>But I do think the asymmetry of the board/pieces is of greater importance than Stan admits. (CK).


Brief overture:

The following two statements are BOTH true ... But INCOMPLETE:
  1. The standard* 8 x8 chessboard is SYMMETRICAL
  2. The same chessboard is ASYMMETRICAL

(* yes, ‘standard’ means the nearest rightmost square is on the right-hand side for BOTH players! White Q square d1 is white on left; Black Q square d8 is black on right. Some of us oldies prefer the English over the Pagan (Algebraic) notation! White’s Q1 = Black’s Q8; vice versa)

Further progress is a problem unless you understand that symmetry and asymmetry are properties that depend on WHICH TRANSFORMATIONs you are APPLYING.

  1. A Rotation of 180 degrees (clockwise or anti-clockwise) about a vertical axis through its midpoint leaves the chessboad looking the same => a symmetrical transformation.
  2. A Rotation of 90 degrees about a vertical axis through its midpoint ALTERS the chessboad’s disposition, INTERCHANGING BLACK/WHITE squares => an asymmetrical transformation.
Each chess PIECE DESIGN (Staunton etc) has its own set of symmetries/assymmetries. But you can play Chess with 32 COINS!
Progress Test: are 1 and/or 2 true for a 7 x 7 ‘chessboard?’

As well as these trivial ‘geometrical’ manipulations, there’s an infinite  number of abstract symmetries/asymmetries, many with physical analogues.  

What about the following KEY transformation (call it BW) to a fully-populated, intitial chess board?:
CHANGE WHITE-to-BLACK/BLACK-to-WHITE applied to all squares AND pieces but NOT to starting RULE? (New White starts):

You’ve effectively achieved a MIRROR reflection (imagine the mirror placed vertically behind the original “black” player). If I’m standing behind the original “white” player I now see in the mirror the reflected “black” player, playing second in the reflected game! So BW and Reflection identically switch first/second player!

This, I repeat, is the ONLY TRUE game-changing Chess asymmetry: white has a marginal STATISTICAL advantage. None of the board/piece/setup conventions OFFER this ADVANTAGE, regardless of mathematical symmetries/asymmetries.

Back to your text:

>Too bad we haven't Dmitri to consult (CK)

As my T-shirt says: “F**k Google. Ask Stan!”

We all miss Dmitri Nabokov, but of  his many, many admired achievements, command of the profound mathematics/physics of symmetry/antisymmetry is not apparent in any publications I’ve encountered. Refs requested.

His dad’s esteemed corpus does often refer to these concepts (always beautifully aphoristically!), but at what is a mathematically trivial level compared with their cosmic implications.

Tongue-in-cheek (advanced readers only ;=)):  
Does ignorance or misogyny explain the absence of EMMY NOETHER (1882-1935) in any of VN’s works?  The greatest female mathematician (so far!) whose eponymous Theorem connects each CONSERVATION LAW with an abstract SYMMETRY group. Their careers overlapped in space-time and suffering. Emma was expelled from Go:ttingen in 1933 (the Nazi’s first wave of anti-Semitic legislation) and ended in the USA (Bryn Mawr, Philadelphia)

Martin Gardener, the late-great maths-amateur popular populariser is a much better source. By all means read the Ambidextrous Universe. The FIRST thing you’ll learn is what I said in my Overture.

The statement “X is asymmetrical” is meaningless/incomplete without adding “ ... (asymmetrical) with respect to some given transformation”

> ... he (MG) does mention that if the universe were not asymmetrical it wouldn't exist. In other words, matter and anti-matter would cancel each other out. (CK)

As reported, this is highly garbled and difficult to unwind. MG is referring to  the well-established CHARGE REVERSAL TRANSFORMATION. (Separately C[harge], [P]arity, and T[ime] REVERSAL are each asymmetric, but combined as CPT, believed to be symmetric).

Each elementary particle in the Standard Model has an ANTI-particle ‘partner’ (electron/positron; proton/anti-proton, neutrino/anti-neutrino, ...).  
With same mass (and other properties) but opposite charge/quantum-spin. Particles and anti-particles are right NOW colliding EVERYWHERE (INCLUDING so-called VACUUMS) by the gaZILLIONS into tiny ‘bursts’ of energy (radiation). The UNIVERSE has NOT disappeared (yet a while) because  these particles are ALSO APPEARING as opposite-C pairs spontaneously in an endless quantum ‘stew.’ Atoms that make up some of our every matter, have corresponding C-transformed atoms = anti-matter. CERN has created millions of Anti-Hydrgen atoms and can observe them for several microseconds (an ETERNITY in quantum terms) before anihilation  ... O dear ...

This is major VN-DIGRESSION. Let me refer you to Wiki
At this time, the apparent asymmetry of matter and antimatter in the VISIBLE universe is one of the greatest unsolved problems in physics
Ending on a VN cum non-Tech Literary-Science note:

Following two quotes are cited in the browsable anthology:

Vladimir Nabokov said of the gap between science and art:
'a mere dimple of a ditch that a small frog could straddle'

Freeman Dyson, end. Chap 1, 'Infinite in all Directions'

"This quick tour of the universe will begin with superstrings and end with butterflies. There will be a couple of intermediate stops on the way. Like Dante on his tour of the Inferno, I find at each level some colorful characters to add human interest to an otherwise intimidating scene. I will not explain what butterflies and superstrings are. To explain butterflies is unnecessary because everyone has seen them. To explain superstrings is impossible because nobody has seen them. But please do not think I am trying to mystify you. Superstrings and butterflies are examples illustrating two different aspects of the universe and two different notions of beauty. Super-strings come at the beginning and butterflies at the end because they are extreme examples. Butterflies are at the extreme of concreteness, superstrings at the extreme of abstraction. They mark the extreme limits of the territory over which science claims jurisdiction. Both are, in their different ways, beautiful. Both are, from a scientific point of view, poorly understood. Scientifically speaking, a butterfly is at least as mysterious as a superstring. When something ceases to be mysterious it ceases to be of absorbing concern to scientists. Almost all the things scientists think and dream about are mysterious...................

On 13/02/2013 23:17, "Carolyn Kunin" <chaiselongue@ATT.NET> wrote:

I was thinking of Lewis Carroll of course (the Red Queen and the Red King) and you are right - something I never seem to get correct is that the Queen is on her own color - so the two queens do oppose each other. The King is a McGuffin anyway.

I rarely play chess - learned by watching my father play. But got quite good at it while hospitalized with nothing else to do. But I do think the asymmetry of the board/pieces is of greater importance than Stan admits. Too bad we haven't Dmitri to consult. Perhaps Martin Gardener in his Ambidextrous Universe discusses chess.

There is always confusion about this amongst us casual players - I for example just learned that the white square must be to the player's right. And few casual players know that it is possible to castle on both the king's (short) side and the queen's (long) side.


p.s I do happen to recall that in Martin Gardener's Annotated Alice, he does mention that if the universe were not asymmetrical it wouldn't exist. In other words, matter and anti-matter would cancel each other out.

From: "stan@bootle.biz" <stan@BOOTLE.BIZ>
Sent: Tue, February 12, 2013 4:35:57 PM
Subject: Re: [NABOKV-L] Ada

Re: [NABOKV-L] Ada CK’s reported ‘King & Queen asymmetry’ will come as a surprise to ALL chess players, both the skilled amateur (like Nabokov/Sirin, author of "Защита Лужина," the ‘worst chess novel ever written!’), and first-day learners!

See http://chess.about.com/od/rulesofchess/ss/Boardsetup.htm

You’ll see that the White Queen, initially at d1, ‘faces/looks-at’ the Red (aka Black) Queen, initially on d8, separated by pawns at d2 and d7. Likewise the two Kings initially ‘face/look-at’ each other along the e-column, from e1 and e8, with pawns at e2 and e7. Both the board and piece-settings are positively dripping with symmetries. These make the game the fairest of all, and ‘boredom’ doesn’t enter into it!

Perhaps the confusion arises because ‘colour’ is assigned to both squares and pieces? But, of course, the White Queen remains White even if she moves to a Red/Black square.

Incidentally, regardless of the arbitrary, physical colours of the pieces, official English ‘chess-speak’ calls the opponents White (making the first move) and Black (responding). This White ‘initiative-ADVANTAGE’ is, in fact, the ONLY GENUINE ASYMMETRY in Chess! Hence, the choice of colour for Game 1 is traditionally a 50-50 random ‘coin-toss.’ Subsequent games, in most tournaments, then alternate who starts so that the ‘White-advantage’ is evened out.

On 11/02/2013 15:45, "Jansy" <jansy@AETERN.US> wrote:

Carolyn described* the asymmetry of how the King and Queen are displayed in a chessboard, with white kings staring at the red queens, aso. Indeed, this must have tickled VN's sense of plot and humor, in particular!
*  {...} As a player of chess, Nabokov is of course intrigued by the play of symmetry (the chess board) and asymmetry (the position of the pieces on the board - in other words, the white king looks at the red queen, not at the red king). If this were not so, the game of chess would be boring indeed.[   ]
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