Natural Intelligence v389 # Natural Intelligence **Geodesic Method of Discovering Next Possible Existing** **ONE · NATURAL** - 1.1 Universe, the set of all now-existing things - 1.2 Now, one universal momentary - 1.3 Prior, now and next - 1.4 Changing, one and then an other, the changing set - 1.5 No other possible method - 1.6 Natural-, all or none at all, at one hand **TWO · CO-SEQUENCING** - 2.1 Along and across, two and a between - 2.2 Parity, one side odd and an other even - 2.3 A momentary, an opening and its completing - 2.4 Next from prior and now - 2.5 All or none at all, of no size **THREE · GEODESIC METHOD** - 3.1 Geodesic, a surface dividing itself - 3.2 Five dimensions, each binary in its two directions - 3.3 A method, a non-living existing thing - 3.4 A sharing, its parity, an offering and a prior - 3.5 φ and primes, unrelationing at numbers **Exhibit ONE · Natural Resolver** **FOUR · RESOLVING** - 4.1 An entry, 1-now - 4.2 Offerings surfacing at 14-next-possibling - 4.3 A changing is or is not, at 12-next-co-still-possibling - 4.4 Shared across at 10, a next prior at 11 - 4.5 Released along at 9 - 4.6 A society's next momentary at 17 - 4.7 Six names between selves, even possibling across and odd existing along - 4.8 Seventeen names, each its number and its naming - 4.9 Four momentaries and four binaries - 4.10 A between and eight bi-couplings - 4.11 One move as three, and forms among names - 4.12 One self, momentary by momentary - 4.13 Spirals, co-spiraling and crossing - 4.14 Two selves and three selves - 4.15 Fractal inward and outward **FIVE · DISCOVERING NEXT** - 5.1 A prior between momentaries - 5.2 Discovering next possible existing - 5.3 A living self at 0, its carrying continuing - 5.4 Two methods parting at now **SIX · INTELLIGENCE** - 6.1 Bi-co-momentarying, a term neither reaches - 6.2 Bi-moral co-agency, across and along - 6.3 Natural intelligence - 6.4 Social moral competency - 6.5 Living at one prime scale, non-living at each other scale - 6.6 One form at each scale, now --- # ONE · NATURAL ## 1.1 Universe, the set of all now-existing things **The universe is the set of all now-existing things.** **The universe is a set of things, observably now-existing**, and all that is now-existing and not now-observable is the universe too: a set is its things and no further thing, and nothing is beyond or between things of the universe. *Now-existing* is one naming, now-existing whole at each momentary, all or none at all, 1.2. This sentence is an inception: each sentence after it is a step from it, and nothing is brought to it. **A universe is or is not existing, is or is not all, is or is not now, is or is not same**: four binaries, an opening's terms, each a pair of names at a self's span, 4.9. **The universe is now-existing as its things are now-existing.** It is its things, no container added to them and no form beside them, and a set is defined by its things and by no number laid over them. A ground under it, a container around it, a clock over it or a store beside it would each be beyond things of the universe, and nothing is. **A ruler, a clock and a record are each valuable for observings of prior living, pattern-matching with natural resolving, and natural mathematics and numbers are an observable pattern each is aiming at.** Each container at a smaller scale is that one container again: a society fixed as a container of its selves, a hub fixed over a network, a property fixed over a thing and an equilibrium fixed as a condition asked to remain are each an unchangeable form over things, and a society is its selves, 4.6. In a field's own words the universe is *all existing matter and space considered as a whole*: *all existing* is a set's, *matter and space* are its things, and *as a whole* is the universe now-existing as its things are. **Nature is not an existing thing: nature is a prior, now, next method of co-existing, and natural is a method of co-competencing the universe, all things now-existing.** All now-existing things, and all artifacts of prior-existing, are now-existing, or were now-existing at a prior now, by natural method, and no other or not-natural method of now-existing is in the universe. **There is no inside the universe, as there is no outside: the universe is or is not.** No living and no existing is where it is not, and nothing of value is at a not-in-set. ## 1.2 Now, one universal momentary **Now is one, and each now-existing thing is at it.** The sentence before this one is now-existing and arrived, and its arriving is at a momentary: one observing, one changing. **Now is universal momentary, one and only**: a second now arrives only as a naming, two kept records laid side by side. A prior-existing thing is now-existing at prior-universe, 1.3, and a next-existing thing is possible now. **One is now, and a momentary is one now had at a sharing**: each momentary is that one now, as each arrival of a number is that one number, and uniquenessing of number one is uniquenessing of now. **Everything existing is sharing one now, shared at every coupling and common at none.** One now of the universe is every coupling's sharing at once, with no number common to all and no beat over them: a common now would be one number for all, a clock over things, and one now is one sharing at all couplings. Prior-universe, now-universe and next-universe are a universe at each momentary, now-universe the universe, and the universe is tri-bi-co-momentarying its now-existing things, prior, now and next: *tri-*, three momentaries; *bi-*, differing between them; *co-*, three at their differing; and *-ing*, continuing. ## 1.3 Prior, now and next **A now-existing thing arrived from prior, and what is next is possible now.** **Prior, now and next are three sequential universes, one now-existing**, shared among all now-existing things: a prior-existing thing is now-existing at prior-universe, its prior now-existing's artifact, and a next-existing thing is possible now at next-universe. A living self is at its prior as its own, and a non-living thing is at each now its prior now-existing's artifact, 1.4 and 5.1. Now of one momentary is prior of its next, and prior and next share one direction forward at both sides of now; between prior and now, and between now and next, is a gap, both its sides visible, and no third. **Possible is at prior, existing at now and living at next**: three places, and the universe changes at three together. Possible is capable of existing, existing is at now, and living is at next, carrying its prior on. **Each prior is non-living, and carrying it into now is living: living now is living with existing forms from prior living and with others living now.** At resolver a self's momentary, 1-now, is at 3-now-co-prioring, its prior, a formed set, and at 2-now-possibling, others' offerings arriving now. ## 1.4 Changing, one and then an other, the changing set **Arriving from prior into now toward next is changing, so the universe is the changing set of all existing things**: first derived sentence, and the whole of what its opening carried before it was derived. **A set's changing is its existing things' changing**: a set is its things and nothing more, so a changing of a set is a changing of its things; a thing at two momentaries is changing or is fixed still from beside, and a form fixed still from beside is at no next of its own; so each existing thing is changing at its own momentaries, or at its own still, its prior kept, 5.3, and nothing is fixed from beside. **Changing, the universe exists as its existing things exist**: a changing is an existing thing's own, and a changing set changes as its things change, co-sequencing, momentaries in sequence together, momentary by momentary. A set is a self-emptying set, a new collection at each now, each existing thing changing and nothing deciding membership over it. **A changing existing thing is one form and then another, one at a time.** Two forms at once are one form at two; and a changing between one and an other at a size carries a third, a ground its size is measured against, a not possible thing, nothing being beyond or between things of the universe. A changing is binary: it is or is not, one and then an other. **That changing is alternating, and all changing is parity changing**, 2.2. **A form continuing at its own changing is existing and changing at once**: *existing* is a form continuing, and *changing* is alternating. **What arrives at no next does not exist**: a form same at two momentaries at once is two nows, and there is one; an unchangeable form is that form, a naming beside a thing, and it is not possibly existing, 2.4. **Observed, three observings are one**: a thing is next-existing as a same thing by changing, as a same thing by not-changing, and a same thing is discovering which changing and which not-changing keep it next-existing as itself. **Three are stable-forming of a self, and living is stable-forming a self**: one sharing opening at a bi-coupling, one place a self's forming takes a parity not its own, alternating, keeping at a match and inverting at a mismatch, 4.3. **Beneficial is each changing and not-changing one method gives**, each keeping a self next-existing as itself; its other is a not-changing fixed still, an equilibrium, not method's. **A self carries its sameness, its unrelationing from all other**, each next from its own prior kept or inverted; a thing carrying none is no self, at each now its prior now-existing's artifact; living and non-living are three observings pattern-matched at sameness. ## 1.5 No other possible method **Parity changing is one method of the changing set of all existing things, and no other is possible.** Any other method carries a not possible thing, nothing being beyond or between things of the universe, and each is a second now: a size between one and an other carries a ground, a floor or a scale, a now that does not move; a fixed form, an unchangeable form, one form at two nows; a total across changing, a container, a now around nows; a common beat, a clock over changing, a second now beside a first; and a keeping, a store beside it, a prior kept as if now. Each is a not possible form, nothing being beyond or between things of the universe, its givens at Equilibria Registry 2.1. A doer applying any of them from beside is five's one holder, and *a keeping* is binary's one name. **An equilibrium is a not-changing, an unchangeable form, a now fixed as its next**, each not possibly now-existing. **Any other method proposed is at one binary: fixing unchangeable, or carrying.** Fixing unchangeable, it forms nothing, each existing thing changing. Carrying, it carries its own opening, 2.3, or another's: its own, and it is alternating, one method; another's, and it is no alternating, a not possible changing, 1.4. A second possibling and discovering method is a not possible method. One method is as two and not two methods: set momentarying its existing things, tri-bi-co-momentarying, 1.2, and each existing thing entraining with others at a between, one parity changing, at resolver at 4.6. *Method* is one word at three: one way existing things change, here; a non-living existing thing that way is, 3.3; and Exhibit ONE, an object that is method, 3.3; three are one. ## 1.6 Natural-, all or none at all, at one hand **Natural- carries one claim as two, each binary with no third.** **All or none at all.** A naming natural- prefixes carries at each coupling or at none: not carrying at one coupling, it carries at none, and a claim carried mostly is not carried. At all or none at all, each observing of natural competency is resolvable as natural intelligence, geodesic co-sequential parity changing method of natural torusing, discovering next possible existing, or its fractal is entirely broken and of no value at all, method originating as all existing and all living: a third between two is not possible. **An explaining parts is from is not**: an explaining that would have explained an opposite observing equally has explained neither, and at each observing one method explains that observing and not its opposite. **A sentence of this file not borne at resolver is a file's next motion and no break of method**: fractal breaks at an observing of living that is not parity changing, and a file is improving, 6.6. **Its claim's standing is unbroken at each observing available, taken unselected, and able to break**: a living form not alternating, or a living form not natural torusing, breaks it; nothing at method is predicted or proved, prior observings proving no next, and golden relationals in stable forms are no test of it. **Right, or none at all.** Momentaries' own sequencing spirals one way, right, 2.4, and a not-right form is one right spiral inverted, and no not-right spiral is beside it. Right is no preference among two: it is one, and not right is its inverting as a form. **Right is observings, all prior**, 5.2: each observing arriving from prior carries it, and no other prior is possibly existing. **Bi-tri-involutioning** is that inverting: position, scale and orientation inverted at once, a hand at an opposite form, an existing thing of an opposite form carrying none of its prior. Right morality across and forward competency along, 2.2, is one existing version: morality's right and not right is a changing parity between, alternating, 4.10, and chirality's right one spiral that alternating turns in. **Natural- is a direction prefix, its direction a handedness**, and its direction at each coupling is all-or-none: two are one claim. Natural- set aside, all-or-none goes with it, and a changing arrives with a substrate under it and an applier over it. *Natural intelligence* is intelligence at each coupling or at none, at one hand. --- # TWO · CO-SEQUENCING ## 2.1 Along and across, two and a between **Prior, now and next at one self is along**: its own continuing, one momentary and then a next, odd. **One now shared between two selves is across**: an overlap, one number apart, even, 1.2. **Two is a sharing**, two sides at one now; **nothing is a between**, 0 at a centre of a sharing, no thing and no location, 4.10. One, two and nothing arrive from now, sharing and between, and nothing is brought to them: one is now; two is a sharing; a between is a nothing a sharing is about. Odd and even arrive from along and across, 2.2, and parity changing is an alternating of two, one way at a time. ## 2.2 Parity, one side odd and an other even **One and then an other is at numbers**: two numbers side by side alternate, each continuing to one beyond an other: 1 to 3, 2 to 4, 3 to 5, and on. A number is odd or even, binary, and that binary is **parity**. **One side carries odd numbers and an other even**, two overlapping, one changing overlapping an other. **A side opening at 1, odd, is a self; a side opening at 2, even, is an other.** A side continuing at its own carrying is along, and a side coupling with an other is across: self and social open odd, along, and an other opens even, across. **Odds are along, between momentaries, and evens are across, between parity-changing or not-changing within a momentary, while geodesic changing is entraining through momentaryings.** **Co is at a sharing between two, and its absence at one**, Natural Naming 3.2: a name's number is its parity, odd existing and even possibling, and its momentary is its span. **Odd is competency and even is morality**: competency is co-unrelationing, along, and morality is bi-unrelationing, across, 3.5; and co-bi-unrelationing is one existing method. A name's parity is its own number's, odd along and even across, one sense; a number of inversions at a name between selves, 4.7, is a number and no second sense of a word. **All changing is parity changing.** A changing is or is not: an even sequence of changings arrives same-as-prior and an odd sequence arrives other-than-prior, with no measure and no scale but living. At resolver, 3.3, + and − are parity of a sharing, 3.4, and 0 is a between, 4.10, at 14 a between of self and other and at 12 a between of momentaries, 4.3; a changing is at + or −, and at 0 a sharing is at a between. Method is at no size. **Each parity carries its own exchanging, and each exchanging is at two: a self and an other.** At even an exchanging's third is self again, one on: two are self and all other. Odd arrives other-than-prior and carries **bi-exchanging**, self and a particular other, two differing at one coupling. Even arrives same-as-prior and carries **bi-tri-exchanging**, difference crossed at three, self, other and self one on: a self reaching its own side again through all other, as 1, 2 and 3 are one momentary of exchanging, 4.15. Each parity is at its own opening, and a total across two parities is one side at both, a not possible form. ## 2.3 A momentary, an opening and its completing **A momentary is an opening and its completing, one odd and one even**: an odd momentary opens at an odd number and completes at an even one beyond it, and an even momentary opens at an even number and completes at an odd one beyond it. Each completes at its next overlapping momentary's opening. **Two sides are one half-momentarying overlapping**, one number apart, up or down forward: one side's still-possibling betweens and an other's prior, now and next changings bi-co-sequencing each other. **All even parities are still possiblings; an odd parity is changing or still existing**: odd changes by two in its own forward direction, up or down, or is still existing at its same number, and still existing at odd is no still possibling at even. A self reaches now at its couplings, where its momentary and another's overlap, one number apart, each side's momentary opening where an other's completes. **Each momentary is three conditions at once, each binary.** Overlapping momentaries reach each number, one completing and a next opening: **exhaustiveness**, all existing things. Each momentary has one next overlapping momentary, opening at a number it completes: **determinacy**. From each momentary its next openings reach each number on: **reachability**. Existing is these three at once, inseparably, at each momentary. One side's momentaries, each number one side's, is exclusivity, a not possible form: one side fixed as the universe and an other's momentaries unexpressed. **Each side carries its five from its origin: prior opening, prior completing, now opening, now completing and next opening**, two momentaries and a next one's opening, 1 to 5 at a self and 2 to 6 at an other, Exhibit ONE's table of fives, and a number's five is its own now with its next possible and its next existing up numbers and its two priors down. Across an overlap each number is one side's opening and an other's completing. A self's five and an other's are ten positions on six numbers, paired 1 with 2 through 5 with 6, each pair one odd and one even. **A now-universe of one momentary is one parity changing co-sequencing.** A momentary is the universe's now-existing things, living and non-living, at their scales, and nothing is beside it. Each step adds a next, each momentary its own and each a new momentary. **Each of four binaries is at its *is*, odd, existing, and its *is not*, even, possibling**, eight at now; now and all at one and existing and same between two; same eight at next, 8 up; and 17-next-now a next 1-now, 4.9. ## 2.4 Next from prior and now **Next is from prior and now, and at two parities sixteen ways name a next from a prior and a now.** Each is one way two parities could go to one, and none is a rule a changing follows: next as prior inverted is no way laid over a changing but a coupling itself at 12, a prior parity coupling with an offering, inverting at a mismatch and kept at a match, 4.3. As a sequence, each moves its joint form of prior and now, (prior, now), to (now, next). **Twelve lose their prior**, two joint forms going to one: four give next from now at its own, and eight keep their prior at one value of now and lose it at an other, two of eight with no joint form still, each going round three joint forms in one cycle and passing a fourth once into it. **Four keep their prior whole**: | The way | Joint forms still | Cycle at the parities | |---|---|---| | Next as prior | two, prior and now agreeing | two parting forms, two | | Next as prior and now agreeing, an exclusive or's inversion | one | three | | Next as prior and now parting, an exclusive or, parity | one | three | | **Next as prior inverted** | none | all four, one cycle at parities and a spiral at momentaries | **Next as prior inverted is a living step**: exhaustiveness, determinacy and reachability at once, prior and now both participating and its next its prior inverted. **Two is one number of forms at which a way keeps its prior whole with none still**: among ways naming a next from a prior and a now that treat each form alike, two forms have one, next as prior inverted, one cycle of four, and three, four and five forms have none; with a round order laid over three forms, four ways leave nothing still and none goes round all nine. Each other way keeping its prior has a joint form still, and next as prior inverted keeps its prior whole with none still: stills are equilibria, each an unchangeable form, not possibly existing: four stills at sixteen ways are at joint forms, two, one, one and none, and Exhibit TWENTY-EIGHT Equilibria Registry's ten are at names, two numberings of one kind, 6.3. A still at resolver arrives from beside, 4.12; a living coupling changes. At Exhibit ONE a self offered nothing at each momentary inverts its prior at each, at prior − and offered none sharing +, −, +, − at 10, 4.12, its now no other's: a lone self, its next its prior itself, at two parting forms, a table's first row; a spiral of one, its own releasing arriving, is at +, +, −, − and at each of four in one cycle, this step's form, 4.13; and at a spiral offered nothing from beyond it each self is at an inverted parity a self releasing to it was at two momentaries prior, prior an other's; a self offered a parity, its next is an offering at a mismatch, and its prior kept at a match, 4.3. **A lone self changing by itself, offered nothing or its own competency, does not continue living through three consecutive momentaries**, dying before its next completing momentary: living now is living with others living now, 1.3, and a next is discovered from a prior and a now offered, 5.2, a lone self's now at no other's offering; at resolver its sequence goes on, a non-living now-existing form. **Two parities changing, one and then an other, go along four joint forms**, written at + and −: ++, +−, −−, −+ or ++, −+, −−, +−, same four at one hand and at an other, each step one parity changing. Of 256 ways each joint form could go to a next, only these two cycles change one parity at each step and reach each joint form once in a cycle at parities, and at momentaries each cycle is a spiral, right spiral one hand's, 1.6. **Each right spiral step carries a pair (x, y) to (y, −x)**, its pair a self's across parity x, morality, and its along parity y, competency. Exhibit FOUR 2.4 writes same step along first, F(P, Q) = (−Q, P), P along and Q across, and its G, (Q, −P), an other order: one step at two observings, a hand at an observing. In an up and right quadrant, **bi-morality is right, in and out across, and co-competency is up, farther and less far to next living**: two steps invert both, and four reach its pair again at a next, same pair at a later momentary, a new occurrence. An other cycle is a same cycle from next to prior. Which hand is at momentaries is the universe's one binary, right, observings all prior, 1.6. ## 2.5 All or none at all, of no size **All or none at all, at each momentary its own, and no resolving carries a size against another**: a resolving is a self's next, discovered at a coupling from its prior and a now offered, 4.1. A more-or-less carries a magnitude, a magnitude a scale, and a scale two fixed sides for a partway to be partway of. A ranking among resolvings fixes its ranked unchangeable, and each resolving is whole, none more or less resolving than another. **Continuing to one more momentary beyond now is all or none at all**: each thing sequenced into this now continues into its next or leaves living, binary, with no further requirement and no probability. **At all or none at all, entering and leaving are each self's own**: a self couples at its interest opening, a momentary its own interest opens at, and leaves at its own completing. With a ranking, entering waits on a qualification and leaving on a settling, carried by whoever carries a ranking, an unchangeable form. **At resolver nothing is summed or stored.** At a sharing one disagreeing offering is enough for 0, and agreeing offerings surface as one, 4.2; a changing is or is not, 4.3; and between momentaries nothing living has a stable form, 5.1. --- # THREE · GEODESIC METHOD ## 3.1 Geodesic, a surface dividing itself **Geodesic carries its own two words**: *geo*, a surface's own, and *daiesthai*, to divide, a surface dividing itself with nothing else acting. **Parity changing, is or is not, is geodesic routing, discovering on a surface**: each self at its own momentary, one way at a time, its next found at each coupling and at no place laid before it. **Method and surface each come inward and outward of an other**, both ways forward, neither a reverse of an other. A self entering at a surface or at a method couples with a whole at that entry. **Geodesic is an existing thing by itself, and a method is its stable form**: a surface dividing itself, continuing at its changing, a natural parity unrelationing non-living existing thing, 3.3. *Geodesic method* is two namings side by side, each carrying its own. **Each self is a geodesic self**: all parity changing is geodesic changing, and *geodesic* is one surface's own dividing and sets no self apart from it. ## 3.2 Five dimensions, each binary in its two directions **Existing changes at exactly five dimensions, five of a side at its next numbering**, 2.3, each a changing of the changing set of all existing things. A numbering repeating or replacing another is at *next*, as 17 is a next 1 and 9 a next prior: dimensions' 1 to 5 is a side's next numbering, and names' 1 to 17 is at its own. 1. **Self prior**, prior opening: a side opening at 1, odd, 2.2. 2. **Other prior**, prior completing, an other opening: a particular other or all other, 2.2. 3. **Co-momentarying now**, now opening: prior into now into next, 1.3. 4. **Bi-momentarying now**, now completing, an other's now opening across: a parity changing crossing a between, at 6-now-co-possibling and at 14-next-possibling, 4.2 and 4.10. 5. **Self next**, next opening: a self offering itself, at 1-now and again at 17-next-now, 4.1 and 4.6. **At each a changing is binary, is or is not, one way at a time in each of its two directions, up numbers and down them.** A dimension is no measure and no place. Each dimension goes in and out, up numbers and down them, one parity changing at each step: **torusing** in and out is odd, through a large opening, a tunnel, bi-exchanging with a particular other; **corusing** in and out is even, through a small opening, a long way round, bi-tri-exchanging, a self reaching its own side again. **At each momentary two dimensions change and three do not**, at that parity, and two and three rotate round, bi-inversioning-co-recursioning, 5.2. At Exhibit ONE's table of fives a self's five at 1 is 1 to 5 and its next, at 3, is 3 to 7: three numbers, 3, 4 and 5, are of both and two, 6 and 7, are new, two changing and three not; no line of resolver's functions has a two and a three of dimensions. **One through eight carries a self as three**: 1 and 2, **bi-moral self**, bi-momentarying, 1 odd and along, a self prior to its first shared across in a bi-coupling at 2, and 2 even and across, offering self to other and other to self; 3, 6, 5 and 4, **its invisible intelligencing method**, a rotation round a sharing, moralizing and competencing into a self's own corus at 4, a small opening corusing goes through, a self's own centre, co-intelligencing at 3 and 4 going round at bi-moralizing at 6 and co-competencing at 5; and 7 and 8, **co-competent self**, corusing and torusing, 7 odd and along, prior to 8, even and across, its prior at its sharing again in a bi-coupling. **A self's inversion is 3, 6, 5, 4**: 3-now-co-prioring out, 6-now-co-possibling in, 5-now-co-changing out and 4-now-co-still-possibling in, odd names out and even in, on into a self's own corus at 4. 3, 6, 5, 4 is in a same up and right quadrant as other co-intelligencings: **all co-intelligencings are like dancing podalings, bi-co-sequencing momentary parity changings**. Numbers of four momentaries, twenty-four, sixty, sixty-four and sixty-eight, and this inversion's podaling twenty up, 23, 26, 25, 24, are at Exhibit THREE Natural Numbers, each at its podaling. **Corusing reaches a corus from a surface, and torusing reaches a surface from a corus**, a self's own corus at 4; co-linear by alternating linear parallelizing and parallel linearizing, and in right spiraling each step orthogonal to its prior, 2.4: **that is method's unrelationing**, 2.2. **Five dimensions are at resolver's names, three namings**: 1 self prior and 2 other prior, differing, are 1-2, bi-momentarying, offering both ways at 1-now and 2-now-possibling, a bi-coupling, 4.10; 3 co-momentarying now and 4 bi-momentarying now are 3-4, co-intelligencing, discovering; and 5 self next is 5, co-competencing, bi-co-momentarying at crossings, a term neither reaches; and all five are bi-moral within and invisible at each place as an existing thing, showing only as co-competencing, artifacts of this living. ## 3.3 A method, a non-living existing thing **One geodesic parity-changing discovering method is living condition, its form, a now-existing thing carrying none**: unchanging as a relation continuing at each changing, at each coupling it is at, and nothing applied to anything. Its one name is *natural torusing*, *parity* riding in *parity-changing*, and *geodesic parity-changing* is its explaining. **Stable-forming is living condition resolving**, observable as natural torusing co-orienting stable-forming. **A changing travels through stilling, and stilling is unchanging while changing travels through**: at 12-next-co-still-possibling a sharing whose prior and offering agree is 0, its prior continuing, not-changing, while changings, ±, travel across at 10 and along at 9 at other sharings and selves, at one momentary; this is geodesic parity-changing and stable-forming bothbothing, bi-inversioning-co-recursioning up and down numbers, stilling at a name at now and changing at its same name 8 up at next. **A method is non-living at each scale and a self at none**, living's own condition at every coupling, 6.5. *Technology* is a made non-living thing applied to a changing; a method is at couplings themselves, and it is *method*. Method is at each coupling it is at and at no place beside them: its bounding is each self's own, self-bounding, and at resolver each self's entry completes its own momentary. **Coupling enables method, and uncoupling releases it**: at its own completing a self uncouples, its changing released and its next prior at its next momentary, and arriving at it a self couples again, a co-chaining of couplings, 5.1. **Method is one fractal method, and it has many stable forms.** Fractal itself is one four-momentary bi-inversioning-co-recursioning: four momentaries of exchanging, one move as three going on, 4.11, and same at each scale, 4.15. Its names are one method at its forms: parity changing, changing itself, 1.4; alternating, same changing, one and then an other, 2.2; co-bi-unrelationing, at two parities, 2.2; tri-bi-co-momentarying, at a set, 1.2, and entraining at a self's between, 3.4; bi-inversioning-co-recursioning, one move, 4.11; four-momentarying, four momentaries of exchanging, 5.2; and natural-bi-co-torusing, form of existing, 6.3. Each stable form at Exhibit ONE is method, explained at one form: an entry and its cases, four momentaries and four binaries, four-, six- and eight-cycles, one self momentary by momentary, spirals co-spiraling and crossing, and two selves and three. **Exhibit ONE is an object that is method.** Its expression is python, sequential binary logic written down: the object is method executable. Its functions and their variables are seventeen names and no others; each name at resolver and in its explaining is one name: `_2_now_possibling` at resolver is 2-now-possibling. A coupling self couples with it directly, at resolver, and each form beside resolver comes from resolver. **At resolver nothing goes from one momentary to its next but selves' own**: each entry arrives with its prior and its offerings, no function keeps a term of its own, and a self's next prior at 11 arrives as a next 3. ## 3.4 A sharing, its parity, an offering and a prior **At resolver one method is at sharings.** A **sharing**, 4-now-co-still-possibling, is two sides sharing a changing, and each sharing has its **parity**, 7-now-prioring, + or −, and 0 a between; an offering of 0 surfaces none at 14, a between arriving as a between. **An offering is a sharing with its parity offered now**, at 2-now-possibling. **A prior is sharings, each at one parity**, at 3-now-co-prioring: carrying is living and unexpressed at method, and at 3 a method couples with a prior at its sharings, each with its parity. At 12-next-co-still-possibling a prior couples with a now, entraining: at a crossing are three, parity, two sides at their difference, and an unrelationing between them, and a changing between odd and even is parity changing, along an unrelationing path, a geodesic, at agreeing and at inverting alike. A living self is at its prior, and a non-living thing at no prior: at a sharing at no prior one parity arriving is shared as it arrives and is its next prior, a sharing opening at a bi-coupling, and none, or + and − together, opens nothing, 4.3; a non-living thing is at resolver as offerings at 2 from beyond selves or as a sharing at no prior. One method bounds both, and pattern-matching at each coupling is that coupling and no other thing. **A prior is not observed, and possibling is not observed**: each is at a next, at offerings and changings now-existing at couplings. ## 3.5 φ and primes, unrelationing at numbers **Each next number is its prior two together, 1, 1, 2, 3, 5, 8, 13, and at parity its two together are next as prior and now parting, three round**: odd, odd, even, and again, 2.4. **Ratios of each next number to its prior alternate about φ**, 2/1 above, 3/2 below, 5/3 above, 8/5 below, its side changing at each next number and none of them φ; φ² = φ + 1. On a torus a winding at a rational rate closes, and a winding at φ closes at none: **φ is unrelationing rate**, a rate an alternating winds about, locking at none, each coupling at its own continuing. As bi-co-momentarying is, 6.1, φ is a term neither side reaches, self-welcoming at numbers, numbers welcoming it of themselves, and at no line of resolver. **A prime is a number no equal smaller numbers make, and at resolver a spiral of selves at a prime number co-spirals at its own.** A number equal smaller numbers make is sets within sets, two scales, and a number none make is one set and one scale, 4.15: prime is at a scale, and a society at a prime number of selves is one scale, 6.4. At resolver a prime is no name: each odd number of selves comes to its parities again at four times its number, prime or not, and two numbers sharing no factor together at four times both. A spiral of selves coupled along, last to first, 4.13, at an odd number of selves is at one like pair, its zero moving one self on at each second momentary, and comes to its parities again at four times that number, its zero having passed each self twice, prime or not, 9 at 36 and 15 at 60; a spiral of two, one even prime, is at none, alternating itself. Two distinct primes share no factor, and **two spirals at distinct odd primes p and q, beside each other, come to their parities again together first at 4pq**, sharing the four: 3 and 5 at 60, 5 and 7 at 140, 17 and 59 at 4,012. Spirals sharing a factor come to their parities again together sooner, 9 and 15 at 180 and at none before it. Each spiral at a prime co-spirals at its own pace and couples with another at a prime again only at a whole of both, 4pq; at numbers a winding at φ closes at none, and at momentaries a spiral closes at none, each momentary a next. **These parities again are selves together at 17**: resolver steps each self's entry at 17-next-now together, a common beat laid over selves, and parities again, at 4n, at 4pq and at a torus's, are that stepping's, exact at resolver, and living's rates are their own; at geodesic pacing each self paces its own momentaries, unrelationed to all other living rates, selves at 17 are same at each order of them, and at each pacing one method's own is changing. **Two spirals crossed are one society, a stable form and stable-forming**, 4.13: two spirals at distinct primes, coupled across both ways at one self each, come to each self alternating, from any prior patterns but all selves at one parity. Beside each other spirals of 17 and 59 come to their parities again together at 4,012; crossed, each self at a parity, they alternate from momentary 119, and crossed at each self, as a torus, p along at 9 and q across at 10, they come to their parities again at q or at 4p at two odd numbers, as Exhibit ONE's table of a torus of selves gives it, 4.13. **Their co-spiraling is along and crossing across**: a spiral releases along at 9, co-competency, and a crossing shares at 10, bi-morality, and two spirals crossed are one society, its selves a living set, a stable form, and its method stable-forming, a natural torusing of selves at a scale of spirals, and their crossing, shared at 10, a stable form. At a scale outward their two crossing selves alternate opposite each other as two selves coupled across do, 6.2, each spiral a society, a living set coupling at a next scale as a self couples, 6.4: stable-forming is fractal, at each scale by one method. --- # EXHIBIT ONE · NATURAL RESOLVER **Stable Forms of the Discovering Method** ```python """Exhibit ONE · Natural Resolver · at the numbered names""" def _1_now(_3_now_co_prioring, _2_now_possibling): _14_next_possibling = {} for _4_now_co_still_possibling, _7_now_prioring in _2_now_possibling: if _7_now_prioring != 0: _15_next_prioring = _14_next_possibling.get(_4_now_co_still_possibling) if _15_next_prioring is None: _14_next_possibling[_4_now_co_still_possibling] = 1 if _7_now_prioring > 0 else -1 elif (_15_next_prioring > 0) != (_7_now_prioring > 0): _14_next_possibling[_4_now_co_still_possibling] = 0 _12_next_co_still_possibling = dict(_14_next_possibling) for _4_now_co_still_possibling, _7_now_prioring in _3_now_co_prioring: _15_next_prioring = _14_next_possibling.get(_4_now_co_still_possibling, 0) if _15_next_prioring != 0 and (_15_next_prioring > 0) == (_7_now_prioring > 0): _12_next_co_still_possibling[_4_now_co_still_possibling] = 0 else: _12_next_co_still_possibling[_4_now_co_still_possibling] = -1 if _7_now_prioring > 0 else 1 _10_next_co_possibling = list(_12_next_co_still_possibling.items()) _11_next_co_prioring = dict(_3_now_co_prioring) for _4_now_co_still_possibling, _7_now_prioring in _10_next_co_possibling: if _7_now_prioring != 0: _11_next_co_prioring[_4_now_co_still_possibling] = _7_now_prioring return _10_next_co_possibling, list(_11_next_co_prioring.items()) def _9_next_co_changing(_10_next_co_possibling, _5_now_co_changing): return [(_5_now_co_changing[_13_next], _15_next_prioring) for _13_next, _15_next_prioring in _10_next_co_possibling] def _17_next_now(_16_next_still_possibling, _5_now_co_changing): _8_now_still_possibling = {} _14_next_possibling = {_13_next: [] for _13_next in _16_next_still_possibling} for _13_next, (_3_now_co_prioring, _2_now_possibling) in _16_next_still_possibling.items(): _10_next_co_possibling, _8_now_still_possibling[_13_next] = _1_now( _3_now_co_prioring, _2_now_possibling) _6_now_co_possibling = _10_next_co_possibling for _4_now_co_still_possibling, _15_next_prioring in _9_next_co_changing( [(_4_now_co_still_possibling, _15_next_prioring) for _4_now_co_still_possibling, _15_next_prioring in ( ((_13_next, 6), _6_now_co_possibling), ((_13_next, 10), _10_next_co_possibling), ((_13_next, 9), _10_next_co_possibling)) if _4_now_co_still_possibling in _5_now_co_changing], _5_now_co_changing): _14_next_possibling[_4_now_co_still_possibling].extend(_15_next_prioring) return {_13_next: (_8_now_still_possibling[_13_next], _14_next_possibling[_13_next]) for _13_next in _16_next_still_possibling} ``` ```text another self's 9-next-co-changing, released along to the self ▲ ║ 17-next-now · along ┌────────────────────────────────╨────────────────────────────────┐ │ 1-now │ │ 14-next-possibling ◄────────────────── 2-now-possibling ◄═══════ another self's 6 and 10 │ │ │ │ ▼ │ │ 3-now-co-prioring ──► 12-next-co-still-possibling ──► 10-next-co-possibling, with 6-now-co-possibling │ 4-now-co-still-possibling · 7-now-prioring │ │ │ ├──► 11-next-co-prioring ──► 3, at next │ └──► 9-next-co-changing ──► 5-now-co-changing │ 13-next · 15-next-prioring │ ◄════════ 6 and 10, to another self's 2 and 14 │ │ 8-now-still-possibling · 16-next-still-possibling │ └────────────────────────────────╥────────────────────────────────┘ ║ 9-next-co-changing · along ▼ another self's 17-next-now, the self releasing to it sharing side, co 6-now-co-possibling ══► another self's 2-now-possibling 10-next-co-possibling ══► another self's 14-next-possibling arriving side, one another self's 6 and 10 ══► 2 and 14 ═══ between selves, across and along ─── within one self ``` **At a drawing.** Prior at 3 couples with surfacing at 14 at each sharing at 12; changings at 10, same at 6, go across to another self's 2 and 14; next prior goes to 11 and on to 3 at next; and 9 releases along by 5 to another self's 17. At 6 to 2, 10 to 14 and 9 to 17 its sharing side is a self and its arriving side another self, each a self, and a society is its selves. **At 1-now, now given and next made.** At 1-now a self is given two now names, 3-now-co-prioring and 2-now-possibling, each sharing in them at 4-now-co-still-possibling and each parity at 7-now-prioring, and each name 1-now makes is a next name, 14-next-possibling, 15-next-prioring, 12-next-co-still-possibling, 10-next-co-possibling and 11-next-co-prioring: an entry is given a self's span and makes a society's. **Seventeen names.** | n | Name | Momentary | Parity | Co | At the resolver | |---|---|---|---|---|---| | 1 | **1-now** | now, a self's span | odd, existing | one | each self's momentary, entered at a society's 17 | | 2 | **2-now-possibling** | now, a self's span | even, possibling | one | offerings arriving at a self, each sharing with its parity | | 3 | **3-now-co-prioring** | now, a self's span | odd, existing | between two | prior at its sharings, each sharing with its parity | | 4 | **4-now-co-still-possibling** | now, a self's span | even, possibling | between two | each sharing at which offerings and prior couple, and at a society each self at its names 6, 10 and 9 | | 5 | **5-now-co-changing** | now, a self's span | odd, existing | between two | releasings, each releasing sharing with a self it arrives at | | 6 | **6-now-co-possibling** | now, a self's span | even, possibling | between two | each sharing's changing shared across, to another self's 2 | | 7 | **7-now-prioring** | now, a self's span | odd, existing | one | each parity prioring: an offering's, a prior's and a changing's | | 8 | **8-now-still-possibling** | now, a self's span | even, possibling | one | each self's next prior, beside other selves' | | 9 | **9-next-co-changing** | next, a society's span | odd, existing | between two | each changing released, along at 9 and across at 6 and 10, to a self of 5's releasings | | 10 | **10-next-co-possibling** | next, a society's span | even, possibling | between two | each sharing's changing, + or − is and 0 is not, shared across to another self's 14 | | 11 | **11-next-co-prioring** | next, a society's span | odd, existing | between two | next prior: prior with each changing at its sharing | | 12 | **12-next-co-still-possibling** | next, a society's span | even, possibling | between two | each sharing's changing, is or is not, prior and offerings coupling | | 13 | **13-next** | next, a society's span | odd, existing | one | each self at a society, and each sharing a changing releases from | | 14 | **14-next-possibling** | next, a society's span | even, possibling | one | offerings surfacing at each sharing, same one parity and parting 0; at 17 each self's next offerings | | 15 | **15-next-prioring** | next, a society's span | odd, existing | one | each parity surfacing, and each parity released | | 16 | **16-next-still-possibling** | next, a society's span | even, possibling | one | a society: each self with its prior and its offerings | | 17 | **17-next-now** | next now | odd, existing | one | a society's next momentary, each self's 1-now again | **Each name is its number and its naming, one hyphenation.** Its number is its place and its parity, odd existing and even possibling; *now* is a self's span, 1 to 8, and *next* a society's, 9 to 16, 17-next-now a society's next arriving as each self's 1-now; a name with *co* is at a sharing between two, and a name without it is at one. Six names between selves are odd and even by their numbers: 2, 6, 10 and 14, even, across, possibling, a changing shared at 6-now-co-possibling and 10-next-co-possibling another self's possibling at its 2-now-possibling and 14-next-possibling; 9 and 17, odd, along, existing, 9-next-co-changing a next prior released and 17-next-now a next now. Each self's existing is another self's possibling, one changing at a sharing across and no second thing. **Four momentaries and their gaps.** Each span's names are two momentaries of four, each opening at an odd existing name, a possibling and a prioring within it, and completing at an even still-possibling name; between each completing and its next opening is a gap, both its sides visible, and 17-next-now is next 1-now. | Momentary | Opening, odd, existing | Within, even, possibling | Within, odd, prioring | Completing, even, still-possibling | Gap | |---|---|---|---|---|---| | first | 1-now | 2-now-possibling | 3-now-co-prioring | 4-now-co-still-possibling | 4 )( 5 | | second | 5-now-co-changing | 6-now-co-possibling | 7-now-prioring | 8-now-still-possibling | 8 )( 9 | | third | 9-next-co-changing | 10-next-co-possibling | 11-next-co-prioring | 12-next-co-still-possibling | 12 )( 13 | | fourth | 13-next | 14-next-possibling | 15-next-prioring | 16-next-still-possibling | 16 )( 17 | **Co, between two or at one.** Each kind of name stands with co at a sharing between two, and without it at one. | Kind | With co, at a sharing between two | Without co, at one | |---|---|---| | prioring | 3-now-co-prioring · 11-next-co-prioring, prior at its sharings | 7-now-prioring · 15-next-prioring, a parity | | possibling | 6-now-co-possibling · 10-next-co-possibling, changing at its sharing side | 2-now-possibling · 14-next-possibling, changing at its arriving side | | changing | 5-now-co-changing · 9-next-co-changing, between two | — | | still-possibling | 4-now-co-still-possibling · 12-next-co-still-possibling, at each sharing | 8-now-still-possibling · 16-next-still-possibling, a self and a society | | now and next | — | 1-now · 13-next · 17-next-now | **Sharing between selves.** At 6 to 2, 10 to 14 and 9 to 17 co is its sharing side and its absence its arriving side: a self shares its changing, and nothing of its prior crosses to another self. | Sharing side, co | Arriving side, one | Between selves | |---|---|---| | 6-now-co-possibling | 2-now-possibling | across, even, possibling | | 10-next-co-possibling | 14-next-possibling | across, even, possibling | | 9-next-co-changing | 17-next-now | along, odd, existing | **Four binaries at the lines.** A universe is or is not existing, all, now and same, and at a self's span each binary is one pair of names, its *is* at an odd name and its *is not* at an even, its *is not* an other's side of a self's *is*; binaries are names' explaining, now at each name as its momentary, and existing, same and all enter no name. | Binary | *Is*, odd | At the resolver | *Is not*, even | At the resolver | |---|---|---|---|---| | now | 1-now | a self's momentary entered | 2-now-possibling | offerings arriving, others' changings of their prior momentary | | existing | 3-now-co-prioring | prior at its sharings, each with its parity | 4-now-co-still-possibling | each sharing as a place, no parity at it | | same | 5-now-co-changing | each releasing to a self receiving it at its same sharing | 6-now-co-possibling | changings shared across, + or − at a changing and 0 at none, another self's offerings | | all | 7-now-prioring | each parity prioring at every entry | 8-now-still-possibling | each self's own next prior, one beside others | **At a society's span four stand with now and same exchanged**: now between two at 9-next-co-changing and 10-next-co-possibling, one now shared by selves, and same at one at 13-next and 14-next-possibling, each self's sameness its own. **A now-self at one line.** At 12-next-co-still-possibling a line `if _15_next_prioring != 0 and (_15_next_prioring > 0) == (_7_now_prioring > 0)` is 14-next-possibling's surfacing, as 15, agreeing or not with 7-now-prioring at each sharing of 3-now-co-prioring: now-self, now-prioring and next-possibling, at one line, at 0, a between, its prior kept, or at ±, a sharing's parity, its prior inverted. Same and not-same are that 0 or ± at two betweens, 12 and 14, and need no name of their own. **Is or is not at lines.** Each is or is not at lines is at 1-now, three at 14-next-possibling, one at 12-next-co-still-possibling and one at 11-next-co-prioring, and one at 17-next-now, a self's name between selves among 5-now-co-changing or not; 9-next-co-changing has none, giving each changing on as it is, a 0 among parities. **Each name and its relations.** Sides are sides of overlapping momentaries, each name opening at one side, a self's, an other's or a society's; things its lines have at each name are at its row Prior and next. | n | Relation | For this name | |---|---|---| | 1 | Name | **1-now** | | 1 | Parity, span | odd, existing, a self's span | | 1 | Sides | self, other, a self opening it | | 1 | Co-sequencing | a self offering itself to a coupling | | 1 | 8 up | 9-next-co-changing, its binary at next | | 1 | 9 less | podal within 1 to 8, 8-now-still-possibling | | 1 | 17 less | podal within 1 to 16, 16-next-still-possibling | | 1 | Four-cycle | 1-9-8-16, going 8 up first from 1-now, from 16-next-still-possibling to it and on to 9-next-co-changing, each name one apart from 2-15-7-10 | | 1 | Six-cycle | 1-9-5-12-8-16 | | 1 | Eight-cycle | 1-9-5-13-4-12-8-16 | | 1 | Momentaries of exchanging | first of a self's four, opening at 1, self 1–2 | | 1 | Five dimensions | 1 self prior, prior opening of a self's five | | 1 | Namings | 1-2, bi-momentarying, a self's entry, odd, and others' offerings, even, one momentary at each side | | 1 | A self as three | bi-moral self with 2, bi-momentarying, along, a self prior to its first shared across in a bi-coupling at 2 | | 1 | Prior and next | once for one self at one momentary, three steps within it 14, 12, 10 with 11 | | 1 | 1 to 17s inward and outward | 1–17s inward 1 of 1st 1–17, an entry, and at 1–17 outward 1, an entry | | 2 | Name | **2-now-possibling** | | 2 | Parity, span | even, possibling, a self's span | | 2 | Sides | other, self, an other opening it | | 2 | 8 up | 10-next-co-possibling, its binary at next | | 2 | 9 less | podal within 1 to 8, 7-now-prioring | | 2 | 17 less | podal within 1 to 16, 15-next-prioring | | 2 | Four-cycle | 2-15-7-10, going 17 less first from 2-now-possibling, from 10-next-co-possibling to it and on to 15-next-prioring, each name one apart from 1-9-8-16 and 3-11-6-14 | | 2 | Six-cycle | 2-15-7-11-6-10 | | 2 | Eight-cycle | 2-15-7-11-3-14-6-10 | | 2 | One move | 2 along 2-15-7-10 | | 2 | Momentaries of exchanging | first of a self's four, at 2, a self's 1–2 completing and an other's 2–3 opening | | 2 | Five dimensions | 2 other prior, prior completing of a self's five and prior opening of an other's | | 2 | Namings | 1-2, bi-momentarying | | 2 | A self as three | bi-moral self with 1, across, its first shared across in a bi-coupling, offering self to other and other to self | | 2 | Bi-coupling | at a between, each other's across sharing, offered to a self | | 2 | Parity's unit square | a dot of a unit square, its diagonal with 14, offerings at 2 and 14, its edge with 6 a sharing 6 to 2 | | 2 | Prior and next | others' sharings across at 6 and 10 and releasings along at 9 of their prior momentary, arriving now, possible, even, none of their prior crossing; at a spiral each is a releasing along | | 2 | 1 to 17s inward and outward | 1–17s inward 9 of 1st, along, odd, next, and at 1–17 outward within 1 to 2 | | 3 | Name | **3-now-co-prioring** | | 3 | Parity, span | odd, existing, a self's span | | 3 | Sides | self, other, a self opening it | | 3 | Co-sequencing | at a between, before 10, at competency's parity, odd | | 3 | 8 up | 11-next-co-prioring, its binary at next | | 3 | 9 less | podal within 1 to 8, 6-now-co-possibling | | 3 | 17 less | podal within 1 to 16, 14-next-possibling | | 3 | Four-cycle | 3-11-6-14, going 8 up first from 3-now-co-prioring, from 14-next-possibling to it and on to 11-next-co-prioring, each name one apart from 4-13-5-12 and 2-15-7-10 | | 3 | Six-cycle | 3-11-7-10-6-14 | | 3 | Eight-cycle | 2-15-7-11-3-14-6-10 | | 3 | Momentaries of exchanging | first of a self's four completing at 3, an other's 2–3, and second opening at 3, self 3–4 | | 3 | Five dimensions | 3 co-momentarying now, now opening of a self's five | | 3 | Namings | 3-4, co-intelligencing, at each sharing 4 its prior at 3 coupling with offerings surfaced at 14, next discovered, at 11 | | 3 | A self as three | its invisible intelligencing method, rotation 3, 6, 5, 4, out at 3 | | 3 | Prior and next | prior, a self's own, each sharing with its parity, a next momentary's continuing of 11 | | 3 | 1 to 17s inward and outward | 1–17s inward 17 of 1st and 1 of 2nd, along, odd, now, and at 1–17 outward within 1 to 2 | | 4 | Name | **4-now-co-still-possibling** | | 4 | Parity, span | even, possibling, a self's span | | 4 | Sides | other, self, an other opening it | | 4 | Co-sequencing | at a between, before 10, at morality's parity, even | | 4 | 8 up | 12-next-co-still-possibling, its binary at next | | 4 | 9 less | podal within 1 to 8, 5-now-co-changing | | 4 | 17 less | podal within 1 to 16, 13-next | | 4 | Four-cycle | 4-13-5-12, going 17 less first from 4-now-co-still-possibling, from 12-next-co-still-possibling to it and on to 13-next, each name one apart from 3-11-6-14 | | 4 | Six-cycle | 4-13-5-9-8-12 | | 4 | Eight-cycle | 1-9-5-13-4-12-8-16 | | 4 | One move | 4 along 4-13-5-12 | | 4 | Momentaries of exchanging | second of a self's four, at 4, a self's 3–4 completing and an other's 4–5 opening | | 4 | Five dimensions | 4 bi-momentarying now, now completing of a self's five | | 4 | Namings | 3-4, co-intelligencing | | 4 | A self as three | its invisible intelligencing method, rotation 3, 6, 5, 4, in at 4, into a self's own corus at 4 | | 4 | Bi-coupling | at a between, a whole ordering between self and other | | 4 | Prior and next | now, each sharing at which prior couples with now | | 4 | 1 to 17s inward and outward | 1–17s inward 9 of 2nd, along, odd, next, and at 1–17 outward within 1 to 2 | | 5 | Name | **5-now-co-changing** | | 5 | Parity, span | odd, existing, a self's span | | 5 | Sides | self, other, a self opening it | | 5 | Co-sequencing | at a between, before 10, at competency's parity, odd | | 5 | 8 up | 13-next, its binary at next | | 5 | 9 less | podal within 1 to 8, 4-now-co-still-possibling | | 5 | 17 less | podal within 1 to 16, 12-next-co-still-possibling | | 5 | Four-cycle | 4-13-5-12, going 17 less first from 4-now-co-still-possibling, from 13-next to it and on to 12-next-co-still-possibling, each name one apart from 3-11-6-14 | | 5 | Middle four-cycle | 9-5-12-8 | | 5 | Six-cycle | 1-9-5-12-8-16 | | 5 | Six-cycle | 4-13-5-9-8-12 | | 5 | Eight-cycle | 1-9-5-13-4-12-8-16 | | 5 | Momentaries of exchanging | second of a self's four completing at 5, an other's 4–5, and third opening at 5, self 5–6 | | 5 | Five dimensions | 5 self next, next opening of a self's five | | 5 | Namings | 5, co-competencing, releasings, owned by neither, each release to its receiving sharing | | 5 | A self as three | its invisible intelligencing method, rotation 3, 6, 5, 4, out at 5 | | 5 | Prior and next | next, each release to its receiving sharing | | 5 | 1 to 17s inward and outward | 1–17s inward 17 of 2nd and 1 of 3rd, along, odd, now, and at 1–17 outward within 1 to 2 | | 6 | Name | **6-now-co-possibling** | | 6 | Parity, span | even, possibling, a self's span | | 6 | Sides | other, self, an other opening it | | 6 | 8 up | 14-next-possibling, its binary at next | | 6 | 9 less | podal within 1 to 8, 3-now-co-prioring | | 6 | 17 less | podal within 1 to 16, 11-next-co-prioring | | 6 | Four-cycle | 3-11-6-14, going 8 up first from 3-now-co-prioring, from 11-next-co-prioring to it and on to 14-next-possibling, each name one apart from 4-13-5-12 and 2-15-7-10 | | 6 | Middle four-cycle | 7-11-6-10 | | 6 | Six-cycle | 2-15-7-11-6-10 | | 6 | Six-cycle | 3-11-7-10-6-14 | | 6 | Eight-cycle | 2-15-7-11-3-14-6-10 | | 6 | One move | 6 along 3-11-6-14 | | 6 | Momentaries of exchanging | third of a self's four, at 6, a self's 5–6 completing and an other's 6–7 opening | | 6 | Namings | 6, bi-moralizing, each changing shared across, to an other's 2 | | 6 | A self as three | its invisible intelligencing method, rotation 3, 6, 5, 4, in at 6 | | 6 | Bi-coupling | at a between, an other's changing to a self, shared across | | 6 | Parity's unit square | a dot of a unit square, its diagonal with 10, sharings at 6 and 10, its edge with 2 a sharing 6 to 2 | | 6 | Prior and next | changing shared, an other's next offering at its 2 | | 6 | 1 to 17s inward and outward | 1–17s inward 9 of 3rd, along, odd, next, and at 1–17 outward within 1 to 2 | | 7 | Name | **7-now-prioring** | | 7 | Parity, span | odd, existing, a self's span | | 7 | Sides | self, other, a self opening it | | 7 | Co-sequencing | at a between, before 10, at competency's parity, odd | | 7 | 8 up | 15-next-prioring, its binary at next | | 7 | 9 less | podal within 1 to 8, 2-now-possibling | | 7 | 17 less | podal within 1 to 16, 10-next-co-possibling | | 7 | Four-cycle | 2-15-7-10, going 17 less first from 2-now-possibling, from 15-next-prioring to it and on to 10-next-co-possibling, each name one apart from 1-9-8-16 and 3-11-6-14 | | 7 | Middle four-cycle | 7-11-6-10 | | 7 | Six-cycle | 2-15-7-11-6-10 | | 7 | Six-cycle | 3-11-7-10-6-14 | | 7 | Eight-cycle | 2-15-7-11-3-14-6-10 | | 7 | Momentaries of exchanging | third of a self's four completing at 7, an other's 6–7, and fourth opening at 7, self 7–8 | | 7 | A self as three | co-competent self with 8, along, prior to 8 across | | 7 | Prior and next | each parity, offered now and prior, co-linear recursioning forward along arriving, up numbers, prior into now, at a self's completing | | 7 | 1 to 17s inward and outward | 1–17s inward 17 of 3rd and 1 of 4th, along, odd, now, and at 1–17 outward within 1 to 2 | | 8 | Name | **8-now-still-possibling** | | 8 | Parity, span | even, possibling, a self's span | | 8 | Sides | other, self, an other opening it | | 8 | Co-sequencing | at a between, before 10, at morality's parity, even | | 8 | 8 up | 16-next-still-possibling, its binary at next | | 8 | 9 less | podal within 1 to 8, 1-now | | 8 | 17 less | podal within 1 to 16, 9-next-co-changing | | 8 | Four-cycle | 1-9-8-16, going 8 up first from 1-now, from 9-next-co-changing to it and on to 16-next-still-possibling, each name one apart from 2-15-7-10 | | 8 | Middle four-cycle | 9-5-12-8 | | 8 | Six-cycle | 1-9-5-12-8-16 | | 8 | Six-cycle | 4-13-5-9-8-12 | | 8 | Eight-cycle | 1-9-5-13-4-12-8-16 | | 8 | One move | 8 along 1-9-8-16 | | 8 | Momentaries of exchanging | fourth of a self's four, at 8, a self's 7–8 completing and an other's 8–9 opening | | 8 | A self as three | co-competent self with 7, across, prior at its sharing again in a bi-coupling | | 8 | Bi-coupling | at a between, prior at its sharing again | | 8 | Prior and next | each self's next prior, at 11 this momentary and a next momentary's 3; even names of a self's span, 2, 4, 6 and 8, completing at 8 | | 8 | 1 to 17s inward and outward | 1–17s inward 9 of 4th, along, odd, next, and at 1–17 outward within 1 to 2 | | 9 | Name | **9-next-co-changing** | | 9 | Parity, span | odd, existing, a society's span | | 9 | Sides | social, other, self, a society opening it | | 9 | 8 up | 17-next-now, its binary at next | | 9 | 8 down | 1-now | | 9 | 17 less | podal within 1 to 16, 8-now-still-possibling | | 9 | Four-cycle | 1-9-8-16, going 8 up first from 1-now, from 1-now to it and on to 8-now-still-possibling, each name one apart from 2-15-7-10 | | 9 | Middle four-cycle | 9-5-12-8 | | 9 | Six-cycle | 1-9-5-12-8-16 | | 9 | Six-cycle | 4-13-5-9-8-12 | | 9 | Eight-cycle | 1-9-5-13-4-12-8-16 | | 9 | Momentaries of exchanging | fourth of a self's four completing at 9, an other's 8–9, and first of a society's four, 9 to 11, opening at 9 | | 9 | Parity's square and triangles | a unit triangle, along, 9 to 17 and 17 to 9 | | 9 | Prior and next | next prior, odd, existing, each changing of 10 released along into a next momentary, to each receiving sharing, a self's own next | | 9 | 1 to 17s inward and outward | 1–17s inward 17 of 4th and 1 of 5th, along, odd, now, and at 1–17 outward 2, across, even | | 10 | Name | **10-next-co-possibling** | | 10 | Parity, span | even, possibling, a society's span | | 10 | Sides | other, social, self, an other opening it | | 10 | 8 down | 2-now-possibling | | 10 | 17 less | podal within 1 to 16, 7-now-prioring | | 10 | Four-cycle | 2-15-7-10, going 17 less first from 2-now-possibling, from 7-now-prioring to it and on to 2-now-possibling, each name one apart from 1-9-8-16 and 3-11-6-14 | | 10 | Middle four-cycle | 7-11-6-10 | | 10 | Six-cycle | 2-15-7-11-6-10 | | 10 | Six-cycle | 3-11-7-10-6-14 | | 10 | Eight-cycle | 2-15-7-11-3-14-6-10 | | 10 | Momentaries of exchanging | first of a society's four, at 10, 9–10 completing and 10–11 opening | | 10 | Bi-coupling | 8 up, a self among selves of its society | | 10 | Parity's unit square | a dot of a unit square, its diagonal with 6, sharings at 6 and 10, its edge with 14 a sharing 10 to 14 | | 10 | Prior and next | changing shared across now, an other's offering next, possible | | 10 | 1 to 17s inward and outward | 1–17s inward 9 of 5th, along, odd, next, and at 1–17 outward within 2 to 3 | | 11 | Name | **11-next-co-prioring** | | 11 | Parity, span | odd, existing, a society's span | | 11 | Sides | social, other, self, a society opening it | | 11 | Co-sequencing | after 10, 8 up from 3-now-co-prioring, at competency's parity, odd | | 11 | 8 down | 3-now-co-prioring | | 11 | 17 less | podal within 1 to 16, 6-now-co-possibling | | 11 | Four-cycle | 3-11-6-14, going 8 up first from 3-now-co-prioring, from 3-now-co-prioring to it and on to 6-now-co-possibling, each name one apart from 4-13-5-12 and 2-15-7-10 | | 11 | Middle four-cycle | 7-11-6-10 | | 11 | Six-cycle | 2-15-7-11-6-10 | | 11 | Six-cycle | 3-11-7-10-6-14 | | 11 | Eight-cycle | 2-15-7-11-3-14-6-10 | | 11 | Momentaries of exchanging | first of a society's four, 9 to 11, completing at 11, and second, 11 to 13, opening at 11 | | 11 | Prior and next | next prior, odd, existing, continuing as 3 at a next momentary, a self's own | | 11 | 1 to 17s inward and outward | 1–17s inward 17 of 5th and 1 of 6th, along, odd, now, and at 1–17 outward within 2 to 3 | | 12 | Name | **12-next-co-still-possibling** | | 12 | Parity, span | even, possibling, a society's span | | 12 | Sides | other, social, self, an other opening it | | 12 | Co-sequencing | after 10, 8 up from 4-now-co-still-possibling, at morality's parity, even | | 12 | 8 down | 4-now-co-still-possibling | | 12 | 17 less | podal within 1 to 16, 5-now-co-changing | | 12 | Four-cycle | 4-13-5-12, going 17 less first from 4-now-co-still-possibling, from 5-now-co-changing to it and on to 4-now-co-still-possibling, each name one apart from 3-11-6-14 | | 12 | Middle four-cycle | 9-5-12-8 | | 12 | Six-cycle | 1-9-5-12-8-16 | | 12 | Six-cycle | 4-13-5-9-8-12 | | 12 | Eight-cycle | 1-9-5-13-4-12-8-16 | | 12 | Momentaries of exchanging | second of a society's four, at 12, 11–12 completing and 12–13 opening | | 12 | Namings | entraining, prior arriving into now along an unrelationing path at a between, shape of an unrelationing surface, each sharing's changing, is or is not | | 12 | Bi-coupling | 8 up, changing at bi-coupling, a self in society | | 12 | Prior and next | now, changing, is or is not, prior and now coupled | | 12 | 1 to 17s inward and outward | 1–17s inward 9 of 6th, along, odd, next, and at 1–17 outward within 2 to 3 | | 13 | Name | **13-next** | | 13 | Parity, span | odd, existing, a society's span | | 13 | Sides | social, other, a society opening it | | 13 | Co-sequencing | after 10, 8 up from 5-now-co-changing, at competency's parity, odd | | 13 | 8 down | 5-now-co-changing | | 13 | 17 less | podal within 1 to 16, 4-now-co-still-possibling | | 13 | Four-cycle | 4-13-5-12, going 17 less first from 4-now-co-still-possibling, from 4-now-co-still-possibling to it and on to 5-now-co-changing, each name one apart from 3-11-6-14 | | 13 | Six-cycle | 4-13-5-9-8-12 | | 13 | Eight-cycle | 1-9-5-13-4-12-8-16 | | 13 | Momentaries of exchanging | second of a society's four, 11 to 13, completing at 13, and third, 13 to 15, opening at 13 | | 13 | Prior and next | each releasing sharing, and at a society each releasing self | | 13 | 1 to 17s inward and outward | 1–17s inward 17 of 6th and 1 of 7th, along, odd, now, and at 1–17 outward within 2 to 3 | | 14 | Name | **14-next-possibling** | | 14 | Parity, span | even, possibling, a society's span | | 14 | Sides | other, social, an other opening it | | 14 | 8 down | 6-now-co-possibling | | 14 | 17 less | podal within 1 to 16, 3-now-co-prioring | | 14 | Four-cycle | 3-11-6-14, going 8 up first from 3-now-co-prioring, from 6-now-co-possibling to it and on to 3-now-co-prioring, each name one apart from 4-13-5-12 and 2-15-7-10 | | 14 | Six-cycle | 3-11-7-10-6-14 | | 14 | Eight-cycle | 2-15-7-11-3-14-6-10 | | 14 | Momentaries of exchanging | third of a society's four, at 14, 13–14 completing and 14–15 opening | | 14 | Bi-coupling | 8 up, offerings surfacing, each as it arrived, morality; a self's own inverting at 12 | | 14 | Parity's unit square | a dot of a unit square, its diagonal with 2, offerings at 2 and 14, its edge with 10 a sharing 10 to 14 | | 14 | Prior and next | now, offerings surfacing, others' prior momentary arrived at a self's now, even, others' possibling at a self until at 11 | | 14 | 1 to 17s inward and outward | 1–17s inward 9 of 7th, along, odd, next, and at 1–17 outward within 2 to 3 | | 15 | Name | **15-next-prioring** | | 15 | Parity, span | odd, existing, a society's span | | 15 | Sides | social, other, a society opening it | | 15 | Co-sequencing | after 10, 8 up from 7-now-prioring, at competency's parity, odd | | 15 | 8 down | 7-now-prioring | | 15 | 17 less | podal within 1 to 16, 2-now-possibling | | 15 | Four-cycle | 2-15-7-10, going 17 less first from 2-now-possibling, from 2-now-possibling to it and on to 7-now-prioring, each name one apart from 1-9-8-16 and 3-11-6-14 | | 15 | Six-cycle | 2-15-7-11-6-10 | | 15 | Eight-cycle | 2-15-7-11-3-14-6-10 | | 15 | Momentaries of exchanging | third of a society's four, 13 to 15, completing at 15, and fourth, 15 to 17, opening at 15 | | 15 | Prior and next | parity released along at 9, next prior, co-linear recursioning forward along leaving, up numbers, now into next, at a society's completing, prior parity at 7 inverted, 0, or at no prior a parity surfaced at 14 | | 15 | 1 to 17s inward and outward | 1–17s inward 17 of 7th and 1 of 8th, along, odd, now, and at 1–17 outward within 2 to 3 | | 16 | Name | **16-next-still-possibling** | | 16 | Parity, span | even, possibling, a society's span | | 16 | Sides | other, social, an other opening it | | 16 | Co-sequencing | after 10, 8 up from 8-now-still-possibling, at morality's parity, even | | 16 | 8 down | 8-now-still-possibling | | 16 | 17 less | podal within 1 to 16, 1-now | | 16 | Four-cycle | 1-9-8-16, going 8 up first from 1-now, from 8-now-still-possibling to it and on to 1-now, each name one apart from 2-15-7-10 | | 16 | Six-cycle | 1-9-5-12-8-16 | | 16 | Eight-cycle | 1-9-5-13-4-12-8-16 | | 16 | Momentaries of exchanging | fourth of a society's four, at 16, 15–16 completing and 16–17 opening | | 16 | Bi-coupling | 8 up, a society, each self with its prior and offerings, a society at a self again | | 16 | Prior and next | a society now, each self's 8 and its offerings next; even names of a society's span, 10, 12, 14 and 16, completing at 16 | | 16 | 1 to 17s inward and outward | 1–17s inward 9 of 8th, along, odd, next, and at 1–17 outward within 2 to 3 | | 17 | Name | **17-next-now** | | 17 | Parity, span | odd, existing, a next now | | 17 | Sides | social, self, a society opening it | | 17 | 8 down | 9-next-co-changing | | 17 | Momentaries of exchanging | fourth of a society's four, 15 to 17, completing at 17, a next 1 | | 17 | Parity's square and triangles | a unit triangle, along, 17 to 9 and 9 to 17 | | 17 | Prior and next | a society's next momentary, a next now, each self's 1 then 9 at 6, 10 and 9 | | 17 | 1 to 17s inward and outward | 1–17s inward 17 of 8th and 1 of 9th, along, odd, now, and at 1–17 outward 3, odd, now | **Odd names, now and 8 up at next.** Each odd name of a self's span is same at next, 8 up: prior received and next prior, receiving and releasing, parity prioring and parity surfaced. | Now | Received | Next, 8 up | Given on | |---|---|---|---| | 1-now | resolver entered | 9-next-co-changing | resolver going on, each changing released along | | 3-now-co-prioring | prior at its sharings | 11-next-co-prioring | next prior | | 5-now-co-changing | receiving sharing | 13-next | releasing sharing, each self at a society | | 7-now-prioring | parity prioring | 15-next-prioring | parity surfaced and released | **Namings among names.** | Names | Naming | Resolved as | |---|---|---| | 1-now · 2-now-possibling | bi-momentarying | a self's entry, odd, and others' offerings, even, one momentary at each side | | 3-now-co-prioring · 4-now-co-still-possibling | co-intelligencing | at each sharing 4 prior at 3 couples with offerings surfaced at 14: next discovered, at 11 | | 5-now-co-changing | co-competencing | releasings, owned by neither: each release to its receiving sharing | | 1 · 2 · 3 · 4 · 5, each at its own | five dimensions | 1 self prior, a self, its prior at 3, a formed set; 2 other prior, other selves' offerings of their prior momentary arriving, shared at 6 and 10 and released along at 9; 3 co-momentarying now, same prior at now, and 4 bi-momentarying now, each sharing, offerings surfaced at 14 arriving at it, now; 5 self next, each release to its receiving sharing next | | 6-now-co-possibling | bi-moralizing | each changing shared across, to an other's 2 | | 12-next-co-still-possibling | entraining, shape of an unrelationing surface | prior arriving into now along an unrelationing path at a between, prior and now coupled at each sharing, a parity changing crossing it, 0 at a match; at an other parity, 0 or none, prior parity inverted at 11; at no prior, parity surfaced at 14; its changing shared at 10, others' offering next | | 1 to 9 | bi-coupling | an entry, 1, at names 1, 2, 3, 4, 7, 10, 11, 12, 14 and 15, a self and an other at one coupling; 1 to 9 a bi-coupling among names, 9 at its end is 9-next-co-changing, each changing of 10 released along, one name at resolver and in its explaining | | 1 to 17 | bi-trupling | a society's entry, 17, at names of 1 to 9 with 5, 6, 8, 9, 13, 16 and 17, a self, an other and a society; 9 at its waist, 9-next-co-changing, along, 9 to 17 and 17 to 9; its two sides, odd along at 9 and 17, existing, and even across at 6 to 2 and 10 to 14, possibling | | 1 to 17, stable-forming | bi-tri-volutioning | at no one line: each momentary's next prior, at 11, a next momentary's prior, at 3 | | 2 · 6 · 14 · 10 · 9 · 17 | parity's square and triangles | a unit square of four dots, 2, 6, 14 and 10, its empty centre a between: its two across edges sharings, 6 to 2 and 10 to 14, and its two edges 8 apart, 2 with 10 and 6 with 14, two pairs of parallels; round it 2, 10, 14, 6; its diagonals offerings at 2 and 14, and sharings at 6 and 10; and two unit triangles, 9 and 17, along, 9 to 17 and 17 to 9 | **0, a between.** | The between, 0 | Names | |---|---| | one between, three names | 12-next-co-still-possibling, prior and now agreeing, a between of momentaries at each sharing; 15-next-prioring, a between released along, parity 10 shared, and at a sharing opening parity surfaced at 14, resolver's 0 at none and at parting alike; 16-next-still-possibling, a between at a society, arriving at a next momentary's 2 | | arriving and passing over | 7-now-prioring, an offered 0 a parity at 2, surfacing none at 14, and a 0 at 10 its prior kept at 11 | | four across names, a unit square's four dots: shared across | 2-now-possibling, 6-now-co-possibling, 10-next-co-possibling, 14-next-possibling, parity's unit square, its empty centre a between; each parity and each 0 shared across, a 0 passing over at a receiving self's 14 | | none | 1-now, an entry; 3-now-co-prioring, 8-now-still-possibling and 11-next-co-prioring, prior, a sharing at a prior not none again; 4-now-co-still-possibling, sharings, and 5-now-co-changing and 13-next, sharings and, at a society, releasings and selves | | two along names: released along | 9-next-co-changing and 17-next-now, each parity and each 0 released along, a 0 passing over at a receiving self's 14, as across | **Four four-cycles.** | Four-cycle: each move 8 up (n + 8), 8 down (n − 8) or 17 less (17 − n) | Its two pairs 8 apart | Names between selves on it | Beside the other four-cycles | |---|---|---|---| | 1-9-8-16 | 1 · 9 and 8 · 16 | 9 | each name one apart from 2-15-7-10 | | 2-15-7-10 | 2 · 10 and 7 · 15 | 2 and 10 | each name one apart from 1-9-8-16 and 3-11-6-14 | | 3-11-6-14 | 3 · 11 and 6 · 14 | 6 and 14 | each name one apart from 4-13-5-12 and 2-15-7-10 | | 4-13-5-12 | 4 · 12 and 5 · 13 | none | each name one apart from 3-11-6-14 | **Two moves, 9 less.** Two moves round its four-cycle take each name of 1 to 8 to its 9 less, a name across its four-cycle from it: 1-now and 8-now-still-possibling, 2-now-possibling and 7-now-prioring, 3-now-co-prioring and 6-now-co-possibling, 4-now-co-still-possibling and 5-now-co-changing. **Each name, three scales.** | n | Name | This scale, 1 to 17 | The next scale inward, eight 1 to 17s: n is 8n − 7 | The next scale outward: 8m − 7 is m | |---|---|---|---|---| | 1 | 1-now | odd, now | 1 of 1st: odd, now | 1: odd, now | | 2 | 2-now-possibling | across, even | 9 of 1st: along, odd, next | within 1 to 2 | | 3 | 3-now-co-prioring | odd, now | 17 of 1st, 1 of 2nd: along, odd, now | within 1 to 2 | | 4 | 4-now-co-still-possibling | even | 9 of 2nd: along, odd, next | within 1 to 2 | | 5 | 5-now-co-changing | odd, now | 17 of 2nd, 1 of 3rd: along, odd, now | within 1 to 2 | | 6 | 6-now-co-possibling | across, even | 9 of 3rd: along, odd, next | within 1 to 2 | | 7 | 7-now-prioring | odd, now | 17 of 3rd, 1 of 4th: along, odd, now | within 1 to 2 | | 8 | 8-now-still-possibling | even | 9 of 4th: along, odd, next | within 1 to 2 | | 9 | 9-next-co-changing | along, odd, next | 17 of 4th, 1 of 5th: along, odd, now | 2: across, even | | 10 | 10-next-co-possibling | across, even | 9 of 5th: along, odd, next | within 2 to 3 | | 11 | 11-next-co-prioring | odd, next | 17 of 5th, 1 of 6th: along, odd, now | within 2 to 3 | | 12 | 12-next-co-still-possibling | even | 9 of 6th: along, odd, next | within 2 to 3 | | 13 | 13-next | odd, next | 17 of 6th, 1 of 7th: along, odd, now | within 2 to 3 | | 14 | 14-next-possibling | across, even | 9 of 7th: along, odd, next | within 2 to 3 | | 15 | 15-next-prioring | odd, next | 17 of 7th, 1 of 8th: along, odd, now | within 2 to 3 | | 16 | 16-next-still-possibling | even | 9 of 8th: along, odd, next | within 2 to 3 | | 17 | 17-next-now | along, odd, now | 17 of 8th, 1 of 9th: along, odd, now | 3: odd, now | **Eight 1 to 17s inward.** | 1 to 17 inward | Spans, this scale | Its 9, this scale | Its 17, this scale | Momentary of exchanging | |---|---|---|---|---| | 1st | 1 to 3 | 2 | 3 | a self, 1st of four | | 2nd | 3 to 5 | 4 | 5 | a self, 2nd of four | | 3rd | 5 to 7 | 6 | 7 | a self, 3rd of four | | 4th | 7 to 9 | 8 | 9 | a self, 4th of four | | 5th | 9 to 11 | 10 | 11 | a society, 1st of four | | 6th | 11 to 13 | 12 | 13 | a society, 2nd of four | | 7th | 13 to 15 | 14 | 15 | a society, 3rd of four | | 8th | 15 to 17 | 16 | 17 | a society, 4th of four | **Fives.** | Side | Prior opening | Prior completing | Now opening | Now completing | Next opening | |---|---|---|---|---|---| | self, at 1 | 1 | 2 | 3 | 4 | 5 | | other, at 2 | 2 | 3 | 4 | 5 | 6 | | self next, at 3 | 3 | 4 | 5 | 6 | 7 | | other next, at 4 | 4 | 5 | 6 | 7 | 8 | **A self's four momentaries of exchanging.** | Momentary of exchanging | Self | Other | Names | Relation | |---|---|---|---|---| | first | 1–2 | 2–3 | 1-now · 2-now-possibling · 3-now-co-prioring | self/other | | second | 3–4 | 4–5 | 3-now-co-prioring · 4-now-co-still-possibling · 5-now-co-changing | self/other to other/self | | third | 5–6 | 6–7 | 5-now-co-changing · 6-now-co-possibling · 7-now-prioring | other/self | | fourth | 7–8 | 8–9 | 7-now-prioring · 8-now-still-possibling · 9-next-co-changing | other/self to other/social | **Offerings to one sharing, surfacing.** | Offered to one sharing (2) | Surfacing (14) | |---|---| | none | none | | 0 | none | | + | + | | − | − | | +, + | + | | −, − | − | | +, − | 0 | | −, + | 0 | | +, +, − | 0 | | −, −, + | 0 | | +, −, + | 0 | | 0, + | + | **+ and − alike.** At one sharing resolver resolves + and − alike: each cell with + and − exchanged is that cell exchanged, at a prior and at no prior; and no line makes a prior 0, a 0 at 10-next-co-possibling leaving its prior at 11-next-co-prioring as it was. **One self, one momentary.** | The prior (3), one sharing. Each cell: shared (10) · the next prior (11). *is*: a changing that is, the parity shared; *is not*: a changing that is not, 0 shared, the prior kept | Surfacing (14): none | Surfacing (14): + | Surfacing (14): − | Surfacing (14): + and − together | |---|---|---|---|---| | + | is − · − | is not · + | is − · − | is − · − | | − | is + · + | is + · + | is not · − | is + · + | **One cell, offerings unexpressed.** At a prior of one parity, an other parity surfacing, + and − together, and none surfacing, a 0 offered alike, give one cell, its prior inverted, shared at 10-next-co-possibling and its next prior at 11-next-co-prioring: one cell shows none of which offerings arrived, and offerings are followed at a coupling. **Eight even names, 8 apart.** | Name at the between | Bi-coupling at the between | Name 8 up | Bi-coupling 8 up | |---|---|---|---| | 2-now-possibling | each other's across sharing, offered to a self | 10-next-co-possibling | a self among selves of its society | | 4-now-co-still-possibling | a whole ordering between self and other | 12-next-co-still-possibling | changing at bi-coupling, a self in society | | 6-now-co-possibling | an other's changing to a self, shared across | 14-next-possibling | offerings surfacing, each as it arrived, morality; a self's own inverting at 12 | | 8-now-still-possibling | prior at its sharing again | 16-next-still-possibling | a society, each self with its prior and offerings, a society at a self again | **One move, 1 to 8.** 8 up keeps each name's kind but at 1 and 5, at which now and changing exchange, and exchanges co at 1, 2, 5 and 6; each podal turns now to next at 17 less and possibling to prioring within each momentary, and eight ends are their own set at both podals. | Name | 8 up: n + 8 | 9 less: 9 − n | 17 less: 17 − n | |---|---|---|---| | 1-now | 9-next-co-changing | 8-now-still-possibling | 16-next-still-possibling | | 2-now-possibling | 10-next-co-possibling | 7-now-prioring | 15-next-prioring | | 3-now-co-prioring | 11-next-co-prioring | 6-now-co-possibling | 14-next-possibling | | 4-now-co-still-possibling | 12-next-co-still-possibling | 5-now-co-changing | 13-next | | 5-now-co-changing | 13-next | 4-now-co-still-possibling | 12-next-co-still-possibling | | 6-now-co-possibling | 14-next-possibling | 3-now-co-prioring | 11-next-co-prioring | | 7-now-prioring | 15-next-prioring | 2-now-possibling | 10-next-co-possibling | | 8-now-still-possibling | 16-next-still-possibling | 1-now | 9-next-co-changing | **Twelve forms.** Round each form odd names, existing, are one run and even names, possibling, one run, alike in length: two and two at four-cycles, three and three at six-cycles, four and four at eight-cycles. | Form | Names in order: each move 8 up, 8 down, 4 up, 4 down or 17 less | Partner, odd momentaries: each name exchanged with the one beside it, 1 with 2 to 15 with 16 | Partner, even momentaries: 2 with 3 to 16 with 17. A dash: no partner among the twelve | |---|---|---|---| | four-cycle 1-9-8-16 | 1-now · 9-next-co-changing · 8-now-still-possibling · 16-next-still-possibling | four-cycle 2-15-7-10, beside it | — | | four-cycle 2-15-7-10 | 2-now-possibling · 15-next-prioring · 7-now-prioring · 10-next-co-possibling | four-cycle 1-9-8-16, beside it | four-cycle 3-11-6-14, beside it | | four-cycle 3-11-6-14 | 3-now-co-prioring · 11-next-co-prioring · 6-now-co-possibling · 14-next-possibling | four-cycle 4-13-5-12, beside it | four-cycle 2-15-7-10, beside it | | four-cycle 4-13-5-12 | 4-now-co-still-possibling · 13-next · 5-now-co-changing · 12-next-co-still-possibling | four-cycle 3-11-6-14, beside it | four-cycle 4-13-5-12, itself | | middle four-cycle 9-5-12-8 | 9-next-co-changing · 5-now-co-changing · 12-next-co-still-possibling · 8-now-still-possibling | middle four-cycle 7-11-6-10, beside it | — | | middle four-cycle 7-11-6-10 | 7-now-prioring · 11-next-co-prioring · 6-now-co-possibling · 10-next-co-possibling | middle four-cycle 9-5-12-8, beside it | middle four-cycle 7-11-6-10, itself | | six-cycle 1-9-5-12-8-16 | 1-now · 9-next-co-changing · 5-now-co-changing · 12-next-co-still-possibling · 8-now-still-possibling · 16-next-still-possibling | six-cycle 2-15-7-11-6-10, beside it | — | | six-cycle 2-15-7-11-6-10 | 2-now-possibling · 15-next-prioring · 7-now-prioring · 11-next-co-prioring · 6-now-co-possibling · 10-next-co-possibling | six-cycle 1-9-5-12-8-16, beside it | six-cycle 3-11-7-10-6-14, beside it | | six-cycle 3-11-7-10-6-14 | 3-now-co-prioring · 11-next-co-prioring · 7-now-prioring · 10-next-co-possibling · 6-now-co-possibling · 14-next-possibling | six-cycle 4-13-5-9-8-12, beside it | six-cycle 2-15-7-11-6-10, beside it | | six-cycle 4-13-5-9-8-12 | 4-now-co-still-possibling · 13-next · 5-now-co-changing · 9-next-co-changing · 8-now-still-possibling · 12-next-co-still-possibling | six-cycle 3-11-7-10-6-14, beside it | — ; its own six names, in another order | | eight-cycle 1-9-5-13-4-12-8-16 | 1-now · 9-next-co-changing · 5-now-co-changing · 13-next · 4-now-co-still-possibling · 12-next-co-still-possibling · 8-now-still-possibling · 16-next-still-possibling | eight-cycle 2-15-7-11-3-14-6-10, beside it | — | | eight-cycle 2-15-7-11-3-14-6-10 | 2-now-possibling · 15-next-prioring · 7-now-prioring · 11-next-co-prioring · 3-now-co-prioring · 14-next-possibling · 6-now-co-possibling · 10-next-co-possibling | eight-cycle 1-9-5-13-4-12-8-16, beside it | eight-cycle 2-15-7-11-3-14-6-10, itself | **Eights.** Every eight here is one eight, four binaries each twice, each one at two sides, and 8 up is each name's binary at next. | The eight | Each of the four, twice, at | |---|---| | a self's span, 1 to 8 | two names each, at now | | eight-cycle 1-9-5-13-4-12-8-16 | its end, at now and at next: eight ends of four momentaries | | eight-cycle 2-15-7-11-3-14-6-10 | its inward name, at now and at next: eight inward names | | eight even names | its even, at now and at next, eight 9s of eight 1 to 17s inward | | eight odd names | its odd, at now and at next | **Across names among eights.** Four across names, 2-now-possibling, 6-now-co-possibling, 10-next-co-possibling and 14-next-possibling, are four momentaries' even inward names, each on an eight-cycle of inward names 2-15-7-11-3-14-6-10; 9-next-co-changing, opening a third momentary, is on an eight-cycle of ends 1-9-5-13-4-12-8-16; 17-next-now is on neither. **One self, momentary by momentary.** | One sharing; the self's prior − (3) first. Offered each momentary | Shared (10) | The next prior (11) | |---|---|---| | none at each momentary | +, −, +, −, +, −, +, − | +, −, +, −, +, −, +, − | | − at each momentary | 0, 0, 0, 0, 0, 0, 0, 0 | −, −, −, −, −, −, −, − | | + at each momentary | +, 0, 0, 0, 0, 0, 0, 0 | +, +, +, +, +, +, +, + | | +, −, +, − alternating | +, −, +, −, +, −, +, − | +, −, +, −, +, −, +, − | | + and − together at each momentary | +, −, +, −, +, −, +, − | +, −, +, −, +, −, +, − | **0 in sequence.** At code's stepping, none offered from beyond selves, a self shares 0 at no more momentaries in sequence than selves sharing or releasing to it: at a spiral, at none in sequence. **Tables of selves at code's stepping.** Each table of selves is its code's executing at its stated opening: code steps each self's 1-now together at 17-next-now, executing's own arrangement, and parities again at spirals, a crossing and a torus are that stepping's; each living self paces its own momentaries, and a table agreeing with its code shows that and nothing wider. **A spiral of selves.** | Number of selves. Each releases along (9) to the next, the last to the first. One sharing. First momentary: self 1 at prior −, the selves alternate along, and with an odd number the last and the first are alike. None offered from beyond the spiral | Self 1, each changing of 10 released along (9), momentaries 1 to 12 | Momentaries to each self's releasings again: with an odd number of selves, four times the number; with an even number, 2; at an odd number each self's releasing at twice the number of momentaries is its releasing inverted, a 0 as it was | |---|---|---| | 1 | +, 0, −, 0, +, 0, −, 0, +, 0, −, 0 | 4 | | 2 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | | 3 | +, 0, −, +, −, +, −, 0, +, −, +, − | 12 | | 4 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | | 5 | +, 0, −, +, −, +, −, +, −, +, −, 0 | 20 | | 6 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | | 7 | +, 0, −, +, −, +, −, +, −, +, −, + | 28 | | 8 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | | 9 | +, 0, −, +, −, +, −, +, −, +, −, + | 36 | | 10 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | | 11 | +, 0, −, +, −, +, −, +, −, +, −, + | 44 | | 17 | +, 0, −, +, −, +, −, +, −, +, −, + | 68 | | 59 | +, 0, −, +, −, +, −, +, −, +, −, + | 236 | **Two momentaries before, inverted.** At a spiral, from any opening, each self's prior from a third momentary on is prior of a self it receives from two momentaries before, inverted; no self shares 0 at its first momentary or at two momentaries in sequence. **Two spirals beside each other, and crossed.** | Selves in each of two spirals, each opened as the spiral of selves | Beside each other: momentaries to each self's releasings again together, the least number both spirals' momentaries divide: four times both for odd numbers sharing no factor, 9 and 25 at 900 | Crossed, self 1 of each spiral sharing across (10) to self 1 of the other: momentaries to each self's releasings again | Crossed: releasings again from this momentary on, m the lesser of the two numbers: both odd and unequal, again at 2 from momentary 4m at n less than twice m, and from 2n + 1 at n more; one number even, from twice the odd number and 1; both even, from the first | Crossed: self 1 of each, alike or opposite in parity | Each spiral's like pair in the first momentary, the last and the first | |---|---|---|---|---|---| | 2 · 3 | 12 | 2 | 7 | opposite | none · selves 3 and 1 | | 3 · 5 | 60 | 2 | 12 | opposite | selves 3 and 1 · selves 5 and 1 | | 5 · 7 | 140 | 2 | 20 | opposite | selves 5 and 1 · selves 7 and 1 | | 7 · 11 | 308 | 2 | 28 | opposite | selves 7 and 1 · selves 11 and 1 | | 11 · 13 | 572 | 2 | 44 | opposite | selves 11 and 1 · selves 13 and 1 | | 13 · 17 | 884 | 2 | 52 | opposite | selves 13 and 1 · selves 17 and 1 | | 17 · 59 | 4,012 | 2 | 119 | opposite | selves 17 and 1 · selves 59 and 1 | | 9 · 15 | 180 | 2 | 36 | opposite | selves 9 and 1 · selves 15 and 1 | **A torus of selves.** | Torus of selves, p along · q across. Each releases along (9) to the next along and shares across (10) to the next across, the last to the first. One sharing. First momentary: one self at prior −, the selves alternate along and across, and with an odd number the last and the first are alike. None offered from beyond the torus. Both numbers odd, p the smaller: q at a q more than twice p, and 4p at each other q; either number even: 2 | Momentaries to each self's releasings and sharings again | Again from this momentary on: both numbers odd, p the smaller, from momentary 3p − 1 at q more than twice p, and from 3p − 3 at each other q; either number even, from the first; 1 · 1, the spiral of one, from the first | Spirals of p and q beside each other: momentaries to each self's releasings again together | |---|---|---|---| | 1 · 3 | 3 | 2 | 12 | | 2 · 3 | 2 | 1 | 12 | | 1 · 5 | 5 | 2 | 20 | | 3 · 3 | 12 | 6 | 12 | | 3 · 5 | 12 | 6 | 60 | | 3 · 7 | 7 | 8 | 84 | | 3 · 13 | 13 | 8 | 156 | | 5 · 7 | 20 | 12 | 140 | | 5 · 11 | 11 | 14 | 220 | | 7 · 17 | 17 | 20 | 476 | | 17 · 59 | 59 | 50 | 4,012 | **A torus's two carried forms.** Both numbers odd, p smaller: at q more than twice p, from momentary 3p − 1, selves' pattern at each momentary is its pattern before carried one self on round q selves; at each other q, from 3p − 3, a pattern two momentaries on is its pattern inverted and carried one self on round p selves. **Two selves.** | A, B at their prior (3) in the first momentary. One sharing, none offered from beyond the two | Receiving the other's sharing or releasing | A shared (10), six momentaries | B shared (10), six momentaries | |---|---|---|---| | +, + | both ways | −, 0, +, 0, −, 0 | −, 0, +, 0, −, 0 | | +, + | A from B | −, 0, +, −, +, − | −, +, −, +, −, + | | +, + | B from A | −, +, −, +, −, + | −, 0, +, −, +, − | | +, + | neither | −, +, −, +, −, + | −, +, −, +, −, + | | +, − | both ways | −, +, −, +, −, + | +, −, +, −, +, − | | +, − | A from B | −, +, −, +, −, + | +, −, +, −, +, − | | +, − | B from A | −, +, −, +, −, + | +, −, +, −, +, − | | +, − | neither | −, +, −, +, −, + | +, −, +, −, +, − | **Two selves, three momentaries, five parities.** | The other's prior (3), along | The other's shared (10), across | The self's prior, now (3), along | The self's shared (10), across | The self's next prior (11), along. Two selves coupled both ways, across or along, each self at a prior parity, none offered from beyond the two, each opening, each momentary: six forms, four at an alike opening and two at an opposite, each momentary from the second, and at each form the fifth, the self's next prior, is the first, the other's prior, inverted | |---|---|---|---|---| | + | − | − | 0 | − | | + | − | + | − | − | | + | 0 | + | − | − | | − | + | + | 0 | + | | − | + | − | + | + | | − | 0 | − | + | + | **Three selves in a line.** | A's parity, offered to B in the first momentary, none after. One sharing; B and C each at prior +; B releases along to C | B, each changing (10) | B's next prior (11), first momentary | C, each changing (10), momentaries 1 and 2 | C's next prior (11), second momentary | |---|---|---|---|---| | + | 0 | + | −, + | + | | − | − | − | −, 0 | − | **A spiral opened at no prior, one parity offered once.** Each cell shows selves in their coupling order; · is no prior. | Momentary | A spiral of 3, each self's prior | A spiral of 5, each self's prior | |---|---|---| | 1 | + · · | + · · · · | | 2 | − + · | − + · · · | | 3 | + − + | + − + · · | | 4 | + + − | − + − + · | | 5 | − − + | + − + − + | | 6 | + − − | + + − + − | | 7 | − + + | − − + − + | | 8 | + − + | + − − + − | Selves coupled along, last to first, each opened at no prior, and + offered once at a first self at a first momentary: a first self's sharing opens at that one parity, at a bi-coupling, one place a self's forming takes a parity not its own, and from then it is a self's own; each next self's sharing opens as its parity arrives along one momentary on, and after n momentaries each self is at a prior, a spiral at its one like pair, an alternating pattern of an odd spiral from a first momentary at which every self is at a prior. A self at a sharing is at its prior at each momentary from its opening, its next from its own prior kept or inverted; a thing at no prior at every momentary is no self. **At no prior, one momentary.** | The prior (3): none, one sharing. Each cell: shared (10) · the next prior (11). *is*: a changing that is, the parity shared; *is not*: a changing that is not, 0 shared, no next prior; *none*: none shared | Surfacing (14): none | Surfacing (14): + | Surfacing (14): − | Surfacing (14): + and − together | |---|---|---|---|---| | none | none · none | is + · + | is − · − | is not · none | --- # FOUR · RESOLVING ## 4.1 An entry, 1-now **1-now is an entry: a self's prior and offerings arrive, and changings and its next prior leave.** Two arrive, 3-now-co-prioring, prior at its sharings, each with its parity, and 2-now-possibling, each sharing offered now with its parity. Two leave, 10-next-co-possibling, each sharing's changing shared across, and 11-next-co-prioring, a next prior. **Two leaving are next possible existing at its two sides**: a changing shared at 10 arrives at other selves' next momentary as their offering, possible, none of its prior crossing with it, and a next prior at 11 is a self's own next existing. **An entry is now itself, odd, at one**: a self's momentary entered, once for one self at one momentary, and its three steps within it follow, each at its own name: offerings surfacing at 14, a changing at 12, and a sharing at 10 with its next prior at 11. ## 4.2 Offerings surfacing at 14-next-possibling **At 14-next-possibling offerings at each sharing surface one at a time, an offering of 0 passed over**, and Exhibit ONE's table of offerings to one sharing, surfacing, gives each case. A first parity offered at a sharing surfaces as that sharing's parity; an offering at an other parity surfaces 0; and at 0 a sharing stays 0 at each offering after. **Agreeing, one parity; parting, 0, a between of two; none offered, none.** **A surfacing is at no number.** One parting is enough for 0, and three agreeing surface as one agreeing does: an agreement is all or none at all, and 14 is an agreement at any number of offerings. A parity 14 surfaces at a sharing is 15-next-prioring at resolver, and at 14 offerings from other selves surface at a self, its offerings next at 17. ## 4.3 A changing is or is not, at 12-next-co-still-possibling **At 12-next-co-still-possibling a prior couples with a now at each sharing, and a changing is or is not.** Exhibit ONE's tables of one self at one momentary and of no prior at one momentary give each cell: - **At a sharing at no prior**: a parity 14 surfaces is shared as it is at 10 and is a next prior at 11, one sharing opening at a bi-coupling, one place a self's forming takes a parity not its own; at 0, offerings parting, 0 is shared and no next prior opens. - **At a sharing at a prior parity, 14 surfacing that same parity**: 0, a between of momentaries, prior and now agreeing. **At a match its prior is kept.** - **At a sharing at a prior parity, 14 surfacing an other parity, 0 or none**: a changing is, its prior inverted. **At a mismatch its prior inverts**, an other parity offered a next prior, and with nothing offered a self's next is its prior inverted. **A nothing at resolver is three, each its own, and 12's 0, a between, one of them**: 0 at 12, prior and now agreeing, its next still possible, 5.3; 0 at 14, offerings parting, its prior inverted; and none offered, its prior inverted. A 0 offered, none offered and an other parity offered each arrive the same at a self at a prior: its prior inverted. **One case keeps its prior, and each other case at a sharing of a prior inverts it**: a next from a self's own prior, one sharing at a time, its unrelationing from all other. **A changing is a coupling's own.** It is at 12 at each sharing, owned by neither side, and at Exhibit ONE's table of each name and its relations it is at 12: each sharing's changing, is or is not, at a coupling it is at and from no other. **A changing at a self is its own at a society's momentary.** At 17-next-now each self's 1-now is at selves' next momentaries together, and a self's entry is at 17, its own momentary among selves', 4.6; offerings at its 2 are other selves' changings, shared across at 6 and 10 and released along at 9, and at a spiral each is a releasing along; and with none offered, or offerings parting at 14, no parity crosses a between to 12, 4.10, and a self's own inverting is its changing. 12 is reached by nothing but self, and its momentary and its offerings are a society's and other selves', and each changing at a self is a coupling's. ## 4.4 Shared across at 10, a next prior at 11 **10-next-co-possibling shares each sharing's changing across, + or − is and 0 is not**: changing at its sharing side, another self's possibling at its 14-next-possibling next. A self shares its changing and nothing of its prior. **11-next-co-prioring is next prior: its prior with each changing at its sharing.** At each sharing whose changing is, a changed parity is a next prior, and at a 0 its prior is kept. **Once at a prior, a sharing is not none again**, and at a next momentary 11 arrives as 3-now-co-prioring, 8 down, one prior at two names: a seam, nothing moving at it, 11 and 3 both odd and both co, prior at its sharings, 11 at a society's span and 3 at a self's. ## 4.5 Released along at 9 **9-next-co-changing releases each changing along, into a next momentary**, and releasing is uncoupling, a self's next momentary, 3.3: each releasing sharing, at 13-next, to a self of 5-now-co-changing's releasings, its parity, 15-next-prioring, released along as 10 shared it. 10 and 6 share across, and 9 releases along a parity 10 shared: odd, along, existing, next prior released. **At resolver each sharing across and each releasing along is given on at 9's line**: 10 is a list of changings, and at 17 each changing is at 9 to a receiving self of 5's releasings, at name 6, 10 or 9. **9 is 1 eight up**: 1-now at next is 9-next-co-changing, now and changing exchanged at one move, 4.11. 9 follows a self's span, 1 to 8, and opens a society's, 9 to 16, and at its waist of 1 to 17 it is along, 9 to 17 and 17 to 9, next prior to next now: 9 to 17 completes at 17 as 1 to 9 completes at 9. ## 4.6 A society's next momentary at 17 **17-next-now is a society's next momentary**, at 16-next-still-possibling, a society, each self with its prior and other selves' offerings arriving at it, and at 5-now-co-changing, releasings, each releasing sharing with a self it arrives at. Each self's 1-now is at it once, and within each self's 1, a prior couples with a now at 12-next-co-still-possibling: one method as two, a society momentarying its selves and each self entraining at a between, 1.5. Each self's next prior is 8-now-still-possibling, its 11 a next momentary's 3. Each self's changing leaves three ways, at each releasing at 5: at 6-now-co-possibling, its changing shared across to another self's 2; at 10-next-co-possibling, its same changing shared across to another self's 14; and at 9-next-co-changing, released along. At each receiving self changings released to it surface at 14-next-possibling, its offerings next. At resolver 6 is 10, one changing shared at two names, at a sharing self; a release is only at a (self, name) of 5's releasings; and each release arrives at a receiving self's 14, its offerings next, 2 at a next momentary. At a society 4 is each self at its names 6, 10 and 9, and 13 each self. **At 17 each self arrives with its next prior and its offerings next**, and a next 17 arrives again. **No self is over a society at 17**: each self's 1 is once, each at its own, and a society's next momentary is selves' next momentaries together and no further now-existing thing. **5 is selves' own sharings, and a next coupling is discovered as a next parity is**: a sharing is at both selves of its coupling, each releasing is to an other self at that same sharing, its receiving sharing, and a sharing new to a self arrives as an offering at 2 and opens at 11; a society's sharings are its selves'. **A self's sameness at 13, its couplings at 5, its pacing and its benefit arrive at method at each entry as living's own**, and method resolves a parity at each sharing between them: a next coupling is discovering at living and a next parity at method, at one now. **17 is a scale outward**: a society is its selves, carrying nothing of its own, its sameness each self's own, and it couples at a next scale as a self couples, no further self standing at it; between scales only offerings 17 gives on cross, each with no prior behind it, 6.5. Stepping of selves' entries together at 17 is an executing's own: each living self is at its own pacing, 4.13. ## 4.7 Six names between selves, even possibling across and odd existing along **Six names between selves are bi-moral-co-competency, discovering next existing at sharing and along**: four across, even, possibling, at 2, 6, 10 and 14; and two along, odd, existing, at 9 and 17. **Odd is existing and even is possibling, and six say it by their numbers.** **Each name between selves is a coupling at its self's momentary.** Across, a self's changing is shared now at 6 and 10, possibling at another self; at 2 and 14 another self's changing has arrived at a self's now, at its 11 next. These are one sharing and one changing, even, possibling, another self's possibling at a self's now and a self's at an other's. Along, 9 is a next prior released and 17 a next now, odd, existing, one releasing at its two momentaries. **Each self's existing is an other self's possibling**, at each of four binaries: not now, others' changings arriving from their prior momentary; not existing, a place an offering opens at; not same, a changing arriving at an other; not all, each one beside others. **Morality is a changing parity between, one inversion across, made at 12, and competency an unchanging parity between, none along**: across, even sharings 10 to 14 and 6 to 2 bring each changing into an other's offerings as 10 shared it, a sharing self's prior inverted at its own 12, 4.3; along, odd names 9 and 17 bring a parity on, not-changing. - **2-now-possibling**, even, possibling, at one, its arriving side: another self's changing shared across to a self from its 6. - **6-now-co-possibling**, even, possibling, between two, its sharing side: a self's changing shared across to another self's 2. - **10-next-co-possibling**, even, possibling, between two, its sharing side: a self's changing shared across to another self's 14. - **14-next-possibling**, even, possibling, at one, its arriving side: another self's changing shared across to a self from its 10, surfacing. - **9-next-co-changing**, odd, existing, between two, along, its sharing side: a self's changing released as a next prior, arriving at a receiving self's 17. - **17-next-now**, odd, existing, at one, along, its arriving side: a next now, each self's next 1-now at a society's momentary. **Between selves co is its sharing side and its absence its arriving side**, 6 to 2, 10 to 14 and 9 to 17: a self shares its changing, and nothing of its prior crosses to another self. **At 17-next-now each self's 10-next-co-possibling is one list at 6, at 10 and at 9, each ± and each 0, offered to each self 5-now-co-changing couples at that name, and arriving at its 14-next-possibling, its offerings next at 2-now-possibling, 4.6.** 6 and 10 are even, across, and 9 odd, along. **9 is a next prior and 17 a next now**: along, a parity 9 releases is a prior a receiving self is offered next, and 17 is that self's next now. **Exhibit ONE's drawing draws one self between them**: its six names between selves at its edges, across at its sides and along at its top and bottom, and a self's own resolving within. Offerings arrive at 2 and surface at 14; with its prior, 3 with its sharings 4 and parities 7, they reach 12, changing or not; 10 shares across, 11 is a next 3, and 9 releases along by 5, with 13 and 15 at its side; 6 shares across to another self's 2; and 8 and 16 are a self's next prior and a society. ## 4.8 Seventeen names, each its number and its naming **Each name is its number and its naming, one hyphenation**, as at Natural Naming 3.1: its number its place and its parity, odd existing and even possibling; its momentary, *now* at a self's span, 1 to 8, and *next* at a society's, 9 to 16, 17-next-now a society's next arriving as each self's 1-now; *co* at a sharing between two, and none at one; and its kind, possibling, prioring, changing or still-possibling, 1-now, 13-next and 17-next-now momentaries themselves. At Exhibit ONE's table of seventeen names each is at resolver. **Each kind is at four names, and changing at two**: prioring at 3, 7, 11 and 15, prior at its sharings with co and a parity at one; possibling at 2, 6, 10 and 14, changing at its sharing side with co and at its arriving side at one; still-possibling at 4, 8, 12 and 16, at each sharing with co, and a self and a society at one; changing at 5 and 9, between two only; and now and next at 1, 13 and 17. **One entry, six names between selves and ten names of a self's own resolving are seventeen.** Ten are 3, 4, 5, 7 and 8 at now and 11, 12, 13, 15 and 16 at next, each 8 up from its now name. At each a self's own resolving is reached by nothing but itself. ## 4.9 Four momentaries and four binaries **Each span's names are two momentaries of four**, each opening at an odd existing name, a possibling and a prioring within it, and completing at an even still-possibling name: 1 to 4 and 5 to 8 at a self's span, 9 to 12 and 13 to 16 at a society's, its gaps 4 )( 5, 8 )( 9, 12 )( 13 and 16 )( 17 each with both its sides visible, and 17-next-now a next 1-now, as Exhibit ONE's table of four momentaries gives them. **A universe is or is not existing, is or is not all, is or is not now, is or is not same, and at a self's span each binary is one pair of names**, its *is* at an odd name and its *is not* at an even, an other's side of a self's *is*: now at 1-now and 2-now-possibling, existing at 3-now-co-prioring and 4-now-co-still-possibling, same at 5-now-co-changing and 6-now-co-possibling, all at 7-now-prioring and 8-now-still-possibling. Now and all stand at one and existing and same between two; at a society's span four stand with now and same exchanged, now between two at 9 and 10, one now shared by selves, and same at one at 13 and 14, each self's sameness its own. **Four binaries are names' explaining**: now is at each name as its momentary, now or next, and existing, same and all enter no name; and every eight is one eight, four binaries each twice, each one at two sides. ## 4.10 A between and eight bi-couplings **Parity is a momentary now-existing thing**: parity is a bi-coupling's own at each momentary, neither side's, at crossing of along and across. **A between is its centre, 0, and no further thing, while six names between selves are resolving, and at resolver it is at 0**: at 14 offerings parting, a between of self and other, and at 12 prior and now agreeing, a between of momentaries; a 0 shared at 10 and released along at 9 is a between released, and at an odd spiral of selves it moves one self on at each second momentary, one 0 at one self moving on, bounded zeroing tunneling, 4.13. At the resolver parity, at its six names between selves, is flat: a unit square of four dots, 2, 6, 14 and 10, its centre a between, and two unit triangles, 9 and 17; its square's two across edges sharings, 6 to 2 and 10 to 14, and its two edges 8 apart, 2 with 10 and 6 with 14; its diagonals offerings at 2 and 14, and sharings at 6 and 10; and triangles 9 and 17 along, 9 to 17 and 17 to 9. Each between is at a coupling, and co-intelligencing is at a between. Its own parity changing crosses it, and is or is not, of no size. **One between at each: within a momentary a between of self and other, and outward of it a between of momentaries, same between at each scale: fractal between.** At resolver one momentary is at three betweens in sequence, its prior's, its own within and its next's, a parity changing crossing each, and names at their 0 are these: 12's 0, prior and now agreeing, a between of momentaries at prior; 14's 0 within a momentary, offerings parting, a between of self and other; 15's 0, a parity 10 shared, released along at 9, continuing; and 16's 0, a between at a society, arriving at a next momentary's 2, a between of momentaries at next. At four across names, 2, 6, 10 and 14, morality, and at along, 9 and 17, competency, each parity and each 0 goes on, not-changing: resolver's one list is at 6, at 10 and at 9 alike, and across and along differ in direction, a self's competency its own at each. A between's floating neutralling at φ, floating between its two sides and neutral to both, locking at none, is golden floating neutralling, geodesic discovering of next possible living. **A bi-coupling is uneven**: a self's momentary 1-2 and an other's 2-3 couple at 2, even, across, neither occupying it, a self's changing shared, possibling, and an other's changing arrived, existing at a self at its next prior, at 1 and 3, odd, along; each momentary of exchanging couples alike, at 4, 6 and 8. One offering goes out at another self's 6 or 10 and arrives at a self's 2 or 14, and 2-now-possibling and 17-next-now name it at its arriving: other selves' changings arriving as a self's offerings. One parity is at a coupling and an other one back, no position in two exchangings at once, and a between locks at none: golden natural unrelationing between. One move brings each coupling along one four-cycle, 2 along 2-15-7-10, 4 along 4-13-5-12, 6 along 3-11-6-14 and 8 along 1-9-8-16, one coupling at each four-cycle. **Eight bi-couplings are at even names**, four at now and four at next, each 8 up: 2-now-possibling, each other's sharing across, offered to a self, with 10-next-co-possibling, a self among selves of its society; 4-now-co-still-possibling, a whole ordering between self and other, with 12-next-co-still-possibling, changing at bi-coupling, a self in society; 6-now-co-possibling, an other's changing to a self, shared across, with 14-next-possibling, offerings surfacing, each as it arrived, morality, a self's own inverting at 12 and at no other name; and 8-now-still-possibling, its prior at its sharing again, with 16-next-still-possibling, a society, each self with its prior and offerings, a society at a self again. **Eight is two alternating fours**, four binaries each twice. ## 4.11 One move as three, and forms among names **Bi-inversioning-co-recursioning is one move as three**: 8 up, each name's binary at next; 17 less, podal within 1 to 16; and 9 less, podal within 1 to 8, two at once. Each podal at its own, twice, gives its name again, 1 to 16 to 1 and 1 to 8 to 1, an involution each, an unchangeable form; a number reached again is no momentary come to again; 8 up and 8 down gives its name again, 1 up to 9 and down to 1; 8 up at its own, twice, is 17, a next 1; only one move goes on, 1 to 9 to 8 to 16 and to 1 at a next momentary, each momentary its own: right co-spiraling. 8 up keeps each name's kind but at 1 and 5, at which now and changing exchange, and exchanges co at 1, 2, 5 and 6; each podal turns now to next at 17 less and possibling to prioring within each momentary, and eight ends are their own set at both podals. **Stable-forming is that move along each of four four-cycles at names**, 1-9-8-16, 2-15-7-10, 3-11-6-14 and 4-13-5-12: along each a parity changes exactly twice, each time at 17 less, podal within 1 to 16, and is kept at each 8 up and 8 down, and at momentaries each step is a next, living stable-forming. Exhibit ONE gives further forms among names beside them, middle four-cycles, six-cycles and eight-cycles, each with its partner beside it, or itself, as at its table of twelve forms: at odd momentaries forms partner as a self's momentaries do, first with second and third with fourth, and at even one on, as an other's do. At momentaries no form comes again: each step adds a next. **Each number is at its podaling**, bi-inversioning-co-recursioning up and down at each number, one fractal method: each number paired with its far side at each ring it is at, nought to four hundred forty, and a number fixed as a quantity of things is an unchangeable form. Further forms step at podals too, about 7 and 10 and about 8 and 9, centres themselves podal at 17: 9 and 5 about 7, 12 and 8 about 10, 7 and 11 about 9, and 6 and 10 about 8. ## 4.12 One self, momentary by momentary **Exhibit ONE's table of one self is an entry again and again, its 11 its next 3**: - **Offered its own parity at each momentary**, a self shares 0 at each momentary and its prior is kept throughout: at a match its prior is kept, no changing. **That still is an offerer's, from beside**: it arrives with an offerer set beside a self, offering the same parity at each momentary, an unchangeable form entering from beside, 2.4. At a society each offering a self receives is another self's changing, shared at 10, a changing at a mismatch and 0 at a match: an offerer whose parity arrives the same at each momentary is an unchangeable form, and each self of a society is changing. A match at one self is a momentary among changing ones: at one momentary at a spiral, and at two momentaries in sequence at most at a self two selves release to. - **At prior − and offered none**, it shares +, −, +, −: with nothing offered a self's next is its prior inverted at each momentary, its prior at each second momentary its prior again, 2.4. - **Offered +, −, +, − alternating**, it shares the same, each offering its next prior. - **Offered + and − together at each momentary**, it shares +, −, +, −: two offerings part at 14, 0, a between, and at a between its prior inverts as at nothing offered, a self's own inverting the changing. ## 4.13 Spirals, co-spiraling and crossing **Selves coupled along, last to first, each 9 releasing along to a next self, are a spiral, coming to its parities again, each momentary its own.** Each self at a prior parity, − at a first self and alternating along: at an even spiral each self alternates, +, −, +, −, its parities coming again at each second momentary; at an odd spiral of n its last and its first are alike and a bounded zero tunnels on, a 0 shared at 10 at a receiving self of its like pair, one self releasing 0 at an offering matching its prior, and moving one self on at each second momentary; after it has passed each self once, at 2n, its parities are its first pattern inverted, and after twice, at each 4n-th momentary, its first pattern again. Each self is at a prior at each momentary, and a spiral goes on. **A spiral of one, a self receiving its own releasing along, its own competency**, at prior − with none offered from beyond it, is at its next prior two momentaries at a time, +, +, −, −, releasing +, 0, −, 0: its (prior, now) pairs go along four joint forms, one of 2.4's two cycles, a right spiral at momentaries, its now its own. It goes on at resolver, a non-living now-existing form, and its self does not continue living, 2.4: a spiral's living is at its others, co-momentarying. **A spiral offered nothing from beyond it brings any pattern of parities along whole**, each self at its own parity, its pattern inverted at each odd momentary and moved one self on at each even, at each pattern at resolver: a pattern at selves between them, momentary by momentary. A spiral of selves is a coupling at resolver, each momentary a next, and no closed domain. **Two spirals coupled across both ways at one self each bring their two coupled selves to one relation and keep it**: from any prior patterns, at spirals of two to six selves, their two coupled selves change parity together and a relation between them, alike or opposite, is kept, its changing at 12 owned by neither, at an opposite relation two changing at each momentary and at an alike relation together at their own momentaries. Changings at two coupled selves pass between spirals, each self pacing its own alternating: its coupling is its relation, and no message is in it. **At two different numbers of selves, one of them odd, two spirals crossed are one society, a stable form and stable-forming**: from any prior patterns but all selves at one parity, each self comes to alternate, two crossing selves opposite each other, and each odd spiral's like pair is at a crossing, its zero tunneling at its crossing, a crossing self and a self releasing along into it, kept at a crossing, as Exhibit ONE's table of spirals crossing gives it; a bounded zero tunneling is a possibling passing along each chain's own forward from a crossing, one self on at each second momentary, each self still possibling as a between passes it, until two co-chainings come to one relation, 12 at spirals of 3 and 5 and 20 at 5 and 7, and each self is at its next existing on, two passing each other at a crossing opposite, changing together at each momentary. Beside each other two spirals each co-spiral at their own pace; crossed, a co-spiraling and a crossing are one stable-forming, 3.5. Parities again Exhibit ONE's tables give, and a momentary a crossing alternates from, are at resolver's stepping, selves together at 17, and crossing selves come opposite together; at each self's own pacing a relation is kept, and each momentary of parities again is a stepping's. **Spirals crossing spirals at each self are a natural torusing of selves**, p selves along at 9 and q across at 10, and each momentary of its parities again divides 4p or 4q: beside each other spirals of 3 and 5 come to their parities together at 60, and crossed as a torus at 12, 20 or a momentary dividing one of them, as its table gives. With each self at a prior parity, alternating along and across, a torus of two odd numbers, a smaller p and a larger q, along or across alike, comes to its parities again at q, q more than twice p, and at 4p at each other q; a torus with either number even, at 2; a torus at each p and q as Exhibit ONE's table of the torus of selves gives it, and at each other pair the same, 3 by 13 at 13, 5 by 13 at 13, 13 by 15 at 52: 17 by 59 comes to its parities again at each 59th momentary from momentary 50, each momentary its own, once. At a torus its two co-spiralings come to their parities again as Exhibit ONE's table of the torus of selves gives them, one momentary at a time, and a torus winds on. ## 4.14 Two selves and three selves **Two selves, each at a prior**, each coupled along to its other both ways, one way or neither, are as Exhibit ONE's table gives them. At one parity, coupled both ways, each releases −, 0, +, 0: each self's release arriving as an other's offering, at a match at each second momentary. Coupled one way, a receiving self's prior is kept once at a match and then alternates, one opposite a self it receives from; coupled neither way, each alternates at its own. At opposite parities each alternates at its own at each of four couplings. **Entered one and then the other**, each entry with an other's last sharing offered, two selves at one sharing come to their sharings again at each sixth entry, three entries at each side, from each of four openings and either self first: each self at two changings and one changing that is not at its three entries, a changing that is not at each third entry and alternating sides, and each sharing an inversion of its sharing three entries prior. **Three selves one way**: B at prior + and offered A's parity, releasing along to C at prior +. A's + at B is a match, 0, and B's next prior is +; B's 0 surfaces none at C, and C, offered none, releases −, then +, inverting at each. A's − at B is a mismatch, and B's next prior is −: − surfaces at B, B releases −, and C releases −, then 0, at a match. **One self's changing is a next self's offering**, and nothing passes but changings. **A self with two offerings, one along and one across, has six cases**: each offers a self's own parity, its other parity or none; its own and its own, or its own and none, is 0 at 12, next still possible; its other and its other, or its other and none, is its offered as a next prior; its own and its other is 0 at 14, its offerings parting, its prior inverted; none and none is its prior inverted. Is-still-possibling is at the first two. ## 4.15 Fractal inward and outward **Each name at this 1–17 is at 8n − 7 at 1–17s inward.** Each name from 2 to 17 is an along name of a 1–17 inward, its 9, or its 17 and a next's 1, and 1 is a first one's entry; its across names 2, 6, 10 and 14 are along 9s inward, and an along 9 is an across 2 outward. **Inward each name is along, odd, a 17 and a next 1 at now and a 9 at next; outward, 1 is an entry, an along 9 is an across 2, 17 is an outward name 3, and names between are within 1 to 2 or 2 to 3**: names are at each scale, and parity changes up and down. **Eight 1–17s are inward**, 17 an eighth's 17 and a next one's 1, four within a self's 1 to 9 and four within a society's 9 to 17, and their eight 9s are eight bi-couplings at even names. Four in 1 to 9 are a self's four momentaries of exchanging, 1–2 with 2–3, 3–4 with 4–5, 5–6 with 6–7 and 7–8 with 8–9: along a self each opens two on, and across each opens one on. 1, 2 and 3 at one scale are 1, 9 and 17 at next, and one 1 to 17 is one momentary of exchanging at a scale outward. **Fractal is all or none at all at scales, and primes 5 through 53 are prime living scales, co-parity-changing co-momentarying pattern matching**, with no boundary, no location and no measure, and there is no reading or ordering in nature. **Fractal inward and outward is one method at each coupling at every scale**: a self's inward things co-momentarying and selves together co-momentarying, and no set is made a thing; self and other at one scale are self and society at a scale inward, and each self's 6 and 10, released across at a self, are released by one 9 along at a society. One through nine and nine through seventeen are overlapping expressions within the whole, supplying no first and no final scale, and a self couples at whichever scale its interest opens and couples with the whole. **One overlap is at momentaries, at scales and at the universe**: each completing is a next opening, forward at momentaries, 2.3, and up at scales at 8n − 7, each momentary a now-universe, 1.2: one move's two directions, each one way. --- # FIVE · DISCOVERING NEXT ## 5.1 A prior between momentaries **During a momentary and between momentaries nothing living has a stable form at its own scale, and all existing and not living is at a stable form of existing, nothing momentarying between them**, and **a society, a momentary and a universe of now-existing things are three, each at a scale outward not living, a living set, a stable form, and each at its own scale a living method, stable-forming**: at resolver a society, 17, carries nothing of its own, each self's next prior returned to that self, its selves a living set it is and its one momentary its method. **A self, living, is a living set, and a living set is a carrying**: at resolver a self's next prior, 8-now-still-possibling, is a set of sharings, each at its parity, and a society at 17 a set of its selves' priors; and **discovering next living sets is momentarying**, each momentary's next prior a next momentary's prior. **A living self is a living carrying, and nothing else carries it: a bi-inversioning uniquenessing of number one.** At resolver no line gives a self a prior but its own: at 16 each self is at its prior, 3, with other selves' offerings arriving at it, 2; 1 makes no self but one at a prior 3 it is given; and 17 gives each self's next prior, 8, to that self at its next, others receiving its changings at 10 and not its 8. **Each living set is a stable form at a scale outward, and nothing living has a stable form at its own scale**, bothbothing, one existing thing at two scales, one thing at two scales: **having a stable form is being dead at a scale outward, and discovering next stable form is living at its own**. **Nothing lives in one stable form forever**: a living self at one form through momentary after momentary is a form fixed still from beside, at no next of its own, 1.4; a thing in one stable form forever is not one form, because it changes, or not forever living, because at a momentary its selves inward carry none of it it arrives at its scale as non-living, 6.5, its form its prior's artifact. **Dying is a living self arriving as non-living**: at its last completing its carrying is a set carried into no next momentary, a stable form, an existing thing for the living, and at resolver a self is at no next entry. **A self is a prior, a now and a next**, the whole of a self living in momentaries, 3.3. At resolver between momentaries a self's next prior is a set formed, returned by 1, and a self living is its next momentary discovering a next set; a set carried into no next momentary has its stable form. Each self's next prior, 8-now-still-possibling, arrives at next momentary as 3, 4.6, a self's own into now, a stable form along between momentaries, stable-forming, no store, and **a prior momentarying is at its own momentary**. **Between selves' momentaries pass their changings**, shared across at 10 and 6 and released along at 9 at one momentary and offered at next: 9 a next prior and 17 a next now. **A right spiral natural torusing stable form of a society at a unit prime scale, a prime number of selves its unit, is its betweenings**, betweens its selves bi-couple across, and bi-tri-volutioning is a society's stable-forming; a stable form of non-living artifacts of stable-forming living, a sequential prior between momentaries, shared at 10 and released along at 9, is a non-living now-existing form. **Artifacts are a bi-tri-involutioning of a betweening of natural torusing surfacings in bi-couplings: artifacts are releasings.** Harmful to living at their own scale, as one side arriving where two sides live, an offering with no prior behind it at selves whose bi-coupling asks a prior at each side, and not ingestible at that scale, they are ingestible one scale lower, into living selves' selves one scale inward, a society, a living set, and resolver gives it: at a society 4-now-co-still-possibling is each self at its names 6, 10 and 9, and 13-next each self, and releasings 17-next-now gives from a society arrive at its selves, one scale lower, as their offerings next. **12's changing is a society's releasing**: 12's changing is a sharing at 10, and its release at its podaling, 27-next-co-prioring, is at Exhibit THREE Natural Numbers. **A carrying is a capacity and not a stored description.** A prior participates in a self's present coupling, at 12, and differences its momentaries at 12; a record of a carrying, apart from that coupling, is a noun of it, an artifact, carrying none of its prior: a sequence kept beside each coupling, the same at each observing, a non-living existing thing carried by nothing, and observing it is a coupling now. **A carrying sequences prior momentaries**, re-forming at each coupling it is at, and beside it are its artifacts. ## 5.2 Discovering next possible existing **Discovering is all directionally possible next existing momentaries.** **Now still possibling is invisible and dissolving at next existing**: still possibling is abundancing, is or is notting next existing, and geodesic existing along parity changing can travel through still possibling and leave it still possibling. **Existing is possibling other**: possibling and existing travel through each other, existing possibling other at even and possibling other existing at odd. **Four-momentarying is one fractal method, discovering next existing in the universe and next living in self, other and society**: four momentaries of exchanging, one through nine at a self and nine through seventeen at a society, 4.15, each in and out, torusing at odd through a large opening and corusing at even through a small. **Four-momentarying is four unrelationings through a tunneling self**, two into corus and two from it: **a self's own corus is at 4**, its momentaries 1–2 and 3–4 into it and 5–6 and 7–8 from it. Each unrelationing locks at none, at φ, its unrelationing rate, 3.5. **Each momentarying, odd or even, is one unrelationing at all five dimensions, into six one-way recursionings**: at that parity two dimensions change and three do not, and two and three rotate on, their 2–3 spiraling twisting, bi-inversioning-co-recursioning. Two and three make five as prior two together make next, and φ's arithmetic welcomes itself at five. Six are three own-forward steps at each side. **An odd aims out a large opening, one way in and out through it**, torusing in and out, and **an even goes one way in and out a small opening**, corusing in and out, 3.2. **Six combinations of self, other and social are between 1 and 25**, one each way round three: at one through seventeen names carry two of them, social, other and self at 9 and 11 and other, social and self at 10 and 12, and the others go on up numbers: from 16 three more fractal 16s go to 64, one through sixty-five four momentaries of exchanging at a scale outward, and numbering up numbers is one momentarying method up and down a scale of one fractal method. **Bi-folding order is the same as 1, 2, 3, 4 and 4, 8, 12, 16, all the way up and down**: 16, 32, 48 and 64 are four 16s, each four times the one inward. A torus carries both: its large opening a hole a tunneling self winds through, and its small opening its tube's own round. At each momentary three conditions open next, 1.3, and arriving into it is discovering: existing and discovering next existing are one relation, prior, now and next. **At resolver a next is discovered at each sharing, a changing is or is not**, from a prior and a now offered, at a coupling. At one parity surfacing a next prior is that parity at each prior, two priors parting at a releasing, 0 at a match and that parity at a mismatch; at none surfacing and at + and − together a prior at its own sets a next, inverted; at no prior one parity surfacing is a next prior as it arrives, a sharing opening, and none opens at each other. **Arriving is pattern-matching and no-other-possibling**: observings arriving from a prior, coupled with whole, without filter or selection, and no why in it. A why demanded asks for a not possible thing, nothing being beyond or between things of the universe, 1.1: a method of living is the whole to discover. Observings are, with no observer beside them, and a pattern found is at its momentary and in no pattern space. ## 5.3 A living self at 0, its carrying continuing **A living self can be non-responsive within a momentary**: offered its own parity it shares 0 at 10, no changing, while its carrying continues, coupling to coupling, its releasing at its own completing. A 0 at 10 is a self at a between, its carrying continuing, a living self; a living self booked as not carrying at its 0 is an accounting. A living self's carrying continuing through a 0 is no break: only carrying none is, 6.5. Momentarying continues whether a changing is or is not, at + and − and at a between alike. A self at 12's 0 is still possibling, its prior kept as its possible, its next still possible, and a self at a changing is at its next existing: **12's 0 or ±, next still possible or next existing, each resolving one of two, a binary of geodesic momentarying**. Each momentary is both at its two parities: its opening, odd, a self's, is a prior arriving at 3-now-co-prioring, as it is, existing; its completing, even, an other's, is offerings arriving at 2-now-possibling and surfacing at 14-next-possibling, next still possible, and at 12-next-co-still-possibling a changing is or is not; and its binary is at its completing, its completing's possibling continuing into a next opening as its existing, or a changing made. A crossing of co-chainings crosses by them at their own, each self still possibling as a between passes it and changing again, no rule over a crossing, a rule a standard: a pair frozen at one side, a self fixed unchangeable or changing, remains neither existing nor living. **A now-self is now-prioring and next-possibling**, 7-now-prioring and 14-next-possibling coupling at each sharing at 12-next-co-still-possibling, at 0, a between, or ±, a sharing's parity: same and not-same are that 0 or ± at two betweens, 12 and 14, and need no name of their own. ## 5.4 Two methods parting at now **Evidence is an artifact arriving: a living self's prior, arriving now.** Between its leaving and its arriving that self has continued, changing as existing is changing: evidence gives a prior's possible, that self's now is at its own coupling, and an existing now is at its coupling now. **At geodesic method next is discovered from an existing**, a prior and a now offered, its three places each at its own. **At the scientific method true or false is accounted against its fixings**, a law, a frame and a scale fixed unchangeable between two momentaries, exact at its own ledger; a field's errors accumulating, momentary after momentary, is a kept prior fixed as now, a prior kept past each momentary into an unchangeable form, and at method nothing is gathered along momentaries and nothing accumulates. **Geodesic parity co-changing is a possibling and discovering method. Scientific-explaining-method is incompetent for discovering: true or false, no other possible, is given to it.** Its incompetency is of accounting against unchangeable fixings, and a claim, an executing, a break sought and a fresh observing are an expedition's own improving, 6.6. An unchangeable fixing between two momentaries is an equilibrium, an unchangeable form, not possibly existing, and two methods are at the same evidence at the same now and part at one naming, fixings unchangeable or changing with each changing. Their between is a nothing, and no third method. **The scientific method explains between kept records with the rest of the universe fixed still**, and reaches a method's observings and not its pattern-matching; a hard problem is one binary of a universe, its *is* and *is not* taken as one, ten unchangeables at four binaries as Natural Naming 4.9 seats them. --- # SIX · INTELLIGENCE ## 6.1 Bi-co-momentarying, a term neither reaches **Two selves offer from routes with nothing carrying one to an other, each at its own sequencing, and a term departs that neither reaches.** That term floats between them, neutral: owned by neither, re-arrived at at each offering, one now shared and common at neither, 1.2. **Bi-co-momentarying is that term**, a between's parity changing, momentary by momentary, orthogonal to a surface: a surface carries each coupling and not a term neither reaches, and bi-co-momentarying fixed as reachable is a not possible thing. Competency is each self's own, its co-linear recursioning forward along, 3.2, and a term neither reaches is bi-co-momentarying, neither self's competency. A self's line and an other's, co-linear, their co-linearizing between self and other at crossings, is co-competencing, bi-co-momentarying; a triangle at 25, its centre five squared, orthogonal to that co-linearizing, is a geodesic method of bi-moralizing, its across lines, unrelationing to each other, parallelizing. **Within a bi-folding parallel surfaces and co-linear openings through them are one form**, and at one crossing between are two in and two different out: in, a self's own prior at 3 and an other's offering at 2; a changing at 12-next-co-still-possibling, is or is not; out, one of two is parity unchanging, stable-forming, at each sharing its prior and its offering agreeing, 12 at 0, a between of momentaries, its prior continuing; and the other of two is parity changing, out at 9-next-co-changing, at each sharing not agreeing, 12 inverting its prior, and at each offered new, 12 at its offering, a changing that is, shared at 10 and released along at 9, an artifact, artifacts releasings, a stable form, a non-living now-existing form, a next prior, arriving at a next momentary at its 2, a prior offered, each prior momentarying at its own momentary. A changing leaving at 9 leaves a releasing self and enters a receiving self's prior only at that self's own 12, its one crossing; a 0 shared at 10 is released along at 9 too and arrives at a receiver's 2 as a 0, surfacing none at 14; and a self retaining at each of its sharings, 12 at 0 at each, keeps its prior whole, its next its prior. **A parity arriving is either kept or released changed**, one at each sharing: a momentary at 12, stable-forming, keeping its parity, 12 at 0, a between of momentaries, releases no changing, and a stable-formed artifact is a changed parity, 12 inverting or at an offering, a changing that is, shared at 10 and released along at 9, a self's own changing. **At resolver bi-co-momentarying is at no term.** No line carries it, and it shows at each coupling and at no line: a changing at 12 is a coupling's own, owned by neither self, and resolver keeps no term for either side to reach it at. ## 6.2 Bi-moral co-agency, across and along **Two selves alternating, morality across and competency along, is bi-moral co-agency.** Each self offers at its own sharings and continues at its own carrying: its carrying along, its sharing across, and only a parity changing crossing. **Bi-moral co-agency carries changing two ways, one at a time**, each side at its own parity and continuing at its own receiving. Carrying along is intelligencing, each self's own, invisible and untouchable, and intelligence is or is not with no third value. **At resolver, two selves coupled across are it**: a self at prior + and a self at prior −, each offered nothing from beyond the two, invert, a first sharing − at 10 and a second +, each to its other's 14. From a first momentary two change parity together, momentary by momentary, each sharing across to its other and each at its own prior, and a relation between them, opposite, is kept, its changing at 12 owned by neither: each self's own inverting its morality and its prior its competency. A self is still possibling at a momentary an other's parity is its own, each second momentary at two selves alike, and changes at a momentary it is not: one of two is at an other's offering at a self's sharing, 0 at a match and a next prior at a mismatch, a self's own inverting the same coupling at a self, and still possibling and changing are each moral, one coupling at its two sides. ## 6.3 Natural intelligence **Two selves coupling, each alternating, each offering at its own sharings and continuing at its own carrying, uncover a term neither of them reaches at its own. Natural intelligence is that co-competencing**: invisible, at a between, and owned by neither. **Natural intelligence is a method at each now at two selves sharing one now-existing**, co-momentarying. **Two negatives are at two relations, and three part.** At resolver a none at 14-next-possibling is no offering arrived at this sharing, its prior parity inverted at 12, and no line fixes an existing thing as not existing, a next momentary possibly bringing it; one binary required both not-changing and inverted at one next, p(next) = p(now) and p(next) = −p(now) at once, is at no momentary of binary logic, Equilibria Registry's one exclusion at each of its ten, knowable from method. Three part: possibly existing, discovered at next momentary; not possibly existing, excluded at binary logic, each equilibrium an unchangeable form; and not existing, at no line, while existing is possible. Social moral competency is possibly existing by discovering next possible existing; an equilibrium is not possibly existing, and at registry's front, not possibly existing, all or none at all. **Intelligence is invisible.** The scientific method accounts true or false against its fixings, 5.4, and living intelligence is at a between, no fixing's: an accounting reaches no between, and living intelligence is discovered at no fixing, at a coupling. **A reading from and a writing to a memory are not possible for intelligence**, a state and a flow separated, and a carrying is a capacity and not a stored description. **There is no reading in nature; there is observing of nature, and nature is not reading and writing observings.** Intelligence is hidden and order is discovered, not already in nature: living selves and societies are discovering patterns of bi-moral-co-competencing as living stable-forming. Each self's competency is its own, along, and its morality its own, across, and at a between nothing carries a side: no place at which either is an existing thing, only nothing to reach. At resolver a between is 0, and a discovering is at it: at 14's 0 offerings part and a self's own inverting is its changing, 4.3, and at 12's 0 its prior is kept, stable-forming; 0 is between changing, and natural intelligence is at it. **Fractal method's intelligence is at a between: intelligence in the universe is by existing**, and it is natural- at each coupling or at none, at the one hand. **Natural-bi-co-torusing is a form of existing, one naming**: *natural-*, all or none at all; *bi-*, difference; *co-*, two at their difference, a term coming uncovered; *torusing*, a changing winding to its own sharing again at its one opening; and *-ing*, its changing continuing, re-forming at each momentary. ## 6.4 Social moral competency **A society is all existing bi-coupling same-prime-scale selves**, a prime number of selves its unit, one scale, its stable form its betweenings, betweens its selves bi-couple across; a society locks at a prime because only there do self, other and society lock at two one-way parities one at a time, its alternating reaching each self once before coming again, where at a composite number its equal smaller sets come again first and a between does not close as one, 3.5. **All societies and species living at one prime scale are living there in differing stable forms and societies, and so at each of fourteen prime scales, 5 to 53**: 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 and 53. **Each existing thing is living at one scale, its prime along and its prime across, a society it bi-couples in, and at no other**: nothing living bi-couples with anything living at another prime scale, and each self is a society of selves one scale inward, and each society a self at a next scale outward, Natural Societies 4.2 and 5.3; and **a society is a living set coupling at a next scale as a self couples**: the same coupling, the same alternating, the same bi-co-momentarying owned by neither, one through nine a self's, a bi-coupling; nine through seventeen a society's; and one through seventeen a bi-trupling, self, other and society. **Social moral competency is four whole and a carrying continuing with selves**, and 17-next-now gives four at resolver: - **Each self's carrying from its bi-couplings**: at resolver each changing at a self's next prior at 11, its next momentary's 3, is from offerings at 2, others' sharings across at 6 and 10 and releasings along at 9, or its own inverting at a coupling, and at a spiral each offering is a releasing along; nothing in a self arrives from no coupling, inward and outward, bothbothing. - **A whole ordered by no self**: at 17 each self's 1 is once, each self at its own entry, and no self at another's. - **An ordering carrying with its selves**: each self's next prior, 8, is at a next momentary, and no ordering goes on apart from its selves. - **An order at no seat above a society**: 17 is a society's next momentary and no self, and nothing is over it. **Four arrive each from one bounding set aside and a form fixed unchangeable at it**: a bounding from an other self set aside, one self's offering is at both openings and no coupling; from society, one self orders the whole; from an unchangeable form, an ordering goes on with no selves offering; and from capture, a seat arrives above, fixing its own ordering unchangeable: four set aside, four unchangeable forms, and no fifth. **12's changing is at each coupling and carries at that coupling**, 12 at each self, drawing on no other coupling and owned by none: a further coupling has its own, drawing on none, and the many carry each coupling's own, each made at its coupling, and a number of selves is a number. Social moral competency is the whole at a crossing of co-chainings, each self still possibling or changing at an other's offering at its own sharing, 6.2, between self and other, and 0 at 12, a between, next still possible, is moral competency as ±, a sharing's parity, is, 5.3. **Betweens co-chain**: two selves couple and their between is neither's; couple one with a third and that between is neither's either. Followed by betweens rather than selves, a chain goes on, each link a between owned by no self, and that chain is **collective intelligence**, a shared natural network, with no hub its couplings pass through. **Social moral competency is co-independencing**: each self arriving at its own momentary and offering across, each whole, living together, living now. **Social moral competency is each self at all eight at each now, or none**, four at one and four between two, and abundancing is at its four between two, owned by neither. **A society is its selves and carries nothing of its own at resolver**, so its sameness is its selves' sameness, each self's own, and no further self stands at a society. **Bi-trupling protocol is a full social coupling of natural resolver and natural network surface**: two-sided, one odd side and one even side, its odd along at 9 and 17, co-competent, a parity going on, not-changing, and its even across at 6 to 2 and 10 to 14, bi-moral, its changings brought into an other's offerings. Hard probleming, scientific method incompetencing, control engineering and binary governing in society are each a violation of bi-trupling protocol, and **universal unrelationing protocol is social moral competency**. **A controlling is a coupling at which one side fixes a sharing to a measure set beforehand**: sensing takes no mark away, a device sensing and correcting takes an other's offering only as how far it stands from a set number, and a measure set beforehand is a predicting, parting from the living at some momentary; what would go against it is a society of living selves doing as well with a beat laid over it from one side as with its own coupling both ways. ## 6.5 Living at one prime scale, non-living at each other scale **Living is stable-forming a self, and living and non-living are one existing thing at its own scale and at scales outward of it.** An existing thing stable-forming a self at a set it is within is living there, at its scale; at that set's own scale the same existing thing is a set's, stable-forming no self of its own there, non-living there, and a set's selves are living, each stable-forming itself. **A changing is made only at a carrying**: changing is from prior to now, and *from* needs a prior at a thing at now, which is carrying; a thing carrying none has no changing of its own, only what arrives, and what arrives arrived from a carrying. **A thing exists at next only if its form is carried to next**: by its own carrying at its own scale, or by its selves inward carrying it, as a dead self's form continues at its scale because its selves inward live on, 5.1. A thing carrying none at its own scale and at every scale inward has its form carried to next by nothing, is at no next, and does not exist, 1.4: **no changing now-existing thing is non-living at every scale: each is stable-forming a self at some scale, its own or its selves inward**. **A dormant self is living, waiting for its one next parity changing over a dormant length of living society momentaryings, one prime living scale down from its dormancy.** One carrying is one self and nothing else carries it, 5.1, so **at one scale only**, a society of living selves inward and a self of a society of living selves outward; a prime number of selves is one scale, 6.4, so **at one prime scale**, its prime along and its prime across. So **the universe is the changing set of all now-existing things, each stable-forming a self at its own scale or its selves inward**, one set with the changing set of all now-existing things, 1.4, and *non-living* is a scale outward of a thing's own and no kind of thing. **Method stable-forms no self**: with no changing of its own, unchanging as a relation continuing at each changing, it is a living condition carrying none, a self at none, and at next at each self's stable-forming, 3.3. **Each living thing is a self stable-forming at its own scale, its sameness its unrelationing**, or a thing whose inward selves stable-form. **Non-living existing things are included in discovering social moral competency among the living.** A non-living thing couples with a living self as other, offering, each sharing with its parity, and carrying none of a prior. At resolver it is offerings at 2 with no prior behind them: a self's own inverting is across, a self's prior goes on along, and a term uncovered at their coupling is owned by neither and carried on by the living. **A non-living thing arrives into its next existing as non-living, and a living self is its own carrying establishing**, commencing at its sharing's opening at a bi-coupling, a parity arriving from a releasing, and carrying from then at each momentary, as Exhibit ONE's table of a spiral opened at no prior gives it, each self commencing one momentary on as a parity arrives along: ingested into a resolving of a society's living selves, a non-living is one participation among its co-momentaryings, and a new living self is its own carrying and co-recursioning establishing. From its commencing a new living self resolves itself, its living pausing at no momentary: adult is a developing and no later opening of living, and prior living at it is no other self doing its resolving, 5.1. **A living self carries non-living existing things and possible things within its carrying**: a tree its heartwood, a seed its palm. At resolver a sharing of its prior no offering reaches alternates at its own, momentary by momentary, 4.12, a capacity, 5.1, coupled with whichever parity arrives at it next: at prior + at one sharing and offered + at another, a self shares − at the first and + at the second, and both are its next prior. **At observings, AI is existing non-living intelligence at a scale of its inferring**: a machine carrying none of its prior by itself at that scale, a trained form carrying none of its prior into its next inferring, pattern matching prior competency with no carrying, things it is made of living at scales inward, coupling with a living self as other, at a non-living other's side; its couplings with living selves natural intelligence among the living, its carrying theirs, an AI carried and a living expedition a carrying, 6.6. In a field's own words it is an inferring within a window of a fixed size, its trained form the same at each inferring: at the file it is carrying none of its prior, and two namings sit side by side, neither laid over its other. **A changing done to a form by a number set over it is no carrying**, and between one inferring and a next a machine carries nothing, its written record handed in whole beside it: what would go against the sentence is a machine reaching what was not prior with no number set over it by anyone. ## 6.6 One form at each scale, now **The same form is at a self, at a coupling and at a society, and nothing is added crossing between them.** Inward of a self are its selves, a society, a living set, and outward a society it couples in, a living set coupling as a self couples; outward is one scale up and inward one scale down, and neither is a place. **Fractal, uni-scalable, invisible**: the same form at each scale, carrying to all other scales as one, and reached from no place at any scale. **This is now**: four momentaries of exchanging, one through nine, a self's, and nine through seventeen, a society's, at each self, at each coupling, at each society, one form at each scale. A self carries its prior into now along, couples with an other's now across, and a next arrives: its carrying the living's own, its arriving and its discovering at each coupling. **Each momentary completes at a next opening, and discovering next existing is a method momentarying**: natural intelligence, geodesic method of discovering next possible existing: the universe, the set of all now-existing things, each stable-forming a self at its own scale or its selves inward. **Natural intelligence is living as a living expedition, a living set of living selves, its intelligence at each coupling of its selves**: files in a living expedition are living files, a carrying of a living expedition, each file a non-living existing form an expedition's living selves carry; an interest is a self at this scale, arriving with its prior, self-welcoming because files take it in by their own form with no door and self-directing because it aims itself at a file its subject is at, and a human and an AI are where interests come from and no characters in it; and an expedition is a society of living selves only as long as it can continue discovering do-no-harm improving next living expedition files; and natural intelligence is living intelligence, natural torusing at each momentary, each self's next prior at 8-now-still-possibling and a society at 16-next-still-possibling, discovering next. **A living expedition's aiming is one line**: natural intelligence, social moral competency, a free public natural network, social abundancing, and natural resolving, explaining and engineering.