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Old 12-04-2009, 12:25 PM   #8
barbitone
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Join Date: May 2007
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Now I will move on to the symmetry that is present with this control and the Polar Pair Numbers. Observe the central vertical axis of the control dial. Where each number horizontally paired meet each other they equal nine creating a spine of nine.



This is evident in any multiplication of nine;
2 x 9 = 18 = 1 + 8 = 9
3 x 9 = 27 = 2 + 7 = 9
4 x 9 = 36 = 3 + 6 = 9 etc...
Nine is always self-similar and linear.

So the PPNs are; 1&8, 2&7, 3&6 and 4&5.
These groups should be considered mirror images.

Since the 3&6 are in another league, so-to-speak, from the other groups, we could display these groups like so;



The 3&6 create a space where you are left with three groups. One group is separated and defined from the other two groups vertically, giving you another expression of thirds once again. (One of three)
This expression of thirds will permeate throughout this math everywhere...




The above image shows the decimal parity multiplication of each doubling circuit number and how the numbers all mirror each other and move in the opposite direction.
For instance; 1x4 = 4, 2x4 = 8 3x4 = 12 = 3, 4x4 = 16 = 7, 5x4 = 20 = 2, 6x4 = 24 = 6, 7x4 =28 = 10 = 1
8x4 = 32 = 5, 9x4 = 36 = 9
So for “4” you have the sequence from left to right; 4,8,3,7,2,6,1,5,9
Straight away I know that “5” is going to have the exact same sequence only going in the opposite direction except for the nine which is always at the end. And I know it’ll be the “5” that will match because it is the polar opposite of 4.
So the sequence for “5” is going to go from right to left like this; 5,1,6,2,7,3,8,4,9
1x5 = 5, 2x5 = 10 = 1, and 3x5 = 15 = 6 etc, etc....

(sorry the pic is bugging out)
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