Bill -- I prefer 'Nimzowitsch', although technically it's the German version. It was at least used by the man himself, after 1920. Earlier, he also used 'Niemzowitsch'. And later, some English-language books, like Reinfeld's 'Hypermodern Chess', rationalized the spelling to 'Nimzovich'. Simpler, but I find it ugly. So 'Nimzowitsch' it is.

As for those opening stats, they're tricky -- they don't take account of an individual's changes in opening over the course of their career, or of variations in success at different times. Nimzo played 1.e4 almost exclusively before 1912; much more rarely in the 1920s, when he was stronger. So his 1.e4 period coincides with a time when he lost more games.

It had to do with the domination of computer analysis and my inability to deal with that given and at the same time knowing you can't do without...

I chose words for that post but didn't like the tone, nor the objective of it...

I was courteous enough to at least mention that, for anyone who might have read it, reacted, or wanted to.

Deleting without notifying has been perfected by one of our famous users; I do not intend to belong to that group.

Bottom line: I am not sure if I want to give "my cents" in the World v GMT game, yet. That was my honest opinion yesterday, but it might change over time.

I might post the relevant position later, if anyone's interested.

<Frogs, Knights on the Rim, and the n-dimensional chessboard>

Generations of chessplayers have been misled by the fact that (locally) the chessboard is square and flat into thinking that the game is played in two dimensions. In fact (as mathematicians such as R.Atkins have observed) the game is played in an n-dimensional space where dimensionality is governed by the position of the pieces, including pawns.

The pieces warp the chessboard space -- much as spacetime is warped by mass in Einstein's general relativity.

Thus a Knight on, say, a4 or e8 is not necessarily 'on the rim' at all. Superficially, it is on the edge or rim of the local 8x8 plane -- but, depending on the squares it can reach and the layout of other pieces, its position can actually be regarded as *central*.

Nimzowitsch glimpsed this when he argued that moves like Nh1 were part of a centralizing scheme -- but he failed to go all the way. That is: a Nh1 is in the corner of the physical board, but is already centralized on the n-dimensional meta-board.

Full mathematical proof, complete with Riemann spaces and Quaternions, to follow when I get around to it.

click for larger view

White has just played 36.Qh8+, to which Dorfman replied 36...Ke7.

If instead 36...Kd7, the line credited to Karpov is 37.e6+! fxe6 (37...Kxe6 loses to 38.Qc8+ Kd6 39.Qb8+ Ke6 40.Qb6+ Ke5 41.Qc5+ Qd5 42.Re1+) 38.Qd4+ Qd5 39.Qa7+ Kd6 40.Qb6+ Kd7, reaching this position:

click for larger view

Now, supposedly "41.b3! and Black has no useful move" (Karpov)

In fact Black has 41...Rh6, which is very useful indeed. It prevents a White winning maneuver with Rf7+ & Rh7, and it leaves White an apparent choice between more queen checks and a move like 42.Qg1 -- none of which seems to lead anywhere for White.

But look instead at 41.a3 -- the same luft for the king, but with a crucial difference. If Black plays 41...bxa3, he loses:

41.a3 bxa3 42.Rf7+ Ke8 43.Rh7 wins, eg 43...Qd1+ 44.Ka2 Qd5+ 45.b3 Qe5 46.Qc6+ Kf8 47.Qc8#

And if 41...Rh6 as in the other (b3) line, then:

41.a3 Rh6 42.Qa7+ Kc6 43.Qa8+ Kb6 44.Qb8+ Kc6 45.axb4 axb4 46.Qxb4 nets a pawn and gives white strong winning chances.

And I see you've just potted the sixteenth virtual meta-red... really going for gold now, yes?

I'll try and behave now and will come back to your detailed lines later but I did get around to run through the game with my engine (grammar?), and was quite annoyed at its eval after the Turm-tausch at move 26/27:

Instead of 40.Qb6+, Fritz indicates that an immediate 40.b3! should win: after 40...Rh6 41.Qb8+ Kc6 42.Rf4 the threat of Rc4+ is deadly, and the black queen can't check on either d4 or e5 following 42...Rh1+ 43.Kb2. Or - 40...Rg4 41.Qb6+ Kd7 42.a4! (42. Rf7+? Ke8 43.Rh7 Qd1+ 44.Kb2 Qd4+ with a queen exchange and draw) and White's attack is decisive.

So instead of 39...Kd6, Kc6 is somewhat better - but then after 40.Qa6+ Kd7 (Kc7 41.a4!), the 41.a3 idea should work in a similar way to the line you gave (White can still win a pawn with axb4 followed by Qa4+).

With all the subtleties involved in checking an exposed king with heavy pieces in different ways, this seems to be a type of position where the brute calculating force of engines would tend to give them a clear advantage over humans.

And yes, this is a type of position where engines are more efficient. Although I think one still needs human oversight, if only to check lines that seem (humanly) plausible, but are bad -- and which for that reason won't show up at all in the engine lines.

And occasionally there are those very deep-ply continuations -- like the rook sac perpetual that wasn't, in the GMAN game -- that require either serious processing power and time, or judicious sliding to find the flaw.

<Dom> Thanks for the Nimzo stuff. I couldn't check the corelation between his age and his opening choices, but as you point out, there's no doubt that as hypermodern theory progressed, he chose 1 e4 less often (though several of his vicoties with 1 e4 in the cfollection I was referring to--and ancient affair compiled buy one Wellmuth) are from the '20s, including a victory over Alekhine at Semmering in '26).

That reminds me of a post by <Thorsson> from the Nickel game:

<There are all sorts of possibilities as to why he played Qb5:

1. It was a genius trap that we have collectively fallen into;

2. It was an out and out blunder;

3. It was a move to see what we'd play knowing he was already lost;

4. It was a move made to maximise the chances of us going wrong in a game that was lost;

5. GMAN was just playing generic active moves without analysis;

6. GMAN is giving us a Xmas present;

7. GMAN has a sure fire method of making us play a blunder at the appropriate point, and he just needs to get the right position;

<<<8. GMAN has a piece in the nth dimension that will suddenly appear on the board with devastating effect;>>>

9. Something else.>

Earlier, I thought 23.Rg6!? looked interesting. It can't be taken (23...fxg6 24.Nxe6 is murderous) -- but black can play something like 23...Bb7, and White may have nothing better than 24.Rg5, the same exchange sac as the game, but with an extra move for black.