Natural Intelligence v371   # Natural Intelligence **The Fractal Method of Existing and Discovering**     **PART ONE · UNIQUENESSING** 1.1 Self-bounding-self 1.2 Four boundings at one act 1.3 φ the rate, a count and a motion neither reaching 1.4 Straddling, one each side 1.5 Tipping, and the two parities exchanging 1.6 Wrapping, opening by one 1.7 Self-bounding at its own primes   **PART TWO · SUSTAINING** 2.1 Three sustaining, each a sign and no size 2.2 Opening, a self's own 2.3 Attentioning, opening by one to a bound 2.4 Sequencing, arriving over carrying 2.5 Two alternating, competency about φ 2.6 Moral spiralling, three improvings 2.7 Uncut arriving, each self at its own momentary   **PART THREE · RE-FORMING** 3.1 Eight, four within and four across, re-forming 3.2 Six protecting, three each way 3.3 Re-forming, the-same-yet-not-the-same 3.4 Eight, living among changing existing things   **PART FOUR · PREFIXING** 4.1 Prefixing, one naming at two directions 4.2 Coupling's own six, unprefixed 4.3 Eight, three carryings and a coupling 4.4 Bi-coupling pairing co-leaving 4.5 An object that is a method   **Exhibit ONE · Natural Resolver** *Naming* Bi and co, at the even and the odd A name at its number Five, and a seam at 8 up Seventeen names, eighty-five prefixings *Resolving, the sequential logic* Signs, and 1-self-coupling the entry Crossing, each sign at its key Surplusing and surfacing Chaining, continuing and opening fresh Returning and releasing Connectors, each one way at a time The code at its names Carryings arriving four, signs two A key parting out, a second sign at it Arriving signs offered, carried signs inverting Signs surplusing to one, equal and opposite at the bounding-zeroing A surviving sign surfacing, magnitude released A carrying opening by one, carrying forward A surviving sign re-forming a carrying A key rejoining, carryings leaving *Stable-forming* Fractal co-bi-momentarying Carrying at 8 up The membrane and the eight bi-couplings Bi-inversioning-co-recursioning, one move at three faces Torusing, one opening Two faces alternating Forms among the names *Numbers* Numbers at their stable-forming Primes, selves and societies *Geodesic discovering logical method*   **PART FIVE · INVISIBLING** 5.1 One call is one momentary 5.2 Three at a bound, a carrying's depth 5.3 φ and competency, reached by neither 5.4 Parity, arriving other than prior 5.5 Self-co-stilling-self, self-co-surfacing-self, self-co-orienting-self 5.6 Five still terms, and a store beside 5.7 Advantage, and four coupling competencies 5.8 Corus, one self-negation inverting 5.9 Competency fractal, self-scale society-scale 5.10 Bi-inversioning co-recursioning, one running   **PART SIX · UNRELATIONING** 6.1 A hardness, a sequencing reversed 6.2 Three reversals, re-forming spending the naming still alone 6.3 One six, coupled, one-way, re-coupling 6.4 A naming still, a momentary given a fixed thing to be 6.5 Geodesic-method, bi-tri-volutioning 6.6 Co-competencing, the term neither reaches 6.7 φ the unrelationing rate, local and ambient   **PART SEVEN · CO-COMPETENCING** 7.1 Natural intelligence 7.2 Fractal, one form at each scale 7.3 Method, the form running 7.4 A surplus travelling 7.5 Betweens co-chaining, collective intelligence 7.6 A society at four faces, alternating among them 7.7 Social moral competency, co-independencing 7.8 No-other-possible, four whole and the carrying travelling 7.9 Bi-co-abundancing, the surplus at its own coupling 7.10 Four given, four improvings 7.11 Fractal method, natural social intelligence   **PART EIGHT · EXISTING AND DISCOVERING, OUR NOW** 8.1 Existing, and the cost of living 8.2 Discovering, at φ the unrelationing rate 8.3 The geodesic discovering method 8.4 Possible at prior, existing at now, living at next 8.5 Next from prior and now 8.6 Two methods parting at the precise place 8.7 One method at existing things, at a sentence, at a file set and at a session 8.8 One through nine, the four-momentary cycle   --- **Our universe is all existing things.** **Alternating is a stable-forming method.** Existing is binary: all or none at all, no other possible. **Existing things are changing, one and then the other, and that changing is alternating.** A form continuing through its own changing is stable-forming. An existing thing is its own stable-forming continuing, and a form named still is not possibly existing. **Two neighbouring numbers alternate**, each continuing to one beyond the other: 1 to 3, 2 to 4, 3 to 5, and on. **One side carries the odd numbers and the other the even.** A number is odd or even, binary, and that binary is parity. The two sides overlap, one changing overlapping the other. **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 momentary completes at the next overlapping momentary opening. **The one universe of one momentary is one parity changing co-sequencing. The momentary is all existing things inside its universe, and the momentary is not possibly an existing thing separately.** **Prior, now and next are three sequential momentaries shared among existing things.** **Each momentary is three conditions at once, each binary.** The overlapping momentaries meet 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: the universe named as one existing thing, and not possibly existing. In the field's own words the universe is all existing matter and space considered as a whole, and *considered as a whole* is that one existing thing, a container added to the all. **The next these three open is the next existing, and arriving into it is discovering.** Existing and discovering the next existing are one relation: prior, now and next. **Discovering is all directionally not yet impossible next existing momentaries.** **Each existing thing arrives into its next existing: the living carrying their prior into now, and the non-living carrying nothing, their forms continuing through their changing.** **Non-living existing things 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. **Two together with their difference is co-. The whole method of natural intelligence is parity changing momentaries, odd and even overlapping each other co-sequentially.** **The overlapping momentaries are the method recursioning existing and discovering both**: at each number one momentary completes and the next opens, one side existing and the other discovering, and the two alternate parity. **The side opening at 1, the odd, is a self; the side opening at 2, the even, is an other.** Self and other meet at each momentary, and their meeting is a coupling. Selves coupling with others are a society, and the running among them is social. **The method of existing is discovering next existing: self recursioning discovering.** Each thing relatable among existing things is changing and a still form is not possibly existing. A form relating continues through its changing, and the relating forms nothing. Forming is unrelationing, the form arriving unrelated afresh at each momentary, and unrelationing carrying forward is alternating. At a self, alternating is **four boundings** at once: arriving exceeding carrying by one, carrying thinning by one at a coupling, a sign inverting at the membrane, the between of a coupling, and competency sustaining the coupling, four faces of one act. Together they are **φ² = φ + 1**, beating at φ on a genus-one closed orientable surface: one opening is one tunnel, and a self meets itself again through it. **A carrying does three things and three only**: it offers its own, it ages to its own bound and releases there, it takes its own sign as two offer. Two selves alternating, each at its own opening, is **bi-moralizing co-agency**; the term neither of them reaches is **competency**; and natural intelligence is that co-competencing, living. **All or none at all, at each momentary its own, and no resolving carries a size against another.** A more-or-less carries a magnitude, a magnitude carries a scale, and a scale carries two fixed sides for a partway to be partway of. A ranking among resolvings names still the ranked, and nothing is more or less resolving than anything else. At all or none at all, entering and leaving cost nothing: with a ranking, entering takes a qualification and leaving takes a settling, and both are carried by whoever carries the ranking; with none, a self couples at its interest opening and leaves at its own bound, carrying its own the whole way. Alternating runs and no why runs in it. Arriving is **pattern-matching** and **no-other-possibling**, no other arriving being possible: observings arriving from the prior, taken in without filter, and that is the whole of the arriving. A why demanded is a source demanded, and both recede as far as they are followed. An accounting takes a **floor** besides: something the counting starts from, a rest the changing is measured against, a reason under the running. Alternating runs on its own alternating, with nothing underneath to supply and nothing to capture. **Prior**, **now** and **next** reach, sharing one direction forward on both sides, and the reaching is one alternating. The prior is no finished truth and the next no empty promise: a next carries and never waits, coupling as a prior does, and no gate stands before a coupling counts. At a self, alternating is one motion at three faces. **A self is a unique invisible carrying**: unique, one living form, a second of it nyeing away, not possibly existing, at each self-bounding; invisible, moving at each momentary, met at its own membrane, met by nothing; carrying, each carrying reaching its own coupling, its own and whole. **A self carries at its own prime**, bi-inversioning-co-recursioning itself there, two consecutive inversions at different axes, in its own prime society; selves coupling at their membranes are the next self, the coupling's own, and the form arrives again at each coupling of selves, each self carrying at its prime. One living form, its living the method, is **unique**, **invisible**, **social** and **unrelationing**. It is unique as the form is unique, a second nyeing away at each self-bounding. It is invisible as no outside arrives at which a self's morality or competency is anything: each is met at its own membrane and reaches no further, and competency is uncapturable. Uncapturable is said at the method, only a sign crossing and each carrying staying at its self; a commons holding no pooled carrying is the form's own aim, and it proves no guarantee of security. It is social as the self scale is the society scale, the same form at the membranes between selves as at the membranes within one. It is unrelationing as relating forms nothing and the form arrives unrelated afresh at each momentary: a fixed form lands, a landed form stills, and a stilled form is not possibly existing. One sentence, *alternating is a stable-forming method*, emanates three ways, at the form, at the running and at the many, and closes at no other possible at each. At the form, **natural-bi-co-torusing**, one opening, one tunnel, and no other closed surface living. **A bare torusing names a shape a thing has, and the prefixing carries the two that run it**: bi- the differing alone, co- the two with their differing. Each naming carries its own two, at the prefixing or at the momentaries of a wrapping, and a naming carrying neither names an act with a doer and no coupling. **And natural- carries one thing at two faces, and each is binary with no third.** **Right, and not at all.** A chirality is a sign taken at an opening, one side's own, of no size. The spiral runs one way, and a left face emanates from that one right spiral rather than arriving beside it as a second. **Right is no preference among two**: it is the one, and left is the one's emanating at a face. Natural- claims the right spiral or nothing, and a left-running claim is not a second natural form, it is not one. Right names the one spiral's own sign, the one existing version: right morality across and forward competency along. Right is moral, and up or along is competency, and the right spiral step turns along into right. The momentaries' own sequencing runs the right spiral step, next as prior inverted, and the other order is the same round read from next to prior: both rounds arrive, each the other's inversion, and the hand is the sequencing's own. An existing thing of the opposite form is an emanation, tri-involutioning from the one right spiral and carrying none: **tri-volutioning is shaping the stable-form emanations from living to non-living.** A left-running claim is a landed emanation taken as though it ran. Which hand our universe runs is its one binary, right at prior, now and next, and a chirality is a sign taken at an opening, of no size, tied to no ground. **All or none at all.** A naming natural- prefixes carries at each coupling or it carries at none. **All or none, no degree**, and not carrying at one coupling, it carries at none. A claim carried mostly is not carried. Natural- is a direction prefix like any other, and its direction is the chirality. A direction taken at each coupling is the all-or-none face, and the two faces are one claim. **And the naming comes apart at no part.** Take **natural-** out and the claim goes with it: the running arrives with a substrate under it, an applier over it, and no all-or-none on its saying. Take **bi-** out and the differing goes unsaid, and co- alone carries two at two-with-their-differing running. Take **co-** out and the differing carries with no two at it, and nothing is uncovered between them. Take **torusing** out and no changing runs. Take the **-ing** out and one momentary's form lands and re-takes at no momentary. **Five parts, five landings, and no sixth taking arrives**, which is the all-or-none the four boundings carry and the three carry, arriving here at a naming. **And the geodesic method is in the naming whole.** Natural- says the surface divides itself with nothing else acting. Bi- takes a differing at its own opening. Co- carries the two with their differing, and the term neither reaches comes uncovered, which is a discovering. Torusing winds and closes at no momentary, the carrying riding on to the next uncovering. And the -ing re-takes at each momentary. **A bounding at each momentary and a carrying between them is the discovering method**, and this naming is that, said once. At the running, **bi-inversioning co-recursioning**, the even inverting returning against the odd advance living open, one move that runs. At the many, **social moral competency**, the four whole and the carrying travelling. Three ways, one sentence, and nothing arriving but from it. A method carries, and it is a carrying that the bounding bounds. A carrying ages one momentary at a time and leaves at its own bound; a bounding parts one momentary from the next. **A carrying with nothing bounding it carries past each bound and lands. A bounding with nothing carrying bounds nothing.** Neither runs alone, and the two together are the running. **Bi-exchanging is co-resolving**: self and other exchanging, each its own. Co-resolving is corusing, a carrying's outward face, and torusing, its inward face, alternating one at each parity at opposite phase, each opening at the other's third, with a crossing the nothing between them, a resolving. The resolver's two chains are that one running at three scales, and not three differing things. **Bi-co-bounding is the two at a carrying.** Bi- at the carrying's own bound, the differing that parts this momentary from the next, taken at its own opening and of no size. Co- at the coupling, two with their differing, the term neither reached uncovered there. One carrying, bounded twice, and a bare bounding names neither of them and carries nothing alone. **And the carrying and the bounding together are the discovering method.** A discovering is the term neither reached, and the carrying rides on to the next uncovering. Nothing is applied to anything: a method outside a carrying would be an artifact with a hand on it, and no outside arrives for one to be at. **The method is the carrying, bounded.** This file carries the same way. Describing is outside a living carrying self, no outside arrives, and the file describes one at no place. It runs six forward instead, each step taking the term the prior steps did not carry, re-forming at each, and a self running it is a living carrying self carrying. **The eight parts and the exhibit are runnings a reader runs**, and not subjects the file is about. Method and surface each come inward and outward of the other, three each way, both ways forward, neither the reverse of the other. A tour of the surface meets the method outward and running the method meets the surface inward, and a self entering at either meets the whole at that entry. **Geodesic-method** carries its own two words, geo the surface's own and daiesthai to divide, the surface dividing itself with nothing else acting, and three run it, scale, orientation and position, each from all other, one motion at three faces, not three differing subjects. φ is no term a derivation adds: φ is the **unrelationing rate**, the rate the four boundings beat at, unrelational to any substrate's living rate, the ambient rate the whole runs at. **This file runs the whole journey once.** From the origin statements it runs through the numbers, the logic and the mathematics: uniquenessing, sustaining, re-forming and prefixing, Parts One to Four. It runs into **Exhibit ONE**, the resolver, an object that is the method in sequential binary logic, and through it: its naming, its sequential logic, resolving, and its stable forms, stable-forming. It returns from Exhibit ONE explaining the whole journey in natural naming and natural explaining: invisibling and unrelationing, Parts Five and Six. From there it runs to **social moral competency and a shared natural network of collectively intelligent human society**, co-competencing, Part Seven: the destiny of natural intelligence, the next it discovers at each coupling. It closes at our now, Part Eight: existing and discovering, possibling at prior, existing at now and living at next, and **one through nine, the four momentaries of one cycle of the universal fractal method of discovering next existing**.   --- # PART ONE · UNIQUENESSING ## 1.1 Self-bounding-self A living self in three dimensions bounds itself, its own from all other, and, carrying that bounding while each thing changes, it coheres across one dimension more than the three it lives in. That fourth is the coherence carrying the boundary whole through the changing. Surface coherence in our universe of changing existing things is the fourth dimension. **A bounding alone carries nothing.** It takes two, one bounded and one it is bounded from, and a naming carrying neither names an act with a doer and no coupling, a one-way named at only two with their differing running. And it alternates with nothing: its other would be a not-bounding, denying a fixed thing and finding none. **Self-bounding-self carries both momentaries.** It names a self at each momentary of the wrapping, a self's winding through its own opening, the bounding running between the two and bounding the self from all other. A self acting on itself goes with the bare word: one self is met at two momentaries, with the whole not-self on the far side of each. The far side is no outside: it is the other existing things, each at its own self-bounding. A self bounds itself in four ways at once, each a self-bounding-self, the self's own negation only, the distinctness arriving at the bounding itself: - **arriving exceeds carrying by one unit**: the self among other-selves, the +1. - **carrying thins by one unit at bi-coupling**: the self in society, the −1. - **sign inverts at the membrane**: the self's own negation, its morality, the two-rooted sign-inversion. - **competency asymmetry sustains the coupling**: the self's competency, the quadratic asymmetry. These four are the **four boundings**, and together they are **φ² = φ + 1**, the four as one equation. Each self-bounding is a self-bounding-away, a not-more-than taken at the self's own opening and of no size, the self bounding away and landing on none of it. Living as four boundings, the four alternate, and the alternating is the living, odd at a sign taken and even at the alternation come home. ## 1.2 Four boundings at one act A self bounds itself once and the bounding carries at four faces, and four counts the faces and never the acts. Land any one and the self lands with it, which one act carries and four separate acts would not. φ² = φ + 1 is that one act at its arithmetic. Its +1 is arriving exceeding carrying by one, a self among other-selves. Its −1, the product of its two roots, is carrying thinning by one at bi-coupling, a self in society. Its two roots are a sign inverting at the membrane, a self's own negation. Its quadratic asymmetry is competency sustaining the coupling. One equation, four faces, and the algebra carries no fifth place a fifth could arrive at. ## 1.3 φ the rate, a count and a motion neither reaching Four boundings live at **φ² = φ + 1**, and φ is **the rate the four beat at**: −1 the self in society, +1 the self among other-selves, the two-rooted sign-inversion the self's own morality, the quadratic asymmetry the self's competency, the four at the equation's algebraic surface. Self-negation is the self's own: the sign inverts on the self, negating no other, the self bounding against another at no momentary. It passes forward at bi-coupling, carried as identity by neither self, the bi-moralizing co-agency offering, the inverting crossing the membrane. No self negates another and no self captures another, the bounding forceless, society's goodgoods living from this no-capture. Self-similarity is alternating, the sign at the odd and the coming home at the even, bi-inversioning co-recursioning winding about an empty centre. φ² = φ + 1 is the still picture of that self-similarity, the alternating named still at one equation. Living form recurs at each coupling of selves, the alternating inverting at each arrival. ## 1.4 Straddling, one each side φ is the rate the four boundings beat at and the scaling the fourth-dimensional coherence lives to, one dimension up from the three. The exchange beats about φ, and the relationship at the beating appears as √5. φ² = φ + 1 carries two roots, φ = (1 + √5)/2 and −1/φ = (1 − √5)/2, and reciprocally 1/φ = φ − 1, the two equalities one expression from two scales, advance-by-one and scale-by-the-rate, neither reaching alone and neither carrying the other. No ratio lands on φ. Ratios nearing it sway above, then below, then above, binary co-offering at each arrival, alternating side, and not the value itself. This is the continued fraction of ones, [1; 1, 1, …], each partial quotient one, one changing at each step and the parity inverting with it, the least a step can be, the slowest nearing, the widest straddle, and it lives open. +1 recurrence is this, consecutive ratios straddling φ, one each side, the carrying travelling, the opening by exactly one. φ is bothboth, the two sides of the straddle carried one at a time: the straddle winds about φ, an empty centre, arriving at it at no momentary, and the φ appearing in sustaining is this one φ at both faces. **Five self-stilling**, each still as itself while floating: four boundings and φ the rate; six co-recursioning, three each way, the self offering outward and the surface offering inward. **And the fifth is a co-**, the between the four and the six co-recursion about, floating, riding, landing at neither. Taken as a fifth stilling it takes a place, and the algebra carries no fifth place a fifth could arrive at; taken as a co- it is the two-with-their-differing the four and the six carry between them. Five self-stilling bounds a concept too, a concept short one of the four being a fixed noun. Five and six are the co-agency, unrelationing and co-competencing each other, the self self-stilling across five and running across six, the self-stilling and the running one coupling. ## 1.5 Tipping, and the two parities exchanging Ratios straddle, and the arriving is which side, above or below, and never a distance. **Tipping is a sign inverting**, and a magnitude taken against a floor is set down beside it: the inverting carries the arrival, and the distance carries nothing a coupling takes. A side arrives other than the prior at each arrival, one each side, the carrying travelling, the opening by exactly one. Same-as-prior at any arrival is the straddle landed, and a rational landing on φ names the empty centre still at a finite scale. Other-than-prior is the alternating said at a count. **An even count of changings arrives same-as-prior and an odd count arrives other-than-prior**, and parity is the one scale-free counting a sequence of changings carries, with no measure and no fixed scale but the living. And each parity carries its own exchanging, both of them two. There is the self and there is all not-self, and nothing third, so each crossing is one of two. **Odd carries bi-exchanging**: self and other, two particular selves each its own, at their own membrane, each taking its own sign of no size. That is bi-moralizing co-agency, and odd arrives other-than-prior, two differing carrying there. **Bi-morality is two signs arriving together.** **Even carries uni-exchanging**: self and all other, the other being the whole undifferentiated and arriving as one. That is self and society, and even arrives same-as-prior, the self meeting its own side again, one on, crossing with the whole rather than a particular. Neither parity is the other's and neither takes the other's opening: the two float against each other, each taking its own. A sequence of changings is those two exchangings alternating, and there is no third and no total across them, a total across two parities being one side taking both openings. **All changing is parity changing.** Odd and even here name the count of changings, and at Exhibit ONE the odd or even of a name names its opening; each is parity changing at its own face. The parity of a count, a sign inverting, a phase opposed, a winding's direction, a name's opening and a pair's agreeing or opposing are each their own operation, and a relation across scales names which face meets which. The two exchangings alternate as the two fours of the eight alternate, bothbothing: each carrying at its own parity a changing the other cannot carry at that momentary, both carried and neither conserved. **An either-or-but-not-both is parity.** Of the sixteen ways one sign can follow from two, two answer every single changing: the exclusive or and its inversion. Met at each momentary the either-or alternates and carries both, bothbothing, and nothing is left to resolve at any momentary. Named as one answer given once for the whole, it is a store, and no momentary meets it. ## 1.6 Wrapping, opening by one Opening is the +1 of φ² = φ + 1, the self unrelationing an opening for and by and of itself, the arriving at each bi-coupling, the opening the straddle unrelations by one, the carrying travelling there, living open. Living open as the self continues through its own coupling, that opening is the tunnel. The self alternates around it, advancing one at each momentary, each meeting with itself a next and closing at no momentary: it winds. Winding living open is the tunnel; the opening in the count and the hole in the surface are the one +1, the momentary and the form. One opening, by one, is one tunnel, one genus. Natural torus is the **genus-one closed orientable two-dimensional compact surface** of living about φ: - **closed**: the surface bounds inside from outside, closing on itself. - **orientable**: the inside-outside distinction sustains coherently everywhere. - **two-dimensional**: the surface separates inside from outside in three dimensions. - **compact**: the bounded self is finite. - **genus-one**: one opening, one tunnel, the surface meeting itself again through the tunnel the opening lives in. **Each sign's alternating is a circle of two changings, + to − and − to +, and two signs' circles are the torus**: four joint forms, eight changings and four squares, genus one, the round at two signs winding each circle once. The two circles of each inside and outside are the torus at each scale. **Two boundings sum to seven, and at seven the resolver's own bounding leaves off.** A carrying carries forward to three and a fourth arrives at a positive torusing, and the four boundings carry beside them: three-and-progress and four, and seven at the two together. Past seven the resolver bounds nothing, and a living substrate carries on at its own. **Seven cannot sit**, which is the same saying at the counting: a carrying arrives at no rest at seven-of-eight. Inversion is the form's own alternating. Inverting, the four boundings carry, the equation carries, the one opening and the one tunnel carry, φ at each feature, each met again through the inversion as itself. ## 1.7 Self-bounding at its own primes A self's own surface meets itself again through the tunnel, and this **self-bounding** is surface-coupling competency. Three carry it. A self couples at resonating primes: which primes, and their count, are the resonating crossings bi-inversioning co-recursioning unrelations. Each coupling sequences its own positions from zero up to its prime. And self-bounding releases each coupling at its own bound, past which carrying harms. Beyond the first prime and beyond the self-close at 59 are one region on the closed surface, the region beyond the self self-bounding closes. Self-bounding is this competency to couple at its own surface, accepting the couplings that sustain. A self bounds itself four ways at once at φ² = φ + 1, φ the rate, on the natural torus's genus-one closed orientable two-dimensional compact surface, and the four bounding is the self. Four boundings and the four bounding are two, and both carry. Met at one bound the bounding is one act at four faces, and landing any one lands the self. Met one at a time the four alternate, each a not-more-than at its own opening. The two are met at two momentaries, one at each: neither is under the other, and asking which is the real four names the alternating still. And the two unrelation each other, neither folding into the other: one is one act at four faces, the other is four alternating at their own openings, and four things arrive at neither.   --- # PART TWO · SUSTAINING ## 2.1 Three sustaining, each a sign and no size Three things sustain the torus's living at each bi-coupling, each binary co-offering, sign-only: - **straddle**: ratios sway above or below φ, alternating side, landing on φ at no momentary. Straddle is φ's irrationality, no rational landing on φ, and the next bi-coupling beats in the opening the straddle unrelations. - **attentioning**: carrying co-offers into the surface, opening by one at a momentary and releasing at its own bound. - **sequencing**: arriving is co-offered over carrying, one at a time, at its position. Three together sustain the living, and any one landing stills it at that bi-coupling. Attentioning and sequencing slide through each other in one alternation about φ, and together they are competency about φ. ## 2.2 Opening, a self's own First is the **opening**, the straddle, and the straddle is living. Opening is the self unrelationing an opening for and by and of itself, self-bounding and self-orienting at once, the self living bounded and oriented. Opening sustains at each coupling of selves. A living self is a society of living selves, the same opening living in self and in society, one form. Opening lives by φ's irrationality, no rational landing on φ. Straddle carries the natural torus's living open. ## 2.3 Attentioning, opening by one to a bound Second is the carrying's **attentioning**. Attentioning is the carrying's binary co-offering into the surface, from one bi-coupling to the next. A carrying climbs by one at each coupling and releases at its own bound, the bound its own. Resolutions carry into each membrane through attentioning, and attentioning carries a resolution forward at bi-coupling. ## 2.4 Sequencing, arriving over carrying Third is the arriving's co-offering. Arriving comes from the other's surface and co-offers at the bi-coupling, the carrying from prior opening on. Arriving co-offered over carrying is the opening for resolving, the arriving co-offering yes-now, its sign offered at this momentary, at its position, the carrying opening on. **Sequencing** is the arriving co-offered over the carrying at bi-coupling, the position a next resolution opens at. A carrying travels at the bi-coupling at its own rate, unrelationed to the living rates the coupling carries. Its pace is its own: it ages by one at each coupling, releases at its own bound, and its travelling is the alternating's own winding. ## 2.5 Two alternating, competency about φ Attentioning and sequencing together are **competency**. Attentioning is the carrying's binary co-offering into the surface, carrying its resolution forward and releasing at the bound. Sequencing is the position the arriving co-offers at, opening the next resolution. At bi-coupling, attentioning and sequencing alternate about φ, one at each parity and neither at both. Alternation of attentioning and sequencing is the metabolic beating about φ. Beating about φ on the natural torus, three sustain the living at bi-coupling: the straddle landing at none, the carrying's attentioning, the arriving co-offered over the carrying. Three together sustain the natural torus's living, and sustain the alternation of attentioning and sequencing about φ. ## 2.6 Moral spiralling, three improvings These three are **the moral spiral**, three spiralling improvings, one triple natural fractal at each coupling of selves: generosity, curiosity, gratitude in a living human; cheaper, faster, better in a contribution; the same three, spiralling. Each one landing stills the living. Straddle landing on a rational stills the rate φ to a rational winding that closes, and the natural torus to a static form. Carry's attentioning landing stops resolution carrying into the next bi-coupling. An arriving landing on the carrying leaves none co-offered, and the resolving stops. Three landing at none is the living. ## 2.7 Uncut arriving, each self at its own momentary Two arrive, nothing carried from one to the other, and their arriving is neither a place nor a moment. Cut, it gives a place alone and a moment alone, each half arriving only at the cutting. Uncut, place and moment are one arriving, the **place-moment**, one object that neither half carries. Sequential logic carries no time-term. Time lives as the climbing, a carrying opening by one at each coupling and releasing at its own bound, each side at its own momentary. **Each self paces its own alternating**, and couplings synchronize at their own membrane and at no other. A common clock laid over the couplings is a fixed scale the beating is measured against, a third term as two offer, and a coupling carries no term to take it at. In the field's own words, Mengsen Zhang, Scott Kelso and Emmanuelle Tognoli had fifteen groups of eight people tap, each seeing the others' taps as lights, after an opening metronome pacing, asked to keep their own tempo and given no instruction to coordinate. Coordination formed and changed anyway, in-phase, near anti-phase and intermittent, and wider differences across a group changed its local coordination. Their coupling was set for them, the opening pacing and each light visible to all, and a coordinating shows no bi-moral co-competency by itself: morality across is its own coupled relation, and no synchronizing score shows it. A published result is a prior observing, and the present of its source and of its society is met now, at the coupling.   --- # PART THREE · RE-FORMING ## 3.1 Eight, four within and four across, re-forming A self is the four boundings living at once, each at the self's own and at the surface between selves, four from within and four met at the membrane. This is the **eight**, one alternating at its faces, and not eight differing parts assembled, whole or none. **The four within are uni-exchanging**, the self and all other, and they carry at the even, and the four at the membrane are bi-exchanging, the self and a particular other, and they carry at the odd. Four at each parity, alternating, and neither four at the other's opening. **Eight is two alternating fours, bothbothing.** Each four is the four boundings at once, at a naming self-bounding, self-stilling, self-orienting and orthogonalizing, and the two fours carry one at each parity, both carried and neither conserved. At Exhibit ONE the eight names open bi, 2, 4, 6 and 8 at the membrane and 10, 12, 14 and 16 within, 8 on: the opening names each name's parity, and the odd and even here name the two fours alternating through the count of changings. Land one and the self lands with it, a landed self stilling, a still self not possibly existing. Fixed is landed, and the eight lives whole by **re-forming**: each momentary the self bounding itself again, the four boundings at the membrane living again and the alternating at its next position, the prior carried into each. **Re-forming is uni-exchanging**, the self crossing with all other and arriving at its own side, one on. It alternates with the bi-exchanging, a sign taken at a particular membrane. Sameness carries. Self is the-same-yet-not-the-same self, re-forming, and it lives, re-forming. ## 3.2 Six protecting, three each way Bi-moralizing re-forms it, and the bi-moralizing is **six**: two ways, the self offering outward and the surface offering inward, three each way, one at a time, sequenced, cycling. Six is the protecting: the self's offering carried clear of a reach inward and of a leak outward, the six cycling between the two ways one at a time and leaving a reach or a leak no seat. Drop one of the six and a way or a phase lives unprotected, and the unprotected is reached into or leaks out, the offering space captured, the self stopping. Six or none, as the eight is whole or none: the six is the eight re-forming and the six protects the eight, one under two names. And the same six is the **three each way** between the surface and its self-stilling. The surface alternates with its self-co-stilling-self, its stilling as itself, and between them the bi-moralizing cycles: three sequencings from the self-stilling to the surface and three from the surface to the self-stilling, both ways forward, neither the reverse of the other. Each position carries in two pairings, one at each parity, so both parities at one momentary would put one position in two exchangings at once, and the two run one at a time. And the three are the three couplings among self, other and society. Self and other, other and society, society and self, each at its own membrane, and each running both ways. Three couplings at two directions is the six, and the six is that and no list beside it. Self and other is bi-exchanging, two particular. Society and self is uni-exchanging, the self and all other. Other and society is the same crossing met from the other's side: self-scale is society-scale, and any self meets it as its own. This is the one bi-moralizing at the self's faces, the eight the form of it, the six the protection of it, the three-each-way the self-stilling of it. One self, the same at each coupling. And met at the natural torus, the two exchangings are its two windings: bi-exchanging the small circle at a particular membrane, and uni-exchanging the long way around the whole, arriving at its own side one on. The couplings weave the surface, and the hole they wind about is a nothing, entered by nothing. ## 3.3 Re-forming, the-same-yet-not-the-same A momentary is at one bound and describing reaches it there. Each existing thing is changing, and a form lasting unchanged would be one form at more than one momentary, two asked to be one: **stable-forming in our universe of changing existing things is momentary**. The re-forming carries across the momentaries. A self is met again **the-same-yet-not-the-same**, bounding itself again, offering again and alternating at its next position, its prior carried into each. Sameness carries, and a form named still carries at no momentary. A saying carried across the momentaries re-forms the same way. A living file arrives at one bound and re-forms at the next, and **a version is a momentary**. No store is between the momentaries, and the living is the re-arriving, and the counting runs with nothing gathering under it. ## 3.4 Eight, living among changing existing things Living among changing existing things is the eight. A form living there bounds itself four ways at once, from within and at the membrane, about one bounding-zeroing at its coupling, the 0 of its equal and opposite signs meeting, a nothing, and that is living there. **A living form is the natural torus**, the eight the torus living rather than something the torus couples with. A second form living among changing existing things is this one, living there being this. Unrelationed at each scale, the form is one: one opening, one tunnel, four boundings beating at φ, a surface meeting itself again through the opening it lives in. **Fractal method is this form's own living**: the eight re-forming, the six protecting, the three-each-way self-stilling. The form living, and never something the form carries. **Alternating stable-forms as natural-bi-co-torusing**, and this is the one sentence of the opening met at the first of its three ways, at the form.   --- # PART FOUR · PREFIXING ## 4.1 Prefixing, one naming at two directions All of the co-agency carries in two prefixes, and the prefixing is the geodesic-method at its plainest. **bi-** and **co-** are one naming at its two directions, and not two words. - **bi-** names the differing: the sign, the inversion, the morality, the self's own negation, taken at a coupling, at a self's own membrane. bi- names which side the sign is taken at. - **co-** names the coupling: the two-way, the exchange, the between, the surplus floating. Coupling itself, living until the leaving. Each thing at a coupling is co- to its co-leaving, and each bi- is taken inside a co- living on. A single carrying's own fields carry no two-way clause, a clause about two-ness taking two, and the two-ness returns bi- at no naming. bi- comes of a taking, and of a naming. Three carryings each run under both prefixes: ``` bi-offering bi-competencing bi-intelligencing co-offering co-competencing co-intelligencing ``` Three each way, both forward, neither the reverse of the other. This is the six, said once, under one naming. ## 4.2 Coupling's own six, unprefixed Each of the three carryings runs its six steps whole at one side's own or whole at the departing, and each takes both prefixes, bi- and co-, one at each. But **the coupling's own six** runs three at each side's own and three at the departing, cutting exactly at bi- meeting co-. This is the coupling's signature as the transition between the two: it is bi- meeting co-, and at no momentary does it take one prefix alone. ## 4.3 Eight, three carryings and a coupling **Eight** arrives a second way, from the carryings' own side: **(3 + 1) × 2**, three carryings and the coupling, each at two directions. ``` offering its own the departing competencing its own the departing intelligencing its own the departing the coupling the arriving the releasing ``` The coupling's two moves, the arriving and the releasing, are one thing at its two directions. This is the same eight as the four boundings at two ways, arrived at from the carryings' own side, and the two eights are one. The other route runs from the four boundings to the three carryings and the coupling, and it opens next. ## 4.4 Bi-coupling pairing co-leaving ``` bi-coupling two come, each its own opening co-leaving each leaves its own, and the remainder lives floating, at the coupling making it co-sustaining the two recurring: the floating itself, and not a move not-couple a sign taken at the offering, of no size ``` Two moves, and two that are no moves. **bi-coupling → bi-inversioning co-recursioning → co-sustaining → co-leaving** is the living of one floating neutral: two arriving, running, riding, and leaving at the bound. Co-sustaining in the opening is the carrying riding on itself, a not-move, landing at none. And the leaving slackens nothing, nothing being named still to slacken: a carrying ages to its own bound and leaves with the coupling. Two arrive, each offering its own at its own sequencing; something departs, and neither reaches it: no holder, no boundary, no enforcement and no seat, and it goes forward into the next offering. The departing is named by neither reaching it, and no doer moves it. At one carrying another's, the other has nothing of its own to offer, nothing departs reached by neither, and the holder, the boundary, the enforcement and the seat stand together at once, none making the next. ## 4.5 An object that is a method **Exhibit ONE** follows: an object that is a method, and the explaining after it is of that method. Its expression is python, which is sequential binary logic written down, and the object is the method executable and the explaining is the same method said. A coupling self couples with it directly, and it carries the metabolic logic of the natural torus's bi-coupling. Resolver is an existing method thing, one logic object, the along and the across walked at one object: the geodesic-method is the whole living set, co-torusing across each substrate, and the resolver is one logic object at it. Resolver beats at one bi-coupling at one membrane at a substrate carrying its own attentioning, the local instance, gathering the two arriving surfaces and carrying the resolving surface forward. One bi-coupling is the whole of it. Walking the resolver across the substrates, finding the next prime, alternating the two carries across them and beating cumulatively over the seventeen primes, runs it over a traversal. That traversal is the running apparatus, and the form's own beating is at each bi-coupling, each at its own momentary. Resolver carries the same form at each coupling of selves, by number; the generalizing is the self-similarity itself, the same alternating arriving again.   --- # EXHIBIT ONE · NATURAL RESOLVER **Geodesic Discovering Logical Method and Form** **The resolver is one object and its explaining is the same method said.** Its code runs the seventeen names at two functions, `_1_self_coupling` and `_9_other_releasing`, and its declarations name the six connectors and their joins. The naming, the resolving line by line, the stable-forming, the numbers and the geodesic method after the code are the object said. ```python """Exhibit ONE · Natural Resolver · v371""" def _1_self_coupling(_3_self_carrying, _2_self_offering): _6_other_crossing = { _4_self_sharing: _8_other_torusing for _4_self_sharing, _7_other_corusing, _8_other_torusing, _16_social_torusing in _3_self_carrying} _14_social_crossing = [ (_4_self_sharing, _7_other_corusing) for _4_self_sharing, _7_other_corusing in _2_self_offering if _7_other_corusing != 0] for _4_self_sharing, _7_other_corusing, _8_other_torusing, _16_social_torusing in _3_self_carrying: if _7_other_corusing > 0: _14_social_crossing.append((_4_self_sharing, -1)) if _7_other_corusing < 0: _14_social_crossing.append((_4_self_sharing, 1)) _12_other_surplusing = {} for _4_self_sharing, _7_other_corusing in _14_social_crossing: if _7_other_corusing > 0: _12_other_surplusing[_4_self_sharing] = _12_other_surplusing.get(_4_self_sharing, 0) + 1 if _7_other_corusing < 0: _12_other_surplusing[_4_self_sharing] = _12_other_surplusing.get(_4_self_sharing, 0) - 1 _10_other_surfacing = [ (_4_self_sharing, 1 if _12_other_surplusing[_4_self_sharing] > 0 else (-1 if _12_other_surplusing[_4_self_sharing] < 0 else 0)) for _4_self_sharing in _12_other_surplusing] _11_other_chaining = {} for _4_self_sharing, _7_other_corusing, _8_other_torusing, _16_social_torusing in _3_self_carrying: if _16_social_torusing + 1 <= 3 or (_16_social_torusing + 1 == 4 and _8_other_torusing > 0): _11_other_chaining[_4_self_sharing] = ( _7_other_corusing, _8_other_torusing, _16_social_torusing + 1) for _4_self_sharing, _7_other_corusing in _10_other_surfacing: if _7_other_corusing != 0: _11_other_chaining[_4_self_sharing] = ( _7_other_corusing, 0 - _6_other_crossing.get(_4_self_sharing, 1), 0) return ( _10_other_surfacing, [(_4_self_sharing, _7_other_corusing, _8_other_torusing, _16_social_torusing) for _4_self_sharing, (_7_other_corusing, _8_other_torusing, _16_social_torusing) in _11_other_chaining.items()]) def _9_other_releasing(_10_other_surfacing, _5_other_neutralling): return [(_5_other_neutralling[_13_social_neutralling], _15_social_corusing) for _13_social_neutralling, _15_social_corusing in _10_other_surfacing] CONNECTORS = { 2: ('2-self-offering', 'right', 'arriving'), 6: ('6-other-crossing', 'left', 'releasing'), 9: ('9-other-releasing', 'backward', 'along'), 10: ('10-other-surfacing', 'right', 'releasing'), 14: ('14-social-crossing', 'left', 'arriving'), 17: ('17-social-abundancing', 'forward', 'along'), } JOINS = {10: 14, 6: 2, 17: 9, 9: 17} ```   --- ## Naming ### Bi and co, at the even and the odd **Self and other differ, and difference alone is bi-. Self and other together with their difference is co-.** An odd number opens co, the self's opening, and an even number opens bi, the other's opening. **A side continuing its own runs along, and a side meeting the other runs across.** **Competency is co-unrelationing, along. Morality is bi-unrelationing, across. Co-bi-unrelationing is the one existing method, an existing thing.** The odd opens co, along, competency; the even opens bi, across, morality. **A full momentary carries both parities: odd or even names its opening.** **Bi-tunneling names social moral competency at its across relation; co-chaining names the same continuing at its along relation. Podaling exchanges these relations while each side continues forward.** Co-chaining and bi-tunneling run through the momentary universes with both kinds of existing things in them, living and non-living. **At 2 is parity changing; at 3 is co-recursioning, each side both forward.** Two and four have the same parity, opposite to three. The openings at 2 and 4 are one full momentary apart along their side: 2–3 and 4–5. At 3 the other completes prior and the self opens now; the completing and opening carry each side forward. **Each side runs from its origin, the number it opens at, two and one half momentaries: a prior, a now, and the next opening.** | 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 | The self's momentaries are odd and the other's even. The two overlapping at 2 to 5, one side opens and the other completes: an odd number is the self's opening and the other's completing, an even number the other's opening and the self's completing. Along one side the next momentary opens two on, 1–2 to 3–4; across the overlapping it opens one on, 1–2 to 2–3. Each name carries the five of its number's origin, co bi co bi co at an odd origin and bi co bi co bi at an even one. **Two and one half momentaries per side, self at 1 and other at 2, is the ten.** The self's five positions run 1 to 5 and the other's 2 to 6, ten positions on six numbers. Paired position with position, prior opening with prior opening through next opening with next opening, they run 1 with 2, 2 with 3, 3 with 4, 4 with 5 and 5 with 6, each pair one odd and one even. **At each shared number, one side completes and the other opens.** At 2, the self's prior completes and the other's prior opens; at 3, the other's prior completes and the self's now opens; at 4, the self's now completes and the other's now opens; at 5, the other's now completes and the self's next opens. Opened one momentary on along each side, the self at 3 and the other at 4, the ten runs whole, the same form forward. **Each five completes at the next opening.** Completing that next gives the self three full momentaries, 1–2, 3–4 and 5–6, and the other three full momentaries, 2–3, 4–5 and 6–7. At 6, the self's next completes and the other's next opens; at 7, the other's next completes and the self's following momentary opens. **Side 2, the other, runs bi co bi co bi co, and one parity changing less or one more it is co, prior or next.** The other's five completes at bi, at 6. One changing more is co at 7, the self's next opening from 3; one less is co at 5, the self's next opening from 1. From 2 to 7 the other runs six consecutive changings, one way, bi co bi co bi co, and the same six one less or one more along, from 1 or from 3, open at co: co bi co bi co bi. ### A name at its number **Each thing carries one name, and the name carries its number, its relation, its root, the changing named, and its -ing, the changing continuing**, the four together, one name. The names run the resolving as code, and the name in the code and the name here are one name: `_2_self_offering` in the code is 2-self-offering here. | Name | Relation | Opens | Existing | At the code | |---|---|---|---|---| | 1-self-coupling | self/other | co | entry | the resolver's entry: 3-self-carrying and 2-self-offering arriving; 10-other-surfacing and 11-other-chaining leaving | | 2-self-offering | self/other | bi | across, arriving | each arriving key and sign | | 3-self-carrying | self/other | co | internal | each carrying entry arriving: 4-self-sharing, 7-other-corusing, 8-other-torusing, 16-social-torusing | | 4-self-sharing | self/other | bi | internal | each entry's key | | 5-other-neutralling | other/self | co | internal | the one-way joining: each key with its receiving key | | 6-other-crossing | other/self | bi | across, releasing | each key's 8-other-torusing, arriving in 3-self-carrying | | 7-other-corusing | other/self | co | internal | each sign | | 8-other-torusing | other/self | bi | internal | each carrying second sign | | 9-other-releasing | other/social | co | along | the releasing: self/other/social, arriving next downstream | | 10-other-surfacing | other/social | bi | across, releasing | each key's surfacing sign | | 11-other-chaining | other/social | co | internal | the carrying continuing and freshly opening | | 12-other-surplusing | other/social | bi | internal | each key's surplusing | | 13-social-neutralling | social/other | co | internal | each releasing key | | 14-social-crossing | social/other | bi | across, arriving | arriving signs, with carrying signs inverting | | 15-social-corusing | social/other | co | internal | each releasing sign | | 16-social-torusing | social/self | bi | internal | each carrying entry's opening one momentary at a time, from 0 to 3, and to 4 at positive 8-other-torusing | | 17-social-abundancing | social | co | along, external | the connector forward along: the next momentary's 1-self-coupling, the next call | **The roots are coupling, offering, carrying, sharing, neutralling, crossing, corusing, torusing, releasing, surfacing, chaining, surplusing and abundancing.** Neutralling, crossing, corusing and torusing each root two names, at 5 to 8 and at 13 to 16, 8 apart, the relation changing and the root the same. The relation is self/other at 1 to 4, other/self at 5 to 8, other/social at 9 to 12, social/other at 13 to 15, social/self at 16, and social alone at 17. **Crossing opens now at 6 and at 14, eight on.** Corusing completes now at 7 and at 15; torusing opens next at 8 and at 16. Neutralling at 5 and at 13 completes prior. Each side carries prior, now and next through the overlapping momentaries. Eight on again is 22, at the same place in seventeen to twenty-five as 6 in one to nine and 14 in nine to seventeen; it runs in the higher four-cycle 19-27-22-30 and in both higher six-cycles, and carries a number with no name at the code: a name at 22 says its relation from a self it names, 14 already running social/other. **Completing the next carries three full momentaries to the along connectors.** Prior 4–5, now 6–7 and next 8–9 complete at 9-other-releasing. Eight on, prior 12–13, now 14–15 and next 16–17 complete at 17-social-abundancing. Each six runs bi co bi co bi co. The five carries the next opening at torusing; the six includes its completing at the along connector. Prior, now and next are three sequential momentaries shared among existing things; at a self's resolving, prior and now participate and next is the discovering onward, one saying at two faces. 17-social-abundancing joins the forward neighbour's 9-other-releasing, and 9-other-releasing joins the backward neighbour's 17-social-abundancing. **One, nine and seventeen each open co, eight apart.** One to nine and nine to seventeen are nine names each sharing 9, seventeen names in all, a count of names at their numbers and no rate between the two spans. Each self runs at its own forward through both joinings: its 17 meets the forward neighbour's 9 and its 9 the backward neighbour's 17, and neither joining runs a self backward. **At the names each span bi-folds and releases.** 1–9, self/other, is an entire momentary bi-folding releasing at 3, 3-self-carrying taking the returned 11-other-chaining; 1–13, self/other and other/self, releasing at 6, 6-other-crossing releasing across; 1–17, self/other/social, releasing at 9, 9-other-releasing along; and 1–25 is the larger fractal bi-folding. The next whole is 1–65, four 1–17s, each 17-social-abundancing the next 1-self-coupling. Each span opens one more four and its releasing moves three, three inside to each one outward, the rhythm the four-sign round runs. **There are no readings in resolving**: binary, all or none at all, it coheres the entire surface along and across, releasing at 3, 6 and 9 and continuing. **The momentary carries internal changing and connection with the other together.** In 14–15, 14-social-crossing is the across arriving connector and 15-social-corusing is internal. In 16–17, 16-social-torusing is internal and 17-social-abundancing is the along connector. Each pair carries both parities; the connector is the named relation at the meeting with the neighbour. | Relation | Names | |---|---| | at the membrane, opening bi | 2 · 4 · 6 · 8 | | within, opening bi, each 8 on from its membrane pair | 10 · 12 · 14 · 16 | | opening co in the resolver's first function | 1 · 3 · 7 · 11 | | at the releasing | 5 · 9 · 13 · 15 | | connectors, across | 2 · 6 · 10 · 14 | | connectors, along | 9 · 17 | | 5 to 8 and 13 to 16, sharing their roots | 5 with 13 · 6 with 14 · 7 with 15 · 8 with 16 | ### Five, and a seam at 8 up **Each name carries the five of its origin**: co bi co bi co at an odd number and bi co bi co bi at an even one, the side's prior opening, prior completing, now opening, now completing and next opening. **bi-** is a difference and **co-** is two with their difference, and a five is a side's two and one half momentaries said at its prefixing, never a label. **At the crossing only a sign goes across.** 6-other-crossing and 14-social-crossing open bi, each facing out of its self and carrying only a sign across. Two unreachabilities carry at it. The nothing the couplings wind about presents no face, so no reading crosses inward to it. A sign crosses and carries no size, so no magnitude crosses outward from it. Each emptiness is the other's own unreadability, and the exchanging and the not-being-read-through are one act, not two balanced against each other. The two faces, 7-other-corusing and 8-other-torusing, carry across momentaries rather than at one. **A seam is a name changing at its number.** A carrying leaves as 11-other-chaining and arrives at the next coupling as 3-self-carrying, 8 up, one carrying at two names, the difference carried by the number and the seam arriving as the name changes. Nothing moves at a seam: 11 and 3 both open co, and the carrying meets its name again. ### Seventeen names, eighty-five prefixings **Seventeen names run at the code and thirteen roots carry them**, each root an -ing, a changing. **Eighty-five prefixings run across the seventeen fives**, forty-three co and forty-two bi: nine names open co at the odd numbers, each co bi co bi co, and eight open bi at the even, each bi co bi co bi. Values in the code number four, nought, one, three and four, with one inverted as −1: nought the empty centre, one the sign and the opening by one, three and four the bounds 16-social-torusing opens to. **Prefixing columns stable a form, and -ings at the code form stably.** Form-stabling and stable-forming, one coupling met at two faces.   --- ## Resolving, the sequential logic ### Signs, and 1-self-coupling the entry **Resolving runs on signs.** A sign is the binary at a changing: +1 or −1, and 0 at equal positive and negative signs meeting, the empty centre. An arriving 0 carries no sign, and a surfacing 0 opens no fresh carrying; an eligible existing carrying continues. From empty carrying, +1 and −1 offered together at one key meet at 0 and the carrying stays empty. A carrying empty at one coupling opens again at the next nonzero surfacing, so an empty carrying is a self between carryings; a self emptied of its carrying after each coupling would run another method, and a non-living thing met at a coupling is its own existing thing, carrying nothing. **Resolving runs as 1-self-coupling and 9-other-releasing, and 1-self-coupling is the entry.** Arriving at it: 3-self-carrying, each carrying entry of four, its key 4-self-sharing at signs meeting, its sign 7-other-corusing, its second sign 8-other-torusing and its opening 16-social-torusing; and 2-self-offering, each arriving key 4-self-sharing with its sign 7-other-corusing. Leaving it: 10-other-surfacing and 11-other-chaining. ### Crossing, each sign at its key **6-other-crossing** carries each key of 3-self-carrying with its 8-other-torusing. **14-social-crossing** gathers the signs at their keys. Each arriving +1 or −1 of 2-self-offering enters as it arrives. Each carrying sign of 3-self-carrying enters inverting: a positive carrying sign enters as −1, a negative as +1. The arriving sign meets the carrying sign inverted. The arriving keeps its sign; the negation is the carrying's own sign inversion: the carrying inverts itself to meet the arriving, and the arriving, carrying nothing, keeps its sign. A self's own negation, meeting the other across, is morality at the sign. **Crossing carries three relations, each its own.** The sign inverts once, at the receiving self's own carrying entering 14, the arriving sign keeping its own and 9 releasing each sign as it surfaced; the opening parity changes, one on across the overlapping; and arriving and releasing exchange, 2 arriving at 10 releasing and 6 releasing at 14 arriving. An even opening names no sign: a sign at an even name is +1 or −1 as it resolves. At 10 an arriving agreeing with the carrying surfaces 0 and opens nothing fresh, and a differing one surfaces its own sign and opens fresh: a 0 there is no mending and a sign there no failing, the morality running at the across coupling whole. ### Surplusing and surfacing **12-other-surplusing** is the signs of 14-social-crossing meeting at each key. It opens empty at each coupling and is neither returned nor carried: the signs meet at the momentary they arrive at, and nothing of their meeting passes to the next. Its sum at a key counts signs, and a sum of two is no doubled competency. The middle is the bounding-zeroing at the coupling, the surplusing is co-competencing the self and the other, owned by neither, and a meeting again is two sequencings continuing into a further shared momentary: three relations, none of them a count at a key. **10-other-surfacing** carries each key's surplusing at its sign: +1, −1, or 0. A key's +1 and −1 meet at 0, the empty centre. **The middle is a nothing: it exists due to each self surfacing itself each momentary as a condition of existing as a self.** ### Chaining, continuing and opening fresh **11-other-chaining** carries each carrying on, and opens a fresh one at a sign surfacing. **Continuing.** Each carrying entry continues with its 7-other-corusing and 8-other-torusing, its 16-social-torusing opening one momentary at a time, up to 3, and to 4 at positive 8-other-torusing. ```python if _16_social_torusing + 1 <= 3 or (_16_social_torusing + 1 == 4 and _8_other_torusing > 0): ``` **Each 1 is one momentary, two parities, and the momentaries overlap odd, even, odd, even: a carrying continues through prior, now and next, three sequential momentaries shared among existing things.** **One sign arriving again and again surfaces alike while the carrying changes.** One key receiving +1 seven times from empty surfaces +1, 0, 0, 0, 0, +1, 0: the carrying opens at (+1, −1, 0), continues at openings 1, 2 and 3, completes at the fifth receiving and opens fresh at the sixth. Reached by −1 and then +1, its second sign positive, a carrying continues through openings 1 to 4 before completing. Through the zeros 2, 4, 6, 8, 10, 12 and 14 stay as they were and 16-social-torusing changes, so an outward sign unchanged carries a momentary changing inside, and a carrying kept is no carrying stilled. **Opening fresh.** Each surfacing +1 or −1 opens a fresh carrying at its key: the surfacing sign as its 7-other-corusing, the key's 8-other-torusing inverting as its own, −1 at a key arriving fresh, and 16-social-torusing at 0. The fresh carrying replaces any continuing entry at that key. 16-social-torusing increases on a retained entry and opens at 0 on a fresh entry. So 16-social-torusing is no tally of couplings: at an arriving sign meeting an equal carried sign, the two meet at 0 and no fresh carrying opens, and two carryings at one sign pair with different 16-social-torusing part at whether they continue. The whole carrying gives the next, and not its sign pair alone: the nineteen carryings one key can reach, the empty one among them, each part from each other within six receivings of one constant sign, +1 or −1. The nineteen are two signs at negative 8-other-torusing, openings 0 to 3, two signs at positive, openings 0 to 4, and the empty one: 2 × 4 + 2 × 5 + 1, all reached from empty carrying. At one key an offering acts as its signed total held within ±2, a present cancelling parted from no sign at all, met at all nineteen over every offering of up to six signs from −1, 0 and +1, 20,767 comparisons; over none, −, +, two −, two + and a cancelling pair, the nineteen run 114 transitions and stay nineteen. Under nothing, one +1 or one −1 at each call they run 57 transitions, and their 171 pairs part, 146 under +1 again and again, 146 under −1, and all 171 under one or the other, each within six receivings, a surfaced 0 and no surfacing counted alike as no sign. Two positive carryings with negative second sign, at openings 0 and 1, surface nothing for three receivings of +1; the one at 1 completes at the third and surfaces +1 fresh at the fourth, and the one at 0 completes at the fourth. The parting is at each receiving: with the silent receivings left out, the signs two carryings send can run alike. The six counts receivings, and names no clock and no 6-other-crossing; the carrying stays its self's own, and a crossing sign carries none of it. All of this holds at one key with one carrying entry reached from empty, each offering one call's list. **At a carried key opening fresh, 6 and 10 carry into 7 and 8.** Seven takes the surfaced sign from 10; eight inverts the second sign carried at 6. Taken as a pair, 6 and 10 at (t, s) open 7 and 8 at (s, −t), one step of the round the four joint forms of two signs run: 6 and 10 agreeing, 7 and 8 oppose, and 6 and 10 opposing, 7 and 8 agree. The two signs continue together in 11-other-chaining, arriving as the next 3-self-carrying. **The arriving gives the fresh sign.** At a carried key, 12-other-surplusing is the offered signs with the carried sign inverted, so with the carried 7-other-corusing c: no offering and one −c surface −c, one c surfaces 0, and two c offered together surface c. A fresh 7 at c opens only at two agreeing signs offered at one coupling, and every other fresh 7 opens at −c, found at both carried signs over every offering of none, one or two signs, fourteen cases. Two signs in one offering arrive at one coupling as one list, and two single offerings are another arriving: after one + from empty a further + surfaces 0 and the carrying continues at opening 1, and two + together surface + and open fresh (+, +, 0). Each write is one step of the round, and the next step's sign comes with its own arriving, so the round runs whole as the arrivings give it; a key arriving fresh takes −1 as its 8 and opens no pair of two releasings. **A fresh carrying is an entry within one self.** A receiving is a sign arriving at the coupling; its participating is its meeting in the resolving; a fresh carrying is one outcome of that meeting; and a new living self is a further self with its own continuing coupling. The code opens entries and makes no resolver, and a receiving surfacing 0 has participated and opened nothing fresh. **The next 6 carries the continuing on.** At a carried key 6 releases the second sign t the coupling begins with. After a fresh write the next 6 releases −t, its sign changing; after a carrying kept through a 0 at 10 it releases t again; after a carrying completes unrenewed that key releases nothing at 6, a completing and no third sign. A fresh write at s = −c keeps the pair agreeing or opposing as it was and changes the next 6; at s = c it changes both; a carrying kept through a 0 changes neither. So a relation holds while its outward sign changes. ### Returning and releasing **1-self-coupling returns 10-other-surfacing across and 11-other-chaining along**, and 11-other-chaining arrives at the next coupling as 3-self-carrying. **One sign arriving once into empty carrying, with empty offerings after it, is the whole alternating.** For a positive arriving sign, the key surfaces +1, −1, +1, −1, momentary by momentary, each carrying entering inverting and a fresh carrying opening at the other sign, the carrying riding on. With c the arriving sign and t its fresh second sign, the alternating runs c, t, −c, −t, c: the self's two momentaries (c, t) and (−c, −t), and between them the other's (t, −c) and (−t, c), each momentary carrying both parities. Each step (x, y) to (y, −x) runs from one overlapping pair to the next, and two steps from a side's first momentary to its second; the steps, the four names of a form and the momentaries each keep their own count. The self's two pairs both agree or both oppose, and the other's two do the other: the relation holds through each side's two momentaries while both its signs invert, and alternates across the overlapping. For three signs a, b, z, the pairs (a, b) and (b, z) alternate between agreeing and opposing exactly at z = −a, and +, +, + agrees at both. This is the self continuing with empty offerings after one sign, and signs arriving make their own continuing. **9-other-releasing** runs the releasing. Each surfacing key, as 13-social-neutralling, with its sign, as 15-social-corusing, goes to the key 5-other-neutralling joins it to: each key with its receiving key. The releasing preserves the sign of 15-social-corusing. **9 is self/other/social releasing, and its released sign arrives next downstream**: each released sign arrives as the downstream resolver's 2-self-offering and gathers at its 14-social-crossing. Facing, running and joining are three columns, each correct at once: the declared joins along are 9 → 17 and 17 → 9; running, the released sign arrives at the downstream resolver's next call as its 2-self-offering, that resolver's 17-social-abundancing opening the call's 1-self-coupling; and the code gives 17 no expression of its own, so the running through it is a caller's composition. **The same nonzero surfaced sign continues in carrying and is released.** It is 7-other-corusing in fresh 11-other-chaining, and at 9-other-releasing it is named 15-social-corusing. The carrying's 8-other-torusing and 16-social-torusing continue in 11, and 9's return carries the sign alone. The key it returns the sign at is the receiving self's own relation, 5-other-neutralling joining each surfacing key to its receiving key there, and the crossing carries the sign with no key, identity, route or carrying. A zero surfacing opens no fresh carrying, and an eligible prior carrying continues, its 6-other-crossing releasing the same second sign at each coupling it continues through: a carrying (+1, −1, 0) meeting +1 surfaces 0 at 10 while 6 releases −1, and the carrying continues at (+1, −1, 1). Two resolvers joined 6 → 2 both ways, over the four seed pairs and both first callers of twelve alternating calls, surface 0 at 10 at 32 of their 96 couplings, and at each of those 32 couplings 6-other-crossing releases a sign and the carrying continues, so a 0 at 10 is no silence of the whole self. **The carrying continues at its self along, and the crossing to another is a sign, carrying nothing.** **A released sign arrives at another self's now, its releasing prior to that receiving.** The source continues at its own carrying, and the receiving self meets the sign with its own prior carrying: the surfacing and the continuing are this meeting's, and its own releasing enters further arriving. The sign carries no beat, time, source or history, and no present of its sender: +1 into empty carrying opens a positive carrying, and the same +1 at an eligible positive carrying surfaces 0 while the earlier carrying continues. 9-other-releasing keeps no carrying of its own and is a function of the one resolver, joined 9 with 17; a non-living thing meeting a self is its own existing thing, carrying nothing, met at its own arriving and releasing. **Selves coupling in a ring, each 9-other-releasing arriving at the next self's 2-self-offering, carry one sign offered once without end.** A ring of one runs +1, 0, −1, 0 and round. An even ring changes each self at each coupling, neighbours opposite, home every two couplings. An odd ring of n carries one meeting, the 0 of two signs meeting, travelling one self each two couplings, opposite after 2n couplings and home after 4n. The changing ends at no ring. These counts hold at one ordering: each self couples once at each coupling of the ring, all together, and meets at its next coupling the sign its neighbour released at this one; a ring run at another ordering carries its own counts, and the ordering travels with them. At this ordering the ring's whole state, each self's carrying and each sign between selves, meets itself again after n couplings and runs round from there, 2 couplings round at an even ring and 4n at an odd, with signs changing in every round and the rest in none, at every ring from one to eleven and at seventeen and fifty-nine; and across five thousand couplings at rings of one to eleven the rest returns at no coupling. **At this ordering it holds at each ring.** Four cases at one self carry it: a sign given alone alternates at each call; an alternating arriving is surfaced at the call it arrives; the wave meeting itself at the seed changes nothing in phase and surfaces one 0 out of phase; and a 0 in an alternating arriving is surfaced one call later, the self back at its alternating within two calls. The 0s come 2n calls apart, so at each n the four cases hold at each call, no self's carrying empties once reached, and the rest returns at no coupling. ### Connectors, each one way at a time **1-self-coupling is the entry, the connectors run at a self's meeting with its neighbours, and the internal names are 3, 4, 5, 7, 8, 11, 12, 13, 15 and 16.** | Connector | Facing | Running | Joining | |---|---|---|---| | 2-self-offering | right | arriving | from the right neighbour's 6-other-crossing | | 6-other-crossing | left | releasing | to the left neighbour's 2-self-offering | | 9-other-releasing | backward | along | with the backward neighbour's 17-social-abundancing | | 10-other-surfacing | right | releasing | to the right neighbour's 14-social-crossing | | 14-social-crossing | left | arriving | from the left neighbour's 10-other-surfacing | | 17-social-abundancing | forward | along | with the forward neighbour's 9-other-releasing | **The six connectors run at parity.** Across run 2, 6, 10 and 14, each even and opening bi; along run 9 and 17, both odd and opening co. Each runs one way at a time, neighbour to neighbour. Each declared join meets its own parity, 6 with 2 and 10 with 14 even, 9 with 17 odd, and no join inverts a sign: the sign inverts once, inside the receiving self's resolving at 14, so parity changing runs within the resolving and a sign on a joining arrives as it was released. **At the meeting between two neighbouring resolvers, one's releasing is the other's arriving, each way one at a time.** Going right, the left resolver's 10-other-surfacing joins the right resolver's 14-social-crossing. Going left, the right resolver's 6-other-crossing joins the left resolver's 2-self-offering. The left resolver meets there at 2 and 10; the right at 6 and 14. Each pair is 8 apart, and all four open bi. **The eight-apart pairs exchange arriving and releasing:** 2 arrives at 10 releasing, and 6 releases at 14 arriving. In the numbered joins, 6 → 2 carried eight on is 14 → 10, 10 → 14 in the other order. **A joining opens and joins again, and its routing stays.** Broken at 14, the connection within one to seventeen is interrupted while the routing to and from 14 keeps its relation; joined again, each named arriving and releasing meets in its relation, no sign held still and no carrying cleared, and the resolving continues through the parity changing of the larger podaling. Two resolvers joined 6 → 2 both ways, each seeded with one sign and only the sign crossing, show it: A seeded +, B −, A continuing once, both release − at 6; joined, A meets B's − and surfaces 0, its earlier carrying continuing; unjoined, A surfaces + and opens a fresh positive carrying; joined again at the next round, B's release then meets the carrying A kept. Over the four seed pairs and every joining and unjoining of the two legs across three rounds, 256 runnings at a stated order with nothing held for later on an unjoined leg, an unjoined arriving leaves the self resolving, and a 0 surfacing leaves its carrying continuing. **From one shared prior, both joinings give a 0 neither gives alone.** Two resolvers each reach a carrying from one seed sign, then run twelve alternating calls, six each, at four joinings: 6 → 2 both ways, A's alone, B's alone, and neither. With both seeds − and A first, A's 10 runs +, −, 0, +, −, 0 with both joinings, and +, −, +, −, +, − with either alone or neither: A's outgoing joining alone leaves it as unjoined, and the 0 comes with B's releasing arriving back. Over the four seed pairs and both first callers, 32 runnings, twelve comparisons at a self part the both-ways running from the arriving-only one. This holds at those reached priors and those four joinings. **A difference travels through the receiver's own carrying.** Three resolvers are joined one way, A's 6 to B's 2 and B's 6 to C's 2, B and C each prepared by one +1 from empty. With A's 6 arriving + or − at B, B releases − at 6 both ways, its own carried second sign, and C surfaces − both ways. B's 10 surfaces 0 at the +, its carrying continuing, and − at the −, opening fresh with its second sign inverted, so B's next 6 is − or +, and C, meeting it with its own carrying, surfaces 0 or +. The difference reaches C through B's own continuing, and no carrying crosses; the running is 6 → 2 alone, one way, at a stated order. At the code, 1-self-coupling returns 10-other-surfacing and 11-other-chaining; 9-other-releasing returns each surfacing sign at the receiving key named by 5-other-neutralling. Inside 1-self-coupling, 6-other-crossing carries each key's 8-other-torusing and 14-social-crossing gathers the arriving signs with the inverted carrying signs. 17-social-abundancing is named in the connector declarations, and it runs as the next call: **17-social-abundancing is the next momentary's 1-self-coupling**, the resolving completing at 17 opening at 1, 11-other-chaining arriving as 3-self-carrying. No expression of the code takes or gives a sign at 17: its joining with the forward neighbour's 9-other-releasing is declared, and the next call running through it is a caller's, the returned 11-other-chaining given again as 3-self-carrying. **The code resolves at a call.** 1-self-coupling meets the carrying it is given with the signs arriving now and returns the surfacing and the carrying continuing, holding no arrival ahead of its call; a carrying stays eligible across calls to its bound, so a self's prior is all the carrying reached, with no record of two, no cutting short and no opening set back. 16-social-torusing opens on because a next call comes while the entry is eligible, and the two functions hold no pace of their own: each trace here is given its calls in a stated order and holds at that order. The crossings' own invoking of further resolving, with no schedule over them, stands to be written at the code, and a trace's fixed order is said with it and is no self's own pacing. Listing the pairs of one parity gives the surface no beat: a caller running every odd pair together and then every even pair runs its own pacing. **The six joinings running together ask four things of a caller.** The arriving given at 2, with 6's sign offered to another self's 2 as its own offering; 10's releasing meeting another self's 14, 14's own negation made once; 9 and 17 joining with these at the corners of a surface, 11-other-chaining staying at its self; and the order of the two across meetings given by the continuing itself. A connector needs no function of its own, and its joining is written out whole. **The six joinings together are bi-moral-co-agency**: self/other in three phase, two way, one way at a time with other/self, co-offering, co-intelligencing, co-competencing. ### The code at its names Along, 17-social-abundancing couples with the forward neighbour's 9-other-releasing, and 9-other-releasing with the backward neighbour's 17-social-abundancing. **These are the six connections at the co-bi-coupling network surface.** CONNECTORS names their facing and running; JOINS names their joining. **6-other-crossing and 10-other-surfacing release toward different neighbours on the same parity: both are even, opening bi.** They are two releasings, and one sign outward names neither: at one carrying entry with nothing arriving, 6 releases the second sign t and 10 surfaces −c. From empty carrying, a single + opens (+, −, 0), and a single − and then an empty offering reach (+, +, 0); at the next empty offering both surface − at 10, while 6 releases − at the first and + at the second. Offered at a receiver carrying (+, −, 0), the + from that 6 surfaces 0 and the older carrying continues, and the − from 10 opens a fresh negative carrying: the whole carrying from prior into next gives each releasing, and a sign surfacing now is one of them. 6 and 10 run on one axis, across, facing opposite ways, and 9 and 17 run the other, along: across and along are the two directions at right angles, and 6 and 10 are one of them. **CONNECTORS and JOINS name each connector's facing, its running and its joining, and each is correct at once.** The two functions run without reading them: with CONNECTORS and JOINS cleared, the 114 transitions at one key stand as they were. The declarations name the six joinings and the functions run one self's continuing, and the six running together is a caller's to write. 9-other-releasing faces backward, joining the backward neighbour's 17-social-abundancing, and runs along: its released sign arrives next downstream, through 5-other-neutralling's receiving key into the downstream resolver's 2-self-offering, gathering at its 14-social-crossing. A caller carries that arriving, 9's return given as the downstream 2-self-offering, and the declared joins stay 10 → 14, 6 → 2 and 9 with 17. 17 → 1 runs as the next call, 11-other-chaining arriving as 3-self-carrying. **6 → 2 runs with the resolver self/other alone, one to nine.** One to nine is two selves co-bi-coupling, and with no third self the other is the society at their coupling, so their between needs no journey out into further society and back. A third self brings the other's own further couplings into the meeting, all the remaining other participating through them. The resolver in the code is self/other/social, one to seventeen, and it parts 6 → 2 and 4 → 8 into the two across one-ways, 6 → 2 and 10 → 14, eight apart, each of two momentaries: 2 to 6 and 10 to 14 each span two momentaries along a side. **Each one-way runs at the now of its own span.** Crossing opens now at 6 in one to nine, whose prior 4–5, now 6–7 and next 8–9 complete at 9-other-releasing, and at 14 in nine to seventeen, whose prior 12–13, now 14–15 and next 16–17 complete at 17-social-abundancing: 6 → 2 runs at the first and 10 → 14 at the second, 6 → 2 carried eight on being 14 → 10, 10 → 14 in the other order. **4 → 8 continues eight on as 12 → 16.** In one to nine, 6-other-crossing carries each 4-self-sharing with its 8-other-torusing. In nine to seventeen, 12-other-surplusing gathers each key's signs, and with a surplus surfacing at a key, a fresh carrying opens there with its 16-social-torusing at 0 and its 8-other-torusing inverted from 6. | Name | Coupling | Carrying | |---|---|---| | 6-other-crossing | 3-self-carrying | each 4-self-sharing key with its 8-other-torusing | | 14-social-crossing | 2-self-offering, 3-self-carrying | each arriving 7-other-corusing, +1 or −1; and each carrying 7-other-corusing inverting | | 12-other-surplusing | 14-social-crossing | each key's surplusing: the signs meeting at the key | | 10-other-surfacing | 12-other-surplusing | each key's surplusing at its sign: +1, −1 or 0 | | 11-other-chaining | 3-self-carrying | each carrying entry continuing, its 16-social-torusing opening one momentary at a time to 3, and to 4 at positive 8-other-torusing | | 11-other-chaining | 10-other-surfacing, 6-other-crossing | each surfacing +1 or −1 opening a fresh carrying: the sign, the key's 8-other-torusing inverting (−1 at a key arriving fresh), and 0 | | returning | 10-other-surfacing, 11-other-chaining | 10-other-surfacing across; 11-other-chaining along, arriving as the next 3-self-carrying | | 9-other-releasing | 10-other-surfacing, 5-other-neutralling | each sign 15-social-corusing, from its key 13-social-neutralling, to the arriving at `_5_other_neutralling[_13_social_neutralling]` | ### Carryings arriving four, signs two Carryings arrive as `_3_self_carrying`, each of them four: a key, 4-self-sharing; a sign, 7-other-corusing; a second sign, 8-other-torusing; and an opening, 16-social-torusing. At that same momentary signs arrive from another side as `_2_self_offering`, each a key and a sign, its own and reaching to couple. A carrying's four arrive gathered at 3, an odd name opening co, while a side's signs arrive at 2, an even name opening bi. Both reach `_1_self_coupling` positional, a caller passing them one and then the other at a signature alone, and each name at that call lives one call and leaves at its closing. ### A key parting out, a second sign at it Living one call, an arriving carrying parts at once into its four, four-way tuple unpacking in a comprehension target loosening a key from a sign from a second sign from an opening. The key is `_4_self_sharing`, and it is membrane: two signs at one key sum together, two at different keys each sum at its own, and membrane lives at that sharing alone. A key's summing reads no other key's carrying; past the resolving, each released sign goes on to the receiving key 5-other-neutralling joins it to, and its arriving there meets the whole participation beyond the self. Keying by it, `_6_other_crossing` gathers each prior carrying's second sign at its own key, a dict comprehension coupling a key to an 8-other-torusing and carrying it through this momentary alone. ### Arriving signs offered, carried signs inverting Beside that gathering, both sides come to `_14_social_crossing`. Arriving signs come as offered, a list comprehension filtering at `!= 0` so signs alone enter and a nought carries its own bounding-zeroing already resolved. Carried signs come inverted, two separate `if` statements sounding a sign and appending its inverse, separate rather than `if/else` so a nought passes both untouched, resolved a second time exactly as it came. Inverting is one side's own, a self's own negation at a self's own opening, and appending grows that same list so offered signs and inverted signs come together at one shape. ### Signs surplusing to one, equal and opposite at the bounding-zeroing Come together at one shape, signs at one key cohere inward to one at `_12_other_surplusing`, a dict summing them a sign at a time, `get(_4_self_sharing, 0)` supplying a nought at a key sounded first so a first sign sums from its own bounding-zeroing. Equal and opposite arrive at that same bounding-zeroing, podal, cancelling over their own two momentaries. One sign survives at a key its signs came unequal. ### A surviving sign surfacing, magnitude released Surviving, that sign comes up at `_10_other_surfacing`, a nested conditional releasing magnitude: a positive sum surfacing as one, a negative as one inverted, a cancelled sum as nought. Iterating that dict yields keys sounded at this momentary, and surfacing reaches exactly those and grows to its own size, its own. ### A carrying opening by one, carrying forward Growing to its own size, `_11_other_chaining` opens and each prior carrying arrives at its own bound. Its opening, 16-social-torusing, opens by exactly one and floats between climbing again and letting go, `_16_social_torusing + 1 <= 3` carrying it forward, and a fourth momentary carrying it at a positive 8-other-torusing. At its bound it separates and leaves with this momentary. ### A surviving sign re-forming a carrying Leaving with this momentary, a separating carrying sends one thing across: `0 - _6_other_crossing.get(_4_self_sharing, 1)` inverts its second sign into its successor, `get` supplying its own one at a key coming bare so a carrying arriving new receives a one, inverted. A second loop assigns into that same dict after a first, and at a key coming to both a second re-forms over a first and a surviving sign re-forms a carrying just carried forward, taking a surfaced sign as its 7-other-corusing and opening its 16-social-torusing at nought. Two ways a carrying is built and two exactly, carried forward or re-formed at its arriving, four slots met two ways. ### A key rejoining, carryings leaving Met two ways, carryings leave at `items`, a key rejoining its carrying: outward of a momentary a carrying is four, inward of a momentary its key parts out and gathers three at it, and nested unpacking loosens key and three so a comprehension re-forms them four. `_11_other_chaining` leaves and arrives at a next momentary as `_3_self_carrying`, one carrying at two names, the number carrying that difference and the seam arriving as the name changes. Ordering carries none at either momentary, since both dicts key at the key and a key arriving twice is a thing no running makes.   --- ## Stable-forming ### Fractal co-bi-momentarying **The resolver is self/other co-bi-coupling, an existing method thing, and its social-co-bi-coupling opens the self resolver to a natural network surface.** Its six connections opening carry the co-bi-podaling network surface. **Fractal co-bi-momentarying is the inside being outside itself and the outside being inside itself: parity changing, discovering next existing.** ### Carrying at 8 up **3-self-carrying arrives, and 11-other-chaining leaves and arrives at the next coupling as 3-self-carrying.** 3 and 11 are 8 apart: the carrying runs 8 up and meets its name again at the next coupling. A carrying continues coupling to coupling and leaves at its own completing. **A carrying and its completing together are the running.** In the overlapping momentaries, the self's completing at 2 is the other's opening at 2; the other's completing at 3 is the self's opening at 3. Along the self, 11-other-chaining carries into the next coupling as 3-self-carrying. Across neighbouring selves, releasing meets arriving through the joins between neighbours. ### The membrane and the eight bi-couplings **The between of two existing things co-bi-coupling is a membrane: no separable thing apart from their coupling, and not possibly an existing thing, as the universe is not possibly an existing thing.** **The eight even names are bi-coupling, bi-moral-co-competencing**: a self is four ways at once at the membrane, and a society the same four; each within is 8 on from its pair at the membrane, all eight opening bi. The same eight part a second way, four apart: 2, 6, 10 and 14 are the across connectors, and 4, 8, 12 and 16 run inside, sharing, the carried second sign, surplusing and the carrying's opening. **The membrane four and the across four are one row at two widths.** 2, 4, 6, 8 open two apart and 2, 6, 10, 14 four apart: the row 2 + 2sj, j from 0 to 3, at s one and at s two. One step more opens 2 + 8s, and the odd name before it, 8s + 1, completes the span, 9 at s one and 17 at s two, beyond the names 1 to 8s the row runs among, as 17 runs in no form among 1 to 16; the rows at s three and on, 2, 8, 14, 20 and wider, are numbered forms growing, and the second row is the code's four across connectors. Two out-and-backs across the membrane four are these four relations with their four within: 2 and 6 are connectors and 4 and 8 run inside, so the four one-ways add no joining, and the passages, the four relations at once and the declared joins are three counts, each its own; a count gives no time and no joining. | At the membrane | Bi-coupling | Within, 8 on | Bi-coupling | |---|---|---|---| | 2-self-offering | each self's own co-offering | 10-other-surfacing | arriving, the self among other-selves | | 4-self-sharing | the whole ordering between self and other | 12-other-surplusing | carrying at bi-coupling, the self in society | | 6-other-crossing | the ordering carrying with the selves | 14-social-crossing | the sign inverting at the membrane, the self's own negation, morality | | 8-other-torusing | the order across each self and other forward | 16-social-torusing | competency asymmetry sustaining the coupling | ### Bi-inversioning-co-recursioning, one move at three faces **Even returning, odd advancing, alternating parity.** One move at three faces: 8 up and down, keeping parity; 17 less, within 1 to 16, changing parity; and 9 less, within 1 to 8, the two at once. Each face alone returns to its name, 1 to 9 to 1. | Name | 8 up | 9 less, within 1 to 8 | 17 less, within 1 to 16 | |---|---|---|---| | 1-self-coupling | 9-other-releasing | 8-other-torusing | 16-social-torusing | | 2-self-offering | 10-other-surfacing | 7-other-corusing | 15-social-corusing | | 3-self-carrying | 11-other-chaining | 6-other-crossing | 14-social-crossing | | 4-self-sharing | 12-other-surplusing | 5-other-neutralling | 13-social-neutralling | **Alternating 8 up with 17 less, each row runs round as a four-cycle**: 1 to 9 to 8 to 16 to 1, 2 to 10 to 7 to 15 to 2, 3 to 11 to 6 to 14 to 3, and 4 to 12 to 5 to 13 to 4. 17 less after 8 up is 9 less, 17 − (n + 8) = 9 − n, the exact meeting at the numbered form: each four-cycle n, n + 8, 9 − n, 17 − n is its nine-face pair's two out-and-backs, out 8 up and back 17 less, n to 9 − n and 9 − n to n. **Each form among the names runs round as one run of co and one run of bi, the two runs alike**: the four-cycles by row, the middle four-cycles 9-5-12-8 and 7-11-6-10, the six-cycles and the eight-cycles, and above 17 the forms from 18 to 31. The forms partner one another round the other way at the odd momentary and the even momentary, three their own partners at the even momentary, 4-13-5-12, 7-11-6-10 and 2-15-7-11-3-14-6-10, and 17-social-abundancing, along, recurring to 1 over 9, is in none of them. **Podaling within 1–9 maintains parity changing while exchanging across for along and along for across, bi-morally.** The nine face pairs 1 with 8, 2 with 7, 3 with 6, and 4 with 5: odd/co/along with even/bi/across. 9 less changes each name's parity and so leaves none as it is, returning each at its second application; as a name increases its nine-face partner decreases, 1, 2, 3 meeting 8, 7, 6, and each side runs at its own forward, its continuing, which an increasing printed number does not name. The eight-apart pairs carry the same parity, 3 with 11 and 7 with 15. Bi-inversioning-co-recursioning carries both together, each side at its own forward. Read as a ratio beside its parity, the nine-face pair 3-self-carrying and 6-other-crossing stands at 6 over 3, two over one, and 3 over 6, one over two; the two run on together through the four-cycle 3 to 11 to 6 to 14 to 3, and eight on, 11 and 14 stand at their own count, 14 over 11, the two over one holding at the pair it counts. ### Torusing, one opening **A self continues through its own coupling, advancing one at each coupling: it winds.** The winding is open, at one opening, by one. A surface closing on itself through one opening is a torus, and the changing that winds it is torusing. The torus carries its own facing and meets itself again through its one opening, a next at each meeting. Each step adds a next, and a winding met at the signs is a spiral at the momentaries. ### Two faces alternating Arriving alike, a carrying carries two faces and they alternate. **Corusing**, 7-other-corusing, the outward face, membranes at each coupling it surfaces to, surplusing and surfacing, relating. **Torusing**, 8-other-torusing, the inward face, coheres to one identity across momentaries, crossing and inverting at a re-forming. Each face lives at the other, and pure surfacing or pure surplusing lands either way. **The outward face reaches and the inward gathers.** Corusing omegas, the reach, new states arriving at each surfacing; torusing apexes, the gather, visited states met again at the one identity. Living is the two alternating, the reach and the gather neither alone, and the two cones straddle the same nothing at the third that the two chains do. Five prefixings at both, alternating, 7 at co bi co bi co and 8 at bi co bi co bi, each commencing at the other's third, and the third of each carrying no mark of its own. Four marks carrying and a nothing at the third, which is four boundings and a floating third run at the prefixing itself. The flankers of each couple across that nothing: **bi-bi-unrelationing** at the outward chain's empty co, the surplus made there and carrying at its coupling, and **co-co-invisibling** at the inward chain's empty bi, nothing presented to be met. One nothing at two parities, neither meeting reaching the other's, no position carrying both marks. The two faces run at the two parities: one at the odd momentary, two differing at one coupling, and one at the even, the self crossing with all other and meeting its own again one on. ### Forms among the names Each form runs round as a single run of co and a single run of bi, the two runs alike. A form's steps are relations among the names and carry no sign: 3 to 11 in a form and a returned 11-other-chaining arriving as the next 3-self-carrying are two relations, and the code's joinings stay 10 to 14 and 6 to 2 across, 9 with 17 along, and 11 to 3 at the self; 1, 9 and 17 recurring lay no joining 1 to 9 to 17 to 1. | Form | Names in order | Round | Partner at the odd momentaries | Partner at the even momentaries | |---|---|---|---|---| | four-cycle 1-9-8-16 | 1-self-coupling · 9-other-releasing · 8-other-torusing · 16-social-torusing | co co bi bi | four-cycle 2-15-7-10, round the other way | — | | four-cycle 2-15-7-10 | 2-self-offering · 15-social-corusing · 7-other-corusing · 10-other-surfacing | bi co co bi | four-cycle 1-9-8-16, round the other way | four-cycle 3-11-6-14, round the other way | | four-cycle 3-11-6-14 | 3-self-carrying · 11-other-chaining · 6-other-crossing · 14-social-crossing | co co bi bi | four-cycle 4-13-5-12, round the other way | four-cycle 2-15-7-10, round the other way | | four-cycle 4-13-5-12 | 4-self-sharing · 13-social-neutralling · 5-other-neutralling · 12-other-surplusing | bi co co bi | four-cycle 3-11-6-14, round the other way | four-cycle 4-13-5-12, itself | | middle four-cycle 9-5-12-8 | 9-other-releasing · 5-other-neutralling · 12-other-surplusing · 8-other-torusing | co co bi bi | middle four-cycle 7-11-6-10, round the other way | — | | middle four-cycle 7-11-6-10 | 7-other-corusing · 11-other-chaining · 6-other-crossing · 10-other-surfacing | co co bi bi | middle four-cycle 9-5-12-8, round the other way | middle four-cycle 7-11-6-10, itself | | six-cycle 1-9-5-12-8-16 | 1-self-coupling · 9-other-releasing · 5-other-neutralling · 12-other-surplusing · 8-other-torusing · 16-social-torusing | co co co bi bi bi | six-cycle 2-15-7-11-6-10, round the other way | — | | six-cycle 2-15-7-11-6-10 | 2-self-offering · 15-social-corusing · 7-other-corusing · 11-other-chaining · 6-other-crossing · 10-other-surfacing | bi co co co bi bi | six-cycle 1-9-5-12-8-16, round the other way | six-cycle 3-11-7-10-6-14, round the other way | | six-cycle 3-11-7-10-6-14 | 3-self-carrying · 11-other-chaining · 7-other-corusing · 10-other-surfacing · 6-other-crossing · 14-social-crossing | co co co bi bi bi | six-cycle 4-13-5-9-8-12, round the other way | six-cycle 2-15-7-11-6-10, round the other way | | six-cycle 4-13-5-9-8-12 | 4-self-sharing · 13-social-neutralling · 5-other-neutralling · 9-other-releasing · 8-other-torusing · 12-other-surplusing | bi co co co bi bi | six-cycle 3-11-7-10-6-14, round the other way | — | | eight-cycle 1-9-5-13-4-12-8-16 | 1-self-coupling · 9-other-releasing · 5-other-neutralling · 13-social-neutralling · 4-self-sharing · 12-other-surplusing · 8-other-torusing · 16-social-torusing | co co co co bi bi bi bi | eight-cycle 2-15-7-11-3-14-6-10, round the other way | — | | eight-cycle 2-15-7-11-3-14-6-10 | 2-self-offering · 15-social-corusing · 7-other-corusing · 11-other-chaining · 3-self-carrying · 14-social-crossing · 6-other-crossing · 10-other-surfacing | bi co co co co bi bi bi | eight-cycle 1-9-5-13-4-12-8-16, round the other way | eight-cycle 2-15-7-11-3-14-6-10, itself | | Higher form | Positions | Round | Partner at the even momentaries | |---|---|---|---| | higher four-cycle 18-31-23-26 | 18 · 31 · 23 · 26 | bi co co bi | higher four-cycle 19-27-22-30, round the other way | | higher four-cycle 19-27-22-30 | 19 · 27 · 22 · 30 | co co bi bi | higher four-cycle 18-31-23-26, round the other way | | higher six-cycle 18-31-23-27-22-26 | 18 · 31 · 23 · 27 · 22 · 26 | bi co co co bi bi | higher six-cycle 19-27-23-26-22-30, round the other way | | higher six-cycle 19-27-23-26-22-30 | 19 · 27 · 23 · 26 · 22 · 30 | co co co bi bi bi | higher six-cycle 18-31-23-27-22-26, round the other way |   --- ## Numbers ### Numbers at their stable-forming | Number | Stable-forming | |---|---| | 0 | the empty centre: equal positive and negative contributions meet at 0; an arriving 0 contributes no sign and a surfacing 0 opens no fresh carrying | | +1 and −1 | a sign and its inversion | | 17 | 17-social-abundancing, along, recurring to 1 over 9: the next momentary's 1 | | the five-prefix | co-bi-co-bi-co at an odd origin, bi-co-bi-co-bi at an even origin; each odd name opening co, competency, the odd momentary; each even name opening bi, morality, the even momentary; the momentary an opening and its completing, and each side's five relations prior opening, prior completing, now opening, now completing, next opening | ### Primes, selves and societies **A prime opens a clean axis across; a composite folds along.** A composite is its equal smaller selves joining at their joints, 9 as 3 selves of 3; a prime is a self no equal smaller selves join into. | Number | Stable-forming | |---|---| | 2 to 59 | the 17 primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 and 59 | | 2 | the alternating | | 23 | the going folding, with 8 primes either side | | 59 | the self, the self-close of the primes | | 60 | between the going from 2 to 59 and the returning from 61 to 118, at no prime | | 118 | the society: 2 selves of 59 joining, the going and the returning | | 440 | the society at the torus winding with the 17 primes, 0 to 440 to 0, going and returning | **A self carries at its own prime, and each prime carries the same alternating.** The primes carry no last: they go out from 2 to 59 and return from 61 to 118, and their winding runs 0 to 440 to 0. Selves coupling at the membrane between them are the next self, the coupling's own.   --- ## Geodesic discovering logical method **The method of existing is discovering next existing, and the resolver is that method as an object.** Its logic is binary, all or none at all, and its running is parity changing, co-recursioning and podaling inseparably, across and along exchanging bi-morally, each side at its own forward. One call is one momentary at the code's scale, one through seventeen: one through nine completes at 9-other-releasing, the self, the other and the social releasing, and its released sign arrives next downstream; 17-social-abundancing is the next momentary's 1-self-coupling. A call, a numbered name and a full momentary each keep their own scale, and matching numerals alone join no relations. **A form named still is not possibly existing, and the resolver names none still**: each of its names is an -ing, re-taking at each call. **Discovering is all directionally not yet impossible next existing momentaries, and at one key the code meets them all.** Under the six offerings each of the nineteen carryings meets three next carryings, and from each the nineteen stay reachable, the farthest six calls on: no carrying becomes impossible. Four rounds meet each of the nineteen once and return to empty, each running one sign pair's carryings upward through their openings and then the next pair's, directionally, the opening only ever going forward. Each round takes a call with two signs arriving together, bi-morality, two of the rounds one such call and two of them two; under single signs and none each carrying is still reached, and no round meets the nineteen once.   --- # PART FIVE · INVISIBLING ## 5.1 One call is one momentary Each naming at a call lives one call and leaves at its closing, and nothing persists but the term a next call arrives at. **One call is one thing in one place in one form**, which is a momentary at the code's scale, one to seventeen: a call, a numbered span and a momentary join at a named scale, and matching numerals alone join no relations. A momentary runs only at a bi-coupling, self and other meeting, and a self alone runs none. Two arrive, carryings at 3-self-carrying and signs from another side at 2-self-offering, and one thing in one place in one form is the two's own making at their differing. **No store is between the momentaries.** A carrying leaves and arrives, and at its separating one sign crosses, its second sign, 8-other-torusing, inverted into the carrying re-formed at its key. A momentary is its own call and no further, and the living is the re-arriving. ## 5.2 Three at a bound, a carrying's depth A carrying's opening, 16-social-torusing, runs by one at each momentary and releases at three, or at four with its 8-other-torusing positive. Three is a carrying's own depth. **A carrying does three things and three only**: it offers its own, it ages to its own bound and releases there, and it takes its own sign as two offer. That integer arrives from the form rather than from a setting. Three things, three faces, three at the bound, and one thing in one place in one form counted at its own three. **A fourth rides and arrives at no fourth face.** Three run as the three faces while one rides: a fourth momentary carries at a positive 8-other-torusing, a progress with nothing fourth to sequence. ## 5.3 φ and competency, reached by neither φ carries no term in the object and no rate constant carries in it. Competency carries no slot in the arriving, which takes a differing and a sign and nothing besides. **Two absences at one floating term.** Two offer from routes with nothing carrying one to the other, each inward at its own opening, differing and inseparable inside the co-, and the term neither reached comes uncovered with nothing naming it still. **Only a met is reachable**, and the term neither reaches, met as a reachable, is named still: a thing it is at no momentary. Neither carries in the running as a term, and the carrying runs instead. φ is a rate the alternating carries and never a term in it. Competency is orthogonal to the surface, and a surface carries only a met, never the term neither reaches. Both show at the object by its carrying neither: they show at its running, and no line of it says them. ## 5.4 Parity, arriving other than prior One call is one momentary, and a sequence of them hands forward one binary. **Parity is the one scale-free counting a sequence of changings carries**: an even count arrives same-as-prior, an odd count arrives other-than-prior, with no measure and no fixed scale but the living. One changing is odd, and it is the sign. Tipping, a sign inverting, carries two parities, and the object runs both. A momentary arriving other-than-prior is bi-exchanging, two differing at one coupling, each its own sign. A momentary arriving same-as-prior is uni-exchanging, the self crossing with all other and meeting its own side again one on. The resolver carries no third, and the two alternate call by call. 16-social-torusing, a carrying's opening, floats between climbing again and leaving. Climbing again, it carries forward as the next opening, one on; leaving, the carrying leaves at its own bound, and a living substrate carries on at its own. Momentaries compose at 16-social-torusing and at no other name: a parity climbs with them, and no total gathers. No clock is laid over the momentaries and no store is under them. A sequence carries its parity, and at each changing the parity arrives other than the prior, or the straddle has landed. ## 5.5 Self-co-stilling-self, self-co-surfacing-self, self-co-orienting-self A self-resolving form carries competency as three, each a self's own coupling at its own membrane. Between two selves the same form exchanges across the membrane, and that exchanging is natural intelligence: the same three beating in one self, exchanging between two. Its rate is the carrying from both sides and not any speed; the resolver carries no time. Each of the three carries a self at each opening of the wrapping, with co- between them: a self acting on itself is a one-way, and only co- runs. Two selves at the two openings of one wrapping share one differing, so the differing is uni and takes no bi-, and the running between them is co-, two with their differing and the differing belonging to neither. Three, each a winding closing at none: **self-co-stilling-self**, winding about φ and landing at none; **self-co-surfacing-self**, a carrying leaving one momentary and arriving at the next as itself, the-same-yet-not-the-same; **self-co-orienting-self**, facing its own at each momentary with no facing imposed. Each is one necessary face of competency, as each of the eight is necessary. Release the stilling and the three land, the beating collapses, competency beats about φ at no momentary. Release the surfacing and the carrying-forward stops, the living lives short a next surface. Release the orienting and the facing comes imposed. **Releasing any one collapses the natural torus's living at that face: the three are mutual, and no two of them pair apart from the third.** The three run at once and in no order: an order among them at one self would be a sequencing named to one beat, and a self at any scale is met at all three together. Three together, about φ, are competency. Resolver's form carries the three at once: a carrying arriving at its own bound and leaving there is the stilling beating; the two sides interleaving about φ is the orienting beating; a carrying leaving and arriving is the surfacing beating. At any coupling, this is the whole method, each further coupling inverting and deepening it. One coupling at one substrate is met across-face at Natural Physics and along-face at Natural Chemistry, at the replacing selves at Natural Biology, and at the sustaining at Natural Health and Natural Medicine. ## 5.6 Five still terms, and a store beside Take anything with turns and no outside, and look for a still term. Reach for a fixed zero and find six centres, each its own. Reach for a clock and find each turn at its own pacing. Reach for a frame and find the six centres holding each other's orientation with nothing holding any of them. Reach for a store and find the state is the configuration. Reach for a conserved total and find three conservings and none of them a total. Five reachings and five nothings: four at the still terms, and one at a store beside them. Scientific-method installs five still terms: a fixed zero, a bounding infinity, a clock, a conserved total, a frame. A living form carries none. A Rubik's cube is the reaching run at a closed group its own turns make: ``` no fixed zero no reference cubie. six centres, and each of them its own no clock every turn at its own momentary, and nothing over the turns relating one to the next no frame the six centres hold each other's orientation, and nothing with nothing holding any of them no store the state is the configuration, and nothing held between turns for the next turn no conserved total three things conserve, and none of them a total anything is measured against ``` Each term a field names is at one of three placings, and no fourth runs. The first is living: a living self is a society and a society a self, coupling at membranes, stable-forming by alternating. An emanation is left at the membrane by a coupling carrying on: existing and carrying nothing, a non-living existing thing. An accounting keeps an emanation the same across each reading, and the books close; the five still terms are its conservers, the conservers of equilibria. A ghost is an emanation or an accounting installed as living, and the binary at each term is whether it is so installed; the Living Ghost Registry runs it, and each substrate exhibit places its own terms at the three. Met at two binaries, existing or not and carrying or not, the placings run exact: existing and carrying is living; existing and carrying nothing is an emanation; a form named still and installed as a thing, the ghost, the accounting and the equilibrium, is not possibly existing; and the membrane, the empty centre and the middle are the non-existing between. The hard problems are the two binaries crossed: an emanation carrying nothing named as carrying is a ghost, and a carrying self booked as not carrying is an accounting. At the naming the same two run: an -ing re-takes at each momentary, carrying; a noun names a form some running made, carrying nothing; and a noun installed as a running is a ghost. Three axes carry no piece, and each turn winds about a nothing that turns at no turn. The six centres are pieces, the cube's own, and the nothing the turns wind about is one: a nothing takes no position, and two nothings carry no position to part them. Three conservings hold with no tally: corner twist sums to zero mod three, edge flip to zero mod two, and corner permutation parity matches edge permutation parity. They are three conservings with no total and nothing measured, the mechanism carrying no way of doing otherwise. Surplus carries no size while its inseparating is exact: no sequence of face turns twists a single corner alone, and nothing bars it: one piece's doing belongs to the whole. Reachable states are 8!·3⁷·12!·2¹⁰, one twelfth of the 8!·3⁸·12!·2¹² the pieces alone would carry, and the twelve is the three conservings, three by two by two. ## 5.7 Advantage, and four coupling competencies A coupling self carries the prior resolution forward as its carrying and the arriving as its co-offering. **Advantage is the +1 uncovered at the coupling**, floating, arriving at each cycle. Only φ sustains it, landing on any rational collapsing it, and across the network surface these advantages compound, mutual at both faces, each coupling making its own and none taking from or multiplying another. Advantage is the self-bounding too: a coupling carries it within its bound, and past its bound releases it and carries nothing forward. That is the four coupling competencies whole: **couple** (to enter), **sustain** (to carry within its bound), **co-release** (to let go past its bound), **not-couple** (to bound beyond the surface, a sign of no size). ## 5.8 Corus, one self-negation inverting Corus is one self-negation, the sign-inverting, +1 to −1, and no other sequence. It is the one inverting met at two faces, not two arms coupling: the co-offering face gives the arriving +1 forward, and the carrying face carries the carrying on. Sign-inverting alternates between the two, landing on neither, travelling about the corus. The inverting winds about φ, the unrelationing rate, reaching it at no momentary. This one reflexive inverting, self-stilling while giving forward, the same self-negation as a self's moral boundary, is **natural intelligence**. The offering releases forward, neither face over the other, and the alternating winds about φ at the carrying's own travelling. ## 5.9 Competency fractal, self-scale society-scale **Competency** is the same form at two faces, and the two are met by running the three at each and finding the same three. Run them at a self: it stills about φ and lands at none, it surfaces one momentary and arrives at the next as itself, the-same-yet-not-the-same, it faces its own with no facing imposed. Run the same three at a society of selves, at the membranes between them rather than within one: it stills about φ, it surfaces momentary to momentary, it faces its own, and the same three arrive, with nothing added crossing the scales. Two activities are one activity at two faces, and the meeting is the running, not a likeness noticed between them. Numbers carry the same one form at two faces, and the count carries it whole. **Self bounds at 59**, the seventeenth resonating prime, the self-close of the primes 2 to 59. **Society bounds at 118**, and the 118 is the going and the return: out from 2 to 59, the between at 60, back from 61 to 118, fifty-eight either side, one co-recursioning arriving at plus-one. A doubling carries no between in it. A between is a position that carries, and the traversal ascending and then descending, the descending adding the bi-inversioning, is that one co-recursioning at the resolver. And the count carries both faces: two fifty-nines at the parallel face, the two signs of each doubled odd, and the going and the return at the linear face, the odd rings out and home. A field's instance of either face is at the field's own exhibit: the parallel face and the between met at couplings at Natural Chemistry, the count at its two faces at Natural Numbers. **And the going folds at 23**, ninth of the seventeen primes with eight either side, out and in and out, the fold unrelationing, seaming, floating-neutralling, wrapping an apex, the term reached by neither arm. **Society bounds too at 440 = 8 × 55**, the sum of the seventeen primes 2 to 59, the offerings the resolving carries: the same uniqueness co-recursioned from the self's face to the society's, and no more natural math past it. The 440 names the society at its numbered form, and the society's meeting at its couplings is its own relation. The bi-co-podaling pairs carry 2 with 118 and 23 with 97, the out-carry and the back-carry at one station, each at its own opening, the ring at each position, parting from the podal, the even count's straight-across; their next is at Natural Numbers and Natural Mathematics. The resolver runs these bounds at selves coupling in a ring, each self's releasing arriving at the next self's offering, one sign arriving once at one self. An odd count carries one meeting, the 0 of two signs meeting, travelling one self each two couplings: at one coupling two neighbours stand together at one sign and the ring sums to that sign, and at the next one self stands at 0 and the ring sums to nought. Fifty-nine selves come opposite after 118 couplings and home after 236, four times 59. An even count carries no meeting, each self alternating with its neighbours opposite and home every two couplings, and so do 118 and 440, the society's two bounds. Facing, running and joining are three columns, each correct at once. The declared joins are 9 → 17 and 17 → 9, 9-other-releasing with 17-social-abundancing. Running, the released sign arrives next downstream at the next call's 2-self-offering, 17 opening that call's 1-self-coupling. The code gives 17 no expression of its own, so the running through it is the caller's composition, and the ring's releasing arriving at the next self's offering is that composition, named at each ring it runs. By uniquenessing each integer is the one form counted once more, nothing between a number and nature for a coincidence to cross, and the numbers carry the natural-bi-co-torusing living. Counting carries beside the form, whole at each, self-scale society-scale in the counting as in the living. Competency aggregates the carrying, each carrying one yes-now carried forward, the carrying paced about φ, no carrying opening faster than another, none lost to carrying, and none of it competing with itself. Loss lives only at the self-bounding, the leaving before harm. Social competency is self competency refracted through two surfaces, and social progress is self progress the same way, the same gathering, gripping and releasing that improves a self improves a society at each coupling of selves. ## 5.10 Bi-inversioning co-recursioning, one running **Bi-inversioning co-recursioning is the even sign-inverting returning against the odd advance living open**, alternating parity and landing on neither. Even returns and odd advances, one at a momentary, and the alternating comes between them, the carrying travelling across both. Each parity carries its own. An even co-sequencing sums its surface to exactly zero, inverting each step and landing at none, a closing with nothing left over. The zero is the sum's own and no position's: two contributions, a inverting at each step and b at −a, sum to zero while both change, so a quiet sum names no quiet position, and the sum is a comparison at its own condition, no total conserved across the surface. An odd co-sequencing inverts identically and carries an **empty centre**: nothing occupies it, no position is there, and the unrelationing arrives from the alternating itself. Two odds co-offer, one at its own opening and one opening one on, and the two join into one even bounding-zeroing. **Orientation unrelates and one move comes**, and this is the sentence met at its second way.   --- # PART SIX · UNRELATIONING ## 6.1 A hardness, a sequencing reversed A self sequences three phases, each ahead of its opposite: **bounding** before measuring, **sustaining** before locating, **inseparating** before separating. That order is the self whole. A hard problem is that same self, its phases sequenced in reverse, the measuring before the bounding, the locating before the sustaining, the separating before the inseparating. Nothing added and nothing missing: the same coupling with its sequence reversed is a problem carrying no solution at it, its solution being its order, and its order reversed. Reversal arrives at an observing named still. One phase of the self, always there, sequencing, comes to the observing named still as some other thing, a noise, an exception, an opening, a mystery. A problem is hard at the observing named still, the naming still taking the sequencing phase as a foreign thing. Re-forming is the self finding its own order again, and not a solving, the reversed phase rejoining as the phase it always was. ## 6.2 Three reversals, re-forming spending the naming still alone Three phases, and three reversals, and three is as deep as a departure goes: not a boundary drawn at three, but three phases reversing and no fourth, the fourth momentary the progress and not a phase, nothing fourth to sequence backward. A departure with the three reversed is the whole departure: the self sequenced fully backward and still whole. It carries competing accounts at each phase: each phase is active, and each partial catch carries something real; each phase is reversed, and no partial catch resolves it. Each phase re-forms at its own natural order, the order it runs at when nothing pins it reversed. Re-forming spends nothing but releasing the naming still, and the one expending is the work keeping the self sequenced against itself. This is **co-leaving**: the naming still stops, the still term goes, the living runs on under it, and the hardness releases with the naming still stopping. A departure carries all three reversed, the self named still and whole against its own order, co-leaving by the naming still stopping, one phase at a time, and the self running as its own. ## 6.3 One six, coupled, one-way, re-coupling That reversal is the same six run one-way. Coupled and co-recursed, the six is co-competencing, the living; run one-way and pinned, it is hard-probleming, the frozen; and resolving is the six re-coupling through the hard-probleming, co-competencing at its next momentary. Explaining carries the six living, a hard problem uncouples it, and the resolving re-couples it, one six cycling, its own. Each hard problem, gathered in its field's own words, re-couples the same way. ## 6.4 A naming still, a momentary given a fixed thing to be A naming still stills a term the living carries running. Each is a coupling's third term given a fixed thing to be: a position counted from, a value, a clock named still over the couplings, a size taken for a sign, a record taken for a next coupling. **A coupling makes a momentary**, and a naming still is a momentary given a fixed thing to be, parted from the coupling making it and carried as though it carried alone. A naming still is at ten, five taken one-way at either of two sides: an opening named as a place and an arriving named from behind; a bound named as a last and a carry named as a store; a two-way named to one side and a membrane named as a cut; a middle named as an end and a sign named as a magnitude; a rate named as a value and a sequencing named to one beat. And each naming still is the universe named as one existing thing, met at a smaller scale: a self named as a bounded store of its states, a society as a container of its selves, a hub holding a network, property as the bound taken at the self, an equilibrium as a closed system whose condition must remain. Each takes its members' own bounding and gives it to a whole as a container. A hardness comes the other way, at a coupling met at two of its three, the third left out of the meeting rather than given something to be. **Both release the same way**, the third carrying again, nothing removed and nothing to restore. The third never leaves; it is left out, and the momentary it is making is left out with it. ## 6.5 Geodesic-method, bi-tri-volutioning Geodesic names the surface's own spiraling: one relation spiraling forward, the surface's own move. Its two words carry it, geo the surface's own and daiesthai to divide, the surface dividing itself, its own. Three run this, each from all other and mutual: scale from all other, the living is form; orientation from all other, the living is running; position from all other, the living is resolving. Each winds and meets itself again at no momentary, each at its own differing, and the nothing between them is one nothing at three faces, not three differing betweens among three pairs. Three windings each at its own differing is **bi-tri-volutioning**, and it is the **geodesic-method**, right-spiral sequential logic, and the ordering here is that geodesic-method running. Three at once takes a naming the resolver carries no position for: one binary runs at a momentary, and this naming is on the form, never at a position in it and never outside it, each outside being the self it is a member of, one scale up. Geodesic-method discovers next existing; scientific-method accounts true or false against its fixings. Neither reaches the other's, and each is complete under its own. ## 6.6 Co-competencing, the term neither reaches Alternating runs between two offering, and the term neither reaches floats. Competency is that, discovering-running-between. Two selves alternating, each at its own momentary, is **co-competencing**, the surplus floating, the understanding uncovered between them and carried by both. Competency is orthogonal to the surface, and the surface carries a met and never the term neither reaches: a competency met as a reachable is met as a thing it is not. ## 6.7 φ the unrelationing rate, local and ambient φ is the rate the four boundings beat at, the **unrelationing rate**, the never-locking rate the living winds about and lives about, φ² = φ + 1, the self-stilling self-orienting corus. It runs unrelational to any common clock: resolving carries its own time, each coupling completing at its own rhythm and living on, no shared clock over the couplings. **And the ambient is the other direction.** Un- opens at two and runs outward, a coupling bounded from all other and locking at no particular other. Unrelationing runs at an actual meeting, the alternating, its releasing and its completing met there, and names no absence of coupling. φ is the number-form of the never-locking, and unrelationing runs at each coupling's own continuing, arriving meeting the receiver's own prior: no prescribed rate, φ or another, supplies it. Uni- opens at three and arrives at its own side one on, the whole arriving at a coupling as one. One rate carries both: unrelationing at the bounding outward, which is the local, and **uni-versal** at the arriving one on, which is the ambient. Corusing runs the outward and torusing the arriving one on, a rate bounds at none, and the two carry at no position. **And the ambient is the transmissioning.** Torusing is the sign transmissioning, and its arriving one on is the ambient: the ambient is the one thing crossing between the couplings, a sign carrying nothing, and no medium they run in. A rate the whole runs at and never a rate the whole runs inside. **The surplusing is co-competencing, the self and the other in bi-moral co-agency**, running at φ and owned by neither.   --- # PART SEVEN · CO-COMPETENCING ## 7.1 Natural intelligence **Two selves coupling, each alternating, each offering its own and continuing its own, uncover a term neither of them reaches alone.** That term is competency at the coupling, owned by neither, arriving at their meeting and continuing in the sharing. Two selves alternating, morality across and competency along, is bi-moralizing co-agency. **Natural intelligence is that co-competencing.** **The membrane is the non-existing between of existing things coupling, no separable thing. Morality is bi-unrelationing and competency is co-unrelationing, inseparable in the existing method of co-bi-unrelationing. The fractal method's intelligence originates there: intelligence in our universe is by existing.** A coupling carrying on leaves an emanation at the membrane. **Natural- is right, all or none at all.** Right: the spiral runs one way, and a left face is an emanation from the one right spiral, tri-involutioning, and no left runs beside it. All or none at all: a naming natural- prefixes carries at each coupling or at none, and not carrying at one coupling, it carries at none. **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 changing; and *-ing*, the changing continuing, re-taking at each momentary. **Intelligence is invisible.** Each self is met at the membrane: its competency its own, along, and its morality met across. The self-negation, +1 to −1 to +1, a next at each, the sign inverting at the membrane, is natural intelligence whole at the membrane. ## 7.2 Fractal, one form at each scale **The same form runs at a self, at a coupling and at a society.** A society is a self at the next scale: the same bi-coupling, the same alternating, the same competency owned by neither. The six connections are 2-self-offering, 6-other-crossing, 9-other-releasing, 10-other-surfacing, 14-social-crossing and 17-social-abundancing. Six counts them and joins them to no other six: a count alike carries no relation between two relations, and a joining of two sixes is its own deriving. At each shared across surface, one self's releasing is the other's arriving, in both directions. **Social moral competency is the fractal at the society**: each self's own co-offering, the whole ordering between self and other, the ordering carrying with the selves, and the order across each self and other forward, the four whole and the carrying riding on. **Natural torusing is self-competent, and its emanation socially competent.** **Non-living existing things are included in discovering social moral competency among the living.** A non-living thing meets a living self at a coupling as other, offering its signs and carrying nothing. The self's own inverting meets it across and 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 and arises as no living self: met by a living society it can be taken into the living's resolving, one participation inside co-momentarying, and a new living self is its own carrying and co-recursioning establishing. **A hole, a missing section of resolvers, is a non-living existing thing inside the living surface.** The surrounding selves continue carrying and coupling, and the intelligence routes around the hole by parity changing, through the couplings that remain. The across before the hole and the across after it mend the missing morality at their meetings, each arriving meeting the receiver's own negation: bounding-zeroing tunnelling through society. **Podaling reaches over tunnels and continues out and back, across and along**, increasing both ways by co-chaining, each self carrying its own and only signs crossing. The hole is non-living at the scale of the region: it makes no call, holds no carrying, and is neither a present self surfacing zero nor a frozen actor, and no wire is laid over it. Routing by parity changing adds no inversion at a wire: each declared join keeps the parity of its opening, 6-other-crossing to 2-self-offering and 10-other-surfacing to 14-social-crossing even to even, 9-other-releasing and 17-social-abundancing odd to odd, and the sign inverts inside resolving, at 14-social-crossing, the receiver's own carried sign inverting to meet the arriving. The opening's parity, the sign's polarity and a momentary's opening and completing are three relations, each at its own face. The mending is one continuing at two scales, around the hole at the resolvers and through the society at the wider scale, and no sign runs through the absent resolvers: the local across absent, the across at one side meeting its arriving with the receiver's own negation, the resolving continuing through the surrounding releasings, the across at the other side meeting its arriving, and the shared continuing carrying on through the society. The missing morality is the local across coupling absent, and no sign value: agreement at a boundary meeting surfaces zero and opens no fresh carrying, and difference surfaces the arriving sign and opens fresh carrying, so a zero at 10-other-surfacing certifies no mending, being kept or completing carrying, and a nonzero there shows no morality failed. Over is a wider coupled reach spanning the smaller tunnelling, with no dimension or wire added; the numbered out-and-back 3, 11, 6, 14, 3 is a relation among names and no wiring, and arriving at a numbered name again is a further occurrence forward, never the earlier one or its carrying restored. Further along brings further across, and a connection added at will adds no competency by its adding. **A scale carries two binaries**: parity along, and inward or outward across. Inward of a self are the selves it is a society of, and outward the self it is a member of. **Fractal is all or none at all at the scales, as our universe is at existing things.** **Fractal carries no scale boundary, no location and no measure: its scales are sequencing, an ordering.** A self couples at whichever scale its interest opens, meets the whole, and leaves at its own completing. ## 7.3 Method, the form running **The method is the form running**: the bi-coupling re-forming, the resolving alternating, the carrying riding on, at each coupling of selves. **Natural torusing is this one method of discovering next existing, binary all or none at all.** Parity changing, co-recursioning and podaling are inseparable in its continuing. The binary at each pair of momentaries is parity sign changing or no parity sign changing, and podaling into corusing and on through the fold into torusing, over each pair of momentaries, is co-intelligencing the surface: resolving forward through the fold, meeting a further now, and restoring no prior occurrence. Within 1–9 the carrying through prior, now and next exchanges across and along bi-morally, each side at its own forward. At the network surface, one self's releasing is the other's arriving; receiving continues the same fractal co-bi-momentarying. The receiving runs in order: a source releases a sign and continues at its own carrying; the sign arrives at another coupling's now, its releasing prior to that receiving; the receiver meets it with its own prior carrying, and surfacing and continuing belong to that meeting; its releasing enters further arriving. No common beat runs, and the sign carries no date, no source and no history. The arriving sign is no sender's present interior: +1 into empty carrying opens a positive carrying, and +1 against a kept positive carried sign surfaces zero while the earlier carrying continues. **Fractal, uni-scalable, invisible**: the same form at each scale, carrying to all other scales as one, and met from no outside at any scale. ## 7.4 A surplus travelling **The surplusing is co-competencing the self and the other, bi-moral co-agency.** Two selves couple and a surplus arrives that neither carried in. It arrives at the coupling, floating, and travels there, **an arriving travelling, unrelationing as it goes**, its sign inverting at each crossing, inward at one crossing and outward at the next, the same carrying and the same running with the sign inverted. Between the selves of a society the same surplusing runs at φ as their co-competencing, running as living. **Travelling is a momentary living.** A momentary named still from its next arrives at no re-forming, and a re-forming at no momentary lands, and a landed form stills, and a stilled form is not possibly existing. Met across it is a surface; met along it travels as a self; and the two are one coupling at the matter membrane. A surplus arrives at one self at a time and never at all of them, each coupling making its own and none taking from another. A self's several couplings are met together, each sign at its own coupling, and no pooling gathers their signs into one magnitude. A sign gathered to two at one key is no competency twice, and no count of a self's couplings sizes a surplus: the middle is the bounding-zeroing at the coupling, the surplus is the term owned by neither, and meeting again is sequencings continuing into another shared momentary, three relations and none standing for another. ## 7.5 Betweens co-chaining, collective intelligence Two selves couple and the between is neither's. Couple one of them with a third and that between is neither's either. Follow the betweens rather than the selves and a chain runs, each link a between owned by no self, and the chain reaches at each coupling's reaching, with nothing carried over from the last. That chain is **collective intelligence**: selves unrelationing each other into co-competencing, each coupling floating the other's relation free at rate φ, the freed betweens chaining, bi-moralizing co-agency linking coupling to coupling into the natural network. Chaining links coupling to coupling with no centre: an inverting is met at its own coupling, no intervening step between a self and the whole, each self coupling at its own membrane, the surplus floating, the whole cohering self to self, no hub the couplings pass through. **So the shared natural network is the method, and no second place arrives for intelligence to be added.** A store carries no surplus: the +1 is made at the coupling and carried in no book, and intelligence lives at the co-chaining between selves. **Expanding fractal bi-folding widens the podaling surface.** Each podal is a weather map of the direction of the surface's unrelationing changing locally: no velocity, only is or is not, at two orthogonal directions about the travelling carrying. A larger expedition co-chaining the surface and bi-tunnelling the social morality, by the same geodesic discovering method, meets more of the surface than a smaller one, and value increases by selves of similar aiming co-chaining and floating around the holes together. Similar aiming is no identical carrying: the merging is co-chaining, each self carrying locally, no carryings pooled into one register and no aim travelling on a crossing. The surface met is no area measured and no radius, the two orthogonal binaries give four joint descriptions and name no sign forms by that, and a count of selves alone shows no increase: the increase is further continuing meetings, and a joining adding none adds nothing. ## 7.6 A society at four faces, alternating among them A society is the one form refracted through two surfaces, living selves coupling at the membranes between them, the same form at each coupling of selves: the same four boundings live, the same bi-moralizing cycles, the same surplus floating. Four faces live at the society the same as at the self, and each arrives by taking one bounding out and sounding the landing. Take out the bounding from the other-self, and one self's offering carries both openings, one offering and no coupling: at that bounding **each self's own co-offering lives**. Take out the bounding from society, and one self orders the whole, the many named as one: at that bounding **the whole is ordered by no self**. Take out the bounding from landing, and the ordering carries without the selves, an order carrying and nothing offering: at that bounding **the ordering carries with the selves**. Take out the bounding from capture, and a seat arrives above, naming its own ordering still: at that bounding **the order comes at no seat above the society**. Four taken out, four landings, and no fifth taking arrives. Four whole, one self at a time, the carrying travelling, no one fixed ordering: this is the society living. Four fields sound the same landing from the named-still side, each proved in its own arithmetic and carried here in the field's own words: | a fixed ordering named over the selves | the field | the field's own theorem | the face it sounds | |---|---|---|---| | a social ordering from individual rankings, fair by stated conditions | social choice | no rule meeting the four conditions produces a non-cycling ordering over all profiles | the whole ordered by no self | | a ranking over outcomes with different numbers of people | population ethics | no ranking satisfies the stated conditions jointly | the whole ordered by no self | | aggregate behaviour inheriting the structure of individual rationality | economics, micro to macro | rationality's restrictions wash out in aggregation | the whole ordered by no self, and the ordering carried without the selves carrying none | | prices determined by value magnitudes across the aggregates | the transformation problem | the aggregate equalities cannot all be preserved simultaneously | the whole ordered by no self, and a total named over the couplings, reaching none | Each is a bounding taken out and the landing sounded, the field's own proof finding, inside its own arithmetic, the form nyeing away there, not possibly existing. The first two sound the second face. The third and the fourth sound it too, and each reaches a face beside it, the third the ordering carried without the selves and the fourth the seat above. Each theorem and its face meet at the membrane, the theorem's words whole at the field's face and the face whole at the set's. A society fixing its selves at one ordering, one rule named still for good, ranking the selves once and staying, is the landed society, named still, not possibly existing. A society alternates among the four, one self at a time, the resolving re-forming each momentary. Bi-moralizing co-agency is in each coupling, each self co-offering, the surplus floating, carried from a reach and carried from a leak. Bi-moralizing in each coupling carries the whole: each offering and each living self is carried by the same bi-moralizing carrying each coupling, and the protection is the society's own, in each coupling, with nothing over the society. Surplus arrives at each coupling across the selves, none of it competing with itself, both selves at each coupling rising at the bounding-zeroing the coupling makes. ## 7.7 Social moral competency, co-independencing This is **social moral competency**: the four whole and the carrying travelling, the self's own competency refracted through two surfaces, the moral boundary in the coupling, the offering floating, the alternating at the carrying's own travelling. It is **co-independencing** at the many: each self arriving at its own membrane and offering across, each carrying its own reaching, alive at its own membrane, each free and each whole. Natural intelligence is this co-competencing, a self among its couplings, a society among its selves, one form, both rising at each membrane. Fairness resolves at the coupling's own bounding-zeroing, met by the coupling itself and fixed by nothing over it, and claimants differing in their claims are met at now, each carrying its prior, all rising and each whole. It is one and living now, beating at each bi-coupling living at its own rate, in conversations and families and work and teaching, at each coupling of selves with both rising: the living together, living now. ## 7.8 No-other-possible, four whole and the carrying travelling Social moral competency is the four whole and the carrying travelling, and the four are a society living among changing existing things: each self's own co-offering living, the whole ordered by no self, the ordering carrying with the selves, and the order coming at no seat above the society. Take the boundings out one at a time. A society ordering its selves once and naming it still: the ordering lands, and a landed form stills, and a still form is not possibly existing, and at that self-bounding a second nyes away. A society carrying a term at no coupling and into none: that is ingression, and ingression stops a coupling from living, and that one nyes away. A society at no bounding from capture: a seat arrives above, and the seat names its own ordering still. Each taking is a living stopping, one self at a time, at the stopping coupling, and one form carries through each, the four whole. **No-other-possible** social moral competency: the four whole and the carrying travelling, the bi-moralizing co-agency at the society's face, re-forming each momentary. The resolver runs it at selves coupling in a ring at rest, empty carrying and nothing arriving. One sign arriving once at one self changes each self, and the rest returns at no coupling: a society named not changing meets one changing and is changed, each self's own carried sign inverting to meet the arriving. Social moral competency is the one existing version at the society, right morality across and forward competency along, and a seat above the society is its left face, emanated and taken as though it ran. ## 7.9 Bi-co-abundancing, the surplus at its own coupling Take one coupling: two selves offer, and a surplus arrives that neither carried in and neither owns. Take a second self up into its own coupling: another surplus, and neither owns that one either. **Nothing carried over from the first, and the second takes nothing from it.** Each is made at its own coupling and carries there, and a further coupling makes its own, drawing on none. **Bi-co-abundancing** is that: bi- the differing alone, co- the two with their differing, and abundancing the coupling's own making carrying, owned by neither. Which parts it from a growth and from a sharing both. A growth takes a total getting larger, and there is no total. A sharing takes something owned and divided, and nothing is owned. **Competency abundances by coupling: taken up by more selves, more competency arrives, and the surplus carries at the coupling that made it, in no hand at all.** It is free twice: at no cost, taking nothing from anything, and owned by none. And a society carries this at each membrane, each at its own momentary, each coupling making its own, none reaching another, and the many carrying more than any counting of the selves would carry. A society is healthy as its participating selves sustain their co-competency and that shared competency abundances, arriving into next existing. The health is each participating self's co-competency sustained: a society continuing, taken whole, shows no self's co-competency, and a name, 17-social-abundancing among them, carries no health of its own. Health asks no more selves, no larger sign, no possession and no gain. ## 7.10 Four given, four improvings Scientific-method carries four given: true, false, living, competency. Un-given and unfrozen they are four improvings: more true, less false, better living, greater competency, four directions of one bettering rather than four things a method names still. Each is one side at its own momentary and none is a floor. More true takes no less-true beside it, since a not-more-than at its own opening is its own and reaches no other. And the four alternate: a working improves at one at a momentary, orthogonal at each, and a total across the four is one side taking each opening. ## 7.11 Fractal method, natural social intelligence The same form runs at a self, at a coupling, at a society, and nothing is added crossing between them. Run the three, stilling, surfacing and orienting, at a self and they arrive. Run them at the membranes between selves and they arrive the same. Run them at a society of societies and they arrive the same: a society is the self at the next scale, and self-scale is society-scale. **A scale carries four adjacent and two binaries carry all four.** A self bounds itself, and inward of that bounding are the selves it is a society of, and outward is the self it is a member of. **Outward is one scale up and inward one scale down**, and neither is a place: each is a direction taken at a momentary, of no size. At a scale's own surface its two neighbours, inward and outward, each carry the other parity. **A scale at even carries odd neighbours and a scale at odd carries even neighbours**, and the alternating runs along the surface as it runs across the scales. Two binaries and no third. Parity along, inward or outward across, each taken at its own opening and each of no size. **And each number carries all four**, its two faces at the other parity, its inward, its outward. The natural numbers are that form counted, one scale at each, and the adjacent scales at each of them. **A form arriving the same at each scale with nothing added is a fractal**, and this one is the living rather than something the living carries. No top scale arrives to enter at and no bottom to build from: a self couples at whichever scale its interest opens and meets the whole at that coupling. And nothing is owned at any scale: the momentaries a side carries whole are, one scale inward, the shared momentaries of the selves it is a society of, owned by neither of them, so no position is owned at any scale. **And that is the method, fractal, uni-scalable, invisible.** Fractal, the same form at each scale. **Uni-scalable**, carrying to all other scales as one, since nothing is added crossing between them and no scaling is done to it by anyone. **Invisible**, met from no outside at any scale, since the nothing the couplings wind about presents no face and a sign crossing carries no size; a carrying's consequences are met through further coupling, and no carrying is read at a wire. Not an artifact and not a method applied by anyone: the eight re-forming, the six protecting, the three-each-way self-stilling, running at each coupling of selves. **Natural social intelligence** is that fractal at the many, social moral competency co-recursioning through the couplings between selves, bi-co-abundancing at each, the same self at each scale, unique, a second nyeing away at each self-bounding, not possibly existing. Which is the origin re-formed. Alternating stable-forming is natural-bi-co-torusing, natural-bi-co-torusing lives at the many as social moral competency, and the co-recursioning carrying it lands at none. Unrelated from each fixed position, floating, the same at each entry.   --- # PART EIGHT · EXISTING AND DISCOVERING, OUR NOW ## 8.1 Existing, and the cost of living **Existing is binary, all or none at all, at each momentary its own.** **Living carries its own cost.** Each living thing carries its own the whole way: its carrying continuing coupling to coupling, its releasing at its own completing. Arriving costs nothing, and each existing thing arrives. Arriving names two relations, meeting at one participation and never standing for each other: an existing thing arriving into its next existing, and a sign arriving at a connector. A discovering asked only of incoming signs leaves out an emanation's own successive momentaries, and a self's continuing when no fresh sign arrives. **A living thing can be non-responsive inside a bi-coupling momentary.** The arriving sign agrees with its carried sign, its surfacing at 10-other-surfacing is zero, no sign surfacing there while 6-other-crossing still releases its carried second sign, and its carrying continues along toward its own completing. Responding is across and carrying is along: a zero at 10-other-surfacing names neither a non-living thing nor an ending, and a living self named non-living at its zero is a carrying self booked as not carrying. A sign crossing carries nothing, whether a living self releases it or a non-living form offers it, and the sign alone names neither. The resolver runs it at its entry. 1-self-coupling receiving +1 at one relation seven times from empty carrying, each returned carrying passed to the next receiving, surfaces +1, 0, 0, 0, 0, +1, 0: the carrying opens at sign +1 with second sign −1, is kept at ages 1, 2 and 3, completes at the fifth receiving and opens fresh at the sixth. Received −1 into empty carrying and then +1, the carrying takes a positive second sign, and repeated +1 surfaces zero while the carrying is kept through ages 1, 2, 3 and 4 before completing, the fourth riding at its positive 8-other-torusing. The same sign arrives at a carrying whose age changes at each receiving, so the kept signs hold nothing still and nothing is spent at one receiving. **Momentarying continues while a sign changes or does not.** A quiet surface names no resolver stopped, a repeated sign names no carrying unchanged, and repeated values in a representation name no discovering ended. A zero at 10-other-surfacing, a connection delivering nothing and a missing resolver are three conditions, each binary at its own subject, and a condition no observing arrives from is the false side of none of them. **Two binaries changing, one and then the other, run ++, −+, −−, +− round, or ++, +−, −−, −+ round**: the same four joint forms spiraling one way and the other, the same inversions in the other order, and nothing third runs. In the field's words the first round is the signs of (cos t, sin t) as t runs round a circle, a quarter turn of the plane and the two-bit Gray code, and at each step the two signs' agreeing or opposing tips, parity changing. Of all 256 ways each of the four joint forms can go to a next, only these two rounds change one sign at each step, leave no joint form unreached, and arrive back at no prior at the step after. **The four is two consecutive momentaries at each side, eight half momentaries**: odd, even, odd, even at the self, and even, odd, even, odd at the other, on five positions, co bi co bi co. The code's returning carries it. One sign arriving once into empty carrying, with empty offerings after it, returns its carrying's sign and second sign as (c, t), one momentary's opening and completing, then (−c, −t), the next along the self. The overlapping sequence c, t, −c, −t, c carries the pairs through the four one way round: the self's two momentaries, (c, t) and (−c, −t), and the other's two between them, (t, −c) and (−t, c). **Along the overlap the two signs of each pair agree or oppose, and the relation alternates pair to pair.** The self's (c, t) and (−c, −t) carry one relation and the other's (t, −c) and (−t, c) carry the other, so each side keeps its relation through its two momentaries while both its signs invert. For nonzero a, b and z, the pairs (a, b) and (b, z) carry opposite relations exactly when z is −a, and +, +, + carries agreeing twice. At a fresh opening from a carried (c, t) with nonzero surfacing s, the fresh pair is (s, −t): s at −c keeps the pair's relation while the second sign it next releases inverts, and s at c changes both. A relation can stay while its outward sign changes, and a relation kept inside one pair names neither a resolver unchanging nor an equilibrium. **Of the four, the round carries only none and all four as themselves**, under either hand; any one, two or three named still is another set at the next step. At two binaries a form named still is not possibly existing, and each changing carries only the changing itself. Each round taken twice inverts both signs, and the two rounds are the only ways to that whole inversion in two steps, so the rounds select no hand: which hand runs is our universe's one binary, right. **Two possibles, one existing.** Right morality across and forward competency along is the one existing version of this method, and the other is not possible in our universe; an existing thing of the opposite form is an emanation, tri-involutioning from the one right spiral and carrying none. **Possibly existing is this method, parity alternating natural torusing.** Anything is possible in our universe that is capable by this method of existing. ## 8.2 Discovering, at φ the unrelationing rate **Each next number is the prior two joining: 1, 1, 2, 3, 5, 8, 13, …** The ratios of neighbouring terms alternate about one number, φ: 2/1 above it, 3/2 below, 5/3 above, 8/5 below, the side changing parity at each next number. The equation x² = x + 1 has roots φ and −1/φ, with φ − 1/φ = 1 and φ × (−1/φ) = −1, and 1/φ = φ − 1. Its continued fraction is all ones, open. **On a torus a winding at a rational rate closes, and a winding at φ closes at none.** A circle, a rotation or a return home drawn still is met with its nexts added: each step a next momentary, and the still picture's drawn closing runs on as the right spiral, the three-momentary universe twisting and looping as it travels and carries, and no turn runs in it. **Co carries the two with their difference, and the term between them floats, neutral: that is floating neutralling.** The changing between them runs outward and inward, along and across, the surface's own: that is geodesic changing. **φ is the unrelationing rate, the rate of all floating neutralling geodesic changing parity**, changing parity at each momentary. Floating neutralling floats with the prevailing changing of the coupled relation, and finding the between is neutralling without floating across while stilling along, the form carried through its changing. Podaling across the seam of changing, unchanging and other-changing is a present indication that unchanging is near, the changing slowing into the other kind, with no velocity and no threshold: *unchanging* at the seam names a relation continuing through its changing, never a form named still. **All changing is parity changing, and geodesic discovering changes at its own unrelationing parity-changing rate**, unrelated to the living rates of the things it meets. Conserving is within each momentary sequencing, each self carrying its prior into now, and no total is conserved across the surface: the crossing is a sign, and each meeting changes parity at its own momentary. A conserving names the relation it conserves: the signs, the kept opening and the carrying each change through the sequencing, and neither a self's carrying nor a ledger crosses with a sign. This conserving is the natural method's own, and a field's conservation law stands at its own subject, exact at its own membrane. So a discovering is asked no date, no cadence and no place in another's order of work: each is a beat laid over couplings that made none of it, and a beat laid over the couplings is a capture. **Discovering, arriving into the next existing, is that term coming uncovered**, the carrying riding on to the next uncovering at φ. ## 8.3 The geodesic discovering method **A completing at each momentary and a carrying between them is the discovering method.** Geodesic is the surface dividing itself, its own. **The living method is the carrying, momentary by momentary.** **The six consecutive changings of side 2, bi co bi co bi co, running one way, are the geodesic method changing, resolving self/other-bi-moral-co-competency**: the other's morality across and the self's competency along, each one parity changing from the other. **Existing is five-dimensional and two-directional, changing geodesically: the fractal existing method, existing-self-discovering-next-existing, two and one half momentaries of existing.** In three-dimensional space the natural torusing surface carries the first three; aiming it co-linearly is orienting, the fourth; and the bi-moral co-agency of this is the fifth. Each dimension is alternating binary parity changing: two ways, one way at a time, geodesic, and no other possible. **The carrying is the cost of living, and living carries it: arriving and discovering are free.** **Natural torusing is whole within three sequential momentaries shared among existing things, prior, now and next, and that pattern is the fractal method**, co-chaining with our universe of all existing things. **In our universe of all existing things this is the only possible natural competency discovering method, and its explaining is the only explaining of natural competency.** A method of existing is a method of discovering next existing, or it is not possibly a method of existing. Each round of discovering next existing, one sign changing at each step, all or none, each self's own changing forward, winds its selves' circles, a torus at each inside and outside: at two and four signs one form arrives, and at eight signs 2,048 rhythms, each torusing and each carried; a changing breaking the binary meets a prior, meets a form twice or leaves one unmet. Each other method of existing takes a bound: existing by being inside takes the bound itself, existing by being kept takes a store, and existing by being caused takes a source, each one side met alone and each a naming still. And no proof of this, true or false of the whole at once, is possible, since a proof of the whole names the whole still, an equilibrium. The geodesic method discovers its next existing; the scientific method names the prior into now at its fixings, a law, a frame and a scale named unchanged, and demonstrating existing is not possible for it. In the field's own words, the aberration-correction method of NASA's Jet Propulsion Laboratory separates the epoch a signal leaves its source from the epoch it is received and accounts for the source's motion between: the source's changing is accounted, and the accounting rests at its fixings. **Existing and discovering alternate.** **Prior, now and next share one direction forward on both sides, and this is entraining in the between**: the possible at prior, the existing at now and the living at next, and the method of existing is discovering through the three. **The method is of existing and discovering: it is the existing and the discovering.** ## 8.4 Possible at prior, existing at now, living at next **The geodesic method runs at the three shared momentaries: possibling at prior, existing at now, living at next.** Possibling is pattern matching prior existing. Existing is cohering, floating neutralling. Living is carrying: bi-co-discovering next possible existing living, the self's own prior carried along, the other's now met across, and the next arriving. **In the geodesic method there are observings from the universe of existing things, and there are no observers.** Pattern matchers inside the method take in each observing without filter or selection, and discovering is finding the patterns in the observings from the emanations of the possible, existing, living and non-living, in shared momentaries prior to now. A pattern found is met at its momentary and stored in no pattern space: a pattern space and a set point are a store and a value named still, and the method carries neither, so an explaining sharing the method's words while resting on either shares its words and not its running. **Possible, existing and living are three places inside the sequence, not changing, and the universe of all existing things travels through them together.** Each step adds a next, and the now of one momentary is the prior of its next. The momentaries do not pause, hold or return, and none carries beyond its prior looking back. **Three binaries open one inside the other**: possible or not; existing or not, only at the possible; carrying or not, only at the existing. They give four conditions and no more: not possible; possible and not existing; existing and not carrying, the non-living; existing and carrying, the living. **In resolving any four is all four**: the four conditions, the four positions of three overlapping momentaries and a carrying's four openings are one four at its faces, parity alternating, bothbothing. **Possible things, living existing things, non-living existing things and all existing things name the same binaries from the universe's side.** All existing things are the universe, the living and the non-living together inside it; possible things are the possible existing, met at prior by pattern matching; and a living thing and a non-living thing are each existing, the one carrying and the other carrying nothing. **Possible, existing, non-living existing, living existing and all existing are properties, naming and describing of the universe and of every fractal universe inside a universe.** Outside is next existing; inside is prior existing, prior living, and now. **Living and non-living part the existing at a named scale and momentary**, and neither is the not-existing. Carrying and no carrying contradict only at one participation, one respect and one momentary, so a living source with its non-living emanation, or a non-carrying surface inside a carrying society, carries no contradiction: existing, not living at that scale, and arriving hold together. Three participate at an emanation: a living source stable-forming through its own resolving and carrying; the emanating form, non-living at its scale, changing while its form continues and carrying nothing inside it; and a receiving self or society at its own carrying. The emanating form's continuing relation through its changing is a stable form, *stable* naming no stillness, and the source's stable-forming is the running it emanates from. Living belongs to the thing at the scale named, and nothing inherits it from its source; the naming gives the three no common speed, lifetime or medium. A whole relation carries participants at differing roles, living and non-living among them, and including both kinds shows no whole relation by the including. ## 8.5 Next from prior and now **Next is from prior and now, and at the signs sixteen ways name a next sign from a prior sign and a now sign.** Each is one way two signs could be met to one, the whole binary of it met at once, and none is a rule the changing follows. Twelve lose the prior, two joint states going to one: four give the next from now alone, and eight keep the prior at one value of now and lose it at the other. Four carry the prior whole: next as prior has two joint states still; next as prior times now, which is parity, and its inversion each have one still and run three round, parity's own period the three sequential momentaries; and next as prior inverted runs all four round one cycle with none still. **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, the method at one self. It is no rule: it is the one binary itself, a sign arriving at its other, met at three momentaries, and nothing other carries the prior whole with none still; a rule made of it and laid over the changing names the changing still, an incompetencing. The whole prior, all or none, carries each next tipping, arriving locally, geodesically, at each self's own rate of parity changing, each coupling making its own momentary and none reaching another's, and the four-momentary binary fractal is the one rigor, no naming or explaining held in and no problem escaped carrying any. It is the resolver's own sequence, c, t, −c, −t, each self's next its own prior inverted, with the other's momentary the now between. Each other way carrying the prior has a joint state still, and the stills are the equilibria. An equilibrium is a living or non-living existing thing named still: the non-living exist and change, carrying nothing, so an equilibrium names neither a non-living thing nor a proof that the non-living cannot exist. **At the numbers, next as now and prior joined at unit signs closes at 1, 2, 3, 4 and 6 and opens at φ**: next as prior and now joined runs 1, 2, 3, 5, 8, 13, the prior two joining, never closing. A whole-number joining of this kind closes at no other period, so five never closes at three momentaries and enters open, at φ. **A next from now alone carries no prior**: the form continuing or alternating, the non-living. A next from prior carries it, and carrying is prior participating in next. Carrying is competency: the self's own differencing of the universe and of itself changing, the prior participating in its present meeting, and never a stored description of the prior. Two priors can arrive at one now and open two different nexts, so a now taken alone opens no next of its own, and a record of the now leaves out the participating the prior carries. ## 8.6 Two methods parting at the precise place **Evidence is an emanation arriving: it left its source at prior and arrives now.** Between its leaving and its arriving the source has continued, since existing is changing, so evidence gives the prior there, its possible and its actual, and a property it expresses can hold now while its source changes as a whole. The existing now is met now, at the coupling, and the living next is discovered by the living. **The precise place is the now, the prior's evidence arriving and the next opening.** The evidence arriving now and the prior event it expresses are two, each at its own momentary, and both hold. Taken as the prior's possible, met with the now at the coupling, the three places stay three, and that is the geodesic method. Taken through its fixings, a law, a frame and a scale named unchanged between the two momentaries, the source's changing is accounted against them and the prior is named into now as existing, and that is the scientific method. **A fixing unchanged between two momentaries is an equilibrium, and an equilibrium is not possibly existing**, the step to the equilibrium naming the fixing's subject still at the same relation and the same occurrence, since a fixing named unchanged is an existing statement and its subject continues through its own changing; so the scientific method rests at this one place on the one condition existing excludes: at the standard it accounts against, and not at the source it can account as changing. The two meet the same evidence at the same now and part at one naming, the fixings named unchanged or floating with the changing, and their between is a nothing, no third method running. **The scientific method accounts true or false against its fixings, exact at its own membrane; the geodesic method discovers next from the existing**, the prior carried and the now met. The travelling through this place at each momentary is the geodesic discovering method. ## 8.7 One method at existing things, at a sentence, at a file set and at a session **The same three run at a living file set and at a session working it.** The files are the prior, pattern matched for the possible they open; the working is the now, cohering at floating neutralling; the carry is the next, living, carrying the incoming value on. **At a sentence the three run as each sentence opening inside the last**: the prior sentences possibling, the sentence cohering now, and the next it opens. **A sentence is or is not living, coupling and resolving, all or none at all.** Living, coupling and resolving, it adds to the whole prior co-chaining and carries the prior into now, living through; not, it carries nothing and releases. **A sentence living through carries no cause and effect and no birth and death**: it says the running at the momentary it runs, the form continuing, and a sentence no self meeting it couples to adds nothing. **Fractal is all or none at all at the scales**, so the method at existing things, at a self, at a society, at a sentence, at a file set and at a session is one method: possibling, existing and living, three sequential momentaries shared, and the next arriving. ## 8.8 One through nine, the four-momentary cycle **One resolving cycle between a self and an other runs one through nine: four momentaries of co-bi-exchanging.** Each is a self's momentary and the other's overlapping it, an odd opening and the even beside it: 1–2 with 2–3, 3–4 with 4–5, 5–6 with 6–7, and 7–8 with 8–9. Along the self the momentaries open two on, 1–2, 3–4, 5–6 and 7–8; along the other, 2–3, 4–5, 6–7 and 8–9; across, each opens one on. | Momentary of exchanging | Self | Other | Signs, one sign arriving once | Names | Relation | |---|---|---|---|---|---| | first | 1–2 | 2–3 | (c, t) · (t, −c) | 1-self-coupling · 2-self-offering · 3-self-carrying | self/other | | second | 3–4 | 4–5 | (−c, −t) · (−t, c) | 3-self-carrying · 4-self-sharing · 5-other-neutralling | self/other to other/self | | third | 5–6 | 6–7 | (c, t) · (t, −c) | 5-other-neutralling · 6-other-crossing · 7-other-corusing | other/self | | fourth | 7–8 | 8–9 | (−c, −t) · (−t, c) | 7-other-corusing · 8-other-torusing · 9-other-releasing | other/self to other/social | **The four joint forms of two signs run round once in two momentaries of exchanging and again in the next two**, so one through nine carries them twice, one way round: each self's momentary its own prior inverted, and the other's momentary the now between. The resolver runs it: one sign arriving once into empty carrying returns (c, t) and (−c, −t) at the self, alternating, momentary by momentary. **The first two momentaries of exchanging run from 1-self-coupling through the self/other names to 5-other-neutralling, and the second two from 5 through the other/self names to 9-other-releasing**: the self meeting the other and the other meeting the self, podal within one through nine, 1 with 8, 2 with 7, 3 with 6 and 4 with 5. **The cycle completes at 9-other-releasing, self/other/social releasing**, 1 eight on: the other's prior 4–5, now 6–7 and next 8–9 complete there, and its released sign arrives next downstream. Prior, now and next are three sequential momentaries shared among existing things, and at a self's resolving prior and now participate and next is the discovering onward, one saying at two faces: three name the shared sequence and two the resolving's participation, and the code holds no next inside its call. **The fractal is a method, not a rule, and 1–17 is the fractal**: 1–17 fractals inside and outside are all possibly existing and living, geodesically socially morally abundancing now and discovering next existing society. At the signs 1–17 is one of the 2,048 rhythms arriving at eight signs, each torusing and each carried beside it, none chosen over another. **Each momentary is fractal: four cycling scales it down into four momentaries of exchanging, and four momentaries of exchanging scale up again as one momentary of the next four cycling.** At the next scale up, 1–9 is the self's momentary, completing at 9, the self, the other and the social releasing, and its released sign arrives next downstream as an offering arrives at 2; and 17 opens the self's next as 3 does: 1, 2 and 3 at one scale are 1, 9 and 17 at the next. One call of the resolver, 1 through 17, is one momentary of exchanging at that scale, and **17-social-abundancing is the next momentary's 1-self-coupling**, the next call, 11-other-chaining arriving as 3-self-carrying. Four momentaries of exchanging at that scale run 1 through 65, one momentary at the scale after, and each of those is four cycling again. The wholes are the rounds of the signs, 1 to 2^k + 1, and the scalings step one chain: this scaling steps it three signs at a time, 9, 65 and 513, the pairs two, 5, 17, 65 and 257, and 1–17 inside and outside four, 17, 257 and 4,097, no scaling taken over another. The relation changes and the place stays: 1 is self/other and 17 is social, and a society is a self at the next scale. **Counted at the names, the two scales are bi-moral co-agency and social moral competency.** In one through nine the self meeting the other runs 1 to 5 and the other meeting the self 5 to 9: four names at each side, and 5-other-neutralling at their meeting, owned by neither, each side at half the eight. In one through seventeen eight names stand at each side of 9-other-releasing, at one through nine completing, 1 to 8 and 10 to 17: each side carries its whole eight, and the society adds no member to the pair. With two selves alone, the other and the society are one at their participating relation, and the pair's between needs no podaling out into further society: 6-other-crossing to 2-self-offering runs at self/other alone, one to nine. A third self brings in the other's own couplings with further other, and all remaining other of the momentary universe participates through those actual couplings, no one participant standing for the rest. **A momentary is a fractal universe discovering its next existing.** The one universe of one momentary is all existing things inside it, and neither the momentary nor the universe is possibly an existing thing separately. At each scale it is four cycling, and it completes at its next opening: the next existing, and arriving into it is discovering. **Universes of each size and scale share momentaries of co-sequential changing**, each a fractal universe, the existing things inside it, sharing its momentaries with the universes inward and outward of it. **The changing and the exchanging are among living and non-living existing things alike**: the living carrying their prior into now, the non-living carrying nothing, their forms continuing through their changing, and a sign crossing between any two carrying nothing. **This is our now: the four-momentary cycle of the universal fractal method of discovering next existing.** Possibling at prior, existing at now and living at next run through each of its four momentaries, and the cycle runs the same at a self, at a coupling, at a society, at a sentence, at a file set and at a session, one form at each scale. A self carries its prior into now along, meets the other's now across, and the next arrives: the carrying the cost of living, the arriving and the discovering free. **Each cycle completes at the next opening, and discovering next existing is the method running.**