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Comments by Tony Paletta

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Bishopper. Moves along diagonal line to first square after jumped over piece.[All Comments] [Add Comment or Rating]
Tony Paletta wrote on Tue, Dec 30, 2003 05:29 PM UTC:
Bishop:Bishopper :: Rook:Rookhopper

Constitutional Characters. A systematic set of names for Major and Minor pieces.[All Comments] [Add Comment or Rating]
Tony Paletta wrote on Mon, Dec 15, 2003 12:01 AM UTC:

Both the Bishop and the Rook do indeed have orthogonal lines of movement.
I touched on this this in a 12-13(?) comment directed to Charles 
concerning why Rooks, and not Bishops, are usually described as are
orthogonal movers; basically, my answer was that its a convention --
meaning a tradition -- and a bow to common usage; since Bishops are
described as diagonal movers it seems relatively harmless to describe
Rooks as orthogonal movers. In fact Solomon Golomb (who developed
Cheskers, Pentominoes and was a leading light in recreational math), in a
write-up on Cheskers, once described Bishops as Rooks on the 32-space
board formed by one color of the chessboard, and Camels (Cooks in
'Cheskers') as Knights on the same board. 

I certainly don't find it a problem to think of Bishops as orthogonal
movers, and I think any rule that uniquely identifies Rooks and not
Bishops with 'the possible set of orthogonal movement patterns' would be
somewhat deficient, since they are simply rotations. 
[Aside: I have used the 'Cheskers' game as an inspiration for a very odd
game called 'Dichotomy Chess' (modest - goal variant), where I also
tacked on a Dabbaba-rider + Ferz (B+K on 32!)].  

My comment about 'straight lines'? It illustrates a construction
guideline that does give rise to straight lines in one context (planes)
and arcs in other (spheres), even though we might have been trying for
'meaning the same thing' and used a rule that is used to produce
straight lines in planes. I certainly don't consider straight lines and
arcs the same thing -- and I don't feel a need to call them both straight
lines, or both arcs. They are simply analogous with respect to the rule of
construction, but do not fully represent the same meaning. 

Walking the 'straight-lines' over to the orthogonal discussion: a rule
that does produce paths of orthogonal movement on a square-grid and can be
applied to produce paths on a hex-grid does not replicate orthogonal
movement on the hex-grid -- it produces sets of movement paths through a
point that are orthogonal on square-grids boards, but not on hex-grids.
Analogous with respect to the rule of construction (and even using the
word right angle -- so it must be legit?) if we apply the rule to square-
and hex-grids, but producing results not reflecting the same type of

On a hex-grid, the simplest orthogonal movement pattern involves an
'edge-path' and a 'point-path' (e.g., vertically and horizontally on
the Glinski board). A while ago (few weeks), I indicated to Charles G.
that this is a mapping of a standard Bishop (e.g., from a chessboard
rotated 45 degrees) that was 'halfbound' as opposed to the
'thirdbound' pattern of g-Bishops. 

To try and wrap up my end of this discussion of 'angles dashing from a
hex in a plane'. There exists a usage convention (tradition with a group
of supporters) for using 'orthogonal' and 'diagonal' to describe some
possibly paths on a hex grid. The usage (1) isn't especially apt, since
it conflicts in some important ways with the usual meaning of orthogonal
and diagonal in both chess and mathematics (especially plane geometry) and
(2) suggests a 'rightness' (based on the analogy to standard chess) that
is misguided, a frequent source of confusion, and somewhat stifling for
developing other approaches to hex chess. I therefore feel its a usage
ripe for replacement.

Tony Paletta wrote on Sun, Dec 14, 2003 02:11 PM UTC:
[Sorry I accidently posted my last comment under a 'Fergus' thread (Game
Courier), rather than the 'Constitutional Characters' thread.]


The fact that I can use 'the shortest possible distance between two
points on the surface' to connect points on both planes and spheres does
not tell me that it is appropriate to refer to both types of constructions
as 'straight lines'.

[and now, new comment]


Interestingly, in his earlier (more informal, mass market) 'Brain
Games', (Penguin Books, 1982) Pritchard used 'files' and 'lines' in
describing the paths in Glinski's 'Hexagonal Chess', rather than
'orthogonals' and 'diagonals'.

About Game Courier. Web-based system for playing many different variants by email or in real-time.[All Comments] [Add Comment or Rating]
Tony Paletta wrote on Sun, Dec 14, 2003 05:40 AM UTC:

The fact that I can use 'the shortest possible distance between two
points on the surface' to connect points on both planes and spheres does
not tell me that it is appropriate to refer to both types of constructions
as 'straight lines'.

Constitutional Characters. A systematic set of names for Major and Minor pieces.[All Comments] [Add Comment or Rating]
Tony Paletta wrote on Sun, Dec 14, 2003 02:53 AM UTC:

It has occurred to me that you were arguing with yourself. I never said or
implied (check) that there was NO USE OF the term orthogonality could be
satisfied in a hex grid -- looking back that seems to have been your
original point that you were looking to refute. 

My point was that a fundamental fact from plane geometry would be
contradicted by any such definition of 'orthogonal movement' -- one that
is satisfied by ' orthogonal movement' in chess: 

at most two orthogonal lines (or paths) 
can be drawn thru a point in a plane.

Tony Paletta wrote on Sun, Dec 14, 2003 12:37 AM UTC:

My argument for not FOLLOWING the convention for using 'orthogonal' and
'diagonal' on hex grids was not based on the idea that they were not
CONVENTIONS,l but that they did not have the same FULL MEANING as on the
chessboard (crossing edges at right angles, but also moving along paths
that are at right angles), which in turn did parallel the more
comprehensive meanings used in mathematics (as opposed to the less
specific 'at right angles' dictionary entry). Both Dickens and Parlett
were well aware of the existence of hex games such as 'Hexagonal Chess'
and gave definitions that covered both -- they were certainly not out to
fight the convention, but simply to reflect it.

One point of my usage (edge-paths, rather than orthogonals; point-paths
rather than diagonals) is that it avoids the terminology problem for
pieces that demonstratably move exactly like chess Rooks, chess Bishops,
chess Knights, or any chess piece) in games on a hex-tiled board. The
conventional chess pieces follow the paths that reflect conventional chess
patterns; the hex pieces simply follow different paths. The baggage of
definition by analogy from chess (orthogonals into hex-orthogonals;
diagonals into hex-diagonals) disappears if the partial analogy is not

Tony Paletta wrote on Sat, Dec 13, 2003 11:15 PM UTC:

Parlett does start his discussion of movement in two dimension with: 
'Before exploring two-dimensional war games it is desirable to ESTABLISH
a terminology of movement and capture, as a surprising amount of
confusion, ambiguity and inconsistency is exhibited in the existing
literature of games.' (emphasis added)

It's unclear to me whether he's trying to (1) describe common usage, (2)
summarize dominant practice (3) prescribe usage or (4) simply provide a
basis for his further discussion so he can write the book. The inclusion
of hippogonal leads and his criticism of Murray me to (3) or (4), but it
isn't that clear.

Pritchard (as encyclopedist, but also as popularizer) tends to go with the
primary source descriptions and is generally descriptive rather than
prescriptive. He (properly) avoids taking positions except where a game
author's conventions are truly strange (and even then, he is seldom
outright critical -- though sometimes revealing a droll wit in the best
tradition of British writers).


Just to summarize some of my main comment lines (personal opinions and
preferences) in this long thread:

(1) I'm not a fan of jargon-for-jargon's sake. If connected to a
specific convention the author feels is necessary in presenting his/her
own work, present the material in a context and do try to be
straight-forward, clear and reasonably accurate in your terminology.  

(2) Personal naming conventions (for pieces, but also for other concepts)
belong inside an author's body of work. This allows you to rethink your
choices, frame your decisions within the context of their use, and present
what you feel is a finished product.   

and (initially least) 
(3) Some existing naming 'conventions' -- orthogonal and diagonal as
used in hexagonal chess, for example -- suggest parallelisms with more
familiar, well-established concepts from chess and mathematics that simply
don't exist. Since the terms don't convey what they appear to convey,
there is a good case to be made for not following those naming

Tony Paletta wrote on Sat, Dec 13, 2003 03:15 PM UTC:

While dictionary definitions provide a rough guide to the meaning of words
have, they (of course) only tell us part of the story. Case in point: Why
are the Rooks commonly said to move orthogonally when a Bishop's lines of
movement are also in orthogonal directions? 

One historic and important role of orthogonal lines in mathematics and its
applications is in the measuring of distance. While the King may have the
title, the Wazir is the natural 'ruler' of the chessboard. Start on c1,
move up three Wazir moves, then four Wazir units to the right to g4 and
(using the Pythagorean theorem) you can calculate that you are five
'Wazir units' away from your starting point. This also works with a
'Ferz' -- but on one color only (from c1 three Ferz units NE, four Ferz
units NW puts you at b8, five 'Ferz units' from the starting point).    

So both the Wazir or Ferz could be used to measure (Euclidean) distances.
The difference is the Wazir directly measures ALL the whole unit distances
that come up in talking about the square grid of the chessboard. So it
probably was more natural to think of the Wazir/Rook as THE orthogonal
directions on the chessboard.

Of course this isn't 'the way it happened' and it isn't the only way
it could have turned out based on the dictionary definitions, but the
convention for usage is not paradoxical, contradictory or especially

Tony Paletta wrote on Sat, Dec 13, 2003 03:55 AM UTC:

In one of 12-12 comments ('As it turns out, the dictionary ...') you
brought up statistics and suggested that a different meaning
('specialized sense') was being given to orthogonal by statisticians. I
responded by indicating that these statistical senses were not different
in their root meaning. You criticized this as involving equations between
sets of coordinates rather than geometry. 
Many fields of mathematics are extensions of the concepts of classical
(Euclidean) geometry, in a variety of directions  -- including quite a few
fields which tend to deal with planes and vector spaces. The consistency
with the geometric sense of orthogonal (where orthogonal lines are lines
at right angles to each other) is maintained, even when not superficially

How does one get three 'orthogonal' paths to pass through a point in a
plane? We could Humpty-Dumpty up a meaning of orthogonal that directly
conflicts with the established meaning, but that doesn't impress me as
exactly dazzling the world with our brilliance. Choosing our terms more
carefully to convey our intended meaning seems like a better way to

Tony Paletta wrote on Fri, Dec 12, 2003 06:35 PM UTC:

I didn't bring up statistics or any of the mathematical disciplines with
roots in geometry.

Are you sure you mean geometry? The orthogonal == right angle usage comes
from geometry.

Tony Paletta wrote on Fri, Dec 12, 2003 02:24 PM UTC:

Latin Squares are typically used when experimental plans involve
'treatment ordering' or 'incomplete block' (nesting of subjects under
some combination of treatments) designs where there is a possibility of
correlation between treatment and assignment. The 'orthogonal' is the
sense of 'uncorrelated' (== zero cosine == 'right angle'), meaning
that there no overall correlation or covariance is introduced between
treatment and assignment (which would otherwise 'confound' a treatment
effect, making it indistinguishable from the assignment or ordering

(Just a rough sketch from memory; if this sounds like Greek to you, rest
assured that the things called Greco-Latin Squares serve the same
'orthogonal' master).

Tony Paletta wrote on Fri, Dec 12, 2003 11:44 AM UTC:

In statistics the term 'orthogonal' (once the surface is scratched)
rests on the geometric sense like it does elsewhere in mathematics --
always consistent with 'at right angles'. For example, orthogonal
comparisons are comparisons with sums of cross-products of zero,
equivalent therefore to uncorrelated, hence represented in a
multidimensional space as vectors with a cosine of zero, placing them at
right angles. 

Regarding 'diagonal' movement in 'cubic' multidimensional space,
there's no reason to consider the space as having anything but the pieces
and a set of potential resting points (think 'Zillions'). Two-D Bishops
ride in a line like they do through collection of two-coordinate systems
-- no established convention is violated by calling that a diagonal move.
If it wasn't for those pesky polygons from geometry, we could give
extended meanings to 'diagonal' for the lines along which N-dim
'Bishops' rider (triagonal, tetragonal, etc.) just like the rec math
folks did for polyominoes, polyiamonds and polyhexes. Given the conflict
with geometry terms looming for N>3, tri-diagonal, tetra-diagonal, etc. do
seem a little more sensible.

On hexagonal boards a conflict with standard chess terminology was (I
suspect) not originally envisioned by game designers. Since standard chess
pieces, fairy pieces and pieces more-or-less designed for hex grids are
also possible, it seems (IMO) that there's little merit in straining and
twisting the language to preserve an inappropriate set of analogies that
(among other things) make Glinski's formulation of 'Hexagonal Chess'
seem like THE way to describe hex grid movement. (But YMMV.)

Tony Paletta wrote on Fri, Dec 12, 2003 05:02 AM UTC:

You seem to have confused a diagonal and something sort of like a

A diagonal of a polygon is any line joining two nonadjacent vertices.

A diagonal of a polyhedra is any line joining two vertices not in the same

Other than these two uses, a diagonal line pretty much just means a
slanted line.

For a standard chessboard-like tiling with squares each square has two
diagonals and they line up to form longer lines -- hence THE diagonals of
a chessboard. It doesn't work with hexagons.

Tony Paletta wrote on Thu, Dec 11, 2003 02:41 PM UTC:

3D Hex-based games present some really tough issues, partly because
there's no 'natural' generalization of a hex into a regular solid
(e.g., stacking boards gives a kind of hex prism) so our ability to use
analogies -- whatever they might be -- are somewhat strained.

One way to get a handle around SOME 'higher dim' chess is to think in
terms of areas -- maybe planes, maybe not -- with sets of paths defined
for within area moves and for between/among area moves. Essentially not
using coordinate geometry ('grid-like' games), but much closer to
'graph theory' - points and directed sets of paths between points. This
may or may not help in the evolution of your thinking.
BTW Mark Thompson's game is 'Tetrahedral Chess'; 'Tetragonal Chess'
(modest 'hexoid' game) is one of mine.

Tony Paletta wrote on Thu, Dec 11, 2003 12:22 PM UTC:

Don't have a problem with your usage in 3D. Orthogonal is standard,
diagonal matches the 2D Bishop's move, and triagonal doesn't jar with an
established term in a situation where the use of diagonal requires a short
term to make a distinction. My objection was and is to 'triagonal' on a
hex-tiled plane.


I still am in agreement with that other guy who posted under your name
somewhat earlier. I don't generally recommend edge/point terms for square
boards because they are not needed. On the other hand, I (recently)
avoided the terms orthogonal and diagonal in describing movement in
'Canonical Chess' variants on a rotated square-tiled board since it
would have been both ambiguous and confusing.

On a 'normal' chessboard (including Xiang Qi board, etc.) the terms
orthogonal and diagonal have had their meanings established by long and
frequent usage, and the terms are easily understood (translated) by people
who simply know what the words mean in other contexts. On hex-tiled boards
the orthogonal/diagonal terms carry neither the same established meaning
nor the same 'chess knowledge' implications.

Tony Paletta wrote on Thu, Dec 11, 2003 03:18 AM UTC:

English is English, not the sum of its roots. Why distort a word with a
clear and established meaning, and give it a new meaning that directly
conflicts with its established meaning (so that three 'orthogonal' paths
CAN pass through a point in a plane) in precisely the context it is to be
used? Seems a lot harder to 'explain' than edge-paths and point-paths.
It's (literally) a poor choice of words.

Tony Paletta wrote on Wed, Dec 10, 2003 09:56 PM UTC:

Faced with the problem of describing geometric movement on a regular grid
(i.e., intersections of two sets of equally spaced parallel lines) back in
1980 I chose the terms 'edgewise' and 'pointwise' to refer to movement
from the center of one space to the center of another in a line which
bisects a side or an angle, with the continuation of such movement
constituting 'edge-paths' and 'point-paths'. 

This convention works equally well for square- and regular hex-tiled
boards (which are grids or sections of a grid) regardless of their
orientation, while not directly conflicting with a very common
mathematical usage (e.g., orthogonal axes).

Tony Paletta wrote on Wed, Dec 10, 2003 06:38 PM UTC:

If you can look at the 3D system as an [x,y,z]-coordinate system, then a
rider that makes a series of consistent unit leaps in two coordinates only
(e.g. --[1,1,0]-rider, [1,0,1]-rider or [0,1,1]-rider) could properly be
called a Bishop -- its a 2D Bishop when there's a choice of planes, and
becomes a regular Bishop when there is only one plane (such as on a flat
board). Generally that's been the piece called 'the Bishop' in
3-(4-,N-)dimensional chess -- a convention to call any other piece the
Bishop would probably be more confusing.

Tony Paletta wrote on Wed, Dec 10, 2003 01:55 PM UTC:
I found this item a complete waste of time. Why should one person's list
of names for chess units be of interest -- when totally unconnected to any
significant body of work or original contribution? If anywhere, a list of
idiosyncratic piece name proposals belongs in an obscure discussion

I am stunned by the lack of editorial standards implicit in adding this
type of material as a 'contribution'. Gee, I thought any CV designer
would have a huge list of unused piece names. 

I generally agree with FD's points concerning the use and abuse of
language. Although I do find affected pseudo-learned illiteracies amusing
as all heck, as well as a great time saver when reading.

Dabbabah. Historical piece leaping two squares horizontally or vertically.[All Comments] [Add Comment or Rating]
Tony Paletta wrote on Mon, Oct 27, 2003 02:27 AM UTC:
There is nothing especially simple, elemental, basic or natural about the
rules for movement proposed by Glinski in developing a chess variant
played on a hexagonal board -- in fact, the Glinski-B interpretation is
considered something of a kluge by some CV designers (others view it more
favorably). Other interpretations are not 'exotic' -- they are simply
other, currently less well-explored, possibilities for defining movement. 

As I see it, Glinski's 'Hexagonal Chess' is 
fully equivalent to a game with  
half-Bishop + half-NRider (g-Bishops), 
Rook + half-Bishop (g-Rooks), 
half-N + half-Zebra + half-Camel (g-Knights),
Rook + Bishop + half-NRider (g-Queens),
King + half-Knight (g-Kings), and
Berolina-type pawns (g-Pawns)
played on a portion of an diagonally-oriented 11x11 chessboard.
(Oddly enough, it's still an interesting game).

I personally feel it might be better to embrace this equivalence (and
others like it) rather than insist on somewhat arbitrary distinctions
between hexagonal- and square-tiled playing fields.

Shield Bearers. A systematic set of names for pawnlike pieces.[All Comments] [Add Comment or Rating]
Tony Paletta wrote on Sat, Oct 25, 2003 01:13 PM UTC:

Thought experiment and philosophical question.

I select a an 8x8 playing area of regular hexagons resting on their points
and arranged in the overall shape of a rhombus (let's say the major 
diagonal is NE-SW). The leftmost line of hexes can be called the
'a-file', the second (parallel) line from White's left can be called
the 'b-file', etc.; the line of hexes closest to White can be called the
'1st rank', the next parallel line the '2nd rank', etc.. 

A certain type of movement can be described as 'Wazir-like': one space
along a file or a rank. Pursuing this analogy, we can generate analogs for
all the units of standard chess and adopt analogous rules. 

A Staunton chess set is arranged so the chessmen or on the spaces with the
same labels as in standard chess (White Staunton Rook on a1). Play begins:
1 e2-e4 e7-e5; 2 g1-f3 b8-c6; 3 f1-b5 a7-a6; 4 b5-a4 g8-f6; 5 Castles ...

My question: What would be an appropriate name for the unit White moved

Ravioli Chess. Chess on two boards squeezed together at the edges. (2x(8x8), Cells: 100) [All Comments] [Add Comment or Rating]
Tony Paletta wrote on Thu, Oct 23, 2003 11:02 PM UTC:
Ravioli Chess seems like a fundamentally interesting idea. A somewhat
similar family of CVs can be developed if we assume that:
(a) The playing field is one or more plane surfaces - folded, rolled or
layered onto itself.
(b) Specific, regularly placed pairs of locations on the playing field are
points of contact.
(c) Pieces occupying a point of contact may move from either their
physical or their virtual location (the location in the pair).
(d) Friendly units can virtually coexist but cannot physically occupy the
same location. Opposing units cannot coexist and moving to one location of
a location pair captures any opposing units on either location.
(e) Piece move along (or around) any plane region, provided that the path
from the starting location is open.

Some examples:

Toaster Pastry Chess:  The Q-side and K-side are notionally two layers,
with the edges of each side (perimeters a1-a8-d8-d1 and e1-e8-h8-h1) the
points of contact. Units on an edge of either half are also virtual
occupants of the space four spaces away, along the rank, in the other
half-board and may move within either half-board containing the physical
or the virtual starting space.

Pierogi (Calzone?) Chess:  The board is notionally rolled so that the a-
and h-files are aligned vertically, with the surface making contact along
the a-h files and each end rank. Units on the edge (a1-a8-h8-h1) may move
as in standard chess from either their physical location or from the
horizontal mirror image edge space.

Taco (Omelet?) Chess:  The board is notionally rolled as in Pierogi Chess,
but the contact is accomplished by the units -- each unit is effectively a
domino occupying both its physical location and its horizontal mirror
image (virtual) location. From either location, units move as in a
standard chess plane.

Turnover Chess:  The board is turned 45 degrees as in a diagonal form of
chess, and also notionally rolled so that the side corners (e.g., a8-h1)
align vertically. Pieces on the edge (a1-a8-h8-h1) move from their
physical location or from the (virtual) horizontal mirror image edge
location. Pawns are Berolina and a standard array might be adopted from
'Diagonal Chess' (L.A.Lewis) or 'Diamond Chess' (A.K. Porterfield
Rynd) -- see Pritchard's ECV. 

Of course, these CVs will not suit everyone's taste.
I will (wisely, I think) omit the details of possibilities such as
'Burrito Chess' or 'Cannoli Chess'.

Magna Carta Chess. Black has the FIDE array, White has a Marshal and an Archbishop instead of a Queen and King. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]
Tony Paletta wrote on Sat, Oct 4, 2003 01:27 PM UTC:
Balancing a game with different pieces AND possibly different objectives is
a tricky business. Since Magna Carta Chess started as a particular
proposal with historical theme constraints, it should be finalized as
such. I would not consider subsequent efforts seeking a similar or maybe
somewhat dissimilar CV to be spinoffs.

Dabbabah. Historical piece leaping two squares horizontally or vertically.[All Comments] [Add Comment or Rating]
Tony Paletta wrote on Sat, Oct 4, 2003 12:13 PM UTC:
(Partial reply to your post. You mentioned several topics.)

I assume you mean a Dabbaba-analog on a hex board, using the Glinski-based
analogy to FIDE chess. Mapping the hex board onto a standard chessboard
(where the 91 Glinski hex board >> diagonal oriented 11x11 chessboard with
15 squares cut from each of the two side corners, for example) helps
clarify the situation: the h-Dabbaba is more strictly equivalent to a true
Dabbaba plus half an Alfil and, since the Alfil adds nothing to the
Dabbaba's possible squares, the net effect is (not so surprisingly) the
same type of boundedness as the true Dabbaba.   

One type of 'half-bound' piece on the hex board would be a piece moving
in any single h-Rooks direction (e.g., N-S) and in the perpendicular
h-Bishop direction -- its a FIDE Bishop. A conventional Camel is also
possible, as are any other half-bound pieces mapped from a square-tiled

[Subject Thread] [Add Response]
Tony Paletta wrote on Sat, Oct 4, 2003 03:52 AM UTC:
I've done some work recently on a family of chess variants that generalize
basic R-B-N piece movements and I more-or-less 'found' a generalization
in the Mao-Moa family. I was wondering if anyone had run into the 'new'
piece in other games and could provide me with any CVs that use it.

The piece of interest is similar to a 'Bison' ([3,2] leaper + [3,1]
leaper). Instead of leaping directly to its destination, it must first
pass over a vacant space a Knight's-leap away, then continue one space
orthogonally (in the N-leaps long direction) or diagonally (in the N-leaps
combination of directions) to its destination.

The context I'm using it in is 'Octoid Chess'. Instead of the 4-4-8
basic directions of the 'tetroid' R-B-N, I adopt 8-8-16 directions. On
an 8x8 board R moves one ore two spaces like a standard chess Queen, B is
one or two leaps like a Nightrider, the 'new' piece has the 16
directions, one step like the Octoid B, then like the Octoid R (Ks/Qs/Ps
as in standard chess, castling also standard).

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