established in such a way so that no diagonal

progressions of array are permitted. The dice array

might be supplied as an example.

But first here the example of the chess knight

journey is supplied. Given the chess board of 64

squares, the chess knight is given 64 unique moves to

complete his journey, without stepping on a past

space, but again how unique or special do these moves

need be?

Several clues for movement can be given, and the

pattern through the first three quadrants can be

easily learned; but it is the fourth quadrant where

complications start. If two knights from opposite

corners of the board started the correct magic

sequence of moves on the board; each knight should be

able to move four times through three quadrants

without interference from the other. If I remember

correctly in the fourth quadrant seven moves instead

of four are made, but I have lost the charts for now

in moving.

Now the question of duplicate, copy, or mirror

image comes up. In this knight jousting game the

first rule becomes first and every square of movement

by the knight is owned, and for the opponent knight

to step there requires future payment of rent. So each

knight by stepping can count on rent from his occupied

square of past movement. In the fourth quadrant each

knight might need to move 7 times before retracing

movemnts through past quadrants, but each quadrant

only holds 16 squares, so it is very likely that in

the fourth quadrant one or the other knights must

conceed and land on a square formerly occupied by the

opponent knight, and thus forfeit some funds for rent

there.

But the special rule of this game is thus, it is

a game for all or nothing, and the payments needed for

rent are inconsequential. All that is required of the

knight is to move 64 times, touching each square as a

new ownership, and the amount of rent required to pay

for this is irrevalent, because if this journey is

completed, everything is won and all recorded rents,

rants and raves, go to the winner.

So each knight could start the game, and one

knight could know the correct magic sequence of moves,

which shows a magic square of 260 for every lateral

layer, but an unbalanced number on the diagonals. And

perhaps more importantly for the knight who gets lost

on his somewhat labyrinth journey, where one wrong

move can mean future entrapment by surrounded past

moves; is the fact that each quadrant contains a

smaller self replicant of the whole or organizational

balance as a smaller magic square summing to 130 in

this example as 16 as the smallest self replicate;

whereupon much larger squares are built. 130 is not a

magic number, it is only the easiest smallest number

to illustrate as a self replicant, and of course

larger numbers are used in larger units of self

replicants. The whole journey can be plotted out to

such a degree that after so many moves are made, it

becomes impossible to make an incorrect move! Talk

about pre-destiny examples!

Now a particular problem comes up in the mirror

image copy. One knight might know the correct

sequence of moves to reach the 64 ending move, but the

other knight in opposition need know nothing, he just

copies the other knights moves mirror image. It would

stand to reason that if this was done, and the rent

actually means nothing because winner takes all, that

whoever moves first must win on the last move. This

also means that even if both knights knew the correct

combination, again whoever was allowed to move first

would win. This makes the game unfair, so more degrees

of freedom must be added.

Now what we might do here to make the problem

more insiduous is to expand the game in three

dimensions. Since we know that each quadrant is

itself a self replicant magic square whose side

additions add to 130 would it not be possible for

these knights to make there progressions though a

three dimensional array of 4X4X4 units? The

possibilty of magic solutions might also be expanded.

However even more obtuse thoughts can follow. A

simple thought and question is brought forward.

Since the magic square knight pattern is known to

provide a balance on lateral additions of numbered

moves, but not a diagonal addition of moves; is it

possible to place those kind of movements on an array

that permits no possible diagonals? Such a thing

might intially seem impossible but think again.

Now a magic cube is the analogy of the magic

square in three dimensions, they are possible starting

with 5 to a side, but not lower. A certain number of

members need be present for the magic balanced

possibility to manifest itself. And added diagonals

are also present on magic cubes whereby the same

example presents itself: the 3 laterals in three

dimensions can add to the balance number, but the

diagonals do not; therefore these examples are

referred to as imperfect magic cubes.

Now what might not be immediately obvious is the

same deception I endured; to mentally think that a

magic cube could be replaced as a three dimensional

array of stacked dice, after all we could look at

these stacked dice with numbers on all 6 sides and at

any of three lateral outside dimensional viewpoints

we can see a row of numbers, and since a magic cube is

possible, why isn't magic dice as an analogy possible?

Here is the difference. On a magic cube each and

every number on the cube is used in three different

rows or combinations in a three different

dimensional combinations of balance. For the magic

dice analogy each dimension of rows uses a different

set of numbers on each dimensional viwpoint, thus it

uses a toal set of numbers three times greater then

what the equivalent magic cube would employ. Since

these combinations are only natures code for maximum

internal capacity to be contained in a sliced coil

construct it should be realized that magic dice

combinations, if they exist should be better examples

for internal capcity methods.

This should also comfort the magic knight moving

in three dimensions for lateral balance since now ALL

of his combinations should be magic or balanced. This

is because in the dice heirarchy no diagonals are

permitted, A unit of three is superimposed on three so

that one point can be made with 3 parts ect. ect.

ect.; but if those diagonals exist they are there,

but I just can't concieve of it yet.

Sincerely

Harvey D Norris

Tesla Research Group; Pioneering the Applications of Interphasal Resonances http://groups.yahoo.com/group/teslafy/