[this text is in process] 12.10.04 Ma Tri Ces t(ree)-races { mom’s trines }   Pythagoras was experientially aware that each of the ordinal numbers was a magical entity, and that the structural manipulation of sums was useless without an intimate understanding of their meanings and natures. Lest we think this nonsense, given our modern predilection to critique all which is not mechanical in nature, I here endeavor to demonstrate a property of numerism in general which is symmetric and, I believe, entirely independent of base. It verifies the uniqueness of each of the natural numbers — 1 through 10 by revealing an amazing symmetry which is progressively elaborated by and for each individual entity. In exploring these algorithms so we discover that ‘decimal numbers are base three three three’ — in general. Only 3, 6, 9, and 12 produce perfect [binary trine pair] repetition. Each of the resultant numeric lists produces a repeating reduction-result, akin to a decimal fraction. Within this fraction lies a startling symmetry. It is my current position that these symmetries represent something akin to the special identity of the numbers examined. The orderly results of the pattern-reductions are as follows — and at the bottom of the page you may explore the numeric demonstrations in long form [proofs] should you care to examine their method and accuracy. o:O:o In trineMath we explored a symmetry created as follows: Begin at -1, 0 or 1 on a linear number-line. Draw a circle around the first 3 integers (may include 0). Sum them. If the result is greater than 9, sum the digits of the results repeatedly until a single digit result is obtained. Continue to the next unique set of 3 integers and proceed. o:O:o I demonstrated that this produces a pattern, such that if we start with 0, we end up with the singular and consistent result of 3. If we begin with 1, we end up with the singular and consistent result of 6. This begs the following question: ‘What would happen if we drew bubbles of other sizes?’ — would they all produce similarly predictable results according to this algorithm? Let’s find out. o:O:o Here’s how these computations function: For both 0 and 1, at the same time... for the whole numbers from 0 to 1000... [this is most easily accomplished in paired columns — see ‘the wedding bands’ at the bottom of this page to see the process] Note: I have extended this work to include the symmetries of -1, however for the sake of simplification I have omitted the complex diagrams of the resulting 27-digit numbers. They are recorded with 2, 4, 5, 7, 8, 10 and 11 below. It would vastly overcomplicate this essay to deal with all three columns — 0 and 1 suffice for illustration. Phase 1: Take n numbers in order at the beginning of the integers and sum them. If the results are greater than 9, sum the digits of the result repetitively until you obtain a single-digit number. Proceed to the next unique set of n integers, repeat. The result is a string of paired integers, which represent the sums of those taken — the number from 0 on the left, 1 on the right. Phase 2: Reduce the resultant sum-pairs by digit-adding. This produces a string of single-digit pairs. Examine the string as though it were a decimal fraction, looking for repetition. Note and record how many positions precede the repetition. If the number of positions is greater than 9, sum the digits of this number. Record the unique digits of the string in sequence [0 side, 1 side, &c]. Take only a single pass between the repetitions as the subject. Add the digits together using normal addition. If the sum is greater than 9, reduce via digit-summing. Record both these values. Digit-sum the resulting number until a single digit entity results. Proceed to the next unique n-sized set of integers.   Phase 3: This process produces 3 ‘lengths’ of numeric entities, those lengths being 9, 2 and 18 in order of arisal. Each of these entities is unique based upon a spiral addition algorithm. Map the spiral for each entity, examining the sums to determine the cardinal identities of each symmetry, such that, for a 9-digit entity we would add the first and last, then the second to the 8th, then the 3rd to the 7th, &c. 9-digit entities will have an agent in the center, 18-digit entities will not. For this reason the 9-d numbers express a unique mode of spirality compared to the more obvious 18-d’s.   Phase 4: Examine the signature pattern resulting from following the bubbles of 2. The result is 246813579 — and represents a unique ordering of the cardinal numbers. For the 18-digit entities, examine how this pattern of numbers is uniquely woven into an orderly yet complexly-wrought pattern. This is most easily accomplished via bracket-graphing. Each of these phases is demonstrated below. o:O:o “Behold brothers and sisters as the noble entirety [1] is born, divided, separated into twins, and complexified amongst many unique peers. Then they are reunited — reunified, and returned to forefront of the pattern. The story of this 1 is the story of your own life, your intelligence, the life of your peers, your nation, your planet and any other scale you might wish to name. It is even the story of our dialogue here today, each sound or letter — number or word — arises from a moving symmetry. Getting a view of this source is tricky when we’re forced to use static figures, but there is lens we may apply to aid us in fashioning a portal which may properly illuminate our quarry. I cannot sufficiently abjure you to remain exceptionally general in your explorations, for the toy we shall examine applies to anything anywhen. The story of this ‘entirety’ to which we shall shortly be numerically introduced is the story of everybeing, told from a perspective we are never allowed to witness clearly. Look deeply into this ancient matter, for it contains a wisdom older and more novel than almost any you may encounter. Let us turn our attentions to the numbers and see what they may reveal. As we do so let us bear in mind that we are after more than abstract sums here — we seek to know the identities of the cardinal numbers — the members of the primordial Decad.” ~#~ [randomness — with wings] 2 Pattern: 246813579 Number of digits: 9 Sum of Digits: 45 Reduction: 9 27 digit pattern resultant from inclusion of the -1 or ‘No One’s’ column: 224668113557992446881335779 = 135 = 9 3 Pattern: 36 Number of digits: 2 Sum of Digits: 9 4 Pattern: 148269472593715836 Number of digits: 18 Sum of Digits: 90 Reduction: 9 In each of the 18-digit [18-d] numbers, the pattern made by 2 is taken twice, and woven in an orderly fashion to produce the a unique ‘identification symmetry’ or ‘resonance’ within each number’s pattern. The 2-pattern: 246813579 Only the digits from 2’s pattern appear, always in a unique and sometimes exotic pattern, and always precisely two pairs of each number from that pattern — no less, no more — for each of the 18-d entities. Note that some patterns are multiply reentrant [more than a single pass is required to complete the weave]. Additionally, each of the other 18-d numbers present a single entity which has to be digit-summed in order to fulfill the spiral symmetry, the exception is 4, the first, which has 3 such numbers. This movement of this single entity as the patterns progress forms a secondary lens that reveals a recursive ‘winding’ effect, occurring in this dimensions ‘between’ the numbers themselves. Follow the single entity requiring summing, and see if you can trace the spin-pattern yourself. ::: The 2-Pattern weave: R to L To Read this and similar figures: Follow the direction-statement [above] and begin on Gold 2, following the black lines. Then start on Black 2 and follow green lines. Gold lines show possible connectivity between the strands but this feature is speculative and I have not examined it numerically. These are precursor renditions. Click the images to explore more accurate renditions on their own page. o:O:o ^ “By reflection via 3, 1 [the entirety] has been made 11 — it hath accrued a hidden double, who travels ahead in time and place. The double arises 4 positions away — in the direction of ‘ahead’. The mystery is that the entirety contains its double. Yet the inversion does not suffice to illumine this matter... ” • 27 digit pattern resultant from inclusion of the -1 or ‘No One’s’ column: 194872659437215983761548326 = 135 = 9 5 Pattern: 168462492795735138 Number of digits: 18 Sum of Digits: 90 Reduction: 9 ::: The 2-Pattern weave: R to L ^ “The double of the entirety steps back, to re-assure assure itself of unity with its sources — it moves back in time — to a position ‘3-ahead’ of its manifest twin.” • 27 digit pattern resultant from inclusion of the -1 or ‘No One’s’ column: 163841628496274952739517385 = 135 = 9 6 Pattern: 63 Number of digits: 2 Sum of Digits: 9 7 Pattern: 317529641853974286 Number of digits: 18 Sum of Digits: 90 Reduction: 9 ::: The 2-Pattern weave: L to R “A stick splits in twain, both pieces spinning a-round their centers. What was outside is now inside — what was inside is now outside — in both the binary pairings on both sticks. Time has thus entangled the brothers — their game is gaining speed, in new dimensions. The entirety has noticed that it’s twin lies at once before and behind it. The next direction is ‘unknown’ — because the uniVerse has changed. A third and invisible stick is shouting at the great nothing at the loudness of light. Where is this rod?” • 27 digit pattern resultant from inclusion of the -1 or ‘No One’s’ column: 531975429864318753297642186 = 135 = 9 8 Pattern: 192132435465768798 Number of digits: 18 Sum of Digits: 36 Reduction: 9 ::: The 2-Pattern weave: L to R “The sticks are splitting infinities now, such that any gesture of either twin results in travel toward re-unification.” • 27 digit pattern resultant from inclusion of the -1 or ‘No One’s’ column: 219321432543654765876987198 = 135 = 9 9 Pattern: 99 Number of digits: 2 Sum of Digits: 18 Reduction: 9 10 Pattern: 911223344556677889 Number of digits: 18 Sum of Digits: 36 Reduction: 9 ::: The 2-Pattern weave: L to R “The brothers 11 are holding hands — yet — what is this miracle? 10 holds the entirety of 11’s cardinal multiples? How could this be? The prodigal twin returns, and their unity brings forth an entirely new dimension of potentials — multiplication.” • 27 digit pattern resultant from inclusion of the -1 or ‘No One’s’ column: 891912123234345456567678789 = 135 = 9 11 Pattern: 135792468 Number of digits: 9 Sum of Digits: 45 Reduction: 9 ::: The 2-Pattern weave: Reverses at this position across the mirror of 9. Was: 246813579 Now: 135792468 “11 is made one, and this entirety is placed 1st. What was last is in the middle, and the rods on either side, with four digits each have exchanged places circularly. The juxtaposition did not happen at this step, however — it was being assembled in every phase, with similar rod-spinning games, at smaller and more complex scales.” • 27 digit pattern resultant from inclusion of the -1 or ‘No One’s’ column: 813357792246681135579924468 = 135 = 9 12 Pattern: 36 Number of digits: 2 Sum of Digits: 9 [The fourth scalar dimension of trines] o:O:o ‘the wedding bands’ These sheets demonstrate how the identity-numbers for each real number above were arrived at. {note: these sheets are about 120k each and run from 0 - 1000} 0 1 2: 1 + 2 = Pattern: 246813579 Sum of Pattern: 45 = 9 Last digit pattern: 13579 Sum of Last digit pattern: 25 = 7 3: 1 + 2 + 3 = Pattern: 36 Sum of Pattern: 9 Last digit pattern: 36251403928170695847 Sum of Last digit pattern: 90 = 9 4: 1 + 2 + 3 + 4 = Pattern: 148269472593715836 Sum of Pattern: 90 = 9 Last digit pattern: 6026824804 Sum of Last digit pattern: 40 = 4 5: 1 + 2 + 3 + 4 + 6 = Pattern: 168462492795735138 Sum of Pattern: 90 = 9 Last digit pattern: 055 Sum of Last digit pattern: 10 = 1 6: 1 + 2 + 3 + 4 + 5 + 6 = Pattern: 63 Sum of Pattern: 9 Last digit pattern: 5117733995 Sum of Last digit pattern: 50 = 5 7: 1 + 2 + 3 + 4 + 5 + 6 + 7 = Pattern: 317529641853974286 Sum of Pattern: 90 = 9 Last digit pattern: 18079685746352413029 Sum of Last digit pattern: 90 = 9 8: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = Pattern: 2132435465768798 Sum of Pattern: 36 = 9 Last digit pattern: 8620640842 Sum of Last digit pattern: 40 = 4 9: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = Pattern: 99 Sum of Pattern: 18 = 9 Last digit pattern: 65768798091021324354 Sum of Last digit pattern: 90 = 9 10: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = Pattern: 911223344556677889 Sum of Pattern: 36 = 9 Last digit pattern: 55 Sum of Last digit pattern: 10 = 1 11: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = Pattern: 135792468 Sum of Pattern: 45 = 9 Last digit pattern: 566778899002233445 Sum of Last digit pattern: 90 = 9 12: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = Pattern: 36 Sum of Pattern: 9 Last digit pattern: 6802468024 Sum of Last digit pattern: 40 = 4 -1: -1 + 0 +1 = Pattern: 93 Sum of Pattern: 12 = 3 Last Digit Pattern: 03928170695847362514 Sum of Last digit pattern: 90 = 9 9   Perhaps from here we might proceed to the next integer after the first in the set, instead of the next unique set? o:O:o : o:O:o : o:O:o links to related material, above close this window to proceed. pax aeternum et illuminatus

cognitive activism : now contents and concept © d. de stefano, 2004