Lewis Carroll's chess problem

One of the strangest books I've ever read is Bach en het Getal (Bach and the Number) by the Dutch authors Kees van Houten en Marinus Kasbergen. The main thesis of the book is that within the music of the great composer J.S. Bach, various messages, numerological clues and strange links hide just behind the surface. A recent article on the chess problem of Lewis Carroll that appeared on Susan Polgar's weblog reminded me of this curious book on Bach.

By Arne Moll

Of course, there are countless books on numerology and esoterics. What's the big deal? After all, who hasn't enjoyed The Da Vinci Code or Foucault's Pendulum? But there's a difference. Dan Brown and Umberto Eco wrote fiction. The books on Bach and Carroll, on the other hand, are very serious indeed. In my opinion, this is surprising. I can barely understand musicians being fooled by bad research, logical fallacies, circular reasonings and wishful thinking, but chess players? Surely they would know better?

The problem

This month, on the 4th of July to be precise, Lewis Carroll fans around the world celebrate the 146th birthday of their favourite story, for that was the day on which the then thirty year old Charles Lutwidge Dodgson (the author's real name) invented a curious story for the entertainment of three little girls, Lorina, Edith and Alice Liddell, on a boat trip near Oxford. Three years later, the story that was to make its author immortal, was published under its current name: Alice's Adventures in Wonderland (1865). In 1871, Carroll wrote an equally brilliant sequel to the story: Through the Looking-Glass and What Alice Found There.

Don't worry, I'm not going to babble at length about my love for Lewis Carroll, my visits to Oxford and Guildford or my Alice collection, however dear these subjects are to me. Chess is one of many themes in Through the Looking-Glass. In the story, Alice enters a giant chess board and meets several chess pieces. She is a White pawn herself, and she will become a Queen by the end of the story. The book even opens with a 'chess problem' and a real diagram. Here it is:



And so, in the chess problem, the story of the book is 'told' by the chess moves of 'Red' and 'White'. As many have noted, the chess problem is seriously flawed from a chess player's perspective. The problem has 10 moves, but Black and 'Red' moves don't alternate, as Carroll himself admits in his preface to the 1897 edition:

The alternation of [the moves] is perhaps not so strictly observed as it might be, and the 'castling' of the three Queens is merely a way of saying that they entered the palace: but the 'check' of the White King at move 6, the capture of the Red Knight at move 7, and the final 'checkmate' of the Red King will be found [...] to be strictly in accordance with the laws of chess.

In earlier editions, Carroll had added a dramatis personae to the problem, in which all 32 pieces of the game were linked to characters in the story, but it created only confusion, and in 1897 (a year before his death) Carroll replaced it with the current preface and that seemed to be the end of it.

But of course, it wasn't. Lewis Carroll and the Alice books have always been an extremely rich source for interpretation, whether sensible or not, and the chess problem proved no different. The problem was discussed in 1910 in British Chess Magazine, and in it, an entire alternative game was composed by Donald M. Liddell (not related to Alice!). The mathematician Martin Gardner dedicates several pages to the problem in his highly recommended The Annotated Alice.

Anatoly Karpov and a mysterious project

The article on Polgar's site mentions a meeting in Lyon, France, on June 26 between former World Champion Anatoly Karpov, the artist Max Schoendorff and a Frenchman named Christophe Leroy.

Anatoly Karpov and Lewis Carroll? Okay, I figured one of these French guys probably knew Karpov personally, and invited him for dinner and a light discussion with a good glass of wine. But I did wonder what this 'mysterious chess game' was all about. I was in for another surprise, because it turned out Leroy has written an entire website on Carroll's chess problem! The press release also published an English version of an article by Leroy on the problem. Now I was genuinely fascinated: could it really be true that an entirely new light had been thrown on this 137 year old chess problem?

To start with, the website mentioned in the press release (in French) is itself rather mysterious. There's some artwork, some photos of coloured chess pieces, and a lot of articles, press releases, and even diagrams, but no clear introduction or a project 'mission'. I looked around on the website a bit, and got the impression the site was made as a teaser to support a book by Leroy about the subject. But was it? The tone of voice of some articles seemed to be a bit tongue-in-cheek, as is the tone of the article mentioned in the press release. For instance, it says that Leroy is 'bewitched'. It made me wonder if the whole project was perhaps just a joke or a parody, rather than a mystery.

I decided to send an e-mail to the English translator of the article, Sylvain Ravot, to ask what it was all about. Were these guys serious? It turned out they were. Ravot e-mailed back:

The only thing I can say in this first and quick answer is that the whole project is very serious.

That was clear enough. And the article itself, too, is rather serious:

In December 2006, 70% of the game were decoded. Convinced that this game was really poetic and deserved to be known and recognized, Christophe claimed: ?¢‚Ǩ?ìI consider it as part of the 'world literary inheritance' with the feeling to have finally found a precious text of the English author ?¢‚Ǩ¬¶"

The enchanting power of numbers

Well, however charming Leroy's enthusiasm, however well-promoted his book, however intriguing his thesis, I beg to disagree. The problem with his article and the whole project is the same problem that Bach and the Number suffers from. Both rely on weak interpretation, factual inaccuracies, wishful thinking and a highly naive belief in the power of numbers. For example, Leroy notes that 42 was Lewis Carroll's favorite number. And he's absolutely right, it was. But he then goes on to suggest that, among other things:

• Carroll lived in Christ Church, Oxford, on number 6, where people could only access it through the 7th stairs, so that 6x7 = 42!
• Carroll died in 1898 because he met Alice Liddell in 1856 (98-56=42!)
• Carroll quit photography in 1880 because he met Alice Liddell in 1856 (80-56=24!)

And these are only three of dozens of "hidden, impressive signatures" within the chess problem. We're actually supposed to believe Carroll choose his own year of death to give us, dear readers, a clue to the solution of his chess problem.

By the way, in Bach and the Number, similarly remarkable conclusions are reached. Bach knew his exact date of death and hid it in some of his works. The authors even calculate the exact number of days Bach has lived (23869) and derive all sorts of wonderful conclusions from it. I won't go too deeply into all this, but interested readers can read a discussion on the book here. It reminded me a lot of some discussions on the existence of Atlantis or aliens. Like words, numbers can mean anything, as Humpty Dumpty would be the first to point out. I, for one, prefer Alice's point of view:

"The question is," said Alice, "whether you can make words mean so many things."

Anyway, why should we multiply numbers in one case, and do subtraction or addition in another? But okay, perhaps these calculations were just a joke...?

Another remarkable discovery is the fact that Lewis Carroll hid his initials (LC) in the chess problem. Now why would he do that anyway? And wouldn't he rather have put his real initials (CLD) in a problem that says something about his private life? But wait, let's not start asking thorny questions yet. Take a look at the diagram again. Don't we see a C-shape in the pieces on the bottom on the diagram: c1,d2, e2, f1? Never mind the C is rotated 90 degrees - we can't be too picky in these matters. Now we're going to find the L. That's a little more difficult, but with enough will-power, we'll manage. Draw a line from the White King on c6 down to the Black King on e4, then go up to the Knight on f5. c6-e4-f5, there you go! It sure looks more like a V-shape to me, but according to Leroy, it's an L allright. And by the way, that pawn on d2, that's Alice, right? Well, notice she's on the fourth (d) file, on the second rank. 4 and 2, makes 42, you see? (Apparently, sometimes we shouldn't multiply or subtract numbers, but just put them behind each other, and the meaning will magically appear!)

The message

So what is the meaning, this hidden message of Carroll? The article says:

After many unsuccessful studies, everything appeared clear overnight: Christophe [Leroy] understood that each piece was actually a living person during Carroll's life.

Leroy then goes on to link not only Alice to the White Pawn on d2 (which is correct), but the White Knight to "a messenger sent by Lewis Carroll, trying to become Alice's dearest knight", the White King to Alice's father, the White Queen to Alice's mother, and the Red Queen to nobody else but Queen Victoria. Oh, and the Red Knight embodies Charles Dodgson. (Note that Leroy mixes Carroll and Dodgson all the time, without explaining why.)

Leroy assumes (as many have done before him) that Carroll wanted to marry young Alice and proposed to her or her parents. In recent years, however, this theory has become under a heavy cloud. Leroy doesn't seem to know this, and is happy to use the old assumption for his own theory:

Indeed, this sacrifice (he is taken by the white Knight: his double) permits him to do another proposal but with new clothes ... White clothes, symbol of marriage ...

So, Carroll hid the fact that he proposed to Alice within the problem. He may never have written anything about it in any of his thousands of letters, or in his books, or even in his diaries, but, by God, did he make it crystal clear in his nonsense problem!

Unfotunately, and needless to say, the whole 'identification' is flawed. For one, Carroll intended himself to be the White Knight, not the Red one, as was proven by Jeffrey Stern in 1990 ["Carroll Indentifies Himself At Last", Jabberwocky Summer/Autumn 1990]. What Queen Victoria has to do with all this, is utterly unclear.

All sorts of problems Enough already! The article suffers from more general problems than the ones I mentioned above. Since we're still assuming the theory is meant to be scientific or at least scholarly, here are a few of the most obvious questions that come to mind:

• Can the theory be falsified? Since neither Carroll nor anyone else ever mentioned a possible hidden solution, by what criteria could we ever say, 'okay, this definitely disproves the theory'?
• Can the theory be tested?
• Can the theory be accepted by someone who disagrees over the fact (such as that Carroll proposed to Alice)? Or does it take 'faith'?
• Why doesn't Occam's Razor apply to the theory?
• Is there a method by which we can reproduce the 'message' or 'meaning' of the chess problem? Or was the solution found by intuition only?
• What does it mean that by 2006, "70% of the game was decoded"? Which 70%? And what was the other 30%? How was the final 30% found? What, in fact, is the code of the game exactly?

Finally, and most importantly, the theory totally lacks facts to back it up. Carroll never wrote about a possible hidden message, not did Alice herself or anyone else. Also, as the 'dramatis personae' from earlier editions shows, Carroll originally intended charcters from the book to resprest the pieces in the problem, not real life persons. As I wrote to Sylvain Ravot:

In my opinion, this fact alone disproves the theory of mr. Leroy, unless he can actually show that Carroll wrote it as a 'decoy' to distract attention from the 'real meaning'.

So far, I have not received an answer.

This can only mean one thing: the project is a joke after all. It has to be. No chess player (and mr. Leroy is a 2200 player who plays for several French clubs) could ever believe this theory. It's a charming, innocent joke, an artistic hoax in the spirit of the great dadaist Marcel Duchamp, who was also a chess player. Let's hope it is. I leave it to the readers to decide whether they like the joke.

Yes, Carroll liked to invent puzzles, but he was not a cryptologist. Yes, he liked riddles, but he was not obsessed with it. He probably was something of a chess enthusiast, but he didn't know much about the game. Yes, he was a romantic, and he was fascinated by young Alice Liddell, but he didn't leave a desperate secret message of failed marriage and love for her in a chess problem. And Christopher Leroy and Sylvain Ravot must surely know this.

What if their not joking, though? We'll be sure to hear more of it. Lack of evidence has never stopped astrologists, Atlantis mysticists or people who believe aliens control the U.S. government. And a book that claims Bach was even more obsessed by numbers than by fugues, can even be found in the best music store in The Netherlands, on the same shelf as the highly serious Interpreting Bach on the Keyboard by Paul Badura Skoda.

But serious interpretations will always be less popular than mysterious ones.