Single Comment

'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.