the phenomena of totality (celestial metaphysics and natural law) 3.6.nb

The Phenomena of Totality

Celestial Metaphysicsand

Natural Law

Being an Inquiryinto

The Noumenal Condition

RC Mann-Price, PhDThe Cambridge School of Pure and Applied Wizardry

(at Cardiff, Wales)

November the 12th, AD 2016

Ten thousand million souls whisper into infinitythe words we know by heart: They are wordsof life giving life (and of hope giving measure)

to the time of us making good purpose.

2 The Phenomena of Totality (Celestial Metaphysics and Natural Law) 3.6.nb

0. SetupTwo systems S and T may vary quite broadly in respect of capacity (under a noumenal type ), and thenagain they might vary only in the minutest features (under some other noumenal type ’). An easy way ofkeeping track of such things is to presuppose a reference condition whose own variation with noumenaltype might easily be standardized.

1. Protocols, Proofs, and Procedures

1.0. The Great NullFor any model of hyperbolicity, there is a model of duality such that the hyperbolic dual applied to themaximal system gives the corresponding null system; it is written 0hyp. The greatest lower bound for thecosystem comprised of all such nulls 0hyp is written 0 g.l.b. all 0hyp , and it is sometimes called thegreat null.

1.1. StandardizationWe have cause to investigate the behavior of an experimental effect: It is the Price-Hecker effectexpressed (I think) in the phenomena associated with anomalous permittivity. The problem here (as Isee it) is that countless bits of minute variation play havoc against a control system built to leverage theoperation of a certain object system, which is a system of definite noumenal type (say, ).

In order to address the bugs and features of this problem, we may peer into each variation (ofnoumenal type using, say, a rule of the form ). And, in the successful handling of this problem, weobtain a partial solution by studying the behavior of the great null 0 (once it is localized over an arbitrarilychosen noumenal ). Moreover, our findings are presented as a standard reference condition givenexpression under the following protocol:

1. 0 ; standard reference condition (setup)

2. eval 0) ; evaluation (at arbitrary noumenal )

3. 0( ) ; effect

4. coloc0 ) ; definition 0 coloc05. coloc(0, ) ; argument form (absorb the filament)6. loc( ,0) ; duality7. loc 0 ; filamentation8. loc 0 ; move parenthesis9. 1 0 ; notation10. 0 ; notation

11. 0 = eval 0) ; equality passes from 2 to 10

1.2. TotalityThe basic result of this section is the description of an ordinary parameter as a totality of indefinite form.We consider, in particular, those parameters (pronounced, nu) whose B-norm is equal to the B-norm of

The Phenomena of Totality (Celestial Metaphysics and Natural Law) 3.6.nb 3

a sort (A, ). Here, the system A is a contact arrow, which is an arrow of the formA : ; ,

where is a given index system, where ' in d, any d : d d is the contact lemma, where is anindex within , and where is a contact within . Also, the system is a weighting arrow, which is anarrow of the form

: ; ,

where is a given index system, where x, x is the real number system, where is anindex within , and where is a real number within . Moreover, the condition

B = A, B,

uses a B-norm [see Appendix B] to show that the following evaluation lies within a B-proximity to :

eval A, .

Furthermore, the approximation of in terms of (A, ) points up an interesting feature of the term coloc0,which distributes 0 over each . And, because this distribution is not well-defined, we may think of itscodomain as a (non-parametric) system of many distributions: It enables our notation to reflect a creativeambiguity in the reference condition 0 , and this condition is expressed by replacing each occurrence ofthe mundane parameter with a symbolic expression of its totality; it is written

0 .

The whole matter is given precision by the totality theorem.

Theorem. totality id coloc0.

Proof. The following steps of logical procession will in sum affirm the result:1. totality ; supposition2. eval totality ; evaluation (at arbitrary noumenal )3. totality( ) ; effect4. ; notation5. 0 ; decomposition (of effect)6. id coloc0 ; operator form7. id coloc0 ; factorization8. eval id coloc0 ; operator form9. id coloc0 ; argument (without evaluation)10. totality( ) = id coloc0 ; equality passes from 3 to 711. totality = id coloc0 ; 10 holds across all noumenals

Of particular interest is the co-location corollary.QED

Corollary. coloc0 totality id

Proof. The system coloc0 splits the system totality, giving the split exact sequence

id id coloc0 coloc0,

which is equal to the canonical reduction sequence

id totality totality id.

Here, the theorem gives totality id coloc0, so that the rules of formation (for a split exact sequence)give the intended result that coloc0 totality id.


QED

1.3. SupportWe ask that a null system 0 be localizable over each noumenal type (say , ', ...), writing 0 1 0together with the support condition supp 0 . This condition is satisfied by the following protocol:

1. = supp(0 ) ; support condition2. = supp( 10) ; definition3. = supp[loc( ,0)] ; localization operator4. = supp[coloc(0, )] ; duality5. = supp[coloc0 )] ; filamentation

6. = supp[0( )] ; 0 coloc0

7. = [supp(0)]( ) ; factorization

This protocol amounts to a logical proof that the composition supp(0) is equal to the identity operator at .

Moreover, because the construction of supp(0) holds independently of any particular value for the noume-

nal type (say, ), we get the result supp(0) = id.

1.4. Combination (a reductive procedure)Two systems (say, S and T) may be combined directly if they share a common null, but not if their respec-tive nulls differ in any way. For, suppose S to have (noumenal) type , with T of type ’, such that and

’ are unequal. Then, the respective nulls 0 and 0 ' will differ, both as standalone systems and (again)as attachments. This means that S and T may combine (as totalities) if their respective types arebrought into a more neutral condition (a more even condition of accord). That is, rather than trying tocompare the proverbial “apples and oranges”, we may normalize S and T relative to their respective nullcurrents. Specifically, we may define the null current for S to be

Wo 0 supp 0 ,

where the standard support condition supp 0 gives the expression Wo 0 . Similarly, the nullcurrent for T is

Wo ' 0 ' supp 0 ' ,

where the condition supp 0 ' ' gives the result Wo ' 0 ' '. Thus, the reducts S/Wo and T/Wo' arecurrent-reduced; they are normalized to one (and the same) standard; and, in consequence, these tworeducts combine directly. This is our reductive procedure.

1.5. A Null Current ProtocolThe null current may be written in terms of the co-localization filament at 0 by considering the expression

0 coloc0. Its reduct relative to the identity operator id may be at the noumenal1. Wo 0 supp 0 ; null current (the definition)2. = 0 ; supp 0 = (support condition)3. = ( 1 0 ; localization (notation)4. = [loc( ,0)]/ ; operator form (notation)


5. = [coloc(0, )]/ ; co-localization (duality)6. = [coloc0 ; filamentation (at 0)7. = coloc0 /id( ) ; identity operator8. = (coloc0 id ( ) ; factorization

9. = (0/id) ; 0 coloc0

10. = eval (0/id) ; evaluation

11. = eval [0/supp(0)] ; supp(0) = id, substitution

12. = eval [(id/supp 0] ; factorization13. = eval [eval0(id/supp)] ; evaluation14. = (eval eval0)(id/supp) ; composition

In order to interpret the argument id/supp as it appears in line 14 of the null current protocol, we say thatthe reduct of the identity operator (relative to the support operator) may be evaluated (with respect to co-

localization over 0, which is written in line 9 as 0), giving the null current density (prior to evaluation overthe noumenal ).

2. Set Theory (A Systematic Approach)

2.1. Intrinsic SetsIn the Godel-Bernays system of axioms, an intrinsic set may be a proper class, but never an improperclass. And, an extrinsic set may be either proper or improper as a class. In the Zermelo-Fraenkel sys-tem of axioms, a set exists if (and only if) it is the reduct of an extension (relative to some foundation).

2.2. Grammar-zeroGrammar-zero is a system of rules about how the parts of an ordinary set hold together. The set may bestrictly extrinsic, it may be purely intrinsic, or it may be a mixture of both extrinsic and intrinsiccomponents.

3. Basic Syntax (The Plumbing of Truth)

3.1. A System of LogisticLogistic is the study of the infrastructure beneath (or within) one or more logics: It is the machinery out ofwhich a logic may unfold its many propositions (and their respective assertions). And, as this machineryworks prior to the instantiation of any particular logic (any particular bit of syntax), we say that logisticoperates at a level of abstraction described by grammar-zero. Similarly, each syntax is said to operate ata level of abstraction described by grammar-one.

3.2. The Sublogistic ContinuumA continuum is a complete, transitive system: It is transitive in the sense of square-inclusion (its arrowpasses from here to there in such a way as to include its own square). It is complete in the sense that no


gap occurs within the transit (its arrow neither skips, jumps, nor hops in any manner of transit). A logisticcontinuum is a system whose reduct (relative to the given logistic) is a continuum. A sublogistic contin-uum is a system which no logistic may reduce to continuum: It is a system which reduces to continuum if(and only if) the reducer is a sublogistic system. Here, a system is sublogistic if its noumenal type liesbeyond the range of any contact parameter: It cannot be covered by the contact lemma

in d, any d : d d .

3.3. The Primitive SystemI am interested in a system of logistic based on the Hilbert-Ackermann axioms: It is a reduction of thesystem due to Hilbert-Ackermann (gotten from Russell and Whitehead’s Principia Mathematica), and it isparenthesis free. Also, there is a second version of this reduced system, and it is called Hilbert-Acker-mann reduced, version two; i.e., HAR2.

3.4. The Grid SystemAn assortment of grids (and of grid-theoretic tools) are used to build a pre-logistic continuum (it is weakerthan a logistic continuum), and we study it as an error grid.

3.4.1. A Character SystemAn idempotent is an arrow p such that p2 p. A grid is a pair of idempotents p0 : X0, X1 X0 andp1 : X0, X1 X1 over a shared domain. Or, loosely speaking, it is the domain X0, X1 itself. A charac-ter system is a grid X0, X1 with sign X0 and character X1, so that a signal is an arrow from X0 to X1. Acharacter grid is a grid X0, X1 for which X0 and X1 do not meet. This means that the character isrestricted to X1 only, and that X0 is free (of character).Remark. The idempotents of a character grid are written p0 free and p1 char, so that we haveX0 free X0, X1 and X1 char X0, X1 .

3.4.2. An Error GridA propagation grid is a character grid X0, X1 with propagation concentrated in X1 only. A propagationis the capacity of a displacement to conduct signal: It is an artifact of transitivity, and it is sometimescalled a displacement current. An error grid is a propagation grid X0, X1 with error propagated in X1only. An error is a discrepancy in the reported value (as opposed to the true value) of a displacement:Its presence is detected by reducing each reported value relative to the true value, and the resultingcurrent is sometimes called an error signal. A logistic continuum is an error grid X0, X1 with X0 isomor-phic to a sublogistic continuum.

3.4.3. Error Signal PropagationIt happens in the course of conducting an experiment (especially an experiment on the anomalouspermittivity) that an initially trivial measure of error may grow to compete with ordinary signal propagation.In fact, the error signal occasionally overwhelms the ordinary signal in such an interesting way that thestudy of error propagation becomes a pursuit in its own right. There are a number of interesting bookson this problem, and my favorite is that of Philip R. Bevington, Data Reduction and Error Analysis for thePhysical Sciences; McGraw-Hill (1969). It is particularly useful in its handling of the dispersion relationfor an experimentally detected resonance. Indeed, it came up in consequence of my work on the experi-mental effect of Compton.


4. Whitehead-Russell Notation

4.1. Predication (with a simple argument)The Whitehead-Russell (WR) formula

. x .fx

reads, “It is the case that for each x, f holds true of x.” This formula is called an assertion, and it is said toassert the proposition

x .fx,

which reads, “For each x, f holds true of x.” Here, the term (x) is called a universal quantifier, and it issaid to instantiate the symbol x universally (in some universe of discourse, say U). Also, the term fx iscalled a predication, and it is said to predicate f of x (in some realm of predication, say R).

4.2. Predication (with a non-simple argument)The WR formula

. , x .f x

reads, “It is the case that for each pair ( ,x), f holds true of the juxtaposition x.” This formula, is said toassert the proposition

, x .f x .

Here, the juxtaposition x is gotten under a passage of the pair ( ,x) to the predication f( x), with a non-simple argument x.

As a nice instance of this formula, we consider the special case that x is a weight (of time), witha system weighted (to varying degree) both in and out of time. Here, time is an active propensity(toward motion, or activity), and a weight of time is a passive propensity (say, energy).

Consonant with this, true motion is active, and apparent motion is passive. True motion is carriednot by frames (nor by their metrics), but true motion is carried by frame-hopping (or by gauge proces-sion). Here, the gauge is a modular system of metrics (with each metric a measure of proximity). Also,gauge procession is likely to derive from parameter acceleration, which expresses a curvature in thedistribution of parameter drift.

5. Sheffer Stroke Notation

5.1. The Parts of a FormulaThe Sheffer formula

p|q

reads “Not both p and q hold true,” where p and q each denote a formula. Here, a formula is a separableexpression: It is studied at a level of abstraction described by grammar-one (which is syntax). Also, anexpression is a bit of whatnot (gotten out of inchoacy): It is a term of logistic which may or may not be


separable, and it is studied at a level of abstraction described by grammar-zero (which is logistic). Whatis more, an expression is said to be separable if one or more of its parts may be parsed into a conditionof preponderance: That is, we ask that the expression may be parsed into a system of entities, where anentity is that which may be considered.

5.2. The Matter of AbstractionThe precise correspondence between mere parsing and actual separation is expressed under a condi-tion of preponderance. The sense of this condition (of preponderance), which may be subliminal(meaning beneath the level of discriminated awareness), is that an otherwise inchoate bit of whatnot maybe raised from a level of inchoate garble to a level of consideration. And, because each level of whatnotappears to succeed some deeper level of abstraction, we get a continuum of logistic running up anddown the entire ladder of abstraction. That is, our notion of a sublogistic continuum penetrates each (andevery) noumenal capacity, resolving its expression into a system of many levels -- many levels ofabstract consideration.

5.3. Consideration

5.3.0. OverviewWithin each sphere of volition, we may identify a condition through which the noumenal matter of anontological process (the one called entelechy) is considered. This condition gives a parametric ambiguityby way of setting up a ground (a noumenal ground). The ambiguity is expressed as a modular latitude(vis-a-vis the localization retract). That is, the parameter is retracted (relative to a localization of the nullover the noumenal), giving a flexible source of control phenomena. Specifically, the ontological processresolves itself over a spectrum (a broad-band spectrum able to adapt its resolving power to the resolutionof any special component). This adaptive process is called specular contraction, and it gives easyaccess to each actionable domain (to each division of active and inactive capacities).

Here it happens that several species of domain interference emerge relative to the inactivecomponent (the homogeneous part of action). In fact, the inactive component seems to propagate aripple effect across multiple universes (collated within a cosmos). Moreover, a broad class of fringeeffects seems to dominate the regime of low-lying complexity, giving rise to an interesting species ofsurface potential supporting the transcritical response of special devices.

Now, each special device is supported by a plexus of many universes, with each such universebearing the translocation of an entirety generated out of a specific module. The specific module lives in ascheme of tension whose underlying ambiguity codes a structured index. And, this index enables eachREM (each random element machine) to navigate its corresponding cosmic plexus. Because of this, weobtain a plexure (an action of the index on its corresponding plexus). Thus, we are able to describe theadaptive filamentation of each cosmos into its respective system of universes. And, this system ofplexure dynamics renders the active part of plexure into totality.

5.3.1. VolitionIn the matter of noumenal capacity (and of abstract resolution), we find the subject of a proposition atwork within its sphere of volition. Actually, this sphere of volition is a hypersphere: It is a nested systemof spheres in which each successive sphere shares a common origin (or attachment, say 0 1 0, withthe null system 0 localized over the noumenal parameter ). The problem, then, in a navigation of anyparticular act of volition consists in the identification of some bit of whatnot (say, w) relative to a given


system S. The overarching process through which this identification is conducted is called consideration,and its definition occurs at three distinct levels of ontological abstraction.

First, a consideration is a relation from an unknown entity e’ to a known entity e”, and it is writtenr : e ' e ". Second, a consideration is the graph of a condition , where this condition is written

: p ' p " p. Third, a consideration is an act of volition through which a bit of whatnot (say, w) is givencorrespondence with a system S, and it is written w::S.

5.3.2. ConditionA condition is a relation of the form : p ' p " p; x,y x,y , where the entity p’ p” is the direct productof two special bits of whatnot (they are p’ and p”), and where the entity p is the cupola related to p’ p”.Here, the term p’ is called the indicative, the term p” is called the predicate, and the direct product p’ p” isa pair of terms which (by virtue of their product) give an entity (it is a preponderant bit of whatnot and, assuch, it may be considered) of the sort drawn forward by the cupola p.

5.3.3. IdentificationAn identification is the noumenal import of a consideration: It is an ontological process through which anoumenal ground (indicated by some value of the parameter ) is established. Specifically, this ontologi-cal process consists in a localization of the null system 0 over . Notice, here, that no particular localiza-tion is distinguished from among the many admissible procedures. Rather, the term 0 is used toembody the null 0 over the parameter in a deliberately ambiguous fashion. In other words, the system0 is ill-defined until some condition of the form

: 0 0 ; a, n n mod a

is introduced, whereby the parameter well-defines the reduct 0 as an object (it is a special primitive,and it serves as an ontolog). Also, notice that the filament a may be expressed as a localization ofover the entity a within . In fact, a is the noumenal retract of over a (vis-a-vis localization). Thus, theterm n mod a is described as the modular retract of the quasi-null n within 0 . Finally, notice that thequasi-null is a loaded bit of : It is a bit of loaded with some local part of the null system 0 (per localiza-tion 1 0 of 0 over ).

5.3.4. Specular contractionAs an example of identification, we may see the process by which a broad spectrum of activity isscanned in massively parallel fashion. We may see how an interesting bit of activity within this spectrumtriggers a focal event to collapse the “resolving power” of a spectrum to a more coherent neighborhood ofthe given bit of activity. To be precise, here, we describe the process of concentrating a broad-bandresolving power to a relatively narrow range of spectral activity as a contraction of that power over anarrow-band window of activity. Specifically, we say that a process of specular contraction is a contrac-tion in the specular domain: Here, a contraction is gauged by a modular system of metrics, where eachmetric is a measure of proximity (which may or may not involve some ancillary notion of distance, as in adistance metric).

5.3.5. Actionable domainAn actionable domain is a domain D (typically a grid, and possibly a direct product) whose embeddedvertical Dactive is actionable over D. Here, we may see the capacity through which an act of volitionrenders some part of D active (together with an ostensible inactive part Dinactive). The point to notice,here, is that mere consideration carries the effect of distinguishing some corollary division of an action-


able domain D into active and inactive parts.

5.3.6. Domain interferenceThe phenomena of domain interference occur in consequence of the division of an actionable domain Dinto an active part Dactive and an inactive part Dinactive. Specifically, the fluxions of Dinactive carry relativelylittle (or no) power, yet they nonetheless convey a homogeneous part of action (much as a DC offsetwould do for an electronic signal). Also, the fluxions of Dactive carry an inhomogeneous part of action(much as an AC signal would do). In other words, the inactive part of D express a gauge-homogeneity,and the active part of D describes the parts of a protoring 1 which run orthogonally across each gauge-homogeneity. Finally, the domain interference is an effect of the inhomogeneous response of D to atranslocation of Y (a scheme of tension whose contact parameter bears the reciprocity : directlyto the gauge ). Evidently, D is a subsystem of the entirety, say Z*, where the zero condition Z is (asusual) an -cosmos (which is a system of many universes, say 10504). What is more, I think that Dinactiveis a subsystem of Z (possibly an amalgam of many universes joined, or overlapping, and giving rise to adensity term on the diffusion of activity from Dactive). Thus, a domain interference is a presumptivelyripple effect across multiple universes within a perturbed -cosmos. In fact (and here is the rub), we mayinvoke the indicial hypothesis [Analysis, page 169] as a means of simplifying the collation T E j tothe form T E j. This move is crucial in the sense that T is the specific agency of comprehension;that is, T passes each behavioral module Ar in the scheme Y (through translocation j and a zero-gaugeE) onto the above gauge .

5.3.7. Fringe effectsGiven the low-lying (but ubquitous) complexity of a domain interference across a cosmos of 10504 uni-verses, we may expect to find a nontrivial layer of (otherwise inexplicable) activity in the surface potentialof each cosmos (each zero condition Z). And, because the active part of an actionable domain D runsorthogonally across the inactive part of D, we may expect that the normal component of each activity at(or proximal to) the cosmic boundary to show a fluctuating system of processes, locally vacillatingbetween outward and inward modes of activity. The corresponding ripples would probably be very slightat first, but with the passage of much activity some measurable bit of coalescing should occur. And,indeed, this is precisely the degree of cosmic-background noise observed in data gleaned from theCOBE-Spitzer experiments. Moreover, since my own predilection for experimentation runs straight awayinto the anomalous permittivity of a medium (either with or without a known dielectric substrate), I feel asthough much of the fringe phenomena is explained by a contribution from the dielectric susceptibility ofthe given medium (especially those with a transcritical density of special polymers). Accordingly, thevalidity of my anticipated experimentation with a parallel-plate condenser (distended of mylar) is hoped toisolate such fringe activity through a number of useful effects. That is, my statement of effect shouldprobably read, “The anomalous permittivity shown by the COBE-Spitzer data may be explained bydomain interference arising from the translocation (and consequent collation) of a medium driven to atranscritical regime of device response.”

5.3.8. Plexus (the indicial reduct)A plexus is the indicial reduct of a cosystem: It is the reduct of a cosystem C relative to the systemwhich gives C index; it is written C C . Notice that a plexus can be written as the final term of a splitexact sequence as follows

C C (exact at C).


To see the appeal of this technique, a plexus of many universes is constructed as follows.

A universe is the image of a module under translocation. The translocation is an arrow of theform j : Y Z; Ar Ur , where the term Ar is the r th behavioral module (an anxiety robot) in the scheme Y= Dom (given a tension : Y), and the term Ur is the translocated entirety of Ar . That is, Ur is ther th specific universe in a cosmos Z. However, this particular decomposition of Z is not unique. For, eachindex r within the -spectrum Q might be replaced by a more arbitrary index drawn out of a given indexsystem . And, because this sort of ambiguity is (in essence) arbitrary, we should expect a component(small, I think) of each fringe effect to express the underlying ambiguity.

Now it happens that each collation (T = E j) may satisfy multiple index systems, so that partialinformation about an individual may not be adequate to distinguish that from another such, say ’.This ambiguity is relevant because the index system (or, possibly, another such ’) specifies thestructure of a suffusion of many universes in Z. That is, each indicial system is equipped with someparticular structure (where a structure is a system of relations). Thus, to each indicial system (a struc-tured index), there is a corresponding plexus in Z. The matter concludes with the following definition:

A cosmic plexus is the plexus of a cosmos Z (the zero condition for a REM -- a random elementmachine); it is written Z Z .

5.3.9. Plexure (the dynamical plexus)A plexure is an action of the form : Z Z . A cosmic plexure is a plexure whose reduct Z Z isgotten from a cosmos Z. If a cosmos Z is considered to evolve under a plexure , and if we have theinactive part Dinactive of an actionable domain D as the non-indicial part of , then we get that Dinactive isisomorphic to the specific null 0 , and that Dactive is isomorphic to (without 0 ). In other words, our littleaction (the plexure) would satisfy the following expression for totality (given the noumenal ): 0 .Here, is the mundane term of action, 0 is the attachment (the specific null), and is the correspondingtotality (given ). What is more, the whole system of domain interference (and fringe effects) falls directlyout of this dynamical arrangement of Z into its translocal plexus. In other words, we have identified asystem of plexure dynamics, and that system is defined as follows.

A system of plexure dynamics is an adaptive filamentation of each cosmos into a correspondingsystem of universes, with the active part of plexure (which is ) rendering (under ) the totality of plexure(which is ).

5.4. The Sheffer BitNow it happens that in the formation of an arbitrary plexure we may encounter mutually exclusive pairs ofnon-overlapping universes. This is a matter of some importance, inasmuch as our tried and true beliefsabout overlaps and underlaps [Bart Kosko] tend to fail in some very interesting ways.

In the first place, our systems bear (in general) very little resemblance to the crisp little objects atwork within the algebraic category of sets. Boundaries and limits are terribly indistinct, tending to trail offinto weak diffusions seeming to vanish at infinity. These vanishingly weak diffusions sometimes returnwith big surprises (even on the other side of infinity). Attributes (if any) tend to warp their way around asystem without any easy sense of uniformity (or even of attachment). Conditions (which are often ill-defined) may attach firmly in one part of a system, and yet slip entirely in another part of the same sys-tem. And, if any species of equipollence might be required, then we are really out of luck: There is asense in which all systems share in an underlying nullity which is everywhere we look, yet nowhere to beseen.

In the second place, the ability of a system S to separate a system S’ from a system S” is rarely


absolute. Rather, there are degrees of separation between S’ and S”, and the expression of thosedegrees may or may not be sensitive to the behavior of S. So, we need a way of gauging sensitivity tothe behavior of a fixed system S. And, we further need a way of gauging the response of a Shefferstroke device relative to changes in the value of S (be the transitions sudden or gradual).

In the third place, two systems S’ and S” that underlap now might readily overlap later. Or, it mayhappen that my data against S’ and S” show that they always underlap, while your data show that S’ andS” always overlap. Strange on the face of it, but useful when probing deeper into the bizarre mysteries ofa general purpose continuum, we consider both views to be accurate reflections of two objective realitiesabout the same pair of systems S’ and S”. And so, to make sense of this type of valency, we propose theparametric specification of a slack system S (sometimes it is T) which, if taken with the pair (S’,S”), givesa triple [S,(S’,S”)] to be studied below. This third system is called the Sheffer bit.

6. Dichotomy

6.1. Dichotomy and TransitionThe age-old problem of dichotomy and transition has been suggested above (by the discussion of separa-tion; i.e., the separation of neighboring systems S’ and S”). And though we are accustomed (in logic) tothe proposition that a logic may be given entirely by a single device (parametrized by a single system,both changeless and insensible to context), we do here consider that the single parameter for a logic beable to change across a cosystem of more than one system. That is, we consider a graduated scale ofadmissible systems (say S, T, etc.) comprising a cosystem C, out of which a veritable plenitude of Shef-fer stroke symbols might be chosen and applied.

The matter is given schematic representation in the following figure:

The most important feature of this figure is, of course, the distinction between the following two scenar-ios: i.) S’ and S” at the level of an S-stroke, and ii.) S’ and S” at the level of a T-stroke. In the firstscenario, we get a device of the form S ' S S " S S',S" whose truth value is positive-definite (we scalethe thing to unity, say the real number one). In the second scenario, we get a device of the formS ' T S " T S',S" which is expected to fail, because its truth value is really very small (we thresholdthe thing to its vanishing point, say the real number zero).

6.2. The FormulaA formula can be given for this machinery on the assumption that our cosystem C is a subsystem of Sys,where Sys is the system of all systems (which is the maximal cosystem). It is enough to write thefollowing:


: C Sys Sys 0, 1 ; S, S ', S " S, S', S" ,

from which we draw the typical filament (using S within C)

S : Sys Sys 0, 1 ; S ', S " S, S', S" .

7. The Universe

7.1. Empirical DataWhat here follows is a study of phenomena accruing to the birth and evolution of a system modelled on aspecial realm of empirical data. It is data observed under the assumption of a wide-open, self-generatingprocess of becoming -- a process of manifesting that which we, in the secrets of a glad heart binding,conceal from the world of change and changing.

The world of us is strong and wild of purpose teeming. It is a world inhabited by strange devices(and inclinations). It is a world grown high beyond every infinity, and it is steeped low into a realm ofsublogistic whatnot (fluxing in and out of pre-existence). And, in the great realm of many systems vacillat-ing between existence and non-existence, we find the one special world of our personal (and transper-sonal) acquaintance: It is a world made stable by folding a suffusion of many worlds into a single entity(like a good solid run of Damascus steel).

Our shared entity of time and space spin-wilding into all nether realm of dauntless hope (and ofobduring fear) does present itself to ordinary experience as the very instance of a single, monolithicuniverse -- the universe. And, in our transit through this heavily enfolded thing of many parts pressedthrough one another (into a suffusion of many worlds), we see ‘the universe’ of our childhood talesverging onward to “the outer limits” of common sense -- to the limits of rational perception.

7.2. RhythmRhythm is a spectral selection mechanism: It is a means of approach through which the diverse parts ofa broadband reality may be chosen, combined, and adapted to any fruitful purpose.

8. The Multiverse and Its Cosmos

8.1. A CosmosA cosmos is the entirety of a certain cosystem: The cosystem is a system of many universes (each ofthe same type, say ), for which reason it is said to be versal. Thus a cosmos is a versal cosystem.

8.2. A MultiverseA multiverse is a system of many universes. There is no assurance that any two universes within asingle multiverse will have the same type. Thus, a multiverse may meet multiple cosmoses, or the wholeof it may subsist in a single cosmos of no particular merit or interest.

8.3. The Alpha-Measure-Verse


An alpha-measure-verse is the system of all universes which are individually of type alpha. It mayinclude more than one alpha-cosmos, and it does itself subsist as a subsystem of infinitely many othersuch species of measure-verse. Accordingly, we enter the study of versal measures with a degree ofcaution (and no small attention to detail), knowing that a general theory of versal measures is yet in theoffing.


Appendices

Appendix A. S-Norm


Appendix B. B-Norm


Appendix C. Sort Routine


Appendix D. Noumenal Forms (The Connection Problem)


Appendix E. Wormhole Grid


Appendix F. Versal Measures


Appendix G. A Rough Simulation


the phenomena of totality (celestial metaphysics and natural law) 3.6.nb

Documents