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| | Page: [Previous] [Next] 1 2 | | (21) Posted by Georgy Evseev [Saturday, Oct 9, 2010 10:45] |
@Oliver
I may only interpret your last message as intentional misleading.
But hoping that it is not so, here are several examples.
G.Fuhlendorf
H.m., BCPS, 1931
 (= 3+3 )
h#3*
1...Rd6 2. Sf5 e3 3. Sd5 Re6#
1. Sc2 Rd5 2. Ke4 Kd6 3. Sd4 Re5#
This is definitely an exact echo (and chameleon one) as all pieces are shifted one row down. (You may see that black knights exchange their places, in a sense, but in this problem it does not matter.)
G.Fuhlendorf
Aachener Anzeiger, 1932
 (= 4+3 )
h#3**
1...Sfd2 2.Sd3 Rf6 3.Se5 Rd6#
1...Sfg5 2.Sc2 Rc1 3.Sd4 Rc5#
1.Sc2 Rb1 2.Kc4 Sed2 3.Kc3 Rb3#
This is also often considered as exact echo, because all the pieces taking part in mating position are placed on exactly same places. The shift and/or rotation is bigger than in previous case. At the same time some people will say that the echo is not exact, because white king and black pawn are not shifted together with all other pieces.
F.Hansson
Eskilstuna-Kuriren, 1932
 (= 4+3 )
h#3*
1...Kf6 2.fe Bg2 3.Kf4 Se2#
1.gh Sc6 2.Kf3 Bf2 3.Kg4 Se5#
This is also an echo, but not exact. While the functions of white knight are the same (check and similar flight control) the mating positions are not exactly matched. The echo would have been exact if the knight arrived on h2 instead of e5.
| | | (22) Posted by Oliver Petrov [Saturday, Oct 9, 2010 17:29]; edited by Oliver Petrov [10-10-13] |
I only quote what is written, nothing more./I am a mere beginner/. I already found the answer to the question I asked from the above article. I didn't know about this article, that's why I asked before.
edit: sorry if I have misled somebody
| | | (23) Posted by Cornel Pacurar [Sunday, Oct 10, 2010 13:16] |
First of all, there seems to be some confusion around “exact echoes” (i.e. “mate on different parts of the board is echo, and the same mate is "exact echo"”) - the answer is simple: regardless their position relative to the board, all related pieces have to be in the same position relative to each other. For instance, White Ka3 Rc1 Black Ka1 and White Kh3 Re1 Black Kh1 are not exact echoes, because in the second position the white rook is at e1 instead of the expected f1. In relation to this, several examples of “pseudo-echoes” can be seen starting page 80 in “500 Triple Echoes in Help play” by Vaclav Kotesovec (http://problem64.beda.cz/silo/kotesovec_500tripleechoes.pdf ).
Beyond semantics and geometry definitions, many problemists do not see “two absolutely identical mating positions” (that is, including identical position relative to the board) to be anything more than just “two absolutely identical mating positions”.
For many they do not even qualify to be labeled as static echoes – while dynamic echoes require that the king is mated on a different square (when of different color we then have what is sometimes called “chameleon echo”) and the final position is either translated, rotated or reflected, static echoes are the ones where the king is mated on the same square, the position being reflected or rotated. See, for instance, “Echoes in long helpmates” by Vaclav Kotesovec (http://problem64.beda.cz/silo/kotesovec_echoesinlonghelpmates_2002.pdf), page 116.
For others (i.e. Dr. J. Niemann), they are a worth-to-be-mentioned small subset, and for others (i.e. George Jelliss) they are a class of their own: “Identity Echoes”:
Indeed, the first 36 problems included by Dr. J. Niemann in his 1950 “Echo Im Hilfsmatt” (http://problem64.beda.cz/silo/niemann_echoimhilfsmatt_1950.pdf) are of this sub-type. Niemann’s classification system includes four types of echoes: Reihenecho, Achsenecho, Punctecho and Reihen- und Achsenecho, where “Reihenecho = Das Echo entsteht durch Verschiebung des Mattbildes in irgend einer Richtung auf dem Brett”. For “two absolutely identical mating positions”, the displacement of the matting position is 0 squares both vertically and horizontally. Take a look at the problems quoted by Niemann, a few of them are quite interesting!
In 1983, in Chessics 15 (http://www.mayhematics.com/p/chessics_15.pdf ) George Jelliss announced an “Exact Echoes Tourney”, and Chessics No. 17 (http://www.mayhematics.com/p/chessics_17.pdf ) is dedicated to exact echoes. George gives examples of the five types of exact echoes that he defines based on isometry (Identity, Translation, Reflection, Rotation and Glide (Transflection)) and gives the following definition: “An EXACT ECHO occurs when ALL the pieces in the two configurations concerned are in the same positions relative to each other, but possibly in a different position relative to the board.” (see page 2). I find this definition misleading, as even assuming that the identity echoes are universally accepted, for the overwhelmingly vast majority of echoes the positions are different relative to the board, thus “possibly in the same position relative to the board” would have been more appropriate… The award is published two years later, in Chessics 23, (http://www.mayhematics.com/p/chessics_23.pdf), page 83. As luck would have it, 25 more years later, on July 21st 2010, George publishes a 50-page booklet which derives from the tourney: “Exact Echoes” - http://www.mayhematics.com/p/exactechoes.pdf . Pages 1 to 8 (including 24 problems) are of interest in relation to this post topic.
To end in a different note, here is a new and very interesting idea of Vaclav Kotesovec, which is based not on symmetry, but on similarity, therefore eliminating “en-passant” the ‘identity echoes’ dilemma: Magnified Echoes!
http://web.telecom.cz/vaclav.kotesovec/kotesovec_magnified_echo_2010.pdf
And, finally, two comments for Ian:
@ Ian RE: “I've only ever seen echoes defined as various types of basic *symmetries* - i.e. translation, reflection, rotation, transflection. If one accepts this, then according to the formal mathematical definition of symmetry, identity is indeed a type of symmetry (albeit of the most trivial kind) hence is an echo.”
George Jelliss claims in Chessics No. 17 that he has coined the term “transflection” (actually also used in spectroscopy) to replace “glide” as one of the five possible distinct transformation types of an echoed configuration, as per the geometrical terminology - I am not quite sure where else have you seen “transflection” associated with echoes?!
@ Ian RE: “Eugene Albert's more recent "Ideal Mate Encyclopedia" (Volume 2) confirms this view.”
I fail to see how Eugen Albert confirms George Jelliss' point of view with regard to identical echoes. Eugene only emphasizes the distance between the matting squares when using that as the primary consideration in setting up the order of arrangement for problems (that is, multi-solution ideal-mates) in IME Vol. 2.
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