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George Duke wrote on Wed, Feb 4, 2009 05:53 PM UTC:
ChessboardMath6 is for other Falcons. (1) OSPREY is the (first) Falcon that
switches back. Now, in the large, all Falcons go to squares removed (2,4)
and (3,4). That's a given, handed down. Others call the squares (1,3) and (2,3), thinking of dynamics in
reality of motion, not of plain statics setting the standard. There will
be over 100 other Falcons different here (and ChessboardMath7 -8 -18 -28: we'll cross that bridge yonder). Osprey follows Rook-lines only
in three legs of noncircuitous route. First leg is to any edge square, thence along the edge to
the same rank or file of the target (2,4) or (3,4) arrival square,
finally ''switching back'' to that very square. Thus either two, three, or four edge squares are mandatory. OSPREY. Here is an
example on 8x10. Departure square b2 moves to b8 (edge) to d8 to d5. That is one way to move b2-d5.
Blocking can occur at any of b3, b4, b5, b6, b7, b8, c8, d8, d7 and d6,
disabling the pathway. OSPREY. (2) Second, ''BISON'' moves directly
without specified pathway, like a DABBABAH or ALFIL, but not to their
(1,3) or (3,3) respectively, instead to regular (2,4) or (3,4) at will. No blocking of BISON in two dimensions.

George Duke wrote on Wed, Feb 4, 2009 06:38 PM UTC:
(3) The Fourriere Falcon, enunciated by Antoine in 2004, operates in two
legs. First Knight leap to (2,3) requires vacancy or the move is
dis-allowed. Second the slide (or leap, according to your preference of
visualization) to the (2,4) or (3,4) square. There is no stopping at (2,3). Fourriere Falcon is handy for
early acclimatization to the fact there are four fundamentals, not three,
lodged as it is in the leaping Horseman. Quick study Antoine subsequently revised the comment omitting the description once he realized within the day the full impact of the regular Falcon modality.

George Duke wrote on Thu, Feb 5, 2009 11:21 PM UTC:
''Being blockable'': I think 70-80 of the following will be being blockable, the essence of the conception and applicable to Bishop and Rook too, the norm after all for 6 of 7 chess pieces. (4) We shall have 100 versions of the piece. The number four version of
Falcon is MARSH HAWK. Marsh Hawk flies low and slowly, a sight to behold.
(Species M.H. suffers from the general loss of amphibeans worldwide as a
result, to M.H., of pointless destructive civilisation
population-exploded.) Like Osprey, switch-backing piece-type M.H. follows
only Rook-lines, but has different modality. MARSH HAWK does have 3 legs like
OSPREY. M.H. first leg is either 2 or 3 or 4 steps in one orthogonal
direction. M.H. can only move to the Camel(2,4) or Zebra(3,4) square from
behind orthogonally one step, or sideways if after two prior legs. So, M.H. second leg, upon 90-degree turn, is also
either 2, 3, or 4. The third leg is the (mandatory) one step switching back another 90
degrees. An example from b2 is b2-b3-b4-b5-b6-c6-d6-d5, thus one way to
move b2-d5, capturing or not. Blocking is possible at any of the
intermediate squares, voiding the pathway.  MARSH HAWK. Properly Northern Harrier (Circus cyaneus).

George Duke wrote on Fri, Feb 6, 2009 06:12 PM UTC:
''Which Falcon?,'' asked a friend ten years ago. ''Peregrine.''
''What, a Horse of a different colour?'' ''Barbary, Gyrfalcon,
Lanner, Laughing...''  ''What's the colour of a different Horse?''
''Behold a pale horse.'' Version (5) of the piece is Pigeon Hawk. P.H.
lacks the middle leg, the split block and split diagonal. P.H. has no S-D-S
or D-S-D. Instead only straight-straight-diagonal, s-d-d, d-d-s and d-s-s
directly to its pathway with no twists. Pigeon hawk you may even see (not so good as she) in your
artificial city, being adaptable, Genus Falco (all of these). Merlin is
the other name, Falco columbarius. Falco derives 1st millennium BCE in
Latin speaking from falx, ''sickle.''  pale horse is the metaphor, n'est-ce pas?

George Duke wrote on Tue, Feb 10, 2009 07:16 PM UTC:
Version (6) Falcon is common Crow (Corvus brachyrhynchos) having only the
split SDS and DSD, like a crooked bishop or crooked rook morphed. Like
intelligent Crow, feeding on leftovers or decay, what the PIGEON HAWK also known as
MERLIN(#4) lacks belongs to the AMERICAN CROW. Look at him in the parking
lot you made of the Earth. He cocks his head repeatedly like ''SDS''
and ''DSD.'' 5 metres away on the ground he knows where you are going: (colon) nowhere. Master of conservation of energy, why fly off, when the
Blockhead is going only inside his square vehicle/building? Call him the
Counting Crow, being better counter than your 4-year-old, as would be expected
of all Corvids genetically. (And of course better counterer constructively than yourself: not saying much at all)

George Duke wrote on Tue, Feb 10, 2009 07:31 PM UTC:
Falcon is first among equals RNBF. Version (7) Falcon Peregrine is the
standard chess piece, one of the four fundamentals, the template actually
from which Rook derives, from which Knight derives, and from which Bishop
derives. Without Falcon, R, N, and B would not exist. PEREGRINE FALCON has the six movement patterns Sraight-Straight-Diagonal, SDD, SDS, DDS, DSS, DSD, in their two
mirrors, making twelve. Knight gets his klutzy fully-functional
striking-degenerate leap from the Falcon beyond, in that Falcon has so
many routes, leaving Knight none whatsoever in plodding placement. 
Knight belongs too, for where would theory be without that necessary real world? Rook takes the Falcon one- and two-step partials to extremities. Bishop the Falcon diagonal one- and two-step partials toward all four extremities, the 4 directions. They depend for their very existence on Falcon being there, the implicate orderer. Peregrine Falcon (Falco peregrinus) clocks at 322 km./hr. the fastest species in the world. 
''The purpose of Life is to break down a gradient.'' --Dorion Sagan

John Smith wrote on Wed, Feb 11, 2009 01:38 AM UTC:
No, you are wrong, Mr. Duke. The truly essential piece is my Gorilla, which
moves 4 King moves, capturing up to one, passing up to one piece. The
Falcon is obviously derived from this, as it only moves thrice, cannot
reverse, and cannot jump. The Knight is derived from it also, for it jumps
for the entire journey, whereas my Gorilla jumps for one step. The Rook and
Bishop extend its steps. It is moreover a superset because it can capture
on any step, rather than the zenith. If you could muster an iota of
intelligence, you could see this for yourself.

George Duke wrote on Mon, Mar 16, 2009 10:37 PM UTC:
Moving some of this to CbM6 from Ramayana, we need to go back to Ramayana
too for how their pieces traverse the Archipelago. ''Thus mathematics
may be defined as the subject in which we never know what we are talking
about, nor whether what we are saying is true.'' --Bertrand Russell. 
How can we be sure of arriving at the equations correctly governing chess
laws? To begin with, Ramayana attributes suggest the proportion
relations:  Buddha:Rook = Bison:Falcon = Rakshasa:Bishop =
Knight:(Mao+Moa). Clever, worthwhile, themed Ramayana has board
unsymmetrical in extreme, and we need to check all our work each step of
the way. Why should Castling and En Passant be both ways? Ramayana
excludes en passant, but if it existed, why not only towards the
Archipelago, right for Yellow and left for Red. On regular 8x8, 8x10, and
10x10, why have castling long and short, instead of only on the Kingside?
Two-side versions of e.p. and castling are too taken for granted. In 4000 CVPage CVs, NOT ONE has en passant and/or castling only to one side of the player or the other, always having both conventionally. (Far lesser rules changes entirely warrant here trivial screed ''new CV'' in fatuous CVPage philosophy: examples from all the historical classics Jetan to Shatranj to Xiangqi. Any tiny change
warrants CV of one's own and more-significant-than-many e.p. and/or
castling only to one flank are open for use if you need it.) Anyway not only piece-movement symmetry and completeness, but these two special rules require real justification mathematically before burdening people with various
rules-sets of the making. ''As far as the laws of mathematics refer to
reality, they are not certain; and as far as they are certain, they do not refer to reality.''  --Einstein

George Duke wrote on Thu, Apr 2, 2009 04:45 PM UTC:
Sheldon Glashow: When I speak of four forces, or you say, ''there are
four forces,'' it reminds me of my fifth grade teacher who told us there
were seven continents.
Eduardo Punset: Wasn't he correct?
Glashow: I had never heard of Australia. I certainly never knew the 
difference between Austria and Australia when my teacher told us there are
seven continents. This is the wrong way around. You, and people in general,
can't know what physicists mean when we say ''four forces.'' People
only know two: if you drop an object it falls to the ground because the
''force of gravity'' exists. And then there is electricity.
Punset: That's true. [from Lynn Margulis & E.P., 2007]
The parallel is that there are four forces, fundamental chess pieces,
making seven units once Rex and Regina embodied, unfulfilled Laeufer-Towers.
And Kasparov, Anand, people in general cannot know Chess until they have
played it extensively, the full quorum, the spectral ROYGBIV, the whole
ball of wax. To real four-force chess, f.i.d.e.-chosen mad queen 8x8 is
kid's play, like a puzzle solved. Or like crude rudimentary markings of C.V.
art never to be taken seriously. Neither serious any more. Addicted to a
measly artifact and its half-truths. Square attitudes: stunted aptitudes:
dimensional deficiency.

George Duke wrote on Sat, Apr 25, 2009 03:21 PM UTC:
Premise: Chess ought to be intellectual competitive sport among
individuals, like Archery or Running. And CVs avoid one-trick ponies. 200
years ago the Slack-Rope Dancers of Johann Maelzel, the Conflagration of Moscow,
and the chess-playing Turk Maelzel bought from Wolfgang von Kempelen
through Napoleon. Pre-computer automata all ushering the machine age with
automatic looms and hot-air balloons, preoccupying the more-than-half-scientific nerdy elite of so recent a day. Computers are
here for now, not yet beginning to be outlawed for good, logical extensions of automata power-driven by Maxwell equations, as of Babbage's theoretical Universal Engine also early 19th century. The Internet. Even if he/she dropped her Math, or Science, major for sociologic Law, or computer science, or business, the near-math types need places to talk shop, let her hair down, picking one another's brains to order. Technocrat-managers, computer-automata, on to surveillance devices, humdrum econometric, and defense-related supercomputers (good for weather). Hence early on CVPage 15 years ago became one among many venues attracting users and/or facilitators. Internet filling every cavity. CVPage (including one sorry nameless case who stressed and inarticulate self-describedly ''projects vomitously'' on other people, the worst sort of offender). All are tolerated where  one  numeric Chess evolv-ed (-ing) is reference point in full speculative variety. [''You don't need a weatherman to know which way
the wind blows.'' --Bob Dylan]

George Duke wrote on Sat, Apr 25, 2009 03:27 PM UTC:
But wait. Historic cultural-rooted CVs actually become fully mathematical under state-of-the-art tooling and treatment -- because they are one-of-a-kind amidst all-purpose math. (As for
example the bogus Shroud of Turin submits to scientific analysis as hardly
over half a millennium old.) Look at OrthoChess herself under the
microscope 100 years now. Before lab testing, ask is the purportedly offered-up ''new CV'' satire? Self-satire? Art or nouveau art? Scientific or subjective tongue-in-cheek? Hostile (to what) or benign? Answer (usually): none of the above. Instead they are to be taken until proven otherwise quasi-artistic self-expression out of the blue. What means but statistico-mathematical to find the rare exceptions? Under scrutiny most CVs in this day could likely turn out to be ham-handed sham products irreverent to origins or direction for the future. Opinion pieces, period pieces many overridden by themes in an excuse. Where is anymore the Sport Chess was intended rather than all Art? Where are the contests of only a decade ago? Unmitigated projection. The effluent society. Conclusion: terminal addiction. Follow-up: Chess, as science and sport both, should stand above every other ''game'': Chatter and scatter, or helter skelter, or pick-up sticks. And not really be subject to comparison at all. It's about like comparing one electric light bulb with a solar flare.

Joe Joyce wrote on Sat, Apr 25, 2009 05:50 PM UTC:
Chess, like geometry, is capable of more than one expression. And I do not
speak of the easy out of 3D, 4D, 1D, fractal, 6, whatever boards. Make
chess as conservative as you want. Only capture by replacement. Always
pawns. Always 2D rectangular board with no holes or other unusual features.
No 'special powers' pieces, as immobilizers, ghosts, neutrals. Just the
old-fashioned, reasonable simple, easy, and obvious pieces have themes,
show directions, indicate blind spots and areas for growth or change. Your
Falcon is one fine example of a fuller, more complete design for chess,
fitting into a design 'hole' in FIDE. Carlos Cetina's sissa is another
such piece, giving another shape to a larger design even if not played on a
larger board than FIDE. He found the rook and bishop hidden in the knight,
and set them freer. Not free, but bound together into one piece, quarks of
the chessboard, they take paths reminiscent of Feynman diagrams, showing
disintegrations of opposing positions. Another vision, distant cousin to
the falcon, the sissa gives a different picture of chess, one of more
power, not less, like the falcon [which, as a shortrange piece, dilutes the
power of the infinite sliders], a picture closer to Seirawan's, or
Capablanca's, for example. But not every apparent Capa variant is exactly
as supposed. One of your games for 2014, Great Shatranj [which does, by the
way, have 10 games completed, and others playing, onsite], appears to be a
Capa variant, but is not. It rejects the concept of infinite sliders [as
much as possible - one must sometimes bow to the demand for rooks, it
seems, but it has eliminated bishops and queens utterly, while retaining
rooks as merely an unnecessary option], and reduces the moves to 1 or 2
squares at a time, while expanding the leaping ability to essentially all
the pieces. This is a theme in a totally different direction, giving a game
which is pure chess and totally different from all the other Capa variants.

George, you're saved by my wife's desire to go out now - more later...
;-) Enjoy!

George Duke wrote on Mon, Apr 27, 2009 10:59 PM UTC:
In early computer days 20
years ago, they used to say 'Garbage in, Garbage out' all the time, now the phrase being
as out of fashion as a Basic Goto. They cleaned up their acT foR gooD, or else it's taken for granted.
D'Arcy Wentworth Thompson: ''It is a remarkable thing, worth pausing to
reflect on, that we can pass so easily and in a dozen lines from molecular
magnitudes to the dimensions of a Sequoia or a whale. Addition and
subtraction, the old arithmetic of the Egyptians, are not powerful enough
for such an operation; but the story of the grains of wheat upon the
chessboard shewed the way, and Archimedes and Napier elaborated the
arithmetic of multiplication.'' [Ed.: British G.B. Shaw always goes
''shew'' too.] Not much point except 75 years ago and before, Chess was
referred to in scholarship it seems about 5 or 10 times as much. Now she is
referred to not mathematically or intellectually but economically once in a
while, a propos some irresponsible ecologically-ignorant capitalist or trader. // Sissa is at the top for originality. The first exception I take to Sissa is duplication of Rook squares. Actually, Sissa's reach to Nightrider squares is better than Nightrider's, because two-path is more interesting than hippety hop.

George Duke wrote on Mon, May 4, 2009 08:49 PM UTC:
CVs as art are novelties. Galileo on novelties: ''In the matter of
introducing novelties. And who can doubt that it will lead to the worst
disorders when minds created free by God are compelled to submit slavishly
to an outside will? When we are told to deny our senses and subject them to
the whim of others? When people devoid of whatsoever competence are made
judges over experts and are granted authority to treat them as they please.
These are the novelites which are apt to bring about the ruin of
commonwealths and the subversion of the state.'' --written by his
handwriting in the margin of own copy of 'Dialogue on the Great World
Systems' [Coincidentally in 1642 only a couple years later Fermat wrote in the margin of a book that proof of Fermat's Last Theorem, Diophantine n > 2, ''Hanc marginis exiguitas non caperet,'' and so Wiles had to prove it in 1993.]

George Duke wrote on Mon, May 4, 2009 09:12 PM UTC:
Now the dissenting view in Copernican-Galilean astronomy [metaphorically to
do with Chess, and unfortunately cv artwork pandered as games, also] was once the majority:
''There are seven windows in the head, two nostrils, two eyes, two ears,
and a mouth; so in the heavens there are two favourable stars, two
unpropitious, two luminaries, and Mercury [the Bishop] alone undecided and
indifferent. From which and many other similar phenomena, such as the seven
metals, which it were tedious to enumerate, we gather that the number of
planets is necessarily seven.'' --Francesco Sizzi in argument against
Galileo's discovery of the satellites of Jupiter

Larry Smith wrote on Tue, May 5, 2009 02:15 PM UTC:
Throughout history there have been occasions where persons have purged
society's database. Libraries burned, authors executed, inventions
destroyed. All for the reason of simplifying their existence and
controlling the common man.

Did this improve mankind's state? Or did this actually cripple mankind's
intellectual evolution? The latter was most likely the case.

Chess has evolved from simplicity to it current complexity. The thinking
person would realize that it will continue to evolve in complexity rather
than slide back into simplicity. If only to continue to challenge the
mind.

Whereas, before the last of half of the twentieth century, most people had little contact with others outside their direct environment. Their exposure to ideas outside that environment was rare or often slow to arrive. Now, with the Net, all those developing concepts which might have gone un-noticed can be presented to an enormous audience. To evaluate and/or play.

No one should be forced to appreciate any particular form of game. This
would be self-defeating of the concept of play. Which is a part of the very nature of humans.

Likewise, those who desire to either promote a particular form of play or
do not appreciate other forms should respect their fellow players. If they desire to apply particular parameters to the development of their
particular games, they are well within their rights. But to demand such
compliance from others is only a high state of hubris.

Consider a mind which has existed within a 'box', surrounding by what it
knows within this domain. If it is allowed to peek outside and view the
infinity of chaotic potential, it may recoil in fear rather than amazement(or amusement). Unable to accept or comprehend. Such a mind should not be harassed to accept such a challenge. Merely pitied.

George Duke wrote on Fri, May 8, 2009 04:13 PM UTC:
I think Smith gets confused because I quote both Galileo and his stupid
accuser and so misses the point.  Now Smith's other history is wrong in
this respect. Oppositely in fact over the past 100 years, with OrthoChess
64 supreme and founding of F.I.D.E. in 1920s, ''Chess'' to the masses
has unfortunately shrunk to one form, played in rapids and blindfold for
''variety.'' It is far cry from Capablanca promoting 8x10 Chess and
playing a large double chess on 8x16, and broadminded Capa's and Lasker's
trying several others. It is far cry from 100 years ago when popular
Kriegspiel was co-equal to OrthoChess among highly-educated. I believe contrary to Smith's assertions, I am constantly relating acceptable CVs to other spheres of learning and challenge.  Smith's comment is further off the mark in that, if you run a test of 100 or 1000 questions, I would shew more knowledge of CVs than probably anyone else in the world (certainly anyone around here, because of knowing 100s of patents too). Appreciation of CVs goes deep in threads CBM-I,  -II ... -VI, and other ongoing threads. The system needed is two-track not artwork alone. CVPage is the bastion of orthodoxy, not George Duke or Seirawan or anybody else, promoting as it does OrthoChess 64 squares 500 years old, often saying the Mad Queen is here for good (very unlikely), to the extent CVPage does nothing with the material it has first collected and then now basely encouraged to proliferate. No one cares about the next CVPage ''CV'' never to be played but bandied as artistic, notwithstanding declining originality across the board. Not to mention increasing insensitivity to prior occasions of uses of pieces and rules by other inventors, involving often mere tweaking of minutiae to claim ''new CV.''  Those are the problems to be taken seriously and in enjoyment.  The pointlessness of Art for art's sake. Instead, let's somehow begin to get the word out that there is some worthwhile material within these pages. Somewhere we can find it, often referred to as the hidden 1-2% of CVs, still remarkably numbering several hundred. Another string of comments attempts that constructively at related user-created ''NextChess-1 -2...''

George Duke wrote on Sat, Jun 27, 2009 03:27 PM UTC:
Maybe Gilman already has SO, Sideways only? Anyway, a new piece class for
Gilman's system can be the Jabberwockies. Gilman's FO has ''directions
moving more ranks forward than files sideways'' in M&Bxx.  Jabberwockies
are *more files sideways than ranks forward*. Betza has some wide-only
Knight that  shows the idea. The class of pieces should be for Gilman's
number '28', because 28 is a perfect number (1+2+4+7+14=28). Some
Jabberwockies are flip pieces, most are not. Flipping is optional at end of
move, or player may flip without moving, in lieu of turn. Understand no
diagonal move is possible. (1) Jabberwocky himself is compound Knight +
Camel. (2) Borogove is flip piece as Knight/ flip mode Wazir. (3)
Bandersnatch is Dabbabah plus Knight. (4) Brilligs are weak Trebouchets(0,3).
(5) Only King may go all 8 standard directions, of which Jabberwockies as a
class only avail E and W. But together all the Jabberwockies, including
promotees, conceivable have more than 8 directions because of the
''oblique infinity'' factor different from that radial east and west.

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