Comments by FergusDuniho

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 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.

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.

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.,

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.

You can see the new graphics in my new Ultima preset. But I plan to touch
them up a bit before sending you bitmaps for Zillions.

Any thoughts on how many games it is reasonable to expect each person in
the tournament to play? Let me offer a suggestion and get feedback. The
tournament could be set up so that each entrant will play in five
subtournaments, each subtournament consisting of eight players. With eight
players to a subtournament, each subtournament would have three rounds,
with four eliminations in the first round and two in the second round. If
each entrant played in five subtournaments, his games would fall between a
minimum of five and a maximum of fifteen. 

As for the logistics of deciding which games entrants would play, the top
five ranked games would be played by everyone if exactly eight people
signed up. If more than eight signed up, then there would be additional
subtournaments, but not everyone would play in each one. Assignments to
subtournaments would be made based on a list of ranked preferences from
each entrant.

Anyway, deciding the exact logistics of the tournament is not as important
right now as it is to decide on a reasonable number of games to be played.
A minimum of five, a maximum of fifteen, and an average of ten seems fine
to me. But I would like to know what other people think.

After doing a bit of math, it looks like the subtournaments method of
running the tournament wouldn't work out well unless we had exactly eight
people in the tournament. For example, if we had nine people, we could not
evenly distribute people among six eight-person subtournaments. At best,
six people would each play in five subtournaments, and three would play in
all six.

One possible alternative is to stick with subtournaments but to put seven
people in some subtournaments. In the case of nine people, three of the
subtournaments could have seven. The one drawback to this alternative is
that some people would have to sit out the first round in a subtournament,
then play against one of the three winners in the next round.

A second alternative is to have some preliminary elimination rounds that
reduce the number in the tournament to eight, then let the eight people
compete in a few subtournaments.

A third alternative is to forego subtournaments and do something else. One
possibility is to just have everyone play so many games, each against a
different opponent, moving first and second in an equal number of games.
Points would be given for wins or draws, and the tournament winner would
be whoever gets the most points. Ties would be broken with an extra game.

These alternatives have been for eight or more. If we get exactly eight, a
set of subtournaments would work well. If we get fewer than eight, then it
may be best to just have everyone play everyone else at something, then
total up points. Depending on how many signed up, people might play two or
three games with each of the others.