword publications, and how that word is clued.

The word COSET appeared 4 times overall, twice in the New York Times, first on 4/2/2000 clued as “Mathematical subgroup” (the clue I used”, then on 12/9/2006 clued as “mathemeatical grouping”.

I did also consult a dictionary, and the definition wasn’t much help because it used the word ‘set’ to define ‘coset’, which I would not have been able to do.

So i figured if the definition was good enogh for Nancy Salomon (the co-constructor of the 4/2/2000 puzzle) and Will Shortz (the editor), then it was good enough for me.

It certainly was not my intent to offend anyone or send them into an uproar, and if I have done so, please accept my apologies. I hope I have explained myself. For future reference, I’d like to say I have consulted a mathematician, so…

Please provide a crossword clue for COSET, keeping in mind that it must reach a general audience (not just mathemeticians), and you must do so in about 30 letters or less. Thanks.

Brilliant! Glad to hear from you. I’ll put my mind to the problem of providing a better clue, if possible.

And don’t mind me being ranty. I don’t mean any slight by it. Overall the puzzle was neat, and I liked the theme. But what’s the internet for if not nitpicking? :D

The clue’s originator, I suppose, might have been taking “subgroup” simply to mean “subcollection of a group”.

I don’t think it’s possible to provide a crossword clue for “coset” (with its standard mathematical meaning) that would actually be solvable/verifiable in itself by a general audience, since I don’t think the word “coset” is one which the layman has ever run across (it would be like trying to provide a general audience clue for “vtable” or “virama” or any other suitably niche piece of jargon for a suitably niche concept) . The best one could do, I think, is some sort of appeal to the word as arising compositionally, if unusually, from a combination of “co-” and “set”, and perhaps using an entirely nonmathematical meaning of “set”; e.g. a clue like “place together” or “arrange a table with a friend”.

(That having been said, slight rewording of the given clue (so as to avoid conflation with the particular technical term “subgroup”) would probably have been acceptable, even pedantically; e.g., “Mathematical group part”)

Those smileys weren’t intentional; just punctuation being misinterpreted.

I suggest “translate of mathematical subgroup” or “mathematical subgroup, translated”, or something similar, if accuracy is what we’re after.

“portion of mathematical group” might be fine?

if you want to shave off a few letters, maybe “piece” or “part” instead….

Well, the defect fixed by “mathematical subgroup, translated” isn’t accuracy, as such, but precision. But yes, that’s better while still suitably simple.

My first professional sale of writing was, at age 12, a crossword puzzle in which many names of Science Fiction authors were embedded. This I sold to the Science Fiction Book Club for $200.00, which, to a 12-year old in 1963, seemed like a lot of money. This is far from the record for youngest professional Science Fiction sale, by the way.

I grew up on the New York Times crosswords which cycled nicely from easy to hard on a weekly basis (hard = Sunday). But my wife grew up on the (London) Times, as did one of my thesis advisors (Oliver Selfridge), both of whom find American crosswords to be almost trivial. I resist explaining the tangled relationship between crosswords, Doubleday, and baseball.

No slight to Shortz intended. What he’s done to the field of Games is wonderful indeed. I resist mentioning that Sir John Suckling invented Cribbage, and had what Isaac Asimov referred to as “the perfect name for a dirty old man.”

I can’t speak to how the NY Times crosswords were arranged back in the Maleska days, but really it’s Friday and Saturday which are the hardest dailies. The Saturday is harder than the (larger) Sunday crossword by at least an order of magnitude.

British crosswords are generally what are called “cryptics” over here. Surely the Sunday puzzle is more or less trivial to inveterate crossword solvers, but I wouldn’t say that American-style crosswords are inherently easier than British-style ones (for it’s possible to construct some real stinkers) — they are simply different. Similarly, one couldn’t say that the Sundays in the Shortz era are necessarily harder or easier than those in the Maleska era; they are just different (the ones edited by Shortz generally contain many more pop references, and hence might prove problematic to those of a certain age).

I love just about any word puzzle, but I’m particularly attracted to acrostics. It’s the dialectic between the grid and clues, and the way the solution can almost bootstrap itself out of sometimes very slender initial data, that gives me a lot of pleasure.

Oh, and Jonathan: you call that resisting? I can’t resist adding that I think it was Groucho Marx who commented on the redundancy of

Peter O’Toole.It goes without saying, and so I won’t.

I resist better since I got married.

My wife, raised as I say on London Times and Edinburgh crosswords does the local Los Angeles Time crosswords rapidly and easily. She commented a few years ago that she’s clearly been in the USA too long, as she had no problem with a TV Guide crossword filled with local celebs and baseball players. She hates baseball, but absorbed a great deal by osmosis.

Speaking of Doubleday/crossword/baseball tangle, I find baseball to be tied with Cricket for the most mathematically fascinating major sport. Google “Pythagorean Theorem of Baseball” for example.

Or these on the OEIS:

A115380 Successive records for the number of home runs scored by a single batter in a single season of (USA) major league baseball.

A121379 Successive records for the number of hits by a single batter in a single season of (USA) major league baseball.

A121403 Decimal expansion of the area of home plate (USA major league baseball) in square inches.

A136407 Valid strings, in lexicographic order, of Balls (“1”) and Strikes (“2”) in a Baseball at bat. Numbers that contain only 1’s and 2’s never exceeding 3 total 2’s or 4 total 1’s, whichever comes first.

Some people have suggested using “translated” — but if I saw that in a crossword I’d assume it was asking for the word for “group” in another language, and I’d try to fit in something like “groupe” (French) or “Gruppe” (German).

Yes — as John said to me privately, “mathematical subgroup, translated” [30 letters] has a kind of cryptic crossword feel to it. I guess you could give the readers a heads-up by sticking a question mark after “translated”, but “coset” is not the kind of light, humorous answer one might expect for that type of clue. So maybe “translate of mathematical subgroup” [31 letters] is preferable in that case.

I think it’s as Todd said earlier: Mark “backed into” a plausible-sounding word, then verified it was a real word. With my son, I’ve recently gotten into the business of crossword construction — to our great delight we’ve sold one puzzle to the Times for an upcoming day — so I’m very sympathetic with the way this happens. The very best constructors miraculously manage to avoid using marginal stuff: obscure or technical words, uncommon abbreviations, unlikely phrases, et al. But for most of us, even in our best efforts there are a handful of such entries.

By the way, there seems to be an affinity between math and crossword puzzle construction. For example, Byron Walden is both a math prof at Santa Clara U. and one of the favorite constructors of those who do the superhard Saturday NYT puzzles.

Congrats, Gary — I’ll keep an eye out. Do you know which day of the week?

Noah Snyder over at Secret Blogging Seminar also evidently enjoys puzzle construction, and also had a puzzle published in the Times.

If any readers are interested in trying their hand at crossword puzzle construction, there’s a downloadable program called Crossword Compiler by Antony Lewis which I think is pretty good. It’s a lot of fun!

Todd, yes we do: Thursday.

Might I suggest ‘Partition of Mathematical Group’.