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The unextinguishable beauty of chess *June 22, 2007*

*Posted by dorigo in Art, chess, games, personal.*

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Very sorry to all of you physics geeks, but here comes yet another post about chess. They come in waves, as my love for the game knows moments of high fever alternating dormant periods.

The title of this post refers to the fact that chess positions, unlike most other human activities, allow us to get to the bare, beautiful truth, and the process can at times give an intense satisfaction. Chess is an art, and it is a science, both in its very peculiar way.

A comment by Derek Slater to my post on the nice queen sacrifice 27.Qc7+!! forced me to analyze the position a while longer. Here is the starting point, after Derek’s proposal of **26. … Nxe5** (instead than the move played in the game, 26….Na7):

Now, says Derek, it seems like white can still play **27.Qc7+ Rxc7 28.Rxc7+ Kd6 29.dxe5+ Bxe5, **

to which can follow 30.R1c6+ Qxc6 31.Rxc6+ Kxc6 31.Nxe5+ K-moves 32.Nxf7.

I agree until 29. … Bxe5 (everything is pretty much forced up to this move), but then white wins with another beautiful, silent move: **30.Rb7!!**

The position shown is a forced win for white. Now, about finding the truth in chess positions: to see that this is a win, one is forced to seep through several exhilarating variations:

1) The dumb defence **30. … Qxb3** loses quickly to **31.Rxb6+ Kd7 32.Nxe5+ Ke8 33.Rb8 mate**. Nothing too artistic here.

2) The more stubborn **30….Qb5** meets instead with a beautiful, long variation, which is prodigious for the fact that every tactical shot works for white: **31.Nxe5! Kxe5 32.Re1 Kd6 33.Bf4 e5**

(33….Kc6 34.Rc7 mate) **34.Bxe5+ Ke6** **35.Nd4+! Nxd4 36.Bxd4+ Kd6 **(tragically, if 36….Kf5 37.Re5+! Kf6 loses the queen to Rxd5, or 37….Kg4 38.h3+ Kf4 39.Rf7 is mate, or 37…. Kf4 38.Rf7 Kg4 39.h3 is also mate) ** 37.Be5+!**

** **

**37. … Ke6** (or 37. … Kc7 38.Rc7 mate)** 38.Bxh8+ Kd6 39.Be5+! Ke6 40.Bd4+ Kd6 41.Rxb6+,** winning the queen and the game.

I find the above cyclic checks with the bishop, to gain time in order to sweep the board clean of black pieces, simply sublime. I had never seen such a “vortex combination” -as these things are sometimes called- in the middle of the board, with the black king forced to play game in order to avoid two different mates on the two sides of the board!

## Comments

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Fantastic! Also in your “stubborn” variation above, after 32.Re1+ Black can throw in 32…Ne3 33.Rxe3+ Kf5 34.Nd4+ Kxg5 35.Nxb5 as yet another interesting way to lose🙂

You are right; this is a wonderful position with so much depth. And Rb7 is an evil, evil move!

p.s. After reading more of your blog – if I’d realized you were a discredited scientific nutjob, I never would have commented in the first place! [JUST KIDDING!🙂 Actually I am inspired to learn more about particles. Thanks for taking time to post further chess analysis.] – Derek

“Chess is an art, and it is a science, …”. Do you mean something like the following and could you give us more on why you think it is a science?

I wonder what a 3D molecularly structured equation of a complete game would look like with both sides’ moves and retaliations displayed in their respective colors to give us a better view of the situation. Could you actually assess and realize a stronger variation and subsequent position based on a model of this type?

As a disappointed physics geek, I would like to point out that chess (if you don’t allow draws) is a determined game. This means that one of either black or white has a strategy that will always win no matter what the other plays. The result is set theoretical and due to an interesting theorem of Gale and Stewart (1953). In computational complexity theory, chess is a finite game and therefore “trivial”.😉

Hi Derek,

true, there are several tactical motives in the position. I guess it is normal when a king goes to e5 with heavy artillery still around.

Feel free to visit – I also find your blog entertaining.

Cheers,

T.

Fred, I like to think at any given chess position as a node in a loosely connected network – connections being moves. Some connections are two-way, some aren’t (you can’t un-castle or un-promote, or even un-capture). Some are white moves, some are black moves. If we imagine to give a color to each node depending on whether there is a path forcibly leading to a win for one side, say white to white wins, black to black wins, and red to draws, we will see the grid lightening up with whole regions of white, of black, and then stacks of “surfaces” – lower-dimensional regions- of white layered with red, and the same with black and red in different regions of the grid. These stacks are positions when the path to the forced win is narrow, and most moves lead to a draw, while only few moves win. It is really a multi-dimensional space which we can think in three-dimensions for our own sake, but we lose sight of the big picture. The topology must be really complex. There are even un-connected regions – positions that cannot be reached by normal moves, but which obey the same general rules of the main space. I believe there is a large number of unconnected regions, actually.

Chess is a science because it is a system where truth exists with certainty, and yet it is complex enough that finding it is usually not possible. That is, we know how to paint small regions of this hyper-grid, but most of it remains unpainted.

Cheers,

T.

… And Charles, I believe I sort of answered to you too with my last answer to Fred. Yes, in a sense it is trivial, but so is the human genome. Still, it is fascinating to study it… Even after cataloging it, we will still have lots to understand about it.

Cheers,

T.

Hi Tommaso,

Of course I was being facetious in calling chess trivial. That’s a nice picture you paint of chess-space. I think the topology is known and it is actually a Baire space although I should stress I am not an expert on this.

Chess is determined if you don’t allow draws because if draws are not allowed, either the black or white part must be topologically closed.

Say white has the winning strategy. If white plays not to lose then he plays so that the next move is always in the white part of the space. If he can’t do this then black actually must have a winning strategy from the beginning. If he can play this way, he must win because the game because the closure of the space means that black can always win in a finite number of moves. By symmetry either black or white must have such a strategy.

Perhaps the possibility of draws are what makes chess non-trivial after all and I hope this doesn’t unweave the rainbow of chess for you.

Best regards,

Charles.

Tomasso – I have one more try (again with no board or analysis engine, so … it may be instantly refuted … but …). After 30.Rb7, how about 30…Ra8.

31.Rxb6+ Kd7 32.Nxe5+ and now black can hide on e8 with his back rank protected.

31.Rcc7 Qxb3 32.Rd7+ Kc6 33.Nxe5+ Kb5 and he’s escaped again.

31.Nxe5 Kxe5 32.Re1+ Kd6 33.Bf4+ e5 34.Bxe5+ Ke6 and the rook is no longer hanging on h8; also 32…Ne3 is worth a try now because after the black king gets to f5, nd4+ is no longer a queen fork.

Hmmm….

Derek

[…] is a truly beautiful chess position, as played and analyzed by Tomasso Dorigo, an Italian theoretical physicist. [Dorigo, do I have […]

Hi Derek,

thank you for still analyzing this position… And for writing about it. I think the easiest is Rxb6 Kd7 Nc5+ and the queen is gone.

Cheers,

T.

[…] Published July 26th, 2007 Science! Previously on Reassembler: Dorigo’s fantastic chess sacrifice and subsequent analytical exchange drew my attention to the world of particle physics. In particle […]

Tommaso,

I don’t play chess (too much unnecessary stress), but yesterday I had the pleasure of teaching a young man how to mate with knight and bishop. He wanted to learn to play beautiful chess and said his ideal is the queen sacrifice. I’m going to see if I can find a cheap copy of “My System”. The post-romantic text by Nimzovich should be a good cure for “beauty in chess” disease. I don’t know more modern books that might be better.

Anyway, though I still don’t play, I am still having fun with the game, which amazes me. My observation of the players who show up to play on the giant chessboard at Crossroads (Redmond, Washington) is that their worst play is with the end game.

The secret to teaching a subject is to break it into elements that have just the right amount of meat on their bones, and the end games are so much nicer to learn than openings or mid game theory. Any time I explain anything about chess to someone I have to begin by making sure that they know a lot less than me, LOL.

Along this line, I’m describing the qubit version of QFT on my blog. I think it makes a better introduction to QFT than the usual scalar field theory introduction. Since one works in a finite quantum space, Feynman diagrams converge to all orders in perturbation theory. Which also means that the method is good for bound state calculations. This is the theoretical foundation behind the formula for the neutrino masses I found.

Hi Carl,

chess is not a stress if you take it the right way… It can be relaxing fun. If you visit http://www.chessclub.com (you will need to download an interface, blitzin, to play) we can have a game online one of these days – my handle there is tonno.

The endgame is usually the part of the game when an observer can most easily spot obvious mistakes, and where the ability of players is most evident. To expert eyes, of course.

I will give a look at your page, but I am less of an expert of QFT than you are at chess…

Cheers,

T.

Tommaso,

I’ve been regularly visiting the chess section of the local used book store and found a copy of Rueben Fine’s classic book on endgames at the bargain price of $2.49. I bought it and gave it to the young man. Hopefully I will eventually see better games played soon.

Whilst doing this, I found an interesting book on Chinese Chess, the version of chess that went east after the invention so long ago in India. I learned the game when I was a boy when Laotian refugees taught me in high school. Since then I regularly play my computer. Playing requires that one learn a few words of written Chinese as that is how the pieces are labeled.

The notation for Chinese Chess is quite fascinating in its own right. The board has 9 vertical columns and 10 ranks. The moving piece is specified according to the column. For the rooks, (called chariots), horizontal movement is specified by defining the beginning and ending column (file). Vertical movement is specified as the number of squares relative to the previous position, with the letter f or b to specify forward or backward. So the notation is split between absolute and relative!

For pieces that move diagonally, like knights and sort of bishops, one specifies f or b, and then, instead of giving the number of squares to move, one specifies the ending column (file). So the designation f3 means forward 3 ranks when the piece is a rook type movement, and it means forward to column 3 when the piece can move on the diagonal. Fortunately, there is no queen, and the king can only move diagonally. Thus all pieces move either on horizontal / vertical, or diagonal.

The best thing about the book is that it includes a table of standard openings. Knowledge of most of them have already been beaten into me by the computer, which is quite good. I may eventually write up a blog entry book report on the book. Right now, I’m busily writing down a description of the standard model symmetries. I’m starting with how quantum numbers fall out of separation of variables in Laplace’s equation when the initial conditions satisfy rotation symmetry. Next will be the rotation group and its Lie algebra. Then how excitations are similar to bound states of fundamental particles. etc.