Chess and music are frequently connected, indeed rightly so. Of celebrated composers, Sergei Prokofiev was a talented player of master strength. Aggressive and tactical in style, the composer of the heroic score for Alexander Nevsky and the romantic ballet, Romeo and Juliet, once defeated Capablanca in a simultaneous display. His surviving games gave ample evidence of his creative abilities over the chessboard.

Jose Raul Capablanca vs. Sergei Prokofiev (simultaneous display)

Sergei Prokofiev vs. Maurice Ravel

Maurice Delage vs. Sergei Prokofiev

In contrast, the avant-garde composer John Cage, learnt chess, primarily in order to communicate osmotically with his artistic hero, Marcel Duchamp. If there was a chessboard parallel to Cage, it was former world champion (1963-1969) Tigran Petrosian at his most mysterious, as British Master Peter Clarke described Petrosianic strategy in his anthology of the Maestros most outstanding games.

Tigran Petrosian vs. Wlodzimierz Schmidt

On playing over the above game for the first time, the following question occurred to me: to what extent is the development of new strategic ideas still possible in modern chess?

Let me attempt to elaborate on this point. A century and a half ago, the profound chess thinker Steinitz systematically collected (for the first time) a wealth of information concerning the positional and strategic elements that go up to make the game of chess. Never before had there existed information (embedded in Steinitzs own games and annotations) concerning the desirability of establishing pawn centres; of seizing the bishop pair; of avoiding pawn weaknesses in ones own camp while inflicting such evils on the adversarys position; of creating a pawn majority on the Q-side, and much more.

The Steinitzian theories were formulated into rules by the Praeceptor Germaniae, Siegbert Tarrasch, and this massive achievement on the part of the German Grandmaster represented the close of the first major stage in the development of chess strategic thought.

Since the time of Tarrasch there have been two more significant movements,bringing with them an advance in our grasp of the strategic possibilities and limitationsofthe chessboard. I mean the Hypermodern revolution and the rise of the dynamic Soviet school of chess.

All three movements, the Classical, the Hypermodern and the Soviet, added something new to our thinking about chess, but, to a very large extent, the two latter movements also embodied a denial of their intellectual ancestor, the Classical school. For example: the theory of the Hypermodern masters (Reti, Grnfeld . . .) concerning the establishment of pawn centres was not so much an entirely new concept (as was the original theory concerning pawn centres) but a reversal, in certain situations, of the Classical rules.

The historical stage reached by modern chess is: the Eclectic.

The best of modern chess has evolved into an amalgam of all previous theories: the classical approach of Boris Spassky; the Romanticism of Tal; nowadays we see top Grandmasters gaily setting up massive pawn centres in true classical style in some of their games , while demolishing identical centres (all according to Reti) in others. Today any strategic idea will gain acceptance if it works, and it is rare that a strategic conception will be condemned on purely abstract grounds without the support of at least some analysis. Everything goes, if it is successful. The following quotation from Peter Clarkes collection of Tals games typifies the modern approach:

A very good rule says that one should avoid weakening ones King position by advancing pawns. However, rules are meant to guide, not to enslave.One of the blessings of present-day chess is thatit is freer than ever from dogma. Many of the most valuable ideas would never have been investigated , had not masters persevered with bad moves. Clarke is referringto Blacks11th move inthevariation:

1. d4 Nf6 2. c4 g6 3. Nc3 Bg7 4. e4 d6 5. f3 O-O 6. Be3 e5 7. Nge2 c6 8. d5 cxd5 9. cxd5 a6 10. Qd2 Nbd7 11. g4 h5

11 h5 is in fact so strong that the whole variation has now been virtually abandoned from Whites side.

So, in view of all this, can we assert that it is still possible for progress to occur in the history of chess ideas, even when we have formulated all the rules and also discovered when it is possible to violate our own formulations? In the present game versus Schmidt, Petrosian provides a possible answer to this creative dilemma. In the previous examples I quoted the Classical rules were reversed for very good and valid reasons (a further example is the good, yet backward, black Q-pawn in certain variations of the Sicilian Defence). If one accepts that chess contains an element of art in its complex make-up then one can perhaps gain some insight into Petrosians mystical conduct of this game.

Against Schmidt, Petrosian certainly reverses all Classical principles, but are the reasons ones which we can recognize as good and healthy?

It is possible to argue that the era of truly creative Western art has now passed and that all which remains for art to achieve is to parody former greatness. Does modern art have truly original statements to make, or is it painfully aware of the achievements of the past, even in its very own act of creation? I would be the last to deny that the work of Mahler contains elements of profound and moving beauty, but structurally this work is dominated by symphonies. If one compares Mahlers 7th or 9th Symphony with any symphony by Mozart, Beethoven or Brahms, one will begin to appreciate the factor of parody concealed in the artistic consciousness of the twentieth century. Examples nearer our own time are Philip Glass, Andy Warhol, and Dmitri Shostakovich, who often creates the effect in his work of laughing at himself (e.g. the pure circus music of Shostakovichs 9th Symphony.) Paradoxically, Shostakovitch had been commissioned by Stalin , no less, after the composers triumph with his Leningrad Symphony, to compose a work celebrating the Soviet victory against Hitler. Even more extreme approaching artistic nihilism are Stockhausen and Cage, in particular the lattersFour Minutes 33 seconds,in which the virtuoso pianist does absolutely nothing during the stipulated time period.

In Petrosians games this artistic crisis is sometimes translated into chess terms. If it is no longer possible to invent ideas that are truly original then it is still possible, as an act of creative defiance, to parody all the Classical rules. In this game Petrosian simply reverses all of good old Dr Tarraschs formulations, as a sheer act of technical virtuosity. This mysterious encounter shows Petrosian mocking all the principles by which other players live, and in a sense this is chess without soul just as so much of modern art lacks true soul. Further we might say that Petrosians play here corresponds to that twentieth-century music which lacks all tonal centre. I suspect that the initial impulses going to create atonal music represented just as much a negative or reversal of traditional tonality as the consciousness of being involved in the genuine process of artistic achievements. As we have seen, Cage goes even further!

I knew Cage and played against him many times, even organising a birthday celebration for him at the Chelsea Arts Club and conspiring with then Vice President, Barry Martin, to present a birthday cake in the shape of DuchampsFontaine, in other words an inverted, white ceramic urinal. On his sad passing, I was invited in December 1993 to deliver his funerary oration at the Museum of Contemporary Art in Los Angeles.

When the German composer Paul Hindemith (1895-1963) wrote his symphonyDie Harmonie der Welt(later to metamorphose into an opera of the same name) I doubt that he had chess in mind. However, there is, I believe a connection.

HindemithsHarmony of the Worldfocuses on the life of astronomer Johannes Kepler (1571-1630) a student of the eccentric Tycho Brahe. Brahe was himself a groundbreaking observer of the universe. He inhabited a castle called the Fortress of the Stars (Uraniborg) and wore a false bronze nose for everyday use, saving his gold and silver prosthetic noses for best. Tychos original nose had been slashed in a duel, not blasted by celestial lightning from the heavens, which so obsessed him.

Kepler led a less dramatic existence, concentrating, without much incident, on establishing the harmonic relationship between earth, the remaining planets and the sun. And this is where chess comes into the equation.

World chess champion Vassily Smyslov once published an anthology of his chessboard masterpieces entitledIn Search of Harmony

a volume, by the way, in which I figure as one of the great mans victims. Chess is an area of human endeavour, which, in common with mathematics and music, allows child prodigies to demonstrate astounding genius. And I suggest that Harmony is the key.

Consider the young Mozart. Among so many other precocious musical achievements, such as composinga Minuet and Trio in G Majoraged five, he was able to reconstruct and transcribe AllegrisMisererefrom memory, having heard the closely guarded score just onceduring a visit to The Vatican. It should be recalled that at the age of fourteen, Mozart also wrote his first opera:Mitridate Re di Ponto, or Mithridates, King of Pontus.

In mathematics alarming precocity was displayed by, for example, Ruth Lawrence, who graduated from Oxford University age thirteen with a starred first class Honours Degree; not to mention John Nunn, who went up to Oxford at the age of fifteen to pursue his mathematical studies. Nunn, who also distinguished himself as a chess-playing prodigy, went on to become a grandmaster and professional player, who numbered even the legendary Anatoly Karpov amongst his scalps.

Indeed, accounts abound of amazingly youthful chess prodigies, including Jos Capablanca who allegedly picked up the moves of the game aged four, simply by watching his father play. Then there was Paul Morphy who at twelve defeated the illustrious European Master Lowenthal, and perhaps most spectacular of all, Bobby Fischer, US champion at the age of fourteen and victor of the so-calledGame of the Centurywhen he was thirteen.

It seems to me that there must be some quality which links chess, music and mathematics. I believe that quality to be an inner harmony which connects all three activities and which the youthful human brain is capable of identifying. The striking factor is that prodigies in chess, music and mathematics are capable of performing at the highest level without significantprior experience.

It would be unthinkable for a child or young teenager to paint like Leonardo da Vinci or write with the depth of Tolstoy or Shakespeare, since the relative life experience would not yet have been accumulated in general such dimensions would be missing. For music, maths and chess, on the other hand, the prodigies appear to be able to leap the chasm of experience and tap directly into an underlying harmony, a harmony which most of us cannot easily perceive.

Apart from John Nunn, who was proficient in both maths and chess from an early age, it is worth noting that Smyslov (World Chess Champion from 1957-1958) was also an accomplished opera singer. Meanwhile, Soviet Chess Grandmaster Mark Taimanov enjoyed a second career as a concert pianist.

With the advent of computers, such as the Demis Hassabis AlphaZero, new dimensions of harmony are now constantly being revealed. At first sight,or to the uninitiated, the moves and strategies of AlphaZero may appear opaque. Queens moved to fantastically improbable attacking squares such ash1, at the rearwards furthest extremity of the board, or sacrifices made for no apparent immediate compensation. Yet the former World Champion Magnus Carlsen has carried out a deep study of the programmes games and drawn advantageous conclusions for his own strategies. Harmony is there and Magnus has located it.

Rays206th book, Chess in the Year of the King , written in collaboration with Adam Black, and his 207th, Napoleon and Goethe: The Touchstone of Genius (which discusses their relationship with chess) areavailable from Amazon and Blackwells.

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Music, chess and the harmonies of the world - TheArticle