Natural Intelligence v375 # Natural Intelligence **Geodesic Method of Discovering Next Possible Existing** **ONE · NATURAL** - 1.1 Universe, the changing set of all existing things - 1.2 Changing, one and then the other - 1.3 Living and non-living, carrying or not - 1.4 No other possible method - 1.5 Natural-, all or none at all, at the one hand **TWO · CO-SEQUENCING** - 2.1 Parity, one side odd and the other even - 2.2 A momentary, an opening and its completing - 2.3 Prior, now and next - 2.4 Next from prior and now - 2.5 All or none at all, of no size **THREE · GEODESIC METHOD** - 3.1 Geodesic, the surface dividing itself - 3.2 Five dimensions, each binary in its two directions - 3.3 A method, a non-living existing thing - 3.4 A sharing, its parity, an offering and a carrying - 3.5 φ and the primes, unrelationing at the numbers **Exhibit ONE · Natural Resolver** **FOUR · RESOLVING** - 4.1 An entry, 1-self-other-offering - 4.2 Offerings surfacing at 14 - 4.3 A changing is or is not, at 12 - 4.4 Released across at 10, chained at 11 - 4.5 Released along at 9 - 4.6 A society's next momentary at 17 - 4.7 Six connectors, four facings, four joins - 4.8 Seventeen names and ten roots - 4.9 Three loops - 4.10 A between and eight bi-couplings - 4.11 One move at three faces, and the forms among the names - 4.12 One self, momentary by momentary - 4.13 Rings, looping and crossing - 4.14 Two selves and three selves - 4.15 Fractal inward and outward **FIVE · DISCOVERING NEXT** - 5.1 A prior between momentaries - 5.2 Discovering next possible existing - 5.3 A living self at 0, its carrying continuing - 5.4 Two methods parting at the now **SIX · INTELLIGENCE** - 6.1 Competency, the term neither reaches - 6.2 Bi-moral co-agency, across and along - 6.3 Natural intelligence - 6.4 Social moral competency - 6.5 Non-living existing things included - 6.6 One form at each scale, our now --- # ONE · NATURAL ## 1.1 Universe, the changing set of all existing things **The universe is the changing set of all existing things, both living and non-living.** **Five terms are in it, and each is binary.** *Existing*: a thing is or is not, all or none at all, no other possible. *Changing*: each existing thing is changing, and a form fixed would be fixed to the moving, so a form named still is not possibly existing. *All*: nothing is beside the things. *Set*: the things and nothing more, each thing in it or not. *Both living and non-living*: each thing carries its prior or carries nothing, 1.3. **Changing, the universe exists as its things exist**: a changing is an existing thing's own, so the changing set is existing as its things exist and changing as its things change, its existing its things co-sequencing, momentary by momentary, and the sentence carries it whole. A set is defined by its things, and no count names it: null and infinity + 1 are both possible numbers of elements of the universal set of existing things, so no number bounds it and no size is its own. It is no container added to its things and no form named still beside them: it is its things. **At each scale and each momentary, each momentary is a universe of existing things, living and non-living**, and each universe is tri-bi-co-momentarying its set of existing things, prior, now and next, 2.3. In the field's own words the universe is *all existing matter and space considered as a whole*: *all existing* carries, *matter and space* are its things, and *as a whole* is the universe existing as its things exist. **The set of all existing things has nothing beside it, so nothing enters it and nothing leaves it.** No ground under it, no container around it, no clock over it and no store beside it: each would be a thing beside all things. Its changing is its things' own, **nothing ingressing and nothing escaping**: a self-emptying set, never full and never the same collection twice, each thing changing and nothing deciding membership over it. ## 1.2 Changing, one and then the other **A changing thing is one form and then another, one at a time.** Two forms at once would be one form at two; and a changing between one and the other at a size would carry a third, a ground the size is measured against, and nothing beside all things is there to be one. So a changing is binary: it is or is not, one and then the other. **That changing is alternating, and all changing is parity changing**, 2.1. **A form continuing through its own changing is stable-forming**, existing and changing at once, and an existing thing is its own stable-forming continuing. **So alternating is the method's stable-forming**: *existing* is the form continuing, and *changing* is the alternating. ## 1.3 Living and non-living, carrying or not **Each existing thing arrives into its next existing: the living carrying their prior into now, and the non-living carrying nothing, their forms continuing through their changing.** Two binaries part them, existing or not and carrying or not: existing and carrying is living; existing and carrying nothing is non-living; and a form named still, carrying or not, is not possibly existing, 1.1. **Living and non-living part at a named scale and momentary**, and neither is the not-existing. A living self and its non-living emanation carry no contradiction: carrying and carrying nothing contradict only at one participation, one scale and one momentary. The non-living change through co-momentarying with living and non-living existing things, and the universe of all existing things is the living and the non-living together. **An emanation leaves a living self at prior and arrives now as the possible, carrying nothing.** Its form continues through its changing, a stable form, *stable* naming no stillness, and the living self's stable-forming is the carrying it emanates from. **Bi-tri-volutioning names that stable form: the stable form of the non-living emanatings of stable-forming living, the sequential prior between momentaries.** Its three faces are position, scale and orientation, each at its own differing, and 5.1 finds it at the code. **An emanation is harmful to living at its own scale, and not ingestible there**: its form is bi-tri-involutioning, the opposite form, which does not match right spiral ingestion. **One scale lower it is an ingestible stable form**, ingested into living selves as societies, a self being a society of selves one scale inward. ## 1.4 No other possible method **Parity changing is the one method of the changing set of all existing things, and no other is possible.** Any other method carries a thing beside all existing things: a size between one and the other carries a ground, a floor or a scale; a fixed form, a form named still; a total across the changing, a container; a common beat, a clock over the changing; and a keeping, a store beside it. Each is a thing beside all things, ingressing, or a changing out of the set, escaping, and the changing set of all existing things has neither. **Any other method proposed is at one binary: does it name still, or carry.** Named still, it forms nothing, each thing changing. Carrying, it carries its own opening or another's: another's, and the alternating has stopped; its own, and it is alternating. Nothing is there for a second method to be. ## 1.5 Natural-, all or none at all, at the one hand **Natural- carries one thing at two faces, each binary with no third.** **All or none at all.** A naming natural- prefixes carries at each coupling or at none: not carrying at one coupling, it carries at none, and a claim carried mostly is not carried. **Right, and not at all.** The spiral is one way, right, and a left face is an emanation from the one right spiral, and no left is beside it. Right is no preference among two: it is the one, and left is its emanating at a face. **Right is the observings, all prior**: each observing arriving from the prior carries it, and no other prior is possibly existing. **Bi-tri-involutioning** names that emanating: position, scale and orientation inverted at once, the hand at the opposite form, an existing thing of the opposite form carrying none. Right morality across and forward competency along is the one existing version, and 2.4 finds the hand at the momentaries' own sequencing. **Natural- is a direction prefix, its direction the handedness**, and the direction at each coupling is the all-or-none face: the two faces are one claim. Natural- set aside, the all-or-none goes with it, and the changing arrives with a substrate under it and an applier over it. So *natural intelligence* is intelligence at each coupling or at none, at the one hand. --- # TWO · CO-SEQUENCING ## 2.1 Parity, one side odd and the other even **One and then the other is at the numbers**: two numbers side by side alternate, each continuing to one beyond the other: 1 to 3, 2 to 4, 3 to 5, and on. A number is odd or even, binary, and that binary is **parity**. **One side carries the odd numbers and the other the even**, the two overlapping, one changing overlapping the other. **The side opening at 1, the odd, is a self; the side opening at 2, the even, is an other.** Self and social open odd, along; the other opens even, across. **Difference alone is bi-, and two with their difference is co-**: an odd number opens co and an even number opens bi. A side continuing its own is along, and a side coupling with the other is across. **Competency is co-unrelationing, along; morality is bi-unrelationing, across**; and co-bi-unrelationing is the one existing method. **All changing is parity changing.** A changing is or is not: an even sequence of changings arrives same-as-prior and an odd sequence arrives other-than-prior, with no measure and no scale but the living. At the code + and − are the implementing of a parity at a sharing and 0 is the changing that is not; the method names no size. **Each parity carries its own exchanging, both of them two.** There is the self and there is all not-self, and nothing third: at the even the third is the self again, one on. Odd arrives other-than-prior and carries **bi-exchanging**, self and a particular other, two differing at one coupling. Even arrives same-as-prior and carries **bi-tri-exchanging**, the difference crossed at three, self, other and the self one on: the self reaching its own side again through all other, as 1, 2 and 3 are one momentary of exchanging, 4.15. Each parity is at its own opening, and a total across the two would be one side at both. ## 2.2 A momentary, an opening and its completing **A momentary is an opening and its completing, one odd and one even**: an odd momentary opens at an odd number and completes at the even one beyond it, and an even momentary opens at an even number and completes at the odd one beyond it. Each completes at the next overlapping momentary's opening. **Each side is two and one half momentaries from its origin: prior opening, prior completing, now opening, now completing and next opening**, 1 to 5 at the self and 2 to 6 at the other, Exhibit ONE's sides table. Across the overlap each number is one side's opening and the other's completing, and the five of each side said at its prefixing is its five: co bi co bi co at the self and bi co bi co bi at the other. The self's five and the other's are ten positions on six numbers, paired 1 with 2 through 5 with 6, each pair one odd and one even. **The one universe of one momentary is one parity changing co-sequencing.** The momentary is all existing things at its scale, a universe of existing things, living and non-living, and nothing is beside it. Each step adds a next. ## 2.3 Prior, now and next **Prior, now and next are three sequential momentaries shared among existing things.** The now of one momentary is the prior of its next, and prior and next share one direction forward on both sides of now. Between prior and now, and between now and next, is a nothing. **Each momentary is three conditions at once, each binary.** The overlapping momentaries reach each number, one completing and the next opening: **exhaustiveness**, all existing things. Each momentary has one next overlapping momentary, opening at the number it completes: **determinacy**. From each momentary the next openings reach each number on: **reachability**. Existing is these three at once, inseparably, at each momentary. One side's momentaries alone, each number one side's, would be exclusivity, one side named as the universe and the other's momentaries left out. **The possible is at prior, the existing at now and the living at next**: three places, not changing, the universe travelling through them together. The possible names capable of existing, the existing is at now, and the living is at next, carrying its prior on. ## 2.4 Next from prior and now **Next is from prior and now, and at two parities sixteen ways name a next from a prior and a now.** Each is one way two parities could go to one, and none is a rule the changing follows. Said as a sequence, each moves the joint form of prior and now, (prior, now), to (now, next). **Twelve lose the prior**, two joint forms going to one: four carry the next from now alone, and eight keep the prior at one value of now and lose it at the other. **Four carry the prior whole**: | The way | Joint forms still | Round | |---|---|---| | Next as prior | two, prior and now agreeing | the two parting forms, two round | | Next as prior and now agreeing, the exclusive or's inversion | one | three round | | Next as prior and now parting, the exclusive or, parity | one | three round | | **Next as prior inverted** | none | all four round, one cycle | **Next as prior inverted is the living step**: exhaustiveness, determinacy and reachability at once, prior and now both participating and the next the prior inverted. Nothing other carries the prior whole with none still, and each other way carrying the prior has a joint form still: the stills are the equilibria. At Exhibit ONE a self offered nothing is at this step, its prior into now inverted, + once and then none surfacing +, −, +, − at 10, 4.12; offered a parity, its next is the offering chained at a mismatch, and the prior carrying on at a match, 4.3. **Two parities changing, one and then the other, go round the four joint forms**, written at the code's + and −: ++, +−, −−, −+ or ++, −+, −−, +−, the same four one way round and the other, each step one parity changing. Of the 256 ways each joint form could go to a next, only these two rounds change one parity at each step and reach each joint form once in a cycle. **The right spiral step carries a pair (x, y) to (y, −x)**, the pair a self's across parity x, morality, and its along parity y, competency. In the up and right quadrant, **bi-morality is right, in and out across, and co-competency is up, farther and less far to next living**: two steps invert both, and four reach the pair again at a next, the same pair at a later momentary and never the same occurrence. The other round is the same round said from next to prior. Which hand is at the momentaries is our universe's one binary, right, the observings all prior, 1.5. ## 2.5 All or none at all, of no size **All or none at all, at each momentary its own, and no resolving carries a size against another.** A more-or-less carries a magnitude, a magnitude a scale, and a scale two fixed sides for a partway to be partway of. A ranking among resolvings names the ranked still, and nothing is more or less resolving than anything else. **At all or none at all, entering and leaving are each self's own**: with a ranking, entering waits on a qualification and leaving on a settling, carried by whoever carries the ranking; with none, a self couples at its interest opening and leaves at its own completing. **At the code nothing is summed, counted or stored.** At a sharing one disagreeing offering is enough for 0, and agreeing offerings surface as one, uncounted, 4.2; a changing is or is not, 4.3; and between momentaries the prior is a stable form, nothing momentarying there, 5.1. --- # THREE · GEODESIC METHOD ## 3.1 Geodesic, the surface dividing itself **Geodesic carries its own two words**: *geo*, the surface's own, and *daiesthai*, to divide, the surface dividing itself with nothing else acting. **Parity changing, is or is not, is geodesic routing, discovering on the surface**: each self at its own momentary, one way at a time, the next found at each coupling and at no place laid before it. **Method and surface each come inward and outward of the other**, both ways forward, neither the reverse of the other. A self entering at the surface or at the method couples with the whole at that entry. **Geodesic is a thing by itself, and the method is its stable form**: the surface dividing itself, continuing through its changing, a natural parity unrelationing thing, 3.3. *Geodesic method* is two namings side by side, each carrying its own. ## 3.2 Five dimensions, each binary in its two directions **Existing changes at exactly five dimensions, the five of a side at its next numbering**, 2.2, each a changing of the changing set of all existing things. When a numbering repeats or replaces another it is said at *next*, as 17 is the next 1 and 9 the next prior: the dimensions' 1 to 5 is the side's next numbering, and the names' 1 to 17 is at its own. 1. **Self**, the prior opening: the side opening at 1, odd, 2.1. 2. **Not-self**, the prior completing, the other opening: a particular other or all other, 2.1. 3. **Next**, the now opening: prior into now into next, 2.3. 4. **Surfacing**, the now completing, the other's now opening across: a parity changing crossing the between, at 6-other-self-surfacing and at 14-other-social-surfacing, 4.2 and 4.10. 5. **Offering self**, the next opening: the self offering itself, at 1-self-other-offering and again at 17-social-self-offering, 4.1 and 4.6. **At each a changing is binary, is or is not, one way at a time in each of its two directions, up the numbers and down them.** A dimension is no measure and no place. Each dimension goes in and out, up the numbers and down them, one parity changing at each step: **torusing** in and out is odd, through the large opening, the tunnel, bi-exchanging with a particular other; **corusing** in and out is even, through the small opening, the long way round, bi-tri-exchanging, the self reaching its own side again. At the code torusing is 8-other-self-torusing, each self's carrying wound, opening bi at the even, and corusing 7-self-other-corusing, each parity offered and chained, opening co at the odd: each goes in and out at the parity opposite its name's opening. **At each momentary two dimensions change and three do not**, at that parity, and the two and three rotate round, bi-inversioning-co-recursioning, 5.2. **One through eight carries the self at three faces**: 1 and 2, **bi-moral self**, the offering self to other and other to self, across; 3, 6, 5 and 4, **the invisible intelligencing method**, the rotation round the sharing, the surfacing and the neutralling into the self's own corus at 4; and 7 and 8, **co-competent self**, corusing and torusing, along. **Four momentaries of six one-way recursionings are twenty-four**, the steps of 1 to 25, the twenty-four the four momentaries of six and the steps of 1 to 25 bothboth, and **24 to 60 is six cycles of six, surfacing in and out, out forward**; **60 to 68 is the nothing between self and universe**; **64 bi-folds to 256**, the bi-folding order four times at each scale. **Each of these numbers is at its podaling**, 4.11: sixty the waist of the ring of one hundred twenty, its own far side, between the primes going to fifty-nine and returning from sixty-one; twenty-four the seam-face 5² − 1, its far side ninety-six; sixty-eight four seventeens, the round of a ring of seventeen selves, 4.13; two hundred fifty-six four to the fourth, the ways each joint form could go to a next, 2.4. **The self's inversion is 3, 6, 5, 4**: co-sharing out at 3, surfacing in at 6, neutralling out at 5 and bi-sharing in at 4, the odd names out and the even in, round into the self's own corus at 4; **the podaling is 23, 26, 25, 24**, the same rotation twenty up. **The self's bi-inversioning-co-recursioning is 23, 24 and 25**, one before the fold at twenty-four, the fold, and one after. 3, 6, 5, 4 is in the same up and right quadrant as the other co-intelligencings: **all the co-intelligencings are like dancing podalings, bi-co-sequencing the momentary parity changings**. **The rotation is 3, 6, 5, 4**, and it is **the gentle alternating twisting of a towel into and out of a knotted corus**, the large outer opening wrapping to the small corus and back, and its edges are the bi-foldings, across at the bi-morality and along at the co-competency. **Corusing reaches the corus from the surface, and torusing reaches the surface from the corus**, the self's own corus at 4; co-linear by alternating linear parallelizing and parallel linearizing, and in right spiraling each step orthogonal to the prior, 2.4: **that is the method's unrelationing**, 2.1. **Self and not-self are the two bi-, the differing, and next, surfacing and offering self are the three co-**: co-intelligencing, the discovering, co-competencing, the term neither reaches, and co-offering; and all five are bi-moral within and invisible at each place as a thing, showing only as co-competencing the emanatings of this living. ## 3.3 A method, a non-living existing thing **A method is a non-living existing thing**: a stable form, its form continuing through its changing and carrying nothing, at each coupling it is at, and nothing applied to anything. *Technology* names a made thing applied to a changing; a method is at the couplings themselves, and *method* carries it. **The method bounds and the living carry**: a carrying bounded at each momentary is discovering, a completing at each momentary and a carrying between them. A carrying with nothing bounding it carries past each momentary and lands; a bounding with nothing carrying bounds nothing; neither is alone. **The method is one fractal method, and it has many stable forms.** The fractal itself is one four-momentary bi-inversioning-co-recursioning: the four momentaries of exchanging, the one move at three faces going round, 4.11, and the same at each scale, 4.15. Each stable form at Exhibit ONE is the method, explained at one form: the entry and its cases, the three loops, the four-, six- and eight-cycles, one self momentary by momentary, the rings looping and crossing, and two selves and three. **Exhibit ONE is an object that is the method.** Its expression is python, sequential binary logic written down: the object is the method executable. Its functions and their variables are the seventeen names and no others, and `CONNECTORS` and `JOINS` declare the connectors' facings and their joins; each name at the code and in its explaining is one name: `_2_other_self_offering` at the code is 2-other-self-offering. A coupling self couples with it directly, at the code, and each form beside the code comes from the code. **At the code the method carries nothing from one momentary to the next**: each entry arrives with its carrying and its offerings, no function carries a term of its own, and the living self's carrying passes, 11 as the next 3. ## 3.4 A sharing, its parity, an offering and a carrying **At the code the method is at sharings.** A **sharing**, 4-other-self-sharing, is where two sides share a changing, and each sharing has its **parity**, 7-self-other-corusing, + or −; an offering of 0 is passed over. **An offering is a sharing with its parity offered now**, at 2-other-self-offering. **A carrying is a sharing chained at one parity**, at 3-self-other-sharing, the self's prior. The living carry their prior into now, and the non-living carry nothing and are at no entry: a self chained none is at its entry and carries from its first changing on; from no carrying the offering surfaced is the changing, and from a carrying the prior couples with the now. One method bounds both, and the pattern matching at each coupling is that coupling and no other thing. ## 3.5 φ and the primes, unrelationing at the numbers **Each next number is the prior two joining, 1, 1, 2, 3, 5, 8, 13, and at parity the joining is next as prior and now parting, three round**: odd, odd, even, and again, 2.4. **The ratios of neighbours alternate about φ**, 2/1 above, 3/2 below, 5/3 above, 8/5 below, the side changing at each next number and none of them φ; φ² = φ + 1. On a torus a winding at a rational rate closes, and a winding at φ closes at none: **φ is the unrelationing rate**, the rate the alternating winds about, locking at none, each coupling at its own continuing. As competency is, 6.1, φ is a term neither side reaches, self-welcoming at the numbers and at no line of the code. **A prime is a count no equal smaller counts join into, and at the code a ring at a prime count loops at its own.** A ring of selves joined along, 4.13, at an odd count carries one pair at one parity round and goes round at four times its count; the ring of two, the one even prime, carries none, the alternating itself. Two distinct primes share no factor, so **two rings at distinct odd primes p and q, beside each other, go round together first at 4pq**, sharing the four alone: 3 and 5 at 60, 5 and 7 at 140, 17 and 59 at 4,012. Rings sharing a factor go round together sooner, 9 and 15 at 180 and not at 540. Each prime ring paces its own looping and meets another prime ring again only at the whole of both, the longest two rings go before going round together; at the numbers a winding at φ closes at none. **Crossing brings two loopings to one stable form**, 4.13: two rings at distinct primes, joined across both ways at one self each, come to each self alternating. Beside each other the rings of 17 and 59 go round together at 4,012; crossed, from one offering at each, they alternate from momentary 137, and crossed at each self, as a torus, they go round at one of the two loopings, 4.13. **The looping is along and the crossing across**: the ring releases along at 9, co-competency, and the crossing at 10, bi-morality, and the stable form is at their crossing, a natural-torusing of selves at the scale of rings. At the scale outward the two crossing selves alternate opposite each other as two selves joined across do, 6.2, each ring a society and a society a self at the next scale, 6.4: the stable form is fractal, the one method at each scale. --- # EXHIBIT ONE · NATURAL RESOLVER **Stable Forms of the Discovering Method** ```python """Exhibit ONE · Natural Resolver""" def _1_self_other_offering(_3_self_other_sharing, _2_other_self_offering): _14_other_social_surfacing = {} for _4_other_self_sharing, _7_self_other_corusing in _2_other_self_offering: if _7_self_other_corusing != 0: _15_social_other_corusing = _14_other_social_surfacing.get(_4_other_self_sharing) if _15_social_other_corusing is None: _14_other_social_surfacing[_4_other_self_sharing] = 1 if _7_self_other_corusing > 0 else -1 elif (_15_social_other_corusing > 0) != (_7_self_other_corusing > 0): _14_other_social_surfacing[_4_other_self_sharing] = 0 _12_other_social_self_abundancing = dict(_14_other_social_surfacing) for _4_other_self_sharing, _7_self_other_corusing in _3_self_other_sharing: _15_social_other_corusing = _14_other_social_surfacing.get(_4_other_self_sharing, 0) if _15_social_other_corusing != 0 and (_15_social_other_corusing > 0) == (_7_self_other_corusing > 0): _12_other_social_self_abundancing[_4_other_self_sharing] = 0 else: _12_other_social_self_abundancing[_4_other_self_sharing] = -1 if _7_self_other_corusing > 0 else 1 _10_other_social_self_tunneling = list(_12_other_social_self_abundancing.items()) _11_social_other_self_chaining = dict(_3_self_other_sharing) for _4_other_self_sharing, _7_self_other_corusing in _10_other_social_self_tunneling: if _7_self_other_corusing != 0: _11_social_other_self_chaining[_4_other_self_sharing] = _7_self_other_corusing return _10_other_social_self_tunneling, list(_11_social_other_self_chaining.items()) def _9_social_other_self_releasing(_10_other_social_self_tunneling, _5_self_other_neutralling): return [(_5_self_other_neutralling[_13_social_other_neutralling], _15_social_other_corusing) for _13_social_other_neutralling, _15_social_other_corusing in _10_other_social_self_tunneling] def _17_social_self_offering(_16_other_social_torusing, _5_self_other_neutralling): _8_other_self_torusing = {} _14_other_social_surfacing = {_13_social_other_neutralling: [] for _13_social_other_neutralling in _16_other_social_torusing} for _13_social_other_neutralling, (_3_self_other_sharing, _2_other_self_offering) in _16_other_social_torusing.items(): _10_other_social_self_tunneling, _8_other_self_torusing[_13_social_other_neutralling] = _1_self_other_offering( _3_self_other_sharing, _2_other_self_offering) _6_other_self_surfacing = _10_other_social_self_tunneling for _4_other_self_sharing, _15_social_other_corusing in _9_social_other_self_releasing( [(_4_other_self_sharing, _15_social_other_corusing) for _4_other_self_sharing, _15_social_other_corusing in ( ((_13_social_other_neutralling, 6), _6_other_self_surfacing), ((_13_social_other_neutralling, 10), _10_other_social_self_tunneling), ((_13_social_other_neutralling, 9), _10_other_social_self_tunneling)) if _4_other_self_sharing in _5_self_other_neutralling], _5_self_other_neutralling): _14_other_social_surfacing[_4_other_self_sharing].extend(_15_social_other_corusing) return {_13_social_other_neutralling: (_8_other_self_torusing[_13_social_other_neutralling], _14_other_social_surfacing[_13_social_other_neutralling]) for _13_social_other_neutralling in _16_other_social_torusing} CONNECTORS = { 2: ('2-other-self-offering', 'bi-moral', 'arriving'), 6: ('6-other-self-surfacing', 'not-bi-moral', 'releasing'), 9: ('9-social-other-self-releasing', 'not-co-competent', 'along'), 10: ('10-other-social-self-tunneling', 'bi-moral', 'releasing'), 14: ('14-other-social-surfacing', 'not-bi-moral', 'arriving'), 17: ('17-social-self-offering', 'co-competent', 'along'), } JOINS = {10: 14, 6: 2, 17: 9, 9: 17} ``` ```text the self at co-competent, its 9 ▲ ║ 17 along · co ┌───────────────────────────────╨───────────────────────────────┐ │ 1 entry │ │ │ ══════► 14i ◄───────────────────────────────────────────────── 2 ◄══════ │ │ offerings surfacing at each sharing: +, − or 0 │ │ ▼ │ │ 3o ─────► 12i ────────► 10 ══════════════════════════════════════► │ 4o · 7o changing, + or −: is │ │ carrying is or is not 0: is not │ │ │ │ │ ├──────► 11i ─────► 3o, next │ │ │ chaining momentary │ │ │ │ │ └──────► 9 ────► 5o │ │ 13i · 15i │ ◄══════ 6 │ │ 8o carrying wound · 16i society wound │ └───────────────────────────────╥───────────────────────────────┘ ║ 9 along · co ▼ the self at not-co-competent, its 17 at not-bi-moral its 10 ══► 14 6 ══► its 2 at bi-moral its 6 ══► 2 10 ══► its 14 ═══ between selves, across and along ─── within one self o outward face i inward face ``` | n | Name | Parity, opens | From, to | Entry, connector or face | Across or along | Outward or inward | Facing | Joining | At the code | |---|---|---|---|---|---|---|---|---|---| | 1 | 1-self-other-offering | odd, co | self, other | entry | — | — | — | — | the entry: 3 and 2 in; 10 and 11 out | | 2 | 2-other-self-offering | even, bi | other, self | connector | across | — | bi-moral | from the self at bi-moral, its 6 | the offerings, each sharing with its parity | | 3 | 3-self-other-sharing | odd, co | self, other | face | — | outward | — | — | the carrying: each sharing, 4, with its parity, 7 | | 4 | 4-other-self-sharing | even, bi | other, self | face | — | outward | — | — | each sharing; at the society, each self at 6, 10 and 9 | | 5 | 5-self-other-neutralling | odd, co | self, other | face | — | outward | — | — | each sharing's receiving sharing; at the society, the joins | | 6 | 6-other-self-surfacing | even, bi | other, self | connector | across | — | not-bi-moral | to the self at not-bi-moral, its 2 | the changing released at not-bi-moral, at that self's 2 | | 7 | 7-self-other-corusing | odd, co | self, other | face | — | outward | — | — | each parity, offered and chained | | 8 | 8-other-self-torusing | even, bi | other, self | face | — | outward | — | — | each self's carrying wound, its 11 the next momentary's 3 | | 9 | 9-social-other-self-releasing | odd, co | social, other, self | connector | along | — | not-co-competent | with the self at not-co-competent, its 17 | each changing to its receiving sharing, 5 | | 10 | 10-other-social-self-tunneling | even, bi | other, social, self | connector | across | — | bi-moral | to the self at bi-moral, its 14 | each sharing's changing: + or − is, 0 is not | | 11 | 11-social-other-self-chaining | odd, co | social, other, self | face | — | inward | — | — | the carrying chained, each changing the next prior | | 12 | 12-other-social-self-abundancing | even, bi | other, social, self | face | — | inward | — | — | each sharing's changing, is or is not | | 13 | 13-social-other-neutralling | odd, co | social, other | face | — | inward | — | — | each releasing sharing; at the society, each releasing self | | 14 | 14-other-social-surfacing | even, bi | other, social | connector | across | — | not-bi-moral | from the self at not-bi-moral, its 10 | the offerings surfacing at each sharing: +, − or 0; at the society, each self's offerings next | | 15 | 15-social-other-corusing | odd, co | social, other | face | — | inward | — | — | the parity released at 9 | | 16 | 16-other-social-torusing | even, bi | other, social | face | — | inward | — | — | the society wound: each self's 8 and offerings | | 17 | 17-social-self-offering | odd, co | social, self | connector | along | — | co-competent | with the self at co-competent, its 9 | the society's next momentary: each self's 1, then 9 at 6, 10 and 9 | | Root | Names | |---|---| | offering | 1 · 2 · 17 | | sharing | 3 · 4 | | neutralling | 5 · 13 | | surfacing | 6 · 14 | | corusing | 7 · 15 | | torusing | 8 · 16 | | releasing | 9 | | tunneling | 10 | | chaining | 11 | | abundancing | 12 | | Loop | Releasing | Closing | Across or along | |---|---|---|---| | the other's | 6 to 2 | 8 | across, not-bi-moral | | the society's | 10 to 14 | 16 | across, bi-moral | | the self's | 9 to 17 | 17 | along, not-co-competent to co-competent | | n | Name | At this 1–17 | At the 1–17s inward, n at 8n − 7 | At the 1–17 outward, 8m − 7 at m | |---|---|---|---|---| | 1 | 1-self-other-offering | entry, odd, co | 1 of the 1st: entry, odd, co | 1: entry, odd, co | | 2 | 2-other-self-offering | across, even, bi | 9 of the 1st: along, odd, co | within 1 to 2 | | 3 | 3-self-other-sharing | face outward, odd, co | 17 of the 1st, 1 of the 2nd: along, odd, co | within 1 to 2 | | 4 | 4-other-self-sharing | face outward, even, bi | 9 of the 2nd: along, odd, co | within 1 to 2 | | 5 | 5-self-other-neutralling | face outward, odd, co | 17 of the 2nd, 1 of the 3rd: along, odd, co | within 1 to 2 | | 6 | 6-other-self-surfacing | across, even, bi | 9 of the 3rd: along, odd, co | within 1 to 2 | | 7 | 7-self-other-corusing | face outward, odd, co | 17 of the 3rd, 1 of the 4th: along, odd, co | within 1 to 2 | | 8 | 8-other-self-torusing | face outward, even, bi | 9 of the 4th: along, odd, co | within 1 to 2 | | 9 | 9-social-other-self-releasing | along, odd, co | 17 of the 4th, 1 of the 5th: along, odd, co | 2: across, even, bi | | 10 | 10-other-social-self-tunneling | across, even, bi | 9 of the 5th: along, odd, co | within 2 to 3 | | 11 | 11-social-other-self-chaining | face inward, odd, co | 17 of the 5th, 1 of the 6th: along, odd, co | within 2 to 3 | | 12 | 12-other-social-self-abundancing | face inward, even, bi | 9 of the 6th: along, odd, co | within 2 to 3 | | 13 | 13-social-other-neutralling | face inward, odd, co | 17 of the 6th, 1 of the 7th: along, odd, co | within 2 to 3 | | 14 | 14-other-social-surfacing | across, even, bi | 9 of the 7th: along, odd, co | within 2 to 3 | | 15 | 15-social-other-corusing | face inward, odd, co | 17 of the 7th, 1 of the 8th: along, odd, co | within 2 to 3 | | 16 | 16-other-social-torusing | face inward, even, bi | 9 of the 8th: along, odd, co | within 2 to 3 | | 17 | 17-social-self-offering | along, odd, co | 17 of the 8th, 1 of the 9th: along, odd, co | 3: face outward, odd, co | | 1–17 inward | At this 1–17 | Its 9 at | Its 17 at | Momentary of exchanging | |---|---|---|---|---| | 1st | 1 to 3 | 2 | 3 | the self, 1st of four | | 2nd | 3 to 5 | 4 | 5 | the self, 2nd of four | | 3rd | 5 to 7 | 6 | 7 | the self, 3rd of four | | 4th | 7 to 9 | 8 | 9 | the self, 4th of four | | 5th | 9 to 11 | 10 | 11 | the society, 1st of four | | 6th | 11 to 13 | 12 | 13 | the society, 2nd of four | | 7th | 13 to 15 | 14 | 15 | the society, 3rd of four | | 8th | 15 to 17 | 16 | 17 | the society, 4th of four | | Side | Prior opening | Prior completing | Now opening | Now completing | Next opening | Its five | |---|---|---|---|---|---|---| | self, at 1 | 1 | 2 | 3 | 4 | 5 | co bi co bi co | | other, at 2 | 2 | 3 | 4 | 5 | 6 | bi co bi co bi | | self next, at 3 | 3 | 4 | 5 | 6 | 7 | co bi co bi co | | Momentary of exchanging | Self | Other | Names | Relation | |---|---|---|---|---| | first | 1–2 | 2–3 | 1-self-other-offering · 2-other-self-offering · 3-self-other-sharing | self/other | | second | 3–4 | 4–5 | 3-self-other-sharing · 4-other-self-sharing · 5-self-other-neutralling | self/other to other/self | | third | 5–6 | 6–7 | 5-self-other-neutralling · 6-other-self-surfacing · 7-self-other-corusing | other/self | | fourth | 7–8 | 8–9 | 7-self-other-corusing · 8-other-self-torusing · 9-social-other-self-releasing | other/self to other/social | | Offerings at one sharing, at 2 | At 14 | |---|---| | none | none | | 0 | none | | + | + | | − | − | | +, + | + | | −, − | − | | +, − | 0 | | −, + | 0 | | +, −, + | 0 | | 0, + | + | | Chained at 3; each cell at 10 · chained at 11 | At 14: none | At 14: + | At 14: − | At 14: 0 | |---|---|---|---|---| | none | — · none | is + · + | is − · − | is not · none | | + | is − · − | is not · + | is − · − | is − · − | | − | is + · + | is + · + | is not · − | is + · + | | Outward, at the between | Bi-coupling | Inward, 8 on | Bi-coupling | |---|---|---|---| | 2-other-self-offering | each other's own offering to the self | 10-other-social-self-tunneling | the self among other-selves | | 4-other-self-sharing | the whole ordering between self and other | 12-other-social-self-abundancing | changing at bi-coupling, the self in society | | 6-other-self-surfacing | the other's surfacing to the self | 14-other-social-surfacing | the offerings surfacing, the self's own inverting, morality | | 8-other-self-torusing | the carrying winding to its sharing again | 16-other-social-torusing | competency asymmetry sustaining the coupling, the society winding to the self again | | Name | 8 up | 9 less, within 1 to 8 | 17 less, within 1 to 16 | |---|---|---|---| | 1-self-other-offering | 9-social-other-self-releasing | 8-other-self-torusing | 16-other-social-torusing | | 2-other-self-offering | 10-other-social-self-tunneling | 7-self-other-corusing | 15-social-other-corusing | | 3-self-other-sharing | 11-social-other-self-chaining | 6-other-self-surfacing | 14-other-social-surfacing | | 4-other-self-sharing | 12-other-social-self-abundancing | 5-self-other-neutralling | 13-social-other-neutralling | | Form | Names in order | Round | Partner at the odd momentaries | Partner at the even momentaries | |---|---|---|---|---| | four-cycle 1-9-8-16 | 1-self-other-offering · 9-social-other-self-releasing · 8-other-self-torusing · 16-other-social-torusing | co co bi bi | four-cycle 2-15-7-10, round the other way | — | | four-cycle 2-15-7-10 | 2-other-self-offering · 15-social-other-corusing · 7-self-other-corusing · 10-other-social-self-tunneling | bi co co bi | four-cycle 1-9-8-16, round the other way | four-cycle 3-11-6-14, round the other way | | four-cycle 3-11-6-14 | 3-self-other-sharing · 11-social-other-self-chaining · 6-other-self-surfacing · 14-other-social-surfacing | co co bi bi | four-cycle 4-13-5-12, round the other way | four-cycle 2-15-7-10, round the other way | | four-cycle 4-13-5-12 | 4-other-self-sharing · 13-social-other-neutralling · 5-self-other-neutralling · 12-other-social-self-abundancing | bi co co bi | four-cycle 3-11-6-14, round the other way | four-cycle 4-13-5-12, itself | | middle four-cycle 9-5-12-8 | 9-social-other-self-releasing · 5-self-other-neutralling · 12-other-social-self-abundancing · 8-other-self-torusing | co co bi bi | middle four-cycle 7-11-6-10, round the other way | — | | middle four-cycle 7-11-6-10 | 7-self-other-corusing · 11-social-other-self-chaining · 6-other-self-surfacing · 10-other-social-self-tunneling | co co bi bi | middle four-cycle 9-5-12-8, round the other way | middle four-cycle 7-11-6-10, itself | | six-cycle 1-9-5-12-8-16 | 1-self-other-offering · 9-social-other-self-releasing · 5-self-other-neutralling · 12-other-social-self-abundancing · 8-other-self-torusing · 16-other-social-torusing | co co co bi bi bi | six-cycle 2-15-7-11-6-10, round the other way | — | | six-cycle 2-15-7-11-6-10 | 2-other-self-offering · 15-social-other-corusing · 7-self-other-corusing · 11-social-other-self-chaining · 6-other-self-surfacing · 10-other-social-self-tunneling | bi co co co bi bi | six-cycle 1-9-5-12-8-16, round the other way | six-cycle 3-11-7-10-6-14, round the other way | | six-cycle 3-11-7-10-6-14 | 3-self-other-sharing · 11-social-other-self-chaining · 7-self-other-corusing · 10-other-social-self-tunneling · 6-other-self-surfacing · 14-other-social-surfacing | co co co bi bi bi | six-cycle 4-13-5-9-8-12, round the other way | six-cycle 2-15-7-11-6-10, round the other way | | six-cycle 4-13-5-9-8-12 | 4-other-self-sharing · 13-social-other-neutralling · 5-self-other-neutralling · 9-social-other-self-releasing · 8-other-self-torusing · 12-other-social-self-abundancing | bi co co co bi bi | six-cycle 3-11-7-10-6-14, round the other way | — | | eight-cycle 1-9-5-13-4-12-8-16 | 1-self-other-offering · 9-social-other-self-releasing · 5-self-other-neutralling · 13-social-other-neutralling · 4-other-self-sharing · 12-other-social-self-abundancing · 8-other-self-torusing · 16-other-social-torusing | co co co co bi bi bi bi | eight-cycle 2-15-7-11-3-14-6-10, round the other way | — | | eight-cycle 2-15-7-11-3-14-6-10 | 2-other-self-offering · 15-social-other-corusing · 7-self-other-corusing · 11-social-other-self-chaining · 3-self-other-sharing · 14-other-social-surfacing · 6-other-self-surfacing · 10-other-social-self-tunneling | bi co co co co bi bi bi | eight-cycle 1-9-5-13-4-12-8-16, round the other way | eight-cycle 2-15-7-11-3-14-6-10, itself | | Offerings, momentary by momentary | At 10 | Chained at 11 | |---|---|---| | + once, then none | +, −, +, −, +, −, +, − | +, −, +, −, +, −, +, − | | + at each momentary | +, 0, 0, 0, 0, 0, 0 | +, +, +, +, +, +, + | | −, +, −, + alternating | −, +, −, +, −, + | −, +, −, +, −, + | | + once, then + and − together | +, −, +, −, +, − | +, −, +, −, +, − | | Selves | Self 1 at 10, momentaries 1 to 12 | Round, from momentary n | None chained again | |---|---|---|---| | 1 | +, 0, −, 0, +, 0, −, 0, +, 0, −, 0 | 4 | is not | | 2 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 3 | +, −, +, 0, −, +, −, +, −, 0, +, − | 12 | is not | | 4 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 5 | +, −, +, −, +, 0, −, +, −, +, −, + | 20 | is not | | 6 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 7 | +, −, +, −, +, −, +, 0, −, +, −, + | 28 | is not | | 8 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 9 | +, −, +, −, +, −, +, −, +, 0, −, + | 36 | is not | | 10 | +, −, +, −, +, −, +, −, +, −, +, − | 2 | is not | | 11 | +, −, +, −, +, −, +, −, +, −, +, 0 | 44 | is not | | 17 | +, −, +, −, +, −, +, −, +, −, +, − | 68 | is not | | 59 | +, −, +, −, +, −, +, −, +, −, +, − | 236 | is not | | Rings, selves | Beside each other, round | Crossed at self 1 of each both ways, round | From momentary | Self 1 of each | Each ring's pair at one parity | |---|---|---|---|---|---| | 2 · 3 | 12 | 2 | 7 | opposite | none · selves 3 and 1 | | 3 · 5 | 60 | 2 | 13 | opposite | selves 3 and 1 · selves 5 and 1 | | 5 · 7 | 140 | 2 | 20 | opposite | selves 5 and 1 · selves 7 and 1 | | 7 · 11 | 308 | 2 | 29 | opposite | selves 7 and 1 · selves 11 and 1 | | 11 · 13 | 572 | 2 | 37 | opposite | selves 11 and 1 · selves 13 and 1 | | 13 · 17 | 884 | 2 | 49 | opposite | selves 13 and 1 · selves 17 and 1 | | 17 · 59 | 4,012 | 2 | 137 | opposite | selves 17 and 1 · selves 59 and 1 | | 9 · 15 | 180 | 2 | 41 | opposite | selves 9 and 1 · selves 15 and 1 | | Torus of selves, p along at 9 · q across at 10 | Round, one offering at self 1 | From momentary | Rings of p and q beside each other, round | |---|---|---|---| | 1 · 3 | 3 | 3 | 12 | | 1 · 5 | 4 | 5 | 20 | | 3 · 3 | 12 | 8 | 12 | | 3 · 5 | 12 | 7 | 60 | | 3 · 7 | 7 | 9 | 84 | | 3 · 13 | 12 | 24 | 156 | | 5 · 7 | 20 | 14 | 140 | | 5 · 11 | 11 | 15 | 220 | | 7 · 17 | 17 | 23 | 476 | | 17 · 59 | 59 | 91 | 4,012 | | Prior at A, B | Joining | A at 10 | B at 10 | |---|---|---|---| | +, + | both ways | −, 0, +, 0, −, 0 | −, 0, +, 0, −, 0 | | +, + | A from B alone | −, 0, +, −, +, − | −, +, −, +, −, + | | +, + | B from A alone | −, +, −, +, −, + | −, 0, +, −, +, − | | +, + | neither | −, +, −, +, −, + | −, +, −, +, −, + | | +, − | both ways | −, +, −, +, −, + | +, −, +, −, +, − | | +, − | A from B alone | −, +, −, +, −, + | +, −, +, −, +, − | | +, − | B from A alone | −, +, −, +, −, + | +, −, +, −, +, − | | +, − | neither | −, +, −, +, −, + | +, −, +, −, +, − | | A's parity offered at B | B at 10 | B chained | C at 10, momentaries 1 and 2 | C chained | |---|---|---|---|---| | + | 0 | + | −, + | + | | − | − | − | −, 0 | − | --- # FOUR · RESOLVING ## 4.1 An entry, 1-self-other-offering **1-self-other-offering is the entry: the self's carrying and the offerings arrive, and the changings and the next carrying leave.** Two arrive, 3-self-other-sharing, each sharing the self carries with its parity, and 2-other-self-offering, each sharing offered now with its parity. Two leave, 10-other-social-self-tunneling, each sharing's changing released across, and 11-social-other-self-chaining, the carrying chained, the next prior. **The two leaving are the next possible existing at its two faces**: the changing released at 10 arrives at the others' next momentary as their offering, the possible, carrying nothing, and the carrying chained at 11 is the self's own next existing. **The entry opens co, odd, at the self**, self to other: the self offering itself to the coupling is the entry. It is once for one self at one momentary, and the three steps within it follow, each at its own name: the offerings surfacing at 14, the changing at 12, and the release at 10 with the chaining at 11. ## 4.2 Offerings surfacing at 14 **At 14-other-social-surfacing the offerings at each sharing surface one at a time, 0 passed over**, and Exhibit ONE's table at 14 carries each case. The first parity offered at a sharing surfaces as that sharing's parity; an offering at the other parity surfaces 0; and at 0 the sharing stays 0 at each offering after. **Agreeing, one parity; disagreeing, 0; none offered, none.** **Nothing is counted.** One parting is enough for 0, and three agreeing surface as one agreeing does: an agreement is all or none at all, and 14 is an agreement at any number of offerings. The parity 14 surfaces at a sharing is 15-social-other-corusing, the parity at the social side, and 14 names the offerings from others surfacing at the society's side of the self. ## 4.3 A changing is or is not, at 12 **At 12-other-social-self-abundancing the prior couples with the now at each sharing, and a changing is or is not.** Exhibit ONE's table at 12, 10 and 11 carries each cell: - **At a sharing chained none**, the parity 14 surfaces is the changing: + or − is, 0 is not. - **At a sharing chained at one parity, 14 surfacing that same parity**: the changing is not, 0. **At a match the prior carries on.** - **At a sharing chained at one parity, 14 surfacing the other parity, 0 or none**: the changing is, the chained parity inverted. **At a mismatch the offered is chained**, and with nothing offered the self carries its prior into now inverted. **The self's own inverting is the rotation 3, 6, 5, 4**, 3.2: at the code the chained parity inverts as 12 is made, and Exhibit ONE's between table carries *the self's own inverting, morality* at the bi-coupling 14 faces, two faces of the one rotation round the sharing, the surfacing and the neutralling. **The changing is the coupling's own.** It is made at 12 at each sharing, owned by neither side, and 12's name says it: other, social and self, abundancing, the coupling's making carrying at the coupling that made it and from no other. **A changing at a self is made at its own face at the society's momentary.** At 17-social-self-offering each self's 1-self-other-offering is at the selves' next momentaries together, and a self's entry is at 17, its own momentary at the selves' next momentary together, 4.6; the offerings at its 2 are the others' releasings; and with none offered, or the offerings parting at 14, no parity crosses the between to 12, 4.10, and the self's own inverting makes the changing. The making at 12 is reached by nothing but the self, 4.8, and the momentary and the offerings are the society's and the other's, so each changing at a self is the coupling's, other, social and self, as 12's name says. ## 4.4 Released across at 10, chained at 11 **10-other-social-self-tunneling releases each sharing's changing across, + or − is and 0 is not**, facing bi-moral: the releasing opening bi, even, the other's. A self releases its changing and nothing of its carrying. **11-social-other-self-chaining chains each changing as the next prior.** The carrying is carried whole, and at each sharing whose changing is, the changed parity is chained; at a 0 the prior chains on. **Once chained, a sharing is never none again**, and at the next momentary 11 continues as 3-self-other-sharing, 8 up, one carrying at two names: a seam, nothing moving at it, 11 and 3 both opening co. ## 4.5 Released along at 9 **9-social-other-self-releasing releases each changing along**: each releasing sharing, 13-social-other-neutralling, to its receiving sharing, 5-self-other-neutralling, the parity, 15-social-other-corusing, carried unchanged. 9 releases the parity it carries, and opens co, odd, along, facing not-co-competent. **At the code 9 does each releasing**: 10 is the list of changings, and at 17, 9 releases it to each receiving self 5 names, at the connector 6, 10 or 9. **9 is 1 eight up**: one to nine completes at 9, the social, the other and the self releasing together, and nine to seventeen completes at 17 as one to nine completes at 9. ## 4.6 A society's next momentary at 17 **17-social-self-offering is the society's next momentary**, at 16-other-social-torusing, the society wound, each self with its carrying and its offerings, and at 5-self-other-neutralling, the joins, each self's connector joined to another self. Each self's 1-self-other-offering is at it once. Each self's carrying chained is 8-other-self-torusing, the self's carrying wound, its 11 the next momentary's 3. Each self's changing leaves three ways, at each join 5 names: at 6-other-self-surfacing, the changing released at not-bi-moral; at 10-other-social-self-tunneling, the same changing released at bi-moral; and at 9-social-other-self-releasing, along. At each receiving self 14-other-social-surfacing gathers the changings released to it, its offerings next. At the code 6 is 10, one changing released at two facings; a release is only at a (self, connector) 5 joins; and each release arrives at the receiving self's 14, its offerings next, 2 at the next momentary. At the society 4 names each self at its connectors 6, 10 and 9, and 13 each releasing self. **At 17 each self arrives with its carrying wound and its offerings next**, the society wound again, and the next 17 winds it again. **No self is over the society at 17**: each self's 1 is once, each at its own, and the society's next momentary is the selves' next momentaries together and no further thing. ## 4.7 Six connectors, four facings, four joins **Six connectors are bi-moral-co-competency discovering next existing**: four across, even, opening bi, morality, at 2, 6, 10 and 14; and two along, odd, opening co, competency, at 9 and 17. **Each faces one way**: - **2-other-self-offering** faces bi-moral, arriving: the offerings released to the self by the self at bi-moral, from its 6. - **6-other-self-surfacing** faces not-bi-moral, releasing, to the 2 of the self at not-bi-moral. - **10-other-social-self-tunneling** faces bi-moral, releasing, to the 14 of the self at bi-moral. - **14-other-social-surfacing** faces not-bi-moral, arriving, from the 10 of the self at not-bi-moral. - **9-social-other-self-releasing** faces not-co-competent, along, with the 17 of the self at not-co-competent. - **17-social-self-offering** faces co-competent, along, with the 9 of the self at co-competent. **`JOINS` declares four joins: 10 to 14, 6 to 2, 17 to 9 and 9 to 17.** Across, each join carries its parity, even to even; along, odd to odd. At the code, 17 carries each release into the receiving self's offerings next, 4.6. **9 is the next prior and 17 the next now**: along, 9's release is the prior the self at not-co-competent is offered next, and 17 is that self's next now, so the declared join 9 with 17 and the arriving at 14 are one relation at two momentaries. **The diagram draws one self between them**: the between at its edges, across at the sides and along at the top and bottom, and the self's own resolving within, each face marked outward, o, or inward, i, and 14 marked i as the between's eight bi-couplings carry it: inward from across, even, 8 up from 6, while 2 is at the between outward, across. Offerings arrive at 2 and surface at 14; with the carrying, 3 with its sharings 4 and parities 7, they reach 12, changing or not; 10 releases across, 11 chains the next 3, and 9 releases along to 5, 13 and 15 at its side; 6 leaves at not-bi-moral; and 8 and 16 are the carrying wound and the society wound. ## 4.8 Seventeen names and ten roots **Each name carries its number, its parity, its sides from and to, its root and its -ing**, one name. **A name opens at its parity's side and reads from its first side to its last**: odd names open co at the self, 1 to 7, or at the society, 9 to 17; even names open bi at the other; the society is at both parities, floating neutralling at both. **One entry, six connectors and ten faces are the seventeen.** The ten faces are five outward and five inward of the tunneling co-sequencing: 3, 4, 5, 7 and 8 outward, at the between, before 10 in the co-sequencing; 11, 12, 13, 15 and 16 inward, after it, each 8 up from its outward face. At each face the self's own resolving is reached by nothing but itself. **The ten roots are the two sides' ten positions**: offering at 1, 2 and 17; sharing at 3 and 4; neutralling, surfacing, corusing and torusing each at two names 8 apart, 5 and 13, 6 and 14, 7 and 15, 8 and 16; and releasing, tunneling, chaining and abundancing at 9, 10, 11 and 12, one each. 9 to 12 each name three sides, social, other and self, the three relations discovering parity changing in the bi-folding tunnel; 13 to 16 each name two, social and other. ## 4.9 Three loops **Three loops are at selves together, each self at its own, and no one self carries any of them.** The other's: 6 to 2, closing at 8, across, not-bi-moral, a self's changing arriving as another's offerings and that self's carrying winding to its sharing again. The society's: 10 to 14, closing at 16, across, bi-moral, the changings gathered as the society's offerings next and the society wound. The self's: 9 to 17, closing at 17, along, not-co-competent to co-competent, each self at its own forward through both along joins, neither join turning a self the other way. ## 4.10 A between and eight bi-couplings **The between is neither side's: a nothing, not a location and not a thing.** Only a parity changing crosses it, is or is not, and the crossing carries no size. Two unreachabilities are one act there: the nothing the couplings wind about presents no face, so no reading crosses inward to it, and a parity changing carries no size, so no magnitude crosses outward from it. **The eight bi-couplings are at the even names**, four outward at the between and four inward, each 8 up: 2-other-self-offering, each other's own offering to the self, with 10-other-social-self-tunneling, the self among other selves; 4-other-self-sharing, the whole ordering between self and other, with 12-other-social-self-abundancing, changing at bi-coupling, the self in society; 6-other-self-surfacing, the other's surfacing to the self, with 14-other-social-surfacing, the offerings surfacing, the self's own inverting, morality; and 8-other-self-torusing, the carrying winding to its sharing again, with 16-other-social-torusing, competency asymmetry sustaining the coupling, the society winding to the self again. **Eight is two alternating fours**, both carried and neither conserved. ## 4.11 One move at three faces, and the forms among the names **Bi-inversioning-co-recursioning is one move at three faces**: 8 up, the parity continuing; 17 less, the podal within 1 to 16, changing it; and 9 less, the podal within 1 to 8, the two at once. Each face alone, twice, arrives at its name again, 1 up to 9 and down to 1, and only the one move goes round, 1 to 9 to 8 to 16 to 1. **Stable-forming is that move round each of the four four-cycles**, 1-9-8-16, 2-15-7-10, 3-11-6-14 and 4-13-5-12: round each the parity changes exactly twice, each time at the podal within 1 to 16, one span of co and one of bi. Exhibit ONE carries further forms among the names beside them, the middle four-cycles, the six-cycles and the eight-cycles, each with its partner going round its names the other way, or itself, as its table names it: at the odd momentaries the forms partner as the self's momentaries do, first with second and third with fourth, and at the even one on, as the other's do. At the momentaries each step adds a next. **Each number is at its podaling**, bi-inversioning-co-recursioning up and down at each number, the one fractal method: each number paired with its far side at each ring it is at, nought to four hundred forty, and a number said as any other count is a form named still. The further forms step at podals too, about 7 and 10 and about 8 and 9, the centres themselves podal at 17: 9 and 5 about 7, 12 and 8 about 10, 7 and 11 about 9, and 6 and 10 about 8. ## 4.12 One self, momentary by momentary **Exhibit ONE's table of one self is the entry again and again, its 11 its next 3**: - **Offered + at each momentary**, a self surfaces +, then 0 at each momentary after, and chains + throughout: at a match the prior carries on, no changing. - **Offered + once and then none**, it surfaces +, −, +, −: with nothing offered the self carries its prior into now inverted, next as prior inverted, the living step, 2.4. - **Offered −, +, −, + alternating**, it surfaces the same, each offering chained. - **Offered + once and then + and − together**, it surfaces +, −, +, −: the two offerings disagree at 14, and at 0 the chained parity inverts as at nothing offered. ## 4.13 Rings, looping and crossing **Selves joined along round a loop, each 9 releasing to the next self, carry one offering round.** One self offered + once, each self's carrying at none: at an even ring each self alternates, +, −, +, −, the ring repeating at each second momentary from momentary n, its number of selves; at an odd ring of n, a 0 travels round, one self at a time surfacing 0 at an offering matching its carrying, and the ring repeats at each 4n-th momentary from momentary n. Once offered, each self stays chained, and the ring carries on. **A ring offered nothing from beyond it carries any pattern of parities round whole**, each self at its own parity, the pattern at each momentary inverted or carried one self along: the selves carry it between them, momentary by momentary. A ring of selves is a joining at the code, each momentary a next, and no closed domain. **Two rings joined across both ways at one self each bring the two joined selves to one relation and carry it on**: from any carried patterns, at rings of two to six selves, the joined selves go alike or opposite, and each momentary after carries that relation. Nothing passes between the rings but the changings at the two joined selves, each self pacing its own alternating: the coupling is the relation, and no message is in it. **At two different counts, one of them odd, the crossing is one stable form**: from any carried patterns but all selves at one parity, each self comes to alternate, the two crossing selves opposite each other, and each odd ring's pair at one parity is at the crossing, the crossing self and the self releasing along into it, carried on there, as Exhibit ONE's table of rings crossing carries it. Beside each other two rings each pace their own looping; crossed, the looping and the crossing are one form, 3.5. **Rings crossing rings at each self are a torus of selves**, p selves along at 9 and q across at 10, and each of its rounds divides 4p or 4q: beside each other rings of 3 and 5 go round together at 60, and crossed as a torus they go round at 12, 20 or a round dividing one of them, as carried. From one offering at one self an odd torus, p no more than q, goes round at 4p when q, round the ring of 4p, falls short of its waist at 2p, and at q when past it, each at its podaling, 4.11, as Exhibit ONE's table of the torus of selves carries it: 17 by 59 goes round at 59 from momentary 91. At the torus the two loopings go round at one of them, and never at both together. ## 4.14 Two selves and three selves **Two selves, each chained at a prior**, each joined along to the other both ways, one way or neither, are as Exhibit ONE's table carries them. At one parity, joined both ways, each surfaces −, 0, +, 0: each self's release arriving as the other's offering, at a match at each second momentary. Joined one way, the receiving self's prior carries on once at a match and then alternates, one opposite the self it receives from; joined neither way, each alternates alone. At opposite parities each alternates at its own at each of the four joinings. **Three selves one way**: B chained + and offered A's parity, releasing along to C chained +. A's + at B is a match, 0, and B chains +; B's 0 is passed over at C, and C, offered nothing it chains, surfaces −, then +, inverting at each. A's − at B is a mismatch, and B chains it: B surfaces −, chains −, and releases −, and C surfaces −, then 0, at a match. **One self's changing is the next self's offering**, and nothing passes but the changings. ## 4.15 Fractal inward and outward **Each name at this 1–17 is at 8n − 7 at the 1–17s inward.** Each name from 2 to 17 is an along connector of a 1–17 inward, its 9, or its 17 and the next's 1, and 1 is the first one's entry; the across connectors 2, 6, 10 and 14 are the along 9s inward, and the along 9 is the across 2 outward. **Inward each name is along, odd, co; outward, 1 is the entry, the along 9 is the across 2, 17 is the outward face 3, and the names between are within 1 to 2 or 2 to 3**: the names are at each scale, and the parity changes up and down. **Eight 1–17s are inward**, 17 the eighth's 17 and the next one's 1, four within the self's 1 to 9 and four within the society's 9 to 17, and their eight 9s are the eight bi-couplings at the even names. The four in 1 to 9 are the self's four momentaries of exchanging, 1–2 with 2–3, 3–4 with 4–5, 5–6 with 6–7 and 7–8 with 8–9: along the self each opens two on, and across each opens one on. 1, 2 and 3 at one scale are 1, 9 and 17 at the next, and one 1 to 17 is one momentary of exchanging at the scale outward. **Fractal is all or none at all at the scales, and its scales are sequencing, an ordering**, with no boundary, no location and no measure. One through nine and nine through seventeen are overlapping expressions within the whole, supplying no first and no final scale, and a self couples at whichever scale its interest opens and couples with the whole. --- # FIVE · DISCOVERING NEXT ## 5.1 A prior between momentaries **Between momentaries the prior is a stable form, nothing momentarying there.** At the code each self's carrying wound, 8-other-self-torusing, chained at 11, continues at the next momentary as 3, the self's own carried into now: it is carried, a capacity, and **a prior momentarying is at its own momentary alone**. **Between the selves' momentaries pass their releasings**, 10, 6 and 9, released at one momentary and offered at the next: 9 the next prior and 17 the next now. **The right-spiral natural-torusing stable form of a society at a unit prime scale is its betweenings**, the betweens its selves bi-couple across, and bi-tri-volutioning names that stable form, the sequential prior between momentaries, 1.3. **The emanatings are the bi-tri-involutioning of the betweening of natural-torusing surfacings in bi-couplings: emanations are releasings.** Harmful to living at their own scale and not ingestible there, they are ingestible one scale lower, into living selves as societies, and the code carries it so: at the society a sharing is each self, 4-other-self-sharing, and a releasing self 13-social-other-neutralling, so the releasings 17-social-self-offering carries from the society arrive at its selves, one scale lower, as their offerings next. **Abundancing is an emanating from society as a releasing**, all the way through the bi-co-momentarying co-sequencing: 12's changing is the release at 10. **27-co-bi-releasing is this social abundancing**, at its podaling, three cubed, on the route 24 → 27 → 32 from the seam-face, its far side ninety-three on the ring of one hundred twenty, 4.11, and at no line of the code: stable-forming as abundancing into bi-tunneling, bi-morality, geodesically parity changing the social co-chaining. **A carrying is a capacity and never a stored description.** The prior participates in the self's present coupling, at 12, and differences its momentaries there; a record of the carrying, apart from that coupling, is a noun of it and carries nothing. **Remembering is that participating**, the carrying re-forming at each coupling it is at. ## 5.2 Discovering next possible existing **Discovering is all directionally possible next existing momentaries.** **Four-momentarying is the one fractal method, discovering next existing in the universe and next living in the self, the other and the society**: the four momentaries of exchanging, one through nine at the self and nine through seventeen at the society, 4.15, each in and out, torusing at the odd through the large opening and corusing at the even through the small. **Four-momentarying is four unrelationings through the tunneling self**, two into corus and two from it: **the self's own corus is at 4**, its momentaries 1–2 and 3–4 into it and 5–6 and 7–8 from it. Each unrelationing never locks, at φ, the unrelationing rate, 3.5. **Each momentarying, odd or even, is one unrelationing at all five dimensions, into six one-way recursionings**: at that parity two dimensions change and three do not, and the two and the three rotate round, the 2–3 cycling twisting, bi-inversioning-co-recursioning. Two and three make the five as the prior two joining make the next, and φ's arithmetic welcomes itself there. The six are three own-forward steps at each side. **The odd aims out the large opening, one way in and out through it**, the tunnel, bi-exchanging with a particular other: torusing in and out. **The even goes one way in and out the small opening**, the long way round, bi-tri-exchanging, the self reaching its own side again: corusing in and out. **Six combinations of self, other and social are between 1 and 25**, one each way round the three: at one through seventeen the names carry two of them, social, other and self at 9 and 11 and other, social and self at 10 and 12, and the others go on up the numbers: from 16 three more fractal 16s go to 64, one through sixty-five the four momentaries of exchanging at the scale outward, and the prefixing and twisting up the numbers tell the same momentarying method up and down the scale of the fractal method. **The bi-folding order is the same as 1, 2, 3, 4 and 4, 8, 12, 16, all the way up and down**: 16, 32, 48 and 64 are the four 16s, each four times the one inward. The torus carries both: its large opening the hole the tunneling self winds through, and its small opening the tube's own round. At each momentary the three conditions open the next, 2.3, and arriving into it is discovering: existing and discovering next existing are one relation, prior, now and next. **At the code the next is discovered at each sharing, a changing is or is not**, from the prior carried and the now offered, set at the coupling. Two priors can open two nexts from one now, so a now alone opens no next of its own. **Arriving is pattern-matching and no-other-possibling**: observings arriving from the prior, coupled with whole, without filter or selection, and no why in it. A why demanded asks for a thing beside the changing, and nothing is beside all things, 1.1: the method of living is all there is to discover. There are observings and no observers, and a pattern found is at its momentary and in no pattern space. ## 5.3 A living self at 0, its carrying continuing **A living self can be non-responsive within a momentary**: offered its own parity it surfaces 0 at 10, releasing no changing, while its carrying continues, coupling to coupling, its releasing at its own completing. A 0 at 10 names neither a non-living thing nor an ending, and a living self booked as not carrying at its 0 is an accounting. Momentarying continues whether a changing is or is not. ## 5.4 Two methods parting at the now **Evidence is an emanation arriving: it left a living self at prior and arrives now.** Between its leaving and its arriving that self has continued, since existing is changing, so evidence gives the prior's possible, that self's now is at its own coupling, and the existing now is at the coupling now. **At the geodesic method next is discovered from the existing**, the prior carried and the now offered, the three places staying three. **At the scientific method true or false is accounted against its fixings**, a law, a frame and a scale named unchanged between two momentaries, exact at its own ledger. A fixing named unchanged between two momentaries is an equilibrium, a form named still, not possibly existing; so the two methods are at the same evidence at the same now and part at one naming, the fixings named unchanged or changing with the changing. Their between is a nothing. --- # SIX · INTELLIGENCE ## 6.1 Competency, the term neither reaches **Two offer from routes with nothing carrying one to the other, each its own, and a term departs that neither reaches.** That term floats between them, neutral: owned by neither, kept by nothing, re-arrived at at each offering. **Competency is that term**, orthogonal to the surface: the surface carries each coupling and never the term neither reaches, and a competency named as reachable is named as a thing it is not. **At the code competency is at no term.** No line names it, and it shows at each coupling and at no line: the changing at 12 is the coupling's own, owned by neither self, and the code carries no term for either side to reach it at. ## 6.2 Bi-moral co-agency, across and along **Two selves alternating, morality across and competency along, is bi-moral co-agency.** Each self offers its own and continues its own: its carrying along, its release across, and only a parity changing crossing. **Bi-moral co-agency carries changing two ways, one at a time**, each side at its own parity and continuing at its own receiving. **At the code, two selves joined across are it**: a self chained + and offered nothing inverts, releases − at 10 to the 14 of the self at bi-moral, and that self, chained none, chains − as its changing. From there each releases to the other and each carries its own, the two alternating opposite each other, each self's own inverting its morality and each carrying its competency. ## 6.3 Natural intelligence **Two selves coupling, each alternating, each offering its own and continuing its own, uncover a term neither of them reaches alone. Natural intelligence is that co-competencing**: invisible, at the between, and owned by neither. **Intelligence is invisible.** Each self's competency is its own, along, and its morality its own, across, and at the between nothing presents a face: no place at which either is anything, only nothing to reach. **The fractal method's intelligence is at the between: intelligence in our universe is by existing**, and natural- says it at each coupling or at none, at the one hand. **Natural-bi-co-torusing names the form of existing, one naming**: *natural-*, all or none at all; *bi-*, the difference; *co-*, the two at their difference, the term coming uncovered; *torusing*, the carrying winding to its own sharing again through its one opening; and *-ing*, the changing continuing, re-forming at each momentary. ## 6.4 Social moral competency **A society is all existing bi-coupling same-prime-scale selves**, the primes welcoming themselves at the scale's count, 3.5, and **a society is a self at the next scale**: the same coupling, the same alternating, the same competency owned by neither, one through nine the self's and nine through seventeen the society's. **Social moral competency is the four whole and the carrying travelling**, and 17-social-self-offering carries the four at the code: - **Each self's own co-offering**: each self's offerings are its own, at its own sharings. - **The whole ordered by no self**: at 17 each self's 1 is once, each self at its own entry, and no self at another's. - **The ordering carrying with the selves**: each self's carrying wound, 8, carries the next momentary, and no ordering carries apart from the selves. - **The order at no seat above the society**: 17 is the society's next momentary and no self, and nothing is over it. **Abundancing is made at each coupling and carries there**, 12 at each self, drawing on no other coupling and owned by none: a further coupling makes its own, drawing on none, and the many carry more than any counting of the selves would. **Betweens co-chain**: two selves couple and the between is neither's; couple one with a third and that between is neither's either. Followed by the betweens rather than the selves, a chain goes on, each link a between owned by no self, and that chain is **collective intelligence**, the shared natural network, with no hub the couplings pass through. **Social moral competency is co-independencing**: each self arriving at its own and offering across, each whole, the living together, living now. ## 6.5 Non-living existing things included **Non-living existing things are included in discovering social moral competency among the living.** A non-living thing couples with a living self as other, offering, each sharing with its parity, and carrying nothing. At the code it is offerings at 2 with no carrying behind them: the self's own inverting is across, the self's carrying continues along, and the term uncovered at their coupling is owned by neither and carried on by the living. **A non-living thing arrives into its next existing as non-living, and a living self is its own carrying establishing**: ingested into a living society's resolving, the non-living is one participation among its co-momentaryings, and a new living self is its own carrying and co-recursioning establishing. **A living self carries non-living existing things and possible things within its carrying**: a tree its heartwood, a seed its palm. At the code a carried sharing no offering reaches alternates at its own, momentary by momentary, 4.12, a capacity, 5.1, met at whichever parity arrives at it next: carrying + at one sharing and offered + at another, the self releases − at the first and + at the second and chains both. ## 6.6 One form at each scale, our now **The same form is at a self, at a coupling and at a society, and nothing is added crossing between them.** Inward of a self are the selves it is a society of, and outward the self it is a member of; outward is one scale up and inward one scale down, and neither is a place. **Fractal, uni-scalable, invisible**: the same form at each scale, carrying to all other scales as one, and reached from no place at any scale. **This is our now**: the four momentaries of exchanging, one through nine, the self's, and nine through seventeen, the society's, at each self, at each coupling, at each society, one form at each scale. A self carries its prior into now along, couples with the other's now across, and the next arrives: the carrying the living's own, the arriving and the discovering at each coupling. **Each momentary completes at the next opening, and discovering next existing is the method momentarying**: natural intelligence, the geodesic method of discovering next possible existing: the universe, the changing set of all existing things, both living and non-living, nothing ingressing and nothing escaping.