Or just human ingenuity at finding patterns in ‘random’ data?

 Cropped from source

Bill Clinton was the 42nd President of the United States. He came close to becoming the first First Gentleman—or whatever we will call the husband of a female president. He is also a fan of crossword puzzles, and co-authored with Victor Fleming a puzzle for this past Friday’s New York Times.

Today we discuss an apparently unintended find in his puzzle. It has a Mother’s Day theme.

The puzzle was widely publicized as having a “secret message” or “Easter egg.” Many crossword puzzles have a theme constituted by the longer answers, but the Friday and Saturday NYT puzzles are usually themeless. They are also designed to be the hardest in a progression that begins with a relatively easy Monday puzzle each week. The online renditions are subscriber-only, but the Times opened this puzzle freely to the public, so you are welcome to try to solve it and find the “hidden” content before we give it away.

## Hidden or Hiding?

In a previous post we featured Margaret Farrar, the famous first crossword editor for the Times, and described how the puzzles look and work. Proper nouns such as CHILE the country, standard abbreviations, and whole phrases are fair game as answers, and they are rammed together without spaces or punctuation. For instance, the clue “Assistance for returning W.W. II vets” in Clinton’s puzzle produces the answer GIBILL. (My own father, returning from the occupation of Japan, completed his college degree under the G.I. Bill.) Some clues are fill-in-the-blank, such as “Asia’s ____ Sea” in the puzzle.

The intended hidden message is formed from three long answers symmetrically placed around the puzzle’s center. It is the signature line from a 1977 Fleetwood Mac song that Clinton has used since his 1992 presidential campaign. If you expected the puzzle to have a theme, these three lines would obviously be it.

An “Easter egg” is a side feature, usually small and local and often, as Wikipedia says, an inside joke. When I printed and did the puzzle over lunch on Friday, I missed the intended content because it wasn’t the kind I was looking for. But I did find something one can call an “Eester gee” involving the three shorter clues and answers mentioned above:

My eye had been drawn by finding Bill in his own puzzle. Winding through him is HILLAREE, indeed in three different ways but with EE in place of Y. Straining harder, one can extract CHEL- from CHILE and get -Sea from the clue for ARAL just underneath to find Chelsea, the Clintons’ only daughter.

Admittedly this is both stilted and cryptic, but it is singularly tied to the former First Family and appropriate just before Mother’s Day. Was this hidden by intent, or was it hiding by accident? Presuming the latter, what does this say about the frequency with which we can find unintended patterns? This matters not only to some historical controversies but also to cases of alleged plagiarism of writing and software code, even this investigation over song lyrics being planted in testimony.

## Where to Draw the Line?

Can we possibly judge the accidental frequency of such subjective patterns? Clinton’s puzzle allows us to experiment a little further. His only grandchild, Chelsea’s daughter, is named Charlotte. Can we find her in the same place?

Right away, CHILE and ARAL give us CHAR in a square, a promising start. There are Ls nearby, but no O. Nothing like “Lenya” or a ‘Phantom‘ reference is there to clue LOTTE. The THREE in our grid is followed by TON to answer the clue, “Like some heavy-duty trucks,” but getting the last four needed letters from there lacks even the veneer of defense of my using the I in CHILE as a connector. Is three tons a “lot”? No doting grandpa would foist that on a child. So we must reject the hypothesis that she is present.

We can attack the CHILE weakness in a similar manner. The puzzle design could have used CHELL, the player character of the classic video game Portal. HILLAREE would still have survived by using the I in Bill. However, the final L would have come below the N in the main-theme word THINKING, and it is hard to find natural answer words ending in NL. So our configuration has enough local optimality to preserve the contention that Chelsea is naturally present. Whether it is truly natural remains dubious, but it dodges this shot at refutation.

Going back, how should we regard the false-start on Charlotte? We should not be surprised that it got started. That she shares the first two letters with Chelsea may have been “correlated” if not expressly purposeful. Such correlations are a major hard-to-handle factor in cases of suspected plagiarism or illicit signaling, as both Dick and I can attest generally from experience.

## Some Historical Crypto

Of course, this is more the stuff of potboilers and conspiracy theories than serious research. That hasn’t stopped it from commanding the input of some of our peers, however. The best-selling 1997 book The Bible Code, following a 1994 paper, alleges that sequences of Hebrew letters at fixed-jump intervals in the Torah—the first five books of the Hebrew Bible—form sensible prophetic messages to a degree far beyond statistical expectation.

The fact that Hebrew skips many vowels helps in forming patterns. For instance, arranging the start of Genesis into a 50-column crossword yields TORaH in column 6, and as Wikipedia notes here, exactly the same happens in column 8 at the start of Exodus. Even just among the consonants, some alleged messages have glitches and skips like ours with HILLAREE and CHILE. Where is the line between patching-and-fudging and true statistical surprise? Our friend Gil Kalai was one of four authors of a 1999 paper delving deep into the murk. They didn’t just critique the 1994 paper, they conducted various experiments. Some were akin to ours above with CHARLOTTE, some could be like trying to find unsavory Clinton associations in the same puzzle, and the largest was replicating many of the same kind of finds in a Hebrew text of War and Peace.

The controversy over the genesis of William Shakespeare’s plays has notoriously involved allegedly hidden messages, most famously stemming from the 1888 book The Great Cryptogram supporting Francis Bacon as their true author. Two other major claimants, Edward de Vere (the seventeenth Earl of Oxford) and Christopher Marlowe, are hardly left out. Indeed, they both get crossword finds in the most prominent place of all, the inscription on Shakespeare’s funerary monument in Stratford, England:

The inscription is singular in challenging the “passenger” (passer-by) to “read” who is embodied within the Shakespeare monument. His tomb proper is nearby in the ground. Supporters of de Vere arrange the six parts of the Latin preface into a crossword and find their man in column 2:

The leftover OL is a blemish but it might not be wasted—it could refer to “Lord Oxford” in like manner to how “Mr. W.H.” in the dedication to Shake-speares Sonnets plausibly refers to Henry Wriothesley, the Earl of Southampton, who was entreated to marry one of Oxford’s daughters throughout 1590–1593.

Supporters of Marlowe volley back in the style of a British not American crossword. Their answer constructs this part of the inscription as a cryptic-crossword clue:

Whose name doth deck this tomb, far more, then cost.

The only name on Shakespeare’s tomb is Jesus, and the Oxford English Dictionary registers ley as an old word for a bill or tax, generically a cost. The answer to the monument’s riddle thus becomes CHRISTO-FAR MORE-LEY, which is within the convex hull of how Marlowe’s name was spelled in his lifetime. The subsequent SIEH, which is most simply explained as a typo for SITH meaning “Truly,” is constructed by modern cryptic-crossword convention as “HE IS returned,” in line with theories that Marlowe’s 1593 murder was actually staged to put him under deep cover in the Queen’s secret service.

What to make of these two readings? The only solid answer Dick and I have is the same as when we are sent a claimed proof of ${\mathsf{P \neq NP}}$ one week and one of ${\mathsf{P = NP}}$ the next:

They can’t both be right.

Or—considering that Marlowe has recently been credited as a co-author of Shakespeare’s Henry VI cycle, and that William Stanley, who completes Wikipedia’s featured quartet of claimants, wound up marrying the above-mentioned daughter of Oxford—perhaps they can.

## Open Problems

Where do you draw the lines among commission, coincidence, and contrivance? Where does my Clinton crossword finding fall?

Happy Mother’s Day to you and yours as well.

[fixed description of Chell character, “seventh”->”seventeenth”, added ref. to song-lyrics case, some wording tweaks]

1. May 15, 2017 2:40 am

Type One or Type Two or Just Plain Typo? — Ay❢ That Is The Question❢

• May 15, 2017 8:12 am

Actually, taking a cue from column 3 of the “Vere” crossword and the Bible code’s treatment of vowels, the answer may be that these patterns somehow have “de-entropy.”

• May 15, 2017 9:08 am

error correcting codes must err
else nature evolution ere deter

• May 15, 2017 9:40 am

(or maybe this way —)

error correcting coding must err
else nature evolution e’er deter