Comments/Ratings for a Single Item

Wow. I just read all the comments for this section, and my eyes and brain
are very tired. I would like to say that the terms orthogonal, diagonal,
and even hippogonal work just fine for me, whether it's on a square
board
or a hex board. When you try too hard to read into things, they become
less
fun, in my opinion. On a lighter note, here's some suggestions for chess
movement directions, which I'm sure are linguistically and
mathematically
incorrect enough to really annoy some people:

Vertizontal, Hedrogonal, Hexaxial, Hipporadial, Horizagonal, Paraheximal,
Gonalogonal, Trigonagonal, Hexohippozontal, Radiogonal, Orthozontal,
Dihedraxial, Hexozontal, Verteximal, Zontifical, Edge-ognal,
Point-edgimal, Side-o-zontal, Polyhedronomical, Rookogonal, Bishagonal,
Knightaxial, Geogonal, Dihippaxial, Extragonal, and of course,         
Tri-di-hippo-horizo-vertico-radio-axio-hexo-agonalogonalogonal-wise

I'm sure these are all thoroughly useless but if you like them you can
have them.

Hippogonal seems a non sequitur to me. Better to describe oblique
(non-radial) directions by their coordinates: thus the Knight, Camel, and
Zebra move along the 2:1, 3:1, and 3:2 obliques respectively. Many others
on the square board are listed in From Ungulates Outwards, which also
gives the formula for duality of moves at 45° to each other. Here are some
reasons to avoid square-board names for hex-specific pieces.
	Matching is more 'obvious' to some than to others. In the all-radial
Wellisch Hex Chess, the diagonal piece (which is short-range) is called a
Knight!
	Many of my piece names use duality, as this is linked to binding. If both
coordinates are odd, as in the Camel, binding is the same as for the Bishop
- inspiring the names Zemel, Gimel, Namel for leapers in other such
directions. Duality on a hex board is entirely different. Extrapolating
from the Glinsky/McCooey use of 'Knight' would give an unbound 'Camel'
but a 'Giraffe' bound to a third of the board.
	It is unwise to ignore the cubic board when dealing with the hex one.
Consider a hex board with cells designated ia1 to ph8. Now consider just
ia1, ja2, jb1, ka3, kb2, kc1, la4, lb3, lc2, ld1 &c.. The diagonals
between those cells are exactly like the orthogonals on a hex board. This
is like the link between just the white squares of a FIDE board and a
board of 7 rows of 2/4/6/8/6/4/2 squares. However the latter transforms
orthogonals to diagonals as well as vv, whereas the cubic-hex
transformation LOSES the original orthogonal. This means that the hex
board does not have the standard diagonal. The diagonal that it does have
transforms from the 2:1:1 oblique, which may explain why Wellisch
considered that direction oblique itself.
	Now consider a hex-prism board of 15 8-cell files in triangular formation
a bc def ghij klmno (used for a variant that I will soon be submitting).
The line k1-l2-m3-n4-o5 is plainly a square-board diagonal but, by
rotation, so is a1-c2-f3-j4-o5. The logical move for a Bishop on this
board would be all such diagonals. With such a range of moves a Bishop
could actually reach the whole board (note j4 and n4 both being reachable
from o5), as could a Camel or Zemel similarly defined by the three planes
of square boards. There is no need or reason to include a same-rank (i.e.
same-hex-board) move; after all, the square-board Bishop has none.

Thanks to everyone for the info on Berse. Were there a 'rating other
comments' list I would select excellent on it! On reflection I have
decided against the change. It does not fit in with my rule of all
radially-enhanced Rooks (as distinct from the Marshal which is
obliquely-enhanced) being female titles. The canine/feline connotations
would particularly conflict with this, by offending both old chivalric
sensibilities and modern feminist ones! Finally I have been considering
extensions of the Crab for a future articles; the name I think most
logical for the 3:2 version of the Barc is Berz, which is just different
enough from Ferz but not from Berse.
Two further comments while I am at it. Firstly HOSTESS in square brackets
is based on a pre-publication layout and I have submitted a correction to
delete it. The correct reference to this name occurs later. Secondly in
Britain it is the other meaning of ounce that is former!

Berse could possibly have its initial roots in bersit, meaning to burst. 
This would explain the term bersim for a flower.

Berse appears to be a form of bersim, which is a flower.

According to Cazaux's book on chess variants (in french) it
is a species of cat, latin name Panthera unica, french once.
Don't know german or english names.

--JKn

Fergus,

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
thing. 

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 P.,

I already responded briefly to this quotation of yours, but now I will
respond in more detail:

'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).'

There are certain problems with using orthogonal to describe lines of
movement that are orthogonal to each other. First, it does not describe a
quality that belongs to any line of movement. Rather, it describes a
quality of the relation between two different lines of movement. Second,
it does not distinguish how a Rook moves from how a Bishop moves. On a
standard chessboard, the Bishop's lines of movement are also orthogonal
to each other, for they too are at right angles to each other.

But if we take an orthogonal line of movement to be a line of movement
that intersects the boundaries of a space at right angles, it describes a
quality of the movement itself, and it distinguishes how a Rook moves from
how a Bishop moves. It also fits well with the very first definition given
in Webster's: 'intersecting or lying at right angles.' It is movement
along a line that intersects the boundaries of spaces at right angles.

Now, if we combine these two senses of orthogonal and call it the FULL
MEANING of orthogonal, as you seem to suggest we should do, we have really
just conflated two independent ideas.

Charles,

We're in agreement on the meaning of orthogonal, but we're not in
agreement on the words standard and nonstandard. You say that nonstandard
means 'different from that used in the standard games'. I disagree. A
standard is a rule or principle that establishes how things should be. For
example, there is a standard that diagonal lines of movement pass through
spaces at their centers and corners. On hexboards it results in different
numbers of diagonals at different angles than it does for square boards,
but it's the same standard. All that's different is the application. We
may call a hexboard a nonstandard application, but it's still the
application of the standard concerning what diagonal lines of movement
are. The inventor of the oldest hex variant may have been ignorant of this
standard, but his ignorance is not an adequate argument against it.

Tony P.

You write: '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'.'

Again, your comments are lacking sufficient context for me to know what
you're talking about. Although this comment was addressed to me, it does
not seem to pertain to anything I have said.

[Sorry I accidently posted my last comment under a 'Fergus' thread (Game
Courier), rather than the 'Constitutional Characters' thread.]

Fergus,

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]

Peter,

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'.

People are still how there can be three orthogonal directions in a plane.
Because they are orthogonal to different things. Orthogonal is shorthand
for orthogonal to the cell boundar[y/ies] crossed. This is true of the
Rook move between square, hex, cubic, and hex-prism cells, and not of
Bishop moves.
Qualifications of diagonal clearly need not be used in a page referring
only to square boards or only to hex ones. Where they are needed standard
is shorthand for 'used in games that are or have been standard in their
part of the world' such as FIDE Chess, Chaturanga, Xiang Qi, and Shogi.
All these use either phyusical square cells or, as in Xiang Qi, something
functionally equivalent, and all use the same diagonal in terms of move
length and colourbinding (again even if squares are not physically
coloured differently). Nonstandard means 'different from that used in the
standard games' in terms of move length and colourbinding. Does anyone
expect a hex or 3d game to ever become a regional standard? Hybrid means
combining orthogonal moves at different angles to each other between
hex-prism cells. Regarding '3 at 90º or 2 at 60º' you must remember to
read it as following 'equal distances in...:' Only 2 hex orthogonal
moves can be mutually at 60º as a third at 60º to one would be at 120º to
the other.That the hex diagonal is not self-evidently a Bishop direction
is demonstrated by the oldest hex variant (Wellisch, 1912), in which there
is no Bishop and Knights move one square hex diagonal (Viceroys in my
terminology - the Queen is my Vicereine and the King a Xiang Qi General).
Noting that the faces of the tetrahedron in Tetrahedral Chess can be seen
as hex boards, it becomes apparent that the same kind of Knight is used
(invented independently, no doubt) there!

Tony P.,

You write: '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,'

That's fine. I have never imagined that this was your argument, though I
do appreciate you giving the clarification.

'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).'

I disagree. Orthogonal and diagonal have the same meaning on a hexboard as
they do on a square board. I see no need for extraneous terms that already
do the job of established terms.

Fergus,

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.

Fergus,

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
followed.

Peter,

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).



All,

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
conventions.

Some anonymous person (Charles Gilman?) writes:

'However, some diagonals have longer shortest moves than others and I
still wish to distinguish between them on that basis. How about equal
distances in...: 2 orthogonal directions at 90º to each other = standard
diagonal; 3 at 90º or 2 at 60º = nonstandard diagonal;'

Do you mean 3 at 60º? A hexagonal board has diagonals along 3 axes.

'2 at 60º AND another at 90º to both = hybrid diagonal?'

What kind of board has that?

'Surely everyone can agree that Hex boards 'have a nonstandard diagonal
but no standard diagonal'.'

No, I don't accept this as a valid distinction. All that's nonstandard
is the board. Given the standard for what diagonal means, diagonals on a
hexboard are as standard as diagonals on a square board. Of course, they
may be less familiar to those who only know the standard board, but
unfamiliar doesn't mean nonstandard.

'First mentions could be clarified in more detail, e.g. (colloquially
called triagonal).'

I'm all for describing movement in detail for nonstandard boards. Even
though I will maintain that the hexagonal Bishop moves diagonally and that
the hexagonal Rook moves orthogonally, I would not say so little in a
description of a game and leave it to the readers to figure out. See my
description of Hex Shogi as an example.

Tony P.,

You wrote: '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.'

Okay, here is why your comments puzzled me. You are entirely mistaken in
your assumption that my comments on equations had anything at all to do
with your comments on the statistical use of orthogonal. In fact, I have
said nothing on the subject of the statistical use of orthogonal since my
one-time mention of it. My comments on equations between sets of
coordinates was on an entirely unrelated thread, in which I was simply
discussing the two different methods for describing piece movement.