1221.00 Integration of Digits
1221.10 Quantifying by Integration: Early in my life, I became interested in the mathematical potentials latent in the methodology of the numerologists. I found myself increasingly intrigued and continually experimenting with digit integrations. What the numerologist does is to add numbers as expressed horizontally; for instance:
Or:
Or:
$59865279171 = 5 + 9= 14 + 8 = 22 + 6 = 28 + 5 = 33 + 2 = 35 + 7 = 42 + 9 = 51 +
1 = 52+ 7 = 59+1= 60 = 6 + 0 = 6$,
Numerologically,
1221.11 Though I was familiar with the methods of the calculus for instance, quantifying large, irregularly bound areasexplorations in numerology had persuaded me that large numbers themselves, because of the unique intrinsic properties of individual numbers, might be logically integratable to disclose initial simplexes of sensorial interpatterning apprehendibility.
1221.12 Integrating the symbols of the modular increments of counting, in the above case in increments of 10, as expressed in the ten-columnar arrays of progressive residues (less than tenor less than whatever the module employed may be), until all the columns’ separate residues are reduced to one integral digit, i.e., an integer that is the ultimate of the numbers that have been integrated. Unity is plural and at minimum two. (See Secs. 240.03; 527.52; and 707.01.)
1221.13 As a measure of communications economy, I soon nicknamed as indigs the final unitary reduction of the integrated digits. I use indig rather than integer to remind us of the process by which ancient mathematicians counting with their fingers (digits) may have come in due course to evolve the term integer.
1221.14 I next undertook the indigging of all the successive modular congruence systems ranging from one-by-one, two-by-two pairs to “by the dozens,” i.e., from zero through 12. (See modulo-congruence tables, Sec. 1221.20.)
1221.15 The modulo-congruence tables are expressed in both decimal and indig terms. In each of the 13 tables of the chart, the little superscripts are the indigs of their adjacently below, decimally expressed, corresponding integers.
1221.16 The number of separate columns of the systematically displayed tables corresponds with the modulo-congruence system employed. Inspection of successive horizontal lines discloses the orderly indig amplifying or diminishing effects produced upon arithmetical integer progression. The result is startling.
1221.17 Looking at the chart, we see that when we integrate digits, certain integers invariably produce discretely amplifying or diminishing alterative effects upon other integers.
One produces a plus oneness;
Two produces a plus twoness;
Three produces a plus threeness;
Four produces a plus fourness.
Whereafter we reverse,
Five produces a minus fourness;
Six produces a minus threeness;
Seven produces a minus twoness;
Eight produces a minus oneness.
Nine produces zero plusness or minusness. One and ten are the same. Ten indigs (indig = verb intransitive) as a one and produces the same alterative effects as does one. Eleven indigs as two and produces the same alterative effects as a two. All the other whole numbers of any size indig to
1221.18 Since the Arabic numerals have been employed by the Western world almost exclusively as congruence in modulo ten, and the whole world’s scientific, political, and economic bodies have adopted the metric system, and the notation emulating the abacus operation arbitrarily adds an additional symbol column unilaterally (to the left) for each power of ten attained by a given operation, it is reasonable to integrate the separate integers into one integer for each multisymboled number. Thus 12, which consists of 1 + 2, = 3; and speaking numerologically, $392
5867 = 4$.
-
= +1 +1
-
= +2 +2
-
= +3 +3
-
= +4 +4
-
= 5-4
-
= 6-3
-
= 7-2
-
= 8 ,
This provides an octave number system of a plus and minus octave and an (outside-out) and an (inside-out) differentiation, for every system has insideness (concave) and outsideness (convex) as well as two polar hemisystems.
-
= 1+1
-
= 2+2
1221.20 Indig Table B: Modulo-Congruence Tables: The effects of integers: One is + 1. Two is +2. Three is +3. Four is +4. Five is. Six is. Seven is. Eight is. Nine is zero; nine is none.
(The superior figures in the Table are the Indigs.)
Congruence in Modulo Zero Integrates to Gain or Lose 0:
0 (Like nine) Qj
Congruence in Modulo One Integrates to Gain I :
Congruence in Modulo Three Integrates to Gain 3:
1 1 2 2 3 3 (Each row gains 3
4 4 5 5 6 6 in each column)
7 7 8 8 9 9 Congruence in Modulo Four Integrates
10 1 ll 2 12 3 +3 to Gain 4:
13 4 14 5 15 6 l 1 2 2 3 3 4 4 (Each row gains 4
16 7 17 8 18 9 5 5 6 6 7 7 8 8 in each column)
19 1 20 2 21 3 9 9 10 1 ll 2 12 3
13 4 14 5 15 6 16 7
17 8 18 9 19 1 20 2 +4
21 3 22 4 23 5 24 6
Congruence in Modulo Five Integrates to Lose 4:
I 1 2 2 3 3 4 4 5 5 (Each row loses 4
6 6 7 7 8 8 9 9 10 1 in each column)
ll 2 12 3 13 4 14 5 15 6
16 7 17 8 18 9 19 1 20 2
21 3 22 4 23 5 24 6 25 7
26 8 27 9 28 1 29 2 30 3
Congruence in Modulo Six Integrates to Lose 3:
I 1 2[^58] [^59] 3[^60] 4[^61] 5 5 6 6 (Each row loses 3
7 7 8 99 jqi j2 j2 3 in each column)
13 4 14 5 15 6 16 7 17 8 18 9
19 1 20 2 21 3 22 4 23 5 24 6 -3
25 7 26 8 27 9 28 1 29 2 30 3
Congruence in Modulo Seven Integrates to Lose 2:
Congruence in Modulo Nine Integrates to No Loss or Gain:
Congruence in Modulo Eleven Integrates to Gain 2:
I 1 2 2 3 3 4 4 5 5 6 s 7 7 8 8 9 9 10* ll 2 (Each row gains 2
12 3 13 4 14 5 15 6 16 7 17 8 18 9 19 1 20 2 21 3 22 4 in each column)
23 5 24 6 25 7 26 8 27 9 28 1 29 2 30 3 31 4 32 5 33 6 34 7 35 8 36 9 37 1 38 2 39 3 40 4 41 5 42 6 43 7 44 8 +2
Congruence in Modulo Twelve Integrates to Gain 3:
55 6s 77 88
17 8 18 9 19 1 20 2
29 2 30 3 31 4 32 5
41 5 42 6 43 7 44 8
9 9 10 1 ll 2 12 3
21 3 22 4 23 5 24 6
33 6 34 7 35 8 36 9
45 9 46 1 47 2 48 3
(Each row gains 3 in each column)
+ 3