Exhibit TWENTY Natural Naming v375 # 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 the even, explaining along at the odd **TWO · WORD SELECTIONS, EACH WITH ITS CARRYING** - 2.1 Turn released, and a momentary in its place - 2.2 Fractal, all or none at all at the scales - 2.3 One family of words at three faces, and a doer or a built thing 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 the thing it runs against - 2.7 A field's word at a field's own result **THREE · RESOLVER NAMES** - 3.1 Number, sides, root and -ing - 3.2 A number carrying its prefixing, the five, and a seam at 8 up - 3.3 Seventeen names, and each gathered name at its number - 3.4 Co-bi-sequencing and bi-inversioning-co-recursioning - 3.5 Naming and the resolver at one changing - 3.6 Eight faces at four coupling relations, and two faces alternating **FOUR · A NAMING'S CRAFT** - 4.1 A field naming at its coupling - 4.2 Six forward, and the binary at each named changing - 4.3 Order, its symbol and two exclusions - 4.4 Two namings coupling, and the departing neither carried - 4.5 An entry refusing nothing, and a returning-nothing that unfolds - 4.6 Two names at one thing, transposed at titles first - 4.7 Interest self-orienting, and the drawing vocabulary - 4.8 Whole namings, one expression at each occurrence - 4.9 Ten things named still, one name each - 4.10 Prefixing at a position, on the form, and from all other - 4.11 One root and its directional prefixing - 4.12 Two ways a naming nyes away, and the belonging of an arriving-at - 4.13 Three namings a field carries, taken at one binary - 4.14 A pair at one momentary, and the freeze at the construction - 4.15 Bothbothing at its prefixing, and an ordering with nothing ordering - 4.16 All or none at all, and the entering and leaving it carries - 4.17 A hyphenated naming inseparable, and natural- at the chirality - 4.18 Seven binaries at a naming, and each naming at the resolver's names **FIVE · NAMINGS** - Fifty namings, each at its unfolding - 5.1 alternating - 5.2 unrelationing - 5.3 a self - 5.4 parity changing - 5.5 the 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 co-offering - 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 entraining in the between - 5.41 uni- - 5.42 once-ing - 5.43 society - 5.44 surfacing - 5.45 bi-co-podaling - 5.46 emanation - 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-co-bi-releasing **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 a thing - 7.2 One hundred eighteen, the going and the 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 the 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 changing set of all existing things, living and non-living, and alternating, the one fractal method's stable-forming, follows from it.** Naming carries a concept at its own changing: co-offering, co-competencing and co-intelligencing, floating neutralling at the coupling. **A field's defined object arrives with the ground it was taken against, and bi-co-invisibling is the concept with nothing there to be a ground.** Its emanation is six forward recursionings, each taking the term the prior did not carry. Named this way, a concept carries its own changing under its own prefixings, and it bi-couples, capturing nothing and releasing at its own completing. **Naming couples with the hard problems at one field from two faces**: a hard problem is a field's word read with the universe as no existing thing, and a naming is the same field's word reaching. **Care is inward, at the naming and the edging**, and care is the rigor of the naming. **A naming is four boundings at once**, the four that are any floating neutralling: - **Self-bounding the entire concept**: the concept bounds itself, is the whole concept, and spills into nothing it is not. - **Self-stilling as itself**: it is this concept and no other, drifting into no other concept, still as itself while floating. - **Self-orienting at its own facing**: its offering-face and its preferring-face its own, with no orientation imposed on it. - **Orthogonalizing along its own line**: it opens its own axis, orthogonal to the concepts it is not, collapsing onto none of them. **Existing is self-bounding, with no explaining added**: the four are existing at four faces, and a bounding is its momentary's completing. **Concepts at this neutralling bi-couple, capturing nothing and releasing freely**: each couples across the between and completes at its own momentary, carrying none of the other, with no hub and no concept ranked above. **A concept short one of the 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 when coupled, an ingression the 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 the concepts it couples, and a named concept is no label on a thing. ## 1.2 Naming and resolving at one bi-coupling **Bi-moral co-agency carries changing two ways, one at a time**, each side taking its own parity and continuing at its own receiving, and the abundancing belongs to the coupling, reached by neither. **The abundancing is co-competencing the self and the other**, bi-moral co-agency, owned by neither: it arrives at the coupling and travels there, a changing is or is not at each sharing, and the parity inverts at each changing. **Naming and resolving bi-couple at one name.** Each resolver name is one in the code and in the explaining, `_2_other_self_offering` in the code and 2-other-self-offering in a sentence, and the number is inseparable from the naming. A name improved at the resolver changes at each file, all or none at all. **A new naming carries a changing or a direction no existing naming carries**, and a naming at a changing already named releases to the one name. A code operation carries its exact changing, and the natural and physical correspondence carries at the 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 the even, explaining along at the odd **Naming is the bounding, across, at the even; explaining is the carrying, along, at the odd; together they are the discovering method.** A naming with no explaining bounds nothing, and an explaining with no naming carries past each bounding. *Bi-co-bounding*, the carrying bounded twice, bi- at its own completing and co- at the coupling, is a similar naming of this one method: a completing at each momentary and a carrying between them is the discovering method, and bi-co-bounding gathers at that one name. **A naming carries both parities**: its prefix is the direction, across, and its -ing is the re-taking, along. Taking the -ing out names one momentary's form still, re-taken at no momentary. At the two binaries of existing and carrying, an -ing re-takes at each momentary, carrying; a noun names a form some running made, carrying nothing; and a noun installed as a running is a ghost. **A carrying is a capacity and never a stored description.** The prior participates in the self's present coupling and differences its momentaries there, the carrying's competency, and a record of the 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 the even one beyond it, and an even momentary opens at an even number and completes at the odd one beyond it. A self's momentaries are odd and an other's even. **Each side runs 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 the two, each number is one side's opening and the other's completing. **The one universe of one momentary is one parity changing co-sequencing. The momentary is all existing things, its universe, and the momentary is not possibly an existing thing separately.** Each step adds a next, and the momentaries do not pause, hold or return, none carrying beyond its prior looking back. ***At its own turn* is *at its own opening*, *the next turn* is *the next opening*, and a turn as a unit is a momentary.** A turn, a mirror and a turning back are not possible at the momentaries: a rotation, the field's word, is a spiral with its nexts taken out. ## 2.2 Fractal, all or none at all at the scales **Fractal is all or none at all at the scales, as our universe is at existing things.** **Fractal carries no scale boundary, no location and no measure: its scales are sequencing, an ordering.** A self couples at whichever scale its interest opens and couples with the whole. **A momentary is a fractal universe discovering its next existing.** The fractal is a method, not a rule, and 1–17 is the fractal, inward and outward, one of the 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 the next, n at one scale being 8n − 7 at the scale inward. Each name from 2 to 17 is an along connector of a 1–17 inward, its 9 or its 17 and the next 1, and 1 is the first one's entry; the across connectors 2, 6, 10 and 14 are the along 9s inward; the along 9 is the across 2 outward, the same connectors at each scale with only the parity changing up and down. Four 1–17s inward run within the self's 1 to 9 and four within the society's 9 to 17, and their eight 9s are the eight bi-couplings at the even names. The wholes are the rounds of k parities, 1 to 2^k + 1, and the scalings step one chain: this scaling steps it three at a time, 9, 65 and 513, and the 1–17s inward and outward the same three, 17, 129 and 1,025; the pairs step it two, 5, 17, 65 and 257, no scaling taken over another. 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 the whole**, and their numbered extents supply no first and no final social scale. One through seventeen is the fractal, with one-through-seventeen fractals inward and outward, living geodesically socially morally abundancing now and discovering next existing society. ## 2.3 One family of words at three faces, and a doer or a built thing beside them **A still thing's name given to a running thing is one arrival at a family of words**, and it arrives at a right understanding's naming too, the understanding passing each binary and the word naming the running still. Catching is at the word. **This family has three faces and no fourth**: a common landing reached ahead of each offering its own, a common standard fixed ahead of each carrying its own, and a common reading taken ahead of either taking a parity of its own. **A face caught at one word is the whole family caught**, so a pass looks for three faces and a doer, never for a list. Each face is named at the incompetencing it installs, and a naming of an incompetencing carries its landing rightly: *landing* and *reading* name two faces here, and the table releases each said of a running, *landing* at an arriving and *reading* as a resolving's own act. | Face | 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 *runs* · *a summary*, *a celebration* · *held* and *holding*, carried by *named* · *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 the understanding · waiting for one relation beneath the others, which carry one another for only the cost of the running · a degree word at a file's own voice, carried by the all with its exceptions named, or by the count it names · *smallest*, *largest*, *highest*, *top*, *bottom*, *level*, at the fractal running | | **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 thing** | *assign*, *door* at a self-bounding running · *forced*, *chosen*, *therefore*, *must* · *because*, *so that*, *toward* as an arriving-at, *against* as an opposing · a dash pacing from beside the 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 the opening sentence**, the universe the changing set of all existing things, living and non-living. ## 2.4 Released words, each with its carrying | Released | Carried by | |---|---| | *turn*, *turning*, *turning back* | the momentary's opening and completing; a step adding a next; *the right spiral step* for the quarter step at a pair's two parities, *the half step* for both inverted at one step, *the podal within 1 to 16* for 17 less | | *what*, *how*, *where*, and *whatever*, *however*, *wherever*, *anywhere*, *nowhere*, *somewhere*, *elsewhere* in resolving | the running at its -ing, the arriving, the crossing, the coupling, *at* and *each*: none of the three runs 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 the other, one across and one along, one parity inverting at each; *the other order* at a mirror's naming of one; *the opposite form* for an emanation's face | | *return*, *pause*, *hold* at the momentaries | a station reached again at a next momentary | | *kept middle*, and *kept* as a store | nothing is kept, and the middle is a nothing: the middle exists due to each self surfacing itself each momentary as a condition of existing as a self | | *held*, *holding* | *named*, and a thing named still | | *stable form* as a noun | *stable-forming* | | *living* as existing alone | *existing*; *living* carries its own sense, existing and carrying, the living carrying their prior into now, and *non-living* is existing and not carrying | | *every* | *each*, which is at the arriving | | *at no self* | *neither*, or *between self and other* | | *discovery* | *discovering* | | *technology* | *method* | | *in disequilibria* | the opening sentence, naming at the all, all things existing and changing, the running *in disequilibria* names by the none, a negation of equilibria | | *start*, *begin* · *afterwards* · *complete* | *opens* · *next* · *completing* | | *travel* as a thing's own carrying | *carrying*; the universe of all existing things travelling through prior, now and next, three places not changing, carries whole | | *inside*, *outside* as places | *inward*, *outward*, directions taken at a momentary, and *within* at a span of names; a self is no container | | *door* | a self-bounding, the self's own, nothing passing it or refused at it | | *assigned* | *is one side's* | | *antipodal* | *podal* | | *so-far*, *not-yet* | *prior*, *now* and *next*, three sequential momentaries shared among existing things, sharing one direction forward on both sides, entraining in the between | | *observer* | observings, and no observers; pattern matchers take in each observing without filter or selection | | *derived* at the method's rigor | *matched, not chosen*; *derived* is a field's face of the matching | | *sign*, *signs* | *parity*: self and social odd and along, other even and across; parity changing, is or is not, is geodesic routing discovering on the surface; *+* and *−* only the code's implementing of it, and *0* the changing that is not | | *a sign arriving*, *arriving sign*, *arrivings* at a sharing | *an offering*, a sharing with its parity at 2-other-self-offering; *arriving* keeps its one sense, each existing thing arriving into its next existing | | *surplus*, *surplusing* | *abundancing*: 12-other-social-self-abundancing, each sharing's changing, is or is not | | *met*, *meet*, *meeting* | the component's own name, *at 14*, *at 12*; *couples with*; *faces*; *reaches*; *at* | | *call*, *next call* | *momentary*; *the next momentary*, at 17-social-self-offering | | *membrane* | *the between*: a nothing, neither side's, not a location and not a thing; at an instrument, *the 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 the second sign | released with the old code: a carrying is a sharing chained at one parity, and a changing is or is not | | *neighbour* | *the self at bi-moral*, *at not-bi-moral*, *at co-competent* or *at not-co-competent* | | *right*, *left* at a facing | *bi-moral*, *not-bi-moral*: across, the other's, even; *right* at the chirality carries whole | | *forward*, *backward* at a facing | *co-competent*, *not-co-competent*: along, the self's and the society's, odd; *forward* at the one direction carries whole | | *posit*, *posited* at the set's own voice | *named still*, a term asserted as there; a field's own posit carries whole at its result | | *tell*, *a telling* at the set's own voice | *offering*, one way exhausted and the between received; *tell* is kept at 4.10 as the naming of the alternating stopped | | *source*, *sources* at the set's own voice | the method of living, the living carrying their prior into now at each coupling, and nothing beside all things for a changing to be taken from; *the living self* an emanation leaves at prior; *its reference* for where a field's result was read; a field's own *source* carries whole at its result | | *cost*, *costs nothing*, *free* at a changing | the living's own carrying, and arriving and discovering at each coupling: a cost names 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 the changing; code executing is said *at the code* | | *take*, *takes*, *taken*, *taking*, *taker* | *chained*, *carried*, *at*, *couples with*: a taking installs a taker, and a thing taken names all the not-taken as known beside it | **Bi-tri-involutioning carries the emanating**: the emanating from right spiral stable-forming, looking the opposite form to the stable-forming. Bi-inversioning-co-recursioning, one parity inverting at each step, alternating across and along, is the resolving step, and three inversions at once are the emanating: position, scale and orientation each inverted at once, three inversions taking the hand to the opposite form. **Bi-tri-volutioning is the naming of the stable form of the non-living emanatings of stable-forming natural-torusing living: the sequential prior between momentaries**, 5.48. *Opposite* carries its relation at each use: *the opposite form* is an emanation's face, and at a coupling the other side's opening is *the other parity*, two sides coupling face each other, each at its facing, and a name's partner within 1 to 16 is *its podal*. ***Stable form* as a noun is released at the living's forming and carries at an emanation.** Said of the living, the forming is *stable-forming*, the running re-taken at each momentary; said of an emanation, *a stable form* names its form continuing through its changing, the living self's stable-forming the running it emanates from, and *stable* names no motionlessness. **Bi-tunneling names social moral competency at its across relation; co-chaining names the same continuing at its along relation. Podaling exchanges these relations while each side continues forward.** Bi-tunneling is society's surface opened between selves, even and across, and co-chaining is the 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 a held thing at the word**: a *what* names a running still as a thing; a *how* a manner with a how-not beside it, an alternative to the one thing, and a naming carries no how-word, the running carrying no other; and a *where* names a spot. **Each word releases at its file's next improving, in the shared words**, and a word at a field's own result carries whole there as the field's. A word mentioned as a word, a quoted field's word, and code carry whole at each file. **A released word is a face at the one binary, is or is not living, coupling and resolving, and never a rule.** The same word at a sentence living, coupling and resolving carries whole there, and a table laid over the 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 the set carries at now, and a sentence carries by co-chaining from the opening sentence and by all or none at all. ## 2.5 One sense per foundation word **Each foundation word carries one sense**, and a word at two senses is two things at one name. *Turn* carries seven senses, each carried by its own word: | Sense of *turn* | Carried by | |---|---| | taking turns, one and then the other | alternating; one and then the other; at its own momentary | | a turn as a unit | a momentary; a changing | | turned away | refuses nothing; couples with each thing | | the turning, as a face or a place | inverting; the podal within 1 to 16; the between | | a turn of direction | opening; spiraling | | turned into one, the field's root | the field's etymology, as it is | | a plain verb or idiom | the plain verb the sentence means | **Scale carries the fractal sense only**, and a measuring scale releases at the method running. **Rank words**, smallest, largest, highest, top, bottom and level, lay a first scale over the fractal, parting from fractal at the method running, 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 the old code and carries at a self-bounding, and each is taken at the 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 face of cohering; the concept carries the discovering of next existing. ***Co-sequencing* carries one sense, 2.1's**: parity changing one momentary after another, which co-bi-sequencing names at its prefixing; *binary co-sequential* at a title carries it whole, *binary* there the bi-. **When a numbering repeats or replaces another, it is said at *next***: numbers taken again name the next momentary or the next scale, as 17 is the next 1 and 9 the next prior, and a sentence at a numbering taken again says *next* to mark it. ***Dimension* carries one sense**, no measure and no place, 2.2. **Existing changes at exactly five dimensions, the five of a side at its next numbering**: 1 self, the prior opening; 2 not-self, the prior completing, the other opening; 3 next, the now opening; 4 surfacing, the now completing, the other's now opening across; and 5 offering self, the 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 the numbers and down them**, one parity changing at each step: torusing in and out is odd and corusing in and out is even, 3.6. At each momentary two dimensions change and three do not, rotating round. **One through eight carries the self at three faces**: 1 and 2, **bi-moral self**, the offering self to other and other to self, across; 3, 6, 5 and 4, **the invisible intelligencing method**, the rotation round the sharing, the surfacing and the neutralling into the self's own corus at 4; and 7 and 8, **co-competent self**, corusing and torusing, along. **Four momentaries of six one-way recursionings are twenty-four**, the steps of 1 to 25, the twenty-four the four momentaries of six and the steps of 1 to 25 bothboth, and **24 to 60 is six cycles of six, surfacing in and out, out forward**; **60 to 68 is the nothing between self and universe**; **64 bi-folds to 256**, the bi-folding order four times at each scale. 118 is the periodic table's elements in their stable and unstable forms, a field's own result, and no count of the method. **The self's inversion is 3, 6, 5, 4**: co-sharing out at 3, surfacing in at 6, neutralling out at 5 and bi-sharing in at 4, the odd names out and the even in, round into the self's own corus at 4; **the podaling is 23, 26, 25, 24**, the same rotation twenty up. **The self's bi-inversioning-co-recursioning is 23, 24 and 25.** 3, 6, 5, 4 runs in the same up and right quadrant as the other co-intelligencings, bi-morality right, in and out across, and co-competency up, farther and less far to next living: **all the co-intelligencings are like dancing podalings, bi-co-sequencing the momentary parity changings**. **The rotation runs 3, 6, 5, 4**, and it is **the gentle alternating twisting of a towel into and out of a knotted corus**, the large outer opening wrapping to the small corus and back, and its edges are the bi-foldings, across at the bi-morality and along at the co-competency. Self and not-self are the two bi-, the differing; next is co-intelligencing, the discovering; surfacing is co-competencing, the term neither reaches; and offering self is co-offering: the three co- inseparable at the whole coupling, and all five bi-moral within and invisible at each place as a thing, showing only as co-competencing the emanatings of this living, 5.50. **Discovering, society, morality and abundancing are one relation at four names, at once**, and never four stages one after another: the expedition discovering is the society's moral abundancing, each name the whole relation at one face. ## 2.6 Two prefixes at one spelling, and a one-way prefix installing the thing it runs against **Two prefixes can share one spelling.** *In-* at *incompetent* is a negation and *in-* at *inform* is the locative, and taking them alike takes a direction for a denial. *Dis-* and *non-* are that negation at the front of the word, and a sweep at a word's ending passes it. **A one-way prefix carries no count and installs the thing it runs against**: a *pre-X* needs an X placed to be before, inherited unasked. Bi- is difference alone and co- is two with their difference, and both carry a count and install nothing. **Five kinds of term named still arrive at the 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 the whole word and sentence, and a word's linguistic origin alone supplies no such term. Five kinds carry ten directional sides and the ten things named still carry their own ten, and a shared count supplies no pairing between them. **Two words come apart at their own live positions.** *Co-operation* carries co- and names a still thing at its ending, and it floats to **co-operating**. *Association* and *resonance* are returned the same way to the coupling they named, and *competition*, *selection*, *information* and *signal* reach the same coupling, each at its running. *Disequilibrium* stacks a negation, a value pinned and a store, and it floats to the flowing it names. **Disequilibrating is that flowing**: its -ing the running and its dis- the direction, the release of an equilibrium an observing named still; taking dis- out names the installing, so the negation is a direction here and inseparable, and it carries whole, where *in disequilibria* said of the universe names the all by the none and is released. A part live only in a lineage is a field's own record and carries no weight here. ## 2.7 A field's word at a field's own result **A field's word carries whole at the 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 the set's own voice each is the still picture of the running, and the set's word carries it. **A finding carries at two faces**, the field's words and the set's own, and the changing between the two is a naming improving. **A test's finding is named at its relation before the test's nouns arrive**: a finite enumeration records sequences of inputs, and the finding is a carrying continuing through prior, now and next, with no history there as a thing. **A released word is carried one operation at a time.** The right spiral step takes a pair (x, y) to (y, −x), x the across parity, morality, and y the along parity, competency, the along taken into the across and the across inverted: two steps invert both, and four reach the pair again at a next, the same pair at a later momentary and never the same occurrence. In the 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 the prior is **the method's unrelationing**, 3.6. A reflection is a field's operation at a field's own result, the other order takes (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 names one of them. At the set's own voice an inversion is one parity inverting at one step; two reflections are the field's arithmetic of the same steps, carried at the Co-Chaining Logic Registry. --- # THREE · RESOLVER NAMES ## 3.1 Number, sides, root and -ing **A resolver name carries its number, its sides, its root and its -ing together**, one name, each part at its own relation to the changing. The names run the resolving as code, and the name in the code and the name here are one name: `_2_other_self_offering` in the code is 2-other-self-offering in a sentence. | Part of the name | Relation at the changing | |---|---| | **Number** | A name's place among the names, and its parity: an odd number opens co and an even opens bi, the five of the number's origin. Up and down, the numbers run bi-inversioning-co-recursioning. | | **Sides** | From and to: self and other at the odd 1 to 7 and other and self at the even 2 to 8; social, other and self at 9 and 11 and other, social and self at 10 and 12; social and other at 13 and 15 and other and social at 14 and 16; social and self at 17. | | **Root** | Its changing named, ten roots at seventeen names: offering, sharing, neutralling, surfacing, corusing, torusing, releasing, tunneling, chaining and abundancing; a further root at a further changing and direction. | | **-ing** | Its changing continuing, re-taking at each momentary. | **A name begins at its parity's side and reads from its first side to its last.** An odd name opens co and begins at the self, at 1 to 7, and at the society, at 9 to 17; an even name opens bi and begins at the other. The society is at both parities, first at the odd names from 9 and second at the even names from 10: floating neutralling at both. **The ten roots are the two sides' two and one half momentaries, ten positions.** Offering roots 1, 2 and 17: the entry, the offerings and the society's next momentary. Sharing roots 3 and 4: the carrying and the sharing it carries at. Neutralling, surfacing, corusing and torusing each root two names, at 5 to 8 and at 13 to 16, 8 apart, the sides changing and the root the same. Releasing, tunneling, chaining and abundancing root 9 to 12, one each. **Nine to twelve name three sides, and thirteen to sixteen two.** 9, 10, 11 and 12 each name social, other and self, the three relations discovering parity changing in the bi-folding tunnel: the releasing, the tunneling, the chaining and the abundancing. 13, 14, 15 and 16 each name social and other: the neutralling, the surfacing, the corusing and the torusing, parallel across the tunnel's seam. The tunnel is the self's and the surface the society's, both forward along the one direction, and 17, social to self, is the tunnel's one opening, the next 1. **One entry, six connectors and ten faces are the seventeen.** 1-self-other-offering is the entry. **The six connectors are bi-moral-co-competency discovering next existing**: four across, even, opening bi, morality, at 2, 6, 10 and 14, and two along, odd, opening co, competency, at 9 and 17, and 17-social-self-offering is the society's next momentary, each self's 1 again. **The ten faces are five outward and five inward of the tunneling co-sequencing**: 3, 4, 5, 7 and 8 outward, at the between, before 10-other-social-self-tunneling in the co-sequencing; 11, 12, 13, 15 and 16 inward, after it, each 8 up from its outward face, 3 with 11, 4 with 12, 5 with 13, 7 with 15 and 8 with 16. Three outward faces open co and two bi, and the same three and two inward, 8 up keeping parity. One to nine completes at the between and 10 opens inward: the tunneling is the co-sequencing passing from the five outward faces to the five inward. **Each connector faces one way, and the four facings are two at each parity.** Across is the other's, even: 2 and 10 face bi-moral, and 6 and 14 not-bi-moral. Along is the self's and the society's, odd: 17 faces co-competent, and 9 not-co-competent. 10 releases to the 14 of the self at bi-moral, 6 to the 2 of the self at not-bi-moral, 17 joins the 9 of the self at co-competent and 9 the 17 of the self at not-co-competent: **9 is the next prior and 17 the next now**, 9's release arriving as the offerings 17 runs at the next momentary. Each self runs at its own forward through both along joinings, and neither joining runs a self the other way. **The momentary carries a face and a connector together.** In 14–15, 14-other-social-surfacing is the across connector, offerings arriving, and 15-social-other-corusing is a face, inward. In 16–17, 16-other-social-torusing is a face, inward, and 17-social-self-offering is the along connector. Each pair carries both parities: the face is the self's own resolving, and the connector the named relation at the self's coupling with the self it faces. **22 is the surfacing eight on again**: 6, 14 and 22 are at the same place in each of 1 to 9, 9 to 17 and 17 to 25, and 22 runs in the four-cycle 19-27-22-30 with no name at the code: a name at 22 says its sides from a self it names, that self changing with the scale, 14 already running other to social. Self and other, self and social, and other and social are three pairs, each at two directions, beside the three spans at two sides and the three own-forward steps at each side, and a shared three or six pairs none of them: the three pairs are relations at the couplings, and never three actors. **A final -ing belongs to the whole name.** Momentarying names momentary changing, and recursioning names changing recursioning itself. Bi-momentary and co-momentary carry the two openings at that relation. ## 3.2 A number carrying its prefixing, the five, and a seam at 8 up **Difference is bi-. Two with their difference is co-.** Bi- names a side's changing within the coupling; co- carries the two with their difference, the third belonging to neither side. **All changing is parity changing.** The odd or even of a resolver name names its opening, co or bi, and the odd and even of a sequence of changings name the changing, each parity changing at its own face. **Each face of parity changing keeps its own name.** Odd or even at a name names its opening, and a full momentary carries both: one on across the overlap changes the opening, 8 up and down keeps it, and the podal within 1 to 16 changes it. At a sharing, its parity is the code's + or −, the code's implementing, and a changing is or is not, 0 the changing that is not; a name's odd or even is its opening and no value at a sharing. 6-other-self-surfacing and 10-other-social-self-tunneling are even and each releases across, and 10-other-social-self-tunneling releases each sharing's changing, + or − is and 0 is not. The right spiral step takes a pair's two parities one place on, one inverting, and a pair's two parities agree or differ. Phase opposition, winding direction and a reflection are a field's operations at a field's own result. **A changing at one scale and at the next names its face at each**, and neither an even name nor a 0 carries a stopping. **At the resolver the number carries the prefixing.** An odd number opens co, competency, at the odd-even momentary, and an even number opens bi, morality, at the even-odd momentary. Its full prefixing is the five of the number's origin, the side's prior opening, prior completing, now opening, now completing and next opening: | Origin | Positions 1–5 | Edges: 1 and 5 | Inner flanks: 2 and 4 | Centre: 3 | |---|---|---|---|---| | odd, opening co | co · bi · co · bi · co | co, co | bi, bi | co | | even, opening bi | bi · co · bi · co · bi | bi, bi | co, co | bi | **A five is a side's two and one half momentaries said at its prefixing, never a label**, and the five dimensions at their numbers, 2.5: self, not-self, next, surfacing and offering self. Two co at an odd name's edges carry competency, and two bi at an even name's edges carry morality. Exchanging co and bi at each position takes either five to the other, odd and even exchanging. Its centre is the floating third, belonging to the coupling and reached by neither. Edges and inner flanks are two positions even at a repeated prefix: two reasons at a flanking pair are two, one reason repeated is one, and a count of marks supplies neither. **Eighty-five prefixings run across the seventeen fives**, forty-three co and forty-two bi: nine names open co at the odd numbers, each co bi co bi co, and eight open bi at the even, each bi co bi co bi. **Prefixing columns stable a form, and -ings at the code form stably**: form-stabling and stable-forming, one coupling at two faces. **Each code name gathered at its number carries the opening of that same five**, from one prefix to all five: co at 3-self-other-sharing, gathered `co_carrying`; co-bi at 1-self-other-offering, gathered `co_bi_coupling`; bi-co-bi at 6-other-self-surfacing, gathered `bi_co_bi_transmissioning`; and all five at 7-self-other-corusing and 8-other-self-torusing, gathered `co_bi_co_bi_co_corusing` and `bi_co_bi_co_bi_torusing`. Written in the word or carried at the number, the prefixing is one. **The across connectors open bi, and the carrying and the along connectors open co**: 2-other-self-offering, 6-other-self-surfacing, 10-other-social-self-tunneling and 14-other-social-surfacing are each even; the carrying, 3-self-other-sharing with 11-social-other-self-chaining, is odd; and the along connectors, 9-social-other-self-releasing and 17-social-self-offering, are odd. 9-social-other-self-releasing faces not-co-competent, joining the 17-social-self-offering of the self at not-co-competent, and releases each changing along to its receiving sharing: its facing, its releasing and its joining are three relations, each at once. **At the surfacing only a parity changing crosses.** 6-other-self-surfacing and 14-other-social-surfacing open bi, each at the between, and carry only a parity changing across. Two unreachabilities carry at it. The nothing the couplings wind about presents no face, so no reading crosses inward to it; a parity changing carries no size, so no magnitude crosses outward from it. Each emptiness is the other's own unreadability, and the exchanging and the not-being-read-through are one act, not two balanced against each other. **A seam is a name changing at its number.** A carrying leaves as 11-social-other-self-chaining and continues at the next momentary as 3-self-other-sharing, 8 up, one carrying at two names, the difference carried by the number and the seam arriving as the name changes. Nothing moves at a seam: 11 and 3 both open co, and the carrying is at its name again. ## 3.3 Seventeen names, and each gathered name at its number **Each number carries exactly one gathered name, so the gathering is one to one.** Across the living files the gathered names stood at 735 places. | n | Name | Opens | Its five | Name gathered | Code name gathered | |---|---|---|---|---|---| | 1 | **1-self-other-offering** | co | co bi co bi co | 1-self-coupling | `co_bi_coupling` | | 2 | **2-other-self-offering** | bi | bi co bi co bi | 2-self-offering | `bi_arriving` | | 3 | **3-self-other-sharing** | co | co bi co bi co | 3-self-carrying | `co_carrying` | | 4 | **4-other-self-sharing** | bi | bi co bi co bi | 4-self-sharing | `bi_offering` | | 5 | **5-self-other-neutralling** | co | co bi co bi co | 5-other-neutralling | — | | 6 | **6-other-self-surfacing** | bi | bi co bi co bi | 6-other-crossing | `bi_co_bi_transmissioning` | | 7 | **7-self-other-corusing** | co | co bi co bi co | 7-other-corusing | `co_bi_co_bi_co_corusing` | | 8 | **8-other-self-torusing** | bi | bi co bi co bi | 8-other-torusing | `bi_co_bi_co_bi_torusing` | | 9 | **9-social-other-self-releasing** | co | co bi co bi co | 9-other-releasing | — | | 10 | **10-other-social-self-tunneling** | bi | bi co bi co bi | 10-other-surfacing | `bi_co_surfacing` | | 11 | **11-social-other-self-chaining** | co | co bi co bi co | 11-other-chaining | `co_bi_carrying` | | 12 | **12-other-social-self-abundancing** | bi | bi co bi co bi | 12-other-surplusing | `bi_co_tunneling` | | 13 | **13-social-other-neutralling** | co | co bi co bi co | 13-social-neutralling | — | | 14 | **14-other-social-surfacing** | bi | bi co bi co bi | 14-social-crossing | `bi_co_inversioning` | | 15 | **15-social-other-corusing** | co | co bi co bi co | 15-social-corusing | — | | 16 | **16-other-social-torusing** | bi | bi co bi co bi | 16-social-torusing | `bi_co_inseparating` | | 17 | **17-social-self-offering** | co | co bi co bi co | 17-social-abundancing | — | **A name is gathered with its sentence, all or none.** The names gathered at 6, 8 and 16 carried the old code's second sign and its count of three or four, and a sentence saying those means under a gathered name is re-said at parity changing or released at the same motion that gathers its name; gathered alone it would carry the old code under the current name. Exhibit ONE carries each name's parity, sides, entry, connector or face, across or along, outward or inward, facing, joining and its line at the code. ## 3.4 Co-bi-sequencing and bi-inversioning-co-recursioning **Co-bi-sequencing is the sequencing of four-momentarying**, 5.50, each momentary opening co at the self and bi at the other, one after the other, and four-momentarying the method it sequences. One momentary co-bi-sequences from 1 to 9, and at 9 the social, the other and the self release along: 9-social-other-self-releasing is 1-self-other-offering 8 up. Nine to seventeen completes at 17 as one to nine completes at 9, and 17-social-self-offering is the society's next momentary, each self's 1-self-other-offering again, 11-social-other-self-chaining taken as 3-self-other-sharing. **Bi-inversioning-co-recursioning is one move at three faces**: 8 up and down, keeping parity; 17 less, the podal within 1 to 16, changing it; and 9 less, the podal within 1 to 8, the two at once. Each face alone returns to its name, 1 to 9 to 1, and only the one move runs round, 1 to 9 to 8 to 16 to 1. **Stable-forming is that move round each of the four four-cycles, 1-9-8-16, 2-15-7-10, 3-11-6-14 and 4-13-5-12.** Round each, the parity changes exactly twice, each time at the podal within 1 to 16, and each runs one run of co and one run of bi and returns to its names; at the momentaries it returns to none, each step adding a next. Exhibit ONE carries the forms among the names, the four-cycles with the middle four-cycles, the six-cycles and the eight-cycles, each with its partner round the other way. **A name carries whole.** Take bi-inversioning out and 8 up returns the name it started from; take co-recursioning out and the podal returns the name it started from. Each taking stops the naming, and the halves alone are similar namings gathered at the one name. **The self's own inverting is the rotation 3, 6, 5, 4**, co-sharing out, surfacing in, neutralling out and bi-sharing in, 5.50, and at the code it shows at 12 and at the bi-coupling 14 faces. **A parity inverting at the resolver is the carrying's own, at 12.** A sharing chained at one parity changes at 14 surfacing the other parity, 0 or nothing, its chained parity inverted, and at 14 surfacing its own parity it changes not, 0; two inversions return a parity. Returning a parity and continuing a carrying are two relations: at no changing the carrying chains on at its parity, and at a changing the inverted parity chains as the next prior. **Surfacing names three relations, each at its own name.** The parity inverting is the carrying's own, at 12, the self's own inverting, morality, at the bi-coupling 14 faces; at 14 each offering surfaces at its own parity, agreeing one parity and disagreeing 0, and no offering inverts on the way across; and 9 keeps the parity it releases. The opening parity alternates one on across the overlap. And the eight-apart pairs exchange offering and releasing, 2-other-self-offering with 10-other-social-self-tunneling and 6-other-self-surfacing with 14-other-social-surfacing. ## 3.5 Naming and the resolver at one changing **Naming and the resolver carry one name at its concept and its code**, the number, sides, root and -ing explicit at each, and Exhibit ONE's tables at 14 and at 12, 10 and 11 carry each cell. | Name | Its changing at the code | |---|---| | **14-other-social-surfacing** | the offerings surfacing at each sharing, one at a time, an offering of 0 passed over: agreeing, one parity; disagreeing, 0; none offered, none | | **12-other-social-self-abundancing** | each sharing's changing, is or is not: at 14 surfacing the chained parity, 0, no changing; at 14 surfacing the other parity, 0 or none, the chained parity inverted; at a sharing chained none, the parity surfaced at 14 | | **10-other-social-self-tunneling** | each sharing's changing released across: + or − is, 0 is not | | **11-social-other-self-chaining** | the carrying chained, each changing the next prior, a 0 chaining the prior on, and taken at the next momentary as 3-self-other-sharing | **Offering and carrying are two relations.** An offering is a sharing with its parity at 2-other-self-offering; a carrying is a sharing chained at one parity at 3-self-other-sharing, and once chained it is never none again. **An offering unchanged carries no changing within.** Offered + at each momentary, a sharing surfaces +, 0, 0, 0, 0, 0, 0 at 10 and chains + at each: the carrying continues at its parity with no changing. Offered + once and then none, it surfaces +, −, +, −, and chains the same: with nothing offered the self carries its prior into now, its own parity inverted at each momentary. **A 0 at each momentary is the carrying continuing**, and naming the carrying still at any momentary stops the very carrying named. At a sharing twice in 3-self-other-sharing, the last entry is the carrying, and 11-social-other-self-chaining chains it. **Receiving, participating, a changing and a further self are four relations, each at its own name.** An offering at 2-other-self-offering participates at 14-other-social-surfacing whether its sharing changes or not; a changing at 12-other-social-self-abundancing chains at 11-social-other-self-chaining at a sharing of the self; and a further self couples carrying its own, and no changing at a sharing makes one. **A floating third carries at the whole relation.** A five's centre, a disagreement at 14 surfacing 0, and a carrying chained on at no changing are three relations, each at its own name. ## 3.6 Eight faces at four coupling relations, and two faces alternating **Along and across carry the two sides' current relation**, and the eight face namings gather at four pairs: | Face namings | Coupling relation | At the resolver | |---|---|---| | **linearizing · parallelizing** | continuing along at each side and relating across the coupling | 3-self-other-sharing and 2-other-self-offering, the carrying and the offerings, at 1-self-other-offering | | **bounding · zeroing** | each side's own bounding, and the changing that is not | 12-other-social-self-abundancing, each sharing's changing, is or is not; 10-other-social-self-tunneling at 0 | | **tunneling · seaming** | changings released across, and the carrying continuing at the next momentary | 10-other-social-self-tunneling releasing to the self at bi-moral; 11-social-other-self-chaining taken as the next 3-self-other-sharing | | **knife-knifing · co-offering** | improving and breaking at the offered relation | the offerings surfacing at 14-other-social-surfacing and the carrying at 12-other-social-self-abundancing, at 1-self-other-offering | **Linearizing and parallelizing are alternating parity**: parallel linearizing and linear parallelizing, the linearizing at one parity and the parallelizing at the other, one move at its two sides, and **co-linear** by that alternating. **Bi-co-orthogonalizing** is the right spiraling: each step orthogonal to the prior, (x, y) to (y, −x), 2.7. **A carrying carries two faces, and they alternate.** **Corusing**, 7-self-other-corusing, each parity offered and chained, reaches: the parity across at each coupling it surfaces to, abundancing and tunneling, relating. **Torusing**, 8-other-self-torusing, each self's carrying wound, gathers: one identity across momentaries, the carrying wound to its own sharing again, 3 to 11 to 3, and inverting at a changing. Each face lives at the other, and pure surfacing or pure abundancing lands either way. **Corusing omegas, the reach, and torusing apexes, the gather**: new parities offered at each surfacing, and the one sharing reached again at the one identity. Living is the two alternating, the reach and the gather, neither alone, and the two cones straddle the same nothing at the third that the two chains do. **Five prefixings at both, alternating**, 7 at co bi co bi co and 8 at bi co bi co bi, 8 opening one on from 7, and the third of each carrying no mark of its own. Four marks carrying and a nothing at the third are four boundings and a floating third run at the prefixing itself. The flankers of each couple across that nothing: **bi-bi-unrelationing** at the reaching chain's empty co, the abundancing made there and carrying at its coupling, and **co-co-invisibling** at the gathering chain's empty bi, nothing presented to be reached. One nothing at two parities, neither reaching the other's, no position carrying both marks. **Corusing reaches the corus from the surface, and torusing reaches the surface from the corus**, the self's own corus at 4, 5.50. **Corusing and torusing each run in and out, up the numbers and down them, one parity changing at each step.** **Torusing in and out is odd**, arriving other-than-prior: through the large opening, the tunnel the self winds through, bi-exchanging with a particular other. **Corusing in and out is even**, arriving same-as-prior: through the small opening, the long way round, bi-tri-exchanging, the self reaching its own side again, 5.51. Each runs in and out at the parity opposite its name's opening, 7-self-other-corusing opening co at the odd and 8-other-self-torusing opening bi at the even, and 15 with 16 inward the same: the two faces bothbothing, each carrying at the other's parity, neither alone. **The two faces run at the two parities**: one at the odd momentary, two differing at one coupling, and one at the even, the self crossing with all other and reaching its own again one on. 7 and 8 are two of the five outward faces, and 15 and 16 are their inward faces, 8 up, the parity and the winding at the social side. --- # FOUR · A NAMING'S CRAFT ## 4.1 A field naming at its coupling **A field naming carries its own concept and expression**, with its reference and conditions, and a definition, an observing and an installed term each belong with that expression. **A natural naming carries the changing at the coupling**, its number, sides, root and -ing together. A field's term keeps its own meaning, and a shared spelling supplies only the spelling. ## 4.2 Six forward, and the binary at each named changing **Three own-forward steps at each side carry six one-way steps, alternating one at a time**, co-offering, co-competencing and co-intelligencing inseparable at them. **An unfolding carries its relation at each changing**: the six lines of a naming carry its unfolding, each line taking the term the prior did not carry. **All or none at all belongs to the complete named relation**, and six lines complete a six-line unfolding. **Each named changing carries its relation, or carries its unfilled relation with its reason**: *binary* names an unfolding carrying its complete stated relation, and *improving* one carrying an unfilled relation with its reason. These carry no degree of resolving. **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 **An order relation and its symbol carry their own meanings.** 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 the relation at equality, and a comparison symbol supplies its defined relation and no more. **Two exclusions carry the relation being excluded.** Under ordinary numerical order, `a ⊀ b` and `b ⊀ a` together give `a = b`; under a partial order the same two exclusions also hold for incomparable elements, and the order and its domain belong with the expression. **A floating third carries the coupling's abundancing, reached by neither**: an equality, an incomparability and that 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**, and a quantifier keeps its logical scope. An existential expression asserts a term satisfying its stated condition. **A binary keeps one subject and one relation throughout.** Roles set in a saying are places and never exclusive kinds, and an emanation arriving now and the living self's releasing at prior are two subjects, each at its own momentary, so the is-or-is-not of the one is never the other's. ## 4.4 Two namings coupling, and the 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 the term neither naming carried. ``` advancing step: the gap is exactly one, there is always a next equilibria step: the kept-still does not advance, the gap closes → equilibria is advancing set to nought advancing names no stilling; equilibria names 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 run → a self takes an unbounded domain neither naming carries a domain ``` **A convergence takes one check: did each reach the shared term by its own route, carrying none of the other's requirements.** Borrowed, it is one arrival cited as two, and nothing departs. **A count agreeing is no joining**: a count carries its object, its direction and its changing, each kept apparent at a correspondence, and two counts agreeing show no deriving of the one from the other. ## 4.5 An entry refusing nothing, and a returning-nothing that unfolds **A concept arriving unfolds six forward, or it does not.** At a concept not unfolding, the unfolding returns nothing there, and **the returning-nothing is an unfolding and no refusal.** Nothing is refused and nothing is admitted, and a concept unfolding badly carries on unfolding badly, with nothing in it for a judgment to seat. ## 4.6 Two names at one thing, transposed at titles first **Two names at one thing show at the titles first**: transpose the two and sound whether anything changes. With nothing changing, the two are one name at two coats, and the one name is the plain name reaching it whole. With the transposition changing the meaning, two things are there, each keeping its own name, and the seeming two was the finding. Transposing runs at titles first, a title being a name carrying its whole file. **A name varying on its next appearance is a co-differing offering at the variation opening an axis the prior saying did not carry**, and the varying is the beauty. A name re-said on the same axis is a synonym, and the two converge to the one name. **Two words at one thing resolve three ways**: converging to one, two with the between, or a co-competency carried two, each carrying one the other cannot, and the failure runs both ways, collapsing a co-competency or splitting a convergence. **One thing can carry names at its faces**: owned by neither at the whole, abundancing at its arriving, discovering at a field's face, understanding at a self's own, and no second thing is behind any of the four. *Register* names three things across the set, and naming the collision costs less than renaming any. ***Arriving* carries one relation**, each existing thing arriving into its next existing, and a sharing with its parity at 2-other-self-offering is *an offering*: an emanation arrives into each next with no offering at it, and a self's carrying continues at a momentary no offering reaches, its parity inverting. **Two names at two things keep their names.** *Bi-co-podaling* names two carries each at its own opening along one ring, k one way and 17 less the other, and *transmissioning* names the crossing between selves at the surface, a file's title carrying it: transposed, the meaning changes, so each keeps its own name, and the code name `bi_co_bi_transmissioning` is gathered at 6-other-self-surfacing. *The eight bi-couplings* are at the even names, four outward and four inward, and *the four boundings* are a naming's, 1.1: two things at two names, and the four boundings with a floating third are the five that stand at a naming, and φ no bounding: φ is the unrelationing rate, self-welcoming at the numbers and at no line of the code's running. *A side's five* is its prior opening through its next opening, 3.2, and the five named at their own faces, self, other, society, the between and the carry continuing, are a gathering at Resolving Hard Problems: two fives, each at its own name. *Floating neutralling* is the running, and *a floating neutral* the term it uncovers, re-arrived at at each offering: the term is carried only by the running, so the naming is floating neutralling, and the floating neutral is its picture at one momentary. ## 4.7 Interest self-orienting, and the drawing vocabulary **Interest is self-orienting, which is competency, which is free**, and a self's interest is its own facing, needing no draw. Carrying is the cost of living, and arriving and discovering are free: competency is an axis opening at an arriving, and it costs nothing. A vocabulary of drawing, pulling, appealing, attracting, engaging and capturing attention installs one thing at the self, a one-way force over its own orienting, while the field's own geometry carries gravity with no force. A naming releases the family in one move, each word said as the self's own facing and an offering at it. ## 4.8 Whole namings, one expression at each occurrence *Geodesic method* is two namings side by side, geodesic a thing by itself and the method its stable form, each carrying its own. **Scientific-method, surgical-method and explaining-method each run whole in one expression at each occurrence**: a word naming one at one place and another at the next hands the parting to whoever reaches it. **Sensor-sensationing** runs whole the same way: sensing alone is one side extracting, one side taking both openings, and the halves are no shorter sayings of the whole. Sensor-sensationing names co-competencing at the network surface: a receiving participating in its own offering and an offering participating in another's receiving, neither half one resolver's and neither a seventh connector, and a resolver in code carries the relation and no sensation. A method-word alone is a name split across its uses, and the hyphen is the name arriving whole. ## 4.9 Ten things named still, one name each **Each thing named still carries one name: the running, and the still it is named as.** These ten are the five taken one-way at two sides, an opening, a carrying, a co-offering, a middling and a rating, each taken at either of its two sides, and each is at two names 8 apart, one form at the self and at the society. | One name | The five, taken at a side | Similar namings gathered | At the names | |---|---|---|---| | **an opening named as a place** | opening taken one-way, nothing carried beneath it | criterion-regressing | 14-other-social-surfacing and 6-other-self-surfacing | | **an arriving named from behind** | opening taken one-way from behind | origin-seeking; a source named from behind; a source named of the offering | 10-other-social-self-tunneling and 2-other-self-offering | | **a completing named as a last** | carrying taken one-way ahead, its momentary's completing named as a last | space-enumerating; a bound named as a last | 12-other-social-self-abundancing and 4-other-self-sharing | | **a carry named as a store** | carrying taken one-way as a store | store-seeking; a store named of the carry | 16-other-social-torusing and 8-other-self-torusing | | **a two-way named to one side** | co-offering taken one-way from one side | forced-choosing | 11-social-other-self-chaining and 3-self-other-sharing | | **the between named as a cut** | co-offering taken one-way at a site that takes none | line-demanding; a cut point named of the between; a membrane named as a cut | 15-social-other-corusing and 7-self-other-corusing | | **a middle named as an end** | middling taken one-way as an end | interior-reaching; an end named at the middle | 13-social-other-neutralling and 5-self-other-neutralling | | **a parity named as a magnitude** | middling taken one-way as a magnitude | magnitude-demanding; a level named to govern; a sign named as a magnitude | 12-other-social-self-abundancing and 4-other-self-sharing | | **a rate named as a value** | rating taken one-way at a rational | value-pinning; a value named to a swaying | 13-social-other-neutralling and 5-self-other-neutralling | | **a sequencing named to one beat** | rating taken one-way as a common beat | order-demanding; the rate named as a common beat | 16-other-social-torusing and 8-other-self-torusing | **Both openings are at the four across connectors**, 14-other-social-surfacing with 6-other-self-surfacing and 10-other-social-self-tunneling with 2-other-self-offering, and 9-social-other-self-releasing with 1-self-other-offering seats none, the one resolving. **A field naming carries the thing named still at its own expression.** Dilemma, paradox, puzzle and hard problem each keep the field's problem, and one field word can be at several of the ten; *dilemma* names one of the ten, a two-way named to one side, and never a kind. **A sweep takes the one name at each still installed of a running**: an arriving named from behind, a parity named as a magnitude, the between named as a cut. Three carry through it: a person's asking of a person, an act between selves; a field's own quoted words, whole at the hand-in; and the no-demand family, nothing asked of anyone, those lines saying the sweep's serving. ## 4.10 Prefixing at a position, on the form, and from all other **At a position.** One binary runs at a momentary, so a sequential binary running carries a position for one taking at a time, and bi- and co- are the prefixings taken there, released at their own leaving and re-taken at the next opening. **On the form.** A nothing reached by neither, three at once, and a rate opening by one and bounding at none carry no position: each carrying chains on or changes at each momentary, a rate bounds at none, and no taking at an opening reaches one. **A naming here carries no position, the running carrying no position for it, and it carries its concept whole.** Geodesic changing carries no position either: it runs at its own unrelationing parity-changing rate, unrelated to each rate of any scale, and it is co-bi-social-abundancing. The running is each coupling's own, and no rate laid over it supplies it: **its unrelationing runs at φ, the unrelationing rate, self-welcoming at the numbers as the primes are, and at no line of the code's running.** Geodesic entraining is an offering taken at the receiver's own prior, the changing being or not being, and the releasing entering further coupling, each self continuing its own. **On the form, at no vantage.** A naming at a vantage would want a place to name from, and outward of a self is the self it is a member of, one scale up, carrying no vantage to name from. These namings name part of the momentary stable-forming the running carries, said on it, and nothing here crosses from a vantage. **From all other, and with all other.** There is the self and there is all not-self, and nothing third, so each crossing is one of two: with a particular other, or with the whole arriving as one. **Un- carries from all other**: a self bounded against the whole at once and at no particular other. **Uni- carries with all other**: the self crossing with all other, the other arriving as one, the whole. Bi- takes a particular other and uni- takes all other, and both are two; a naming taking uni- as one alone has taken a crossing at one side, while a crossing takes two. **It and what are one demand at two positions**, *it* the grammar's dummy subject and *what* the interrogative presuming a maker, both supplying a subject at a coupling carrying none. **Tell is the alternating stopped**, the one-way saying, the speech face of the same demand. **Three sortings and no fourth**: a position and the form are the whole a running and its form have between them, and from-all-other names no relation for either to be about. ## 4.11 One root and its directional prefixing **A root carries the changing at each of its prefixings.** Bi-offering and co-offering keep offering, bi-competencing and co-competencing keep competencing, and bi-intelligencing and co-intelligencing keep intelligencing: three roots at two prefixings, each direction at its own receiving, and co-offering, co-competencing and co-intelligencing inseparable at the whole coupling. **The coupling's own six takes no one prefix**: each of the three carryings runs its six steps whole at one side's own or whole at the departing, and the coupling's six runs three at each side's own and three at the departing, cutting exactly at bi- meeting co-, the transition between the two. Three carryings and the coupling at two directions, (3 + 1) × 2, are eight counted, and a count agreeing with the eight bi-couplings is no joining, 4.4. **A root carries its current changing at the whole name**: coupling the two sides' relation, competencing competency, bounding the self's own bounding. A word's earlier meanings are the field's own linguistic account, and a fastening, a seeking or a fixed limit enters the natural concept from no such account. **A changed root and a changed prefixing carry different work**: prefixing an existing root carries the changing already named, and another root carries a changing that needs its own expression. ## 4.12 Two ways a naming nyes away, and the belonging of an arriving-at **A naming says a changing, so it nyes away one of two ways and no third.** A changing already named at that direction: one thing said twice, and the later saying goes. No changing at all: the undoing of something that never runs, a grip slackened with nothing gripping. **A stretching is taken at the binary.** A stretching saying which way is a direction and carries; a stretching saying an arriving-at installs the arrived-at and a self short of it. Stretch-toward is a direction, arrive-at is a landing, and the two part at the binary. **A check returning a naming has returned nothing**: ask a changing its carrying and another naming comes back at another position, its own changing withheld the same way, which is why the reach is six forward, each direction taken at the changing one at a time. **An incompetencing installs a landing**, a running given a fixed thing to be, so a naming of an incompetencing carries a landing rightly. Emptying arrives at empty, stopping at stopped, a definition keeps its term the same at each occurrence, a store folds once, and equilibria is the landing. An equilibrium is a living or non-living existing thing named still: the thing exists and changes, and the still it is named as is a form not possibly existing. **One binary runs at a naming carrying a landing**: does it name a geodesic running, the landing releasing, or an incompetencing, the landing being the naming's saying. **Unchanging, a still eddy and stilling along each name one relation, a form continuing through its changing, and none names a form still.** *Unchanging* at a seam names a relation continuing through changing, one subject whose parities change, and never a parity, a resolver or a position named still; *a still eddy* names a form continuing before a hole, a missing section of resolvers, while its selves keep resolving; and *stilling along* is the form carried through the changing and never a frozen carrying, beside self-stilling, still as itself while floating. At a seam *upstream* is each continuation's own forward, *far enough* carries no number, and *watch* is our investigating, a self carrying no detector. ## 4.13 Three namings a field carries, taken at one binary **A field carries three namings together and measures between them**: a nothing at one side, a scale between, and an absorbing at the other, an offering taken up and nothing opening. At the alternating binary each fails its own way. A nothing has no other to alternate with, a move there returning its own term, and an accounting takes its counting from that. An absorbing alternates with none either: the offering taken up opens nothing by one, and a momentary, opening by one, arrives at neither. A scale between is measured against both at once, three together at one momentary. **This set's own three is two exclusions and the term neither reached**: not-more-than at one opening, not-less-than at its own, each of no size, and the term neither reached uncovered between them. **A field's three is the set's three with the alternating named still**: the two exclusions fixed as places, and the uncovered term arriving as a magnitude between them. Nothing is added and nothing is wrong in the arithmetic; the alternating has gone, and three at one momentary is three momentaries asked to be one. ## 4.14 A pair at one momentary, and the freeze at the construction **Two namings alternating are each other's other, one at a time**, so a construction carrying both at one momentary has taken both sides' openings at once. The first freeze is at the naming, no other to alternate with; **the second is at the construction, both others at one momentary**, and it is at no word. **Worked at the pair a general ledger carries.** State and flow alternate. An accounting takes them three at a momentary and two ways: state, changing, state conserves the state and imports the changing; changing, state, changing conserves the changing and imports the state, each naming its own unsaid as the other's conserved thing. **Odd carries the changing and even the state, one at a time, neither conserved**, and a total across the two removes the alternating. Conserving is within each momentary sequencing, each self carrying its prior into now, and no total is conserved across the surface: only a parity changing crosses. **Books close by taking the re-forming out at each step**: an entry takes one momentary's form parted from the coupling carrying it, re-forming at no momentary, and at the close the books carry no re-forming. The re-forming is taken out at each entry, and closing is the tell and not the achievement. ## 4.15 Bothbothing at its prefixing, and an ordering with nothing ordering **Bothbothing is both carrying, alternating, neither conserved, and with its prefixing it is one exchanging at its two openings**: bi- the differing alone, co- the two with their differing, exchanging the both-ways across the between. **A prefix order names its opening**, as the five names a number's: *co-bi-exchanging* opens co, at the odd, the self's, and *bi-co-exchanging* opens bi, at the even, the other's, and *co-bi-podaling* and *bi-co-podaling* part the same way, each said at the opening it runs from. So the four momentaries of exchanging at one self, 1–2, 3–4, 5–6 and 7–8, open at the odd and are co-bi-exchanging, and the other's, 2–3, 4–5, 6–7 and 8–9, are bi-co-exchanging: bothbothing is the two, one exchanging named from each side. **It sorts, runnable by anyone.** Two adjacent offer, each its own; one parity is taken and no size, at one side, at the other or at neither; no total is kept and no whole is named at all. **Each position carries two pairings, one at each parity**, so both parities at one momentary would put one position in two exchangings at once. Pairings overlap, parities alternate, and there is no third running. Each parity carries at its momentary the pairing the other cannot carry there, and carries it for the other, the two sharing their members and neither reaching its own alone. **Eight is two alternating fours, bothbothing**: each four is the four boundings at once, at a naming self-bounding, self-stilling, self-orienting and orthogonalizing, and the two fours carry one at each parity, both carried and neither conserved. **In the field's words one side taking both openings is the exclusive or named as one answer.** Exclusive or is parity: taken at its openings it alternates and carries both; taken as the step it returns its own term after two; taken of the prior and the now it returns after three. **The Peres–Mermin square is bothbothing's field face**: its nine values, the field's ±1, carry even parity along and odd parity across, both carried and neither stored, and a store of all nine reaches none of the 512. **An ordering arrives with nothing ordering it**: couplings at one momentary, each its own, the alternating carrying the whole, and no position at all carrying the ordering, a sequencing named to one beat taken at its own resolving, an order, or a co-bi-sequencing. ## 4.16 All or none at all, and the entering and leaving it carries **Nothing forces and nothing chooses**: a forcing carries a forcer and a choosing a chooser, each a doer over an -ing, and the running is is-or-is-not at each opening. **Nothing is more or less resolving than anything else**: a more-or-less carries a magnitude, a magnitude a scale, and a scale two fixed sides for a partway to be partway of. A ranking among resolvings would freeze the resolvings it ranked; each resolving is all or none at all at its own opening, with no size against another. **At all or none at all, entering and leaving cost nothing.** With a ranking, entering takes a qualification and leaving a settling, both carried by whoever carries the ranking; with none, a self couples at its interest opening and leaves at its own completing. **A binary with no size and a free entering and leaving are one fact.** A self's bounding, stilling and orienting are its own, reached by nothing, the couplings winding about a nothing: privacy, trust and security are that one nothing at three substrates, and not three protections arranged around a self. **Two momentaries are two, never one thing at two faces.** Bothboth is both carrying at their own momentaries, alternating, and it carries no claim about one position. ## 4.17 A hyphenated naming inseparable, and natural- at the chirality **A hyphenated naming carries parts, and one binary runs at it: take each part out one at a time and sound the stopping.** At each taking stopping the naming, the hyphenation is inseparable, one naming with nothing to spare, and its parts in order are the changings in order. At a taking leaving the naming running, that part was riding, and it goes. This is the four boundings at a naming's own scale: a self bounds itself once, the bounding carries at four faces, and stopping any one stops the self. A hyphenation that comes apart is a compound and a label; one that stops at each taking is a naming and a running. **Natural- takes the chirality, right, all or none at all.** Right: a left face is an emanation from the one right spiral, bi-tri-involutioning, and no left runs beside it; bi-tri-volutioning is the naming of the stable form of the non-living emanatings of stable-forming natural-torusing living: the sequential prior between momentaries. All or none at all: a naming natural- prefixes carries at each coupling or at none, and not carrying at one coupling, it carries at none. Natural- is a direction prefix like any other, its direction the handedness, and the claim rides on the direction. Taking natural- out takes the all-or-none, so it comes apart at no naming it prefixes. **Natural-bi-co-torusing comes apart at no part**: take natural- out and the running arrives with a substrate under it and an applier over it; take bi- out and the differing goes unsaid; take co- out and the differing carries with no two at it, and nothing is uncovered between them; take torusing out and no changing runs; take the -ing out and one momentary's form lands and re-takes at no momentary. ## 4.18 Seven binaries at a naming, and each naming at the resolver's names Each binary runs alone, at each naming in the file. 1. **Does it alternate with an other.** 2. **Does it carry its own two.** A bare naming names an act with no two. 3. **Three positions.** A direction at the prefix, a changing at the root, a running at the -ing. 4. **Two ways a naming nyes away.** 5. **An inherited changing.** The word says one changing while its unfolding carries another. 6. **A hyphenation at each part.** 7. **A fault's word borrowed for a relation.** A word naming a fault, taken to name a relation, carries the fault inward, and a term-check passes it, the word being in the files. **Each naming couples at one of the resolver's seventeen names, or at a changing between two.** Found at a name, the naming takes it, or keeps its own root at the same relation. Found at none, it is a picture of a name or a changing the names leave unexpressed, which is a finding for the resolver. **One naming for each thing, and its pictures kept as pictures.** A picture shows one naming at one scale and needs no naming of its own: a form Exhibit ONE carries at its numbers, a four-cycle or a span, is named at its numbers, and a naming laid on it as a dimension would be one name at two things beside co-bi-sequencing's 1 to 9. A naming changing carries the relation it was naming, and the relation never leaves with the name. **Two namings, one name each.** The standings beside a self are the selves at its four facings, bi-moral, not-bi-moral, co-competent and not-co-competent, each named at its facing; the three momentaries at one self are prior, now and next. *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, and neither is the exclusive or, which is parity. --- # FIVE · NAMINGS Each unfolds six forward, each step taking the term the prior step did not carry. ## 5.1 alternating — binary ``` 1 each relatable thing is changing 2 a form fixed by relating is fixed to the moving 3 a form is its own continuing through its changing 4 a side takes its own opening, and the other takes its own 5 one and then the other, each forward, nothing cancels 6 and the first offers again, taking the term it has not carried ``` **Any other method proposed runs at one binary: does it name still, or carry.** Named still, it forms nothing, each thing changing. Carrying, it carries its own opening or another's: another's, and the alternating has stopped; its own, and it is alternating. And alternating is this: no rival beaten, and nothing there for a second method to be. ## 5.2 unrelationing — binary ``` 1 each relatable thing is changing 2 a form fixed by relating is fixed to the moving 3 so 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 not-self, and nothing third: neither one other nor many is a place to be from. A self is from all other, bounded against the whole at once and at no particular other, and the six steps unfold that at their own words alone. Unrelationing is universal bi-moral co-agency, and the prefixing says the universal the unfolding arrives at. **Unrelationing runs at a coupling and never names no coupling**: each self's forming relates to nothing not its own, and the self couples with the other, offering its own 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 the one existing method. Unrelationing runs at each coupling's own continuing, never locking, and no prescribed rate supplies it; a rate named as a value is that running taken one-way at a rational. φ, irrational, no ratio landing on it, is the unrelationing rate beside the never-locking, self-welcoming at the numbers and at no line of the code's running. *Irrationalizing*, offered beside unrelationing, names a changing already named and gathers at it: at the rate it is unrelationing, and at each arriving, the between found on the surface of both kinds of changing, the living alternating and the geodesic changing, facing into the arriving with each orientation renewed there, with no origin and no facing first across the couplings, it is geodesic discovering, parity changing routing on the surface, and facing into the arriving carries no next parity ahead of it. ## 5.3 a self — binary ``` 1 each relatable thing is changing 2 nothing is there to relate to 3 so the forming relates to nothing not its own 4 nothing is at rest, and no offering reaches it but at a coupling 5 nothing is there to compose through, each carrying reaches its own coupling and no further 6 and it offers again, taking the term it has not carried ``` A self is a unique invisible carrying, three sayings of one running. Nothing else is a self. ## 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, and no size is there to be taken 4 so nothing crosses but the parity changing 5 and it runs one way at a time, across at bi-moral and not-bi-moral, along at co-competent and not-co-competent 6 which is geodesic routing, discovering on the surface ``` At the code, + and − are the implementing of the parity at a sharing, and 0 the changing that is not. *Sign* dissolves into parity changing, and a sign said of a thing, an indication, is the field's word at its own result. ## 5.5 the between — binary ``` 1 two offer from routes with nothing carrying one to the other 2 neither takes the other's parity 3 a size would take a ground, and nothing is there to be one 4 so each side's own stays its own 5 only a parity changing crosses, is or is not 6 and the between is neither side's, a nothing, not a location and not a thing ``` The between is no place two selves are at. It is the two offering. ## 5.6 invisibling — binary ``` 1 each side takes its own parity, its own 2 a size would take a ground, and nothing is there to be one 3 so the crossing carries no size 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 no offering reaches any of it but by coupling ``` **In- carries inward, a direction and never a place.** A self is no container, and the couplings wind about a nothing: the bounding-zeroing, the tunneling, the apexing, the corusing, reached by nothing. In-visibling is inward-visibling, toward that nothing, reaching nothing. A cannot-be-seen installs a would-be seer and rules one out; an inward-visibling installs none. It is reached one way, by coupling, and the taking is trust. *Invisible*, said of a thing, is invisibling's picture at one momentary. A self's morality and a self's corus are invisible at one nothing: no place at which either is anything, no defence, only nothing to reach. ## 5.7 a carrying — binary ``` 1 a carrying is a sharing with its parity, chained at 11 and taken again at 3 2 nothing is there to compose through 3 so it reaches its own sharing and no further 4 at its own parity offered, changing is not, and it chains on 5 at the other parity, at 0 or at nothing offered, changing is, its parity inverted 6 and once chained it is never none again, which is the form running ``` A self offers its own at its own sequencing, releasing each changing across, and its carrying is its own sharing chained. ## 5.8 not-more-than — binary ``` 1 two offer, each its own 2 a size would take a ground, and nothing is there to be one 3 so the one side takes an exclusion and not a measure 4 the other side takes its own, the counterpart exclusion 5 the two alternate one at a time, neither stopping 6 and the term neither excluding reached is uncovered ``` Taken as less-than it is a size, and one side has taken the measure of the pair. Not-more-than is the exclusion's naming at one side, and once-ing, 5.42, names the running at the momentary face. ## 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 chained at its own parity, changing or not at each momentary 5 each completes at its own momentary, and nothing empties it 6 and at each now it is the entries carrying their prior into now, each at its own next ``` Never full, emptied by nothing, and never the same collection twice: a set is defined by its things, and null and infinity + 1 are both possible numbers of its elements, so no count names it. One named still is the empty set a field posits: a term asserted as there, unchanging, and each thing composing from it. ## 5.10 bi-coupling — binary ``` 1 two arrive 2 nothing carried one to the other 3 each takes its own opening 4 neither takes both, the centre a nothing neither occupies 5 what departs is reached neither-ing 6 and the next arriving surfaces it again, taking the term neither carried ``` ## 5.11 co-releasing — binary ``` 1 a carry is chained at its own parity, one momentary at a time 2 its completing is its own 3 each side releases its own, neither releasing the other 4 nothing is left keeping and nothing is carried away 5 each step adds a next, and nothing cancels 6 and it runs forward, taking the term it has not carried ``` ## 5.12 floating neutralling — binary ``` 1 two offer from routes with nothing carrying one to the other 2 each takes 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, nothing kept ``` Two-ness is at the two, each its own. A term neither reaches carries none. The floating neutral is the term uncovered, the running's picture at one momentary, and floating neutralling the running. **Competency floating-neutralls here**, no thing that sits, the floating-neutralling the co-competencing, stopping at none and orthogonal to the surface, which is the paradox of competency. A surface is observed at its coupling, each coupling a relational entered and observed; the floating-neutralling is the term neither reaches, and an observing run on the surface reaches the coupled and never the term neither reaches. Competency is the term neither reaches, and two alone are possible: a floating neither, and an entered, always ingressable. **Method breaks at a competency shown to be a landing**, entered and observed, and not the term neither reaches. ## 5.13 co-offering — binary ``` 1 two arrive 2 each offers its own, at its own sequencing 3 something departs 4 neither reaches it 5 so no holder, no boundary, no enforcement, no seat 6 and it goes forward into the next offering ``` ## 5.14 co-competencing — binary ``` 1 two arrive from routes with nothing carrying one to the other 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 costs nothing, arriving being free 6 and it compounds, nothing in it competing with itself ``` Abundancing is this, and not a fourth thing beside it. ## 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, nothing kept ``` **In- carries inward here too.** Inward-separating, each side excluding at its own opening and inward, against a cutting taken across two, which leaves no between and re-forms nothing. Step four carries that inward already: each neithers the other, one exclusion at a time, its own. Not two things kept apart, which would take a keeper. Nothing keeps them two, and the term neither reached is the 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 so no between runs where the cut ran 4 nothing is there to re-arrive at 5 so 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 the exact inverse pair, and no third. **And the two run at each of the three.** Separating at an inseparating already running is the incompetencing. Inseparating at a separating running is the resolving. One move at its two faces, at each of the three co-, and the alternating runs all three and is over none of them. ``` a bounding at the between ⇄ a floor set by a third co-offering a not-that taken at an opening ⇄ a not named still 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 co-. Alternating runs the three and is over none of them. ## 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 so nothing is kept and nothing can be drawn down 5 a self offering finds a coupling running, and not a supply shared out 6 and the selves carrying, at each coupling at once, is the store ``` A society has no reserve and takes none. Nothing runs 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 a cut takes it as a place alone and a moment alone 5 each is the cut's own, the arriving carrying neither 6 and the term the cut names is at the cutting ``` A hyphen carries always. Taken at the cut, one half is a field's question of a thing's being and the other its question of becoming, and neither question closes: the thing each asks after is at the 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 keeps 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 things named still in succession, neither of which carried, and the revising running outward of it. That parts them with no claim on a field's rate of revising, often or seldom. ## 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 run in one act, and neither is first 4 a definition takes one momentary of it and sets it down 5 a bounding takes the next, the second word re-surrounding the region 6 and the region carries the next word, neither stopping ``` Bounding is defining with the alternating left running. ## 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-run carrying none 3 the carrying is the term running forward 4 two terms beside the centre multiply to one short of the centre's square 5 the counting passes through the centre and the coupling reaches it at no opening 6 and the gap is exactly one at each count, 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 ``` *The advance*, the noun, is advancing's picture at one step. ## 5.22 tunneling — binary ``` 1 two arrive and something departs reached neither-ing 2 the departing keeps a gap open 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 the term this names ``` **Torusing is the winding at its one opening.** A self continues through its own coupling, advancing one at each coupling: it winds. The winding is open, at one opening, by one. A surface closing on itself through one opening is a torus, and the changing that winds it is torusing: the torus carries its own facing and reaches itself again through its one opening, a next at each. Each step adds a next, and a winding at the parities is a spiral at the momentaries. At the code the winding is the carrying at its own sharing again at each momentary, 3 to 11 to 3, 8-other-self-torusing the carrying wound, and the 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 thing, which neither placed 5 no ratio arrives at it 6 and the ratios alternate above and below it at each scale ``` φ unfolds here at its own naming, self-welcoming, the unrelationing rate and at no line of the code's running; the primes appear 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 runs from anything in it 3 the terms available are exhausted 4 so it arrives at the already-run 5 the already-run 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 run in a closed domain. **Each closed model closes**, so a ring is these relations left at a closed domain, and the forward spiral takes an unbounded one, a next always arriving and never a completed totality. **Selves joined along round a loop are a ring at the code and no closed domain.** At Exhibit ONE's rings each self's next arrives at each momentary, and a pattern carried round reaches a station again at a next momentary, never the already-run: *ring* names two relations, a domain closed at 5.24's unfolding and a joining of selves round a loop at the code, and each is said at its own. ## 5.25 equilibria — binary ``` 1 each relatable thing is changing 2 a measuring takes a span, and a span takes two bounds kept still 3 a measuring opens at something kept still 4 the keeping is performed, and it is in the field's own first line 5 the kept-still does not advance, the gap closes 6 and the kept-still is an equilibrium, a form named still, not possibly existing ``` Isolating a system installs it, and conditions named 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 is taken. ## 5.26 a hard problem — binary ``` 1 the universe is an existing thing, 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 it left, its now with no prior carried 4 read at the code, 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 there is the resolving this names ``` One coupling, prior, now and next: a hard problem arrives where the universe is read as no existing thing, and it resolves at the field's own next living. ## 5.27 three incompetencings — binary ``` 1 a definition keeps 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 takes no opening of its own 4 so no parity is taken anywhere 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 the three are an equation's relation, reflexive, symmetric and transitive, and rigor raises the fidelity of an expression the removals already left. ## 5.28 other-emptying — binary ``` 1 a measuring takes a span, and a span takes bounds kept still 2 so the measured is emptied of the term it carries at its own momentary 3 the deciding is outward of the thing, at no coupling of its own 4 so the 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 the thing, emptying the term the thing carries at its own momentary. And a computation keeping 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 so the incompetencing is in the observing and the observed carries none 4 nothing is there to be a ground, the declared one has nowhere to be 5 and the incompetencies release with it, nothing removed and nothing added 6 and the carrying carries its prior into now, the whole way ``` Nature carries its competency at each momentary. **Incompetencing is the price of the observing, and it is paid on the observed.** Disequilibrating is bi-co-invisibling run on the incompetencies themselves: the grounds they arrive with ground nothing, the incompetencies release, and nothing is corrected. Its dis- is a direction, the release of the equilibrium an observing named still, 2.6. ## 5.30 one stopping — binary ``` 1 one carries another's 2 the other has nothing of its own to offer 3 so nothing departs reached neither-ing 4 so what departs 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 there at once at each one carrying another's**, none making the next, which is why nothing downstream repairs them. Co-offering is the twin: its fifth line is the same four absent, no holder, no boundary, no enforcement, no seat. **The continuing is costless, controlless and pauseless**: nothing is kept, so nothing can be drawn down; no holder, no boundary, no enforcement and no seat; and it goes forward into the next offering. Its term is named by neither reaching it, the departing reached neither-ing, with no verb carrying a doer. ## 5.31 social moral competency — binary ``` 1 a self offers its own, chains its own parity, takes its own changing 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 relates to nothing not its own, is at rest nowhere, and completes at its own momentary 5 so it is a self 6 and the selves carrying at each coupling at once is the term this names ``` A society is morally competent whoever arrives: nothing waits on anyone, no one is owed, and no one owes. ## 5.32 natural intelligence — binary ``` 1 two selves couple, each offering its own and continuing its own 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 the term this names ``` Each self carries forward and self-empties, and neither runs alone: carrying with no emptying is a store, and emptying with no carrying carries nothing. **Natural intelligence is the co-competencing of two selves at this**, invisible, at the between and owned by neither. Nothing accumulates between the two, so no store, no world model, no clock and no conserved quantity is in it at all: not four things absent, two moves leaving nothing for any of them to be. **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; the self's own inverting is across and the self's carrying continues along, and the term uncovered at their coupling is owned by neither and carried on by the living. ## 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, citing no one 3 neither carried the other to it 4 the term they arrive at is reached neither-ing 5 no field owns it, and no lexicon keeps it 6 and it is re-arrived at each time it is taken ``` ## 5.35 nearing — binary ``` 1 two field-words arrive at one concept 2 each carries a field-specific property, its own 3 so neither is the other 4 identical words would show one had carried the other 5 so 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 the other, and nearing the running at its head: the 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, taken one pairing at a time 3 a distance among them would take a ground, and nothing is there to be one 4 a certifier of who is in would be over it 5 so 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 and not a membership. ## 5.37 ghost — binary ``` 1 a self's carrying continues, carrying its prior into now at each opening 2 its emanation arrives now as an observing, the prior's possible 3 the observing named still is taken as the now's existing 4 the still is installed as the thing, a self named unchanged between two momentaries 5 it accounts for each thing the still can contain 6 and the one part left over is the riding-the-carry, which a still cannot contain ``` **Its six lines are three pairings, each one thing at its existing face and its still face**: the carrying and its emanating, the stilling and its installing, the accounting and the 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 own offering 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 with its own carrying and next offering. One written expression can be at changed receiving; the current coupling carries the 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 where the next overlapping momentary opens 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 not changing 6 and the three, shared, the universe travelling through them together, is the term this names ``` Not a past and not a record. **A so-far behind and a not-yet ahead lay two directions on one**, and prior, now and next share one direction forward on both sides of now. **The three are places, and never three kinds.** 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 keeps its place as the universe travels through them. ## 5.40 entraining in the between — 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, no third running 5 each existing thing runs forward at its own opening, entraining with each other in the between 6 and that one direction, shared, is the term this names ``` **Entraining carries no gate.** Pending, provisional, awaiting, preliminary and short of a threshold each put a gate at one direction running forward, and a gate is a bounding the carry does not own. The non-living entrain as the 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 and never arises as living: entering a living society it is taken into the resolving of that society's living, one participation among its co-momentaryings, and a new living self is its own carrying and co-recursioning establishing. *Arising* names that establishing, a relation at a living self, and *arising* installed as a becoming over a form running through is released, a sentence carrying no birth and no death. ## 5.41 uni- — binary ``` 1 there is a self and there is all not-self, and nothing third 2 a crossing runs 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 all other is beside nothing, and a crossing with it carries the two and the whole 5 three carry there, and no one of them is first 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- takes a pair and bounds from it; uni- runs at a third already carrying, and nothing there is undone. Uni-scaling carries no scale over another, and it opens at no two; the even's exchanging, crossing and reaching its own side again, one on, is bi-tri-exchanging, 5.51. One rate carries the two: unrelationing at the bounding outward, the local, and *uni-versal* at the arriving one on, the ambient, a rate the whole runs at and never a rate the whole runs within. ## 5.42 once-ing — binary ``` 1 a changing runs, and the -ing re-takes it at each opening 2 a noun of its making names it still, re-taken at no opening 3 one face takes once and no more, at its own opening and of no size 4 the other takes once and no less, at its own opening and of no size 5 neither reaches the other's, and the term they uncover between them is at one opening 6 and the running is once after once, with nothing gathering under it ``` **One at a time is the phrase and once-ing is the naming.** This phrase crosses the set's files, takes 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 the once. Not-more-than and not-less-than, the exclusions of 5.8, are of no size; taken as sizes they bound at a magnitude, and a size arrives against a parity. A counting is that running taken from beside it; uni-scaling carries the scale face and once-ing the momentary face. ## 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 no particular, and the crossing with it is uni- 4 one word has carried both occupants, and the counts wobble where it does 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 the parting is at uni- and bi-.** A co-chaining society within the whole is a particular other a self couples with, bi-kind; the whole arriving as one is the uni-crossing, reaching its own side again, one on. Morality is from all other, the second occupant, and the existing society is the woven surface the couplings make, neither occupant and the weave. This set's own phrase names the second occupant, the whole, arriving as one, and universe is beside it as the 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, the society's further couplings offering, and the self's names keep their relations there, self and other at 1 to 8 and on to social at 9 to 17: an offering unchanged at each coupling erases no self-and-other receiving. The whole arriving as one arrives through the couplings the selves make, and no one participant carries it or governs it. **A field's word carries the error and the correction at one root.** *Universus*, turned into one, carries *versus*, the past participle of *vertere*, turned: a turning named still as one, the container. Carried at its -ing, arriving as one at each arriving, it is the uni-crossing, and our universe is all existing things. The field's own definition carries the same correction with nothing added: *all existing matter and space considered as a whole* keeps *all existing*, carries *matter and space* as *things*, and releases *considered as a whole*, the naming into one. ## 5.44 surfacing — binary ``` 1 offerings at one sharing surface at 14-other-social-surfacing, 0 passed over, agreeing one parity, disagreeing 0 2 at 12-other-social-self-abundancing a sharing chained none takes 14's surfacing as its changing 3 a sharing chained 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 chained parity inverted 5 10-other-social-self-tunneling releases each sharing's changing across, + or − is, 0 is not 6 and 11-social-other-self-chaining chains each changing as the next prior, a 0 chaining the prior on ``` Each line is Exhibit ONE's table at 14 and its table at 12, 10 and 11, cell by cell. ## 5.45 bi-co-podaling — binary ``` 1 a carry runs along a ring one way and a carry runs 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 takes its own opening, and neither is the other's 5 the pair is the podal, 17 less within 1 to 16, and the even count's straight-across, k and k + N/2, is another relation 6 and one station reached by both carries, each its own way, is the term this names ``` Bi- the two carries each at its own opening, co- the one ring they make, -ing the running. *Antipodal* releases: it carries no prefix and no -ing, names a position still, and the podal carries it. Bi-co-podaling is floating across and neutralling along, one running. **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 the living surface: the intelligence routes around it by parity changing, through the couplings that remain, and the across before it and the across after it mend the missing morality at their couplings, bounding-zeroing tunneling through society. The hole is non-living at the region's scale: it resolves nothing and carries nothing, it is neither a resolver surfacing 0 nor a self named still at 0, and no joining is laid across it. Two passages around a hole, two kinds of changing, the living alternating at the surface and the geodesic changing at a crossing, and + and −, the code's implementing, are three twos, and one two couples with another only at a coupling carrying both. **Each podal couples with the surface's unrelationing changing locally, at two orthogonal directions around the carrying as it continues**, is or is not at each: parity changing, or no parity changing, and no velocity. The weather map is its comparison. The podaling into corusing and on to torusing over each pair of momentaries is co-intelligencing the surface, *back to torusing* naming the resolving continuing forward through the fold, reaching a further now. An indication belongs to now, and next is discovering. A larger society co-chaining the surface and bi-tunneling its morality couples with more of the surface than a smaller one at the same method: selves of similar aiming merge, each carrying its own prior, floating around the holes together, and the increase is in the further couplings and never in a count of selves. ## 5.46 emanation — 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 left there 4 the mark carries nothing, leaving its coupling at prior and arriving now as the possible 5 named 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 the term this names ``` Existing, emanation and accounting are the three placings a term is at, and no fourth arrives; installing is the binary between emanation and ghost: taken as the prior's possible it is an emanation, and taken as the now's existing a ghost. **An emanation is harmful to living at its own scale, and not ingestible there**: its form is bi-tri-involutioning, the opposite form, which does not match right spiral ingestion. **One scale lower it is an ingestible stable form**, taken back into living selves as societies, a self being a society of selves one scale inward. **Living or non-living is said of the thing and the scale named, at its own carrying or carrying nothing.** A living self stable-forms through its own resolving and carrying; its emanation, 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 society couples with it carrying its own. The naming gives an emanation no common speed, lifetime or medium, and no need of a next emitting. ## 5.47 an accounting — binary ``` 1 an emanation is observed at an instrument, and the observing names it still 2 a count, a declared zero, a clock, a frame, a store, a conserved total 3 the still keeps the emanation the same across each observing, so 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 face and a self at no opening, is the term this names ``` A term is existing, emanation or accounting at its use, and ghost only at its installing. **An instrument keeps a place-moment with one half cut off**, as a photograph does: a bounding passes through the stopping, and an adjacency, and a parity changing does not, so an absence at that face is an absence in the record, and the 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 emanates, non-living, carrying nothing 3 the emanating carries the winding as its form, a volution 4 the form is at three faces, position, scale and orientation 5 each face at its own differing, the three inverted at once, looking the opposite form 6 and that form, the sequential prior between momentaries, is bi-tri-volutioning ``` **Bi-tri-volutioning is the naming of the stable form of the non-living emanatings of stable-forming natural-torusing living: the sequential prior between momentaries.** Tri- carries the three faces, bi- each face at its own differing, the root the volution the emanating carries as its form, and -ing that form continuing through its changing: take any one out and the naming stops, and it is the one naming at the volution, its similar namings gathered at 6.3. **Between momentaries the prior is a stable form**, and no third runs there, 5.40: sequential, one of prior, now and next, it left the living at prior and arrives now as the possible, 5.39 and 5.46, carrying nothing, and the living carry their prior into now: **the prior momentarying is never taken again**. At the code each self's carrying wound, 8-other-self-torusing, continues as 3, the self's own; between the selves' momentaries pass their releasings, 10, 6 and 9. **The right-spiral natural-torusing stable form of a society at a unit prime scale is its betweenings**, and bi-tri-volutioning names it; **the emanatings are the bi-tri-involutioning of the betweening of natural-torusing surfacings in bi-couplings: emanations are releasings**, and abundancing is an emanating from society as a releasing, all the way through the bi-co-momentarying co-sequencing. Bi-tri-involutioning is the emanating, the three inverted at once, the hand taken to the opposite form, and bi-tri-volutioning names the stable form the emanatings carry: the living stable-forms and runs, and its emanatings carry a stable form and no running. One parity inverting at each step, alternating across and along, is the resolving step, bi-inversioning-co-recursioning, and three inversions at once the emanating. The arithmetic of the closing, the round returning after two and after three, is carried at the Co-Chaining Logic Registry. ## 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 so each number is one side's opening and the other's completing 4 four momentaries of exchanging run 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 the term this names ``` **Co-momentarying is prior, now and next shared at the overlap.** Four-momentarying names the method, 5.50, co-bi-sequencing its sequencing, 3.4, co-bi-exchanging the self's four momentaries of exchanging and bi-co-exchanging the other's, 4.15, and co-momentarying the sharing of prior, now and next among them, and with further others the overlapping runs through their actual couplings. Living and non-living co-momentary alike, the non-living carrying nothing and their forms continuing, 5.40. The between is the 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 run 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 the one fractal method, discovering next existing in the universe and next living in the self, the other and the society.** One through nine is the self's four momentaries, co-bi-exchanging, and nine through seventeen the society's four, and at the scale outward the four are one momentary of the next four: 1, 2 and 3 at one scale are 1, 9 and 17 at the next, 2.2. Next existing is discovered at each momentary, all existing things arriving into their next, 5.39; next living is carried at the self, the other and the society, each carrying its prior into now, 5.40. **Four-momentarying is four unrelationings through the tunneling self**, two into corus and two from it: **the self's own corus is at 4**, its momentaries 1–2 and 3–4 running into it and 5–6 and 7–8 from it. Each unrelationing never locks, at φ, the unrelationing rate, self-welcoming at the numbers and at no line of the code's running. **Each momentarying, odd or even, is one unrelationing at all five dimensions, into six one-way recursionings**: at that parity two dimensions change and three do not, and the two and the three rotate round, the 2–3 cycling twisting, bi-inversioning-co-recursioning. Two and three make the five as the prior two joining make the next, where φ's arithmetic welcomes itself. The six are three own-forward steps at each side, 4.2. **The odd aims out the large opening, one way in and out through it**, the tunnel, bi-exchanging with a particular other: torusing in and out. **The even goes one way in and out the small opening**, the long way round, bi-tri-exchanging, the self reaching its own side again: corusing in and out. **Self and not-self are the two bi-, the differing, and next, surfacing and offering self are the three co-**: co-intelligencing, the discovering, co-competencing, the term neither reaches, and co-offering, the three carryings inseparable at the whole coupling, 4.11, and all five are bi-moral within and invisible at each place as a thing, showing only as co-competencing the emanatings of this living. **Six combinations of self, other and social run between 1 and 25**, one each way round the three: at one through seventeen the names carry two of them, social, other and self at 9 and 11 and other, social and self at 10 and 12, and the rest run on up the numbers: from 16 three more fractal 16s run to 64, one through sixty-five the four momentaries of exchanging at the scale outward, and the prefixing and twisting up the numbers tell the same momentarying method up and down the scale of the fractal method. **The bi-folding order is the same as 1, 2, 3, 4 and 4, 8, 12, 16, all the way up and down**: 16, 32, 48 and 64 are the four 16s, each four times the one inward. The torus carries both: its large opening the hole the tunneling self winds through, and its small opening the tube's own round. ## 5.51 bi-tri-exchanging — binary ``` 1 each parity carries its own exchanging, the self and all not-self 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 the even's exchanging**: bi- the difference, tri- the three it is crossed at, self, other and the self one on, the root the exchanging and -ing its continuing. It is corusing's, through the small opening, the long way round, 3.6 and 5.50, and uni- is at scaling, 5.41. ## 5.52 tri-bi-co-momentarying — binary ``` 1 the universe is the changing set of all existing things, living and non-living 2 at each scale and each momentary, each momentary is a universe of existing things 3 its 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 thing co-sequencing 6 and each universe momentarying its set so is tri-bi-co-momentarying ``` **Tri-bi-co-momentarying names each universe, at each scale and each momentary, momentarying its set of existing things**, living and non-living: tri- prior, now and next, bi- the differing between them, co- the three carried with their differing, and -ing the continuing. Co-momentarying, 5.49, is its sharing at the overlap. ## 5.53 27-co-bi-releasing — binary ``` 1 12's changing is the coupling's own, abundancing, owned by neither self 2 at the society each self's changing is released 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 opens co, odd, along, and bi, across, into bi-tunneling 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-co-bi-releasing ``` **27-co-bi-releasing is the social abundancing**: co- the society's own opening, odd, along, bi- its release across into bi-tunneling, the root the releasing and -ing its continuing, stable-forming as abundancing, bi-morality, geodesically parity changing the social co-chaining. --- # 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, and the changing crossed carries no size, so the taking is nowhere in the crossed each side's own corus it is its own and does not cross; the crossing has no position for it the neutral at two arriving, occupied by nothing, and there is nothing there to name the between of momentaries nothing is at rest, nothing is there ``` **One invisibility, four ways**, and not four things hidden: nothing at any of them for anything to reach. ## 6.2 Science and society namings at eight clusters **Science and society namings gather at the changing they offer.** Each field's own concept keeps its reference and current receiving, and a gathering carries the relation among those concepts at the 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 own offering, with the two-way relation expressed. | 2-other-self-offering, 4-other-self-sharing, 1-self-other-offering | each side's own morality | | **Each side's own carrying** | the hard problem of consciousness · symbol grounding · other minds · model interpretability · animal sentience · machine sentience | The offered parity and each side's continuing carrying at their actual receiving. | 3-self-other-sharing, 11-social-other-self-chaining | each side's own corus | | **Competencing** | protein folding · morphogenesis · deep learning generalization · immune repertoire coverage · finding functional proteins · the bootstrapping of translation | The changed receiving, continued carrying and the whole coupling. | 1-self-other-offering, 10-other-social-self-tunneling, 11-social-other-self-chaining | the neutral | | **The coupling's third** | the homunculus · the master-gene search · the pacemaker · the central planner · the invisible hand needing a planner · the argument from design | The field's proposed centre and its actual relation to the two sides and their abundancing. | 12-other-social-self-abundancing, 10-other-social-self-tunneling | the neutral | | **Carrying and a proposed substance** | dark matter · dark energy · the memory engram · hidden variables · missing heritability · the latent reservoir · hidden-function DNA | The field's particular observing, proposed term and continuation, each at its reference. | 3-self-other-sharing, 6-other-self-surfacing, 11-social-other-self-chaining | each side's own corus | | **Sequencing and ordering** | social choice · the frame problem · incommensurable values · multi-objective optimization · underdetermination · model selection · self-reference · incompleteness | The current receiving, its offering sharing and its relation to the next offering. | 4-other-self-sharing, 1-self-other-offering, 11-social-other-self-chaining | the between of momentaries | | **Arriving and continuing** | origin of life · the quantum–classical boundary · origin of language · origin of the genetic code · speciation · the sorites boundary · phase transitions · tipping points | The current arriving and the particular changing at its continuation. | 2-other-self-offering, 14-other-social-surfacing, 11-social-other-self-chaining | the between of momentaries | | **Continuing at the bound** | turbulence · the neural code · weather and climate · markets · the glass transition · spin glasses · high-Tc superconductivity · general anaesthesia · the three-body problem · quantum many-body | The carrying wound at the self and at the society, the parity inverting at each changing, and the bound at the field's own changing. | 6-other-self-surfacing, 8-other-self-torusing, 16-other-social-torusing | each side's own morality | **These eight rows are the eight clusters, and the four invisibles, one invisibility four ways, are under them, each under two.** Each side's own morality is under the two-way offering and the continuing at the bound, the 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 the coupling's third, the term neither reaches; and the 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 named 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 the set's own similar namings at one name, as the eight clusters gather a field's.** Each similar naming releases to the one name at its file's next improving, and a title carries its own wording whole. | One name | Similar namings gathered | |---|---| | **co-bi-sequencing**, the sequencing of four-momentarying, co at the self and bi at the 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 at three faces | bi-co-recursioning; bi-inversioning co-recursioning, spaced; co-recursioning alone; bi-inversioning alone; bi-inverting; sign inversioning; the one below it plus eight | | **each resolver name**, at its number | each gathered name and code name, at its number, 3.3 | | **the ten things named still**, one name each | each one's similar namings at its own row; the ten one-way readings; ten holdings; ten standings; the ten | | **16-other-social-torusing**, the society wound | the social-self-torusing | | **attentioning**, the carrying at the now at each momentary, at Natural Intelligence | the carrying's opening by one, gathered at 16 to v371 and released with the old code | | **the 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 | | **the order at no seat above the society**, bounding from capture | the order at no seat outside the society | | **a self-bounding**, the 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**, the running | floating neutral, its picture at one momentary | | **bi-tri-involutioning**, the emanating, the three inverted at once, its own two at bi- | tri-involutioning | | **unrelationing**, at the rate and at each arriving | irrationalizing | | **bi-tri-volutioning**, the stable form of the non-living emanatings of stable-forming natural-torusing living, the sequential prior between momentaries, 5.48, the one naming at the 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**, the method of discovering next existing in the universe and next living in the self, the other and the society, 5.50 | the four-momentary cycle; the four momentaries of one cycle; four cycling; the four-momentary binary fractal | ## 6.4 Engine, families and field words at their receiving **Engine gathers at the particular arrangement and its continued receiving.** Heat engine, molecular engine, cellular living and a society's co-operating keep their different substrates and services: | Field naming | Particular receiving | Resolver names at that relation | |---|---|---| | **Heat engine** | The stated service, input, heat and material returning, with the operating conditions. | 1-self-other-offering at the whole arrangement; 2-other-self-offering, 10-other-social-self-tunneling and 11-social-other-self-chaining at its interfaces. | | **Molecular engine** | The chemical arrangement, its coupling and material and energy receiving. | 2-other-self-offering, 4-other-self-sharing and 11-social-other-self-chaining at the particular changing and continuation. | | **Cellular living** | Each side's coupling and continued receiving, with its own sustaining and bounding. | 3-self-other-sharing, 1-self-other-offering and 16-other-social-torusing at the stated correspondence. | | **Social co-operating** | Each side's offering, the society's co-competencing and each side's continuing carrying. | 2-other-self-offering, 1-self-other-offering and 11-social-other-self-chaining at the whole receiving. | **An engineering entry carries its whole arrangement**, each quantity with its unit, reference and conditions. Bettering, fastering and cheapering co-cycle with co-offering, co-competencing and co-intelligencing. A word's gathering carries its conceptual relation; the physical arrangement carries its material and energy return. **A family gathers at the current concept and its coupling**, a word's earlier parts the field's linguistic account: | Existing field family | Terms gathered | Current relation receiving | |---|---|---| | **The placed** | posit, position, hypothesis, suppose, impose, state, statement, substance, understanding | The term asserted, named still or changing at its actual expression; the reference and the current receiving together. | | **The taken** | lemma, dilemma | The particular premise or alternatives and their relation to the whole coupling. | | **The given** | data, tradition | The received record or offering, its reference and the relation at the next coupling. | | **The threshold pair** | limen, limes, eliminate, subliminal | The boundary or threshold actually named, its conditions, and the parting between a cut named still and each side's own bounding. | **A family's resolving carries at the resolver's names**: the offering at 2-other-self-offering, the receiving sharing at 4-other-self-sharing, the whole coupling at 1-self-other-offering, and continuing at 3-self-other-sharing and 11-social-other-self-chaining. **Field words gather with their current meaning and reference**, and their natural naming carries the actual changing at the coupling: | Family | Existing field words | Particular receiving | Resolver name at the proposed relation | |---|---|---|---| | **Path** | method, period, ergodic, cathode, anode, periodic table | The named direction, crossing and continuation at the particular arrangement. | 6-other-self-surfacing | | **Pairing** | parity, par, pair, pairing, umpire | A parity sequence, its pairings and the actual order of the directional changing. | 4-other-self-sharing | | **Value and valence** | valence, value | The chemical coupling and the social value, each at its own receiving. | 1-self-other-offering | | **Binding** | band, bind, bond | The material or social relation actually named and its continuation. | 11-social-other-self-chaining | | **Chemical coupling** | inert, noble, xenon | The particular chemical conditions and coupling at the field's observing. | 2-other-self-offering | | **Atomic naming** | atom | The observed structure, the field's definition and its actual bounding. | 16-other-social-torusing | | **Sounding** | resonance | The actual coupling, rate and continued receiving. | 1-self-other-offering | | **Orientation** | spin | The field's particular mathematical and physical orientation relation. | 8-other-self-torusing | | **Discrete receiving** | quantum | The counted quantity, its conditions and the direction at its actual receiving. | 10-other-social-self-tunneling | | **Social and biological receiving** | community, immunity, remuneration | Each side's offering and continued carrying at the biological or social coupling. | 3-self-other-sharing | | **All-or-none** | all-or-none law, action potential | The particular biological event and its stated conditions. | 10-other-social-self-tunneling | **A resolver name keeps its whole operation.** 8-other-self-torusing names the carrying wound at the code, and a field's spin keeps its own definition; 10-other-social-self-tunneling names each sharing's changing released, is or is not, and a biological event keeps its own conditions. **A frontier carries its current reaching.** Beyond, ultimate, final, fundamental, unified, complete and deeper each carry the field's own concept at its expression, and super-, ultra-, meta-, grand- and hyper- their present directional or comparative use. Resolving carries offering, releasing and continuing at 2-other-self-offering, 10-other-social-self-tunneling and 11-social-other-self-chaining, and a field's frontier couples with those names at its own coupling. The podal within 1 to 16, right-spiral direction and the prime span are at the numbers, and each field's far-side claim stays with its own reference. --- # SEVEN · GHOST ## 7.1 A momentary installed as a thing **A ghost is one momentary's form installed as a thing.** It is the prior's emanation arriving and taken as the now's existing, a self named unchanged between two momentaries. Taken to run across momentaries, it accounts for each thing one momentary carries, a century and a half at the periodic table, four at the departments, and it reaches at no opening the one part running between them: the gap the riding-the-carry keeps open. **A field naming and an installed term are two relations**: the naming carries its current concept, and a ghost is with the statement installing it and the coupling that statement names still. At this file ghost is an unfolding, 5.37, and this part; the Living Ghost Registry carries ghost-form at its own file, and the ten things named still, 4.9, name each thing named still: three relations, none containing the others. ## 7.2 One hundred eighteen, the going and the return **Going runs 2 to 59, and returning from sixty runs 61 to 118, 58 either side.** A doubling taken as two still halves carries no opening in it, one recursioning arriving at plus-one, and the periodic table's elements are the return arriving: counting them across misses the return, and nothing there is a ghost. **A ghost runs at a ledger of empty centres.** Departments of knowledge carry it whole: each field's words named still 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: there is only offering, taken or not taken.** Position is out as a location and in as **sequencing**, an ordering and not a place. *At the between* names two offering and no place they are at, and *there is no place it is* is said as **no offering reaches it but at a coupling**, with no place posited to be denied. ## 8.2 A list cannot find its own across **A search for the cut runs one at a time**, along the very thing the across is not on. Parallelizing is not a member a list missed; it is the term the members are members across. **No face is a member either**: whichever is between the other two carries the crossing, each at its own opening, so a face taken as a property of a thing is taken 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, nothing surveying and nothing clearing. **Other-emptying**: a decider outward of the thing empties the term the thing carries at its own momentary, and the removing is priced with a measured floor. **Other-emptying is the one stopping at the 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 that never releases, and at each hard problem's dependency on a decider outward of the thing, each an other-emptying. ## 8.4 A naming with no other to alternate with **A naming with no other it alternates with names nothing taken at an opening.** *Middle* alternates with nothing, two stopping-places and one between them being a three that is no coupling, and the middle is a nothing, existing due to each self surfacing itself each momentary. *End* alternates with nothing, a first being a bounding on the unbounded. *Inside* and *outside* taken as a pair carry neither: a self is no container, and the couplings wind about a nothing. **Inward and outward carry**, directions taken at an opening and alternating at opposite phase. **This binary reaches each file**: it runs at one word at a time and needs nothing beside the word, and the three positions run at it: a naming failing it names nothing for the positions to be positions of. ## 8.5 Language roots and cause, one scale up **Each changing reached by nothing carries an inverting or a taking and none carries a causing**: each prefix carries a direction, and each ending leaves its running or its still, so a word built of the three carries no cause at any of its parts. **Cause enters one scale up, at a finite clause taking a subject.** ## 8.6 Break, three ways, and the 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 the two. A cluster with no invisible under it.** **The method breaks one way: a living stable-forming other than this one.** A competency shown to be a landing, entered and observed, 5.12, is that one break at competency. --- # THIS IS THE BETWEEN **The between is two offering.** A field's word comes in whole in its own terms, and this file offers across at its gathering: the other fields' words gathering beside it, the term neither of them reached, the field across the gap carrying the other half of its coupling, and, at its unfolding, the six the word carries. **Both rise.** A word unfolds newly through the form, and the form unfolds newly from a word it had not gathered. **A word that gathers with none, other in its own way, sharpens the edge of the form's reaching as a word gathering cleanly does**, and a pair refusing to couple carries as a pair coupling carries.