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Comments by MarkThompson
Right, I'm not talking about simply ZIPping the files and sending them, which I wouldn't call encryption at all. I mean using the kind of tools they have on secure servers, which I believe use RSA encryption. I've never needed to get software to do this on my own, but I've heard there's a tool called PGP (for Pretty Good Privacy) that does RSA for you. RSA is the algorithm based on Fermat's Little Theorem, and on the difficulty of factoring huge numbers that are products of two huge primes. It was written up in a Scientific American column in the 1970's, and the Dept. of Defense got all bothered and tried to suppress it on the grounds that it described for a mass audience an encryption technique that would be impossible for their biggest brains to crack. If RSA were not secure, there would be profound implications to the security of online purchasing. If any mathematician found a way to break it, he would make a name for himself by publishing it. No one has.
'Wouldn't it be, in fact, impossible to move the rook 'through' an attacked position? Since the only position the rook goes 'through' is the one position where the King is going to end up.' Not when you're castling Queenside. Then the King ends the move on square c1, the Rook on d1. The Rook passes over b1 and the King does not. The King always moves two squares when castling to either side.
As I read it, the 'Anglican Bishop' designation was really meant to fit into the 'British' theme of the game, and the piece's powers I presume were chosen to resemble a usual Chess Bishop but also be sufficiently different to justify a different name, and the 'colourbinding-celibacy' analogy was merely an offhand remark for helping people remember the rules. It seems surprising that people are so interested by this throwaway comparison to spend so much time analyzing it, when it has no bearing at all on the game. The same rules might easily have been written without making that particular analogy. The topic here is chess variants, or else I would remark how, as a Roman Catholic, I'm always amazed at how fascinated non-Catholics are in anything connected with the practice of priestly celibacy.
Personally, I prefer names that are 'real' nouns, but chosen with as much logic as possible. For instance, a Queen isn't called a Rook-Bishop, so I feel a Marshall shouldn't be called a Rook-Knight. The room this leaves for logic isn't very great, but I'd be inclined to give, for instance, names suggesting greater importance, authority, or strength to pieces that are more powerful: for example, 'Empress' would be a reasonable name for Q+N, but not for (say) B+N. I would give clerical names to pieces whose chief move is diagonal, such as 'Priest' to a one-step diagonal mover (um, that's a Ferz? or an Alfil? I can never remember). I like Cardinal for B+N, and would use Archbishop for a Bishop with a one-step orthogonal move. Animal names are well reserved for leaping pieces like Knights, Camels, Zebras, etc. But the problem with all this is that there seems to be no way to get everyone to agree to use the same terms, and some pieces already have several different names that each have considerable tradition behind them.
'It is also problematic to qualify Catholic for the Pope's followers. Calling them Roman is inaccurate as there is now complete separation between the Vatican, a political entity independent of all others, and Rome, the capital of an Italy with no established religion.' Nevertheless, we call ourselves Roman Catholics. It is inaccurate to call England 'England' since its inhabitants are no longer exclusively Angles. It is inaccurate to call French Fries French since the dish originated in Belgium. Etc., etc., but none of this matters, because derivation is one thing and meaning is another. I am a Roman Catholic, thank you very much, and I would prefer to go on describing my religion by the term that everyone in Christendom already knows.
The PBM system seems to have a bug in the routines that color the board. When I try to change the colors in the preset for Hexagonal Chess from magenta, yellow, and cyan to orange, olivedrab, yellow, the colors that show up on the board are instead three shades of green; and there are blue patches all around the board's border, as if they landed one tile away from where they should have landed. Here's the URL it gave me for accessing my board: play.php?game%3DGlinski%27s+Hexagonal+Chess%26set%3Dsmall%26patt erns%3D%3A+%2A%26hexcolors%3Dorange+olivedrab+yellow%26cols%3D11% 26code%3D1prnqb%2F2p2bk%2F3p1b1n%2F4p3r%2F5ppppp%2F11%2F-PPPPP5%2 F--R3P4%2F---N1B1P3%2F----QB2P2%2F-----BKNRP1%26rules%3D%2Fhexago nal.dir%2Fhexagonal.html%26board%3D201.012.120.%26shape%3Dvhex
You say there are 33 pieces on a board of 169 (13x13), and many of them have varying powers, and the Fisher in particular has powers that vary according to the color of square it occupies. This leads me to speculate that the pieces begin all on the dark (or all on the light) squares of the first 5 ranks of each side of the board, including the corner squares, and that the ones whose powers vary, ALL vary (like the Fisher) based on the color square they occupy. At the start of the game, moving your pieces onto the other color of square 'develops' them, giving them powers that will make them more useful in the middle game. If this is really how the initial arrays are set up, gaining extended diagonal movement would be handy.
Amazons is already implemented for e-play at Richard's pbem server, you know.
My two cents' worth is that 'orthogonal' (as used in game rules) and 'triagonal' are 'terms of art,' useful in descriptions of game rules and hardly anywhere else, and therefore known to people interested in games but not to most others (including lexicographers). I'm mildly interested to learn from the discussion here that their derivations are probably based on confusions, but this doesn't diminish them in my regard. Lots of good words were originally coined ineptly. Any attempt to replace 'orthogonal' with 'lateral,' or 'triagonal' with 'vertexal,' or with any other new coinages, is more likely to create confusion than remove it.
I've seen the word triagonal on the Yahoo 3-D Chess Group many times, always meaning the same thing, and I don't remember anyone having to ask what it meant. I didn't know what it meant when I first joined that group but I quickly figured it out. It made sense to me immediately when I thought about it; I consider 'triagonal' to be as clear and apt as 'tromino,' coined by analogy with 'domino,' with perfect insouciance toward etymological correctness. As long as the word is being used in the context of a 3-D cubical grid I don't see what confusion can result. I agree Gilman's comment, applying it to a 2-D hexagonal grid, seems confused, but then his usages are idiosyncratic (which, indeed, is the whole point of his article).
Orthogonal is used in the study of Latin Squares to mean two Latin Squares like the following: 1 2 3 4 2 1 4 3 3 4 1 2 4 3 2 1 and 1 2 3 4 3 4 1 2 4 3 2 1 2 1 4 3 which are orthogonal because when you combine the symbols in each cell, all possible ordered pairs result: 11 22 33 44 23 13 41 32 34 43 12 21 42 31 24 13 Sets of orthogonal Latin Squares are useful in the design of scientific experiments, or for generating 'magic' squares. Anyway, this is a technical usage of the word orthogonal that may be grounded in the 'at right angles' meaning, but if so I think it's very tenuous. So I feel it gives more aid and comfort to those of us who believe drafting orthogonal to use the way we do in rule descriptions is okay.
No, the first-move doublestep option is only for non-capturing moves. So a pawn that begins on g2 can only move to g3 or g4 (if not obstructed) or capture on f3 or h3 (if an enemy piece is there). Your idea might make an interesting chess variant, though.
As I understand the term, a gambit is a tactic in which a player offers a material sacrifice in exchange for what he hopes is a positional advantage. Familiar openings like the 'Queen's Gambit' involve playing a pawn to a square where the opponent can take it. (Queen's Gambit means the pawn offered is on the Queen's side.) But taking the pawn, presumably, gives the gambit-player a better position. They speak of openings such as 'Queen's Gambit Accepted,' in which the other player takes the pawn, and 'Queen's Gambit Declined,' in which he doesn't. I don't think I've heard of any openings in which a unit of greater value than a pawn is offered. 'Gambit' has entered the language as a word used in general conflict situations, for risky maneuvers like this.
Jared, I believe the cells of the board shown here are topologically connected in the same way as the rhombic dodecahedron tiling you mention. Only the topological form of the board is relevant to play, so I wouldn't think that the translated rules would be enlightening ... if I'm visualizing correctly what you have in mind, I think it would be far harder to understand what the game is about. The trouble is that in any diagram I can imagine, you can only see a cross-section of each level, which prevents the full geometric form of the 3D cell from being seen. If you have 3D raytracer software you might be able to demonstrate it. I'd be interested in seeing that too. The ideal thing would be a virtual reality board, that players would see by donning those goggles that present stereoscopic 3D images that you can see all sides of by moving your head. When those become commonplace I predict a lot of wonderful 3D games will get implemented on them. I still haven't seen that technology, but I hope someday to use them to play Renju on a 'tetrahedral' board of order 13 or so. Charles, I'm reading your post for about the tenth time and am starting to figure out what you're talking about. You say 'square roots' but I believe you mean 'squares.' The base 36 business was confusing to me but you're really just doing it for compactness, so you can indicate each distance (or its square root) by a single character. And your use of 'coprime' doesn't seem to match the meaning I understand by that word. But I'm interested to see that the cells to which a knight at your origin can move are all labelled as distance sqrt(3) from the origin - well, that would make sense, just as a FIDE knight's moves are all sqrt(5) in length. Okay, I'm starting to follow your arithmetic - and I'm surprised, I wouldn't have guessed that the centers of cells in a rhombic dodecahedral grid would have distances whose squares are integers - though now that you point it out, I don't see why not. I'm not sure how playable your proposals for Unicorns and Nightriders would be on this grid -- it seems to me that to give them sufficient scope to practice their powers the board would have to be considerably larger and so have a huge number of cells, and a IMO game whose board has too many cells becomes too complicated to be interesting, because the moves have so many consequences no human player can foresee them; hence, it turns into a game of chance rather than skill. However, many people disagree with me, and I would be glad to see other game developers try their hand at this grid. If you're inspired, go for it!
Larry, your idea of showing the cells as points where color-coded lines of movement intersect works well with another idea I've been turning over in my mind. I've never been quite satisfied with the 'Dababantes' that I used as Bishops in this game -- they're color-bound, but that's about the only way they resemble chess Bishops. What I've been thinking of is to designate three of the six lines through each cell as 'rook lines' and the other three as 'bishop lines'. This would make rooks weaker than they were in Tetrahedral Chess, and Bishops would have really equal power to Rooks. In your xiangqi-style board representation, the rook lines might be colored red and the bishop lines blue. If the seven squares of level I where the White pieces begin are considered to be in an 'east-west' row and the seven squares of level VII are in a 'north-south' row, then I would make north-south and two of the vertical edges 'rook lines,' and east-west and the other two vertical edges 'bishop lines.' Neither the rook line edges nor the bishop line edges would make a triangle on the surface of the tetrahedron; they would be symmetrical with one another. And then, I would arrange the Black pieces differently from the White pieces, putting rooks in place of bishops and vice versa, because the orientation of the levels on which the two sides begin would in effect 'turn a rook into a bishop,' if you see what I mean. (Sorry, it's hard to describe without a diagram.) But this is just thinking out loud in public, I haven't tried any of it out yet.
Jared: Are you still going to have the two armies start on opposite edges of the board? That was what prompted me to orient it as I did in my diagrams, rather than the usual idea of a tetrahedron resting on its base. I look forward to seeing your variant. One could also use the basic rhombic dodecahedron grid as a playing space with something other than a tetrahedron as the overall shape of the board. For example one could chop off the corners and make either an octahedral board, or (by chopping smaller pieces) a board with 4 hexagonal and 4 triangular sides. I calculate that an order-6 octahedron would have 146 cells.
Jared: Ah! I think I see (why you're using an order-4 octahedron). Very timely! But opposite faces will have only space for 10 pieces, and the armies are already only separated by 2 layers, if I'm imagining it right. That would mean rather small armies for the space available.
Charles, after reading your latest about the rhombic dodecahedral grid, I thought to look up 'rhombic dodecahedron' in the invaluable Penguin Dictionary of Curious and Interesting Geometry, where I found the following tidbits you might find interesting: 'rhombic dodecahedron: Take a three-dimensional cross formed by placing six cubes on the faces of a seventh. Join the centres of the outer cubes to the vertices of the central cube. The result is a rhombic dodecahedron. ... From the original method of construction, it follows that rhombic dodecahedra are space-filling.' [etc.] Indeed, if you imagine space filled with alternating black and white cubes, and perform the construction by dividing up the white cubes into six pyramids apiece and affixing them onto their black cube neighbors, you get the r. d. grid, and this supports your observation that the grid is conceptually identical to the cubic grid with the white cubes removed.
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There is a zrf for Shafran's Hexagonal Chess. It's on the Zillions site listed under 'Hexagonal Chess.'
Playing on squares doesn't bother me, but I would suggest that -- since the player has to make his own 9 x 10 board anyway -- there is no good reason to make the squares checkered dark and light, because this game doesn't have diagonal sliders. I would probably shade the two fortresses, and maybe also mark the squares that constitute the Elephant's domain with a dot in the middle or something. But the idea of introducing Xiang Qi to westerners with a more western-appearing set sounds reasonable.
People like chess variants for lots of reasons, and some prefer the more exotic variants that depart from usual chess with unusual pieces or rules: you don't find that in Millennium Chess. But, without diminishing the exotics, I like the more modest variants also. I've played this one and found it to be pretty good. And yes, it did seem to improve my skills at usual chess, at least temporarily -- or at least my confidence level. When you come back to 8x8 after a few games you have this strange feeling: 'Why, this game will be SIMPLE!' I haven't tried the other variants that are approximately double width and so I can't opine on how this one compares with them. I once communicated briefly with the inventor, who said that while developing M.C. he tried other versions (among them, 8x16) and rejected them. He says having two rooks in the center of the board is too much power there. I expect the choice among wide chesses will also come down to personal tastes.
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