The value of five-finger exercises and pawn endings
One of the things I disliked most in my childhood was piano practice. Not that I disliked playing the piano; in fact, I spent quite a lot of time sitting at the piano and playing things through. But I did very little practising. Playing scales, or other keyboard exercises, were things I almost never did. Partly, this was because my piano teacher (whom I liked very much and to whom I owe a great deal) did not teach me how to practise, nor explained to me why practising is important, and how it differs from playing pieces through and hoping that by repetition you will play them better.
Much the same was true of my early experiences of playing chess. I learned the moves from my father; I played at a club at school and later for a club in the local league; but all I ever did was play games. I did try to memorise some common opening moves (which I found very difficult to do beyond the second or third move), but no-one ever suggested to me that playing chess might be a skill that required practising.
The proverb, “Practice makes perfect” therefore intrigues me. What exactly is practice? Is it just playing a piece on the piano again and again, or playing games of chess as often as possible, with the hope in both cases that improvement will be the inevitable result? Or is there more to it than that? Equally, what does it mean to play music, or to play chess, “perfectly”? Is that even possible? And will it result from proper practice?
My attitude to piano practice changed abruptly and forever when I was sent to a new teacher as part of starting my music studies at university. That teacher was Phyllis Palmer, who is something of a legend amongst those who ever studied with her. At my first lesson, she told me that the piece I played to demonstrate my standard was badly chosen, my posture was dreadful, and my technique was poor. She also introduced me to a book of piano exercises, recommending I try the easiest two. “These,” she remarked, “are what a professional would use for the whole of their career.”
What do you do when you practise?
Here is one of those piano exercises by Dohnányi to which the redoubtable Phyllis Palmer introduced me:
When I first saw this, it looked trivially easy. You put your five fingers on the five white notes C, D, E, F and G, and only use one hand (to begin with; you add the other hand, an octave lower, later). You keep one note depressed while you play the others. The pattern changes by one note in each bar until it repeats itself. Easy.
Then I tried playing it. I couldn’t.
Nowadays, I often start a practice session with this exercise, which trains your fingers to move independently, and makes them stronger. It is an exercise that shows the value of practising.
Now here is a chess position to which, a year or two earlier, an older member of my chess club introduced me:
“What do you think of this position?” He asked me. “It’s Black to move.”
“It looks like a dead draw,” I replied.
“Quite right. Try and play it out.”
Since Black’s king can’t go forwards, I moved it one square backwards. “Ah!” said the older player who then, in a few more moves, forced my king into the corner, took all Black’s pawns, and won.
The position should indeed be a draw. But of Black’s five legal moves, four lose. It is a position which shows the value of practising.
Five-finger exercises and pawn endings
There is an affinity between five-finger exercises and pawn endings like the ones above. They enable you to develop the kind of ability which underlies much more complex tasks, which however cannot be attempted unless the “practice” task is completely mastered.
The piano exercise by Dohnányi is not a great piece of music, but if you can play it perfectly, then your fingers will be able to attempt the counterpoint of a Bach fugue or the figuration of a Chopin Étude. Equally, the pawn ending is not a great game of chess; but if you know how to draw and not lose the ending, you will be able to tread a path through real, tricky endgames.
Both kinds of exercise look deceptively simple. The first bar of the Dohnanyi exercise is fairly easy, in fact; the second bar is a lot harder, and the third bar really takes practising. Pawn endings share this deceptive quality. Here is an apparently symmetrical, equal position; White is to move. It is a win for White.
On the other hand, if the kings are anywhere except in the corners, the result is different:
White to move. A draw.
White to move. Another draw.
And here is a similar position where, if White is to move then White will win, while if Black is to move then Black can draw:
How do you practise?
Now that I am no longer a child, and thanks to Phyllis Palmer’s accurate assessment of my weaknesses, I enjoy practising the piano. A regime of Dohnányi’s A Legfontosabb Ujjgyakorlatok [Essential Finger Exercises] and Bach’s immensely beautiful, immensely tricky 48 Preludes and Fugues (Book 1 in odd-numbered years, Book 2 in even-numbered years) will keep me happy for the rest of my life, I should think.
Practising chess technique used to be more laborious, requiring books of puzzles, endgame studies, and the like, as well as a board and pieces (unless you could play blindfold, which I cannot). That, however, has been entirely changed by the internet. Nowadays, a regime of practising using an internet chess site is a direct parallel to practising a musical instrument. The examples above were endgame puzzles; here is an example from Chess.com’s training website, where you need to remember basic pawn technique to win an ending that looks as if it comes from a real-life chess game:
I try to practise every day. Like Schumann, I try to make Bach my “daily bread”. In chess, I am still very poor at endgames, partly because I prefer to practise tactical puzzles which reinforce the kind of pattern recognition I waxed lyrical about in Creating patterns.
I certainly don’t manage to practise the piano every day, but I do usually manage to practise chess tactics (which takes a lot less time). And in both realms, there is no doubt that my technique has become a lot more secure.
So, does practice make perfect?
No, of course it doesn’t. At least, not in the sense that I will ever become a pianist to rival András Schiff or a chess player to rival Magnus Carlsen. However, what practice can perfect is that underlying technique that can allow you to aspire at least to competence. Ninety-nine times out of a hundred I can play that Dohnányi exercise as well as anyone; and ninety-nine times out of a hundred I can draw a drawn pawn endgame, or win a won pawn endgame. It is practice that enables me to stop worrying about the routine business of playing the right notes or choosing reasonable moves, and get on with the rewarding business of interpreting great music or formulating chess strategy. But in both contexts, that is true only if I keep practising, daily if possible.
Even a professional pianist or a professional chess player has to practise – in fact, professionals practise an awful lot more than I do or could. It was Phyllis Palmer herself who first gave me that well-worn adage: “An amateur practises until they can get it right. A professional practises until they can’t get it wrong.”
The number of novels that centre on the game of chess is small, but it does include works by some significant authors. I have already traced the role of music in Nabokov’s chess novel, The Luzhin Defense. Perhaps the most-discussed chess novel is Stefan Zweig’s Schachnovelle, translated as The Royal Game and, more simply, Chess. Zweig’s novella does not allot a large role to music, which is perhaps surprising, since Zweig grew up and lived in Vienna from the 1880s until his exile in the 1930s. Zweig was a librettist for the composer Richard Strauss, and possessed a large collection of music manuscripts, including Mozart’s handwritten catalogue of his own works. It is clear from Zweig’s autobiography The World of Yesterday, however, that for him, the music of Vienna was equated with the culture destroyed by the advance of National Socialism. His Schachnovelle, written in 1941, is among other things a protest against the philistinism of modern Europe in which music can no longer sound. Shortly after completing it, Zweig and his wife committed suicide.
So once again my exploration of music, chess and their common themes leads me back to the Vienna of the fin-de-siècle. And this is also the setting of the novel on which this post focuses, Carl Haffner’s Love of the Draw, published in 1998 by the contemporary Austrian author Thomas Glavinic. It is a short novel, and well worth reading. I advise you to get a copy if you have read this far into this blog post. It is also a straightforwardly historical novel, based on one of the most notable matches ever played for the chess world championship.
The match in question was between Carl Schlechter (1874-1918), one of the the strongest players of his day, and Emanuel Lasker (1868-1941), the second World Chess Champion. The match took place in 1910. It was a ten-game match, with the first five games played in Vienna, where Schlechter was born and lived, and the second five in Berlin, Lasker’s home city.
The match was tied, and according to the rules agreed before its start, Lasker retained the title. Lasker was extremely fortunate: Schlechter led 1-0 at the half-way point of the match, and Lasker only managed to achieve the tie by winning the last game, in which Schlechter first had the advantage, and then mis-played a drawn position. Few would doubt that Schlechter was the one player who seriously rivalled Lasker’s status as World Champion in the twenty-seven years that he held the title between defeating Wilhelm Steinitz in 1894 and losing to José Raul Capablanca in 1921.
Schlechter had only one weakness as a player, which was his tendency to accept offers of a draw. From that stems the title of Glavinic’s novel.
Music in the names
One might wonder why Glavinic decided to rename the protagonist of the novel “Carl Haffner” rather than “Carl Schlechter”. “Schlechter”, after all, could be a motivated name, since it means “worse” in German. Nearly all the characters based on historical people appear in propria persona: Emanuel Lasker, of course, along with famous players of the day such as Janowski, Marshall and Tarrasch; but in the first chapter we meet Carl Haffner’s clubmates, the lesser-known chess masters Max Weiss and Hugo Fähndrich, and all the members of the Vienna Chess Club seem to appear under their own names.
There are just two characters based on real people whose names have been changed. One is Haffner himself, of course, and the other is the first person we meet in the book, Georg Hummel, the chess correspondent of the Neue Freie Presse, editor of the Wiener Schachzeitung and a notable chess player in his own right. Hummel is based on Georg Marco (1863-1923), who was indeed one of the strongest players in the world in the 1890s, and whose match with Carl Schlechter in 1893 marked the beginning of Schlechter’s international recognition. The ten-game match finished with every game drawn.
Glavinic, then, has chosen to rename two characters, presumably because his fictionalised versions of them depart from what is known of their historical counterparts (although as far as I can discover, we know remarkably little about either Schlechter or Marco). What is notable, though, is that both the names he uses have musical resonances. The name Haffner suggests two works by Mozart: the “Haffner Serenade” and the “Haffner Symphony”. Both were written for Mozart’s friend and contemporary, the Salzburg aristocrat Sigmund Haffner. And the name Hummel suggests Johann Hummel (1778-1837) the composer and virtuoso pianist of much the same period as Mozart. Mozart lived in Vienna; the Haffner Symphony was premiered there. Hummel worked in Vienna, as Director of the Imperial Military Music School.
Music, then, is in the background of the novel – in what literary critics might call its intertext. Or perhaps Glavinic’s choice of fictional names is pure coincidence, plucked out of his Viennese subconscious.
The suggestion of a musical as well as a Viennese background to the novel becomes stronger, however, when the role of music in the narrative is considered.
Music in the background
It would be an exaggeration to say that music plays a central role in Glavinic’s novel. However, the role it does play is significant. Glavinic renames his protagonist so that Carl Haffner can have a fictional family background and fictional formative experiences. Chapters narrating his Bildung alternate with those narrating the chess world championship, which are simply an imaginative re-telling of the Schlechter / Lasker match.
There are three family members who together define Carl’s personality, and music plays a significant part in all three relationships.
The successful grandfather
Carl’s grandfather Rudolph is a comic playwright whose greatest opportunity was being invited to write the libretto for Johann Strauss II’s operetta Die Fledermaus. He flunks the chance: “Failing to grasp the importance of his task, he supplied Strauss with a poor, half-hearted piece of work.” Glavinic is adapting history here: the libretto for Die Fledermaus, to this day the most popular operetta of all time, was in fact written by a real Carl (not Rudolph) Haffner, who was indeed a well-known comic playwright. And the writer credited as the lesser co-author of the libretto, Richard Genée, later claimed that he had to completely rewrite the original text and that he had never even met Haffner.
The Rudolph Haffner of Glavinic’s novel, although successful, fails to understand the significance of music, as the incident with Die Fledermaus demonstrates. He forces his son Adalbert to learn the violin, which Adalbert detests. Adalbert (the fictional Carl’s father) becomes completely alienated by his father, and leaves home on his twenty-first birthday with the words “I’m off to play some music”. He then earns his living by playing the violin in Viennese wine gardens. He marries, without telling his father, and Carl is born.
The drunken father
Adalbert is a violent drunk who does not love his wife and hardly provides for his family. Eventually, he elopes with a barmaid, produces a half-sister for Carl and dies in poverty. His abandonment of his wife and child, the most significant and traumatic event of Carl’s childhood, is narrated as the meeting-point of (reader, you guessed it) music and chess:
On the evening after that eventful night [when he decided to leave his family], Adalbert took out his fiddle and played it in one of the wine gardens where he was still welcome. Although completely out of practice, he soon got into his stride because he wanted to play. Not the cloying taproom melodies he detested so heartily, but classical music of a wild and passionate nature. He played as if possessed by the devil. No one in the establishment had ever heard the like.
The next day, with Carl’s hand in his and the money he had earned in his pocket, he called on Samuel Gold, who ran a bookshop not far from the Gasthaus zum Hirschen. He put some coins on the counter and told the bookseller, without more ado, that the money was all he had. It would have to suffice to equip Carl with a chessboard, a set of chessmen to go with it, and the principal textbooks on playing the game.
(Carl Haffner’s Love of the Draw, p. 70)
Samuel Gold, incidentally, is a real historical personage: he was a composer of chess problems who in 1887 became the thirteen-year-old Carl Schlechter’s first (and only) chess tutor.
The loving half-sister
Finally, there is Lina Bauer, Carl’s half-sister (the product of Adalbert’s elopement) and the person Carl seems to care about more than any other. He spends the evening before the match with Lasker with her, when “She played his favourite piece on the piano before he left.” And when the match moves to Berlin for its second half, he again spends the evening before his departure with Lina:
After they had a snack lunch together, she sat down at the piano. […] He didn’t know why, but he felt nothing for any woman, apart from the one who was playing his favourite tune at that moment.
(Carl Haffner’s Love of the Draw, p. 88)
The piano that Lina plays is itself an emblem of Carl’s love for her:
Carl watched Lina grow up with warm-hearted affection. When he asked her what she wanted most of all, she confessed that she dreamed of playing the piano. Carl paid for her piano lessons. Meantime, he scrimped and saved until he had amassed enough money for a second-hand concert grand. He did not mind limiting himself to one meal a day and wearing a thin, threadbare jacket in winter. The day on which the piano was delivered meant more to him than any victory ceremony.
(Carl Haffner’s Love of the Draw, p. 138)
Music runs, then, as a background to the story of three generations of the Haffner family. It is also just about the only activity that interests Carl other than chess. The evening before the final game of the match, which Carl has only to draw to become World Champion, he spends in the smoking-room of his hotel:
Carl’s attention was focused on a figure in a black tailcoat. A lean, angular man of melancholy mien, he went over to the piano and bowed. Carl, who knew the cheerful piece he proceeded to play, listened spellbound. […] Carl’s excited reflections on the world championship were challenged, and eventually defeated, by the music.
(Carl Haffner’s Love of the Draw, pp. 146-47)
What is the music doing?
I do not know whether Thomas Glavinic is a musician. He is certainly a good chess player, as his entry in the FIDE international database of chess players proves.
He does not describe the games between Haffner and Lasker, as they are played, by using musical metaphors (unlike Nabokov). However, music is the inescapable subtext of the entire book. There is a kind of counterpoint between chess and music which sets in relief questions such as playing for love or playing for money; performing because others require it or because you are driven to perform; dedicating your life, with significant personal sacrifice, to an activity that is not ultimately productive of anything except beauty. These questions define the life of Carl Haffner, as they apply to chess; they also define the lives of his father, and to some extent his grandfather and half-sister, as they apply to music. Perhaps Schlechter’s unsuccessful bid to become World Champion was the most musical moment of chess history.
It is now a year since I began this blog, so I thought it was time that I thanked everyone who has taken the time to read any of the posts which have been appearing at the rate of about one per month (this is in fact the fourteenth).
I was asked recently whom I thought I was writing for. It was (and is) a very difficult question to answer. The truth is that I write these posts for myself, of course. I remain fascinated by the connections between the human activities of chess and music, and I am sure I shall remain so.
What has been gratifying, though, has been the discovery that others share my fascination – enough to read this blog, at least. In the twelve months that I have been posting, more than 500 visitors have paid this site a visit. More surprisingly to me, the site has been viewed from a total of 55 different countries across the world. Most of you come from the UK or the USA, of course; but this is my opportunity to hail whoever you are from Estonia, Honduras, Kenya, Palau and elsewhere who have stumbled across this blog at least once.
I do know some of my readers, who are club-mates from Cowley Chess Club, colleagues from The Open University (which has had an extremely eventful year since this blog started, although I would not claim any causation either way), and friends prepared to indulge me. But I have also made friends through writing here: I suspect that Greece features high up in the list of countries where the blog has been read mainly because I have come to know Achilles Zographos since his excellent book was recommended to me. If you haven’t read his book, at least read my book review: Music and Chess (Achilleas Zographos). And I have become at least a Facebook friend of Richard James, whose book with Mike Fox, The Even More Complete Chess Addict, and whose own chess and music posts remain constant sources of inspiration.
Finally, as I begin a second year of these blog posts, I do want to reassure my readers that I haven’t exhausted my topic. I am rather well aware that it has been quite some time since I last posted (when I answered the question Did Beethoven play chess?). Partly this has been due to the demands of earning a living during troubled times for my employer; partly it has been because the post on which I have been working for some time, a return to the Vienna of the early twentieth century and Arnold Schoenberg, has led me down paths I did not suspect and which have taken time to pursue (including attempting to translate a lengthy academic article written in German). But rest assured that my thoughts on Schoenberg will appear before long, and that I have plenty more musico-caissic topics to write up.
I want to answer the question, “Did Beethoven play chess?” because several people claim that he did. I remarked on this fact in my Book review: Music and Chess (Achilleas Zographos), where Beethoven is listed as one of the many chess-playing musicians of history.
Now, I am not an expert on Beethoven’s biography; I learned my lesson there when I speculated on the genesis of one of his works in a research paper, and discovered that a pre-eminent Beethoven scholar was in the audience. And I would love it if Beethoven turned out to have been a devotee of the Royal Game; Viennese classical music is under-represented on that score. Mozart’s favoured game was billiards; Haydn was not (as far as I know) among the ranks of chess-playing composers. Any excitement at finding the chess games of F. Schubert in book indexes is dispelled by learning that František Schubert was a Czech chess master who once beat Richard Réti, but was no relation of Franz Schubert.
There is no reason why Beethoven might not have played chess, after all: the first chess book in German was published in 1795 by a Viennese contemporary of his; the chess-playing automaton known as “The Turk” was one of the wonders of the age; Napoleon himself (whom Beethoven admired for a long time, although he lost faith in him when Napoleon became a dictator as self-declared Emperor) certainly was a keen chess player.
Tracing the evidence
I had, however, never come across any evidence that Beethoven even knew the moves of the game, let alone took a serious interest in it. And so I was fascinated to see him in the list of names in Achilleas Zographos’s recent book. When I expressed some dismay in my review at the lack of evidence presented to support his inclusion, the author himself paid me the courtesy of a reply, and made two helpful suggestions: one was to consult a book I should have thought of myself, The Even More Complete Chess Addict by Mike Fox and Richard James (which I have mentioned many a time in earlier posts), and other was to take a closer look at footnote 18 on page 26 of Music and Chess: Apollo meets Caïssa.
Turning to Fox & James first, they too ascribe a love of chess to Beethoven. But they are quite circumspect about it:
Jostling for a place among the reserves [of a fantasy musicians’ chess team] would be Schumann […] Mendelssohn […] Richard Strauss [… twenty other musicians are listed]. And, according to The Polish History of Chess, Chopin and Beethoven.(Fox & James, p. 33)
So they give a single source, which is another book rather than any primary evidence from Beethoven’s letters and so forth. After some further exploration, I identified “The Polish History of Chess” as Z Szachami Przez Wieki I Kraje (Jerzy Gizycki, Warszawa 1984). Courtesy of the Bodleian Library, I summoned it up and discovered that Fox & James were quite right: Beethoven and Chopin are both mentioned. But they are only mentioned once. Here is the paragraph, together with what I, Google Translate, and my good friend Geoff Chew (a musician who really does speak Polish) made of it:
Wielu szachistów można snaleźć pośród muzyków. Kompozytorem był słynny szachista francuski Philidor. Królewską grę znał Beethoven i Chopin. W posiadaniu doktora Jerzego Goreckiego, prawnuka Mickiewicza, znajdował się zabytkowy okrąkły stolik drewniany w naturalnym czerwonym kolorze, na którym, według jego oświadwicz i Fryderyk Chopin (od 1978 roku w zbiorach Museum Literatury w Warszawie).
Many chess players can be found among musicians. The famous French chess player Philidor was a composer. The royal game was known by Beethoven and Chopin. Dr. Jerzy Gorecki, great-grandson of Mickiewicz, possessed an old, round, wooden chess table in a natural red colour, on which Mickiewicz was said to have played Fryderyk Chopin (since 1978 in the collection of the Museum of Literature in Warsaw).
(Gizycki, p. 228)
This doesn’t get us much further. There is real anecdotal evidence given that Chopin played chess at least once with the poet Mickiewicz (whose lyrics he set to music), but nothing more than another bald assertion that Beethoven was a chess enthusiast.
So that left me with Achilleas Zographos’s footnote. Here it is:
The main sources for this list are the articles by Wall, Bill; Musicians and Chess; 8/8/2013, chessmaniac.com, and by Silver, Albert; Musical giants and chess; 3/7/2015, Chessbase.
Consulting these two online articles (both well worth reading, by the way) yielded less in the way of historiographical evidence than I had hoped. The second of them doesn’t mention Beethoven at all, although it does have a photo of David Bowie playing chess with Catherine Deneuve.
Bill Wall’s article, though, does mention Beethoven. Here is what it says:
Ludwig van Beethoven (1770-1827), the German composer and pianist, was a chess player. He was a good friend of Johann Maelzel, the builder of one of the first chess automatons.
That’s all. No mention of a source, but there is some detail. Beethoven’s “good friend” Johann Maelzel seems to be the link.
Maelzel’s mechanical marvels
Johann Nepomuk Maelzel (1772-1838) is one of the more colourful characters of music history. He was an inventor who settled in Vienna in 1792 (the same year as Beethoven), and soon afterwards began to display his “panharmonicon”, a kind of mechanical organ which played orchestral music. Maelzel was aiming to profit out of the popularity of automata of all kinds, especially automata which could play musical instruments. Maelzel and Beethoven met in 1812 or 1813, and the inventor persuaded the famous composer to write a “Battle Symphony” for his panharmonicon. Beethoven did so, and then expanded and arranged it for a regular orchestra (it was written in between the Seventh and Eighth symphonies). The “Battle Symphony”, or Wellington’s Victory at Vittoria as the orchestral version is called, was premiered, along with the Seventh Symphony, in two charity concerts organised by Maelzel in 1814 to raise funds for Austrian soldiers wounded and maimed in conflict. At this time, Maelzel also invented several ear trumpets in an attempt to help Beethoven’s progressive deafness.
To describe Maelzel as Beethoven’s “good friend”, though, is sadly not quite accurate. There was a violent quarrel following the concerts arranged by Maelzel, over the rights to Beethoven’s “Battle Symphony”, which Maelzel wanted to play on his tour to the rest of Europe with his panharmonicon. Beethoven describes him thus:
[…] his low and disloyal character is displayed in expressions such as the following: “I shit on Vienna and I’ll see to it that people in London are told that here in Vienna one is paid 10 gulden” […] Maelzel is an ill-bred fellow, quite uneducated and without refinement.
(Letter to Dr Carl, Edler von Adlersburg, July 1814: The Letters of Beethoven, trans. Emily Anderson, London: Macmillan, 1961, Vol. I, letter 485, p. 461)
Beethoven also describes Maelzel’s ear trumpets as “not of any real use” and accuses Maelzel of stealing his work.
There seems to have been some sort of reconciliation, however, since Beethoven was very impressed by the one of Maelzel’s inventions which you may own yourself: the musical metronome. From 1817, Beethoven started to put metronome indications on his works to indicate the speed he wanted. How accurate Maelzel’s metronome was, and how realistic Beethoven’s expectations were of performers as his deafness became complete, are things still vigorously debated to this day.
So, if “good friend” doesn’t really fit the bill as far as Beethoven’s relationship with Maelzel goes, what about the other claim by Bill Wall, that Maelzel was “the builder of one of the first chess automatons”? This too, unfortunately, isn’t quite true. The automaton in question was in fact the most famous of all chess-playing machines before Deep Blue, known as “The Turk”.
The automaton could move the pieces on a chess board, and appeared to be able to beat any human opponent. It was a marvel of its age, and exhibited all over Europe.
It was not, however, built by Maelzel. Its inventor was in fact a Hungarian called Wolfgang von Kempelen, who first demonstrated it to Empress Maria Theresa in 1770. Maelzel bought it from Kempelen in 1804, a good few years before he met Beethoven. Maelzel repaired it, and exhibited it to Napoleon in Vienna in 1809. He then took it to Milan, where he sold it for a huge profit to Napoleon’s stepson, Eugène de Beauharnais. A few years later he managed to buy it back, and took it to Paris and then London on the European tour over which he and Beethoven fell out so badly.
The Turk was a remarkable machine, but it was a fake as far as playing a game of chess was concerned. You can see in the photograph the compartment on the right where a small grandmaster had to be concealed to control the machine’s moves. This subterfuge meant that Maelzel had to hire short, impoverished chess masters (of which, then as now, there was a ready supply) wherever he exhibited the machine. Napoleon was actually defeated by Johann Allgaier, the strongest player in Vienna in Beethoven’s day, whom I mentioned earlier as the author of the first chess tutor in German.
So, did Beethoven play chess?
It has been an interesting search through published books on chess, and a fascinating encounter with that entrepreneur, inventor and showman Johann Maelzel. But there is, I am afraid, no evidence at all that Beethoven did have an enthusiasm for chess.
The English translation of Beethoven’s letters runs to three thick volumes (I quoted Beethoven’s view on Maelzel’s character from them earlier). I have looked through them all, and there are no mentions of chess, or The Turk, in any of the letters involving Maelzel, and no mention anywhere of Allgaier (who was known in the city as well as being the inhabitant of The Turk). No mention either of François-André Philidor, a contemporary of Beethoven and by far the best-known chess-playing musician of that or any other time.
Sadly, I have to conclude that the assertions with which I began, that the composer of The Eroica symphony, Fidelio, and Wellington’s Victory had a particular interest in the battle of the wooden soldiers over the sixty-four squares, are without evidential basis. The search has emphasised to me the pitfalls of wishful thinking, which can undo your attacks over the chessboard as easily as your search for historical truth.
Books on chess are a curious genre. There are an awful lot of them, they are very hard to find in libraries. They nearly all fall into one of a few categories. Books on openings. Books on improving your chess technique. Collections of games (by an individual, or from a world title match, or from a significant tournament).
And that is about it. What all these books share as a quality is that they are absolutely incomprehensible to anyone who is not a keen chess player. I have many of them, and if I leave them lying around, members of my family ask me when I am going to read a “proper” book.
There are just two kinds of exceptions to this rule, and these exceptions contain my favourite kinds of chess book. The first is chess biography or autobiography: Korchnoi’s Chess is my life is worth reading as much for its picture of the privations of the siege of Leningrad as for its depiction of one of the most obdurate personalities ever to have graced the game. Emanuel Lasker: The life of a chess master (J. Hannak) is a riveting account of an extraordinary personality. But the second kind of exception to the normal run of chess literature is my favourite: books which take chess into other realms, such as literature or film (see my earlier post on Nabokov’s The Luzhin Defence), or the anecdotal and eccentric (by far my favourite is The Complete Chess Addict by Mike Fox and Richard James, and its enlarged version The Even More Complete Chess Addict). And now – joy of joys! – the chess publisher Russell Enterprises has presented a book on exactly the topic of this blog.
The first thing I want to say about this book is that you should definitely get yourself a copy, if you are reading this blog. I need to put that first, because I could hardly fail to welcome a publication such as this. Having said that, there are of course lots of things here which I would have put differently or with which I don’t quite agree. But these are the kinds of things one should discuss over a convivial drink, not reasons for disparaging the book.
Achilleas Zographos (since I contacted him, this blog has gained Greece as a new country in its stats profile) is a much better chess player than I am (he is a FIDE trainer) and also a much better performer (he is a concert pianist). There are times when his perspective is clearly that of a performer rather than a composer. But there are a lot of things I like about his book.
Things I like about this book
The author is clearly a man after my own heart, with a taste for the quirky and occasionally bizarre which I love. Perhaps all of us who love both chess and music as arts are similar in that way. He has compiled a huge quantity of anecdotes and information of the sort I find fascinating. Quite a lot of it I knew already (unsurprisingly); Fox & James (see above) are frequently cited as a source for anecdotes. But there is plenty in the book which I didn’t know: for instance, I didn’t know the sixteenth-century Italian poem which invented the dryad Schacchia, goddess of chess, and the eighteenth-century English poem in which she acquired the name Caïssa (the poems are described here); I had never come across Guido van der Werve’s chess piano (here is his concerto in three movements); and I did not know that GM Levon Aronian, who is about to compete in the 8-player knockout to determine the next World Title Candidate, has a passion for jazz.
The book is sumptuously illustrated. At the back are links for internet sources for the illustrations and YouTube videos. Sadly, some of these links seemed to be broken when I tried them; but I loved the quality of the illustrations reproduced. Trying to download one of the illustrations led me on an interesting detour. On p. 128 is printed a lovely canvas by Kandinsky, with the title Schach-Theorie [Chess Theory], and the date 1937. I did not know that Kandinsky (one of my favourite artists and a collaborator with the composer Arnold Schoenberg) had an interest in chess. When I found that the link at the back of the book seemed to be broken, I tried an internet search for the painting, and discovered that it has two quite different attributions. The canvas is owned by the Guggenheim Museum in New York, where it has the title Graceful Ascent and the date 1934.
I have to say that Graceful Ascent seems more convincing as a title, although there are some details near the top of the canvas that could conceivably be chess pieces.
So where do the probably false title and date come from? Further internet searching turned up what seems the likely source, and a wonderful anecdote. In 1937, the year that many of Kandinsky’s paintings were confiscated by the Nazis and displayed in the Exhibition of Degenerate Art, a retrospective of his work was displayed in the Swiss city of Bern. The city was home to another of the Bauhaus artists, Paul Klee, and the exhibition was to be the last time that the two artists met (Klee was seriously ill and died in 1940). According to the Bern artist Peter Matter, the two giants met in front of Kandinsky’s work Schach-Theorie, and both were seized by a sudden desire to go back to Klee’s house and play each other at chess. So perhaps the internet translation of Matter’s diary is the source of the misattribution. And perhaps it was a different canvas: both Klee and Kandinsky produced other works at that time that suggest the game of chess much more clearly to me (hover your mouse to see the titles).
Klee, ‘Überschach’ (1937)
Kandinsky ‘Trente’ (1937)
So this is probably an error, as far as the content of the book goes; but I could hardly complain at that, since it sent me on a rewarding hunt which enabled me to place these two alongside Schoenberg as artists enthusiastic for the Royal Game.
Things I don’t like so much about this book
Most of the things I am less impressed with in the book are not the fault of its author. While the publisher should be applauded for commissioning this work, the author is not writing in his native language, and the services of a copy-editor would have improved it as a text to read. Infelicities such as “At the moment of writing” (rather than “At the time of writing”, p. 13); or grammatical lapses such as Steinitz’s “systematic, scientific approach of the game” (rather than “…approach to the game”, p. 21), are frequent and irritating. My annoyance at the blurb on the back cover engendered an earlier blog post, Prodigies: the preserve of music and chess? although I did discover on p. 39 that it was the American grandmaster Edward (not the World Champion Emanuel) Lasker who originally commented on child prodigies as a phenomenon of chess, music and mathematics.
Things that puzzle me in this book
There are a lot of lists in this book. That is no bad thing in itself; I like lists. The last chapter, ‘Quotations’ is in fact just a list of good quotations, which ought to delight designers of chess-related t-shirts.
Other lists are more intriguing. For instance, Beethoven appears in a long list of musicians who had a passion for chess on pp. 23–24; he is mentioned a dozen times elsewhere (the book has a good index), but always just as an emblem of “the great composer”; nowhere are we told the source for believing he had an interest in the game of chess. My scan through the several hefty volumes of his letters could find no mention of it at all; but I would love to know what evidence there is.
But lastly, the thing which puzzles me most about this book is actually the way that it compares the technical elements of chess and music. Several times, the author’s love for the quirky leads him to the most extraordinary chess compositions to illustrate the most ordinary elements of music. One is the study by Petrovic which is presented as an example of the role of rhythm and tempo in chess:
Another is the beautiful but totally bizarre study by van Reek which illustrates the musical idea of ‘texture’:
But the puzzlement I felt reading through the lengthy chapter entitled ‘Components’ which works its way through ‘Time, rhythm and tempo’, ‘Melody and movement’, ‘Harmony’, ‘Texture’, ‘Structure’, and ‘Timbre / colour’ turned from slight annoyance to perfect calm with the realisation that this most difficult of fields, making detailed and persuasive comparison of the technical aspects of the arts of chess and music, is left open to my own blog to attempt. Keep reading my posts here to see how well I get on with trying.
Patterns analysed by the Réti brothers in music and in chess
It is hardly controversial to say that both chess and music rely on the recognition of recurrent patterns. Is this a trivial observation? Or is there a deeper connection in terms of the kinds of patterns that structure and make meaningful the experience of playing the game of chess or listening to a work of music? Does the observation that both activities rely on pattern recognition actually indicate a cognitive similarity between the two arts?
This post explores these questions. In this I am once again guided by the Réti brothers whom I introduced in Réti the Modernist: Rudolph, the pioneer of music analysis, and Richard, the visionary chess grandmaster.
It is one thing to say that chess and music both require pattern recognition; quite another to define what constitutes a “pattern” in this context. To begin with, I am going to work with two different kinds of pattern: firstly, general patterns that are found everywhere and without which the piece of music or game of chess doesn’t make sense; and secondly, individual patterns that define specific examples in either field. The first category comprises patterns that define well-formed pieces of music or legitimately played games of chess; the second category comprises patterns that are memorable enough to act as “signatures” for their author (whether a composer or a chess player).
I am in fact much more interested in the second kind of pattern than in the first; but please bear with me while I start with a comparison of generic, universal patterns in chess and in music.
Checkmates and cadences
Beginning students of music, and beginning chess players, are alike taught certain basic patterns as the essential first step towards understanding how the respective arts of composing and chess-playing work. Every game of chess aims towards a checkmate; every piece of music aims towards a final cadence. Admittedly, here I am talking about tonal music in the Western tradition; but that is going to be my focus for this post. Other posts have considered atonal music, such as that of Réti’s friend (and chess player) Arnold Schoenberg (see Réti the Modernist).
Sticking with tonal music, here is a cadence:
To repeat the point that this is the place where students of composition begin, this example (with the analysis underneath the staves) is taken from my own Open University module. I suggest you sign up for it now: it’s called Inside Music.
There are many different ways of approaching a cadence. Here are two:
And here is one from a real piece of music that you might recognise:
Just as there are many ways of approaching a cadence, there are many ways of approaching a checkmate. Here are four, which all aspiring chess players have to learn (hover your mouse over each to see its caption):
The back rank mate
The knight with bishop mate
The rook with bishop mate
The rook with knight mate
These are all patterns which recur again and again, in many different forms (whether you are thinking of pieces of music or of chess games). They are meaningful: the meaning of the patterns in music is to signify the end of a phrase, or the end of the whole piece; the meaning of the chess patterns is to signify the end of the game. In both cases, these patterns accord with Wolfgang Köhler’s definition of a pattern in Gestalt psychology, which is that their meaning is different from that of the components of the pattern: the individual notes forming harmonies in accordance with the rules of tonal composition, or the individual pieces moving in accordance with the rules of chess. It is the pattern itself that signifies ‘cadence’ or ‘checkmate’, and this makes it a Gestalt.
The Réti brothers and pattern recognition
The patterns just identified are generic: they are learned by students because they have a level of generality that makes them recognisable in innumerable contexts. What fascinated both the Réti brothers was the recurrence of patterns which have a quite different level of individuality, so that instead of signifying something general, they identify something unique.
In both cases (music and chess) the relevant Réti identifies these patterns as the signature of the creator of the artwork in question. These patterns personalise the musical work or the game of chess, and in each case this was a significant innovation in the understanding of the field. Rudolph Réti was one of the first thinkers (along with Schoenberg and a few others) to develop a theory of how patterns in melody shape a work of music; a topic strangely absent from the centuries of theory of harmony, tonality and form. And Richard Réti was one of the first thinkers (along with Nimzowitsch and a few others) to develop a theory of manoeuvring pieces not in order to win material or deliver checkmate, but in order to create a better pattern to their disposition.
Rudolph Réti and patterns in Schumann
Let’s start with the older brother, Rudolph, and his analysis of a wonderful work by another chess-fanatical musician, Robert Schumann (1810-56).
The work in question is Kinderszenen [Scenes of Childhood], a multi-piece consisting of thirteen short individual pieces written in 1838 while Schumann was engaged to be married to Clara Wieck (her father was opposing the match). Rudolph Réti devotes a whole chapter of one of his books to this work (Rudolph Réti, ‘Schumann’s Kinderszenen: A “Theme with Variations”’ in The Thematic Process in Music (Macmillan: New York 1951) pp. 31–55).
With a work like Kinderszenen, it is always worth asking whether the pieces are entirely separate from each other, linked just by a general mood summed up in the title of the whole collection; or whether there is some musical connection between them that links them together. Rudolph Réti sets about demonstrating that a single “musical idea”, an individual pattern of notes, links together all the pieces. This pattern is found in the melody that begins the first of the pieces, which is called “Von fremden Ländern und Menschen” [“Of Distant Lands and Peoples”]. Réti doesn’t actually think that the opening melody of the work is the “basic pattern” that unites the whole. It is the first individualised example of a “basic pattern” that is ideal, abstract: it underlies all its individual occurrences in the work, but isn’t identical to any of them. Réti infers the “basic pattern” from the opening melody and its slightly altered repeat at bars 14-15.
You can hear the great pianist Vladimir Horowitz (1903–89) perform the piece here: his sensitive playing of these pieces depicting the carefree days of childhood, as an old man (the concert was recorded in 1987), is suitably elegiac.
Having identified this “basic pattern”, Réti sets about discovering it in every single one of the pieces that make up the Kinderzszenen. Here it is in the melody of No. 2, ‘Curiose Geschichte’ [‘Curious Story’]:
As Réti points out, the basic pattern here uses exactly the same notes as in the first piece, even though the key has changed from G major to D major.
Horowitz’s performance of this piece is well worth hearing, although the link here lacks video:
And here is the same basic pattern in possibly the best-known of the Kinderszenen, No. 7, ‘Träumerei’ [‘Daydreaming’], where Réti finds it in the middle of the theme, transposed down from G major to F major:
Horowitz’s performance is spellbinding:
Réti also thinks he can detect the basic pattern at its original pitch, in the middle of the texture rather than in the melody, at the climax near the end of the piece. Personally, I think this is pushing things a bit; but it shows Réti’s deep belief that the basic shape recurs everywhere:
I’ve circled in red the notes that Réti thinks make the basic shape; the first two are both in the first chord, but played one after the other according to the arpeggiation marking included by Réti; presumably it was in the edition he owned, since it isn’t in Schumann’s original edition. Horowitz plays the chord as Schumann wrote it, without arpeggiation; but he did have huge hands.
Richard Réti’s brilliant checkmate pattern
One thing that certainly does make playing chess a different kind of thing from writing music is that no-one who uses an idea from one of the great players of the past is going to be accused of plagiarism. If I were to write a piece that started with the “basic pattern” used by Schumann in the Kinderszenen, I would at the very best be credited with a conscious hommage to the nineteenth-century master. If I ever manage to reproduce Richard Réti’s most famous mating pattern, I would not only be delighted, but my chess-playing friends would congratulate me.
The pattern in question comes from a game Réti played against Savielly Tartakower in 1910. Over their careers, these two grandmasters played each other many times: Réti won on fifteen occasions, Tartakower on fifteen, and a further fourteen games were drawn. But this game is the best known. Réti won in just eleven moves. The game was played in Vienna, where both chess masters lived. Réti was 21, Tartakower 23. After eight moves, the game had reached the following position:
Tartakower had just taken Réti’s knight on e4 with his own knight [8…KtxKt], apparently winning a piece, although White can regain it with the move Re1 [R-K1]. However, Réti had set a trap: White wins, with mate in three moves.
DON’T CONTINUE UNTIL YOU HAVE GUESSED THE MOVE!!
The move Réti had foreseen was Qd8+!! [Q-Q8ch!!]:
Black can take the white queen — in fact, that is the only legal move — but then a double check from bishop and rook simultaneously, Bg5+ [B-Kt5ch], leads (depending on how the king moves) to one of two very pleasing checkmates:
The mate played in the game
The alternative possible mate
The game became well known. However, one has to wonder whether Réti knew a game played sixty years earlier in a box at a Paris opera house between Paul Morphy, the world’s strongest player of the time, and two French aristocrats:
Morphy’s stunning win was, like Réti’s, a queen sacrifice leading to that same rook-and-bishop mating pattern:
The queen sacrifice
The story of this game is told in more detail here.
Or perhaps Réti knew a game of 1864, a defeat for another top player of his day, Ignaz von Kolisch:
Once again, a queen sacrifice leads to checkmate, this one even more like that in Réti’s game:
The queen sacrifice
Whether Réti knew these earlier games or not, it is as I remarked a fortunate aspect of playing chess that no-one is bothered by accusations of plagiarism. Certainly not Georges Koltanowski, who arrived at the following position on his way to becoming Belgian chess champion of 1923. Black has just played Qxh2 [QxQR2] and is threatening Qa1 [Q-QR1] checkmate:
By now, the winning combination should be familiar:
The queen sacrifice
Finally, a more recent game between two strong amateurs:
This time, it was Black (Rene Gralla, a Hamburg lawyer and rock journalist who has interviewed Mick Jagger, Ringo Starr, and others) who unleashed the ‘Réti combination’:
The queen sacrifice
So that is five games, played over a span of nearly 150 years, all as it were variations on a recognisable theme.
So far, all these chess patterns have led to checkmates. They can only happen on the rarest of occasions, and are so memorable that they are associated with Richard Réti’s name, simply because his win against Tartakower became well-known.
But these chess patterns are not really like the patterns observed by Richard’s brother in the music of Schumann. To find a kind of pattern that can properly be called a Gestalt pattern that carries the sign of its creator’s authorship, we really need to look at the most complex phase of a chess game, the ‘middlegame’: the phase between the opening (roughly the first dozen moves or so, in which generally each side tries to move each piece no more than once), and the endgame, where just a few pieces strive to hold a draw or deliver checkmate.
One would think that the middlegame in chess is unique in each game, and so it would not be possible to create patterns more complex than very general rules (“control the centre”, “find a square for a knight where it cannot be attacked by an enemy pawn”). Richard Réti, however, showed that even in the middlegame it is possible to create a recognisable pattern that recalls his authorship whenever it it seen.
Richard Réti’s middlegame pattern
Like so many memorable creations in chess and in music, the middlegame pattern that bears Réti’s name was invented in Vienna. Réti’s opponent was called Fischer (absolutely no relation to his much better-known namesake born twenty years later). Here is the position in which Réti’s genius came up with a unique manoeuvre:
This is what chess players call a “closed” position, with all the pieces and pawns still on the board. Réti has played the “Réti opening”, positioning both of his bishops at the sides of the board and leaving the centre squares free of white pieces.
In this position, Réti came up with a startling idea. He moved his rook from c1 [QB1], in order to slide his queen right into the corner of the board:
Réti vs Fischer, move 11
Réti vs Fischer, move 12
This is modernism in chess: from what appears to be the very worst square from which the most powerful piece can operate, Réti hopes to influence the long diagonal that runs from that square to the far corner of the board. In this closed position, the long diagonals are the straight lines from one side of the board to the other with the least number of obstructing pawns on them:
The pattern is more than just an inventive and unusual disposition of the pieces. It is a Gestalt, a shape with meaning: the curious position of the white queen aims to dominate the game by controlling the long diagonal leading to the enemy king.
Fischer was a local amateur player competing in the annual Vienna tournament; Réti was an acknowledged grandmaster. So it is hardly surprising that Réti won this game. However, later that same year, he was playing in the strongest tournament organised, at Karlsbad. Here, facing one of the strongest players in the world, Akiba Rubinstein, the following position arose:
Réti reproduced his idea from the Vienna tournament, this time creating two lines of attack into the enemy camp:
Once again, the pattern was the basis of a winning strategy. Like Schumann’s recognisable motif that holds together all the pieces of Kinderszenen, Réti’s motif not only had perfect meaning in the context of the games in which he played it, but was also memorable and unusual enough to carry his signature, as it were. It is “Réti’s middleground pattern”.
The following year, Réti again played in the strongest tournament organised, this time in New York. He faced the former World Champion, Emanuel Lasker:
Once again, Réti manoeuvred his pieces to create a new line of attack into the enemy camp:
Lasker, a superb defender, prevented Réti’s idea from bearing fruit. Later in the game, after Réti had sacrificed rook for knight in an attempt to break open Lasker’s fortress, the following position arose:
With typical inventiveness, Réti tried playing the motif from the other corner:
The game was a terrific struggle, which Réti eventually lost. Lasker went on to win the tournament by a clear 1½ points, ahead of the reigning World Champion, José Capablanca.
In the plagiarism-free world of chess, even motifs forever identified with their creator are free for all to use. Capablanca himself, more than a decade later, was faced with the following position against another strong grandmaster:
By now, it should come as no surprise to see the pattern created by Capablanca’s next two moves:
This may have been some sort of hommage to Réti, who had died in 1929; but it was still the basis of a winning strategy for Capablanca.
Conclusion: patterns and meaning
I have tried to point out several times that the significance of the kinds of patterns I have been exploring, in music as well as in chess, is that they have meaning. They are not just pleasing configurations of chess pieces or of musical sounds; they are what a psychologist might term a Gestalt: a pattern whose meaning is different from the meaning of the individual components which constitute it.
This appeal to psychology is not accidental. Schumann’s music evokes more than just simple pleasure at its melodic beauty: it summons forth the world of childhood experience, tempered by memory and nostalgia (particularly the way that the aged Horowitz plays it).
Equally, when Lilienthal saw Capablanca move his queen to the corner square of the board, the gesture must have had a psychological effect: Lilienthal was just too young to have played Réti, and Capablanca signalled with the “Réti manoeuvre” that he was employing against him the kind of “hypermodern” attack Capablanca was himself famous for having refuted time and again by his legendarily precise play. It was Lasker who first wrote about the importance of psychology in chess; he would select not necessarily the objectively best move in a position, but the strategy he thought best suited to his opponent. One of his dictums was “Chess is not an art, or a science, but a struggle”.
The Réti brothers were alike in many ways, and we know from Rudolph that they discussed the similarity of their ideas regarding chess and music. The topic of pattern recognition is probably the one in which their ideas came closest to each other. It is no accident that it was the topic that enabled both brothers to become great theoreticians in their respective fields.
This short blog post is inspired by a statement I read this week in the publisher’s blurb for what looks to be an interesting book, Music and Chess: Apollo meets Caissa (Achilleas Zographos, Milford: Russell Enterprises 2017). This is not a review of the book – you can expect one of those in due course – and, with one book to my own name, I know better than to attribute what you read in the blurb to the author of the book. It is printed on the back cover, and also on all the websites from which the book can be purchased. Here it is:
It has long been recognized that there are only three major areas of human endeavor which produce prodigies: music, chess and mathematics.
Is this true? I found myself wondering (a) whether this assertion is justified, and (b) whether it does indeed demonstrate an innate connection between these three fields in particular.
I shall have to leave to one side the question of definitions of the terms “prodigy” and “major areas of human endeavour”. After all, this is a piece of advertising copy rather than a philosophical proposition. But the more I looked at it, the odder it seemed.
Are there prodigies outside of music, chess and maths?
If “prodigy” means someone who attains mastery of a field at a very young age, it seems to me that there are other “areas of human endeavour” which produce this phenomenon. I can think of three straight away:
Sport in general. Even without turning to womens’ gymnastics in the 1970s, when it seemed that mastery of the sport was the province only of pre-pubescent girls, exceptional talent in many sports shows itself very early indeed. I remember reading an anecdote of John McEnroe’s father throwing a baseball for his five-year-old son to hit in Central Park, when a passer-by asked whether the talented midget worked in a circus. Wayne Rooney was the top goal-scorer in his father’s local pub football league at the age of nine.
Acting. The number of incredibly talented child actors is long indeed. Shirley Temple was the highest-paid actress in Hollywood before retiring at the age of 22 and becoming a diplomat (American Ambassador to Ghana and Czechoslovakia). Mark Lester, Macaulay Culkin, and more recently, Daniel Radcliffe and Emma Watson all demonstrate that exceptional talent can show itself early and stay with its owner into adulthood.
Romantic poets. They may not have been children, but the whole movement of Romantic poetry in the early nineteenth century was certainly the province of teenagers: Keats, Shelley, arguably Byron, Wordsworth and Coleridge, all produced their best work in their teens or perhaps early twenties.
Are the greatest musicians and chess players always child prodigies?
It is undeniable that some of the greatest musicians, and some of the greatest chess players, were also child prodigies. In chess, the clearest example is the third World Champion, José Raul Capablanca (1888–1942), whose ability was reported in the Cuban press before his fifth birthday.
In music, the obvious candidate is of course Wolfgang Amadeus Mozart (1756–1791), who learned to play the piano at three, was touring Europe with his father as a soloist before his tenth birthday, and composed his first symphony at the age of nine.
However, these two are not typical. Indeed, Richard Réti was of the opinion that Capablanca’s exceptional talent (his predecessor as World Champion, Emanuel Lasker, and his successor, Alexander Alekhine, both rated him as the greatest player of all time) stemmed from the fact that he learned the game so early, so that it was like a “native language” to him. Much the same could be said of Mozart. But many other great chess players learned the game later: for instance, Emanuel Lasker (eleven), one of his challengers for the World title, Carl Schlechter, (thirteen), another World Champion, Mikhail Botvinnik (twelve). Equally, while most musicians begin playing early in life, exceptional talent may not show itself until much later. Had Beethoven died at the same age as Mozart (35), he would have left just three symphonies, no operas, and only one set of string quartets.
When do artists reach their peak?
While some chess players and some musicians do show exceptional talent as children, this does not mean that they attain the greatest heights at that age. While most sportsmen and sportswomen reach their peak in their twenties or thirties (as I believe is true for some mathematicians), this hardly means that they are prodigies when they do, or have to have been prodigies in order to excel. Bobby Fischer learned the game of chess at the age of six, was hailed as the best player in America when he was thirteen, but did not become World Champion until he was 29. Chess and music are both reassuring (to people like me) in that age can be defied by the greatest exponents: Emanuel Lasker, having held the title of World Champion longer than anyone else (27 years), returned to competitive chess at the age of 66, having lost his fortune in Hitler’s persecution of Jews; he attained third place at the Moscow tournament of 1935, remaining unbeaten, defeating Capablanca (who came fourth), and ending just a half-point behind the winners (Botvinnik and Salo Flohr). The pianist Alfred Brendel caused dismay in the world of music when he announced his retirement at the age of 75, still considered by many to be the greatest living performer. The composer Havergal Brian produced his thirty-first and thirty-second symphonies at the age of 92.
Are chess, music and maths linked?
To me, the most irritating aspect of the statement with which I started this post is that I agree with its basic contention, which is that there is cognitive similarity between the intellectual skills and mental stimulation that chess, music and mathematics all provide. But I don’t think that this guarantees that talent in any of these fields must necessarily show itself in childhood. Nor do I think these are the only “areas of human endeavour” in which prodigies occur. Nor do I think that some competence in any of these fields is impossible for those who, like me, attempt in their middle life to apply the hard work and practice to these activities which they were incapable of mustering earlier on.