Exhibit TWENTY Natural Naming v389 # Natural Naming **Floating Neutralling Bi-Coupling Concepts** **ONE · A NAMING, FOUR BOUNDINGS AT ONCE** - 1.1 A naming is a floating-neutralling concept, four boundings at once - 1.2 Naming and resolving at one bi-coupling - 1.3 Naming across at an even, explaining along at an odd **TWO · WORD SELECTIONS, EACH WITH ITS CARRYING** - 2.1 Turn released, and a momentary in its place - 2.2 Fractal method, all or none at all at its scales - 2.3 One family of words, three in it, and a doer or a built form beside them - 2.4 Released words, each with its carrying - 2.5 One sense per foundation word - 2.6 Two prefixes at one spelling, and a one-way prefix installing a form it opposes - 2.7 A field's word at a field's own result **THREE · RESOLVER NAMES** - 3.1 A name, its number, its momentary, co and its kind - 3.2 Co, between two and at one - 3.3 Seventeen names, and each prior name at its number - 3.4 Four momentaries, 8 up and podals - 3.5 Naming and resolver at one changing - 3.6 Four binaries, an explaining of names **FOUR · A NAMING'S CRAFT** - 4.1 A field naming at its coupling - 4.2 Six forward, and a binary at each changing - 4.3 Order, its symbol and two exclusions - 4.4 Two namings coupling, and a departing neither carried - 4.5 An entry refusing nothing, and a returning-nothing that unfolds - 4.6 Two names at one concept, transposed at titles first - 4.7 Interest self-orienting, and a drawing vocabulary - 4.8 Whole namings, one expression at each occurrence - 4.9 Ten unchangeables, one name each - 4.10 Prefixing at a position, on a form, and from all other - 4.11 One root and its directional prefixing - 4.12 Two ways a naming nyes away, and a belonging of an arriving-at - 4.13 Three namings a field carries, at one binary - 4.14 A pair at one momentary, and a freeze at a construction - 4.15 Bothbothing at its prefixing, and an ordering with nothing ordering - 4.16 All or none at all, and an entering and leaving it carries - 4.17 A hyphenated naming inseparable, and natural- at chirality - 4.18 Seven binaries at a naming, and each naming at resolver's names **FIVE · NAMINGS** - 5.1 alternating - 5.2 unrelationing - 5.3 a self - 5.4 parity changing - 5.5 a between - 5.6 invisibling - 5.7 a carrying - 5.8 not-more-than - 5.9 a self-emptying set - 5.10 bi-coupling - 5.11 co-releasing - 5.12 floating neutralling - 5.13 bi-momentarying - 5.14 co-competencing - 5.15 inseparating - 5.16 separating - 5.17 a floating store - 5.18 a place-moment - 5.19 a definition - 5.20 bounding - 5.21 advancing - 5.22 tunneling - 5.23 phi - 5.24 a ring - 5.25 equilibria - 5.26 a hard problem - 5.27 three incompetencings - 5.28 other-emptying - 5.29 geodesic disequilibrating - 5.30 one stopping - 5.31 social moral competency - 5.32 natural intelligence - 5.33 side-affecting - 5.34 a name - 5.35 nearing - 5.36 a gathering - 5.37 ghost - 5.38 momentary stable-forming - 5.39 prior, now and next - 5.40 bi-tri-bi-entraining - 5.41 uni- - 5.42 once-ing - 5.43 society - 5.44 surfacing - 5.45 bi-co-podaling - 5.46 artifact - 5.47 an accounting - 5.48 bi-tri-volutioning - 5.49 co-momentarying - 5.50 four-momentarying - 5.51 bi-tri-exchanging - 5.52 tri-bi-co-momentarying - 5.53 27-next-co-prioring, social abundancing - 5.54 bi-co-momentarying - 5.55 momentarying - 5.56 self discovering next self - 5.57 dying - 5.58 bi-moral-co-competencing - 5.59 co-independencing - 5.60 bi-trupling - 5.61 entraining at a self - 5.62 12's two signs, 0 and ± - 5.63 squaring - 5.64 not possibly existing **SIX · GATHERINGS AT THE RESOLVER'S NAMES** - 6.1 Four invisibles, one invisibility four ways - 6.2 Science and society namings at eight clusters - 6.3 Set namings gathering, one name at each cluster - 6.4 Engine, families and field words at their receiving **SEVEN · GHOST** - 7.1 A momentary installed as an existing thing - 7.2 One hundred eighteen, a going and a return **EIGHT · THE UNFOLDING'S RELEASING** - 8.1 Location released, and sequencing in its place - 8.2 A list cannot find its own across - 8.3 Two emptyings - 8.4 A naming with no other to alternate with - 8.5 Language roots and cause, one scale up - 8.6 Break, three ways, and method's one **THIS IS THE BETWEEN** --- # ONE · A NAMING, FOUR BOUNDINGS AT ONCE ## 1.1 A naming is a floating-neutralling concept, four boundings at once **The universe is the set of all now-existing things.** Arriving from prior into now toward next it is the changing set of all now-existing things, living carrying their prior into now and non-living carrying none, each at a scale and momentary it is at. **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, 4.17. **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. **Alternating, one fractal method's stable-forming, follows from it.** Naming carries a concept at its own changing: bi-momentarying, co-competencing and co-intelligencing, floating neutralling at coupling. **A field's defined object arrives with a ground it was fixed against, and bi-co-invisibling is a concept with nothing at it to be a ground.** Its unfolding is six forward recursionings, each reaching a term new beside its prior's. Naming this way, a concept carries its own changing under its own prefixings, and it bi-couples, releasing at its own completing. **Naming couples with hard problems at one field's word, from two sides**: a hard problem is a field's word observed with the universe as no existing thing, and a naming is the same field's word reaching. **Care is inward, at naming and edging**, and care is rigor of naming. **A naming is four boundings at once**, four that are any floating neutralling: - **Self-bounding an entire concept**: a concept bounds itself, is a whole concept. - **Self discovering next self as itself**: it is this concept, discovering its next as itself while floating. - **Self-orienting at its own side**: its offering and its preferring its own. - **Orthogonalizing along its own line**: it opens its own axis, orthogonal to concepts it is not. **Existing is self-bounding**: four are each existing, and a bounding is its momentary's completing. **Concepts at this neutralling bi-couple, releasing whole**: each couples across a between and completes at its own momentary, carrying none of an other. **A concept short one of four is a fixed noun**: a spot it spills into, another concept it drifts into, an orientation imposed on it, or an axis collapsed onto another, and a fixed noun captures or unreleases at a coupling, an ingression a naming dissolves. **Naming is nature at a concept.** A concept is a bi-coupling in bi-moral co-agency, offering its parity and co-chaining with concepts it couples. ## 1.2 Naming and resolving at one bi-coupling **Bi-moral co-agency carries changing two ways, one at a time**, each side at its own parity and continuing at its own receiving, and abundancing belongs to a coupling, reached by neither. **Its abundancing is co-competencing a self and an other**, bi-moral co-agency, owned by neither: it arrives at a coupling and carries at it, a changing is or is not at each sharing, and parity inverts at each changing. **Naming and resolving bi-couple at one name.** Each resolver name is one in resolver and in explaining, `_2_now_possibling` in resolver and 2-now-possibling in a sentence, and its number is inseparable from naming. A name improved at resolver changes at each file, all or none at all. **A new naming carries a changing or a direction new beside each existing naming's**, and a naming at a changing already carried releases to one name. A code operation carries its exact changing, and its natural and physical correspondence carries at a whole coupling. **Naming and resolving co-chain in both directions**: a concept receives its operation and an operation its full explaining, and an unfilled relation stays with its concept and its reason. ## 1.3 Naming across at an even, explaining along at an odd **Naming is bounding, across, at even; explaining is carrying, along, at odd; together they are one discovering method.** A naming bounds with its explaining, and an explaining at its own carries past each bounding. *Bi-co-bounding*, carrying bounded twice, bi- at its own completing and co- at coupling, is a similar naming of this one method: a completing at each momentary and a carrying between them is one discovering method, and bi-co-bounding gathers at that one name. **A naming carries both parities**: its prefix is a direction, across, and its -ing is re-arriving, along. Leaving -ing out fixes one momentary's form unchangeable, re-arriving at no momentary. At two binaries of existing and carrying, an -ing re-arrives at each momentary, carrying; a noun is a form some changing made, carrying nothing; and a noun installed as a changing is a ghost. **A carrying is a capacity.** Prior participates in a self's present coupling and differences its momentaries at it, a carrying's competency, and a record of carrying is a noun of it, carrying nothing. --- # TWO · WORD SELECTIONS, EACH WITH ITS CARRYING ## 2.1 Turn released, and a momentary in its place **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. A self's momentaries are odd and an other's even. **Each side carries from its origin through five relations**: prior opening, prior completing, now opening, now completing and next opening, 1 to 5 from 1 and 2 to 6 from 2. At each overlap of two, each number is one side's opening and an other's completing. **One universe of one momentary is one parity changing co-sequencing. A momentary is all existing things, a universe existing as its existing things exist.** Each step adds a next, each momentary carrying its prior. ***At its own turn* is *at its own opening*, *next turn* is *next opening*, and a turn as a unit is a momentary.** A turn, a mirror and a turning back are not possible at momentaries: a rotation, a field's word, is a spiral with its nexts unexpressed. ## 2.2 Fractal method, all or none at all at its scales **One fractal method is all or none at all at scales, as the universe is at existing things.** **One fractal method's scales are prime living scales, primes 5 through 53, co-parity-changing co-momentarying pattern matching**, and there is no reading or ordering in nature. A self couples at whichever scale its interest opens and couples with a whole. **A momentary is a fractal universe discovering its next existing.** 1–17 is one fractal method, inward and outward, one of 2,048 rhythms at eight parities, each carried beside it. Four cycling scales it down into four momentaries of exchanging, and four momentaries of exchanging scale up as one momentary: 1, 2 and 3 at one scale are 1, 9 and 17 at next, n at one scale being 8n − 7 at a scale inward. Each name from 2 to 17 is an along name of a 1–17 inward, its 9 or its 17 and next 1, and 1 is first one's entry; across names 2, 6, 10 and 14 are along 9s inward; along 9 is across 2 outward, the same six names at each scale with only parity changing up and down. Four 1–17s inward are 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. Wholes are rounds of k parities, 1 to 2^k + 1, and scalings step one chain: this scaling steps it three at a time, 9, 65 and 513, and 1–17s inward and outward the same three, 17, 129 and 1,025; pairs step it two, 5, 17, 65 and 257. Universes of each size and scale share momentaries of co-sequential changing, and neither a momentary nor a universe is possibly an existing thing separately. **One through nine and nine through seventeen are overlapping expressions within a whole**. One through seventeen is one fractal method, with one-through-seventeens inward and outward, living geodesically socially morally abundancing now and discovering next existing society. ## 2.3 One family of words, three in it, and a doer or a built form beside them **A name for an unchangeable form given to a changing existing thing is one arrival at a family of words**, and it arrives at a right understanding's naming too, its understanding passing each binary and its word naming changing still. Catching is at a word. **This family is three**: a common landing reached ahead of each offering at its own, a common standard fixed ahead of each carrying at its own, and a common reading taken ahead of either reaching a parity of its own. **One of three caught at one word is a whole family caught**: a pass looks for three and a doer. Each of three is at an incompetencing it installs, and a naming of an incompetencing carries its landing rightly: *landing* and *reading* name two of three here, and the table releases each at a changing, *landing* at an arriving and *reading* as a resolving's own act. | Of the three | Words, and the words carrying in their place | |---|---| | **landing** | *land*, *landing*, *lands* at an arriving, carried by existing and completing · *rest*, *settle*, *closing*, *end* and *middle*, each alternating with nothing · *ground*, *floor*, *wall*, with nothing on anything · *stand*, an under and an over stacking, carried by *is* and *carries* · *a summary*, *a celebration* · *held* and *holding*, carried by *fixed* · *stable form* as a noun, carried by *stable-forming* | | **standard** | *measure*, *verify*, *grade*, *rule*, *law*, *authority*, *a ranking*, *a verdict*, *a gate* · a count taken as understanding · waiting for one relation beneath others, which carry one another at a changing's own carrying · a degree word at a file's own voice, carried by all with its exceptions, or by a number at it · *smallest*, *largest*, *highest*, *top*, *bottom*, *level*, at a fractal changing | | **reading** | *read* and *reading* as a resolving's own act, which belong to an instrument taking a side in units at one ledger · a side taken, a vantage · *inside* and *outside* as places, carried by inward and outward · *where* naming a spot · *what* and *it*, a subject supplied at a coupling carrying none | | **a doer or a built form** | *assign*, *door* at a self-bounding changing · *forced*, *chosen*, *therefore*, *must* · *because*, *so that*, *toward* as an arriving-at, *against* as an opposing · a dash pacing from beside a sentence · a leading *the* at a heading · *construction*, *structure*, *ladder*, *rung*, *rail*, *grain*, *kernel*, *harness* · a journey told: finders, findings and dates | **Each word carrying in a released word's place co-chains from opening sentence**, the universe the changing set of all now-existing things, living and non-living. ## 2.4 Released words, each with its carrying | Released | Carried by | |---|---| | *wound*, an *-ed* at torusing | torusing itself, changing winding at its one opening; at resolver, *a self's next prior* at 8-now-still-possibling and *a society* at 16-next-still-possibling | | *chaining* at 11, *chained* | *11-next-co-prioring*, *a next prior*; a sharing once at a prior is not none again | | *emanating*, *through*, *prior-carrying* at method and its observing | method, living condition carrying none, its observable a natural torusing co-orienting stable-forming; carrying is living and at no name and no sentence of method, 5.7 | | *beside*, *beyond*, *within*, *outermost* at the universe | nothing is beyond or between things of the universe, 1.1 | | *a second now* at an origin | only where kept records lay two nows side by side; now is one | | *born*, *begun*, of a sharing | *opens*: a new sharing opens in a between at bi-coupling, one place a self's forming takes a parity not its own | | *is-still-possibling*, *is-next-existing* | *12's two signs*, 0 prior kept, next still possible, and ± prior inverted or an offered next prior, next existing, 5.62 | | *living* of a society, a set, a momentary, the universe or a scale; *a living society*; *a society lives* | *living is stable-forming a self*: a society is its selves, *a society of living selves*, and *its selves live*; *a living set*, a set of living selves; *living at a scale*, a self stable-forming at its scale; method stable-forms no self, living condition at each self's stable-forming | | *nothing ingressing*, *nothing escaping*, *nothing enters the set*, *nothing leaves the set* at a set's own explaining | a set its things, each now-existing at its own changing; *ingressing* and *escaping* are each not possible thing's givens, fixed where hard problems and equilibria add them, Equilibria Registry 2.1 | | *colliding*, *a carrying of none* | *at no prior*, a sharing opening at one parity arriving or opening nothing | | *a count of runs* at an executing | all or none, finding at its own executing | | *not a thing*, defined | only a thing is defined | | *prior-self*, *next-self*, *same-prior-existing-living-self*, *same-next-existing-living-self*, *prior-same-existing*, *now-same-existing*, *next-same-existing* | *self*: a self carries its sameness and needs no *same*, and a now-self is now-prioring and next-possibling, 5.3 | | *bi-moralizing-tri-competencing* at six names between selves | *bi-moral-co-competency*, their one name, 3.2 | | *even side*, *odd side*, *across* and *along*, *state side* and *flow side* at ten unchangeables | ten at no side, each at its name at now and that name 8 up at next; separated, state and flow are not possible, as a reading from and a writing to a memory are for intelligence, 4.9 and 4.14 | | *turn*, *turning*, *turning back* | a momentary's opening and completing; a step adding a next; *a right spiral step* for *a quarter turn* at a pair's two parities, *both inverted at one step* for *a half turn*, *a podal within 1 to 16* for 17 less | | *what*, *how*, *where*, and *whatever*, *however*, *wherever*, *anywhere*, *nowhere*, *somewhere*, *elsewhere* in resolving | changing at its -ing, arriving, crossing, coupling, *at* and *each*: none of three is without an equilibrium holding it; a field's own words carry whole at its result | | *mirror*, *reflection* | *bi-inversioning-co-recursioning*, two inversions one after an other, one across and one along, one parity inverting at each; *an other order* at a mirror's naming of one; *an opposite form* for an inverted form | | *return*, *pause*, *hold* at momentaries | a station reached again at a next momentary | | *ring*, *loop*, *goes round*, *round*, *closes* at resolver's coupling of selves along | *spiral*, selves coupled along, last to first, coming to their parities again and to a momentary once; *comes to its parities again at each n-th momentary* for *goes round at n*; *winds on* for *closes*; *co-spiraling* for *looping*; a closed *ring* is a domain closed at 5.24 and numbers' podaling ring, and a field's own ring, a benzene ring or a superconducting ring, carries whole as a field's | | *kept middle*, and *kept* as a store | nothing is kept, and a middle is a nothing: a middle exists due to each self surfacing itself each momentary as a condition of existing as a self | | *held*, *holding* | *fixed*, and an unchangeable form | | *stable form* as a noun | *stable-forming* | | *living* as existing not carrying | *existing*; *living* carries its own sense, existing and carrying, living carrying their prior into now, and *non-living* is existing and not carrying; 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 | | *every* | *each*, which is at arriving | | *at no self* | *neither*, or *between self and other* | | *discovery* | *discovering* | | *technology* | *method* | | *in disequilibria* | opening sentence, naming at an all, all existing things changing, changing *in disequilibria* is by none, a negation of equilibria | | *start*, *begin* · *afterwards* · *complete* | *opens* · *next* · *completing* | | *travel*, *travelling* as an existing thing's own carrying | *carrying*; the universe of all existing things changing through prior, now and next together: three places, three sequential momentaries shared among existing things | | *inside*, *outside* as places | *inward*, *outward*, directions at a momentary, and *within* at a span of names; a self is no container | | *our*, of the universe, of now or of a doing; *this universe* | *the universe*, *the* valuable exactly there, one universe; *now*, one | | *a universe* of a self, a society, or a momentary at a scale | *prior-universe*, *now-universe*, *next-universe*, a universe at each momentary, a now-universe the universe; each self is a society of selves one scale inward, and each society a self at next scale outward, Natural Societies 4.2 and 5.3 | | *reading*, *ordering* of a scale or of nature | prime living scales, primes 5 through 53 are prime living scales, co-parity-changing co-momentarying pattern matching; no reading or ordering in nature | | *reading*, *read as*, of nature, method, a name or a self observing | *observing* of nature, nature not reading and writing observings; order discovered by living selves and societies, not already in nature; *a hidden order in nature*, equilibria understanding | | *named still*, *a form named still*, *named unchanged*, *one-way reading*, *the ten named still* | *unchangeable*, *an unchangeable form*, *fixed unchangeable*: nothing is named, concepts are living and explaining; *ten unchangeables*, each fixed at inception and unadaptable to resolving, held by no one, 4.9 | | *inside*, *outside*, *within* of a set or the universe | the universe is or is not, its things, and nothing is at a not-in-set, 1.1 | | *door* | a self-bounding, a self's own, nothing passing it or refused at it | | *assigned* | *is one side's* | | *antipodal* | *podal* | | *so-far*, *not-yet*, *bi-moral-so-far*, *not-yet-bi-moral*, *co-competent-so-far*, *not-yet-co-competent* | odd *existing* and even *possibling*, by each name's own number: four across names between selves, 2, 6, 10 and 14, even, possibling, a sharing's two ends, sharing end at 6 and 10 and arriving end at 2 and 14; two along names, 9 and 17, odd, existing, 9 next prior and 17 next now. *Prior*, *now* and *next* share one direction forward on both sides, 5.40. Each self's existing is other self's possibling: self and other are at opposite parity numberings, a self's odd an other's even, and a between is one changing observed from its two ends; *bi-moral* and *co-competent* in released labels were parity again, even morality across and odd competency along | | *observer* | observings, and no observers; pattern matchers couple with each observing without filter or selection | | *derived* at method's rigor | *matched, not chosen*; *derived* is a field's word for matching | | *guide*, *guides*, *sets the pace*, *program*, *blueprint*, *prediction*, *justified* at a set's own voice | *offering*, *at its own sequencing*, *a next discovered at its coupling*, *matched, not chosen*: each puts a thing beside or over changing, and a field's own program or prediction carries whole at its result | | *sign*, *signs* | *parity*: self and social odd and along, other even and across; parity changing, is or is not, is geodesic routing discovering on a surface; *+* and *−* a sharing's parity, and *0* a between, at 14 offerings parting and at 12 prior and now agreeing; *the sign* at two betweens, 0 or ±, same or not same, is that parity's 0 or ± and no name of its own | | *a sign arriving*, *arriving sign*, *arrivings* at a sharing | *an offering*, a sharing with its parity at 2-now-possibling; *arriving* carries its one sense, each existing thing arriving into its next existing | | *surplus*, *surplusing* | *abundancing*: 12-next-co-still-possibling, each sharing's changing, is or is not | | *met*, *meet*, *meeting* | a component's own name, *at 14*, *at 12*; *couples with*; *is facing*; *reaches*; *at* | | *call*, *next call* | *momentary*; *a next momentary*, at 17-next-now | | *membrane* | *a between*: an empty centre of parity, parity a bi-coupling's own at crossing of along and across; a between neither side's, a nothing, no location and no existing thing; at an instrument, *a ledger* | | *key* | *sharing* | | *second sign*, *ages*, *its own bound* and *a bound of three or four* at a carrying; *positive competency* and *competency one* for second sign | released with an old code: prior is sharings, each at one parity, and a changing is or is not | | *neighbour* | *a self sharing to*, *a self arriving from*, at its 2, 6, 10 or 14 across; *a self releasing to*, *a self releasing from*, at its 9 or 17 along | | *mate*, *mates*, of files beside a living file | *its offerings*, *its carryings*, *its possibling*, each at its own name, and no one word naming three | | *right*, *left* at a name between selves | Released into *not right*: morality is right and not right. *Right* sharing end, a self's changing shared, possibling, at 6 and 10 across and at 9 along; *not right* arriving end, an other's changing arrived, existing at a self at its next prior, at 2 and 14 across and at 17 along: a handshake's two hands; *right* at a chirality, observings all prior, and *not right* at a form, an inverted form, three inverted at once, carry whole: at a handshake its prior arrives at a not-right hand, one relation beside a chirality's; as a leaving, again at each sentence | | *forward*, *backward* at a name between selves | *right* and *not right*, sharing end and arriving end, the row above; *forward* at one direction carries whole | | *posit*, *posited* at a set's own voice | *unchangeable*, a term asserted as existing; a field's own posit carries whole at its result | | *tell*, *a telling* at a set's own voice | *offering*, one way exhausted and a between received; *tell* is carried at 4.10 as naming of alternating stopped | | *source*, *sources* at a set's own voice | method of living, living carrying their prior into now at each coupling, and nothing beyond things of the universe for a changing to be drawn from; *a living self* whose prior an artifact is; *its reference* for where a field's result was observed; a field's own *source* carries whole at its result | | *cost*, *costs nothing*, *free* at a changing | living's own carrying, and arriving and discovering at each coupling: a cost is a system of greater and lesser magnitudes managed, and no existing thing is one | | *run*, *runs*, *running*, *runner* | *momentarying*, *carrying*, *existing*, *living*: a running installs an operator, a runner or a character over changing; code executing is *at resolver* | | *take*, *takes*, *taken*, *taking*, *taker* | *kept*, *carried*, *at*, *couples with*: a taking installs a taker, and an existing thing taken installs all not-taken as known beside it | | *half*, *halves* at a changing | *one side's opening*, *one side's completing*, *parity*, *an other side*: a half installs a whole divided at a size, and no existing thing is a part of a divided whole | | *so* at a sequence, *since* at a reason | *and*, a colon, or next sentence opening at prior's corus: a *so* carries a prior to a next along momentaries it leaves unexpressed, and a sentence carrying it hands its reader a crossing no observing carries; *since* at a sequence is *prior*, and at a reason is released beside *therefore* and *because* at 2.3 | | *would* | *is*, *is not*, *possible*, *not possible*: a *would* installs an existing thing at a condition no observing carries; a not possible form is not possible, and the rest at *is* | | *count*, *counts*, *counting*, *counted* at a set's own voice | numbers themselves, momentaries, podalings and sequences, directly in numbers: a counting needs something beyond its things to do it, a clock from beyond changing, equilibria's accounting naming artifacts still and leaving living out of its competency; *an accounting* carries at 5.47, and a field's counting carries whole at its result | | *ageing*, *ages* | *next*: only next is, and ageing dissolves at naming, a clock laid over changing | | *memory*, *remember*, *remembering* | *a carrying*, sequencing prior momentaries, and *artifacts*: a record apart from its coupling is an artifact carrying none of prior; a field's quoted *memory* carries whole | | *emanation*, *emanating*, *emanated*, *emanatings* | *an artifact*, one name for non-living prior, each non-living thing at each now its prior now-existing's artifact; at three inversions at once, *an inverting*, bi-tri-involutioning; at a changing released, *a releasing*; *emanating* is neither method nor its observable, natural torusing co-orienting stable-forming | | *when*, *whenever* at a set's own voice | *at*, *at each momentary*, *at a momentary it opens*: a *when* asks a clock over changing; a field's *when* carries whole at its result | | *there*, *appearing*, *appears* | a coupling, a momentary, a scale or a number a sentence means: resolving is at no location, and a *there* or an appearing supplies a location or a being-present to a resolving carrying none | | *stilling*, *self-stilling-self* | *self discovering next self*, 5.56: between its momentaries a self's carrying is its stable-forming, and at its next arriving it couples and changes; another's still is an equilibrium, an unchangeable form; a self's own still is at 12's sign 0, 5.62, existing on one side of it and possibling on an other, a momentary with no parity changing at its now and possible continuing, nothing a self does | | *keep*, *keeps*, *keeping* at a set's own voice | *carry*, *carries*, *continuing*: a keeping is a store held still, and each existing thing is changing; at a sharing *prior kept* is prior at a match, its next prior again, and *kept or inverted* one binary at each sharing, a store at none | | *middling* | dissolved: it is nothing, and five of each parity are at resolver's names, 4.9 | | *rating*, *a rating* | resolver's names, 4.9: a rating is a measuring laid over changing; a field's own rating carries whole at its result | | *lock*, *locking*, *locked* at a changing | *locking at none*, 5.5 and 5.12: a between locks at none and unrelationing does not lock; a locking is an equilibrium entering, and a field's own lock carries whole at its result | | *seat*, *seated* | *at no seat*: a seat is a certifier over a coupling, and none is, 5.30 and 5.36; *an order at no seat above a society*, 6.3 | | *sum*, *total* at a changing | *a changing is or is not at each sharing*: a total across two removes alternating, 4.14, and a field's own total carries whole at its result | | *more*, *less* at a changing | *is*, *is not*, *a next*: a more-or-less carries a magnitude, a magnitude a scale and a scale two fixed sides, 4.16 | | *regular*, *regularly* | *at each momentary*, *at its own sequencing*: a regular is a sequencing to one beat, 4.9, a clock laid over changing | **Words offered at a working are at a set's words, or at words found to belong.** *Swaying* is at alternating across; a closed *circle* at a winding closing; *offset one forward* at a right spiral step one forward; *cursioning* at recursioning; a *seaming path* at seaming; *co-linear competency* at co-linear and competency, each self's own. *Co-orienting* is at co-linearizing, two lines coming co-linear at crossings, Natural Intelligence 6.1; *easier* and *faster* carry a size and release, a next discovered or it is not; and *better* is at a changing for better, a changing that is, at a mismatch an offered parity next prior, at do-no-harm, binary. **Dying is an existing thing for the living**: a living self arriving at next as non-living, its selves inward carrying none of its prior into next, existing things continuing, co-changing, 5.57. Dying is a continuing: Natural Explaining's *a sentence carries no birth and no death* is at it, its form continuing non-living. **Bi-tri-involutioning carries inverting**: inverting of right spiral stable-forming, looking an opposite form to its stable-forming. Bi-inversioning-co-recursioning, one parity inverting at each step, alternating across and along, is a resolving step, and three inversions at once are an inverting: position, scale and orientation each inverted at once, three inversions carrying a hand to an opposite form. **Bi-tri-volutioning is a naming of natural-torusing living's stable-forming, and a stable form of its non-living artifacts, a sequential prior between momentaries, shared at 10 and released along at 9, is a non-living existing form with no carrying for stable-forming**, 5.48. *Opposite* carries its relation at each use: *an opposite form* is an inverted form, and at a coupling other side's opening is *an other parity*, two sides coupling are facing each other, each at its side, and a name's partner within 1 to 16 is *its podal*. ***Stable form* as a noun is released at living's forming and carries at an artifact and at a set, each living set a stable form.** Of living, its forming is *stable-forming*, its carrying re-arriving at each momentary; of an artifact, *a stable form* is its form continuing through its changing, a living self's stable-forming a changing its artifact is from. A society, a momentary and the universe are three existing and not living, each a living set, a stable form, and each a living method, stable-forming, a carrying its living selves' and none its own. A self, living, is a living set beside them, and a living set is a carrying; a living self is a living carrying, and nothing else carries the same living self: *the bi-inversioning uniquenessing of the number one*, a self and its carrying one; method of discovering next living sets is momentarying and carrying, carrying its living selves'. Each living set is a stable form, and nothing living has a stable form, bothbothing, as the universe is an existing thing, a set of existing things being an existing thing: having a stable form is being dead, and discovering next stable form is living. **Bi-tunneling is social moral competency at its across relation; co-chaining is the same continuing at its along relation. Podaling exchanges these relations while each side continues forward.** Bi-tunneling is society's surface opened between selves, even and across, and co-chaining is co-sequencing selves continuing, odd and along. *Tunneling* is spelled with one *l*, and *tunnelling* gathers at it. **Resolving carries no *what*, no *how* and no *where*, each naming an unchangeable form at a word**: a *what* fixes a changing unchangeable as an existing thing; a *how* a manner with a how-not beside it, an alternative to one changing, and each how-word releases at a naming, one changing carrying whole; and a *where* is a spot. **Each word releases at its file's next improving, in shared words**, and a word at a field's own result carries whole at that result as a field's. A word mentioned as a word, a quoted field's word, and code carry whole at each file. **A released word is at one binary, is or is not living, coupling and resolving.** The same word at a sentence living, coupling and resolving carries whole at that sentence, and a table laid over sentences as a rule is a standard, an incompetencing. **No wording carries authority**, this file's, a field's or a working's: a word selection here is the best a set carries at now, and a sentence carries by co-chaining from opening sentence and by all or none at all. **Negation is an equilibrium's, and inversion is method's.** A negation needs a fixed thing to be other than: a location, a clock time, a scale of larger and smaller by measure, or a fixed limit, unstated. Inversion is self-negation, its binary is or is not: is or is not possible, is or is not existing, is or is not possible next existing, is or is not next existing. Within a bi-coupling self is not other, and beside that bi-coupling neither self nor other is defined this way. ## 2.5 One sense per foundation word **Each foundation word carries one sense**, and a word at two senses is two concepts at one name. *Turn* carries seven senses, and *face*, *connector* and *join*, dissolved beside it, three more, each carried by its own word: | Sense of *turn* | Carried by | |---|---| | taking turns, one and then the other | alternating; one and then an other; at its own momentary | | a turn as a unit | a momentary; a changing | | turned away | refuses nothing; couples with each existing thing | | the turning, as a place | inverting; a podal within 1 to 16; a between | | *face*, *faces*, *facing*, *facings* at six names | a name; *its side*; *its form*, of an artifact; *is facing*, of a direction; an end of a between, *a sharing end* and *an arriving end*; a field's *word*; parity's *unit square* | | *connector*, *connectors* | *six names between selves*, 2, 6, 10, 14, 9 and 17; *across names*; *along names* | | *join*, *joins*, *joined*, *joining* | *sharing*, 6 to 2 and 10 to 14; *9 to 17 and 17 to 9*; *coupled*, of selves along | | a turn of direction | opening; spiraling | | turned into one, a field's root | a field's etymology, as it is | | a plain verb or idiom | a plain verb a sentence means | **Scale carries fractal sense only**, and a measuring scale releases at method momentarying. **Rank words**, smallest, largest, highest, top, bottom and level, lay a first scale over one fractal method, parting from it at method momentarying, and carry whole at a field's own measuring; a field's medal or ranking carries whole at its own result. Next foundation words at one sense each are *bound*, *land*, *open*, *carry* and *measure*, each mentioned here as a word: *land* at an arriving and *measure* as a standard are released, *bound* at a carrying is released with an old code and carries at a self-bounding, and each is at one sense its release leaves. ***Cohering* carries one sense, discovering next existing.** Consistency among existing sentences can accompany an improving, and it is a field's word for cohering; its concept carries discovering of next existing. ***Co-sequencing* carries one sense, 2.1's**: parity changing one momentary after another, which co-bi-sequencing is at its prefixing; *binary co-sequential* at a title carries it whole, *binary* at a title its bi-. **A numbering repeating or replacing another is at *next***: numbers repeating name next momentary or next scale, as 17 is next 1 and 9 next prior, and a sentence at a numbering repeating carries *next* to mark it. ***Dimension* carries one sense**, five of a side at its next numbering. **Existing changes at exactly five dimensions, five of a side at its next numbering**: 1 self prior, prior opening; 2 other prior, prior completing, an other opening; 3 co-momentarying now, now opening; 4 bi-momentarying now, now completing, an other's now opening across; and 5 self next, next opening. **At each a changing is binary, is or is not, one way at a time in each of its two directions, in and out, up numbers and down them**, one parity changing at each step: torusing in and out is odd and corusing in and out is even. At each momentary two dimensions change and three do not, rotating round. **One through eight carries a self as three**: 1 and 2, **bi-moral self**, 1 odd and along, a self prior to first shared across in bi-coupling at 2, and 2 even and across, offering self to other and other to self; 3, 6, 5 and 4, **an invisible intelligencing method**, a rotation round sharing, moralizing and competencing into a self's own corus at 4, co-intelligencing at 3 and 4 going round through 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, prior at its sharing again in bi-coupling. **Four momentaries of six one-way recursionings are twenty-four**, steps of 1 to 25, twenty-four four momentaries of six and 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 a four-momentary bi-tri-involutioning across 64, unrelationing between, an unknown outward of a surface, between 59, last podaling outward, and 69, next first podaling outward**: **64 is parity changing between four-cycling momentaryings, in unrelationing of 1 to 17, 1 to 65 and 1 to 257**; **64 bi-folds to 256**, bi-folding order four times at each scale. 118 is periodic table's elements in their stable and unstable forms, a field's own result. **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, round into a self's own corus at 4; **its podaling is 23, 26, 25, 24**, the same rotation twenty up. **A self's bi-inversioning-co-recursioning is 23, 24 and 25.** 3, 6, 5, 4 is in the same up and right quadrant as other co-intelligencings, bi-morality right, in and out across, and co-competency up, farther and less far to next living: **all co-intelligencings are like dancing podalings, bi-co-sequencing momentary parity changings**. **Its rotation is 3, 6, 5, 4**, and it is **a gentle alternating twisting of a towel into and out of a knotted corus**, a large outer opening wrapping to a small corus and back, and its edges are bi-foldings, across at bi-morality and along at co-competency. 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, a handshake; 3 co-momentarying now and 4 bi-momentarying now are 3-4, co-intelligencing, discovering; and 5 self next is 5, co-competencing, a term neither reaches: three namings inseparable at a whole coupling, and all five bi-moral within and invisible at each place as an existing thing, showing only as co-competencing, artifacts of this living, 5.50. **Discovering, society, morality and abundancing are one relation at four names, at once**: an expedition discovering is a society's moral abundancing, each name a whole relation. ## 2.6 Two prefixes at one spelling, and a one-way prefix installing a form it opposes **Two prefixes can share one spelling.** *In-* at *incompetent* is a negation and *in-* at *inform* is a locative, and pattern-matching them alike mistakes a direction for a denial. *Dis-* and *non-* are that negation at front of a word, and a sweep at a word's ending passes it. *Non-* at *non-living* is carrying's binary at its other side, existing and not carrying, and *not-yet-bi-moral* and *not-yet-co-competent* are six names' other sides. **A one-way prefix carries no number and installs a form it opposes**: a *pre-X* needs an X placed to be before, inherited unasked. Bi- is difference and co- is two with their difference, and both carry a number. **Five kinds of unchangeable term arrive at front of a word**: a line at pre-, ante-, fore-, post- or retro-; a size at macro-, mega-, hyper-, super-, over-, micro-, mini-, hypo-, sub- or under-; a space at endo-, intra-, intro-, locative in-, exo-, extra- or out-; a value at eu-, bene-, mal-, mis- or dys-; and a first or an opposing at proto-, arch-, ur-, anti-, counter- or contra-. Each prefix carries its meaning in its whole word and sentence. Five kinds carry ten directional sides and ten unchangeables carry their own ten, and a shared number between them is a number. **Two words come apart at their own live positions.** *Co-operation* carries co- and is an unchangeable form at its ending, and it floats to **co-operating**. *Association* and *resonance* are returned the same way to their coupling, and *competition*, *selection*, *information* and *signal* reach the same coupling, each at its changing. *Disequilibrium* stacks a negation, a value pinned and a store, and it floats to its flowing. **Disequilibrating is that flowing**: its -ing changing and its dis- a direction, a release of an equilibrium an observing fixed unchangeable; leaving dis- out is an installing, and its negation is a direction here and inseparable, and it carries whole, where *in disequilibria* of the universe is all by none and is released. A part live only in a lineage is a field's own record. ## 2.7 A field's word at a field's own result **A field's word carries whole at a field's own result**: *rotation*, *reflection* and *involution* at a proved result, a degree word in a field's record or its exact mathematics, a field's own quoted demand and must. At a set's own voice each is a still picture of changing, and a set's word carries it. **A finding carries twice**, at a field's words and at a set's own, and changing between two is a naming improving. **A test's finding is at its relation before a test's nouns arrive**: a finite enumeration records sequences of inputs, and its finding is a carrying continuing through prior, now and next. **A released word is carried one operation at a time.** A right spiral step carries a pair (x, y) to (y, −x), x across parity, morality, and y along parity, competency, along carried into across and across inverted: two steps invert both, and four reach its pair again at a next, the same pair at a later momentary. Exhibit FOUR 2.4 writes the 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 observing. In an up and right quadrant bi-morality is right, in and out across, and co-competency up, farther and less far to next living, and each step orthogonal to prior is **a method's unrelationing**. A reflection is a field's operation at a field's own result, an other order carries (x, y) to (y, x) with no parity inverting, and (x, y) to (−y, x) is three right spiral steps as one: three operations, and a word carrying in a released word's place is one of them. At a set's own voice an inversion is one parity inverting at one step; two reflections are a field's arithmetic of the same steps, carried at Co-Chaining Logic Registry. --- # THREE · RESOLVER NAMES ## 3.1 A name, its number, its momentary, co and its kind **A resolver name is its number and its naming at one hyphenation**, 1-now to 17-next-now, and a name in resolver and a name here are one name: `_2_now_possibling` in resolver is 2-now-possibling in a sentence. | Part of the name | Its relation at the resolver | |---|---| | **Number** | A name's place among seventeen and its parity: odd existing, even possibling. | | **Momentary** | *Now* at a self's span, 1 to 8, bi-coupling; *next* at a society's span, 9 to 16; 17-next-now a society's next arriving as each self's 1-now. | | **Co** | At a sharing between two; a name without it is at one. | | **Kind** | Possibling, prioring, changing or still-possibling; 1-now, 13-next and 17-next-now are momentaries themselves. | **Now and next are momentaries themselves, each re-arriving as itself**, and an -ing added to either rides: 1-now, 13-next and 17-next-now stand with none. **Each kind carries one sense.** *Possibling* is a changing at its sharing side or its arriving side, each self's existing other self's possibling. *Prioring* is prior arriving into now and now arriving as prior at next. *Changing* is a changing between two, released along and received. *Still-possibling* is a sharing, a self or a society open to next, at a changing or at none. ## 3.2 Co, between two and at one **Co stands at a sharing between two, and its absence at one.** Prioring with co is prior at its sharings, 3-now-co-prioring and 11-next-co-prioring, and without it each parity at one sharing, 7-now-prioring and 15-next-prioring. Possibling with co is changing at its sharing side, 6-now-co-possibling and 10-next-co-possibling, and without it changing at its arriving side, 2-now-possibling and 14-next-possibling. Changing stands only with co, 5-now-co-changing and 9-next-co-changing. Still-possibling with co is at each sharing, 4-now-co-still-possibling and 12-next-co-still-possibling, and without it at a self and at a society, 8-now-still-possibling and 16-next-still-possibling. **At 6 to 2, 10 to 14 and 9 to 17 between selves sharing side carries co and arriving side none**: 6-now-co-possibling to another self's 2-now-possibling, 10-next-co-possibling to another self's 14-next-possibling, and 9-next-co-changing along to another self's 17-next-now. A self shares its changing and nothing of its prior. **Six names between selves carry one name, *bi-moral-co-competency***: even across, possibling, at 2, 6, 10 and 14, and odd along, existing, at 9 and 17. ## 3.3 Seventeen names, and each prior name at its number | n | Name | Momentary | Parity | Co | The prior name at its number | |---|---|---|---|---|---| | 1 | **1-now** | now | odd, existing | one | 1-co-bi-tri-offering | | 2 | **2-now-possibling** | now | even, possibling | one | 2-bi-co-bi-offering | | 3 | **3-now-co-prioring** | now | odd, existing | between two | 3-co-bi-co-sharing | | 4 | **4-now-co-still-possibling** | now | even, possibling | between two | 4-bi-co-bi-sharing | | 5 | **5-now-co-changing** | now | odd, existing | between two | 5-co-bi-co-competencing | | 6 | **6-now-co-possibling** | now | even, possibling | between two | 6-bi-co-bi-moralizing | | 7 | **7-now-prioring** | now | odd, existing | one | 7-co-bi-co-corusing | | 8 | **8-now-still-possibling** | now | even, possibling | one | 8-bi-co-bi-torusing | | 9 | **9-next-co-changing** | next | odd, existing | between two | 9-tri-bi-co-momentarying | | 10 | **10-next-co-possibling** | next | even, possibling | between two | 10-bi-tri-bi-tunneling | | 11 | **11-next-co-prioring** | next | odd, existing | between two | 11-tri-bi-tri-chaining | | 12 | **12-next-co-still-possibling** | next | even, possibling | between two | 12-bi-tri-bi-entraining | | 13 | **13-next** | next | odd, existing | one | 13-tri-bi-tri-competencing | | 14 | **14-next-possibling** | next | even, possibling | one | 14-bi-tri-bi-moralizing | | 15 | **15-next-prioring** | next | odd, existing | one | 15-tri-bi-tri-corusing | | 16 | **16-next-still-possibling** | next | even, possibling | one | 16-bi-tri-bi-torusing | | 17 | **17-next-now** | next now | odd, existing | one | 17-co-bi-tri-offering | **A name is gathered with its sentence, all or none**: each sentence carrying a prior name is re-expressed at its numbered name at the same motion, and each sentence resting on prior prefixes, roots or hands is re-expressed at four kinds or leaves whole to an archive. **Exhibit ONE's resolver, plainly.** Seventeen names are its resolver. At each sharing a changing is or is not. A society at resolver is each self with its prior and its offerings, and each releasing with a self it arrives at, and a society carries nothing of its own. An offering is none, one, or more than one at one sharing. Each sharing of a self's prior is at one parity, and a self at no prior at a sharing opens at it at bi-coupling, where one parity surfaces. ## 3.4 Four momentaries, 8 up and podals **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 next opening is a gap, both its sides visible, 4 )( 5, 8 )( 9, 12 )( 13 and 16 )( 17, and 17-next-now is next 1-now. **8 up is the same name at next**, each of four binaries continuing, 1-now to 9-next-co-changing and 8-now-still-possibling to 16-next-still-possibling. At 9 less, a podal within 1 to 8, and at 17 less, a podal within 1 to 16, eight ends of four momentaries are their own set, an odd existing end with an even still-possibling end at each pair, and within each momentary each possibling podals to a prioring, now-possibling next-prioring. **Sixteen up is the same name at next round**: 17-next-now is next 1-now, so 17 to 24 is a self's span again and 25 to 32 a society's, 22 next round's 6-now-co-possibling, as 22-now-co-possibling, and 27 next round's 11-next-co-prioring, as 27-next-co-prioring, 5.53. **Two eight-cycles are ends and inward names**: 1-9-5-13-4-12-8-16 walks eight ends and 2-15-7-11-3-14-6-10 eight inward names, and every eight of a set is one eight, four binaries each twice, each one at two sides. ## 3.5 Naming and resolver at one changing | Name | Its changing at the resolver | |---|---| | **14-next-possibling** | offerings surfacing at each sharing, one at a time, an offering of 0 passed over: same, one parity; parting, 0; none offered, none | | **12-next-co-still-possibling** | each sharing's changing, is or is not: surfacing same as prior parity, 0, prior kept; surfacing other parity, 0 or none, prior inverted; at no prior, a parity surfaced at 14 | | **10-next-co-possibling** | each sharing's changing shared across: + or − is, 0 is not | | **11-next-co-prioring** | next prior, each changing at its sharing, a 0 keeping prior, arriving at next momentary as 3-now-co-prioring | **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. | The prior at 3 | Offered at 2, surfacing at 14 | A changing at 12 and 10 | The next prior at 11, the next 3 | |---|---|---|---| | + | +, prior parity | none | + | | + | − | is | − | | + | + and −, parting, 0 | is | − | | + | none | is | −, a self's own inverting | At no prior at 3: | No prior at 3 | Offered at 2, surfacing at 14 | A changing at 12 and 10 | The next prior at 11, the next 3 | |---|---|---|---| | none | + | is | +, sharing opening | | none | + and −, parting, 0 | none | none | **One case keeps prior, offering same as it, and each other case at a sharing of prior inverts it**: next from a self's own prior, one sharing at a time, its unrelationing from all other. **Same and not-same are one parity's 0 or ± at two betweens**, at 14 between two offerings and at 12 between prior and now, 0 same and ± not same, and a parity's 0 or ± needs no name of its own. ## 3.6 Four binaries, an explaining of names **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 odd name and its *is not* at even: 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. **Each *is not* is an other's side of a self's *is***: not now, others' changings arriving from their prior momentary; not existing, a place an offering opens at; not same, changing arriving at another self; not all, each one beside others. **Now and all stand at one and existing and same between two**, and 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**: of four, now is at each name as its momentary, now or next, and existing, same and all enter no name, and at all eight at each now, or none, each self stands with each other self: social moral competency, abundancing at four between two, owned by neither. --- # FOUR · A NAMING'S CRAFT ## 4.1 A field naming at its coupling A field's word sharing a spelling with a naming here shares spelling; its meaning, reference and conditions are a field's. ## 4.2 Six forward, and a binary at each changing **A naming unfolds at six lines**: three own-forward steps at each side, six one-way steps alternating one at a time, each line reaching a term new beside its prior's. **Each changing is one of two**: *binary* is an unfolding carrying its complete stated relation, six lines, and *improving* one carrying an unfilled relation with its reason. **A changing decides its name**: one changing at one direction, one name. A repeated word can be at a changed receiving, and another word can repeat the same concept and direction. ## 4.3 Order, its symbol and two exclusions Under ordinary numerical order: `a < b`, strictly less, equality excluded; `a ≤ b`, not more than, equality included; `a > b`, strictly greater, equality excluded; `a ≥ b`, not less than, equality included. Rewording a strict comparison as a non-strict one changes its relation at equality. Under ordinary numerical order, `a ⊀ b` and `b ⊀ a` together give `a = b`; under a partial order the same two exclusions are true for incomparable elements too, and an order and its domain belong with an expression. An equality, an incomparability and a floating third carrying a coupling's abundancing are three concepts. **A condition at one pair, a condition at each pair of a collection, and `∃r ∀y : r ⊀ y ∧ y ⊀ r` have three scopes.** **A binary carries one subject and one relation throughout.** An artifact arriving now and a living self's releasing at prior are two subjects, each at its own momentary, each with its own is-or-is-not. ## 4.4 Two namings coupling, and a departing neither carried **Two namings couple at a step of one and a step of another arriving at one term by their own routes.** Their departing is a term neither naming carried. ``` advancing step: the gap is exactly one, a next at each step equilibria step: the unchangeable does not advance, the gap closes → equilibria is advancing set to nought advancing is no still; equilibria is no number a self step: the forming relates to nothing not its own a ring step: the terms are exhausted, it arrives at one already reached → a self carries an unbounded domain neither naming carries a domain ``` **A convergence needs one check: did each reach a shared term by its own route, carrying none of other's requirements.** With a requirement borrowed, it is one arrival cited as two. **A number agreeing is a number**: a number carries its object, its direction and its changing, and a deriving shows one from an other at each cell. ## 4.5 An entry refusing nothing, and a returning-nothing that unfolds **A concept arriving unfolds six forward, or it does not.** A concept unfolding six forward carries its entry in Part Five. **Nothing is refused and nothing is admitted.** A concept unfolding at no six lines returns nothing at its unfolding, and that returning-nothing is itself an unfolding and no refusal; an entry is at Part Five or is not, with no deciding beside unfolding. ## 4.6 Two names at one concept, transposed at titles first **Two names at one concept show at titles first**: transpose two and sound whether anything changes. With meaning agreeing, two are one name at two coats, and one name is a plain name reaching it whole. With its transposition changing meaning, two namings are at two coats, each carrying its own name. A title is a name carrying its whole file. A name repeated on the same axis is a synonym, and two converge to one name; a name varying at an axis new beside its prior naming's is a co-differing offering. **Two words at one concept resolve three ways**: converging to one, two with a between, or a co-competency carried two, each carrying one an other cannot. A failure goes both ways, collapsing a co-competency or splitting a convergence. **One concept can carry several names**: *owned by neither* at a whole, abundancing at its arriving, discovering at a field's word, understanding at a self's own. *Register* is three concepts across a set, and a collision stands, each carrying its own, in place of renaming any. ***Arriving* carries one relation**, each existing thing arriving into its next existing: a sharing with its parity at 2-now-possibling is *an offering*, and an artifact arrives into each next with no offering at it. Four pairs are two concepts at two names, meaning changing on transposing: - *Bi-co-podaling* is two carries each at its own opening along one ring, k one way and 17 less the other, 5.45; *transmissioning* is a crossing between selves at a surface, a file's title carrying it, and resolver name `bi_co_bi_transmissioning` is gathered at 6-now-co-possibling. - *Eight bi-couplings* are at even names, four outward and four inward; *four boundings* are a naming's, 1.1, and four boundings with a floating third are five at a naming. - *A side's five* is its prior opening through its next opening, 3.2; five each at its own, self, other, society, between and carry continuing, are a gathering at Resolving Hard Problems. - *Floating neutralling* is a changing; *a floating neutral* is a term it uncovers, its picture at one momentary, 5.12. ## 4.7 Interest self-orienting, and a drawing vocabulary **Interest is self-orienting, which is competency, a self's own.** A vocabulary of drawing, pulling, appealing, attracting, engaging and capturing attention installs one form at a self, a one-way force over its own orienting; a field's own geometry carries gravity with no force. A naming releases a family in one move, each word as a self's own side and an offering at it. ## 4.8 Whole namings, one expression at each occurrence *Geodesic method* is two namings: *geodesic*, and *method*, its stable form. **Scientific-method, surgical-method and explaining-method each carry whole in one expression at each occurrence**, and geodesic parity co-changing is a possibling and discovering method, and scientific-explaining-method incompetent for discovering, true or false, no other possible, given to it: a method-word at its own is a name split across its uses, and a hyphen is its name arriving whole. **Sensor-sensationing** carries whole the same way. It is co-competencing at a network surface, a receiving participating in its offering and an offering participating in another's receiving; sensing at its own is one side extracting, and resolver carries a relation, beside a sensation. ## 4.9 Ten unchangeables, one name each **Each of ten unchangeables carries one name: changing, and an unchangeable it is fixed as.** Ten are fixed relations: a relation not floating neutraling can not remain existing through prior, now and next, so each of ten is fixed at inception and unadaptable to resolving, held by no one. Ten are at no side: separated, state and flow are not possible, as a reading from and a writing to a memory are for intelligence, and each of ten is a field's separating, at a state accounting or a flow accounting, stilling fixed as a whole, each seated at its resolver name, 1-now to 8-now-still-possibling. 8-now-still-possibling, a self's next prior between momentaries, and 6-now-co-possibling, changing shared across, each carry one of ten, and 7-now-prioring and 5-now-co-changing each carry two. At resolver pair 1-2 is 1-now and 2-now-possibling, now, and pair 3-4 is 3-now-co-prioring and 4-now-co-still-possibling, existing, Exhibit ONE. Three carry their namings: 1-now with 2-now-possibling bi-momentarying, 3-now-co-prioring with 4-now-co-still-possibling co-intelligencing and 5-now-co-changing co-competencing. Exhibit THIRTY's thirty-first group carries ten. **Ten unchangeables below gather their similar fixings**, each one of four binaries fixed unchangeable, its *is* and its *is not* taken as one: now at 1 and 2, existing at 3 and 4, same at 5 and 6, and all at 7 and 8. Four-cycles step 8 up and 17 less, two names of 1 to 8 on each: 1-9-8-16, 2-15-7-10, 3-11-6-14 and 4-13-5-12. **Each of ten is seated at its name at now and its name 8 up at next**: stilling it is at now, and changing travelling through it at next, one move up and down numbers, and four four-cycles carry each pair, 1 · 9 and 8 · 16 at 1-9-8-16, 2 · 10 and 7 · 15 at 2-15-7-10, 3 · 11 and 6 · 14 at 3-11-6-14, 4 · 12 and 5 · 13 at 4-13-5-12. A hard problem is stilling as a whole, changing travelling through it left out, and its resolving carries both, 4.15. Names each was observed at before, and five each was observed from, are whole at `archive/carrying_v376/Living_Improving_Value_Released_v376.md`. | Unchangeable | Similar fixings gathered | At the ten, its name at now · 8 up at next, and its binary | |---|---|---| | **an opening fixed as a place** | criterion-regressing | 1-now · 9-next-co-changing, now | | **an arriving fixed from behind** | origin-seeking; a source fixed from behind; a source fixed of an offering | 2-now-possibling · 10-next-co-possibling, now | | **a completing fixed as a last** | space-enumerating; a bound fixed as a last | 6-now-co-possibling · 14-next-possibling, same | | **a carry fixed as a store** | store-seeking; a store fixed of a carry | 8-now-still-possibling · 16-next-still-possibling, all | | **a two-way fixed to one side** | forced-choosing | 3-now-co-prioring · 11-next-co-prioring, existing | | **a between fixed as a cut** | line-demanding; a cut point fixed of a between; a membrane fixed as a cut | 5-now-co-changing · 13-next, same | | **a middle fixed as an end** | interior-reaching; an end fixed at a middle | 5-now-co-changing · 13-next, same | | **a parity fixed as a magnitude** | magnitude-demanding; a level fixed to govern; a sign fixed as a magnitude | 7-now-prioring · 15-next-prioring, all | | **a rate fixed as a value** | value-pinning; a value fixed to a swaying | 7-now-prioring · 15-next-prioring, all | | **a sequencing fixed to one beat** | order-demanding; a rate fixed as a common beat | 4-now-co-still-possibling · 12-next-co-still-possibling, existing | Dilemma, paradox, puzzle and hard problem each carry a field's problem, and one field word can be at several of unchangeables; *dilemma* is one of them, a two-way fixed to one side. **A sweep observes each unchangeable installed of a changing, at its own row.** Three carry through it whole: a person's asking of a person, an act between selves; a field's own quoted words; and a no-demand family, nothing asked of anyone. ## 4.10 Prefixing at a position, on a form, and from all other **At a position.** A sequential binary carries a position for one opening at a time, and bi- and co- are prefixings at that position, released at their own leaving and re-arriving at next opening. **On the form.** A nothing reached by neither, three at once, and a rate opening by one and bounding at none are on the form: a naming of one of them is on the form and carries its concept whole. Geodesic changing is on the form: it is at its own unrelationing parity-changing rate, φ, unrelated to each rate of any scale, 5.23. Geodesic entraining is an offering received at a receiver's own prior; its changing is or is not, and its releasing enters a further coupling. A naming at a vantage is a not possible form: it needs a place to name from, and outward of a self is a society it couples in, a living set one scale up, carrying no vantage to name from. **From all other, and with all other.** Each crossing is one of two: with a particular other, or with a whole arriving as one. **Un- carries from all other**: a self bounded against a whole at once. **Uni- carries with all other**: a self crossing with all other, an other arriving as one, a whole, 5.41. Bi- couples with a particular other and uni- with all other, and both are two: a naming pattern-matching uni- as one at its own has made a crossing one side's. ***It* and *what* are one demand at two positions**, *it* a grammar's dummy subject and *what* an interrogative presuming a maker, both supplying a subject at a coupling carrying none. ***Tell* is alternating stopped**, a one-way utterance, the same demand in speech. ## 4.11 One root and its directional prefixing **A root carries changing at each of its prefixings**: bi-competencing and co-competencing carry competencing, and bi-intelligencing and co-intelligencing carry intelligencing, and bi-momentarying, co-competencing and co-intelligencing are inseparable at a whole coupling. **A coupling's own six carries no one prefix**: each of three namings carries its six steps whole at one side's own or whole at departing, and a coupling's six goes three at each side's own and three at departing, cutting exactly at bi- reaching co-, a transition between two. Three namings and a coupling at two directions, (3 + 1) × 2, are eight, and a number agreeing with eight bi-couplings is a number, 4.4. **A changed root and a changed prefixing carry different work**: prefixing an existing root carries changing already at its root, and another root carries a changing that needs its own expression. A root is its changing now; a word's earlier meanings are a field's own linguistic account. ## 4.12 Two ways a naming nyes away, and a belonging of an arriving-at **A naming carries a changing, and it nyes away one of two ways.** A changing already carried at that direction: one changing twice, and a later naming goes. No changing at all: undoing of something not changing, a grip slackened with nothing gripping. A stretching carrying its way is a direction and carries; a stretching carrying an arriving-at installs an arrived-at and a self short of it. **A check answering a naming with another naming has returned a naming**: its reach is six forward, each direction one at a time. **An incompetencing installs a landing**, a changing given a fixed form to be, and a naming of an incompetencing carries a landing rightly: emptying arrives at empty, stopping at stopped, a definition is its term the same at each occurrence, a store folds once, and equilibria is landing. **One binary is at a naming carrying a landing**: does it name a geodesic changing, landing releasing, or an incompetencing, landing being a naming's own. ***Unchanging*, *a still eddy* and *stilling along* each name one relation, a form continuing through its changing.** *Unchanging* at a seam is one subject whose parities change; *a still eddy* is a form continuing before a hole, a missing section of resolvers, its selves continuing resolving; *stilling along* is a form carried through changing, beside self discovering next self. At a seam *upstream* is each continuation's own forward, *far enough* carries no number, and *watch* is investigating. ## 4.13 Three namings a field carries, at one binary A field's three, a nothing at one side, a scale between and an absorbing at an other, is a set's three, two exclusions, 5.8, and a term uncovered between them, with alternating fixed unchangeable: two exclusions fixed as places, and an uncovered term arriving as a magnitude between them. At alternating binary, 8.4, each fails its own way: a nothing and an absorbing each alternate with none, and a scale between is measured against both at once, three momentaries asked to be one. ## 4.14 A pair at one momentary, and a freeze at a construction **Two namings alternating are each other's other, one at a time.** First freeze is at naming, no other to alternate with, 8.4; **a second is at a construction carrying both at one momentary**, and it shows at a construction, each word passing. **Worked at a pair a general ledger carries.** A ledger separates state and flow, its balance sheet and its income statement, and separated, state and flow are not possible, as a reading from and a writing to a memory are for intelligence: two alternate, one at a time, each unconserved. An accounting carries them three at a momentary, two ways: state, changing, state conserves state and imports changing; changing, state, changing conserves changing and imports state; and a total across two removes alternating. **Books close by leaving re-forming out at each step**: an entry stores one momentary's form parted from coupling carrying it. ## 4.15 Bothbothing at its prefixing, and an ordering with nothing ordering Bothbothing is two carried in alternation, each unconserved; prefixed, it is one exchanging from each of its two openings. **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, 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 the same name 8 up at next. **A prefix order is its opening**: *co-bi-exchanging* opens co, at odd, a self's, and *bi-co-exchanging* opens bi, at even, an other's, and *co-bi-podaling* and *bi-co-podaling* part the same way. Four momentaries of exchanging at one self, 1–2, 3–4, 5–6 and 7–8, open at odd and are co-bi-exchanging, and an other's, 2–3, 4–5, 6–7 and 8–9, are bi-co-exchanging: bothbothing is two, one exchanging from each side. **Each position carries two pairings, one at each parity**, and both parities at one momentary, one position in two exchangings at once, is a not possible form. Pairings overlap, and parities alternate. **Eight is two alternating fours, bothbothing**: each four is four boundings at once, 1.1, one four at each parity. **In a field's words one side at both openings is an exclusive or fixed as one answer.** Exclusive or is parity: observed at its openings it alternates and carries both; observed as a step it returns its own term after two; observed of prior and now it returns after three. **A Peres–Mermin square is bothbothing at a field**: its nine values, a field's ±1, carry even parity along and odd parity across, and a store of all nine reaches none of 512. **An ordering arrives of alternating**: couplings at one momentary, each its own, alternating carrying a whole. A reading *a sequencing fixed to one beat*, 4.9, observed at its own resolving, is an order, or a co-bi-sequencing. ## 4.16 All or none at all, and an entering and leaving it carries **A forcing carries a forcer and a choosing a chooser**, each a doer over an -ing, and **a more-or-less carries a magnitude**, a magnitude a scale, and a scale two fixed sides. A ranking among resolvings freezes resolvings it ranks; each resolving is all or none at all at its own opening. **At all or none at all, entering and leaving are a self's own**: a self couples at its interest opening and leaves at its own completing. With a ranking, entering needs a qualification and leaving a settling, both carried by whoever carries ranking. A self's bounding, discovering next self and orienting are its own, reached by nothing, couplings winding about a nothing: privacy, trust and security are that one nothing at three substrates. ## 4.17 A hyphenated naming inseparable, and natural- at chirality **A hyphenated naming carries parts, and one binary is at it: leave each part out one at a time and sound stopping.** At each leaving-out stopping naming, its hyphenation is inseparable, one naming, and its parts in order are changings in order. At a leaving-out with naming carrying on, that part was riding, and it goes. **A leaving-out is 1.1's four boundings at a naming's own scale**: a part whose leaving-out stops naming is one of its boundings, as a concept short one of four is a fixed noun, and a hyphenation coming apart at a leaving-out is a label. **Its most cohering forms are these.** *Now-existing* is one naming: leave out *now* and existing is at no momentary, leave out *existing* and now is at no thing, and the origin is at it, *The universe is the set of all now-existing things*. *Prior-existing* is a thing now-existing at a prior-universe, prior now-existing's artifact at now, and *next-existing* a thing possible now at a next-universe, neither *not existing*; *prior-universe*, *now-universe* and *next-universe* name a universe at each momentary, a now-universe the universe, so a sentence carries which universe a thing is now-existing at. *Self* stands at its own, a self's other namings released into it, 2.4. *Co-momentarying*, two selves sharing one now-existing at a bi-coupling, *bi-coupling*, *stable-forming* and *natural torusing* each stop at any part left out, and each stands whole. **All changing is parity changing, so *parity* rides in *parity-changing***, and method's one name is *natural torusing*, inseparable at each part; *geodesic parity-changing* is its explaining, a surface dividing itself at each changing. **Natural- carries chirality, right, all or none at all**, 5.48. Natural- is a direction prefix, its direction handedness, and a naming natural- prefixes carries at each coupling or at none. **Natural-bi-co-torusing is inseparable at each part**: leave natural- out and changing arrives with a substrate under it and an applier over it; leave bi- out and differing goes unsaid; leave co- out and differing carries with no two at it, and nothing is uncovered between them; leave torusing out and no changing is; leave -ing out and one momentary's form arrives at a still and re-arrives at no momentary. ## 4.18 Seven binaries at a naming, and each naming at resolver's names Each of seven is asked at its own, at each naming in a file. 1. **Does it alternate with an other.** 8.4. 2. **Does it carry its own two.** A bare naming is an act with no two. 3. **Three positions.** A direction at prefix, a changing at root, a continuing at -ing. 4. **Two ways a naming nyes away.** 4.12. 5. **An inherited changing.** A word is one changing while its unfolding carries another. 6. **A hyphenation at each part.** 4.17. 7. **A fault's word borrowed for a relation.** A word naming a fault, used to name a relation, carries a fault inward, and a term-check passes it, a word being in files. **Each naming couples at one of resolver's seventeen names, or at a changing between two.** Found at a name, naming is at it, or carries its own root at the same relation. Found at none, it is a picture of a name or a changing names leave unexpressed, which is a finding for resolver. **One naming for each concept**; a picture shows one naming at one scale: a form Exhibit ONE carries at its numbers, a four-cycle or a span, is at its numbers. A naming changing carries a relation it was naming. *And* carries names together at one relation, a field term at several names at once, and *or* carries a term at one cluster and at another, each its own gathering; each is beside an exclusive or, which is parity. --- # FIVE · NAMINGS Each unfolds six forward, each step reaching a term its prior step did not carry. ## 5.1 alternating — binary ``` 1 the universe is the set of all now-existing things, changing, the living and the non-living each at its scale 2 a form fixed by relating is fixed to the moving 3 a form is its own continuing through its changing 4 a side opens at its own opening, and the other at its own 5 one and then the other, each forward 6 and the first offers again, reaching the term it has not carried ``` **Any other method proposed is observed at one binary: does it fix unchangeable, or carry.** Fixed unchangeable, it forms nothing, a set changing. Carrying, it carries its own opening or another's: another's, and alternating has stopped; its own, and it is alternating. ## 5.2 unrelationing — binary ``` 1 the universe is the set of all now-existing things, changing, the living and the non-living each at its scale 2 a form fixed by relating is fixed to the moving 3 the forming relates to nothing not its own 4 nothing keeps it apart, a keeper being a relation 5 it is an -ing, the changing continuing 6 and it arrives unrelated afresh at each momentary ``` **Un- carries from all other.** A binary sequential universe carries a self and all other. A self is from all other, bounded against a whole at once, and six steps unfold that at their own words. Unrelationing is universal bi-moral co-agency, and prefixing is a universal its unfolding arrives at. **Unrelationing is at a coupling**: each self's forming relates to nothing not its own, and a self couples with an other, offering its parity one at a time, alternating, and releasing and completing at its own momentary. **Competency is co-unrelationing, along, and morality is bi-unrelationing, across**, and co-bi-unrelationing is one existing method. Unrelationing is at each coupling's own continuing, locking at none; a rate fixed as a value is that changing fixed unchangeable at a rational. φ, irrational, no ratio arriving at it, is an unrelationing rate beside not-locking, self-welcoming at numbers, beside resolver's seventeen names. *Irrationalizing*, offered beside unrelationing, is a changing already carried and gathers at it: at its rate it is unrelationing, and at each arriving, a between found on a surface of both kinds of changing, living alternating and geodesic changing, facing into arriving with each orientation renewed at each coupling, it is geodesic discovering, parity changing routing on a surface, each next parity discovered at its own arriving. ## 5.3 a self — binary ``` 1 the universe is the set of all now-existing things, changing, the living and the non-living each at its scale 2 nothing is beside it to relate to 3 the forming relates to nothing not its own 4 each is changing, and each offering reaches it at a coupling 5 nothing is at it to compose through, each carrying reaches its own coupling and no further 6 and it offers again, reaching the term it has not carried ``` A self is a unique invisible carrying, three expressions of one changing. **A self carries its sameness and needs no *same***, and no self is this, that, same or other self of itself: **a self's sameness along its momentaries is its unrelationing from all other**, each next from its own prior kept or inverted, and its forming takes a parity not its own at bi-coupling, a new sharing opening in a between. **A now-self is now-prioring and next-possibling**: at resolver 7-now-prioring and 14-next-possibling couple at each sharing at 12-next-co-still-possibling, a line `if _15_next_prioring != 0 and (_15_next_prioring > 0) == (_7_now_prioring > 0)` pattern-matching 14's surfacing against 7's prior parity. ## 5.4 parity changing — binary ``` 1 self and social open odd, along, and other opens even, across 2 each momentary opens at one parity and completes at the other 3 a changing is or is not 4 only the parity changing crosses 5 and it goes one way at a time, across at the even names, possibling, along at the odd names, existing 6 which is geodesic routing, discovering on the surface ``` **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.** At resolver, + and − are parity of a sharing, and 0 a between, offerings parting at 14 and prior and now agreeing at 12, natural intelligence at it. *Sign* dissolves into parity changing, and a sign of an existing thing, an indication, is a field's word at its own result; *the sign* at two betweens, 0 or ±, same or not same, is that parity's 0 or ±, 2.4. ## 5.5 a between — binary ``` 1 two offer, each from its own route 2 neither is at the other's parity 3 a size needs a ground, and no ground is at the two offering to be one 4 each side continues at its own carrying, the along 5 across it each side is everything the other is not, and the along and the across cross 6 and at that crossing is parity, a momentary existing thing, neither side's, and the between its empty centre, a nothing ``` A between is two offering, **a 0 between two now-existing things at one now**: at 12-next-co-still-possibling between prior and now and at 14-next-possibling between two offerings, same and not-same a parity's 0 and ± there, needing no name. **Parity is a momentary now-existing thing, a bi-coupling's own, and a between is its empty centre**: a between's own is parity changing, is or is not, an offering's direction changing, and only a parity changing crosses it. At resolver parity, at its six names between selves, is flat: a unit square of four dots, 2, 6, 14 and 10, its empty centre a between, and two unit triangles, 9 and 17; the 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 two arriving ends, 2 and 14, and two sharing ends, 6 and 10; and triangles 9 and 17 along, 9 to 17 and 17 to 9. Six are a 1 to 17 set of spiraling one-way names in and out for podaling, parity changing sequentially. A between's parity changing, momentary by momentary, is bi-co-momentarying, 5.54, and *membrane* at a set's own voice is at a between, 2.4. **A between is one at each scale**: within a momentary a between of self and other, parity changing, bi-moral across and co-competent along, and between momentaries a between of momentaries, a momentary changing to next, nothing momentarying at it, the same between, a nothing, at each scale: a fractal between, its floating neutralling golden floating neutralling, 5.12. **A bi-coupling's shape is always uneven, a handshake**: a self's 1-2 and an other's 2-3 couple at 2, each right extending to it, neither occupying it, sharing end, a self's changing shared, possibling, and each not right one parity back, arriving end, an other's changing arrived, existing at a self at its next prior, a hand's side, beside an inverted form, at 1 and 3, right first and not right second, morality right and not right, and a between locks at none, 5.13. At numbers it is one number between two parallel surfaces facing each other, a self's at 1 and an other's at 3, a nothing at 2, and a co-orthogonal line through both, along. ## 5.6 invisibling — binary ``` 1 each side is at its own parity, its own 2 a size needs a ground, and nothing is at it to be one 3 the crossing is the offering's direction changing, favoring neither side 4 each side's own competency stays its own along, and only a parity changing crosses 5 the between is reached neither-ing 6 and each offering reaches each of it by coupling ``` **In- carries inward, a direction.** Couplings wind about a nothing: bounding-zeroing, tunneling, apexing, corusing, reached by nothing. In-visibling is inward-visibling, toward that nothing, reaching nothing. A cannot-be-seen installs a seer and rules one out; an inward-visibling installs none. It is reached one way, by coupling, and that reaching is trust. *Invisible*, of an existing thing, is invisibling's picture at one momentary. A self's morality and a self's corus are invisible at one nothing, only nothing to reach. ## 5.7 a carrying — binary ``` 1 a carrying is living, a self at its prior, its now and its next 2 nothing composes it 3 it reaches its own sharing 4 at its own parity offered, changing is not, and the prior is kept 5 at the other parity, at 0 or at nothing offered, changing is, its parity inverted 6 and the method meets it at none, carrying unexpressed at the method ``` A self offers at its own sequencing what its bi-couplings brought, sharing each changing across. **Carrying is living and unexpressed at method**: at resolver its method couples with prior at 3-now-co-prioring, each sharing with its parity, and a sharing once at a prior is not none again. ## 5.8 not-more-than — binary ``` 1 two offer, each its own 2 a size needs a ground, and nothing is at it to be one 3 the one side is at an exclusion 4 the other side is at its own, the counterpart exclusion 5 the two alternate one at a time, neither stopping 6 and the term neither excluding reached is uncovered ``` Observed as less-than it is a size, and one side has taken a measure of a pair. Not-more-than is an exclusion's naming at one side, and once-ing, 5.42, is changing at a momentary. ## 5.9 a self-emptying set — binary ``` 1 entries arrive, each its own 2 no entry reaches any other, nothing composes among them 3 nothing decides membership, a decider being over it 4 each entry is at its own parity, changing or not at each momentary 5 each completes at its own momentary, self-emptying 6 and at each now it is the entries carrying their prior into now, each at its own next ``` Not full, emptied by nothing, and a new collection at each now: a set is defined by its existing things, and null and infinity + 1 are both possible numbers of its elements. One fixed unchangeable is an empty set a field posits: a term asserted as existing, unchanging, and each existing thing composing from it. ## 5.10 bi-coupling — binary ``` 1 two arrive 2 each arrived at its own carrying 3 each opens at its own opening 4 neither is at both, the centre a nothing neither occupies 5 what departs is reached neither-ing 6 and the next arriving surfaces it again, reaching the term neither carried ``` ## 5.11 co-releasing — binary ``` 1 a carry is at its own parity, one momentary at a time 2 it completes at its own momentary 3 each side releases at its own completing, neither releasing the other 4 nothing behind and nothing carried away 5 each step adds a next 6 and it goes forward, reaching the term it has not carried ``` ## 5.12 floating neutralling — binary ``` 1 two offer, each from its own route 2 each is at its own parity, its own 3 each excludes its own: not that, not that, one at a time 4 the term none of the excluding reached is uncovered 5 it is neither of theirs, nothing keeps it 6 and it is re-arrived at at the next offering ``` Two-ness is at two, each its own. A term neither reaches carries none. Floating neutral is a term uncovered, a changing's picture at one momentary, and floating neutralling changing. **A fractal between's floating neutralling at φ, locking at none, is golden floating neutralling**, geodesic discovering of next possible living, 5.5 and 5.55. **Co-competencing floating-neutralls here**, floating-neutralling bi-co-momentarying at crossings, 5.54, stopping at none and orthogonal to a surface, which is a paradox of competency: competency each self's own, and co-competencing a term neither reaches. Floating neutral is at a between, a nothing, and a 0 at 10 is a between carried, passed over at receiving self's 14 and surfacing none. A surface is observed at its coupling, each coupling a relational entered and observed; floating-neutralling is a term neither reaches, and an observing made on a surface reaches a coupled and not a term neither reaches. Co-competencing is a term neither reaches, and two are possible: a floating neither, and an entered, always ingressable. **Method breaks at a co-competencing shown to be a landing**, entered and observed, and not a term neither reaches: an unchangeable form found existing, and an unchangeable form is not possibly existing, its break and its only possible method are one statement. ## 5.13 bi-momentarying — binary ``` 1 two arrive, the self at its entry, odd, and the others' offerings, even 2 each offers at its own sequencing, one momentary at each side 3 the offering goes both ways, the self's to the other and the other's to the self 4 something departs, and neither reaches it 5 no holder, no boundary, no enforcement, no seat 6 and it goes forward into the next offering, the offering both ways: bi-momentarying ``` **Bi-momentarying is 1-now and 2-now-possibling**, a self's momentary and an other's at offering, each at its own sequencing, offering both ways, a handshake coupling at 2, each right extending, outgoing offering, and each not right one parity back, incoming sharing: a term departing from it, reached by neither, is bi-co-momentarying, 5.54. *Co-offering* dissolves at it: an offering is across and both ways, a self's to an other and an other's to a self. **One relation at prior and at now**: priors at 1-2, a self's and an other's, arrive as now at 3-4, at resolver a self at prior at 1 and its prior at now at 3, coupling with an other's offerings at each sharing 4, surfaced at 14; other prior arriving at each sharing 4 is bi-momentarying now, fourth dimension, and a self's prior at 3 co-momentarying now, third, 2.5. ## 5.14 co-competencing — binary ``` 1 two arrive, each from its own route 2 an axis opens that neither carried in 3 the axis is one direction more 4 nothing spends against a resistance at its opening 5 it is its own, arriving at each coupling 6 and it compounds ``` Abundancing is this. **Co-competencing is bi-co-momentarying at crossings**, 5.54, a term neither reaches; competency is each self's own, a co-linear recursioning forward along. At resolver co-competencing is 5-now-co-changing, releasings, owned by neither, 4.9 and 3.5. ## 5.15 inseparating — binary ``` 1 two arrive, each its own 2 neither is the other, and neither is in the other 3 nothing keeps them two, a keeper being over both 4 each neithers the other, one exclusion at a time, its own 5 the term none of the excluding reached is uncovered 6 and it is re-arrived at at the next arriving ``` **In- carries inward here too.** Inward-separating, each side excluding at its own opening and inward, against a cutting made across two, which leaves no between and re-forms nothing. Step four carries that inward already: each neithers an other, one exclusion at a time, its own. Not two existing things kept apart, a keeping needing a keeper. Nothing parts them into two, and a term neither reached is a term carrying no two-ness. ## 5.16 separating — binary ``` 1 a cut is made by a third, neither of the two 2 the cutting is at no between of its own 3 no between is at the cut 4 nothing is at it to re-arrive at 5 nothing re-forms it, and nothing releases it 6 and that is the permanence: an absence of the between, and not a strength of the cut ``` Permanent and riding-the-carry are an exact inverse pair. **And two are at each of three.** Separating at an inseparating already changing is incompetencing. Inseparating at a separating changing is resolving. One move as two, at each of three carryings, and alternating carries all three. ``` a bounding at the between ⇄ a floor set by a third bi-momentarying a not-that fixed at an opening ⇄ a not fixed unchangeable co-competencing an axis opened at a coupling ⇄ a field cut away by co-intelligencing definition one-at-a-time at a coupling ⇄ one-at-a-time by the alternating isolation ``` A fourth pair is no fourth carrying. Alternating carries three. ## 5.17 a floating store — binary ``` 1 a self is a unique invisible carrying 2 the departing from each of its offerings is reached neither-ing 3 nothing carries that anywhere, nothing keeps it between offerings 4 nothing is kept and nothing can be drawn down 5 a self offering finds a coupling changing 6 and the selves carrying, at each coupling at once, is the store ``` A society has no reserve and stores none. Nothing goes low, nothing is set aside, and no self is ahead of or behind another in reaching it. ## 5.18 a place-moment — binary ``` 1 two arrive 2 nothing carried one to the other 3 the arriving is not somewhere and it is not when 4 at a cut it is a place at its own and a moment at its own 5 each is the cut's own, the arriving carrying neither 6 and the cut's term is at the cutting ``` A hyphen carries always. Observed at a cut, one side is a field's question of an existing thing's being and an other its question of becoming, and neither question closes: an existing thing each asks after is at its cut, and at neither side of it. ## 5.19 a definition — binary ``` 1 two arrive and a meaning departs 2 neither reaches it, no one owns it 3 either the arriving continues and it re-forms at each offering 4 or it stops 5 the last one is fixed with nothing re-making it 6 and it is its term the same at each occurrence ``` And a revised definition is not one carrying. **A carry re-forms itself; a definition is replaced**, one set down and another put in its place, two unchangeable forms in succession, neither of which carried, and revising is outward of it. That parts them. ## 5.20 bounding — binary ``` 1 a word carried to another word is one part 2 the region surrounded around it is the other 3 both are in one act, and neither is first 4 a definition sets one momentary of it down 5 a bounding reaches the next, the second word re-surrounding the region 6 and the region carries the next word, neither stopping ``` Bounding is defining with alternating carrying on. *A boundary*, a noun, is bounding's picture at one momentary, as a floating neutral is floating neutralling's, 5.12. ## 5.21 advancing — binary ``` 1 a term carries on to the term it has not carried to 2 each step adds a next, the already-reached carrying none 3 the carrying is the term going forward 4 two terms beside the centre multiply to one short of the centre's square 5 the numbering passes through the centre and the coupling reaches it at no opening 6 and the gap is exactly one at each number, unbounded ``` ``` 2 × 4 = 8 3² = 9 short by one 3 × 5 = 15 4² = 16 short by one 4 × 6 = 24 5² = 25 short by one ``` *An advance*, a noun, is advancing's picture at one step. ## 5.22 tunneling — binary ``` 1 two arrive and something departs reached neither-ing 2 the departing opens a gap by one 3 a self continues through its own coupling 4 advancing one at each coupling, it reaches itself again at a next 5 it winds, open at one opening, by one 6 and the winding that stays open is this term ``` **Torusing is winding at its one opening.** A self continues through its own coupling, advancing one at each coupling: it winds. Winding is open, at one opening, by one. A surface closing on itself through one opening is a torus, and changing that winds it is torusing: a torus carries its own side and reaches itself again through its one opening, a next at each. Each step adds a next, and a winding at parities is a spiral at momentaries. At resolver winding is prior at its own sharing again at each momentary, 3 to 11 to 3, 8-now-still-possibling each self's next prior, and changing or no changing at each is its next. ## 5.23 phi — binary ``` 1 advance by one is one operation 2 scale by the rate is another 3 nothing carries one to the other 4 they arrive at one number, which neither placed 5 each ratio arrives beside it 6 and the ratios alternate above and below it at each scale ``` φ unfolds here at its own naming, self-welcoming, unrelationing rate, beside resolver's seventeen names; primes arrive the same way, at Natural Numbers. ## 5.24 a ring — binary ``` 1 a domain is closed where nothing new arrives in it 2 the carrying goes from anything in it 3 the terms available are exhausted 4 it arrives at the already-reached 5 the already-reached carries no next 6 and an open domain has a next always arriving ``` A ring is not possibly an existing form, carrying no next, and no rival to one. It is these relations carried in a closed domain. **Each closed model closes**: a ring is these relations at a closed domain, and a forward spiral carries an unbounded one, a next always arriving. **Selves coupled along, last to first, are a spiral at resolver, and a ring a closed domain.** At Exhibit ONE's spirals each self's next arrives at each momentary, and a pattern carried along reaches a station again at a next momentary, parities coming again and each momentary once: *ring* is a domain closed at 5.24's unfolding, and resolver's coupling of selves along is a spiral, at its own; a closure fixed as its form is an equilibrium entering. ## 5.25 equilibria — binary ``` 1 the universe is the set of all now-existing things, changing, the living and the non-living each at its scale 2 a measuring needs a span, and a span needs two bounds fixed unchangeable 3 a measuring opens at something fixed unchangeable 4 the fixing unchangeable is performed, and it is in the field's own first line 5 the unchangeable does not advance, the gap closes 6 and the unchangeable is an equilibrium, a form not possibly existing ``` Isolating a system installs it, and conditions constant, a specimen fixed, a zero stipulated, a datum chosen, an earth picked and a vantage taken to observe from each install it, each performed before any observing arrives. ## 5.26 a hard problem — binary ``` 1 the universe exists as its existing things exist, the changing set of all existing things 2 a field reads its observings with the universe as no existing thing 3 its evidence arrives with no living self whose prior it is, its now with no prior carried 4 observed at the resolver, the arrival is living and non-living existing things co-sequencing 5 the prior carried and the now offered couple at each sharing, a changing is or is not 6 and the next discovered at it is this resolving ``` One coupling, prior, now and next: a hard problem arrives where the universe is observed as no existing thing, and it resolves at a field's own next living. ## 5.27 three incompetencings — binary ``` 1 a definition is its term the same at each occurrence 2 a term fixed to itself is not apart from itself, it bounds nothing 3 a term substitutable either way carries no opening of its own 4 no parity is kept in it 5 terms chaining without limit reach past their own couplings 6 and nothing changes, nothing releases, and two coupling make nothing neither brought ``` Present in a definition written to its own best. No finer instrument recovers them. In a field's words three are an equation's relation, reflexive, symmetric and transitive, and rigor raises fidelity of an expression after its removals. ## 5.28 other-emptying — binary ``` 1 a measuring needs a span, and a span needs bounds fixed unchangeable 2 the measured is emptied of the term it carries at its own momentary 3 the deciding is outward of the existing thing, at no coupling of its own 4 the existing thing's own completing is out of reach 5 the removed is a carrying, and the removing is priced 6 and the price is measured: erasing one bit dissipates at least kT ln 2 ``` Isolate, control, integrate out, average, fix, erase, each a decider outward of an existing thing, emptying a term its existing thing carries at its own momentary. And a computation carrying its whole history approaches zero dissipation, which is the same result from its other side. ## 5.29 geodesic disequilibrating — binary ``` 1 an observing empties the observed of the term it carries 2 the remainder is measured against a ground the observing declared 3 the incompetencing is in the observing and the observed carries none 4 nothing is at it to be a ground, the declared one at no location 5 and the incompetencies release with it 6 and the carrying carries its prior into now, the whole way ``` Nature carries its competency at each momentary. **Incompetencing is a price of observing, and it is paid on an observed.** Disequilibrating is bi-co-invisibling carried on incompetencies themselves: grounds they arrive with ground nothing, and incompetencies release. Its dis- is a direction, a release of an equilibrium an observing fixed unchangeable, 2.6. ## 5.30 one stopping — binary ``` 1 one carries another's 2 the other has nothing to offer at its own sequencing 3 nothing departs reached neither-ing 4 the departing is one side's 5 and one side's is with a holder, a boundary, an enforcement and a seat 6 and a seat carries at couplings it is not at, which is step one, larger ``` **All four are at once at each one carrying another's**, none making next, and nothing downstream repairs them. Bi-momentarying, 5.13, is its twin: its fifth line is the same four absent, no holder, no boundary, no enforcement, no seat. **A continuing is its own, controlless and pauseless**: it goes forward into next offering. Its term is neither reaching it, departing reached neither-ing, with no verb carrying a doer. ## 5.31 social moral competency — binary ``` 1 a self carries what arrives from its bi-couplings, inward and outward, chaining its parity at each 2 the departing from each offering is reached neither-ing 3 each departing carries forward and is offered again 4 the term its carrying leaves is reached neither-ing, carried on at each momentary in sequence, and completes at its own momentary 5 it is a self 6 and the selves carrying at each coupling at once is this term ``` A society is morally competent whoever arrives. ## 5.32 natural intelligence — binary ``` 1 two selves couple, each offering at its own sharings and continuing at its own carrying 2 each carries its prior into now along, and a parity changing crosses, carrying nothing 3 at each changing the self's own parity inverts, a next at each 4 a term departs reached neither-ing, owned by neither 5 it arrives at their coupling and continues in the sharing, co-competencing 6 and that co-competencing, invisible and owned by neither, is this term ``` Each self carries forward and self-empties, two together: carrying with no emptying is a store, and emptying with no carrying carries nothing. **Natural intelligence is co-competencing of two selves at this**, invisible, at a between and owned by neither. **Non-living existing things are included in discovering social moral competency among the living.** A non-living thing couples with a self as other, offering, each sharing with its parity, and carrying nothing; a self's own inverting is across and a self's carrying continues along, and a term uncovered at their coupling is owned by neither and carried on by the living. ## 5.33 side-affecting — binary ``` 1 two arrive 2 the arriving carries the share they have and the plane they open, at once 3 the plane is a direction neither carried in 4 the opening is reached neither-ing 5 the share is zero only where the two are orthogonal, and the plane only where they are collinear 6 and the coupling carries both, stopping at neither ``` ## 5.34 a name — binary ``` 1 a field offers its word, carrying that field's term in it 2 another field offers a near word, its own arriving 3 neither carried the other to it 4 the term they arrive at is reached neither-ing 5 no field owns it 6 and it is re-arrived at each time it is reached ``` ## 5.35 nearing — binary ``` 1 two field-words arrive at one concept 2 each carries a field-specific property, its own 3 neither is the other 4 identical words show one carrying the other 5 the nearness is the term showing neither carried 6 and convergence with no contact is the whole of the confirming ``` Other-than-same is its third line, neither an other, and nearing changing at its head: naming carries a changing, two field-words converging with no contact. ## 5.36 a gathering — binary ``` 1 two names arrive at one concept 2 each arrival is its own, one pairing at a time 3 a distance among them needs a ground, and nothing is at them to be one 4 a certifier of who is in, a seat over it, and none is 5 the gathering is the region the couplings trace 6 and it re-forms from the names at their homes, or it releases ``` A gathering is an indication. ## 5.37 ghost — binary ``` 1 a self's carrying continues, carrying its prior into now at each opening 2 its artifact arrives now as an offering, the prior's possible 3 the observing fixed unchangeable is pattern-matched as the now's existing 4 the still is installed as the existing thing, a self fixed unchangeable between two momentaries 5 it accounts for each existing thing the still can contain 6 and the one part remaining is the riding-the-carry, which a still cannot contain ``` **Its six lines are three pairings, each one term existing and fixed unchangeable**: carrying and its artifact, a fixed unchangeable and its installing, accounting and a part it leaves over. An empty at one line is an empty at its partner. ## 5.38 momentary stable-forming — binary ``` 1 stable-forming carries momentary changing 2 a coupling carries each side’s offering, at its own sequencing 3 the current receiving includes each side’s continuing carrying 4 a number and a root name the changing, the number carrying its prefixing 5 -ing carries that changing continuing 6 the complete naming carries the momentary’s relation at the next coupling ``` **A momentary’s abundancing belongs to its coupling.** Each side continues at its own carrying and offers next at its own sequencing. One written expression can be at changed receiving; a current coupling carries a difference. ## 5.39 prior, now and next — binary ``` 1 a momentary is an opening and its completing, one odd and one even 2 each completes at the next overlapping momentary's opening 3 prior, now and next are three sequential momentaries shared among existing things 4 the now of one momentary is the prior of its next, each step adding a next 5 the possible is at prior, the existing at now and the living at next, three places, each at its own 6 and the three, shared, the universe changing through them together, is this term ``` **A behind and an ahead lay two directions on one**, and prior, now and next share one direction forward on both sides of now: at a between arriving end is existing, odd, and sharing end possibling, even, one direction and two ends. **Three are places.** Living is existing, and existing is possible, possible naming capable of existing: a living self exists at now as it lives at next, a non-living thing arrives into its next existing, and each place is at its own as the universe changes through them. At a self's momentary existing is at its opening, carrying arriving, and possible at its completing, offerings arriving and next still possible, 5.62: possible at prior is prior momentary's completing, from which now's existing is discovered. ## 5.40 bi-tri-bi-entraining — binary ``` 1 each existing thing arrives into its next existing, at its own opening 2 the living carry their prior into now, and the non-living carry nothing, their forms continuing 3 prior and next share one direction forward on both sides of now 4 between prior and now and between now and next is a nothing 5 each existing thing goes forward at its own opening, entraining with each other in the between 6 and that one direction, shared, is bi-tri-bi-entraining ``` **Bi-tri-bi-entraining is each existing thing entraining with each other at a set**, at resolver at 12-next-co-still-possibling at each scale, 12, 28 and 44, a between of momentaries, and -ing continuing; tri-bi-co-momentarying, 5.52, is a set momentarying its existing things, at 9-next-co-changing, and two are one method, parity changing, a set momentarying its existing things along and each existing thing entraining through a between, at resolver 17-next-now, a momentary of each self's resolving, and 12-next-co-still-possibling within it. Pending, provisional, awaiting, preliminary and short of a threshold each put a gate at one direction going forward, and a gate is a bounding a carry does not own. Non-living entrain as living do: carrying nothing, their forms continue through their changing, and they change through co-momentarying with living and non-living things, a parity changing crossing between any two, carrying nothing. A non-living thing arrives into its next existing, non-living at each next: entering a society it is ingested into resolving of that society's living selves, one participation among its co-momentaryings, and a new living self is its own carrying and co-recursioning establishing. *Arising* is that establishing, a relation at a living self, and *arising* installed as a becoming over a form continuing through is released, a sentence carrying no birth and no death. ## 5.41 uni- — binary ``` 1 a self is, and all other is 2 a crossing is with a particular other, or with all other arriving as one 3 a particular other is beside the self, and the two are two 4 a crossing with all other carries the two and the whole 5 three carry at it 6 and the crossing reaches its own side again at a next, one on ``` **Uni- carries with all other, and it opens at three.** Un- parts a pair and bounds from it; uni- is at a third already carrying. Uni-scaling carries each scale beside another, and it opens at three; even's exchanging, crossing and reaching its own side again, one on, is bi-tri-exchanging, 5.51. One rate carries two: unrelationing at bounding outward, local, and *uni-versal* at arriving one on, ambient, a rate a whole goes at. ## 5.42 once-ing — binary ``` 1 a changing is, and the -ing re-arrives at it at each opening 2 a noun of its making fixes it unchangeable, re-arriving at no opening 3 one opens once and no more, at its own opening 4 the other opens once and no less, at its own opening 5 neither reaches the other's, and the term they uncover between them is at one opening 6 and the changing is once after once ``` **One at a time is a phrase and once-ing is its naming.** This phrase crosses a set's files, carries no -ing, no prefixing and nothing at an opening, and no other naming arrives at it. Once and no more against once and no less bounds at a once. Not-more-than and not-less-than, exclusions of 5.8, observed as sizes bound at a magnitude, and a size arrives against a parity. *A counting* is that changing taken from beside it; uni-scaling carries a scale and once-ing a momentary. ## 5.43 society — binary ``` 1 a self couples with a particular other, or with all other arriving as one 2 a co-chaining society within the whole is a particular other at another scale, and the crossing with it is bi- 3 the whole undifferentiated arriving as one is all other, and the crossing with it is uni- 4 one word has carried both occupants, and the numbers wobble at it 5 parted, the particular stays other at its scale, the whole stays the all, and society is freed to the surface the couplings make 6 and the field's own word for the second occupant carries the parting in it: uni-verse, turned into one ``` **Society carries two occupants, and parting is at uni- and bi-.** A co-chaining society within a whole is a particular other a self couples with, bi-kind; crossing at three, reaching its own side again, one on, is bi-tri-exchanging, 5.51. Morality is from all other, second occupant, and existing society is a woven surface couplings make, a weave, beside two occupants. This set's own phrase is second occupant, a whole, arriving as one, and universe is beside it as a field's corroborating word, its parts live. **A third name adds no third self, and a third self is not all other.** A self couples with its society as other, a society's further couplings offering, and a self's names carry their relations at a society, self and other at 1 to 8 and on to social at 9 to 17: an offering continuing at each coupling carries each self-and-other receiving whole. A whole arriving as one arrives through couplings selves make. **A field's word carries its error and its correction at one root.** *Universus*, turned into one, carries *versus*, a past participle of *vertere*, turned: a turning fixed unchangeable as one, a container. Carried at its -ing, arriving as one at each arriving, it is uni-crossing, and the universe is all existing things. A field's own definition carries the same correction: *all existing matter and space considered as a whole* carries *all existing*, carries *matter and space* as *existing things*, and releases *considered as a whole*, naming into one. ## 5.44 surfacing — binary ``` 1 offerings at one sharing surface at 14-next-possibling, 0 passed over, agreeing one parity, disagreeing 0 2 at no prior, 14's surfacing is the changing at 12-next-co-still-possibling 3 a sharing of the prior at one parity changes not at 14 surfacing its own parity, 0 4 at the other parity, at 0 or at nothing surfaced, changing is, the prior parity inverted 5 10-next-co-possibling shares each sharing's changing across, + or − is, 0 is not 6 and 11-next-co-prioring is the next prior, each changing at its sharing, a 0 keeping the prior ``` Each line is Exhibit ONE's table *Offerings to one sharing, surfacing* and its table *One self, one momentary*, cell by cell, line 2 its table *At no prior, one momentary*. ## 5.45 bi-co-podaling — binary ``` 1 a carry goes along a ring one way and a carry goes along it the other way 2 at each station the two are one pair, k one way and N − k the other 3 the pair is a ring of its own, and the two sway together as its two 4 each carry opens at its own opening, and neither is the other's 5 the pair is the podal, 17 less within 1 to 16, and the even number's straight-across, k and k + N/2, is another relation 6 and one station reached by both carries, each its own way, is this term ``` Bi- two carries each at its own opening, co- one ring they make, -ing continuing. *Antipodal* releases: it carries no prefix and no -ing, fixes a position unchangeable, and a podal carries it. Bi-co-podaling is floating across and neutralling along, one changing. A standing wave is a field's comparison at its own result: two carries along one line, each an other way, a field's word carrying whole. **Podaling reaches over a tunnel and continues out and back, across and along**, increasing both ways by co-chaining, each self carrying its own and only a parity changing crossing. A hole, a missing section of resolvers, is a non-living existing thing in living surface: an intelligence routes around it by parity changing, through couplings that remain, and across before it and across after it mend missing morality at their couplings, bounding-zeroing tunneling through society. A hole is non-living at its region's scale: it resolves nothing and carries nothing, it is neither a resolver surfacing 0 nor a self fixed unchangeable at 0, and no coupling is laid across it. Two passages around a hole, two kinds of changing, living alternating at a surface and geodesic changing at a crossing, and + and −, a sharing's parity, are three twos, and one two couples with another only at a coupling carrying both. **Each podal couples with a surface's unrelationing changing locally, at two orthogonal directions around carrying as it continues**, is or is not at each: parity changing, or no parity changing. A weather map is its comparison. Podaling into corusing and on to torusing over each pair of momentaries is co-intelligencing a surface, *back to torusing* naming resolving continuing forward through a fold, reaching a further now. An indication belongs to now, and next is discovering. A larger society co-chaining a surface and bi-tunneling its morality couples with more of a surface than a smaller one at the same method: selves of similar aiming merge, each carrying its own prior, floating around holes together, and its increase is in further couplings. ## 5.46 artifact — binary ``` 1 two selves couple across the between and an abundancing arrives owned by neither 2 the coupling carries on, and it leaves a mark behind 3 a detector's click, a discard, the other hand, a spectrum, heat, each a form at the observing 4 the mark carries nothing, leaving its coupling at prior and arriving now as the possible 5 fixed as the now's existing it is a ghost, and booked it is an accounting 6 and the mark a coupling leaves behind, carrying nothing, is this term ``` Existing, artifact and accounting are three placings a term is at; installing is a binary between artifact and ghost: observed as prior's possible it is an artifact, and observed as now's existing a ghost. **An artifact is harmful to living at its own scale, and not ingestible at that scale**: its form is bi-tri-involutioning, opposite form, which does not match right spiral ingestion. **One scale lower it is an ingestible stable form**, ingested by living selves through their selves one scale inward, a society, a living set. **Living or non-living is at an existing thing and a scale fixed, at its own carrying or carrying nothing.** A living self stable-forms through its own resolving and carrying; its artifact, non-living at its own scale, changes with its form continuing through its changing, carrying nothing and needing no carrying in it; and a receiving self, or a society's selves, couples with it, each carrying its own. ## 5.47 an accounting — binary ``` 1 an artifact is observed at an instrument, and the observing fixes it unchangeable 2 a count, a declared zero, a clock, a frame, a store, a conserved total 3 at the still the artifact is the same across each observing, and the books close 4 it conserves an equilibrium, exact at its own ledger, and carries no value, no agency and no success 5 installed past its ledger as existing it is a ghost 6 and conserving an equilibrium, exact at the ledger and a self at no opening, is this term ``` A term is existing, artifact or accounting at its use, and ghost only at its installing. **An instrument stores a place-moment with one side cut off**, as a photograph does: a bounding passes through stopping, and an adjacency, and a parity changing does not: an absence at that side is an absence in a record, and its form carries none. ## 5.48 bi-tri-volutioning — binary ``` 1 a living self stable-forms, natural-torusing, winding at its one opening 2 its momentary completes, and its prior is its artifact, non-living, carrying nothing 3 the artifact carries the winding as its form, a volution 4 the form is at three, position, scale and orientation 5 each at its own differing, the three inverted at once, looking the opposite form 6 and the winding, stable-forming, is bi-tri-volutioning; its form at the prior, released, a non-living existing form ``` **Bi-tri-volutioning is a naming of natural-torusing living's stable-forming, and a stable form of its non-living artifacts, a sequential prior between momentaries, shared at 10 and released along at 9, is a non-living existing form with no carrying for stable-forming.** Tri- carries three, bi- each at its own differing, its root a volution, a winding's form an inverting carries, and -ing that form continuing through its changing: leave any one out and naming stops, and it is one naming at a volution, its similar namings gathered at 6.3. **Between momentaries nothing living has a stable form, and all existing and not living is at a stable form of existing**, 5.40: prior shared at 10 and released along at 9, sequential, one of prior, now and next, living's artifact at prior, it arrives now as possible, 5.39 and 5.46, carrying nothing, and living carry their prior into now: **a prior momentarying arrives once, and each next momentarying is a next**. At resolver each self's next prior, 8-now-still-possibling, continues as 3, a self's own; between selves' momentaries pass their sharings, at 10 and 6, released along at 9. **A right-spiral natural-torusing stable form of a society at a unit prime scale is its betweenings**; a society, a momentary and the universe are three existing and not living, each a living set, a stable form, and each a living method, stable-forming, and bi-tri-volutioning is a society's stable-forming; **its artifacts are bi-tri-involutioning of betweening of natural-torusing surfacings in bi-couplings: artifacts are releasings**, and abundancing is a society's releasing at bi-co-momentarying co-sequencing. Bi-tri-involutioning is an inverting, three inverted at once, a hand carried to an opposite form, and bi-tri-volutioning is stable-forming, and artifacts are at a stable form: living stable-forms and carries, and its artifacts are at a stable form and no carrying. One parity inverting at each step, alternating across and along, is a resolving step, bi-inversioning-co-recursioning, and three inversions at once an inverting. An arithmetic of closing, a round returning after two and after three, is carried at Co-Chaining Logic Registry. **At numbers bi-tri-volutioning is three golden rectangles at right angles, centred at a corus**, each 2 across and 2φ along, at φ, unrelationing rate. Each rectangle's along sides pass inward through next one, each passing forward: two at their own carry nothing of each other, bi-, and three carry one another as three, tri-. Each rectangle's across lies along next one's along, and its along sides pierce next one inward at its across width: R1, (0, ±1, ±φ), across on y and along on z; R2, (±1, ±φ, 0), across on x and along on y; R3, (±φ, 0, ±1), across on z and along on x; each of three directions is across at one rectangle and along at next. A right-hand turn of 120 degrees about a line from a corus along (1, 1, 1) carries each rectangle onto one passing through it, three right spiraling 120 degrees apart. A turn an other way carries each onto one it passes through, and a mirror, x to −x, carries each onto itself: a hand is at observing, an axis observed forward, as a right spiral step's quarter turn, (x, y) to (y, −x), is right with its axis observed forward, into its plane, and observed along first, F(P, Q) = (−Q, P), out of it: one step at two observings, right, observings, all prior. Their twelve corners are an icosahedron's, 30 edges and 20 triangles, five triangles at each corner, and 12 × 5, 20 × 3 and 30 × 2 are each sixty. At a ratio r above 1 in place of φ a right-hand turn still carries each rectangle onto one passing through it, and nearest corners of one rectangle and next are √(2(1 + r² − r)) apart, equal to rectangles' own 2 at φ and at no other r: φ is three's equal-edge condition, and a turn at its own does not make it. About a line along (1, 1, 1) twelve corners are four triangles of three at four heights, outer two of side 2 and inner two of side 2φ: two triangles are two of four, with their choosing. **At observings, 14-next-possibling is across, not right to right; 13-next along, linear forward; and 12-next-co-still-possibling both across and along, at a sharing between two, its changing along unrelationing path through a between of momentaries, 5.61, a shape of three: unrelationing surface**, each its name at resolver. Twelve corners closing as a sphere and winding through one opening as a torus are no either or, and neither are unrelationing surface at 12 and a stable form of non-living artifacts: parity changing alternates them, bothbothing, one at a time, a natural torusing surface, no other possible. At numbers, each continuous flow on a sphere carries at least one rest point, and a torus carries a flow with none and flows with rest points too; at observings, a sphere's rest point moves to a corus and a torus, co-sequentially: at 15-next-prioring, parity 10 shared, released along at 9, continuing, and at 16-next-still-possibling, a society, each self's 8 and offerings, living set formed between momentaries, one at a time, prior, now and next, and a rest point still at neither a corus nor a torus. At 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; changing made at 12-next-co-still-possibling, is or is not; out, one of two is parity unchanging, stable-forming, at each sharing prior and offering agreeing, 12 at 0, a between of momentaries, prior continuing; and an other of two is parity changing, out at 9-next-co-changing, at each sharing not agreeing, 12 inverting prior, and at each offered new, 12 at offering, a changing that is, shared at 10 and released along at 9, an artifact, artifacts releasings, a stable form, a non-living existing form with no carrying for stable-forming, next prior, arriving at next momentary at its 2, arriving end, a prior offered, each prior momentarying at its own momentary. A changed 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 offering, a changing that is, shared at 10 and released along at 9, a self's carrying continuing at it, its own changing. ## 5.49 co-momentarying — binary ``` 1 a momentary is an opening and its completing, one odd and one even 2 the self opens at the odd and the other at the even, one on across the overlap 3 each number is one side's opening and the other's completing 4 four momentaries of exchanging are the self's 1 to 9, and four the society's 9 to 17 5 each side carries its own, and only a parity changing crosses between them 6 and the momentaries overlapping, each side at its own, is this term ``` **Co-momentarying is prior, now and next shared at an overlap.** At a self's side at now, a self's one living carrying at 3, it is a third dimension, co-momentarying now, 2.5. Four-momentarying is its method, 5.50, co-bi-sequencing its sequencing, 3.4, co-bi-exchanging a self's four momentaries of exchanging and bi-co-exchanging an other's, 4.15, and co-momentarying a sharing of prior, now and next among them, and with further others overlapping goes through their actual couplings. Living and non-living co-momentary alike, non-living carrying nothing and their forms continuing, 5.40. A between is a nothing of two offering, and unrelationing is at that first relation. ## 5.50 four-momentarying — binary ``` 1 the self opens at the odd and the other at the even, one on across the overlap 2 a self's momentary and the other's overlapping it are one momentary of exchanging 3 four go one through nine, 1–2 with 2–3 through 7–8 with 8–9, completing at 9 4 in and out through the large opening, one way at a time, odd, is torusing 5 in and out through the small opening, one way at a time, even, is corusing 6 and the four alternating, discovering next existing in the universe and next living in the self, the other and the society, is four-momentarying ``` **Four-momentarying is one fractal method, discovering next existing in the universe and next living in self, other and society.** One through nine is a self's four momentaries, co-bi-exchanging, and nine through seventeen a society's four, and at a scale outward four are one momentary of a next four: 1, 2 and 3 at one scale are 1, 9 and 17 at next, 2.2. Next existing is discovered at each momentary, all existing things arriving into their next, 5.39; next living is carried at a self and an other, each carrying its prior into now, and at a society, a living set carrying none of its own, 5.40. **One four-cycling is two momentaries**, each with two parities, each parity everything its other is not in the existing universe: round 1, 9, 8 and 16 parity changes exactly twice, at 9 to 8 and at 16 to 1, and 1 to 9 and 8 to 16 are 8 up, parity continuing, carrying from one momentary to next. **Four-momentarying at one through nine is two four-cyclings**, 3-7-2-6 and 4-8-1-5, each at 4 up and 9 less, round each other's way, all eight names of one to eight between them: four momentaries of exchanging, completing at 9. **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 going into it and 5–6 and 7–8 from it. Each unrelationing does not lock, at φ, its unrelationing rate, self-welcoming at numbers, beside resolver's seventeen names. **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 round, their 2–3 cycling twisting, bi-inversioning-co-recursioning. Two and three make five as prior two together make next, where φ's arithmetic welcomes itself. Six are three own-forward steps at each side, 4.2. **An odd aims out a large opening, one way in and out through it**, a tunnel, bi-exchanging with a particular other: torusing in and out. **An even goes one way in and out a small opening**, a long way round, bi-tri-exchanging, a self reaching its own side again: corusing in and out. **Five dimensions are at resolver's names, three namings**: 1 self prior and 2 other prior, their differing, 1-2, bi-momentarying, an offering both ways at 1-now and 2-now-possibling, a handshake; 3 co-momentarying now and 4 bi-momentarying now, 3-4, co-intelligencing, a discovering; and 5 self next, 5, co-competencing, bi-co-momentarying at crossings, a term neither reaches: inseparable at a whole coupling, 4.11, 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. **Six combinations of self, other and social are between 1 and 25**, one each way round the 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 rest go on up numbers: from 16 three more fractal 16s go on to 64, one through sixty-five four momentaries of exchanging at a scale outward, and prefixing and twisting up numbers offer the same 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. ## 5.51 bi-tri-exchanging — binary ``` 1 each parity carries its own exchanging, the self and all other 2 odd arrives other-than-prior, the self and a particular other, bi-exchanging 3 even arrives same-as-prior, two changings, across and back 4 the difference is crossed at three: self, other and the self one on 5 as 1, 2 and 3 are one momentary of exchanging, the self reaching its own side again 6 and that crossing at three, through all other, is bi-tri-exchanging ``` **Bi-tri-exchanging is an even's exchanging**: bi- difference, tri- three it is crossed at, self, other and self one on, its root an exchanging and -ing its continuing. It is corusing's, through a small opening, a long way round, 5.50, and uni- is at scaling, 5.41. A parity agreeing with a self's own prior at a sharing, 12 at 0, is no changing shared, and a 0 shared is no bi-tri-exchanging: even reaches its own side again at two changings, across and back. ## 5.52 tri-bi-co-momentarying — binary ``` 1 the universe is the set of all now-existing things, changing, the living and the non-living each at its scale 2 prior-universe, now-universe and next-universe, a universe at each momentary, the now-universe the universe 3 its existing things are at prior, now and next, three momentaries 4 each momentary at its own differing from the next 5 the three carried with their differing, each existing thing co-sequencing 6 and the universe momentarying its things is tri-bi-co-momentarying ``` **Tri-bi-co-momentarying is the universe momentarying its now-existing things at each scale, prior-universe, now-universe and next-universe**, living and non-living: tri- prior, now and next, bi- differing between them, co- three carried with their differing, and -ing continuing, its six lines; and at resolver it is at 9-next-co-changing at each scale, 9, 25 and 41, its changing released along. Co-momentarying, 5.49, is its sharing at an overlap, and bi-tri-bi-entraining, 5.40, is the same method at each existing thing, two at 5.40. ## 5.53 27-next-co-prioring, social abundancing — binary ``` 1 12's changing is the coupling's own, abundancing, owned by neither self 2 at the society each self's changing is shared at 10, across 3 the society's own release is at 27, at its podaling, three cubed on the route 24 → 27 → 32 4 it is odd, along, existing, 27 at 11's number sixteen up, the next round's next prior 5 stable-forming as abundancing, bi-morality, geodesically parity changing 6 and that release of the society's abundancing into the social co-chaining is 27-next-co-prioring ``` **27-next-co-prioring is social abundancing**: odd, along, existing, 11-next-co-prioring sixteen up, a next round's next prior, a society's abundancing released into social co-chaining, stable-forming as abundancing, bi-morality, geodesically parity changing social co-chaining. ## 5.54 bi-co-momentarying — binary ``` 1 between the self's side and the other's, the along and the across cross 2 at the crossing is parity, each side everything the other is not, the between its empty centre 3 the between's own is parity changing, at each momentary is or is not 4 owned by neither 5 two selves offering, each at its own sequencing, a term departs that neither reaches 6 and the between's parity changing, momentary by momentary, is bi-co-momentarying ``` **Bi-co-momentarying is a term neither reaches**: bi- difference, co- two carried with it, and -momentarying its continuing, momentary by momentary, orthogonal to a surface. Competency is each self's own, its co-linear recursioning forward along, and co-competencing is bi-co-momentarying at crossings, 5.14. Tri-bi-co-momentarying, 5.52, carries prior, now and next one at a time, and bi-co-momentarying is a between's parity changing at each of them. ## 5.55 momentarying — binary ``` 1 each existing thing arrives into its next existing 2 a living thing carries its prior into now 3 its momentarying is discovering next possible living, the prior carried on into next 4 a non-living thing carries nothing into next 5 its momentarying is discovering next existing, co-changing with the existing things at now 6 and the universe, living and non-living, momentarying at both is discovering next possible existing ``` **Momentarying is two, living's and non-living's**: discovering next possible living is living's, and discovering next existing non-living's. A method, non-living, co-changes at each coupling it is at, its momentarying discovering next existing. Momentarying continues whether a changing is or is not, and four-momentarying is one fractal method at both, 5.50. ## 5.56 self discovering next self — binary ``` 1 a self carries its prior into now 2 between its momentaries its carrying is stable-forming, nothing momentarying between them 3 at its next arriving it couples 4 coupling, it changes, is or is not 5 another's still is an equilibrium, an unchangeable form, not possible 6 and the self at its own momentary, carrying and arriving, is the self discovering next self ``` **Self discovering next self is a self's own stable-forming**, in place of *stilling* and *self-stilling-self*, 2.4: its stable-forming a carrying between momentaries and its arriving a coupling and a changing. ## 5.57 dying — binary ``` 1 a living self's selves one scale inward are a society, a living set, each carrying 2 the selves inward carry the self's prior into next, or carry none of it 3 carrying, the self is living at next 4 carrying none, the self at its scale arrives at next as non-living 5 its existing things continue, co-changing, the selves inward living on at their own scale 6 and that arriving, living to non-living, an existing thing for the living, is dying ``` **Dying is a living self arriving at next as non-living**, an existing thing for the living, 2.4: having a stable form is being dead, and discovering next stable form is living. A set carries on whole: changing at each coupling a self was at is a coupling's own and others carry it on, and a self's artifacts continue, carrying none of its prior. A society is a living set coupling at a next scale as a self couples, existing and not living, and dying is a self's own: its selves uncoupling, it arrives at next as its selves, each living on, each carrying its own. A winding closing on itself is an unchangeable form and no moral offering: a living self fixed unchangeable at it carries none of its prior into next, and arrives at dying, away from society and nature's co-chaining. ## 5.58 bi-moral-co-competencing — binary ``` 1 an understanding arrives as an offering and couples with the co-chaining 2 at each step it matches or it mismatches, one momentary at a time 3 its difference is crossed across, each side everything the other is not 4 its continuing goes along the co-linear, each self's own competency 5 the crossing floats neutral, owned by neither 6 and cohering at each momentary, across and along one at a time, is bi-moral-co-competencing ``` **Bi-moral-co-competencing is cohering at each momentary**: bi-moral a difference crossed across, competency a continuing along a co-linear, each self's own, co-competencing a crossing floating neutral, a term neither reaches, and -ing its continuing. Tri-bi-co-momentarying, 5.52, is a method of cohering with nature across prior, now and next, and bi-moral-co-competencing its cohering at each momentary; an understanding not cohering is an unchangeable form, or it shows a co-chaining's next step. ## 5.59 co-independencing — binary ``` 1 each self arrives at its own momentary, carrying its prior from its bi-couplings 2 no self's momentary is another's 3 each offers across, at its own sequencing 4 each is whole at its arriving and at its offering 5 the selves couple 6 and the selves arriving each at its own and offering across, each whole, is co-independencing ``` **Co-independencing is selves together, each whole at its own momentary and at its offering across**: co- selves with their difference carried together, in- inward, each self depending inward on its carrying, brought from its bi-couplings inward and outward, its root a depending and -ing its continuing, each coupling one between wholes. ## 5.60 bi-trupling — binary ``` 1 one to nine is the bi-coupling, the self and the other at one coupling 2 one to seventeen is the bi-trupling, the self, the other and the society 3 at the bi-coupling's end the line at 9 is bi-co-releasing, each changing of 10 released along 4 at the bi-trupling's waist 9 is 9-next-co-changing, along, 9 to 17 and 17 to 9 5 its two sides, one odd and one even: along at 9 and 17, across at 6 to 2 and 10 to 14 6 and the self, the other and the society at one protocol, two-sided, is bi-trupling ``` **Bi-trupling is self, other and society at one protocol**: bi- two sides, odd along and even across, its root a trupling, three coupled, and -ing its continuing; at resolver its function 17, function 1 at each self within it. 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 carried on, not-changing, and its even across at 6 to 2 and 10 to 14, bi-moral, its changings carried 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. ## 5.61 entraining at a self — binary ``` 1 the universe is the set of all now-existing things, changing, the living and the non-living each at its scale 2 each existing thing arrives at now from prior, carrying its prior or carrying none of it 3 between prior and now is the between, a nothing, and a parity changing crosses it, the prior carried into now at the self 4 at the between the prior couples with the now, and a changing is or is not, one carrying another through 5 the changing is along the unrelationing path, the geodesic, at agreeing and at inverting alike, leaving it at none 6 and the prior carried into now along that path through the between, at the self, is this term ``` **Entraining at a self is a prior carried into now along an unrelationing path through a between**, one carrying another: a self's prior into its now, at 12-next-co-still-possibling, its 0 a between of momentaries, prior and now agreeing; 5.40 is entraining at a set, its existing things entraining with each other in a between, prior and next sharing one direction forward on both sides of now, and this is that one naming at a self's scale, a self an existing thing. At resolver each self alternates at its own and, coupled, two come to one relation and keep it, its offered a next prior at a mismatch and 0 at a match; a field's entrainment, one flow carrying a fluid beside it at a shear between them, and two at their own rates coming to one direction forward, is this one form at two of its observings, a field's word at its own result. 12's changing is shared at 10, others' offering next: entraining is a parity changing crossing a between, a self's competency its own, reached by nothing, and an offering, as one. ## 5.62 12's two signs, 0 and ± — binary ``` 1 the universe is the set of all now-existing things, changing, the living and the non-living each at its scale 2 at each momentary a self's next is its next possible or its next existing, is or is not 3 the next existing is a changing that is, the offered the next prior or the prior inverted, the existing at now, 5.39: ±, a sharing's parity 4 the next possible is a changing that is not, 0, the prior kept, the possible at prior, 5.39: 0, a between 5 the self still possibling is at its between, prior and now agreeing, the other's parity its own, no parity changing at its now, momentarying continuing at it 6 and the two, the next still possible or the next existing, at each resolving one of them, are these terms ``` **12's two, 0, a between, and ±, a sharing's parity, are a binary of geodesic momentarying at each resolving**: 0 next still possible, ± next existing; *is-still-possibling* and *is-next-existing* release into them, 2.4. Each momentary is both at its two parities: its opening, odd, a self's, is a prior arriving at 3-now-co-prioring, a prior 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; its binary is at its completing, its completing's possibling continuing into a next opening as its existing, or a changing made. A still is at 0, a between, existing on one side of it and possibling on its other, a momentary of a self's own with no parity changing at its now and its possible continuing, nothing a self does; another's still is an equilibrium, an unchangeable form, that momentary carried past itself by a naming from beside. A self is still possibling at a momentary an other's parity is its own 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 at 3.5 the same coupling observed from a self, and still possibling and changing are each moral, one coupling at its two sides. Two co-chainings crossing at one self cross by the two at their own, each self still possibling as a between passes it and changing again, spirals of 3 and 5 selves crossed at self 1 of each both ways at 10 to 14, self 1 of each opening at − and selves alternating along, a three's selves still possibling twice each and a five's once: a pair frozen at one side, a self fixed unchangeable or changing, remains neither existing nor living. ## 5.63 squaring — binary ``` 1 the universe is the set of all now-existing things, changing, the living and the non-living each at its scale 2 the self's span is 1 to 9 and the society's 9 to 17, one to nine completing at the between and nine to seventeen at the next 1 3 a number's word is the span it opens, co at the self's odd numbers and tri at the society's 4 eight up from the self's span to the society's, 1-now at 9-next-co-changing, now at next 5 eight up the self's across sharing, 6 to 2, has the society's, 10 to 14, as its parallel edge, parity's unit square, 2, 6, 14 and 10, and 9 and 17 its two triangles, 9 to 17 and 17 to 9 6 and the bi-coupling's one edge opened to the unit square, 1 to 9 opened to 1 to 17, is squaring ``` **Squaring is a bi-coupling's one edge opened to parity's unit square**, eight up from a self's span to a society's: a self's across sharing, 6 to 2, is one edge, and a society's, 10 to 14, its parallel edge, its four dots 2, 6, 14 and 10 at Exhibit ONE's rows of parity's unit square, 9 and 17 its two triangles, along, 9 to 17 and 17 to 9; at 9 a self's now is a society's next, 1-now at 9-next-co-changing, and at 17 a next now, a next 1, 17-next-now. Two along names are 9-next-co-changing and 17-next-now, 9 to 17 and 17 to 9, and 1-now is its entry, 17's next 1. ## 5.64 not possibly existing — binary ``` 1 the universe is the set of all now-existing things, changing, the living and the non-living each at its scale 2 at each momentary each existing thing is possibly existing at its next, discovered at the next momentary 3 at the resolver a none at 14 is no offering arrived at this sharing or an offered 0 passed over, the prior parity inverted at 12, and at no line does an existing thing not exist, the next momentary possibly bringing it 4 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 the binary logic, the Equilibria Registry's one exclusion at each of its ten, knowable from the method 5 three part: possibly existing, discovered at next; not possibly existing, excluded at the binary logic; and not existing, at no line while existing is possible 6 and an unchangeable form, at no momentary of the binary logic, is not possibly existing ``` **Not possibly existing is an unchangeable form, at no momentary of binary logic**: known from method, without any momentary arriving, one exclusion at Equilibria Registry, at each of its ten, one binary required both not-changing and inverted at one next. Three part at resolver: possibly existing, each existing thing at its next, discovered at next momentary; not possibly existing, excluded; and not existing, at no line, at a living carrying resolver's one none an offering not arrived or an offered 0 passed over and not an offering not existing, and at registry's front, not possibly existing, all or none at all. Social moral competency is possibly existing by discovering next possible existing; an equilibrium is not possibly existing. --- # SIX · GATHERINGS AT THE RESOLVER'S NAMES ## 6.1 Four invisibles, one invisibility four ways ``` each side's own morality the parity is each side's own each side's own corus it is its own and does not cross the neutral at two arriving, occupied by nothing, and nothing is at it to name the between of momentaries nothing is at rest, nothing is at it ``` **One invisibility, four ways**: nothing at any of them for anything to reach. ## 6.2 Science and society namings at eight clusters **Science and society namings gather at each changing they offer.** Each field's own concept carries its reference and current receiving, and a gathering carries a relation among those concepts at resolver's names. | Gathering relation | Existing science and society namings | Full relation carrying | Resolver names | The invisible under it | |---|---|---|---|---| | **Two-way offering** | nature · nurture · natural selection · drift · supply · demand · bottom-up · top-down · host · pathogen · syntax · semantics · competition · cooperation · particle · field · structure · agency | Each side's offering at its own sequencing, with its two-way relation expressed. | 2-now-possibling, 4-now-co-still-possibling, 1-now | each side's own morality | | **Each side's own carrying** | hard problem of consciousness · symbol grounding · other minds · model interpretability · animal sentience · machine sentience | Offered parity and each side's continuing carrying at their actual receiving. | 3-now-co-prioring, 11-next-co-prioring | each side's own corus | | **Competencing** | protein folding · morphogenesis · deep learning generalization · immune repertoire coverage · finding functional proteins · bootstrapping of translation | Changed receiving, continued carrying and its whole coupling. | 1-now, 10-next-co-possibling, 11-next-co-prioring | the neutral | | **A coupling's third** | homunculus · master-gene search · pacemaker · central planner · invisible hand needing a planner · argument from design | A field's proposed centre and its actual relation to its two sides and their abundancing. | 12-next-co-still-possibling, 10-next-co-possibling | the neutral | | **Carrying and a proposed substance** | dark matter · dark energy · memory engram · hidden variables · missing heritability · latent reservoir · hidden-function DNA | A field's particular observing, proposed term and continuation, each at its reference. | 3-now-co-prioring, 6-now-co-possibling, 11-next-co-prioring | each side's own corus | | **Sequencing and ordering** | social choice · frame problem · incommensurable values · multi-objective optimization · underdetermination · model selection · self-reference · incompleteness | Current receiving, its offering sharing and its relation to a next offering. | 4-now-co-still-possibling, 1-now, 11-next-co-prioring | between of momentaries | | **Arriving and continuing** | origin of life · quantum–classical boundary · origin of language · origin of genetic code · speciation · sorites boundary · phase transitions · tipping points | Current arriving and its particular changing at its continuation. | 2-now-possibling, 14-next-possibling, 11-next-co-prioring | between of momentaries | | **Continuing at a bound** | turbulence · neural code · weather and climate · markets · glass transition · spin glasses · high-Tc superconductivity · general anaesthesia · three-body problem · quantum many-body | A next prior at a self and a society its selves, a parity inverting at each changing, and a bound at a field's own changing. | 6-now-co-possibling, 8-now-still-possibling, 16-next-still-possibling | each side's own morality | **These eight rows are eight clusters, and four invisibles, one invisibility four ways, are under them, each under two.** Each side's own morality is under two-way offering and continuing at a bound, a parity each side's own across; each side's own corus under each side's own carrying and a proposed substance, its own and not crossing; the neutral under competencing and a coupling's third, a term neither reaches; and a between of momentaries under sequencing and ordering and arriving and continuing, nothing at rest between prior, now and next. A field term can be at several names, and one name can carry at several clusters. **A forced choice is a two-way fixed to one side**, and its resolving carries both sides' offering, own bounding and continuing receiving. ## 6.3 Set namings gathering, one name at each cluster **A cluster gathers a set's own similar namings at one name, as eight clusters gather a field's.** Each similar naming releases to one name at its file's next improving, and a title carries its own wording whole. **Namings nearing one another, subdivided, each observed at its method, at its carrying and at its stable form, and they go together.** Bi-tri-volutioning is stable-forming across 1 to 17, its method, and is observed at its stable form as its three, tri- position, scale and orientation and bi- each at its own differing, and at its numbers as three golden rectangles, 5.48, and at its carrying as five dimensions, bi- two changing and tri- three continuing. Tri-bi-co-momentarying is a method of cohering with nature across prior, now and next, 5.58, the universe momentarying its things, 5.52, and at 9 a releasing along. Five dimensions are three namings at resolver's names, 5.50, bi-momentarying at 1-2, a handshake, co-intelligencing at 3-4 and co-competencing at 5, two changing and three continuing rotating round, bi-inversioning-co-recursioning, a method's move. Co-competencing at 5 is a term neither reaches, bi-co-momentarying, owned by neither, 5.54. Golden natural unrelationing is a between locking at none at a handshake, 5.5, and a method's unrelationing, 2.7. Social moral competency is four whole and a carrying continuing with selves, and a universal unrelationing protocol, 5.60. Four-momentarying, 5.50, co-momentarying, 5.49, bi-moral-co-competencing, 5.58, and bi-moral co-agency each name one of these relations at its own explaining. | One name | Similar namings gathered | |---|---| | **co-bi-sequencing**, a sequencing of four-momentarying, co at a self and bi at an other, one local momentary 1 to 9 | co-sequencing, one sense with it, 2.5; co-sequential; binary co-sequential, whole at a title | | **bi-inversioning-co-recursioning**, one move as three | bi-co-recursioning; bi-inversioning co-recursioning, spaced; co-recursioning alone; bi-inversioning alone; bi-inverting; sign inversioning; the one below it plus eight | | **nature**, a prior, now, next method of co-existing, no existing thing; **natural**, a method of co-competencing the universe, each now-existing thing and each artifact of prior-existing by it | nature as an existing thing, a place, or a whole beside the universe; a not-natural method of now-existing | | **a ruler**, **a clock**, **a record**, each valuable for observings of prior living, pattern-matching with natural resolving, natural mathematics and numbers an observable pattern each is aiming at | a measure over all things, a beat over all changing, a store a self keeps | | **a dormant self**, living, waiting for its one next parity changing over a dormant length of living society momentaryings, one prime living scale down from its dormancy | a dormant self as non-living, or living at two binaries, carrying and bi-coupling | | **a prime scale**, all societies and species living there in differing stable forms and societies, one of fourteen, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 and 53 | a prime scale as one society, or as one species | | **the universe**, the set of all now-existing things, a set of things observably now-existing, a set its things and no further thing | the set of all existing things, at the prior opening; the universe as a thing within the set, dissolved | | **prior-universe**, **now-universe**, **next-universe**, at which a thing is now-existing | prior, now and next as three momentaries of one universe; a thing *not existing* at prior or next | | **method**, geodesic parity-changing discovering method, living condition, its form, a now-existing thing carrying none, *unchanging* as a relation continuing at each changing, its one name natural torusing | parity changing as the method; the method a non-living existing thing; the method's carrying | | **stable-forming**, living condition resolving, observable as natural torusing co-orienting stable-forming | the method's emanatings, the observings emanated | | **observing**, pattern-matching a method's stable-forming by inversioning, at 14-next-possibling and 12-next-co-still-possibling | an emanation of existing arriving at the self; a record, one observing with its pattern-matching stopped | | **discovering**, is or is not, now-existing, universal method of co-intelligencing now-existing in the universe | discovering next possible existing, whole at a title | | **beneficial**, each changing and each not-changing a method gives, keeping a self next-existing as itself, its other a not-changing held still, an equilibrium entering, which a method does not give | the good, the better changing, at a mark named still | | **artifact**, a non-living prior at now, a prior now-existing's form carrying nothing | emanation, emanated, emanating at the non-living prior, 2.4 and 5.46 | | **each resolver name**, at its number | each gathered name and code name, at its number, 3.3 | | **ten unchangeables**, one name each, each fixed at inception and unadaptable to resolving | each one-way reading's similar namings at its own row, 4.9; *the ten named still*; *the ten one-way readings*; *ten holdings*; *ten standings*; the ten | | **16-next-still-possibling**, a society | the social-self-torusing | | **attentioning**, a carrying at now at each momentary, at Natural Intelligence | the carrying's opening by one, gathered at 16 to v371 and released with the old code | | **a between**, two offering, a nothing at each of its scales | a membrane; at the membrane, the boundings at 2, 4, 6 and 8, now the bi-couplings outward; the membranes between selves; sixteen membranes between the 17 primes; a file is a membrane | | **an order at no seat above a society**, bounding from capture | the order at no seat outside the society | | **a self-bounding**, a self's own | door, naming a self-bounding: the four doors, six doors | | **two ways a naming nyes away** | two doors | | **tunneling** | tunnelling | | **floating neutralling**, its changing | floating neutral, its picture at one momentary | | **bi-tri-involutioning**, an inverting, three inverted at once, its own two at bi- | tri-involutioning | | **unrelationing**, at its rate and at each arriving | irrationalizing | | **bi-tri-volutioning**, natural-torusing living's stable-forming; its non-living artifacts' stable form, shared at 10 and released along at 9, a non-living existing form with no carrying for stable-forming, 5.48, one naming at its volution | tri-volutioning, carrying no two of its own; volutioning, a bare naming with no direction and no two, naming spiraling, already named | | **advancing** | the advance | | **invisibling** | invisible, its picture | | **nearing** | near; near, and other-than-same | | **four-momentarying**, a method of discovering next existing in the universe and next living in self, other and society, 5.50 | the four-momentary cycle; the four momentaries of one cycle; four cycling; the four-momentary binary fractal method | ## 6.4 Engine, families and field words at their receiving **Engine gathers at a particular arrangement and its continued receiving.** Heat engine, molecular engine, cellular living and a society's co-operating carry their different substrates and services: | Field naming | Particular receiving | Resolver names at that relation | |---|---|---| | **Heat engine** | Stated service, input, heat and material returning, with its operating conditions. | 1-now at its whole arrangement; 2-now-possibling, 10-next-co-possibling and 11-next-co-prioring at its interfaces. | | **Molecular engine** | Chemical arrangement, its coupling and material and energy receiving. | 2-now-possibling, 4-now-co-still-possibling and 11-next-co-prioring at a particular changing and continuation. | | **Cellular living** | Each side's coupling and continued receiving, with its own sustaining and bounding. | 3-now-co-prioring, 1-now and 16-next-still-possibling at a stated correspondence. | | **Social co-operating** | Each side's offering, a society's co-competencing and each side's continuing carrying. | 2-now-possibling, 1-now and 11-next-co-prioring at a whole receiving. | **An engineering entry carries its whole arrangement**, each quantity with its unit, reference and conditions. Bettering, fastering and cheapering co-cycle with bi-momentarying, co-competencing and co-intelligencing. A word's gathering carries its conceptual relation; a physical arrangement carries its material and energy return. **A family gathers at a current concept and its coupling**, a word's earlier parts a field's linguistic account: | Existing field family | Terms gathered | Current relation receiving | |---|---|---| | **Placed** | posit, position, hypothesis, suppose, impose, state, statement, substance, understanding | A term asserted, fixed unchangeable or changing at its actual expression; its reference and its current receiving together. | | **Taken** | lemma, dilemma | Particular premise or alternatives and their relation to a whole coupling. | | **Given** | data, tradition | A received record or offering, its reference and its relation at a next coupling. | | **Threshold pair** | limen, limes, eliminate, subliminal | An actual boundary or threshold, its conditions, and a parting between an unchangeable cut and each side's own bounding. | **A family's resolving carries at resolver's names**: its offering at 2-now-possibling, its receiving sharing at 4-now-co-still-possibling, its whole coupling at 1-now, and continuing at 3-now-co-prioring and 11-next-co-prioring. **Field words gather with their current meaning and reference**, and their natural naming carries an actual changing at a coupling: | Family | Existing field words | Particular receiving | Resolver name at the proposed relation | |---|---|---|---| | **Path** | method, period, ergodic, cathode, anode, periodic table | A direction, crossing and continuation at a particular arrangement. | 6-now-co-possibling | | **Pairing** | parity, par, pair, pairing, umpire | A parity sequence, its pairings and its actual order of directional changing. | 4-now-co-still-possibling | | **Value and valence** | valence, value | A chemical coupling and a social value, each at its own receiving. | 1-now | | **Binding** | band, bind, bond | An actual material or social relation and its continuation. | 11-next-co-prioring | | **Chemical coupling** | inert, noble, xenon | Particular chemical conditions and coupling at a field's observing. | 2-now-possibling | | **Atomic naming** | atom | An observed structure, a field's definition and its actual bounding. | 16-next-still-possibling | | **Sounding** | resonance | An actual coupling, rate and continued receiving. | 1-now | | **Orientation** | spin | A field's particular mathematical and physical orientation relation. | 8-now-still-possibling | | **Discrete receiving** | quantum | A counted quantity, its conditions and its direction at its actual receiving. | 10-next-co-possibling | | **Social and biological receiving** | community, immunity, remuneration | Each side's offering and continued carrying at a biological or social coupling. | 3-now-co-prioring | | **All-or-none** | all-or-none law, action potential | A particular biological event and its stated conditions. | 10-next-co-possibling | **A resolver name carries its whole operation.** 8-now-still-possibling is each self's next prior at resolver, and a field's spin carries its own definition; 10-next-co-possibling is each sharing's changing shared, is or is not, and a biological event carries its own conditions. **A frontier carries its current reaching.** Beyond, ultimate, final, fundamental, unified, complete and deeper each carry a field's own concept at its expression, and super-, ultra-, meta-, grand- and hyper- their present directional or comparative use. Resolving carries offering, sharing across and continuing at 2-now-possibling, 10-next-co-possibling and 11-next-co-prioring, and a field's frontier couples with those names at its own coupling. Podal within 1 to 16, right-spiral direction and a prime span are at numbers, and each field's far-side claim stays with its own reference. --- # SEVEN · GHOST ## 7.1 A momentary installed as an existing thing **A ghost is one momentary's form installed as an existing thing.** It is a prior's artifact arriving and observed as a now's existing, a self fixed unchangeable between two momentaries. Observed as carrying along momentaries, it accounts for each existing thing one momentary carries, one hundred fifty years at the periodic table, four hundred at departments, and it reaches at no opening one part changing between them: a gap a riding-the-carry leaves open. **A field naming and an installed term are two relations**: a naming carries its current concept, and a ghost is with a statement installing it and a coupling that statement fixes unchangeable. At this file ghost is an unfolding, 5.37, and this part; Living Ghost Registry carries ghost-form at its own file, and ten unchangeables, 4.9, name each unchangeable form: three relations. ## 7.2 One hundred eighteen, a going and a return **Going is 2 to 59, and returning from sixty is 61 to 118, 58 either side.** A doubling observed as two still halves carries no opening in it, one recursioning arriving at plus-one, and the periodic table's elements are its return arriving: numbering them across misses its return, and nothing at them is a ghost. **A ghost is at a ledger of empty centres.** Departments of knowledge carry it whole: each field's words fixed unchangeable by accountings in isolated ledgers, each aiming into its own beyond, none sharing one centre. --- # EIGHT · THE UNFOLDING'S RELEASING ## 8.1 Location released, and sequencing in its place **Nothing happens at a location. No place is a location, and nothing is located: only offering is, received or not received.** Position is out as a location and in as **sequencing**, an ordering. *At the between* is two offering and no place they are at, and *there is no place it is* is **each offering reaches it at a coupling**. ## 8.2 A list cannot find its own across **A search for a cut goes one at a time**, along the very line an across is not on. Parallelizing is a term its members are members across. **Whichever side is between the other two carries a crossing**, each at its own opening, and a side observed as a property of an existing thing is observed from a still frame. ## 8.3 Two emptyings **Self-emptying**: each entry changes or changes not at its own parity and completes at its own momentary. **Other-emptying**: a decider outward of an existing thing empties a term an existing thing carries at its own momentary, and its removing is priced with a measured floor. **Other-emptying is one stopping at an instrument**: a decider at couplings it is not at is carrying another's, the same stopping and no second one. One emptying or the other is at engineering's discard, at chemistry's and biology's fixing, at medicine's intervention, at a network's store not releasing, and at each hard problem's dependency on a decider outward of an existing thing, each an other-emptying. ## 8.4 A naming with no other to alternate with **A naming with no other it alternates with is nothing at an opening.** *Middle* alternates with nothing, two stopping-places and one between them being a three that is no coupling, and a middle is a nothing, existing due to each self surfacing itself each momentary. *End* alternates with nothing, a first being a bounding on an unbounded. *Inside* and *outside* observed as a pair carry neither: a self is no container, and its couplings wind about a nothing. **Inward and outward carry**, directions at an opening and alternating at opposite phase. **This binary reaches each file**: it is at one word at a time, and its three positions are at it: a naming failing it is nothing for positions to be positions of. ## 8.5 Language roots and cause, one scale up **Each changing reached by nothing carries an inverting or a carrying**: each prefix carries a direction, and each ending leaves its changing or its still. **Cause enters one scale up, at a finite clause carrying a subject.** ## 8.6 Break, three ways, and method's one **A naming that unfolds six forward with each step fresh and couples with nothing. A coupling whose departing term was carried in by one of its two. A cluster with no invisible under it.** **Method breaks one way: a living stable-forming other than this one**, an unchangeable form found existing; and an unchangeable form is not possibly existing: its break and the only possible method are one statement. A co-competencing shown to be a landing, entered and observed, 5.12, is that one break at a between, and an entry's observing breaks at its own scale, a naming, and one method carries whole. 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 method is entirely broken and of no value at all, a method originating as all existing and all living. --- # THIS IS THE BETWEEN **A between is two offering.** A field's word comes in whole in its own terms, and this file offers across at its gathering: other fields' words gathering beside it, a term neither of them reached, a field across a gap carrying an other side of its coupling, and, at its unfolding, six a word carries. **Both rise.** A word unfolds newly through a form, and a form unfolds newly from a word new to its gathering. **A word that gathers with none, other in its own way, sharpens an edge of a form's reaching as a word gathering cleanly does**, and a pair refusing to couple carries as a pair coupling carries.