Where does the knight go?

0 | Chess Event Coverage
Where goes the knight?Australia has a surface of 7,617,930 km², (2,941,299 square miles), making it the 6th biggest country in the world. However, currently there are only three Australian grandmasters on the FIDE rating list (the 4th retired not long ago). How is this possible?

I think I have found the solution to one of the greates enigmas in the world of chess: why Australia has so few grandmasters. And no, I'm not talking about population (around 22 million) or density (which puts the country on a modest 232nd spot). No, I think it's because Australians just don't know the rules well enough. Well, that's one explanation - there might be a deeper one which I'll come to at the end of this post.

It's one specific rule the Australians seem to have problems with: how the knight moves. And indeed, it's not easy. Especially kids, when learning chess for the first time, have trouble with what Donner called "the most paradoxical of all chess pieces". Rooks go straight, bishops along a diagonal, the queen, well, she's very lucky because she can do both, but the knight... How to explain? One straight, one diagonal, that's not easy. My 5 year old niece can't remember it very well, and thinks she can only go forward with her knights (a problem some strong players encounter throughout their career, by the way).

So what's the fuzz about? Well, in the first round of the Sydney International Open, the following happened.

Alan Ansell (1968) - GM Darryl Johansen (2457) Sydney International Open, 07.04.2010 Ansell-Johansen Position after 31...fxe5

Here Ansell played the illegal (well, to most of us at least) move 32.Nf4-h2?!! and... play continued: 32...Rb4 33.Nf3 (The knight is suddenly perfectly placed for the kingside attack) 33...Nh5 34.Ng5 Nf6 35.Ne6 and the grandmaster resigned.

And this was not just an incident. Last year, in the same tournament, something very similar happened.

Sarah Anton (1718) - Paul Broekhuyse (2118) Sydney International Open 2009 Sarah Anton - Paul Broekhuyse Position after 53...Kf6

Here Anton played 54.Nf5-Nd7?!! and Broekhuyse resigned the game as indeed there's nothing to play for when the queen drops.

For other pieces it may be very clear how they move, but many people more educated than my niece have pondered over the question where, and how exactly, the knight goes. In fact, it has been questioned whether the knight actually goes. As Donner argues in Schaakbulletin 60, November 1972, the pieces don't 'go', as 'going' is to follow a path, and along the way all points are passed chronologically. From a geometrical point of view, this is not the case in chess, because 'no points are passed'. So for a bishop on b2 'going' to f6, more than one move is needed. (The bishop 'went' from b2 via d4 to f6.)

More interesting is Donner's point that although optically other pieces may reach much further than the knight, it's in fact the knight that triumphs in a certain way. Whereas queens, bishops and rooks follow lines (horizontally, vertically or diagonally) that are finite, the knight in fact follows an infinite circle! This is what Paul Janse wrote about as well, in a February 1992 article for the club magazine of the Amsterdam chess club MEMO (which was merged into different chess clubs over the years):

The Circle And Caissa contemplated King, Queen, Rook and Bishop, and she saw that it still was not good enough. She put a cross on the d4 square and asked herself: what are the nearest fields not attacked by any piece I put on the square? She saw that these were the fields b3, b5, c6, e6, f5, f3, e2 and c2. And She consulted the Greek philosopher Pythagoras, who announced her that those squares are at a distance of √5 from square d4. And then Caissa created the Knight, as the piece that precisely covers the squares at a distance of exactly √5. And She saw that these squares describe a circle centered around the knight itself, with the Holy √5 as the radius, and she saw that it was good. The fifth day.

Perhaps it's too easy to explain the happenings in Australia as a lack of understanding of the knight, or even the knowledge of the chess rules. Maybe there's something else going on. Something that would make us realize that the Australian players are in fact much more advanced than we are.

This week Chessbase generously allows chess players the opportunity to solve tough scientific problems, such as the danger of the Large Hadron Collider at CERN generating micro black holes, and the Fermi paradox. In today's post they embbed Richard Feynman's analogy of "understanding nature" and chess, which we'll do here as well, as it might explain all of the above.


Australian chess players seem to have been the first to have realized that in some situations, the knight may go two squares diagonally. Following a fundamental scientific method, they're most interested in the thing that doesn't fit, the part that doesn't go according to what you expected. The Australians seem to have discovered a new revolution in the physics of chess.


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