tag:blogger.com,1999:blog-8425130739244783400.post1079888100015767775..comments2023-10-05T11:54:07.030-05:00Comments on Creative Science & Philosophy: Intuition and Error Correction CodesL. Edgar Ottohttp://www.blogger.com/profile/00525169618204198073noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-8425130739244783400.post-89429104872807562892012-03-29T21:48:33.057-05:002012-03-29T21:48:33.057-05:00I have called combination movements through three ...I have called combination movements through three space 4or2 2or1 1or4 as rooks, 4and2 2and1 1and4 are knights which attack the cells the queen does so in a sense is logically opposite but the queen is not limited to one move in one direction. <br /><br />Now for single movements, 4 or 2 or 1 for a given piece I call bishops. But in four space we combine 8 4 2 1 for a board of 1024 cells. A unicorn (or perhaps Magus) we have 842 421 214 142 for rooks, 8 or 4 or 2 or 1 for bishops now that leaves the six combinations 84 42 21 18 82 41 I designate as the Magi or Unicorns.<br /><br />8 means moving thru a cube in four space which is like the face of a hypercube in a board lattice. In higher space if I use this terminology new classes arise. 1 3 3 1 for a queen moving from a corner through three faces in three space or three edges or the diagonal point or staying where it is. But in four space it is 1 4 6 4 1 following Pascal's triangle.<br /><br />The unicorn acts like the normal non-knight chess pieces of restricted moves. Of course we can continue this to a few higher dimensions but these are probably best played on 2D boards. <br /><br />Thank you for the question. My first chess game designs way back were so complicated my friend Rick in high school said only it could be played between two computers.<br /><br />Sometimes I think imagining a set of cubes is harder than four space once you get used to it and the algebra does help, I mean the number of ways a queen might move from a center of a cube would be 3 to the nth, or the analog to Pascal's triangle that goes 1 12 144 1 6 12 8 1 8 24 32 16 ... which is the count of the sub parts of the square things (orthogons). so for a cube we have 1 cube 6 faces 12 edges and 8 points to move through.<br /><br />It is all very Euclidean and flat at this stage but it can get rather complicated. (even beyond the non-euclidean geometry) but this is the sort of thing we should do in discrete programming if it is to be a logical extension of such space games.<br /><br />Now I will just mention quantum chess hehe<br /><br />cheers, let me know if you need anything between jobs.<br /><br />The PeSlaL. Edgar Ottohttps://www.blogger.com/profile/00525169618204198073noreply@blogger.comtag:blogger.com,1999:blog-8425130739244783400.post-33787314298983604042012-03-29T18:03:47.493-05:002012-03-29T18:03:47.493-05:00What does the unicorn do? Does it move through the...What does the unicorn do? Does it move through the chess plane easier than the queen?Ottohttps://www.blogger.com/profile/15414551321408036318noreply@blogger.com