--- Frederick Sparber <[EMAIL PROTECTED]> wrote: > Jones Beene asks. > > > " "Seven" is a number that is entrenched in > mysticism at many levels - but why? " > > Because it is the result of dividing the "42", the > answer Arthur Dent got when he asked the computer > the meaning of life by 6 ? > > http://www.bbc.co.uk/cult/hitchhikers/guide/answer.shtml > > > If you want the"Ultimate Answer" sooner, ask Jed. > :-) > > Frederick One needs a certain amount of numbers in order to balance them into a magic square state. This of course is taking the array from an ordered sequential state into a so called "magic" state; where all horizontal, vertical and diagonal combinations add to the same number. To find what this "average" number is going to be we merely find the summation of the diagonals when they are placed in the sequential uniform ordering state. The smallest square would be 4 numbers where the diagonals add to 5. However it is impossible to balance this smallest square. We cannot rearrange these 4 numbers so that any combination adds to 5. The first square that can be balanced uses 9 numbers, where one of the diagonals contains 1,5,9 which adds to 15. The solution itself is quite unique, over 4000 combinations of which only one is correct: but depending on our perpective it can be shown 8 different ways as reflections, and half of these reflections are duplicates. If we now take the same analogy into 3 dimensions and attempt to form a "magic cube", we must use 27 numbers for the smallest 3 sided cube; of which one of the four diagonals reads 1,14,27 which sums to 42. If that magic cube could be perfectly balanced, all the sums would add to 42. But as it turns out the best that can be made is lateral combinations that will add to 42, the diagonals cannot be brought to balance because the cube is too small. Thus the first magic cube is an imperfect one, since the diagonals cannot be made to balance. On two dimensions the magic square constructions show that the two diagonals interchange positions with the two laterals that bisect the center: but with a three dimensional cube we find an impossibility for interchange since the are four diagonals but only three laterals that bisect the center number, which does not move to a new position. One cannot interchange four sums with three. Because of this for many years I considered the magic cube an impossibility, but I had not accounted for larger sized cubes. In fact the square that has an even number of elements on its sides has a totally different regimen for solving its solution. Now there is not a single element in the center, but rather a code of four numbers in the center. This code can be turned into an oscillation so that it replicates the conditions for balance by using four adjacent groups of four. Thus at once I recognized that perhaps a perfect magic cube might be had using a cube with four elements to a side, but apparently even this cube is too small. I then started work with balancing a cube with 8 elements to a side, for a total of 512 elements where I then posed this question to vortex list, has a magic cube ever been constructed? Thanx for the answers there, a 1976 Scientific American article shows that it can be done, but I have not yet read this article. Since these things have already been accomplished I abandoned my efforts to find the solution to the 512 element balanced cube. I do not know if this is the smallest perfect magic cube, I will eventually have to get to a university library and find the cited Scientific American article to find what was deduced there. But in any case the special quality of the number 42 can be defined as the first number that can be used to form a sum for an imperfect magic cube. Sincerely Harvey D Norris.
Tesla Research Group; Pioneering the Applications of Interphasal Resonances http://groups.yahoo.com/group/teslafy/
