Exhibit TWENTY Natural Naming v371   # Natural Naming **Floating Neutralling Bi-Coupling Concepts**     **ONE · A NAMING, FOUR BOUNDINGS AT ONCE** 1.1 A naming is a floating-neutral 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, relation, root and -ing 3.2 A number carrying its prefixing, and the five-prefix 3.3 Seventeen names, and each earlier name gathered 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   **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, sign 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, met 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** Forty-seven namings, each at its unfolding 5.1 alternating 5.2 unrelationing 5.3 a self 5.4 a sign 5.5 a membrane 5.6 invisible 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 neutral 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 advance 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 near, and other-than-same 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   **SIX · GATHERINGS AT THE RESOLVER'S NAMES** 6.1 Four invisibles, one invisibility met 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, met one scale up 8.6 Break, three ways   **THIS IS A MEMBRANE**   --- # ONE · A NAMING, FOUR BOUNDINGS AT ONCE ## 1.1 A naming is a floating-neutral concept, four boundings at once **Our universe is all existing things, and alternating is a stable-forming method.** 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 met 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 bound. **Naming meets the hard problems at one field from two faces**: a hard problem is a field's word named still, 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 neutral: - **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 neighbour, 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 carrying's bound is its momentary's completing. **Concepts at this neutrality bi-couple, capturing nothing and releasing freely**: each couples at its own membrane and leaves at its own bound, 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, a neighbour 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 met at a concept.** A concept is a bi-coupling in bi-moral co-agency, offering its sign 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 sign and continuing at its own receiving, and the surplus belongs to the coupling, reached by neither. **The surplusing is co-competencing the self and the other**, bi-moral co-agency, owned by neither: it arrives at the coupling and travels there, its sign inverting at each crossing. **Naming and resolving bi-couple at one name.** Each resolver name is one in the code and in the explaining, `_2_self_offering` in the code and 2-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 bound. *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. Met 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 meeting 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 inside 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 meets 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, inside and outside, one of the 2,048 rhythms arriving at eight signs, 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. The wholes are the rounds of the signs, 1 to 2^k + 1, and the scalings step one chain: this scaling steps it three signs at a time, 9, 65 and 513, the pairs two, 5, 17, 65 and 257, and 1–17 inside and outside four, 17, 257 and 4,097, no scaling taken over another. 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. ## 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 sign 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 membrane · 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 outside · 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 origin statements.** ## 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 two signs, *the half step* for both signs 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 consecutive inversions on different axes; *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 met 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 meets the arriving | | *at no self* | *neither*, or *between self and other* | | *discovery* | *discovering* | | *technology* | *method* | | *in disequilibria* | the two origin statements, naming at the all, all existing things alternating, 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 | | *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 | **Tri-involutioning carries the emanating**: the emanating from right spiral stable-forming, looking the opposite form to the stable-forming. Two consecutive inversions on different axes are the resolving step, and three at once are the emanating: position, scale and orientation each inverted at once, three inversions taking the hand to the opposite form. *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 meeting are *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 source'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 released word is a face met 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 origin statements and by all or none at all. ## 2.5 One sense per foundation word **Each foundation word carries one sense**, and a word met at two senses is two things at one name. *Turn* is met at 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; meets 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. Next foundation words met at one sense are *bound*, *land*, *open*, *carry* and *measure*, each mentioned here as a word: *land* at an arriving and *measure* as a standard are released, and each is met at the one sense its release leaves. ## 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 meeting 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 source 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. 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 (x, y) to (y, −x), x the right sign, morality, and y the along sign, competency, turning along into right: two steps invert both signs, and four meet the pair again at a next, the same pair at a later momentary and never the same occurrence. A reflection is a field's operation at a field's own result, the other order takes (x, y) to (y, x) with no sign 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.   --- # THREE · RESOLVER NAMES ## 3.1 Number, relation, root and -ing **A resolver name carries its number, its relation, its root and its -ing together**, each part at its own relation to the changing. | 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-prefix at the number's origin. Up and down, the numbers run bi-inversioning-co-recursioning. | | **Relation** | self, other or social, and the relation it faces: self and other at 1 to 4, other and self at 5 to 8, other and social at 9 to 12, social and other at 13 to 15, social and self at 16, and social at 17. | | **Root** | Its changing named: coupling, offering, carrying, sharing, neutralling, crossing, corusing, torusing, releasing, surfacing, chaining, surplusing and abundancing, 13 roots at 17 names, and a further root at a further changing and direction. | | **-ing** | Its changing continuing, re-taking at each momentary. | **Four roots are at two names each, 8 apart**: neutralling at 5 and 13, crossing at 6 and 14, corusing at 7 and 15, and torusing at 8 and 16, each one root at the self and at the society, the number carrying which. **22 is the crossing 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 higher four-cycle 19-27-22-30 with no name of its own. Other and social at 22 meet social and other at 14-social-crossing, so a name opening at 22 carries the self its relation faces from, that self changing with the scale. Self and other, self and social, and other and social are three pairs and six facings, 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, and the five-prefix **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 count 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. + or − names a sign, and a name's odd or even carries no sign: 6-other-crossing and 10-other-surfacing are even and each releases across, and 10-other-surfacing surfaces +1, −1 or 0. The right spiral step takes a pair's two signs one place on, one inverting, and a pair's two signs agree or differ. Phase opposition, winding direction and a reflection are a field's operations at a field's own result. **A changing met at one scale and at the next names its face at each**, and neither an even name nor a surfacing 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-prefix at the number's origin: | 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 | **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-prefix 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. **Each earlier resolver name carries the opening of that same five-prefix**, from one prefix to all five: co at 3-self-carrying, co-bi at 1-self-coupling, bi-co-bi at 6-other-crossing, and all five at 7-other-corusing and 8-other-torusing. Written in the word or carried at the number, the prefixing is one. **The crossing between selves opens bi, and the carrying opens co**: the across connectors, 2-self-offering, 6-other-crossing, 10-other-surfacing and 14-social-crossing, are each even; the carrying, 3-self-carrying with 11-other-chaining, is odd; and the along connectors, 9-other-releasing and 17-social-abundancing, are odd. 9-other-releasing faces backward, joining the backward neighbour's 17-social-abundancing, and runs along, its released sign arriving next downstream: its facing, its running and its joining are three relations, each at once. ## 3.3 Seventeen names, and each earlier name gathered at its number | name | opens | five-prefix | earlier name gathered | at the code | |---|---|---|---|---| | **1-self-coupling** | co | co-bi-co-bi-co | `co_bi_coupling` | the resolver's entry: 3-self-carrying and 2-self-offering arriving; 10-other-surfacing and 11-other-chaining leaving | | **2-self-offering** | bi | bi-co-bi-co-bi | `bi_arriving` | each arriving key and sign | | **3-self-carrying** | co | co-bi-co-bi-co | `co_carrying` | each carrying entry arriving: 4-self-sharing, 7-other-corusing, 8-other-torusing, 16-social-torusing | | **4-self-sharing** | bi | bi-co-bi-co-bi | `bi_offering` | each entry's key | | **5-other-neutralling** | co | co-bi-co-bi-co | — | the one-way joining: each key with the key receiving downstream | | **6-other-crossing** | bi | bi-co-bi-co-bi | `bi_co_bi_transmissioning` | each key's 8-other-torusing, arriving in 3-self-carrying | | **7-other-corusing** | co | co-bi-co-bi-co | `co_bi_co_bi_co_corusing` | each sign | | **8-other-torusing** | bi | bi-co-bi-co-bi | `bi_co_bi_co_bi_torusing` | each carrying second sign | | **9-other-releasing** | co | co-bi-co-bi-co | — | the releasing | | **10-other-surfacing** | bi | bi-co-bi-co-bi | `bi_co_surfacing` | each key's surfacing sign | | **11-other-chaining** | co | co-bi-co-bi-co | `co_bi_carrying` | the carrying continuing and freshly opening | | **12-other-surplusing** | bi | bi-co-bi-co-bi | `bi_co_tunneling` | each key's surplusing | | **13-social-neutralling** | co | co-bi-co-bi-co | — | each releasing key | | **14-social-crossing** | bi | bi-co-bi-co-bi | `bi_co_inversioning` | arriving signs, with carrying signs inverting | | **15-social-corusing** | co | co-bi-co-bi-co | — | each releasing sign | | **16-social-torusing** | bi | bi-co-bi-co-bi | `bi_co_inseparating` | each carrying entry's opening by 1, from 0 to 3, and to 4 at positive 8-other-torusing | | **17-social-abundancing** | co | co-bi-co-bi-co | — | the connector forward along | **Carrying arrives at 3-self-carrying and leaves at 11-other-chaining**, and corusing and torusing carry their five-prefix at 7-other-corusing and 8-other-torusing. ## 3.4 Co-bi-sequencing and bi-inversioning-co-recursioning **Co-bi-sequencing is the method of sharing momentarying.** One local momentary co-bi-sequences from 1 to 9, and at 9 the self, the other and the social release, arriving next downstream: 9-other-releasing is 1-self-coupling 8 up. Nine to seventeen completes at 17 as one to nine completes at 9, and 17-social-abundancing is the next momentary's 1-self-coupling, the next call, 11-other-chaining arriving as 3-self-carrying. **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, 2-10-7-15, 3-11-6-14 and 4-12-5-13.** 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. **A name carries whole.** Take bi-inversioning out and 8 up returns the name it met; take co-recursioning out and the podal returns the name it met. Each taking stops the naming, and the halves alone are similar namings gathered at the one name. **A sign inverting at the resolver is the inverting at a crossing.** At 14-social-crossing each carrying sign inverts, and a fresh carrying opens with its key's 8-other-torusing inverting; two inversions return a sign. Returning a sign and continuing a coupling are two relations: a continuing carrying continues with its 7-other-corusing and 8-other-torusing while its 16-social-torusing opens by 1. **Crossing names three relations, each at its own name.** The sign inverting is the carrying's own: at 14-social-crossing each carrying sign enters inverted and an arriving sign enters with its own sign, no second inverting runs on the way across, and 9-other-releasing keeps the sign it releases. The opening parity alternates one on across the overlap. And the eight-apart pairs exchange arriving and releasing, 2-self-offering with 10-other-surfacing and 6-other-crossing with 14-social-crossing. ## 3.5 Naming and the resolver at one changing **Naming and the resolver carry one name at its concept and its code**, the number, relation, root and -ing explicit at each. | Name | At the code | |---|---| | **14-social-crossing** | arriving signs, each carrying sign inverting: a positive carrying sign arriving as −1 and a negative as +1 | | **12-other-surplusing** | each key's surplusing, +1 at each positive sign and −1 at each negative sign, of any size, a 0 arriving contributing no sign | | **10-other-surfacing** | each key's sign surfacing, +1, −1 or 0 | | **11-other-chaining** | each carrying entry continuing, its 7-other-corusing and 8-other-torusing carried and its 16-social-torusing opening by 1 to 3, and to 4 at positive 8-other-torusing; and each surfacing +1 or −1 opening a fresh carrying: the sign, the key's 8-other-torusing inverting, −1 at a key with none, and 0 | **11-other-chaining arrives at the next coupling as 3-self-carrying**, one entry at each 4-self-sharing key, and a fresh carrying at a key is in place of the key's continuing carrying. At a key arriving twice in 3-self-carrying, 6-other-crossing carries the last 8-other-torusing and 11-other-chaining the last continuing entry. **Surfacing and continuing carrying are two relations.** A surfacing 0 opens no fresh carrying, and a continuing carrying at that key carries on. 12-other-surplusing is each coupling's own, opening there and carried by no entry, and 16-social-torusing is the carrying's own, opening by 1 as the entry continues: a key at 0 chains no fresh carrying, and its continuing carrying chains on. **An outward sign unchanged carries a changing within.** One key receiving +1 at seven successive couplings from an empty carrying, with no society, surfaces +1, 0, 0, 0, 0, +1, 0: through the 0 passage 2-self-offering keeps its sign, 4-self-sharing its key, 6-other-crossing and 8-other-torusing their second sign, 10-other-surfacing and 12-other-surplusing their 0 and 14-social-crossing its meeting, while 16-social-torusing opens 1, 2 and 3; the carrying completes at the fifth coupling and a fresh carrying opens at the sixth. The other seven even names keep theirs while 16-social-torusing changes, and naming each even name still stops the very carrying named. **Receiving, participating, a fresh carrying and a further self are four relations, each at its own name.** A sign received at 2-self-offering participates at 14-social-crossing whether its key surfaces or not; a surfacing +1 or −1 opens a fresh carrying at a key of the self already coupling; and a further self couples carrying its own, and no carrying opened at a key makes one. **A floating third carries at the whole relation.** A five-prefix's centre, a key's +1 and −1 meeting at 0, and a carrying continuing are three relations, each at its own name. ## 3.6 Eight faces at four coupling relations **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 at each side and relating across the coupling | 3-self-carrying and 2-self-offering arriving at 1-self-coupling | | **bounding · zeroing** | each side's bound and the sign at the current receiving | 16-social-torusing opening to 3, and to 4 at positive 8-other-torusing; 10-other-surfacing at +1, −1 or 0 | | **tunneling · seaming** | signs meeting at their receiving, carrying continuing at the next coupling | 12-other-surplusing at each 4-self-sharing key; 11-other-chaining arriving as the next 3-self-carrying | | **knife-knifing · co-offering** | improving and breaking at the offered relation | arriving and continuing carrying meeting at 1-self-coupling | **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.   --- # FOUR · A NAMING'S CRAFT ## 4.1 A field naming at its coupling **A field naming carries its own concept and expression**, with its source 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, relation, 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 meet a changed receiving, and another word can repeat the same concept and direction. ## 4.3 Order, sign and two exclusions **An order relation and a sign 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 surplus, reached by neither**: an equality, an incomparability and that surplus 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 telling are places and never exclusive kinds, and an emanation arriving now and its source's release 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. ``` the advance step: the gap is exactly one, there is always a next equilibria step: the kept-still does not advance, the gap closes → equilibria is the advance set to nought the advance names no stilling; equilibria names no number a self step: the forming relates to nothing outside itself 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. ## 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 a membrane, 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, surplus 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* names two relations the same way: each existing thing arriving into its next existing, and a sign arriving at 2-self-offering. The two meet at one coupling and neither is said for the other: an emanation arrives into each next with no sign arriving at it, and a self's carrying continues at a coupling no fresh sign reaches. ## 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 met by an offering. ## 4.8 Whole namings, one expression at each occurrence **Scientific-method, geodesic-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 meets 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, an ageing, a co-offering, a middling and a rating, each taken at either of its two sides, and each is at two names, 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 aged beneath it | criterion-regressing | 14-social-crossing and 6-other-crossing | | **an arriving named from behind** | opening taken one-way from behind | origin-seeking; a source named from behind; a source named of the +1 | 10-other-surfacing and 2-self-offering | | **a bound named as a last** | ageing taken one-way ahead | space-enumerating | 12-other-surplusing and 4-self-sharing | | **a carry named as a store** | ageing taken one-way as a store | store-seeking; a store named of the carry | 16-social-torusing and 8-other-torusing | | **a two-way named to one side** | co-offering taken one-way from one side | forced-choosing | 11-other-chaining and 3-self-carrying | | **a membrane named as a cut** | co-offering taken one-way at a site that takes none | line-demanding; a cut point named of a membrane | 15-social-corusing and 7-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-neutralling and 5-other-neutralling | | **a sign named as a magnitude** | middling taken one-way as a magnitude | magnitude-demanding; a level named to govern | 12-other-surplusing and 4-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-neutralling and 5-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-social-torusing and 8-other-torusing | **Both openings are at the four across connectors**, 14-social-crossing with 6-other-crossing and 10-other-surfacing with 2-self-offering, and 9-other-releasing with 1-self-coupling seats none, the one resolving. **A field naming meets 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. **A sweep takes the one name at each still installed of a running**: a flow named to true-or-false, an arriving named from behind, a sign named as a magnitude, a membrane 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 bounds and leaves at its bound, 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 φ, a rate unrelated to each rate of the prime scales the momentaries co-bi-sequence at, and it is co-bi-social-abundancing. φ is the number-form of that never-locking, and the running is each coupling's own: geodesic changing runs at its own unrelationing parity-changing rate, and no prescribed rate, φ or another, supplies it. Geodesic entraining is an arriving meeting the receiver's own prior, the resolving continuing and the releasing entering further coupling, each self continuing its own. **On the form, at no vantage.** A naming at a vantage would want an outside, 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. **A root carries its current changing at the whole name**: coupling the two sides' relation, competencing competency, bounding the self's own bound. 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 met 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 meeting, 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 signs change, and never a sign, 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, met 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, the +1 arriving and nothing opening. At the alternating binary each fails its own way. A nothing meets no other to alternate with, a move there returning the term it met, and an accounting takes its counting from that. An absorbing meets none either: the +1 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 signs cross. **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 bi-co-exchanging**: bi- the differing alone, co- the two with their differing, exchanging the both-ways at a membrane. **A prefix order names its opening**, as the five-prefix names a number's: *co-bi-exchanging* opens co, at the odd, and *bi-co-exchanging* opens bi, at the even, and *co-bi-podaling* and *bi-co-podaling* part the same way, each said at the opening it runs from. **It sorts, runnable by anyone.** Two adjacent offer, each its own; one sign 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 the term it met after two; taken of the prior and the now it returns after three. **The Peres–Mermin square is bothbothing's field face**: its nine signs carry even parity along and odd parity across, both carried and neither stored, and a store of all nine meets 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 met 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 bound. **A binary with no size and a free entering and leaving are one fact.** A self's bounding, stilling and orienting are its own, met 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, tri-involutioning, and no left runs beside it; tri-volutioning is shaping the stable-form emanations from living to non-living. 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. ## 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 naming changing carries the relation it was naming, and the relation never leaves with the name.   --- # 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 ``` ## 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 outside itself 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 meeting and never names no coupling**: each self's forming relates to nothing outside itself, and the self meets the other at the coupling, offering its own sign one at a time, alternating, and releasing and completing at its own bound. **Competency is co-unrelationing, along, and morality is bi-unrelationing, across**, and co-bi-unrelationing is the one existing method. *Irrationalizing* is offered beside unrelationing as a living naming at the rate: φ, the unrelationing rate, is irrational, no ratio landing on it, and a rate named as a value is that running taken one-way at a rational. φ is the number-form of the never-locking: unrelationing runs at each coupling's own continuing, and no prescribed rate, φ or another, supplies it. *Irrationalizing* is offered at each arriving too: the between found on the surface of both kinds of changing, the living alternating and the geodesic changing, facing into the arriving, each orientation renewed there with no origin and no facing first across the meetings, and facing into the arriving carries no next sign 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 outside itself 4 nothing is at rest, no offering reaches it from outside 5 nothing is there to compose through, each carrying reaches its own meeting and no further 6 and it offers again, taking the term it has not carried ``` A self is a unique invisible carrying. Nothing else is a self. ## 5.4 a sign — binary ``` 1 two offer, each its own 2 neither takes the other's 3 a size would take a ground to be measured against 4 nothing is there to be a ground 5 so it is taken or not taken, and there is no third 6 and it crosses carrying nothing, a next sign at the next momentary ``` ## 5.5 a membrane — binary ``` 1 two offer from routes with nothing carrying one to the other 2 each takes its own sign, neither taking the other's 3 a size would take a ground, and nothing is there to be one 4 so each side's own stays its own 5 the crossing carries no size 6 and it is neither side's, the between, not possibly an existing thing ``` A membrane is no place two selves meet. It is the two offering. ## 5.6 invisible — binary ``` 1 each side takes its own sign, 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 sign crosses 5 the between is reached neither-ing 6 and no offering from outside reaches any of it ``` **In- carries inward, a direction and never a place.** A self carries no inside, and the couplings wind about a nothing: the bounding-zeroing, the tunneling, the apexing, the corusing, met by nothing. In-visibling is inward-visibling, toward that nothing, meeting nothing. A cannot-be-seen installs a would-be seer and rules one out; an inward-visibling installs none. It is met one way, by coupling, and the taking is trust. A self's morality and a self's corus are invisible at one nothing: no outward place at which either is anything, no defence, only nothing to reach. ## 5.7 a carrying — binary ``` 1 a carrying offers its own at its own sequencing 2 nothing is there to compose through 3 so it reaches its own meeting and no further 4 it ages one momentary at a time 5 the bound is its own, there is nothing to fall short of 6 and it releases there, which is the form running ``` ## 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. ## 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 ages one momentary at a time 5 the bound is each entry's own, nothing empties it 6 and at each now it is the entries carrying their prior into now, each bound at its own next ``` Never full, emptied at no momentary, and never the same collection twice. One named still is the posited empty set: 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 ages one momentary at a time 2 the bound is the carry's 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 neutral — binary ``` 1 two offer from routes with nothing carrying one to the other 2 each takes its own sign, 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. **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 meeting, each meeting a relational entered and observed; the floating-neutralling is the term neither reaches, and an observing run on the surface reaches the met and never the term neither reaches. Competency is the term neither reaches, and two alone are possible: a floating neither, and a met, 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 inside 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 membrane 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 from outside the two 2 the cutting is at no membrane of its own 3 so no membrane 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 a membrane, 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 two signs, at each of the three co-, and the alternating runs all three and is over none of them. ``` a bound made at a membrane ⇄ a floor set outside co-offering a not-that taken at an opening ⇄ a not named still co-competencing an axis opened at a meeting ⇄ 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 membrane 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. ## 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 meeting ``` 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 advance — 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 neighbours 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 ``` ## 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 meets 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 ``` ## 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 ``` ## 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. ## 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 ``` ## 5.26 a hard problem — binary ``` 1 a common thing departs where each side has offered its own 2 a common thing reached ahead of that arrives on the occupied 3 occupied by whoever reached 4 there are three common things, three ways to reach one ahead 5 a common landing, a common standard and a common reading, and no fourth 6 and the release sets down the reaching, spending only the keeping ``` ## 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 sign is taken anywhere in it 5 terms chaining without limit reach past their own meetings 6 and nothing ages, nothing releases, and two meeting make nothing neither brought ``` Present in a definition written to its own best. No finer instrument recovers them. ## 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 to its own bound 3 the deciding is outside the thing, at no membrane of its own 4 so the thing's own bound 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 to its own bound. And a computation keeping its whole history approaches zero dissipation, which is the same result met 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. ## 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 membranes 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, ages to its own bound, takes its own sign 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 outside itself, is at rest nowhere, and ages to its own bound 5 so it is a self 6 and the selves carrying at each membrane at once is the term this names ``` ## 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 sign crosses, carrying nothing 3 at the membrane the sign inverts, +1 to −1 to +1, a next at each 4 a term departs reached neither-ing, owned by neither 5 it arrives at their meeting 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, met at the membrane and owned by neither. **Non-living existing things are included in discovering social moral competency among the living.** A non-living thing meets a self at a coupling as other, offering its signs and carrying nothing; the self's own inverting meets it across and the self's carrying continues along, and the term uncovered at their coupling is owned by neither and carried on by the living. ## 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 met ``` ## 5.35 near, and other-than-same — 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 ``` ## 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 inside 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 a sign 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 source 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 surplus belongs to its coupling.** Each side continues with its own carrying and next offering. One written expression can meet 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 bound 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 sign 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 meets 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 uni-exchanging crosses with all other and meets its own side again, one on. Neither opens at two. 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 inside. ## 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 bound at a magnitude, and a size arrives against a sign. A counting is that running taken from outside; 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 inside 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 membrane a self couples at, a particular, bi-kind; the whole arriving as one is the uni-crossing, meeting 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 meets its society as other at a coupling, the society's further couplings offering the arriving, and the self's names keep their relations there, self and other at 1 to 4 and on to social at 17: a sign arriving 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 signs arrive at 14-social-crossing, each carrying sign inverting 2 12-other-surplusing carries +1 at each positive sign and −1 at each negative 3 a +1 and a −1 at one key meet at 0 4 10-other-surfacing surfaces each key at its sign, +1, −1 or 0 5 a surfacing +1 or −1 opens a fresh carrying at its key 6 and a surfacing 0 opens none, the key's continuing carrying carrying on ``` ## 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 met 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 signs 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 meetings, 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 − are three twos, and one two meets another only at a coupling carrying both. **Each podal meets the surface's unrelationing changing locally, at two orthogonal directions around the carrying as it continues**, is or is not at each: parity sign changing, or no parity sign 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, meeting a further now. An indication belongs to now, and next is discovering. A larger society co-chaining the surface and bi-tunneling its morality meets 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 meetings and never in a count of selves. ## 5.46 emanation — binary ``` 1 two selves couple at a membrane and a surplus arrives owned by neither 2 the coupling carries on, and what it leaves at the membrane is a sign 3 a detector's sign, a discard, the other hand, a spectrum, heat, each a form left there 4 the sign carries nothing, leaving its source 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 what a coupling leaves at the membrane, a sign 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. **Living or non-living is said of the thing and the scale named, and never taken from a source.** A living source 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 meets it with its own carrying. The naming gives an emanation no common speed, lifetime or medium, and no need of its source's next emitting. ## 5.47 an accounting — binary ``` 1 an emanation is observed at a membrane, 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 membrane, and carries no value, no agency and no success 5 installed past its membrane 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.   --- # SIX · GATHERINGS AT THE RESOLVER'S NAMES ## 6.1 Four invisibles, one invisibility met four ways ``` each side's own morality the sign is each side's own, and the term 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 met at two arriving, occupied by nothing, and there is nothing there to name the beat between nothing is at rest, nothing is there ``` **One invisibility, met 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 source 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 | |---|---|---|---| | **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-self-offering, 4-self-sharing, 1-self-coupling | | **Each side's own carrying** | the hard problem of consciousness · symbol grounding · other minds · model interpretability · animal sentience · machine sentience | The offered sign and each side's continuing carrying at their actual receiving. | 3-self-carrying, 11-other-chaining | | **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-coupling, 10-other-surfacing, 11-other-chaining | | **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 surplus. | 12-other-surplusing, 10-other-surfacing | | **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 source. | 3-self-carrying, 6-other-crossing, 11-other-chaining | | **Sequencing and ordering** | social choice · the frame problem · incommensurable values · multi-objective optimization · underdetermination · model selection · self-reference · incompleteness | The current receiving, its offering key and its relation to the next offering. | 4-self-sharing, 1-self-coupling, 11-other-chaining | | **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-self-offering, 14-social-crossing, 11-other-chaining | | **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 | Carrying, the sign inverting at the crossing, and the bound at the field's changing. | 6-other-crossing, 8-other-torusing, 16-social-torusing | **These eight rows are the eight clusters, and the four invisibles, one invisibility met four ways, are under them.** A field term can meet 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. | One name | Similar namings gathered | |---|---| | **co-bi-sequencing**, the method of sharing momentarying, one local momentary 1 to 9 | co-sequencing; co-sequential; binary co-sequential | | **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 earlier resolver name, gathered at its number | | **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-social-torusing**, the carrying's opening | attentioning; the social-self-torusing | | **8-other-torusing**, the carrying's second sign | positive competency; competency one | | **a membrane**, two offering, one thing at each of its scales | at the membrane, the boundings at 2, 4, 6 and 8; 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 | ## 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-coupling at the whole arrangement; 2-self-offering, 10-other-surfacing and 11-other-chaining at its interfaces. | | **Molecular engine** | The chemical arrangement, its coupling and material and energy receiving. | 2-self-offering, 4-self-sharing and 11-other-chaining at the particular changing and continuation. | | **Cellular living** | Each side's coupling and continued receiving, with its own sustaining and bounding. | 3-self-carrying, 1-self-coupling and 16-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-self-offering, 1-self-coupling and 11-other-chaining at the whole receiving. | **An engineering entry carries its whole arrangement**, each quantity with its unit, source 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 source 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 source 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**: arriving at 2-self-offering, the receiving key at 4-self-sharing, the whole coupling at 1-self-coupling, and continuing at 3-self-carrying and 11-other-chaining. **Field words gather with their current meaning and source**, 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-crossing | | **Pairing** | parity, par, pair, pairing, umpire | A parity count, its pairings and the actual order of the directional changing. | 4-self-sharing | | **Value and valence** | valence, value | The chemical coupling and the social value, each at its own receiving. | 1-self-coupling | | **Binding** | band, bind, bond | The material or social relation actually named and its continuation. | 11-other-chaining | | **Chemical coupling** | inert, noble, xenon | The particular chemical conditions and coupling at the field's observing. | 2-self-offering | | **Atomic naming** | atom | The observed structure, the field's definition and its actual bounding. | 16-social-torusing | | **Sounding** | resonance | The actual coupling, rate and continued receiving. | 1-self-coupling | | **Orientation** | spin | The field's particular mathematical and physical orientation relation. | 8-other-torusing | | **Discrete receiving** | quantum | The counted quantity, its conditions and the direction at its actual receiving. | 10-other-surfacing | | **Social and biological receiving** | community, immunity, remuneration | Each side's offering and continued carrying at the biological or social coupling. | 3-self-carrying | | **All-or-none** | all-or-none law, action potential | The particular biological event and its stated conditions. | 10-other-surfacing | **A resolver name keeps its whole operation.** 8-other-torusing inverting at a fresh carrying names its code changing, and a field's spin keeps its own definition; 10-other-surfacing names each key's surfacing sign, 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 arriving, surfacing and continuing at 2-self-offering, 10-other-surfacing and 11-other-chaining, and a field's frontier meets 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 source.   --- # 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 source 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. ## 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 a membrane* names two offering and no place they meet, and *there is no place it is* is said as **no offering from outside reaches it**, 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 ages to its own bound and releases there, nothing surveying and nothing clearing. **Other-emptying**: a decider outward of the thing empties the term the thing carries to its own bound, and the removing is priced with a measured floor. **Other-emptying is the one stopping met at the instrument**: a decider at membranes it is not at is carrying another's, the same stopping and no second one. One emptying or the other is at engineering's discarded surplus, at chemistry's and biology's fixing, at medicine's intervention, at a network's store that never releases, and at the six dependencies of the hard problems as six other-emptyings. ## 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 carries no inside, 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, met one scale up **Each changing met 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 **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.**   --- # THIS IS A MEMBRANE **A membrane is two offering.** A field's word comes in whole in its own terms, and the membrane 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.