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Man and Beast 04: Generalised Generals. Systematic naming of part-symmetric coprime radial pieces.[All Comments] [Add Comment or Rating]
Bn Em wrote on Thu, Oct 9, 2014 06:37 PM UTC:
"Motorcyclists may be disappointed that the name Goldwing is not used!"

Wouldn't a Goldwing simply be a wing which can also make one step in the remaining Goldgeneral directions? Likewise for e.g Silvermitre, Brasswing, Foresthorn, etc.

Greg Strong wrote on Tue, Feb 1, 2011 02:11 AM UTC:
Way too much drama 'round here

🕸Fergus Duniho wrote on Tue, Feb 1, 2011 01:33 AM UTC:
Thanks for the heads up. The fischerplayed person is writing in the same style as the recently banned George Duke. I have merely blocked his comment instead of deleting it so that other editors may ascertain whether it is him.

Earl wrote on Tue, Feb 1, 2011 12:47 AM UTC:
He's Baaaaack

Somebody wrote on Mon, Jan 31, 2011 04:49 PM UTC:
[This comment is hidden pending review. It will eventually be deleted or displayed.]

Man and Beast 04: Generalised Generals. Systematic naming of part-symmetric coprime radial pieces.[All Comments] [Add Comment or Rating]
George Duke wrote on Sun, Jun 28, 2009 08:09 PM UTC:
That cubic Ferz triangulates. Take 8 cubes 2x2x2 labelled ccw below 1-2-3-4 and above '1' 5-6-7-8 ccw. Ferz goes 2->7->5->2, or else 2742, or 2572, or 2542, or 2452 or 2->4->7->2. There are no more starting with cube-2. Since any of the other seven cubes can begin similar patterns, there are (6x8) 48 possible Ferz triangulating sequences in 2x2x2. It's the ''normal'' thing, literally and figuratively as Gilman would say, since there are several pathways. Noticing 336 (and 392) familiarly as 8x7x6 and 8x7x7, here there are 8 concocted starting cubes, and since triangulating involves two more different cubes, 7, then 6 with the last step the same numbered cube as the first, so 8x7x6x1 possibilities. 336 thus represents # cube-sequences without regard to the Ferz move-rule in quasi-minimal 2x2x2. Real Ferz actually has the above 48 of this maximum 336 possible. Now 336 is the same number in Falcon USP5690334 as number of square-based pathways 2-D  allowed Jetan's Chieftain with no ''doubling back,'' with 392 also for less restricted Chieftain interpretation. There in the text over a decade now, (8x7x7) and (8x7x6) the elements are the 8 chess directions of each step in Chieftain's three-step pathways. Falcon uses precisely 48 of Chieftain's 336 (or 392, depending on strict or loose interpretation of Chieftain). It is well-known Falcon has those exact 48 pathways to her 16 squares. Dis-allowing 135 degrees is another way to arrive at only 336 rather than 392. In computing pathways 336 for Chieftain three-steps, it matters whether changes of direction are 135- or 90-degree and exact orthogonal-diagonal order and positioning, not allowing revisiting spaces already passed over;  but those are the numbers reached arithmetically on sufficently-large lay-out, 10x10 being ideal. Cubes 2x2x2 and squares 10x10 and both numbers 48 and 336 out from their very different geometries.  After all, Gilman's ND root-3 shows important comparability between space-filling squares and hexagons in that number; so such other more-so tailored parallels are not surprising from cubic and square geometries taken together. 48 and 336 paired and emerging in different contexts, one cubic, the other one ordinary flat decimal board in compelling pre-cognitive patterning.

George Duke wrote on Sun, Jun 28, 2009 07:36 PM UTC:
Not interested in speculative ''far-ranging'' conversations with no touchstone but self-interest, that belong in Game Courier scores, where they also detract, I am set to emphasize analysis. Please continue in Philosophy and later some succinct couple sentences may sum up a week's talk. (1) Gilman has at least 5 geometries: square, hexagonal, cubic, hex-prism, tetrahedral. The goal is to describe hex-prism and tetrahedral with some same depth as Gilman. (2) Simplicities having gotten lost in discussion: one-stepper cubic through faces is Wazir, diagonals Ferz, triagonals Viceroy. FO versions of these are Point, Cross, and Saltire. (3) One-stepper rank-switching Silver General cannot triangulate in squares. Gold General is Wazir + Cross. Silver General is Ferz + Point. The latter is in cubes, where rank-switching does not necessarily prevent triangulation. Colourbound Ferz cannot triangulate in squares, but cubic Ferz triangulates. On hex boards Unicorn and Viceroy are clearly bound to 1/3, and that holds for hex-prism because by themselves there is no provision to switch levels. (4) In practice of designing 3-D CVs -- not particularly upheld by Gilman's nomenclative system -- we recommend for these simplest radials in a piece-type solo directions of Wazir-Rook, or else Ferz-Bishop, or else Viceroy-Unicorn; or all three at once in (probably) powerful piece. Using only two directions in a radial compound, (o+d), or (o+t), or (d+t) will lessen clarity whenas piece-types other than simple radials admit to the congregation.

George Duke wrote on Fri, Jun 26, 2009 10:21 PM UTC:Excellent ★★★★★
First comment here for Gilman's Generalized Generals. (1)If you think of new Pawn or Pawn enhancement to mid-power piece, chances are up to 50-50 it has already been named or catalogued by Gilman. (2) If you think of any Mutator you imagine you've invented, probably Betza already has it described, or else Neto; or Betza inspired someone else to implement such Mutator by now. For these are the end times. (3) FERZ triangulates in cubes but not in squares. That is because in cubes Ferz uses any edge including ones orthogonal to each other. (4) SEABISHOP sounds like the great thoroughbred Seabiscuit 1933-1947. Suppose SEABISHOP in cubes to be ROOK + FERZ + SALTIRE. (Gilman may correct the name for this related tri-compound; using the example does not hinge on the name per se.) SALTIRE from 'M&B01' references with POINT and CROSS. We are talking cubic now and Gilman cleverly goes back and forth by way of SD and ND, so we get used to all geometries at once. Back at 'M&B01' just view a cube from front and POINT is in your face through faces, just that, Point-like one-stepping Wazir-like. CROSS SD in the same orientation, staring into the face of a cube looks like cross Bishop-like, and SALTIRE ND is triagonal one-stepper ''cross-wise'' to your same eyes. All these are FO (Forward) because we already have their omni-directional names as Wazir, Ferz and Viceroy (M&B01). (5) Returning to 'M&B04', why have a rather weak FO SALTIRE with strong Rook and all-way Ferz in tri-compound SEABISHOP? Because it makes just as much sense to have all three directions as only 2 of 3 built in. The logic of 3-D is either orthogonal, or diagonal, or triagonal, or else all three in a piece-type; the only other possibilities being o-d and d-t and o-t. Gilman calls 'd' SD standard diagonal and 't' ND triagonal, that I use in ''Multi-path Chess Pieces.'' We'll have to merge somewhat later Betza's Funny Notation and Gilman's in areas of overlap and also where Gilman diverges from concise Betza linguistics. (6) When you have symmetric and FO compounds in any geometry, the FO aspects may get fresh start over and over after the symmetric leg ''backpedals'' as much as possible in actual play. Gilman in 'M&Bxxs' seldom discusses actual play except formally as triangulating etc. (7) Gilman is saying in the paragraph starting ''Now it gets complicated'' that some CVs other than Tunnelshogi and 3DMinishogi have illogical promotions. What are they?

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