Check out Janggi (Korean Chess), our featured variant for November, 2024.

Enter Your Reply

The Comment You're Replying To
Tony Paletta wrote on Fri, Dec 12, 2003 11:44 AM UTC:
Fergus,

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.)

Edit Form

Comment on the page Constitutional Characters

Conduct Guidelines
This is a Chess variants website, not a general forum.
Please limit your comments to Chess variants or the operation of this site.
Keep this website a safe space for Chess variant hobbyists of all stripes.
Because we want people to feel comfortable here no matter what their political or religious beliefs might be, we ask you to avoid discussing politics, religion, or other controversial subjects here. No matter how passionately you feel about any of these subjects, just take it someplace else.
Avoid Inflammatory Comments
If you are feeling anger, keep it to yourself until you calm down. Avoid insulting, blaming, or attacking someone you are angry with. Focus criticisms on ideas rather than people, and understand that criticisms of your ideas are not personal attacks and do not justify an inflammatory response.
Quick Markdown Guide

By default, new comments may be entered as Markdown, simple markup syntax designed to be readable and not look like markup. Comments stored as Markdown will be converted to HTML by Parsedown before displaying them. This follows the Github Flavored Markdown Spec with support for Markdown Extra. For a good overview of Markdown in general, check out the Markdown Guide. Here is a quick comparison of some commonly used Markdown with the rendered result:

Top level header: <H1>

Block quote

Second paragraph in block quote

First Paragraph of response. Italics, bold, and bold italics.

Second Paragraph after blank line. Here is some HTML code mixed in with the Markdown, and here is the same <U>HTML code</U> enclosed by backticks.

Secondary Header: <H2>

  • Unordered list item
  • Second unordered list item
  • New unordered list
    • Nested list item

Third Level header <H3>

  1. An ordered list item.
  2. A second ordered list item with the same number.
  3. A third ordered list item.
Here is some preformatted text.
  This line begins with some indentation.
    This begins with even more indentation.
And this line has no indentation.

Alt text for a graphic image

A definition list
A list of terms, each with one or more definitions following it.
An HTML construct using the tags <DL>, <DT> and <DD>.
A term
Its definition after a colon.
A second definition.
A third definition.
Another term following a blank line
The definition of that term.