Comments/Ratings for a Single Item

Since I so cleverly made the initial posting unreachable by using the
'&', I'll graciously/shame-facedly re-post the original post, a quote
from D C Dennett:

'If we want to know what the answer to a question in, lets say,
multiplication is, we can all sit down and calculate, but we may not all
agree because some people may get it wrong. But we have got a very good way
of determining, now, this is objectively the right answer. But it really
does depend on people converging on the same answer. If they didn’t,
mathematics would be a very different sort of endeavor. But we can achieve
that sort of convergence, that sort of consensus. And we can do that too on
empirical, factual matters, like, what water is; yes, its H2O. That’s a
fact, no question about it. But there are other questions- not just ethical
questions- where agreement has a different sort of status. Is chess a
better game than checkers, or will the game of chess be better if the king
can move two spaces rather than one? Now, there is evidence that can be
amassed on both sides of the issue. And in the end we might find that no
consensus could be achieved, no matter how much people learned about the
variant ways of playing chess. The preferability of one game over the other
would be a matter of opinion and that would be a subjective matter. But
notice that its not subjective in the sort of wild sense. It could be
perfectly objective that chess would not be improved by a rule that said
that the pawns could be moved up to five spaces at a time. Everybody agrees
that that’s a much worse game. It just does not warrant playing.'

Daniel C. Dennett - Nirmukta interview May 2009

Thanks to Uri Bruck for pointing this out. It seems clear that Dr. Dennett
is thinking either of rather small boards when he is considering 'chess',
or of the 4-square spacing between the 2 lines of pawns, when he comments
about 5-square pawns. I will also point out his use of the word 'could'
in 'It could be perfectly objective that...', giving himself wiggle room.

George, the first question you asked was about area-effect pieces: 'How is
''two-step bent nightrider'' Joyce mentions an example of an area
effect piece, as Joyce describes it?' 

The traditional western chesspieces are highly linear. Even the pawns are
'slow linear', if you think about it. The only pieces that aren't purely
linear are the knight and the king. The knight, which has a sort of
circular footprint, attacks a sort of 2D limited area, rather than some
undetermined number of squares along a straight line. This is an example of
an area-effect piece. The king is a weaker example. It does just hit a
small square area, the squares immediately around it. This can be seen as
an area effect, but you can also consider the king merely a fragile,
degenerate queen [in the chess and mathematical senses, of course.] The
knightzee's footprint [diagrams courtesy of J Good]: 

o o 2 o 2 o 2 o o
o 2 o 2 o 2 o 2 o
2 o o 1 o 1 o o 2
o 2 1 2 o 2 1 2 o
2 o o o N o o o 2
o 2 1 2 o 2 1 2 o
2 o o 1 o 1 o o 2
o 2 o 2 o 2 o 2 o
o o 2 o 2 o 2 o o

It doesn't go far, but it goes wide. The bent Hero and Shaman pieces are
also examples of area effect pieces that are complementary. From the center
of a 7x7 square, they cover all the squares that a zebra does not:

S Z S H S Z S
Z S H H H S Z
S H S H S H S
H H H O H H H
S H S H S H S
Z S H H H S Z
S Z S H S Z S

These represent one sort of area effect piece. The planar pieces in Prince
are another sort.

'What does Joyce mean by ''planar, cubic, quartic, quintic'' in his
current comment at Charles Gilman's glossary to 'M&Bxxs'?' Well, if you
won't accept that it's just a little psychobabble a la my more famous and
very distant relative, then I'll confess it is a quick extension of the
idea of planar pieces on a cubic board to higher and higher dimensions. 

There are already several 4D games around, and even 5D and 6D. 'Planar'
has become the 2D piece designation, and 'cubic' is clearly something in
3D. While you might prefer something like 'quadric' to 'quartic' for a
piece that must make all minimum-distance 4D moves on a 4D or higher board,
what would you call a piece that moves in 5 dimensions, rather than
'quintic'? 

The non-frivolous point is that these pieces, if we are here and now
discussing them, are already being tried out on strange-looking chessboards
hidden in dark corners by people who know the meanings of words like
'hippogonal' and 'triagonal'. Heck, on a 4x4x4x4, a piece that moves 1,
a wazir, can be extended to moving 1 in 2D, 3D, and 4D by using the most
restrictive blocking rules. So the 4D 'wazir', a 'hyperzir' can move
like a ferz, if the 2x2 square defined by the start and end squares is
empty, allowing it to move 1,1 - but both ways. Likewise, it could move
1,1,1, and go to the opposite corner of a 2x2x2 cube, if all other 6 cubes
are empty. We can extend ever upward, to a 16-position tesseract, and a
32-position whateveritis in 5D... 

There. I think I've described a whole new class of pieces, based on a
unit that can move 1 square in any and every direction, up to the limits of
the dimensionality of the board it's on. ;-) Now here's a headache: the
piece I described started as a wazir, capable of moving 1 square at a time,
to every square on the board. Put a hyperferz together, that has the same
properties as the 'hyperzir', and also the same properties as the ferz,
in that it's bound to a regular subset of the board, a multidimensional
lattice. Enjoy.

One of the humorous Chess articles I have read was about the different ways
that the Knight's move was described over the centuries. Sorry, I do not
absolutely recall the book that it was in(I believe that it was in Mensa's
book on Chess).

It gave a large variety of examples, each more convoluted the next. All
took a bit of careful consideration(or at least diagrams) to work out their
logic. Some just made the reader go sparrow.

I bring this up as an example, so that hopefully developers will avoid
re-hashing particular descriptives. Thus continuing the confusion of
particular pieces.

BTW, my description of a Knight move is a translation to the opposite
corner cell of a 2x3 area. Is it better than others? Maybe not. But I
really like it. ;-)

Gee, Larry, don't you know the only description of the knight's move is
'out 2 and over 1'? (Or was that up 1 and over 2?) Anyway, that has to be
the description because that's how you count the move out in 4D chess. So
we gotta use my way... not. There are many ways to describe the moves of
pieces, and many reasons why the movement rules are written the way they
are. But without some standards, no one will know what the heck anyone else
has done. 

Still, alternative ways to describe moves will be used for the foreseeable
future. And actually, that knight move description is true of my version of
Hyperchess. Unless I can give everyone 4D glasses with the game rules, the
only real way to figure the knight's move in 4D is to count it out. Thus,
'2 and 1', rather than a 2x3 rectangle, which is much harder to visualize
on a 4D board. And it points out the real problem we have of defining moves
so that others can understand them. 

I would propose a very simple system, based on the footprints of the
pieces, to give the exact shape/pattern of the move, and hope against hope
that is enough. Otherwise, the task is monumental, and needs several people
with different talents, most likely. I can assure you one is not enough,
nor are two, unless they have an amazing amount of time to work on it and
discuss the project. [You might check out the attempt at the CVwiki; it's
an illustration of the difficulties involved.]

The problem is that I don't really believe there is a very simple system
to do this, so we're screwed, so to speak. We'd [most likely] have to use
'atoms' into which the pieces are broken down, and the pieces would have
to also have 'flavors', like mode of capture, method[s] of transit from
beginning location to ending, whether it's self-moving or requires
activation to do anything, special features, eg: royal...

Yeah, I remember an on-line argument between some individuals about the
'diagonal' descriptive in hexagonal games. One insisted that it was
improper because not only did the target cell have a tenuous connection to
the starting cell but that it involved the shift of three axes on the
field(rather than two) and thus the term 'diagonal' was insufficient.
Another even argued that there were no 'diagonal' moves on the hexagonal
field, merely leaps to orthogonally-connected cells.

There was much venom, and an excessive use of mathematics. In the end,
common use may have won. Few(and there are still some) will now argue about the term 'diagonal' in the description of this form of translation on the hexagonal field.

Perception is probably the greatest factor in game descriptions. How does
a designer relate their concepts to the potential player in such a way that
they can easily visualize them? Building upon common ground is probably a
sound approach. Verbal logic, with minimal use of mathematical
formulae(which some players may have a dis-advantage), is a positive.
Consistency, at least within a given ruleset, is also a necessity.

How many chess variants can dance on the head of a pin?

All of then Rich. After all, they are just thoughts without mass, lots of
efemeral ideas wich a few ones become solid and materialize in boards and
pieces.

The lack of mass could explain the apparent lack of traction of any
particular variant of FIDE chess to get positioned as 'the next chess'.

In the pursuit of mathematical definitions for games and their pieces, one
of the basic qualities, often over-looked, is fun. Primarily because it is
impossible to fully quantify, but also it is very subjective.

Allow me to point out a game which I find quite enjoyable. This is V. R.
Parton's Royal Fury. One which he claimed as a futuristic form of Chess.
It contains many pieces of power, both strong and strange. Therefore it is
un-forgiving in its play. One mistake can lead to disaster.

I had written a Zillions implementation, primarily for my personal
use(since it can be difficult to find human opponents who were willing to
risk such a game), to test out the potential of this game. And discovered
its high level of aggravation(a quality which I thoroughly enjoy). Also,
that Zillions was really not up to the task of prosecuting a good form of
play with this game.

I even tried various alternate set-up patterns to see if there was an
optimum. And discovered that Parton's was most probably the best(at least
in comparison to those I had attempted). So I now accept its master's
wishes.

Like Nemoroth, Royal Fury has pieces which affect and are affected by
other pieces. This can be a source of great frustration for many new
players. Yet I find this quality of frustration(primarily within myself)
again enjoyable.

I point all this out to demonstrate an aspect in the nature of fun. Not as
an absolute value but simply as a subjective facet. Other might not enjoy
such games, nor should they be forced to play such(this would be seriously
contrary to the nature of fun). But there are many in this world, whose
population is numbered in billions, who might enjoy an occasional game of
Royal Fury.

Here's something interesting:

http://www.comedycentral.com/videos/index.jhtml?videoId=222671&title=games-the-annihilator

Hey, Larry. You realize what you've done, don't you? I can think of at
least 2 people*, right off the top of my head, that would put that piece in
a game, but I will mention neither Jeremy nor Carlos [as opposed to carlos]
by name. 

*besides you, of course ;-)

Joe writes: 'Gee, Larry, don't you know the only description of the knight's move is 'out 2 and over 1'? (Or was that up 1 and over 2?) Anyway, that has to be the description because that's how you count the move out in 4D chess.'

On the other hand, the nonleaping Horse in Xiangqi first moves one space orthogonally followed by one more space diagonally outward. And according to the rules of Wormhole Chess, 'The Knight moves as a Knight in FIDE Chess, one space orthogonally, then one space in an outward diagonal direction, jumping over intervening pieces.' While the Knight ignores any pieces occupying the squares it passes over, it still must follow the underlying geometry of the board. In Wormhole Chess this board geometry is constantly changing, so the exact definition of the Knight's move will affect its destination squares.

Are any of those special annihilator pieces still available for purchase?