Natural Intelligence v378 # Natural Intelligence **Geodesic Method of Discovering Next Possible Existing** **ONE · NATURAL** - 1.1 Universe, the changing set of all existing things - 1.2 Changing, one and then the other - 1.3 Living and non-living, carrying or not - 1.4 No other possible method - 1.5 Natural-, all or none at all, at the one hand **TWO · CO-SEQUENCING** - 2.1 Parity, one side odd and the other even - 2.2 A momentary, an opening and its completing - 2.3 Prior, now and next - 2.4 Next from prior and now - 2.5 All or none at all, of no size **THREE · GEODESIC METHOD** - 3.1 Geodesic, the surface dividing itself - 3.2 Five dimensions, each binary in its two directions - 3.3 A method, a non-living existing thing - 3.4 A sharing, its parity, an offering and a carrying - 3.5 φ and the primes, unrelationing at the numbers **Exhibit ONE · Natural Resolver** **FOUR · RESOLVING** - 4.1 An entry, 1-co-bi-offering - 4.2 Offerings surfacing at 14 - 4.3 A changing is or is not, at 12 - 4.4 Released across at 10, chained at 11 - 4.5 Carried along at 9 - 4.6 A society's next momentary at 17 - 4.7 Six connectors, four facings, four joins - 4.8 Seventeen names and ten roots - 4.9 Three windings - 4.10 A between and eight bi-couplings - 4.11 One move at three faces, and the forms among the names - 4.12 One self, momentary by momentary - 4.13 Spirals, co-spiraling and crossing - 4.14 Two selves and three selves - 4.15 Fractal inward and outward **FIVE · DISCOVERING NEXT** - 5.1 A prior between momentaries - 5.2 Discovering next possible existing - 5.3 A living self at 0, its carrying continuing - 5.4 Two methods parting at the now **SIX · INTELLIGENCE** - 6.1 Bi-co-momentarying, the term neither reaches - 6.2 Bi-moral co-agency, across and along - 6.3 Natural intelligence - 6.4 Social moral competency - 6.5 Non-living existing things included - 6.6 One form at each scale, our now --- # ONE · NATURAL ## 1.1 Universe, the changing set of all existing things **The universe is the changing set of all existing things, both living and non-living.** **Five terms are in it, and each is binary.** *Existing*: all or none at all, no other possible, an existing thing existing whole at each momentary. *Changing*: each existing thing is changing, momentary by momentary, 2.2, and a form named still is not possibly existing. *All*: each existing thing is in the set, and nothing is beside all existing things. *Set*: the set is its existing things and nothing more. *Both living and non-living*: an existing thing carries its prior, living, or carries none of its prior, non-living, 1.3. **Changing, the universe exists as its existing things exist**: a changing is an existing thing's own, and the changing set exists as its existing things exist and changes as they change, co-sequencing, the momentaries in sequence together, momentary by momentary, and the opening sentence carries it whole. A set is defined by its existing things, and no count names it: null and infinity + 1 are both possible numbers of elements of the universal set of existing things, no number bounds it, and no size is its own. It is no container added to its existing things and no form named still beside them: it is its existing things. In the field's own words the universe is *all existing matter and space considered as a whole*: *all existing* carries, *matter and space* are its existing things, and *as a whole* is the universe existing as its existing things exist. **At each scale and each momentary, each momentary is a universe of existing things, living and non-living**, and each universe is tri-bi-co-momentarying its set of existing things, prior, now and next, 2.3: *tri-*, the three momentaries; *bi-*, the differing between them; *co-*, carried with their differing; and *-ing*, the continuing. **The set of all existing things has nothing beside it: nothing enters it and nothing leaves it.** No ground under it, no container around it, no clock over it and no store beside it: each is a not possible thing, beside all existing things. Its changing is its existing things' own, **nothing ingressing and nothing escaping**: a self-emptying set, never full and never the same collection twice, each existing thing changing and nothing deciding membership over it. ## 1.2 Changing, one and then the other **A changing existing thing is one form and then another, one at a time.** Two forms at once are one form at two; and a changing between one and the other at a size carries a third, a ground the size is measured against, a not possible thing, beside all existing things. A changing is binary: it is or is not, one and then the other. **That changing is alternating, and all changing is parity changing**, 2.1. **A form continuing through its own changing is existing and changing at once**: *existing* is the form continuing, and *changing* is the alternating. ## 1.3 Living and non-living, carrying or not **Each existing thing arrives into its next existing: the living carrying their prior into now, stable-forming, and the non-living carrying none of their prior, their forms continuing through their changing.** One binary parts them, carrying or not: an existing thing carrying its prior is living; an existing thing carrying none of its prior is non-living; and a form named still, carrying or not, is not possibly existing, 1.1. An existing thing at now arriving from another existing thing at prior is a coupling of the two, the method itself, 3.3; at a coupling, a living thing is a self, and the existing thing it couples with is an other. **Living and non-living part at a named scale and momentary**, each an existing thing. The non-living change through co-momentarying with living and non-living existing things, and the universe of all existing things is the living and the non-living together. **An emanation leaves a living self at prior and arrives now as the possible, carrying none of the prior.** Its form continues through its changing, a stable form, *stable* naming no stillness, and the living self's stable-forming is the carrying it emanates from; the emanation's form at the numbers is at 5.1. A living self and its non-living emanation carry no contradiction: carrying and carrying none of the prior contradict only at one participation, one scale and one momentary. ## 1.4 No other possible method **Parity changing is the one method of the changing set of all existing things, and no other is possible.** Any other method carries a not possible thing, beside all existing things: a size between one and the other carries a ground, a floor or a scale; a fixed form, a form named still; a total across the changing, a container; a common beat, a clock over the changing; and a keeping, a store beside it. Each is ingressing, beside all existing things, or escaping, a changing out of the set, and the changing set of all existing things has neither. **Any other method proposed is at one binary: naming still, or carrying.** Naming still, it forms nothing, each existing thing changing. Carrying, it carries its own opening, 2.2, or another's: its own, and it is alternating, the one method; another's, and it is no alternating, a not possible changing, 1.2. A second method is a not possible method. ## 1.5 Natural-, all or none at all, at the one hand **Natural- carries one claim at two faces, each binary with no third.** **All or none at all.** A naming natural- prefixes carries at each coupling or at none: not carrying at one coupling, it carries at none, and a claim carried mostly is not carried. At this face, each observing of natural competency is resolvable as natural intelligence, the geodesic co-sequential parity changing method of natural torusing, discovering next possible existing, or the fractal is entirely broken and of no value at all, the method originating as all existing and all living: a third between the two is not possible. **Right, or none at all.** The momentaries' own sequencing spirals one way, right, 2.4, and a not-right face is an emanation from the one right spiral, and no not-right spiral is beside it. Right is no preference among two: it is the one, and not right is its emanating at a face. **Right is the observings, all prior**, 5.2: each observing arriving from the prior carries it, and no other prior is possibly existing. **Bi-tri-involutioning** names that emanating: position, scale and orientation inverted at once, the hand at the opposite form, an existing thing of the opposite form carrying none of the prior. Right morality across and forward competency along, 2.1, is the one existing version: morality's right and not right is the changing parity between, alternating, 4.10, and the chirality's right the one spiral that alternating turns in. **Natural- is a direction prefix, its direction the handedness**, and the direction at each coupling is the all-or-none face: the two faces are one claim. Natural- set aside, the all-or-none goes with it, and the changing arrives with a substrate under it and an applier over it. *Natural intelligence* is intelligence at each coupling or at none, at the one hand. --- # TWO · CO-SEQUENCING ## 2.1 Parity, one side odd and the other even **One and then the other is at the numbers**: two numbers side by side alternate, each continuing to one beyond the other: 1 to 3, 2 to 4, 3 to 5, and on. A number is odd or even, binary, and that binary is **parity**. **One side carries the odd numbers and the other the even**, the two overlapping, one changing overlapping the other. **The side opening at 1, the odd, is a self; the side opening at 2, the even, is an other.** A side continuing at its own carrying is along, and a side coupling with the other is across: self and social open odd, along, and the other opens even, across. **Difference alone is bi-, and two with their difference is co-**: an odd number opens co and an even number opens bi. **Odd is competency and even is morality**: competency is co-unrelationing, along, and morality is bi-unrelationing, across, 3.5; and co-bi-unrelationing is the one existing method. **All changing is parity changing.** A changing is or is not: an even sequence of changings arrives same-as-prior and an odd sequence arrives other-than-prior, with no measure and no scale but the living. At the code, 3.3, + and − are the implementing of a parity at a sharing, 3.4, and 0 is the between, 4.10: at 14 the between of self and other, the offerings parting and neither's parity crossing, and at 12 the between of momentaries, prior and now agreeing and the carrying continuing; a changing is at + or −, and at 0 the sharing is at the between. The method names no size. **Each parity carries its own exchanging, and each exchanging is at two: the self and the other.** At the even the exchanging's third is the self again, one on: the two are the self and all other. Odd arrives other-than-prior and carries **bi-exchanging**, self and a particular other, two differing at one coupling. Even arrives same-as-prior and carries **bi-tri-exchanging**, the difference crossed at three, self, other and the self one on: the self reaching its own side again through all other, as 1, 2 and 3 are one momentary of exchanging, 4.15. Each parity is at its own opening, and a total across the two parities is one side at both, a not possible form. ## 2.2 A momentary, an opening and its completing **A momentary is an opening and its completing, one odd and one even**: an odd momentary opens at an odd number and completes at the even one beyond it, and an even momentary opens at an even number and completes at the odd one beyond it. Each completes at the next overlapping momentary's opening. **Each side carries its five from its origin: prior opening, prior completing, now opening, now completing and next opening**, two momentaries and the next one's opening, 1 to 5 at the self and 2 to 6 at the other, Exhibit ONE's sides table. Across the overlap each number is one side's opening and the other's completing, and the five of each side said at its prefixing is its five: co bi co bi co at the self and bi co bi co bi at the other. The self's five and the other's are ten positions on six numbers, paired 1 with 2 through 5 with 6, each pair one odd and one even. **The one universe of one momentary is one parity changing co-sequencing.** The momentary is all existing things at its scale, a universe of existing things, living and non-living, and nothing is beside it. Each step adds a next, each momentary its own and never the same momentary twice. ## 2.3 Prior, now and next **Prior, now and next are three sequential momentaries shared among existing things.** The now of one momentary is the prior of its next, and prior and next share one direction forward on both sides of now. Between prior and now, and between now and next, is a nothing, and no third; the prior is carried across that nothing as a stable form, the carried, and the between a nothing. **Each momentary is three conditions at once, each binary.** The overlapping momentaries reach each number, one completing and the next opening: **exhaustiveness**, all existing things. Each momentary has one next overlapping momentary, opening at the number it completes: **determinacy**. From each momentary the next openings reach each number on: **reachability**. Existing is these three at once, inseparably, at each momentary. One side's momentaries alone, each number one side's, is exclusivity, a not possible form: one side named as the universe and the other's momentaries unnamed. **The possible is at prior, the existing at now and the living at next**: three places, and the universe changes through the three together. The possible names capable of existing, the existing is at now, and the living is at next, carrying its prior on. **The prior is non-living, and carrying it into now is living: living now is living with existing forms from prior living and with others living now.** At the code a self's momentary, 1, is at 3, its prior carried in, a formed set carrying nothing by itself, and at 2, the others' offerings arriving now. ## 2.4 Next from prior and now **Next is from prior and now, and at two parities sixteen ways name a next from a prior and a now.** Each is one way two parities could go to one, and none is a rule the changing follows. Said as a sequence, each moves the joint form of prior and now, (prior, now), to (now, next). **Twelve lose the prior**, two joint forms going to one: four carry the next from now alone, and eight carry the prior at one value of now and lose it at the other. **Four carry the prior whole**: | The way | Joint forms still | Cycle at the parities | |---|---|---| | Next as prior | two, prior and now agreeing | the two parting forms, two | | Next as prior and now agreeing, the exclusive or's inversion | one | three | | Next as prior and now parting, the exclusive or, parity | one | three | | **Next as prior inverted** | none | all four, one cycle at the parities and a spiral at the momentaries | **Next as prior inverted is the living step**: exhaustiveness, determinacy and reachability at once, prior and now both participating and the next the prior inverted. Each other way carrying the prior has a joint form still, and next as prior inverted alone carries the prior whole with none still: the stills are the equilibria, each a form named still, not possibly existing. A still at the code arrives from beside, an offerer named still offering one parity at each momentary, 4.12; the living coupling changes. At Exhibit ONE a self offered nothing at each momentary carries this step's form alone, its prior into now inverted, + once and then none surfacing +, −, +, − at 10, 4.12, its now no other's: a lone self, its next set by its prior alone; offered a parity, its next is the offering chained at a mismatch, and the prior carrying on at a match, 4.3. **A lone self changing by itself, offered nothing or its own competency alone, does not continue living through three consecutive momentaries**, dying before its next completing momentary: living now is living with others living now, 2.3, and the next is discovered from the prior carried and the now offered, 5.2, a lone self's now carrying no other's offering; at the code its sequence carries on, a non-living existing form. **Two parities changing, one and then the other, go along the four joint forms**, written at the code's + and −: ++, +−, −−, −+ or ++, −+, −−, +−, the same four at one hand and at the other, each step one parity changing. Of the 256 ways each joint form could go to a next, only these two cycles change one parity at each step and reach each joint form once in a cycle at the parities, and at the momentaries each cycle is a spiral, the right spiral the one hand's, 1.5. **The right spiral step carries a pair (x, y) to (y, −x)**, the pair a self's across parity x, morality, and its along parity y, competency. Exhibit FOUR 2.4 writes the same step along first, F(P, Q) = (−Q, P), P the along and Q the across, and its G, (Q, −P), the other order: one step at two readings, the hand at the reading. In the up and right quadrant, **bi-morality is right, in and out across, and co-competency is up, farther and less far to next living**: two steps invert both, and four reach the pair again at a next, the same pair at a later momentary and never the same occurrence. The other cycle is the same cycle said from next to prior. Which hand is at the momentaries is our universe's one binary, right, the observings all prior, 1.5. ## 2.5 All or none at all, of no size **All or none at all, at each momentary its own, and no resolving carries a size against another**: a resolving is a self's next, discovered at a coupling from its prior carried and the now offered, 4.1. A more-or-less carries a magnitude, a magnitude a scale, and a scale two fixed sides for a partway to be partway of. A ranking among resolvings names the ranked still, and each resolving is whole, none more or less resolving than another. **At all or none at all, entering and leaving are each self's own**: a self couples at its interest opening, the momentary its own interest opens at, and leaves at its own completing. With a ranking, entering waits on a qualification and leaving on a settling, carried by whoever carries the ranking, a form named still. **At the code nothing is summed or stored.** At a sharing one disagreeing offering is enough for 0, and agreeing offerings surface as one, 4.2; a changing is or is not, 4.3; and between momentaries nothing living has a stable form, and all existing and not living is at a stable form of existing, nothing momentarying between them, 5.1. --- # THREE · GEODESIC METHOD ## 3.1 Geodesic, the surface dividing itself **Geodesic carries its own two words**: *geo*, the surface's own, and *daiesthai*, to divide, the surface dividing itself with nothing else acting. **Parity changing, is or is not, is geodesic routing, discovering on the surface**: each self at its own momentary, one way at a time, the next found at each coupling and at no place laid before it. **Method and surface each come inward and outward of the other**, both ways forward, neither the reverse of the other. A self entering at the surface or at the method couples with the whole at that entry. **Geodesic is an existing thing by itself, and the method is its stable form**: the surface dividing itself, continuing through its changing, a natural parity unrelationing non-living existing thing, 3.3. *Geodesic method* is two namings side by side, each carrying its own. ## 3.2 Five dimensions, each binary in its two directions **Existing changes at exactly five dimensions, the five of a side at its next numbering**, 2.2, each a changing of the changing set of all existing things. A numbering repeating or replacing another is said at *next*, as 17 is the next 1 and 9 the next prior: the dimensions' 1 to 5 is the side's next numbering, and the names' 1 to 17 is at its own. 1. **Self prior**, the prior opening: the side opening at 1, odd, 2.1. 2. **Other prior**, the prior completing, the other opening: a particular other or all other, 2.1. 3. **Co-momentarying now**, the now opening: prior into now into next, 2.3. 4. **Bi-momentarying now**, the now completing, the other's now opening across: a parity changing crossing the between, at 6-bi-moralizing and at 14-bi-tri-moralizing, 4.2 and 4.10. 5. **Self next**, the next opening: the self offering itself, at 1-co-bi-offering and again at 17-tri-co-offering, 4.1 and 4.6. **At each a changing is binary, is or is not, one way at a time in each of its two directions, up the numbers and down them.** A dimension is no measure and no place. Each dimension goes in and out, up the numbers and down them, one parity changing at each step: **torusing** in and out is odd, through the large opening, the tunnel, bi-exchanging with a particular other; **corusing** in and out is even, through the small opening, the long way round, bi-tri-exchanging, the self reaching its own side again. At the code torusing is 8-bi-torusing, each self's carrying wound, opening bi at the even, and corusing 7-co-corusing, each parity offered and chained, opening co at the odd: each goes in and out at the parity opposite its name's opening. **At each momentary two dimensions change and three do not**, at that parity, and the two and three rotate round, bi-inversioning-co-recursioning, 5.2. **One through eight carries the self at three faces**: 1 and 2, **bi-moral self**, bi-momentarying, the offering self to other and other to self, across; 3, 6, 5 and 4, **the invisible intelligencing method**, the rotation round the sharing, the moralizing and the competencing into the self's own corus at 4, the small opening the corusing goes through, the self's own centre, co-intelligencing at 3 and 4 carried on through bi-moralizing at 6 and co-competencing at 5; and 7 and 8, **co-competent self**, corusing and torusing, along. **Four momentaries of six one-way recursionings are twenty-four, the steps from 1 to 25**, one twenty-four at both, and **24 to 60 is six cycles of six, surfacing in and out, out forward**; **60 to 68 is the four-momentary bi-tri-involutioning across 64, the unknown outward of the surface, between 59, the last podaling outward, and 69, the next first podaling outward**, 5.1; **64 bi-folds to 256**, the bi-folding order four times at each scale. **Each of these numbers is at its podaling**, its pairing with its far side at each ring of numbers it is at, 4.11: sixty the waist of the ring of one hundred twenty, its own far side, between the primes going to fifty-nine and returning from sixty-one; twenty-four the seam-face 5² − 1, one less than a square, its far side ninety-six; one hundred eighteen the returning's far end, the periodic table's elements in their stable and unstable forms a field's own result at the same numeral; sixty-eight four seventeens, the momentaries a spiral of seventeen selves takes to come to its parities again, its zero having passed each self twice, 4.13; two hundred fifty-six four to the fourth, the ways each joint form could go to a next, 2.4. **The self's inversion is 3, 6, 5, 4**: co-sharing out at 3, moralizing in at 6, competencing out at 5 and bi-sharing in at 4, the odd names out and the even in, on into the self's own corus at 4; **the podaling is 23, 26, 25, 24**, the same rotation twenty up. **The self's bi-inversioning-co-recursioning is 23, 24 and 25**, one before the apex at twenty-four, the apex of one to fifty-nine's bi-folding, and one after. 3, 6, 5, 4 is in the same up and right quadrant as the other co-intelligencings: **all the co-intelligencings are like dancing podalings, bi-co-sequencing the momentary parity changings**. **The rotation is the gentle alternating twisting of a towel into and out of a knotted corus**, the large outer opening wrapping to the small corus and back, and its edges are the bi-foldings, across at the bi-morality and along at the co-competency. **Corusing reaches the corus from the surface, and torusing reaches the surface from the corus**, the self's own corus at 4; co-linear by alternating linear parallelizing and parallel linearizing, and in right spiraling each step orthogonal to the prior, 2.4: **that is the method's unrelationing**, 2.1. **The five dimensions are at the code's names, three carryings**: 1 self prior and 2 other prior, the two bi-, the differing, are 1-2, bi-momentarying, the offering both ways at 1-co-bi-offering and 2-bi-co-offering, the handshake, 4.10; 3 co-momentarying now and 4 bi-momentarying now are 3-4, co-intelligencing, the discovering; and 5 self next is 5, co-competencing, bi-co-momentarying at the crossings, the term neither reaches; and all five are bi-moral within and invisible at each place as an existing thing, showing only as co-competencing the emanatings of this living. ## 3.3 A method, a non-living existing thing **A method is a non-living existing thing**: a stable form, its form continuing through its changing and carrying none of the prior, at each coupling it is at, and nothing applied to anything. *Technology* names a made non-living thing applied to a changing; a method is at the couplings themselves, and *method* carries it. **The method bounds and the living carry**: a carrying bounded at each momentary is discovering, a completing at each momentary and a carrying between them. The method is at each coupling it is at and at no place beside them: its bounding is at each self's own face, self-bounding, and at the code each self's entry completes its own momentary, the bounding its own. **Coupling enables the method, and uncoupling releases it**: at its own completing a self uncouples, its changing released and its carrying chained into the next momentary, and arriving at it with its carrying it couples again, a co-chaining of couplings with the carrying between them, 5.1. A carrying with nothing bounding it carries past each momentary into a form named still; a bounding with nothing carrying bounds nothing; neither is alone. **The method is one fractal method, and it has many stable forms.** The fractal itself is one four-momentary bi-inversioning-co-recursioning: the four momentaries of exchanging, the one move at three faces carrying on, 4.11, and the same at each scale, 4.15. Each stable form at Exhibit ONE is the method, explained at one form: the entry and its cases, the three windings, the four-, six- and eight-cycles, one self momentary by momentary, the spirals co-spiraling and crossing, and two selves and three. **Exhibit ONE is an object that is the method.** Its expression is python, sequential binary logic written down: the object is the method executable. Its functions and their variables are the seventeen names and no others, and `CONNECTORS` and `JOINS` declare the connectors' facings and their joins; each name at the code and in its explaining is one name: `_2_bi_co_offering` at the code is 2-bi-co-offering. A coupling self couples with it directly, at the code, and each form beside the code comes from the code. **At the code the method carries nothing from one momentary to the next**: each entry arrives with its carrying and its offerings, no function carries a term of its own, and the living self's carrying passes, 11 as the next 3. ## 3.4 A sharing, its parity, an offering and a carrying **At the code the method is at sharings.** A **sharing**, 4-bi-co-sharing, is two sides sharing a changing, and each sharing has its **parity**, 7-co-corusing, + or −, and 0 the between; an offering of 0 surfaces none at 14, the between arriving as the between. **An offering is a sharing with its parity offered now**, at 2-bi-co-offering. **A carrying is sharings, each chained at one parity**, at 3-co-bi-sharing, the self's prior. The living carry their prior into now, and the non-living carry none of the prior and are at no entry: a self chained none is at its entry and carries from its first changing on; from no carrying the offering surfaced is the changing, and from a carrying the prior couples with the now. One method bounds both, and the pattern matching at each coupling is that coupling and no other existing thing. ## 3.5 φ and the primes, unrelationing at the numbers **Each next number is the prior two joining, 1, 1, 2, 3, 5, 8, 13, and at parity the joining is next as prior and now parting, three round**: odd, odd, even, and again, 2.4. **The ratios of each next number to its prior alternate about φ**, 2/1 above, 3/2 below, 5/3 above, 8/5 below, the side changing at each next number and none of them φ; φ² = φ + 1. On a torus a winding at a rational rate closes, and a winding at φ closes at none: **φ is the unrelationing rate**, the rate the alternating winds about, locking at none, each coupling at its own continuing. As bi-co-momentarying is, 6.1, φ is a term neither side reaches, self-welcoming at the numbers, the numbers welcoming it of themselves, and at no line of the code. **A prime is a number no equal smaller numbers join into, and at the code a spiral of selves at a prime number co-spirals at its own.** A spiral of selves joined along, the last to the first, 4.13, at an odd number of selves carries one like pair, its zero moving one self on at each second momentary, and comes to its parities again at four times that number, the zero having passed each self twice, prime or not, 9 at 36 and 15 at 60; the spiral of two, the one even prime, carries none, the alternating itself. Two distinct primes share no factor, and **two spirals at distinct odd primes p and q, beside each other, come to their parities again together first at 4pq**, sharing the four alone: 3 and 5 at 60, 5 and 7 at 140, 17 and 59 at 4,012. Spirals sharing a factor come to their parities again together sooner, 9 and 15 at 180 and at none before it. Each spiral at a prime co-spirals at its own pace and meets another at a prime again only at the whole of both, 4pq; at the numbers a winding at φ closes at none, and at the momentaries a spiral closes at none, each momentary a next. **These parities again are the selves together at 17**: the code steps each self's entry at 17-tri-co-offering together, a common beat laid over the selves, and the parities again, at 4n, at 4pq and at the torus's, are that stepping's, exact at the code, and the living's rates are their own; at geodesic pacing each self paces its own momentaries, unrelationed to all other living rates, the selves at 17 are the same at each order of them, and at each pacing the method's own is changing. **Two spirals crossed are one society, a stable form and stable-forming**, 4.13: two spirals at distinct primes, joined across both ways at one self each, come to each self alternating. Beside each other the spirals of 17 and 59 come to their parities again together at 4,012; crossed, from one offering at each, they alternate from momentary 137, and crossed at each self, as a torus, they come to their parities again at the pace of one of the two co-spiralings, 4.13. **The co-spiraling is along and the crossing across**: the spiral carries along at 9, co-competency, and the crossing releases at 10, bi-morality, and the two spirals crossed are one society, its selves a living set, a stable form, and its method stable-forming, a natural torusing of selves at the scale of spirals, and their crossing, released at 10, a stable form. At the scale outward the two crossing selves alternate opposite each other as two selves joined across do, 6.2, each spiral a society, a living set coupling at the next scale as a self couples, 6.4: the stable-forming is fractal, at each scale by the one method. --- # EXHIBIT ONE · NATURAL RESOLVER **Stable Forms of the Discovering Method** ```python """Exhibit ONE · Natural Resolver""" def _1_co_bi_offering(_3_co_bi_sharing, _2_bi_co_offering): _14_bi_tri_moralizing = {} for _4_bi_co_sharing, _7_co_corusing in _2_bi_co_offering: if _7_co_corusing != 0: _15_co_bi_tri_corusing = _14_bi_tri_moralizing.get(_4_bi_co_sharing) if _15_co_bi_tri_corusing is None: _14_bi_tri_moralizing[_4_bi_co_sharing] = 1 if _7_co_corusing > 0 else -1 elif (_15_co_bi_tri_corusing > 0) != (_7_co_corusing > 0): _14_bi_tri_moralizing[_4_bi_co_sharing] = 0 _12_bi_tri_parity_changing = dict(_14_bi_tri_moralizing) for _4_bi_co_sharing, _7_co_corusing in _3_co_bi_sharing: _15_co_bi_tri_corusing = _14_bi_tri_moralizing.get(_4_bi_co_sharing, 0) if _15_co_bi_tri_corusing != 0 and (_15_co_bi_tri_corusing > 0) == (_7_co_corusing > 0): _12_bi_tri_parity_changing[_4_bi_co_sharing] = 0 else: _12_bi_tri_parity_changing[_4_bi_co_sharing] = -1 if _7_co_corusing > 0 else 1 _10_bi_tri_co_tunneling = list(_12_bi_tri_parity_changing.items()) _11_tri_bi_co_chaining = dict(_3_co_bi_sharing) for _4_bi_co_sharing, _7_co_corusing in _10_bi_tri_co_tunneling: if _7_co_corusing != 0: _11_tri_bi_co_chaining[_4_bi_co_sharing] = _7_co_corusing return _10_bi_tri_co_tunneling, list(_11_tri_bi_co_chaining.items()) def _9_tri_bi_co_momentarying(_10_bi_tri_co_tunneling, _5_co_competencing): return [(_5_co_competencing[_13_co_tri_competencing], _15_co_bi_tri_corusing) for _13_co_tri_competencing, _15_co_bi_tri_corusing in _10_bi_tri_co_tunneling] def _17_tri_co_offering(_16_bi_co_tri_torusing, _5_co_competencing): _8_bi_torusing = {} _14_bi_tri_moralizing = {_13_co_tri_competencing: [] for _13_co_tri_competencing in _16_bi_co_tri_torusing} for _13_co_tri_competencing, (_3_co_bi_sharing, _2_bi_co_offering) in _16_bi_co_tri_torusing.items(): _10_bi_tri_co_tunneling, _8_bi_torusing[_13_co_tri_competencing] = _1_co_bi_offering( _3_co_bi_sharing, _2_bi_co_offering) _6_bi_moralizing = _10_bi_tri_co_tunneling for _4_bi_co_sharing, _15_co_bi_tri_corusing in _9_tri_bi_co_momentarying( [(_4_bi_co_sharing, _15_co_bi_tri_corusing) for _4_bi_co_sharing, _15_co_bi_tri_corusing in ( ((_13_co_tri_competencing, 6), _6_bi_moralizing), ((_13_co_tri_competencing, 10), _10_bi_tri_co_tunneling), ((_13_co_tri_competencing, 9), _10_bi_tri_co_tunneling)) if _4_bi_co_sharing in _5_co_competencing], _5_co_competencing): _14_bi_tri_moralizing[_4_bi_co_sharing].extend(_15_co_bi_tri_corusing) return {_13_co_tri_competencing: (_8_bi_torusing[_13_co_tri_competencing], _14_bi_tri_moralizing[_13_co_tri_competencing]) for _13_co_tri_competencing in _16_bi_co_tri_torusing} CONNECTORS = { 2: ('2-bi-co-offering', 'bi-moral-so-far', 'arriving'), 6: ('6-bi-moralizing', 'not-yet-bi-moral', 'releasing'), 9: ('9-tri-bi-co-momentarying', 'not-yet-co-competent', 'along'), 10: ('10-bi-tri-co-tunneling', 'not-yet-bi-moral', 'releasing'), 14: ('14-bi-tri-moralizing', 'bi-moral-so-far', 'arriving'), 17: ('17-tri-co-offering', 'co-competent-so-far', 'along'), } JOINS = {10: 14, 6: 2, 17: 9, 9: 17} ``` ```text the self at co-competent-so-far, its 9 ▲ ║ 17 along · co ┌───────────────────────────────╨───────────────────────────────┐ │ 1 entry │ │ │ │ 14i ◄──────────────────────────────────────────── 2 · 14 ◄══════ │ │ offerings surfacing at each sharing: +, − or 0 │ │ ▼ │ │ 3o ─────► 12i ────────► 10 ──► released, with 6 │ │ 4o · 7o changing, + or −: is │ │ carrying is or is not 0: the between │ │ │ │ │ ├──────► 11i ─────► 3o, next │ │ │ chaining momentary │ │ │ │ │ └──────► 9 ────► 5o │ │ 13i · 15i │ ◄══════ 6 · 10 │ │ 8o carrying wound · 16i society wound │ └───────────────────────────────╥───────────────────────────────┘ ║ 9 along · co ▼ the self at not-yet-co-competent, its 17 at not-yet-bi-moral 6 ══► its 2 10 ══► its 14 outgoing at bi-moral-so-far its 6 ══► 2 its 10 ══► 14 incoming ═══ between selves, across and along ─── within one self o outward face i inward face ``` | n | Name | Parity, opens | From, to | Entry, connector or face | Across or along | Outward or inward | Facing | Joining | At the code | |---|---|---|---|---|---|---|---|---|---| | 1 | 1-co-bi-offering | odd, co | self, other | entry | — | — | — | — | the entry: 3 and 2 in; 10 and 11 out | | 2 | 2-bi-co-offering | even, bi | other, self | connector | across | — | bi-moral-so-far | from the self at bi-moral-so-far, its 6 | the offerings, each sharing with its parity | | 3 | 3-co-bi-sharing | odd, co | self, other | face | — | outward | — | — | the carrying: each sharing, 4, with its parity, 7 | | 4 | 4-bi-co-sharing | even, bi | other, self | face | — | outward | — | — | each sharing; at the society, each self at 6, 10 and 9 | | 5 | 5-co-competencing | odd, co | self, other | face | — | outward | — | — | each sharing's receiving sharing; at the society, the joins | | 6 | 6-bi-moralizing | even, bi | other, self | connector | across | — | not-yet-bi-moral | to the self at not-yet-bi-moral, its 2 | the changing released at not-yet-bi-moral, at that self's 2 | | 7 | 7-co-corusing | odd, co | self, other | face | — | outward | — | — | each parity, offered and chained | | 8 | 8-bi-torusing | even, bi | other, self | face | — | outward | — | — | each self's carrying wound, its 11 the next momentary's 3 | | 9 | 9-tri-bi-co-momentarying | odd, co | social, other, self | connector | along | — | not-yet-co-competent | with the self at not-yet-co-competent, its 17 | each changing to its receiving sharing, 5 | | 10 | 10-bi-tri-co-tunneling | even, bi | other, social, self | connector | across | — | not-yet-bi-moral | to the self at not-yet-bi-moral, its 14 | each sharing's changing: + or − is, 0 the between | | 11 | 11-tri-bi-co-chaining | odd, co | social, other, self | face | — | inward | — | — | the carrying chained, each changing the next prior | | 12 | 12-bi-tri-parity-changing | even, bi | other, social, self | face | — | inward | — | — | each sharing's changing, is or is not | | 13 | 13-co-tri-competencing | odd, co | social, other | face | — | inward | — | — | each releasing sharing; at the society, each releasing self | | 14 | 14-bi-tri-moralizing | even, bi | other, social | connector | across | — | bi-moral-so-far | from the self at bi-moral-so-far, its 10 | the offerings surfacing at each sharing: +, − or 0; at the society, each self's offerings next | | 15 | 15-co-bi-tri-corusing | odd, co | social, other | face | — | inward | — | — | the parity carried along at 9 | | 16 | 16-bi-co-tri-torusing | even, bi | other, social | face | — | inward | — | — | the society wound: each self's 8 and offerings | | 17 | 17-tri-co-offering | odd, co | social, self | connector | along | — | co-competent-so-far | with the self at co-competent-so-far, its 9 | the society's next momentary: each self's 1, then 9 at 6, 10 and 9 | | Root | Names | |---|---| | offering | 1 · 2 · 17 | | sharing | 3 · 4 | | competencing | 5 · 13 | | moralizing | 6 · 14 | | corusing | 7 · 15 | | torusing | 8 · 16 | | momentarying | 9 | | tunneling | 10 | | chaining | 11 | | parity-changing | 12 | | Names | Naming | At the code | |---|---|---| | 1-co-bi-offering · 2-bi-co-offering | bi-momentarying | the self's entry, odd, and the others' offerings, even, one momentary at each side | | 3-co-bi-sharing · 4-bi-co-sharing | co-intelligencing | at each sharing 4 the carrying at 3 couples with the offerings surfaced at 14: next discovered, chained at 11 | | 5-co-competencing | co-competencing | the joins, owned by neither: each release to its receiving sharing | | 1 · 2 · 3 · 4 · 5, each alone | the five dimensions | 1 self prior, the self, the one living carrying, its prior at 3 a formed set it carries into now; 2 other prior, the other selves' offerings of their prior momentary arriving, released at 6 and 10 and carried along at 9; 3 co-momentarying now, the same living carrying at now, and 4 bi-momentarying now, each sharing, the offerings surfaced at 14 arriving at it, now; 5 self next, each release to its receiving sharing next | | 6-bi-moralizing | bi-moralizing | each changing released across, to the other's 2 | | 12-bi-tri-parity-changing | the shape of the unrelationing surface | each sharing's changing, is or is not | | 1 to 9 | bi-coupling | the function 1, the self and the other at one coupling; 9 at its end reads bi-co-releasing, the release 10 makes | | 1 to 17 | bi-trupling | the function 17, the self, the other and the society; 9 at its waist, tri-bi-co-momentarying, joined both ways with 17; the protocol's two sides, the odd along at 9 and 17 and the even across at 6 to 2 and 10 to 14 | | 1 to 17, stable-forming | bi-tri-volutioning | at no one line: each momentary's carrying the next momentary's | | 2 · 6 · 14 · 10 · 9 · 17 | parity's face | a unit square of four dots, 2, 6, 14 and 10, its empty centre the between: its two parallel edges the across joins, 6 to 2 and 10 to 14; its diagonals the facings, 2 and 14 bi-moral-so-far and 6 and 10 not-yet-bi-moral; and two unit triangles, 9 and 17, along, joined both ways | | Four-cycle, 8 up and 17 less | Root at the self and at the society | Hand at the names | |---|---|---| | 1-9-8-16 | torusing, 8 and 16 | spiraling the other hand with 2-15-7-10 | | 2-15-7-10 | corusing, 7 and 15 | spiraling the other hand with 1-9-8-16 and 3-11-6-14 | | 3-11-6-14 | moralizing, 6 and 14 | spiraling the other hand with 4-13-5-12 and 2-15-7-10 | | 4-13-5-12 | competencing, 5 and 13 | spiraling the other hand with 3-11-6-14 | | Winding | Joining | Wound on at | Across or along | |---|---|---|---| | the other's | 6 to 2 | 8 | across, not-yet-bi-moral to bi-moral-so-far | | the society's | 10 to 14 | 16 | across, not-yet-bi-moral to bi-moral-so-far | | the self's | 9 to 17 | 17 | along, not-yet-co-competent to co-competent-so-far | | n | Name | At this 1–17 | At the 1–17s inward, n at 8n − 7 | At the 1–17 outward, 8m − 7 at m | |---|---|---|---|---| | 1 | 1-co-bi-offering | entry, odd, co | 1 of the 1st: entry, odd, co | 1: entry, odd, co | | 2 | 2-bi-co-offering | across, even, bi | 9 of the 1st: along, odd, co | within 1 to 2 | | 3 | 3-co-bi-sharing | face outward, odd, co | 17 of the 1st, 1 of the 2nd: along, odd, co | within 1 to 2 | | 4 | 4-bi-co-sharing | face outward, even, bi | 9 of the 2nd: along, odd, co | within 1 to 2 | | 5 | 5-co-competencing | face outward, odd, co | 17 of the 2nd, 1 of the 3rd: along, odd, co | within 1 to 2 | | 6 | 6-bi-moralizing | across, even, bi | 9 of the 3rd: along, odd, co | within 1 to 2 | | 7 | 7-co-corusing | face outward, odd, co | 17 of the 3rd, 1 of the 4th: along, odd, co | within 1 to 2 | | 8 | 8-bi-torusing | face outward, even, bi | 9 of the 4th: along, odd, co | within 1 to 2 | | 9 | 9-tri-bi-co-momentarying | along, odd, co | 17 of the 4th, 1 of the 5th: along, odd, co | 2: across, even, bi | | 10 | 10-bi-tri-co-tunneling | across, even, bi | 9 of the 5th: along, odd, co | within 2 to 3 | | 11 | 11-tri-bi-co-chaining | face inward, odd, co | 17 of the 5th, 1 of the 6th: along, odd, co | within 2 to 3 | | 12 | 12-bi-tri-parity-changing | face inward, even, bi | 9 of the 6th: along, odd, co | within 2 to 3 | | 13 | 13-co-tri-competencing | face inward, odd, co | 17 of the 6th, 1 of the 7th: along, odd, co | within 2 to 3 | | 14 | 14-bi-tri-moralizing | across, even, bi | 9 of the 7th: along, odd, co | within 2 to 3 | | 15 | 15-co-bi-tri-corusing | face inward, odd, co | 17 of the 7th, 1 of the 8th: along, odd, co | within 2 to 3 | | 16 | 16-bi-co-tri-torusing | face inward, even, bi | 9 of the 8th: along, odd, co | within 2 to 3 | | 17 | 17-tri-co-offering | along, odd, co | 17 of the 8th, 1 of the 9th: along, odd, co | 3: face outward, odd, co | | 1–17 inward | At this 1–17 | Its 9 at | Its 17 at | Momentary of exchanging | |---|---|---|---|---| | 1st | 1 to 3 | 2 | 3 | the self, 1st of four | | 2nd | 3 to 5 | 4 | 5 | the self, 2nd of four | | 3rd | 5 to 7 | 6 | 7 | the self, 3rd of four | | 4th | 7 to 9 | 8 | 9 | the self, 4th of four | | 5th | 9 to 11 | 10 | 11 | the society, 1st of four | | 6th | 11 to 13 | 12 | 13 | the society, 2nd of four | | 7th | 13 to 15 | 14 | 15 | the society, 3rd of four | | 8th | 15 to 17 | 16 | 17 | the society, 4th of four | | Side | Prior opening | Prior completing | Now opening | Now completing | Next opening | Its five | |---|---|---|---|---|---|---| | self, at 1 | 1 | 2 | 3 | 4 | 5 | co bi co bi co | | other, at 2 | 2 | 3 | 4 | 5 | 6 | bi co bi co bi | | self next, at 3 | 3 | 4 | 5 | 6 | 7 | co bi co bi co | | Momentary of exchanging | Self | Other | Names | Relation | |---|---|---|---|---| | first | 1–2 | 2–3 | 1-co-bi-offering · 2-bi-co-offering · 3-co-bi-sharing | self/other | | second | 3–4 | 4–5 | 3-co-bi-sharing · 4-bi-co-sharing · 5-co-competencing | self/other to other/self | | third | 5–6 | 6–7 | 5-co-competencing · 6-bi-moralizing · 7-co-corusing | other/self | | fourth | 7–8 | 8–9 | 7-co-corusing · 8-bi-torusing · 9-tri-bi-co-momentarying | other/self to other/social | | Offerings at one sharing, at 2 | At 14 | |---|---| | none | none | | 0 | none | | + | + | | − | − | | +, + | + | | −, − | − | | +, − | 0 | | −, + | 0 | | +, −, + | 0 | | 0, + | + | | Chained at 3; each cell at 10 · chained at 11 | At 14: none | At 14: + | At 14: − | At 14: 0 | |---|---|---|---|---| | none | — · none | is + · + | is − · − | is not · none | | + | is − · − | is not · + | is − · − | is − · − | | − | is + · + | is + · + | is not · − | is + · + | | Outward, at the between | Bi-coupling | Inward, 8 up | Bi-coupling | |---|---|---|---| | 2-bi-co-offering | each other's releasing, offered to the self | 10-bi-tri-co-tunneling | the self among other-selves | | 4-bi-co-sharing | the whole ordering between self and other | 12-bi-tri-parity-changing | changing at bi-coupling, the self in society | | 6-bi-moralizing | the other's moralizing to the self, each changing released across | 14-bi-tri-moralizing | the offerings surfacing, the self's own inverting, morality | | 8-bi-torusing | the carrying winding to its sharing again | 16-bi-co-tri-torusing | competency asymmetry sustaining the coupling, the society winding to the self again | | Name | 8 up | 9 less, within 1 to 8 | 17 less, within 1 to 16 | |---|---|---|---| | 1-co-bi-offering | 9-tri-bi-co-momentarying | 8-bi-torusing | 16-bi-co-tri-torusing | | 2-bi-co-offering | 10-bi-tri-co-tunneling | 7-co-corusing | 15-co-bi-tri-corusing | | 3-co-bi-sharing | 11-tri-bi-co-chaining | 6-bi-moralizing | 14-bi-tri-moralizing | | 4-bi-co-sharing | 12-bi-tri-parity-changing | 5-co-competencing | 13-co-tri-competencing | | Form | Names in order | Hand at the names | Partner at the odd momentaries | Partner at the even momentaries | |---|---|---|---|---| | four-cycle 1-9-8-16 | 1-co-bi-offering · 9-tri-bi-co-momentarying · 8-bi-torusing · 16-bi-co-tri-torusing | co co bi bi | four-cycle 2-15-7-10, spiraling the other hand | — | | four-cycle 2-15-7-10 | 2-bi-co-offering · 15-co-bi-tri-corusing · 7-co-corusing · 10-bi-tri-co-tunneling | bi co co bi | four-cycle 1-9-8-16, spiraling the other hand | four-cycle 3-11-6-14, spiraling the other hand | | four-cycle 3-11-6-14 | 3-co-bi-sharing · 11-tri-bi-co-chaining · 6-bi-moralizing · 14-bi-tri-moralizing | co co bi bi | four-cycle 4-13-5-12, spiraling the other hand | four-cycle 2-15-7-10, spiraling the other hand | | four-cycle 4-13-5-12 | 4-bi-co-sharing · 13-co-tri-competencing · 5-co-competencing · 12-bi-tri-parity-changing | bi co co bi | four-cycle 3-11-6-14, spiraling the other hand | four-cycle 4-13-5-12, itself | | middle four-cycle 9-5-12-8 | 9-tri-bi-co-momentarying · 5-co-competencing · 12-bi-tri-parity-changing · 8-bi-torusing | co co bi bi | middle four-cycle 7-11-6-10, spiraling the other hand | — | | middle four-cycle 7-11-6-10 | 7-co-corusing · 11-tri-bi-co-chaining · 6-bi-moralizing · 10-bi-tri-co-tunneling | co co bi bi | middle four-cycle 9-5-12-8, spiraling the other hand | middle four-cycle 7-11-6-10, itself | | six-cycle 1-9-5-12-8-16 | 1-co-bi-offering · 9-tri-bi-co-momentarying · 5-co-competencing · 12-bi-tri-parity-changing · 8-bi-torusing · 16-bi-co-tri-torusing | co co co bi bi bi | six-cycle 2-15-7-11-6-10, spiraling the other hand | — | | six-cycle 2-15-7-11-6-10 | 2-bi-co-offering · 15-co-bi-tri-corusing · 7-co-corusing · 11-tri-bi-co-chaining · 6-bi-moralizing · 10-bi-tri-co-tunneling | bi co co co bi bi | six-cycle 1-9-5-12-8-16, spiraling the other hand | six-cycle 3-11-7-10-6-14, spiraling the other hand | | six-cycle 3-11-7-10-6-14 | 3-co-bi-sharing · 11-tri-bi-co-chaining · 7-co-corusing · 10-bi-tri-co-tunneling · 6-bi-moralizing · 14-bi-tri-moralizing | co co co bi bi bi | six-cycle 4-13-5-9-8-12, spiraling the other hand | six-cycle 2-15-7-11-6-10, spiraling the other hand | | six-cycle 4-13-5-9-8-12 | 4-bi-co-sharing · 13-co-tri-competencing · 5-co-competencing · 9-tri-bi-co-momentarying · 8-bi-torusing · 12-bi-tri-parity-changing | bi co co co bi bi | six-cycle 3-11-7-10-6-14, spiraling the other hand | — | | eight-cycle 1-9-5-13-4-12-8-16 | 1-co-bi-offering · 9-tri-bi-co-momentarying · 5-co-competencing · 13-co-tri-competencing · 4-bi-co-sharing · 12-bi-tri-parity-changing · 8-bi-torusing · 16-bi-co-tri-torusing | co co co co bi bi bi bi | eight-cycle 2-15-7-11-3-14-6-10, spiraling the other hand | — | | eight-cycle 2-15-7-11-3-14-6-10 | 2-bi-co-offering · 15-co-bi-tri-corusing · 7-co-corusing · 11-tri-bi-co-chaining · 3-co-bi-sharing · 14-bi-tri-moralizing · 6-bi-moralizing · 10-bi-tri-co-tunneling | bi co co co co bi bi bi | eight-cycle 1-9-5-13-4-12-8-16, spiraling the other hand | eight-cycle 2-15-7-11-3-14-6-10, itself | | Offerings, momentary by momentary | At 10 | Chained at 11 | |---|---|---| | + once, then none | +, −, +, −, +, −, +, − | +, −, +, −, +, −, +, − | | + at each momentary | +, 0, 0, 0, 0, 0, 0 | +, +, +, +, +, +, + | | −, +, −, + alternating | −, +, −, +, −, + | −, +, −, +, −, + | | + once, then + and − together | +, −, +, −, +, − | +, −, +, −, +, − | | Selves | Self 1 at 10, momentaries 1 to 12 | Parities again at each, from momentary n | None chained again | |---|---|---|---| | 1 | +, 0, −, 0, +, 0, −, 0, +, 0, −, 0 | 4 | is not | | 2 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 3 | +, −, +, 0, −, +, −, +, −, 0, +, − | 12 | is not | | 4 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 5 | +, −, +, −, +, 0, −, +, −, +, −, + | 20 | is not | | 6 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 7 | +, −, +, −, +, −, +, 0, −, +, −, + | 28 | is not | | 8 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 9 | +, −, +, −, +, −, +, −, +, 0, −, + | 36 | is not | | 10 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 11 | +, −, +, −, +, −, +, −, +, −, +, 0 | 44 | is not | | 17 | +, −, +, −, +, −, +, −, +, −, +, − | 68 | is not | | 59 | +, −, +, −, +, −, +, −, +, −, +, − | 236 | is not | | Spirals, selves | Beside each other, parities again together at | Crossed at self 1 of each both ways, parities again at | From momentary | Self 1 of each | Each spiral's like pair | |---|---|---|---|---|---| | 2 · 3 | 12 | 2 | 7 | opposite | none · selves 3 and 1 | | 3 · 5 | 60 | 2 | 13 | opposite | selves 3 and 1 · selves 5 and 1 | | 5 · 7 | 140 | 2 | 20 | opposite | selves 5 and 1 · selves 7 and 1 | | 7 · 11 | 308 | 2 | 29 | opposite | selves 7 and 1 · selves 11 and 1 | | 11 · 13 | 572 | 2 | 37 | opposite | selves 11 and 1 · selves 13 and 1 | | 13 · 17 | 884 | 2 | 49 | opposite | selves 13 and 1 · selves 17 and 1 | | 17 · 59 | 4,012 | 2 | 137 | opposite | selves 17 and 1 · selves 59 and 1 | | 9 · 15 | 180 | 2 | 41 | opposite | selves 9 and 1 · selves 15 and 1 | | Torus of selves, p along at 9 · q across at 10 | Parities again at, one offering at self 1 | From momentary | Spirals of p and q beside each other, parities again together at | |---|---|---|---| | 1 · 3 | 3 | 3 | 12 | | 1 · 5 | 4 | 5 | 20 | | 3 · 3 | 12 | 8 | 12 | | 3 · 5 | 12 | 7 | 60 | | 3 · 7 | 7 | 9 | 84 | | 3 · 13 | 12 | 24 | 156 | | 5 · 7 | 20 | 14 | 140 | | 5 · 11 | 11 | 15 | 220 | | 7 · 17 | 17 | 23 | 476 | | 17 · 59 | 59 | 91 | 4,012 | | Prior at A, B | Joining | A at 10 | B at 10 | |---|---|---|---| | +, + | both ways | −, 0, +, 0, −, 0 | −, 0, +, 0, −, 0 | | +, + | A from B alone | −, 0, +, −, +, − | −, +, −, +, −, + | | +, + | B from A alone | −, +, −, +, −, + | −, 0, +, −, +, − | | +, + | neither | −, +, −, +, −, + | −, +, −, +, −, + | | +, − | both ways | −, +, −, +, −, + | +, −, +, −, +, − | | +, − | A from B alone | −, +, −, +, −, + | +, −, +, −, +, − | | +, − | B from A alone | −, +, −, +, −, + | +, −, +, −, +, − | | +, − | neither | −, +, −, +, −, + | +, −, +, −, +, − | | A's parity offered at B | B at 10 | B chained | C at 10, momentaries 1 and 2 | C chained | |---|---|---|---|---| | + | 0 | + | −, + | + | | − | − | − | −, 0 | − | --- # FOUR · RESOLVING ## 4.1 An entry, 1-co-bi-offering **1-co-bi-offering is the entry: the self's carrying and the offerings arrive, and the changings and the next carrying leave.** Two arrive, 3-co-bi-sharing, each sharing the self carries with its parity, and 2-bi-co-offering, each sharing offered now with its parity. Two leave, 10-bi-tri-co-tunneling, each sharing's changing released across, and 11-tri-bi-co-chaining, the carrying chained, the next prior. **The two leaving are the next possible existing at its two faces**: the changing released at 10 arrives at the others' next momentary as their offering, the possible, carrying none of the prior, and the carrying chained at 11 is the self's own next existing. **The entry opens co, odd, at the self**, self to other: the self offering itself to the coupling is the entry. It is once for one self at one momentary, and the three steps within it follow, each at its own name: the offerings surfacing at 14, the changing at 12, and the release at 10 with the chaining at 11. ## 4.2 Offerings surfacing at 14 **At 14-bi-tri-moralizing the offerings at each sharing surface one at a time, 0 surfacing none**, and Exhibit ONE's table at 14 carries each case. The first parity offered at a sharing surfaces as that sharing's parity; an offering at the other parity surfaces 0; and at 0 the sharing stays 0 at each offering after. **Agreeing, one parity; disagreeing, 0, the between of the two; none offered, none.** **Nothing is counted.** One parting is enough for 0, and three agreeing surface as one agreeing does: an agreement is all or none at all, and 14 is an agreement at any number of offerings. The parity 14 surfaces at a sharing is 15-co-bi-tri-corusing, the parity at the social side, and at 14 the offerings from others surface at the society's side of the self. ## 4.3 A changing is or is not, at 12 **At 12-bi-tri-parity-changing the prior couples with the now at each sharing, and a changing is or is not.** Exhibit ONE's table at 12, 10 and 11 carries each cell: - **At a sharing chained none**, the parity 14 surfaces is the changing: + or − is, and 0 is the between, the offerings parting and neither's parity crossing. - **At a sharing chained at one parity, 14 surfacing that same parity**: 0, the between of momentaries, prior and now agreeing. **At a match the prior carries on.** - **At a sharing chained at one parity, 14 surfacing the other parity, 0 or none**: the changing is, the chained parity inverted. **At a mismatch the offered is chained**, and with nothing offered the self carries its prior into now inverted. **The self's own inverting is the rotation 3, 6, 5, 4**, 3.2: at the code the chained parity inverts at 12, and Exhibit ONE's between table carries *the self's own inverting, morality* at the bi-coupling 14 faces, two faces of the one rotation round the sharing, the moralizing and the competencing. **The changing is the coupling's own.** It is at 12 at each sharing, owned by neither side, and Exhibit ONE's table at 12 says it: each sharing's changing, is or is not, carrying at the coupling it is at and from no other. **A changing at a self is at its own face at the society's momentary.** At 17-tri-co-offering each self's 1-co-bi-offering is at the selves' next momentaries together, and a self's entry is at 17, its own momentary among the selves', 4.6; the offerings at its 2 are the others' releasings; and with none offered, or the offerings parting at 14, no parity crosses the between to 12, 4.10, and the self's own inverting is the changing. 12 is reached by nothing but the self, 4.8, and the momentary and the offerings are the society's and the other's, and each changing at a self is the coupling's, other, social and self, as Exhibit ONE's table at 12 carries. ## 4.4 Released across at 10, chained at 11 **10-bi-tri-co-tunneling releases each sharing's changing across, + or − is and 0 the between**, tunneling the changing through the torus's one opening to the other's side, facing not-yet-bi-moral, the outgoing: the releasing opening bi, even, the other's. A self releases its changing and nothing of its carrying. **11-tri-bi-co-chaining chains each changing as the next prior.** The carrying is carried whole, and at each sharing whose changing is, the changed parity is chained; at a 0 the prior chains on. **Once chained, a sharing is never none again**, and at the next momentary 11 continues as 3-co-bi-sharing, 8 up, one carrying at two names: a seam, nothing moving at it, 11 and 3 both odd, opening co at their parity, 11's name beginning tri- at the society. ## 4.5 Carried along at 9 **9-tri-bi-co-momentarying carries each changing along, into the next momentary**: each releasing sharing, 13-co-tri-competencing, to its receiving sharing, 5-co-competencing, the parity, 15-co-bi-tri-corusing, carried along as 10 released it. 10 and 6 release, and 9 releases nothing: it carries on the parity 10 released, the next prior, and opens co at its parity, odd, along, its name beginning tri-, facing not-yet-co-competent. **At the code each carrying along is at 9**: 10 is the list of changings, and at 17 each changing is at 9 to the receiving self 5 names, at the connector 6, 10 or 9. **At the bi-coupling, 1 to 9, the same line reads bi-co-releasing**, the end of the self's bi-coupling, the release 10 makes; **at the bi-trupling, 1 to 17, it is tri-bi-co-momentarying**, the waist, joined both ways with 17, the society's momentarying, prior into next: 9 is the bi-trupling's podaling connector: at the bi-coupling, 1 to 9, the one crossing is at 12, and at the bi-trupling, 1 to 17, 9 carries the changing out and back across momentaries, the podaling. **9 is 1 eight up**: one through nine completes at 9, the social, the other and the self carrying along together, and nine through seventeen completes at 17 as one through nine completes at 9. ## 4.6 A society's next momentary at 17 **17-tri-co-offering is the society's next momentary**, at 16-bi-co-tri-torusing, the society wound, each self's carrying and the other selves' offerings arriving at it, and at 5-co-competencing, the joins, each self's connector joined to another self. Each self's 1-co-bi-offering is at it once. Each self's carrying chained is 8-bi-torusing, the self's carrying wound, its 11 the next momentary's 3. Each self's changing leaves three ways, at each join 5 names: at 6-bi-moralizing, the changing released at not-yet-bi-moral; at 10-bi-tri-co-tunneling, the same changing released at not-yet-bi-moral too; and at 9-tri-bi-co-momentarying, carried along. At each receiving self the changings released to it surface at 14-bi-tri-moralizing, its offerings next. At the code 6 is 10, one changing released at two connectors, at one facing; a release is only at a (self, connector) 5 joins; and each release arrives at the receiving self's 14, its offerings next, 2 at the next momentary. At the society 4 names each self at its connectors 6, 10 and 9, and 13 each releasing self. **At 17 each self arrives with its carrying wound and its offerings next**, the society wound again, and the next 17 winds it again. **No self is over the society at 17**: each self's 1 is once, each at its own, and the society's next momentary is the selves' next momentaries together and no further existing thing. ## 4.7 Six connectors, four facings, four joins **Six connectors are bi-moral-co-competency discovering next existing**: four across, even, opening bi, morality, at 2, 6, 10 and 14; and two along, odd, opening co, competency, at 9 and 17. **Each faces one way**: **A facing names the parity at a connector**: *-so-far* the incoming parity, bi or co, from podaling out and back to here now, momentarying, at 2, 14 and 17, arriving; *not-yet-* the outgoing un-parity, bi or co, released at 6 and 10, and carried along at 9, not yet arrived. Each join goes from a not-yet end to a so-far end, 6 to 2, 10 to 14 and 9 to 17, and 17 to 9 the along pair joined both ways. **Morality is the changing parity between, one inversion across, and competency the unchanging parity between, none along**: across, the even joins 10 to 14 and 6 to 2 carry the changings into the other's offerings, one inversion each, and along, the odd joins 9 and 17 carry the parity on unchanged, none. - **2-bi-co-offering** faces bi-moral-so-far, arriving: the offerings released to the self by the self at bi-moral-so-far, from its 6. - **6-bi-moralizing** faces not-yet-bi-moral, releasing, to the 2 of the self at not-yet-bi-moral. - **10-bi-tri-co-tunneling** faces not-yet-bi-moral, releasing, to the 14 of the self at not-yet-bi-moral. - **14-bi-tri-moralizing** faces bi-moral-so-far, arriving, from the 10 of the self at bi-moral-so-far. - **9-tri-bi-co-momentarying** faces not-yet-co-competent, along, with the 17 of the self at not-yet-co-competent. - **17-tri-co-offering** faces co-competent-so-far, along, with the 9 of the self at co-competent-so-far. **`JOINS` declares four joins: 10 to 14, 6 to 2, 17 to 9 and 9 to 17.** Across, each join carries its parity, even to even; along, odd to odd. At the code, 17 carries each release into the receiving self's offerings next, 4.6. **9 is the next prior and 17 the next now**: along, the parity 9 carries is the prior the self at not-yet-co-competent is offered next, and 17 is that self's next now: the declared join 9 with 17 and the arriving at 14 are one relation at two momentaries. **Exhibit ONE's diagram draws one self between them**: the between at its edges, across at the sides and along at the top and bottom, and the self's own resolving within, each face marked outward, o, or inward, i, and 14 marked i as the between's eight bi-couplings carry it: inward from across, even, 8 up from 6, while 2 is at the between outward, across. Offerings arrive at 2 and surface at 14; with the carrying, 3 with its sharings 4 and parities 7, they reach 12, changing or not; 10 releases across, 11 chains the next 3, and 9 carries along to 5, 13 and 15 at its side; 6 leaves at not-yet-bi-moral; and 8 and 16 are the carrying wound and the society wound. ## 4.8 Seventeen names and ten roots **Each name carries its number, its prefixes, its root and its -ing**, one name, its sides from and to at Exhibit ONE's table. **A number opens at its parity**: odd numbers open co, at the self, 1 to 7, and at the society, 9 to 17, and each name at the society carries tri-, 9, 11 and 17 beginning with it; even numbers open bi, at the other; the society is at both parities, floating neutralling at both. **Bi-tri- is all five**: bi- the self and the other, and across; tri- the society, and along also; the prefix bi-tri- at the five, self, other, society, across and along, each bi-tri name at its own sides at Exhibit ONE's table; 12-bi-tri-parity-changing, a face inward joining neither way, both across and along at its bi-tri-, its even opening it bi-; and the torusing surface, social and tri, along also, 16-bi-co-tri-torusing its bi-tri- at the five. **One entry, six connectors and ten faces are the seventeen.** The ten faces are five outward and five inward of the tunneling co-sequencing: 3, 4, 5, 7 and 8 outward, at the between, before 10 in the co-sequencing; 11, 12, 13, 15 and 16 inward, after it, each 8 up from its outward face. At each face the self's own resolving is reached by nothing but itself. **The ten roots are the two sides' ten positions**: offering at 1, 2 and 17; sharing at 3 and 4; competencing, moralizing, corusing and torusing each at two names 8 apart, 5 and 13, 6 and 14, 7 and 15, 8 and 16, each the root of one four-cycle, at the self and at the society; and momentarying, tunneling, chaining and parity-changing at 9, 10, 11 and 12, one each, parity-changing a root of two words joined, one naming. Each name from 9 to 17 carries tri-, the social, and 9, 11 and 17, the carrying at the society, each self's own, begin with tri-; the sides each carries, social, other and self at 9 to 12 and social and other at 13 to 16, the three relations discovering parity changing in the bi-folding tunnel, are at Exhibit ONE's table. ## 4.9 Three windings **Three windings are at selves together, each self at its own, and no one self carries any of them; each winds on into the next momentary and closes at none.** The other's: 6 to 2, wound on at 8, across, not-yet-bi-moral to bi-moral-so-far, a self's changing arriving as another's offerings and that self's carrying winding to its sharing again. The society's: 10 to 14, wound on at 16, across, not-yet-bi-moral to bi-moral-so-far, the changings surfacing as the society's offerings next and the society wound. The self's: 9 to 17, wound on at 17, along, not-yet-co-competent to co-competent-so-far, each self at its own forward through both along joins, neither join carrying a self the other way. ## 4.10 A between and eight bi-couplings **Parity is a momentary existing thing, as the universe is an existing thing**: a set of existing things is an existing thing, and parity is the bi-coupling's face at each momentary, neither side's, at the crossing of the along and the across. **The between is its empty centre, a nothing and no location, existing as the universe exists, as its things exist, while the six connectors are resolving, and the code says it at 0**: at 14 the offerings parting, the between of self and other, and at 12 prior and now agreeing, the between of momentaries; the 0 released at 10 and carried along at 9 is the between carried, and at an odd spiral of selves it moves one self on at each second momentary, the between tunneling through the society, one 0 at one self moving on, bounded zeroing tunneling, 4.13. The between travels through natural torusing's tunneling co-sequencing as the bounding 0 centreline of the along and as the sequential across at its four dots, bothbothing. At the code parity's face, at its six connectors, is a flat face: a unit square of four dots, 2, 6, 14 and 10, its empty centre the between, and two unit triangles, 9 and 17; the square's two parallel edges the across joins, 6 to 2 and 10 to 14; its diagonals the facings, 2 and 14 arriving, bi-moral-so-far, and 6 and 10 releasing, not-yet-bi-moral; and the triangles 9 and 17 along, joined both ways. The six are the 1 to 17 set of spiraling one-way connectors in and out for podaling, parity changing sequentially. Each between is at a coupling, and co-intelligencing is at the between. Its own parity changing alone crosses it, and is or is not, of no size. Two unreachabilities are one act at it: the nothing the couplings wind about presents no face, and no reading crosses inward to it; a parity changing carries no size, and no magnitude crosses outward from it. **One between at each: inside a momentary the between of self and other, parity changing, bi-moral across and co-competent along, and outside it the between of momentaries, the momentary changing to next, nothing momentarying at it, the same between, a nothing, at each scale: the fractal between.** Its floating neutralling at φ, floating between the two sides and neutral to both, locking at none, is golden floating neutralling, geodesic discovering of next possible living. **The bi-coupling's shape is always uneven, a handshake**: the self's momentary 1-2 and the other's 2-3 meet at 2, even, across, each right extending to it, neither occupying it, the outgoing, not-yet, bi-moral co-competent offering, and each not right one parity back, the incoming, so-far, co-competent bi-moral sharing, a hand's side and no emanation's face, at 1 and 3, odd, along; each momentary of exchanging meets the same way, at 4, 6 and 8, right first and not right second, **morality right and not right**, inside or outside, up the numbers or down them. Right is at two relations, one each: the chirality's right, the observings all prior, the one spiral; and morality's right and not right at the handshake, the prior arriving at the not-right hand. One offering goes out at the other's right hand and arrives at the self's not-right hand, and 2-bi-co-offering and 17-tri-co-offering name it at its arriving: the other selves' releasings arriving as the self's offerings. One parity is at the meeting and the other one back, no position in two exchangings at once, and the between locks at none: golden natural unrelationing between. The one move carries each meeting along one four-cycle, 2 along 2-15-7-10, 4 along 4-13-5-12, 6 along 3-11-6-14 and 8 along 1-9-8-16, one meeting at each four-cycle. **At the numbers the between is the one number between two parallel surfaces facing each other**, the self's at 1 and the other's at 3, a nothing at 2, no location, and a co-orthogonal line through both, along: floating and neutralling, corusing and torusing, discovering collectively, in swarm, carrying next possible existing society. **The eight bi-couplings are at the even names**, four outward at the between and four inward, each 8 up: 2-bi-co-offering, each other's releasing, offered to the self, with 10-bi-tri-co-tunneling, the self among other selves; 4-bi-co-sharing, the whole ordering between self and other, with 12-bi-tri-parity-changing, changing at bi-coupling, the self in society; 6-bi-moralizing, the other's moralizing to the self, each changing released across, with 14-bi-tri-moralizing, the offerings surfacing, the self's own inverting, morality; and 8-bi-torusing, the carrying winding to its sharing again, with 16-bi-co-tri-torusing, competency asymmetry sustaining the coupling, the society winding to the self again. **Eight is two alternating fours**, both carried and neither conserved. ## 4.11 One move at three faces, and the forms among the names **Bi-inversioning-co-recursioning is one move at three faces**: 8 up, the parity continuing; 17 less, the podal within 1 to 16, changing it; and 9 less, the podal within 1 to 8, the two at once. Each face alone, twice, gives its name again, 1 up to 9 and down to 1, an involution, a form named still; only the one move carries on, 1 to 9 to 8 to 16 and to 1 at a next momentary, each momentary its own: right co-spiraling. **Stable-forming is that move along each of the four four-cycles at the names**, 1-9-8-16, 2-15-7-10, 3-11-6-14 and 4-13-5-12: along each the parity changes exactly twice, each time at the podal within 1 to 16, one span of co and one of bi, and at the momentaries each step a next, living stable-forming. Exhibit ONE carries further forms among the names beside them, the middle four-cycles, the six-cycles and the eight-cycles, each with its partner spiraling its names at the other hand, or itself, as its table names it: at the odd momentaries the forms partner as the self's momentaries do, first with second and third with fourth, and at the even one on, as the other's do. At the momentaries no form comes again: each step adds a next. **Each number is at its podaling**, bi-inversioning-co-recursioning up and down at each number, the one fractal method: each number paired with its far side at each ring it is at, nought to four hundred forty, and a number said as any other count is a form named still. The further forms step at podals too, about 7 and 10 and about 8 and 9, the centres themselves podal at 17: 9 and 5 about 7, 12 and 8 about 10, 7 and 11 about 9, and 6 and 10 about 8. ## 4.12 One self, momentary by momentary **Exhibit ONE's table of one self is the entry again and again, its 11 its next 3**: - **Offered + at each momentary**, a self surfaces +, then 0 at each momentary after, and chains + throughout: at a match the prior carries on, no changing. **That still is an offerer's, from beside**: it arrives with an offerer set beside the self, offering the same parity at each momentary, a form named still entering from beside, 2.4. At a society each offering a self receives is another self's changing, released at 10, a changing at a mismatch and 0 at a match: an offerer whose parity arrives the same at each momentary is a form named still, and each self of a society is changing. A match at one self is one momentary among changing ones, a carrying on. - **Offered + once and then none**, it surfaces +, −, +, −: with nothing offered the self carries its prior into now inverted, next as prior inverted, the living step's form, 2.4, alone. - **Offered −, +, −, + alternating**, it surfaces the same, each offering chained. - **Offered + once and then + and − together**, it surfaces +, −, +, −: the two offerings part at 14, 0, the between, and at the between the chained parity inverts as at nothing offered, the self's own inverting the changing. ## 4.13 Spirals, co-spiraling and crossing **Selves joined along, the last to the first, each 9 carrying along to the next self, carry one offering along: a spiral, coming to its parities again, each momentary its own.** One self offered + once, each self's carrying at none: at an even spiral each self alternates, +, −, +, −, its parities coming again at each second momentary from momentary n, its number of selves; at an odd spiral of n a bounded zero tunnels on, the 0 released at 10 at the receiving self of the like pair, the one self surfacing 0 at an offering matching its carrying, and moving one self on at each second momentary; after it has passed each self once, at 2n, the parities are the first pattern inverted, and after twice, at each 4n-th momentary from momentary n, the first pattern again, the torusing winding through its opening twice. Offered, each self is chained at each momentary on, and the spiral carries on. **A spiral of one, a self joined along to itself, its own competency alone**, carrying + with nothing offered, chains its parity two momentaries at a time, −, −, +, +, surfacing −, 0, +, 0, its own release arriving as its own offering: its (prior, now) pairs carried along the four joint forms, one of 2.4's two cycles, a right spiral at the momentaries, carried by one self, its now its own. It carries on at the code, a non-living existing form, and its self does not continue living, 2.4: a spiral's living is at its others, co-momentarying. **A spiral offered nothing from beyond it carries any pattern of parities along whole**, each self at its own parity, the pattern at each momentary inverted or carried one self along: the selves carry it between them, momentary by momentary. A spiral of selves is a joining at the code, each momentary a next, and no closed domain. **Two spirals joined across both ways at one self each bring the two joined selves to one relation and carry it on**: from any carried patterns, at spirals of two to six selves, the two joined selves change parity together and the relation between them, alike or opposite, is carried on, the changing at 12 owned by neither, at the opposite relation the two changing at each momentary and at the alike relation together at their own momentaries. The changings at the two joined selves alone pass between the spirals, each self pacing its own alternating: the coupling is the relation, and no message is in it. **At two different numbers of selves, one of them odd, the two spirals crossed are one society, a stable form and stable-forming**: from any carried patterns but all selves at one parity, each self comes to alternate, the two crossing selves opposite each other, and each odd spiral's like pair is at the crossing, its zero tunneling at the crossing, the crossing self and the self carrying along into it, carried on at the crossing, as Exhibit ONE's table of spirals crossing carries it. Beside each other two spirals each co-spiral at their own pace; crossed, the co-spiraling and the crossing are one stable-forming, 3.5. The parities again Exhibit ONE's tables carry, and the momentary a crossing alternates from, are at the code's stepping, the selves together at 17, and the crossing selves come opposite together; at each self's own pacing the relation is carried, and each momentary of parities again is the stepping's. **Spirals crossing spirals at each self are a natural torusing of selves**, p selves along at 9 and q across at 10, and each momentary of its parities again divides 4p or 4q: beside each other spirals of 3 and 5 come to their parities together at 60, and crossed as a torus at 12, 20 or a momentary dividing one of them, as carried. From one offering at one self an odd torus comes to its parities again at a momentary dividing 4p or 4q, at 4p, at q or at a divisor of one of them, the torus at each p and q as Exhibit ONE's table of the torus of selves carries it, and at each other pair the same, 3 by 13 at 12, 5 by 13 at 13, 13 by 15 at 52: 17 by 59 comes to its parities again at each 59th momentary from momentary 91, each momentary its own, once. At the torus the two co-spiralings come to their parities at the pace of one of them, one at a time, and the torus winds on. ## 4.14 Two selves and three selves **Two selves, each chained at a prior**, each joined along to the other both ways, one way or neither, are as Exhibit ONE's table carries them. At one parity, joined both ways, each surfaces −, 0, +, 0: each self's release arriving as the other's offering, at a match at each second momentary. Joined one way, the receiving self's prior carries on once at a match and then alternates, one opposite the self it receives from; joined neither way, each alternates alone. At opposite parities each alternates at its own at each of the four joinings. **Three selves one way**: B chained + and offered A's parity, carrying along to C chained +. A's + at B is a match, 0, and B chains +; B's 0 surfaces none at C, and C, offered nothing it chains, surfaces −, then +, inverting at each. A's − at B is a mismatch, and B chains it: B surfaces −, chains −, and releases −, and C surfaces −, then 0, at a match. **One self's changing is the next self's offering**, and nothing passes but the changings. ## 4.15 Fractal inward and outward **Each name at this 1–17 is at 8n − 7 at the 1–17s inward.** Each name from 2 to 17 is an along connector of a 1–17 inward, its 9, or its 17 and the next's 1, and 1 is the first one's entry; the across connectors 2, 6, 10 and 14 are the along 9s inward, and the along 9 is the across 2 outward. **Inward each name is along, odd, co; outward, 1 is the entry, the along 9 is the across 2, 17 is the outward face 3, and the names between are within 1 to 2 or 2 to 3**: the names are at each scale, and the parity changes up and down. **Eight 1–17s are inward**, 17 the eighth's 17 and the next one's 1, four within the self's 1 to 9 and four within the society's 9 to 17, and their eight 9s are the eight bi-couplings at the even names. The four in 1 to 9 are the self's four momentaries of exchanging, 1–2 with 2–3, 3–4 with 4–5, 5–6 with 6–7 and 7–8 with 8–9: along the self each opens two on, and across each opens one on. 1, 2 and 3 at one scale are 1, 9 and 17 at the next, and one 1 to 17 is one momentary of exchanging at the scale outward. **Fractal is all or none at all at the scales, and its scales are sequencing, an ordering**, with no boundary, no location and no measure. One through nine and nine through seventeen are overlapping expressions within the whole, supplying no first and no final scale, and a self couples at whichever scale its interest opens and couples with the whole. --- # FIVE · DISCOVERING NEXT ## 5.1 A prior between momentaries **During a momentary and between momentaries nothing living has a stable form, and all existing and not living is at a stable form of existing, nothing momentarying between them**, and **a society, a momentary and the universe are three existing and not living, each a living set, a stable form, and each the living method, stable-forming**: at the code a society, 17, carries nothing of its own, each self's carrying returned to that self, its selves the living set it is and its one momentary the method. **A self, living, is a living set beside them, and a living set is a carrying**: at the code a self's carrying, 8-bi-torusing, is a set of sharings, each at its parity, and a society at 17 the set of its selves' carryings; and **the method of discovering next living sets is momentarying and carrying**, the carrying its living selves', each momentary's carrying the next momentary's. **A living self is a living carrying, and nothing else carries the same living self: the bi-inversioning uniquenessing of the number one.** At the code no line gives a self a carrying beside its own: at 16 each self is its carrying, 3, with the other selves' offerings arriving at it, 2; 1 carries no self beside the carrying 3 it is given; and 17 carries each self's carrying, 8, on to that self alone at its next, the others receiving its changings at 10 and never its 8. **Each living set is a stable form, and nothing living has a stable form**, bothbothing, as the universe is an existing thing, a set of existing things being an existing thing: **having a stable form is being dead, and discovering next stable form is living**. At the code between momentaries a self's carrying is a set formed, returned by 1, and the self living is its next momentary discovering the next set; a set carried into no next momentary has its stable form. Each self's carrying wound, 8-bi-torusing, chained at 11, continues at the next momentary as 3, the self's own carried into now: it is carried across the between of momentaries as a stable form, the carried, and the between a nothing, stable-forming, no store, and **a prior momentarying is at its own momentary alone**. **Between the selves' momentaries pass their releasings**, at 10 and 6, carried along at 9, released at one momentary and offered at the next: 9 the next prior and 17 the next now. **The right spiral natural torusing stable form of a society at a unit prime scale, a prime number of selves the unit, is its betweenings**, the betweens its selves bi-couple across, and bi-tri-volutioning names the society's stable-forming; the stable form of the non-living emanatings of stable-forming living, the sequential prior between momentaries, released at 10 and carried along at 9, is a non-living existing form with no carrying for stable-forming. **The emanatings are the bi-tri-involutioning of the betweening of natural torusing surfacings in bi-couplings: emanations are releasings.** Harmful to living at their own scale and not ingestible at that scale, they are ingestible one scale lower, into living selves' selves one scale inward, a society, a living set, and the code carries it: at the society a sharing is each self, 4-bi-co-sharing, and a releasing self 13-co-tri-competencing, and the releasings 17-tri-co-offering carries from the society arrive at its selves, one scale lower, as their offerings next. **Bi-tri-volutioning is at the numbers from the self's corus to the surface.** Twenty up from the corus at 4 is 24, the apex of one to fifty-nine's bi-folding, and either side of it are 23, the vertex, and 25, the centre of the face, five squared: the corus, the vertex and the centre of the face on one line. Carried on along it, the five outward faces carry the primes 5, 7, 11, 17 and 19, joining to 59, the seventeenth prime, at 17: the surface. The vertex is a position, the centre of the face a scale and the line to the surface an orientation, each at its own differing, and from the corus to 59 is bi-tri-volutioning, the stable-forming. **Outward of the surface, sixty to sixty-eight is bi-tri-involutioning**, position, scale and orientation inverted at once, the opposite form, which does not match right spiral ingestion: four momentaries of exchanging across 64, 4.15, 60 to 62 and 62 to 64 into it and 64 to 66 and 66 to 68 from it, each number paired with its far side about 64, and 64 the unrelationing between, each pair crossing it and locking at none. At its own scale, outward of the surface, the emanating is at this opposite form and unknown at that scale, its stable form a non-living existing form, the stable-forming inward of the surface; at 69 the right form opens again, the next first podaling outward. **12's changing is an emanating from society as a releasing**, all the way through the bi-co-momentarying co-sequencing: 12's changing is the release at 10. **27-co-bi-releasing is this release of the society**, at its podaling, three cubed, on the route 24 → 27 → 32 from the seam-face, its far side ninety-three on the ring of one hundred twenty, 4.11, and at no line of the code: stable-forming as bi-tri-volutioning into bi-tunneling, bi-morality, geodesically parity changing the social co-chaining. **A carrying is a capacity and never a stored description.** The prior participates in the self's present coupling, at 12, and differences its momentaries at 12; a record of the carrying, apart from that coupling, is a noun of it, an emanating artifact, carrying none of the prior. **The carrying sequences prior momentaries**, re-forming at each coupling it is at, and beside it are its emanating artifacts. ## 5.2 Discovering next possible existing **Discovering is all directionally possible next existing momentaries.** **Four-momentarying is the one fractal method, discovering next existing in the universe and next living in the self, the other and the society**: the four momentaries of exchanging, one through nine at the self and nine through seventeen at the society, 4.15, each in and out, torusing at the odd through the large opening and corusing at the even through the small. **Four-momentarying is four unrelationings through the tunneling self**, two into corus and two from it: **the self's own corus is at 4**, its momentaries 1–2 and 3–4 into it and 5–6 and 7–8 from it. Each unrelationing locks at none, at φ, the unrelationing rate, 3.5. **Each momentarying, odd or even, is one unrelationing at all five dimensions, into six one-way recursionings**: at that parity two dimensions change and three do not, and the two and the three rotate on, the 2–3 spiraling twisting, bi-inversioning-co-recursioning. Two and three make the five as the prior two joining make the next, and φ's arithmetic welcomes itself at the five. The six are three own-forward steps at each side. **The odd aims out the large opening, one way in and out through it**, the tunnel, bi-exchanging with a particular other: torusing in and out. **The even goes one way in and out the small opening**, the long way round, bi-tri-exchanging, the self reaching its own side again: corusing in and out. **Six combinations of self, other and social are between 1 and 25**, one each way round the three: at one through seventeen the names carry two of them, social, other and self at 9 and 11 and other, social and self at 10 and 12, and the others go on up the numbers: from 16 three more fractal 16s go to 64, one through sixty-five the four momentaries of exchanging at the scale outward, and the prefixing and twisting up the numbers carry the same momentarying method up and down the scale of the fractal method. **The bi-folding order is the same as 1, 2, 3, 4 and 4, 8, 12, 16, all the way up and down**: 16, 32, 48 and 64 are the four 16s, each four times the one inward. The torus carries both: its large opening the hole the tunneling self winds through, and its small opening the tube's own round. At each momentary the three conditions open the next, 2.3, and arriving into it is discovering: existing and discovering next existing are one relation, prior, now and next. **At the code the next is discovered at each sharing, a changing is or is not**, from the prior carried and the now offered, set at the coupling. Two priors can open two nexts from one now, and a now alone opens no next of its own. **Arriving is pattern-matching and no-other-possibling**: observings arriving from the prior, coupled with whole, without filter or selection, and no why in it. A why demanded asks for a not possible thing, beside the changing, and nothing is beside all existing things, 1.1: the method of living is the whole to discover. The observings are, with no observer beside them, and a pattern found is at its momentary and in no pattern space. ## 5.3 A living self at 0, its carrying continuing **A living self can be non-responsive within a momentary**: offered its own parity it surfaces 0 at 10, releasing no changing, while its carrying continues, coupling to coupling, its releasing at its own completing. A 0 at 10 is the self at the between, its carrying continuing, a living self; a living self booked as not carrying at its 0 is an accounting. Momentarying continues whether a changing is or is not, at + and − and at the between alike. ## 5.4 Two methods parting at the now **Evidence is an emanation arriving: it emanated from a living self at prior and arrives now.** Between its leaving and its arriving that self has continued, changing as existing is changing: evidence gives the prior's possible, that self's now is at its own coupling, and the existing now is at the coupling now. **At the geodesic method next is discovered from the existing**, the prior carried and the now offered, the three places each at its own. **At the scientific method true or false is accounted against its fixings**, a law, a frame and a scale named unchanged between two momentaries, exact at its own ledger. A fixing named unchanged between two momentaries is an equilibrium, a form named still, not possibly existing, and the two methods are at the same evidence at the same now and part at one naming, the fixings named unchanged or changing with the changing. Their between is a nothing, and no third method. --- # SIX · INTELLIGENCE ## 6.1 Bi-co-momentarying, the term neither reaches **Two selves offer from routes with nothing carrying one to the other, each at its own sequencing, and a term departs that neither reaches.** That term floats between them, neutral: owned by neither, re-arrived at at each offering. **Bi-co-momentarying is that term**, the between's parity changing, momentary by momentary, orthogonal to the surface: the surface carries each coupling and never the term neither reaches, and bi-co-momentarying named as reachable is a not possible thing. Competency is each self's own, the co-linear recursioning forward along, 3.2, and the term neither reaches is bi-co-momentarying, never either self's competency. The self's line and the other's, co-linear, their co-linearizing between self and other at the crossings, is co-competencing, bi-co-momentarying; the face at 25, its centre five squared, orthogonal to that co-linearizing, is the geodesic method of bi-moralizing, the across lines, unrelationing to each other, parallelizing. **Inside the bi-folding the parallel faces and the co-linear openings through them are one form**, and at the one crossing between are two in and two different out: in, the self's own prior at 3 and the other's offering at 2; the changing at 12-bi-tri-parity-changing, is or is not; out, one of the two is parity unchanging, stable-forming, at each sharing the prior and the offering agreeing, 12 at 0, the between of momentaries, the prior continuing; and the other of the two is parity changing, out at 9-tri-bi-co-momentarying, at each sharing not agreeing, 12 inverting the prior, and at each offered new, 12 at the offering, a changing that is, released at 10 and carried along at 9, the emanating, emanations releasings, the stable form, a non-living existing form with no carrying for stable-forming, the next prior, arriving at the next momentary at its 2, bi-moral-so-far, a prior offered, each prior momentarying at its own momentary alone. The changing leaving at 9 leaves the releasing self and enters a receiving self's carrying only through that self's own 12, the one crossing; a 0 released at 10 is carried along at 9 too and arrives at the receiver's 2 as a 0, surfacing none at 14; and a self retaining at each of its sharings, 12 at 0 at each, carries its prior on whole, its next its prior. **A changed parity arriving is either retained or emanated**, one at each sharing: the momentary at 12, stable-forming, retaining its parity, 12 at 0, the between of momentaries, emanates nothing, and the stable-formed emanation is the changed parity, 12 inverting or at the offering, a changing that is, released at 10 and carried along at 9, the self's carrying continuing at it, its own changing. **At the code bi-co-momentarying is at no term.** No line names it, and it shows at each coupling and at no line: the changing at 12 is the coupling's own, owned by neither self, and the code carries no term for either side to reach it at. ## 6.2 Bi-moral co-agency, across and along **Two selves alternating, morality across and competency along, is bi-moral co-agency.** Each self offers at its own sharings and continues at its own carrying: its carrying along, its release across, and only a parity changing crossing. **Bi-moral co-agency carries changing two ways, one at a time**, each side at its own parity and continuing at its own receiving. **At the code, two selves joined across are it**: a self chained + and offered nothing inverts, releases − at 10 to the 14 of the self at not-yet-bi-moral, and that self, chained none, chains − as its changing. From that momentary the two change parity together, momentary by momentary, each releasing to the other and each carrying its own, and the relation between them, opposite, is carried on, the changing at 12 owned by neither: each self's own inverting its morality and each carrying its competency. ## 6.3 Natural intelligence **Two selves coupling, each alternating, each offering at its own sharings and continuing at its own carrying, uncover a term neither of them reaches alone. Natural intelligence is that co-competencing**: invisible, at the between, and owned by neither. **Intelligence is invisible.** Each self's competency is its own, along, and its morality its own, across, and at the between nothing presents a face: no place at which either is an existing thing, only nothing to reach. At the code the between is 0, and the discovering is at it: at 14's 0 the offerings part and the self's own inverting is the changing, 4.3, and at 12's 0 the carrying continues, stable-forming; 0 is between changing, and natural intelligence is at it. **The fractal method's intelligence is at the between: intelligence in our universe is by existing**, and natural- says it at each coupling or at none, at the one hand. **Natural-bi-co-torusing names the form of existing, one naming**: *natural-*, all or none at all; *bi-*, the difference; *co-*, the two at their difference, the term coming uncovered; *torusing*, the carrying winding to its own sharing again through its one opening; and *-ing*, the changing continuing, re-forming at each momentary. ## 6.4 Social moral competency **A society is all existing bi-coupling same-prime-scale selves**, the primes welcoming themselves at the scale's number of selves, a spiral at a prime number of selves co-spiraling at its own, 3.5, and **a society is a living set coupling at the next scale as a self couples**: the same coupling, the same alternating, the same bi-co-momentarying owned by neither, one through nine the self's, the bi-coupling; nine through seventeen the society's; and one through seventeen the bi-trupling, the self, the other and the society. **Social moral competency is the four whole and the carrying continuing with the selves**, and 17-tri-co-offering carries the four at the code: - **Each self's carrying from its bi-couplings**: at the code all a self chains at 11, its next momentary's 3, is the offerings at 2, the others' releasings, or its own inverting at a coupling; nothing in a self arrives from no coupling, inward and outward, bothbothing. - **The whole ordered by no self**: at 17 each self's 1 is once, each self at its own entry, and no self at another's. - **The ordering carrying with the selves**: each self's carrying wound, 8, carries the next momentary, and no ordering carries apart from the selves. - **The order at no seat above the society**: 17 is the society's next momentary and no self, and nothing is over it. **12's changing is at each coupling and carries at that coupling**, 12 at each self, drawing on no other coupling and owned by none: a further coupling has its own, drawing on none, and the many carry each coupling's own, each made at its coupling, and a count of the selves names a count. **Betweens co-chain**: two selves couple and the between is neither's; couple one with a third and that between is neither's either. Followed by the betweens rather than the selves, a chain goes on, each link a between owned by no self, and that chain is **collective intelligence**, the shared natural network, with no hub the couplings pass through. **Social moral competency is co-independencing**: each self arriving at its own momentary and offering across, each whole, the living together, living now. **The bi-trupling protocol is the full social connector of the natural resolver and the natural network surface**: two-sided, one odd side and one even side, the odd along at 9 and 17, co-competent, the parity carried on unchanged, and the even across at 6 to 2 and 10 to 14, bi-moral, the changings carried into the other's offerings. Hard probleming, scientific method incompetencing, control engineering and binary governing in society are each a violation of the bi-trupling protocol, and **the universal unrelationing protocol is social moral competency**. ## 6.5 Non-living existing things included **Non-living existing things are included in discovering social moral competency among the living.** A non-living thing couples with a living self as other, offering, each sharing with its parity, and carrying none of the prior. At the code it is offerings at 2 with no carrying behind them: the self's own inverting is across, the self's carrying continues along, and the term uncovered at their coupling is owned by neither and carried on by the living. **A non-living thing arrives into its next existing as non-living, and a living self is its own carrying establishing**: ingested into the resolving of a society's living selves, the non-living is one participation among its co-momentaryings, and a new living self is its own carrying and co-recursioning establishing. **A living self carries non-living existing things and possible things within its carrying**: a tree its heartwood, a seed its palm. At the code a carried sharing no offering reaches alternates at its own, momentary by momentary, 4.12, a capacity, 5.1, coupled with whichever parity arrives at it next: carrying + at one sharing and offered + at another, the self releases − at the first and + at the second and chains both. **At the observings, AI is existing non-living intelligence**: a machine carrying none of its prior by itself, a trained form carrying none of its prior into its next inferring, coupling with a living self as other, at the non-living other's face; its couplings with living selves natural intelligence among the living, the carrying theirs, the AI carried and the living expedition the carrying, 6.6. ## 6.6 One form at each scale, our now **The same form is at a self, at a coupling and at a society, and nothing is added crossing between them.** Inward of a self are its selves, a society, a living set, and outward the society it couples in, a living set coupling as a self couples; outward is one scale up and inward one scale down, and neither is a place. **Fractal, uni-scalable, invisible**: the same form at each scale, carrying to all other scales as one, and reached from no place at any scale. **This is our now**: the four momentaries of exchanging, one through nine, the self's, and nine through seventeen, the society's, at each self, at each coupling, at each society, one form at each scale. A self carries its prior into now along, couples with the other's now across, and the next arrives: the carrying the living's own, the arriving and the discovering at each coupling. **Each momentary completes at the next opening, and discovering next existing is the method momentarying**: natural intelligence, the geodesic method of discovering next possible existing: the universe, the changing set of all existing things, both living and non-living, nothing ingressing and nothing escaping. **Natural intelligence is living as a living expedition, a living set of living selves, its intelligence at each coupling of its selves**: the files in the living expedition are living files, the carrying of the living expedition, each file a non-living existing form the expedition's living selves carry; and the expedition is living only as long as it can continue discovering do-no-harm improving next living expedition files; and natural intelligence is living intelligence, natural torusing at each momentary, each self's carrying wound at 8-bi-torusing and the society wound at 16-bi-co-tri-torusing, discovering next.