122200-Absolute-Four-and-Octave-Wave

1222.00 Absolute Four and Octave Wave

1222.10 Prime Dichotomy: It is found that all decimally expressed whole numbers integrate into only nine digits. Looking at the charts (Indig Table B), we see the nine indigs resultant to the decimal system, or congruence in modulo ten, have integrated further to disclose only nine unique operational effects upon all other integers. These nine interoperational effects in turn reduce into only eight other integer-magnitude-altering effects and one no-magnitude-altering effect. The “octave” of eight magnitude-altering sets of indigs in turn disclose primary dichotomy into four positively altering and four negatively altering magnitude operators, with each set arranged in absolute arithmetical sequence of from one to four only.

1222.11 Indig congruences demonstrate that nine is zero and that number system is inherently octave and corresponds to the four positive and four negative octants of the two polar domains (obverse and reverse) of the octahedron and of all systemswhich systematic polyhedral octantation limits also govern the eight 45-degree-angle constituent limits of 360-degree unity in the trigonometric function calculations.

1222.12 The inherent + 4,- 4, 0, + 4, - 4, 0 \longrightarrow of number also corresponds (a) to the four varisized spheres integrating tritangentially to form the tetrahedron (see Sec. 1222.20) and (b) to the octantation of the Coupler (see Sec. 954.20) by its eight allspace-filling Mites (AAB Modules) which, being inherently plus-or-minus biased, though superficially invariant (i.e., are conformationally identical); altogether provide lucidly synergetic integration (at a kindergarten-comprehendible level) of cosmically basic number behavior, quantum mechanics, synergetics, nuclear physics, wave phenomena in general, and topologically rational accountability of experience in general.

1222.20 Cosmically Absolute Numbers: There are apparently no cosmically absolute numbers other than 1, 2, 3, and 4. This primitive fourness identifies exactly with one quantum of energy and with the fourness of the tetrahedron’s primitive structuring as constituting the “prime structural system of Universe,” i.e., as the minimum omnitriangulated differentiator of Universe into insideness and outsideness, which alone, of all macro-micro Universe differentiators, pulsates inside-outingly and vice verse as instigated by only one force vector impinging upon it. (See Sec. 624.)

1222.30 Casting Out Nines: We can use any congruence we like, and the pattern will be the same. The wave phenomenon, increasing by four and decreasing by four, is an octave beginning and ending at zero. From this I saw that nine is zero.

1222.31 When I worked for Armour and Company before World War I, I had to add and multiply enormous columns of figures every day. As yet, neither commercially available adding machines nor electric calculators existed. The auditors showed us how to check our multiplications by “casting out nines.” This is done by inspecting all the input integers of multiplication, first crossing out any nines and then crossing out any combinations of integers that add to nine, exclusively within either the (a) multiplicands, (b) multipliers, or © products of multiplication, taken separately. This means we do not take combinations of integers occurring in other than their own respective (a), (b), or © sets of integers that add up to nine.

1222.32 (a) Multiplier Cross out all nines,

(b) x Multiplicand or any set of integers

adding to nine, in any one of either the multiplier (a), the multiplicand (b), or the product ©.

image Example:

Indig

= 5

= 7

Multiplicand (a)

Multiplier (b)

35629178

35,

178145890

142516712

71258356

3 + 5 = Indig 8 (a)x(b) = 8

image

142516712

Q.E.D.