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Planes of Existence~ ~ ~

Interactive Devicing(under)

The Echelon Protocol

(with a polar estimate of)

Specific Tension

RCMP, Echelon SystemsFrom: June the 1st, AD 2016

To: June the 17th, AD 2016

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Draft A23.Planes of Existence: Interactive Devicing(The Echelon Protocol)

Abstract. A temporal fabric X is deviced by a system V, with W < V < W*, where W*=Support(X) and W=Zero(W*). A probe of W gives an echelon (W',W"), with primary hypothesis W' and with adjunct effect W". A collation theta binds the known W" to the unknown W', under the formula theta: Echelon --> Error; (W',W") |--> theta(W',W"). The device Vtheta fuses each echelon, giving the special correspondence W'::W"; theta. It is written

Vtheta(W',W") = V(W',W"; theta) = W'::W"; theta.

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Table of Contents

Part 0 ~ Title & Permission

Proemic. These Are The Things.. Item 0. Title Page Item 1. Permission Key Item 2. Abstract Item 3. Table of Contents

Part 1 ~ Preface & Four Chapters (A-D)

Preface. The Ontological Problem

Chapter A. Noumenal Interpretation Section 0. Introductory Matter, Measures of Entelechy Section 1. Temporal Excitation Section 2. Remark, Inducing the Noumenal Section 3. Noumenal Hypothesis Section 4. Interpretation, Ontological Analysis Section 5. Remark

Chapter B. The Ideas Section 6. The Eleven Ideas, Setup Section 7. The Eleven Ideas, A Generic Wormhole Device

Chapter C. Four Divisions Section 8. Zero Division, The Noumenal Intrinsic Section 9. Zero Division, Noumenal Capacity Section 10. Zero Division, Noumenal Coordinates Section 11. First Division, Non-existence Section 12. Second Division, Pre-existence (Dragon) Section 13. Second Division, Pre-existence (Module) Section 14. Second Division, Pre-existence (Echelon) Section 15. Second Division, Pre-existence II Section 16. Second Division, Pre-existence III Section 17. Third Division, Existence

Chapter D. Ontological Extension

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Section 18. Fourth Division, Existential Immediacy Section 19. Fifth Division, Multiplex Contingency Section 20. Sixth Division, Vertical Interaction Section 21. Seventh Division, Ontological Combination Section 22. Eighth Division, Transcendental Expression Section 23. Ninth Consideration, Source of Becoming Section 24. Tenth Consideration, Periphery of Becoming

Part 2 ~ Appendices & Collectanea

Appendices. The Echelon Protocol Appendix A. Specify conditions of use (parametric similitude) Appendix B. Entity conditions of operation (noumenal similitude) Appendix C. Concretize conditions (noumenal embedding) Appendix D. Rectify noumenal implication (special pullback grid setup) Appendix E. Transmit grid (quiver) Appendix F. Co-ordinate echelon validity (zero condition) Appendix G. Fuzzy wiggle the zero condition (zero gauge) Appendix H. Protoring the gauge condition (gauge homogeneity, control factor)

Collectanea. Some Loose Ends Item A. Vital Procession Item B. Measures of Entelechy Item C. Bundle Exact Sequence Item D. Pair Receptor Item E. The General Domain Item F. Advanced Operating System Item G. Distribution Item H. Binomial Arrow Item I. Special Utility Item J. Echelon Pair Receptor (EPR) Item K. Device Realization Item L. Fusion & Diffusion Item M. Diffusion Across A Heterogeneous Substrate Item N. Interactive Devicing Item O. The Zero Diffusion Item P. Wormhole Perturbation Item Q. Early Alpha Measure Theory Item R. Review of Contents

Part 3 ~ Experiment

Experiment. Mylar Propagator Experiment One. Dielectric Capacity In Mylar (Field-Theoretic Interaction)

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Part 1~


Four Chapters (A-D)

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RCMP, Echelon Systems

Preface: The Ontological Problem

The title of this paper is "planes of existence". It was chosen to orient the reader to a consideration of the ontological problem: It is the diverse range of continuum through which the noumenal world may be brought to manifest each matter hosted within the phenomenal world.

The subtitle of this paper opens with the phrase "interactive devicing". Here, the term devicing refers to a process through which two systems (an echelon) might fuse relative to a third system (a binding condition U). Thus, a device is a process (with condition) under which an echelon is fused to form a correspondence (articulated by the given condition). Also, the term interactive refers to any back-and-forth activity between a primary S, and its adjunct T, within an echelon (S,T). Thus, interactive devicing is a process through which a correspondence is set up relative to (the polarization of) any fluxion across an echelon.

The subtitle continues with the phrase "the echelon protocol". This general protocol is a devicing procedure relegated to the appendices (there are eight). This procedure is used to describe the specific process through which a given echelon is deviced, or set up, as a correspondence. Its development is articulated with detailed reference to the key systems entailed in the running of a 'random element machine (rem)'.

The subtitle concludes with the phrase "specific tension". Here, the notion of a tension is defined to be an impeded fluxion, where the fluxion is defined to be a processive extension (from small to large, done bit by bit), and where the impedance is defined to be a dithered noumenality -- the noumenality is a noumenal contact embedding used to type a host system S (the primary within an echelon). Also, the term specific is used to indicate a prime r of the well-defined reduct host/type. Thus, a specific tension might be interpreted as an anxiety -- an (S,r)-module, where (S,r) is the r-th prime echelon.

Therefore, the full title of this paper "planes of existence - interactive devicing (under) the echelon protocol (with a polar estimate of) specific tension" is understood to propose the following study of means and their use: The ontological problem (a transitum X of planes Xr) is used to set up a correspondence (an echelon (S,r) fused under some binding condition U); a random element machine (rem) articulates the development, and the noumenal tension is resolved into a system of echelon-modules which form the echelons fused to get a system of correspondences -- a struct.

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Chapter A. Noumenal Interpretation

Section 0. Introductory Matter, Measures of Entelechy

This paper studies some features of the arrow M: alpha --> S (monic), with alpha a subsystem of d: d --> d, and with S an arbitrary system. Special language is used to keep the constructions in a narrative mode, and the definitions recede into each narrative excursion through the dictionary (for a random element machine).

For instance, the arrow d: d --> d is called a contact engine; the parameter alpha in d is called a contact, a contact system, a noumenal contact, or simply a noumenal; the host S is called a host system, or a noumenal host; and, the arrow M: alpha --> S (monic) is called a noumenality, a noumenal embedding, or simply an embedding. In the pages which follow, we speak freely of these things, showing only casual concern for the underlying machinery.

Thus, our basic problem (the 'planes of existence') is addressed through an underlying noumenality M: alpha --> S (monic), while the noumenal interaction (above ground) binds life to existence, existence to noumenality, and noumenality to a working contact engine. In fact, our approach evokes within each vital process a bit of ontological interaction with each plane of existence. The interactions are understood in consequence of the following definitions:

An echelon system is a system of echelons populating each plane of existence. An entelechy is a vital process of extended consequence (both noumenal and extra-noumenal). The application to interactive devicing begins with the relatedness of an entelechy S to each echelon, with S unfolding its attribute system T, giving the echelon (S,T). And, if we think that the mechanism which pairs S and T into an echelon (S,T), then we may dig about for a mechanism, say

lambda: Sys x Sys --> Echelon; (S,T) |--> (S,T)lambda.Here, the subscript lambda assumes a value of 0 or 1, indicating either exclusion (0) or inclusion (1) of the argument (S,T) as an echelon. And, should we desire a special calculus within the system of all echelons, written Echelon, then we appeal to Echelon for a subsystem

Lambda = {(S,T)lambda, selection mechanism lambda}.Also, to each instance of lambda, there is a bundle filaments running through the planes of existence; this lambda-bundle gives the desired echelon-calculus.

Finally, it must be noted that the unfolding of a noumenal entelechy S (with the usual extension into all consequence) manifests a system T of phenomena, where both S and T are interpreted relative to an as yet unspecified zero condition Z. Here, the ontological status of an unspecified condition Z is that of a quiescent ground which exists (qua ground) but whose specific nature appears open for development (as need should dictate).

Therefore, when we speak of a measure of entelechy, we are speaking of a measure group whose ground condition is established and operational, but not explicitly represented. We feel that this type of latitude (or wiggle room) allows us to treat freely of the slip and mix of space and time within a primordial realm of indefinite reality: It's just another trip!

Section 1. Temporal ExcitationHere we begin with the supposition that each plane of existence can be treated (despite

all contingency, and uncertain probability) as being no less real (or valid) than any other plane within a given realm of ontological consideration. We suppose that the means of normalizing

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diverse measures of range and scope (of validity) are admissible to the formalism unfolding within this paper. And, thus, we conclude that we have the capacity to peer into each realm of possibility, limited only by the adequacy of our navigational apparatus. That is, we feel that the apparatus developed here should be adequate to the level of abstraction encountered within each target realm. And, just in case the matter has fallen short of abundant clarity, we now consider the specific system of abstraction imposed by a fundamental peek at excitable systems in general, and at the excitation of a logistic system in particular.

A key bit of phenomenological data is expressed through a system of metrics (measures of proximity). A gauge 'beta' is used to keep track of the metrics, and this beta constrains the range of values admissible for the parameter 'alpha'. This constraint is expressed under a phenomenological reciprocity defined as follows. A reciprocity is a system of correspondence between a noumenal alpha and a gauge beta: It is an arrow † from alpha to beta, and it is given by a rule of correspondence that passes each entity a within alpha to its corresponding value, which is a metric b in beta; it is written †: alpha --> beta; a |--> b. Here, the evaluation of † at an entity a (in alpha) returns a metric b (in beta), and the identity b=†(a) sets up; it is established!

The next step is to set up an arrow of excitation relative to each species of temporal extension. In general, we may treat an arbitrary extension (of the temporal sort) by resolving its logistic density into a parametric system of filaments, with each filament given below as a 'b-logistic density'. The argument theta within each such density is called the collation (a binding condition, or error signal).

The error signal 'theta' is studied, in vivo, under an implicit arrow; it is the logistic density for an arrow of temporal extension, and it is written

rho-bar(theta) = 1/[1+exp(theta)].The parametrized version of the standard-normal density uses a metric b in gauge beta as a parameter giving the b-filament, which we call the b-logistic density; it is written

rhob-bar(theta) = 1/[1+exp(theta)]b.This rhob-bar belongs to an excitable system, which is the quiescent gauge condition written as a bundle of metric-filaments

rhobeta-bar = {rhob-bar, b in beta}.The problem of interpreting the parameter b across the square-braces is a delicate

matter, and it involves some explicit machinery for the filamentation of a complex system -- a system which may or may not form an arrow. Each arrow of excitation taub is parametrized by a metric b in a gauge beta, and the effect of its evaluation at rhobeta-bar (relative to a gauge beta) gives the phenomenological condition, whose rule of correspondence gives the result

taub(rhobeta-bar) = rhob.The arrow of excitation is written

tau: R-bar --> R; rhobeta-bar |--> rhobeta,and it holds for each gauge beta.

The behavior of this entelechy S is studied under each reduction (of noumenal type), where each variation on type well-defines a corresponding variation on the reduct; the general reduct is written entelechy/alpha, where the entelechy is taken to be a system of indefinite type, and where each value of the parameter 'alpha' (another system) is taken to be a particular instance of the noumenal type.

A simulation for this arrangement is configured (under the standard system, a system of codes) as follows. The system of entelechy is coded S; the noumenal type of S is coded alpha; the noumenal object entelechy/type is coded S/alpha; the primary subsystems of S/alpha are coded abstractly as individual parameters r (the noumenal primes); and, the primes are gathered into a class of primes called the spectrum Q = {primes r of S/alpha}.

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A noumenal form is an entity of noumenal origin; it lives in the spectrum of an entelechy S (type alpha), and we say that it is a prime of the (noumenal) object S/alpha -- it is a primitive idea of S (type alpha). In fact, the primes of S/alpha (within Q) are precisely the primitive ideas of S (type alpha). Moreover, the subsystems of S/alpha are the ideas of S (type alpha): The two are identical (nothing is missed; this result extends the important Schroeder-Bernstein theorem). [cf. Paul Halmos, Naive Set Theory]

Section 2. Remark,Inducing the Noumenal

The general reduct entelechy/alpha gives instance to the abstract reduct entelechy/type, by inducing the noumenal alpha as an instance of noumenal type.

Section 3. Noumenal HypothesisThe matter continues through the construction of a general reduct. The key idea is that

of hypothesis, and it occurs because an arbitrary system forms no object (it is not well-defined). And, since objects are believed to be ubiquitous in nature, it would seem natural to suppose a mechanism through which an object might occur within a given system (or within an environment for a given system). More particularly, we may say that a given system S is the environment of each of its subsystems S'; or, more especially, we may say that each system S' in the given environment S is a reduct of S relative to some hypothesis about S. And here the matter becomes precise.

A short exact sequence is a pair of arrows S' --> S and S --> S", such that Image(S'-->S) = Kernel(S-->S"); it is written S' --> S --> S" (exact). Here, the system S' is called the initus, the system S" is called the terminus, and the system S is called the pivot. A split exact sequence is a short exact sequence S' --> S --> S" (exact), such that S is the direct sum of S' and S"; it is written S' --> S --> S" (split exact), with direct sum S = S'+S". Here, the arrow S' --> S is called the insertion, and the arrow S --> S" is called the reduction.

A hypothetical sequence is a split exact sequence S' --> S --> S" (split exact) for which the insertion S' --> S is monic; it is written S' --> S --> S" (hypothetical). Here, S" = S/S' is called the reduct, S' is called the hypothesis, and S is called the environment. A noumenal sequence is a hypothetical sequence whose hypothesis is a noumenal 'alpha'; it is written

alpha --> S --> S/alpha (noumenal).Here, the system alpha is called the noumenal hypothesis, the (noumenal) environment S is called the host, and the reduct S/alpha is called the (noumenal) object.

Before passing into the sequel, we close this section with a useful observation: A (general) object is a well-defined system. Thus, a noumenal object may be characterized as a general object that is well-defined by its hypothesis alpha on the environment S from which it is drawn.

Section 4. Interpretation,Ontological Analysis

To introduce the proper matter of ontological analysis, let us say that an idea is a noumenal form (section zero). Let us add that within each parametric transitum of ideation (i.e., each noumenal system of ideas), a subsystem comprised of the primitive ideas may be

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considered: It is the system of primes within the environment X (the parametric transitum of ideation). In fact, each noumenal prime attaches to its corresponding semantic primitive, and Q is a system included in X (but not necessarily subsumed). The problem is that while both Q and X are deduced relative to the same primary noumenal 'alpha', they may as systems be typed by incompatible secondary noumenals nu(Q) and nu(X). And, should the matter require further analysis, we may introduce an abstract derivation through which to relate each value of nu to alpha. The issue seems to be a matter of relative valuation, and it falls nicely into the venue established by Alpha Measure Theory (mine, 1993). The setup is written

evalQ(nu;alpha) = eval(Q,nu;alpha) = alpha-eval(Q,nu) = nualpha(Q),where the filament nualpha(Q) = nu(Q#alpha) is forced by a species of interpretation given by the arrow

#: Sys x P --> Sys; (Q,alpha) |--> #(Q,alpha),so that evaluation gives the identity #(Q,alpha) = Q#alpha.

The arrow # is sometimes called the interpretation, and its use is seen to govern the secondary noumenal of a system relative to its primary noumenal. Therefore, in the handling of any derived system, we need to know not only the primary and secondary noumenalities, but also the implicit between them: This (within the limits given here) is the essence of all interpretation, and it seems to operate at a level of grammar which is neither syntax (grammar-one), semantics (grammar-two), nor semiotics (grammar-three); rather, the matter is entirely epinetic (grammar-four). Consequently, we have arrived at the fourth (and final) natural grammar (the remaining three run beyond anything of specific nature -- anything of noumenal character): The definition follows. An epinetic grammar is a grammar of interpretation; it is a comprisal of grammars one, two and three restricted only by interpretation, which is the noumenal evaluation of specific nature.

Section 5. RemarkAll interpretation is noumenal!

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Chapter B. The Ideas

Section 6. The Eleven Ideas,Setup

With a feasible model of interpretation in hand, we may turn to some very general sorts of idea. And, in order to facilitate the handling of this generality, we begin with the attachable notion of a primitive idea as follows. A primitive idea is a noumenal prime (within the spectrum Q of a well-defined system S/alpha of ideas). Here, we have used the definition that a prime subsystem is a subsystem r whose alpha-reduct (r/alpha) is trivial (giving only r itself, or the null 0S).

Therefore, we may resolve our noumenal system S (of type alpha) into its noumenal primes r of S/alpha to get a spectrum Q of primitive ideas. Moreover, because S resolves into ideas (a parametric transitum X of ideation), we may reduce S (idea by idea) through each respective mode of existence, arriving at a system of eleven categories -- the eleven ideas.

The eleven ideas are the primary modes of ideation (the noumenal primes). They express the principal aspects (the modes of ideation) through which a noumenal entelechy interacts with each existence (each plane of existence). Each plane of existence is arranged into a system of contingencies which, by virtue of entelechy, give each mode (of ideation) is characteristic range (and agency) of functioning.

Here, each idea resolves an existence into a system of contingencies; they are ontological contingencies given as echelon-planes (the so-called levels of contingency), and they are expressed as measurable bits of existential tension -- tiny little fragments which may or may not contribute to a particular anxiety. In turn, the anxieties resolve into modules, and the modules contribute to a zero system Z -- the gauge condition preceding a gauge 'beta'. The resulting echelon system is a system of nine divisions appended by two considerations on the nature of life, and of becoming:

Section 7. The Eleven Ideas,A Generic Wormhole Device

The zero division concerns the subtle matter of that which precedes any possible existence. The first division concerns the nature of that which does not, and can not, exist. The second division addresses that whose potential to exist is measurable. The third division gives criteria for that which does exist; these existents are the ontologs of my study, and their existence qua ontologs well-defines many systems: These well-defined systems are sometimes called objects.

The fourth division expands the criteria for existence into ideas on those special ontologies which exist with immediacy; it introduces the doctrine of ontological necessity -- a modern variation on "the ontological argument". The fifth division postulates the matter of things which exist on multiples planes of contingent reality. The sixth division combines the prior five into a system of vertical interaction across their constituent potentials to exist -- their ontological potentials. The seventh division arranges categories and classes of ontological combination discovered within the sixth division. And, the eighth division is a transcendental meta-division governing the expression of life among the first seven divisions. There is a ninth consideration, but it forms no proper division, and its concern runs chiefly into the source of becoming within

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each division (zero through eight). A tenth consideration does not properly exist, except inasmuch as there might be a periphery to the ninth consideration.

Finally, we may group divisions zero through eight into a "nine-point circle", aggregating considerations nine and ten as two further objects within the constellation. Here, the ninth consideration gives a well-defined geometric point (a source of becoming), an ill-defined generic point (the periphery of becoming): This genericity is of the sort used to study the Algebraic Geometry of a system; we use it to device a wormhole switch, and this is our generic wormhole device (as advertised).

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Chapter C. Four Divisions

Section 8. Zero Division,The Noumenal Intrinsic

An intrinsic is that which has no specific nature; its noumenal sense is comprehensive. There being no distinction of part or place, an intrinsic is (to the extrinsic view of things) indiscernible from any particular thing; it is not visible. On the other hand, if we could see things through an eye that is whole, then an intrinsic would be immediately distinguished from the extrinsic world; the intrinsic would appear simple, whole and all-embracing.

Notice further that the noumenal perspective departs markedly from the phenomenal perspective: From a strictly phenomenal viewpoint, the realm of possibility for a purely noumenal entity vanishes with identity. On the phenomenal view, no entity may be derived from 'noumenal whatnot'. The phenomenal position maintains the view that our noumenal realm is the hallmark of fantasy, illusion, falsity, and wrong-headedness. In fact, the strict phenomenalist position concerning each noumenal reality, within which we may arrange and transact our affairs, is a simple matter of delusion arising out of some pathological loss of objectivity.

Section 9. Zero Division,Noumenal Capacity

In the general case, the question of existence resolves into an (inconsistent) system of ideas: Each idea resolves into a noumenal form which may or may not attach to some corresponding phenomenal range of expression. Thus, each particular idea may or may not be susceptible of consideration, where each type of expression is indicated by a noumenal parameter. In other words, the susceptibility of a noumenal form to consideration depends (obviously enough) on the type of consideration proposed. Therefore, to each idea I there corresponds a system S of entities, where each entity e of S has a capacity ce(I;alpha) given by evaluating the e-th capacity of the noumenal parameter alpha. That is, the capacity of an idea I to be considered is measured in terms of its filaments, which are indicated by each entity e, and the type of consideration proposed to do the measuring is parametrized by the noumenal parameter alpha; the whole of it is written

c: Gamma(Entity,Idea) x Noumenal --> Capacity; (e,I;alpha) |--> c(e,I;alpha),where Entity is system of all entities, Idea is the system of all ideas, Noumenal is the system of all noumenals, and Capacity is the system of all capacities. Also, the grid operation Gamma is invoked to accommodate a interrelatedness between each idea I of Idea and the subsystem of Entity. The typical filament of c is written, for each e in Entity,

ce: Idea x Noumenal --> Capacity; (I;alpha) |--> c(e,I;alpha).Here, the measure of consideration that may be given to any particular idea (noumenal,

phenomenal, or mixed) is expressed by its susceptibility chiI to each type of consideration -- to each noumenal type alpha. Thus, I distinguish among the parts of an idea which are considerable, which have capacity, and whose capacity is measurable.

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Section 10. Zero Division,Noumenal Coordinates

Finally, the condition of comprehension is a noumenal condition whose each instance is characterized by a locus (the intrinsic) and its scope of instantiation (range of influence), and whose every generality is given by a vertical abstraction against each instance. Thus, to each syllogism, be it categorical or transcendental, there corresponds a coordinate range of validity within the noumenal plane: It is a coordinate plane whose horizontal axis (the abscissa) is delineated as the axis of instance, and whose vertical axis (the ordinate) is delineated as the axis of generality.

Section 11. First Division,Non-existence

An extrinsic is that which is not intrinsic; it is that whose specific nature may or may not be indicated (in some noumenal sense). A measurable is that whose specific nature may be indicated (in some noumenal sense). An immeasurable is that whose specific nature may not be indicated (in any noumenal sense).

An entity is that which may be considered. A non-entity is that which may not be considered. A bit of whatnot is that which may or may not be considered; it is that whose capacity to be considered is measurable.

A ponderable is a measurable bit of whatnot. A decidable is a ponderable of decidable measure; it is that whose measure of capacity (to be considered) may be reduced to some indicatable value. An imponderable is that which is not ponderable (as in the imponderable void -- the inviat, that through which nothing may pass).

Section 12. Second Division,Pre-existence (Dragon)

A thing is that which can be indicated. An ontolog is a thing which can be well-indicated. The scala are neutrino-like fields made passive into transit -- passive with a switch under which the passivation evaporates, like a zero noise being lifted; the resulting field is active and binding: It is readily subtracted, together with whatever fields (such as time continuum) to which it may already have bound itself. [The intended use of this result was a scanning module for the treatment of cancer under 'neutrino field therapy', given a reliable neutrino field source: I do not know of one!]

A dragon is a scale-bundle, where the scale concept is illustrated by the preceding scala, and where the bundle is a pivot for the local exact sequence with a grid for its initus and with a spectrum for its terminus. A scale is an attachable locus (with extension): It is a 'metric system' (S,T) attached at a locus (possibly noumenal alpha) that defines the reduct (S/locus,T; locus), and it is regarded as a locale echelon (whose similar instances are distributed the density of locale 'rho'). The metric system is derived below (section eight), and the density of locale is presented in its sequel (section nine).

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Section 13. Second Division,Pre-existence (Module)

A quiver is a system of correspondence between a grid Gamma(X0,X1) and a display system X2: It is an arrow 'psi' that points from Gamma(X0,X1) to X2, and it is given by a rule of correspondence that passes each grid element u in Gamma(X0,X1) to a corresponding display element v in X2; it is written psi: Gamma(X0,X1) --> X2; u |--> v, and the effect of this arrow is written v = psi(u).

A module is a quiver of the form Gamma(X0,X1) --> X1; it is a quiver whose display system X2 is identical to the dependent system X1, giving the condition X2 = X1. To see why this might matter to a physicist, we consider the behavior of each X0-filament (over X1). Let the independent variable r in X0 index a filament over Gamma(X0,X1), and let the r-th filament display its image in X2 (=X1). Then, this filament is given simply by the implicit arrow gamma(r), which is an extension of r in X0 to a subsystem of X1. In fact, we can formalize this trick by writing Imr(gamma) = gamma(X0|r) = gamma(r), provided that the details of cohesion (relative to the restriction X0|r may be safely swept under the null system 0 within X0).

The explicit upshot of all this machinery is that our module depends in a very sensitive way upon the behavior of its host environment -- the quiver psi. In fact, should we care to document the total modular effect associated with the formation of a behavioral group of filaments over X1, then we must recognize within the familiar adjoint (a group of transitive filaments) the hidden work of this quiver. Moreover, because our transitivity is merely a filamentation of the alpha-additivity (via alpha-associativity), it follows that the entire framework assumed of group theory embeds very nicely within our formalism for the alpha-measure group 'pi'.

Finally, we close with the definition of a classical module as follows. A Cartesian (direct) module is a module whose grid reduces to a Cartesian (direct) product; it is written X0xX1 --> X1, where X0xX1 is the direct product of the systems X0 and X1.

Section 14. Second Division,Pre-existence (Echelon)

A fusion is a system V comprised of two systems, S and T, together with arrows S-->V (epic) and T-->V (epic); this fusion is sometimes written V(S,T). A special fusion is a fusion V(S,T) that is conditioned by a parameter U; it is written V(S,T;U). [A16. The First Echelon: section four, "Fusion"]

An echelon is a pair of systems (S,T), together with a condition U whose satisfaction gives a special fusion V(S,T;U). Relative to this special fusion, the term (S,T) is called the argument; the term U is called the parameter; the term (S,T;U) is called an argument with parameter; and, this argument with parameter is sometimes called an echelon of grammar. [A16. The First Echelon: section five, "Echelon"]

Section 15. Second Division,Pre-existence II

To get a proper metric system, a bit of echelon machinery is invoked: An echelon-module is a module whose grid is the fusion of an echelon; X0 is the primary, X1 is the adjunct, and Gamma(X0,X1) is the fusion of their echelon (X0,X1). A gauge specialization is an arrow K from the system (Sys x Sys) of all pairs of systems to the system P' of all gauge homogeneities;

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it is written K: (beta x Sys x Sys) --> P'; (b,S,T) |--> (S,T)b, where the protoring P' (= secular inverse of the contact lemma P).

A metric system is a metric-cofilament of a gauge specialization K; it is written k: beta --> P'; b |--> K(b,-,-). Thus, a consonance is gotten by taking the value K(b,-,-) to be the frame of our 'metric system' in the provisional case; i.e., k(b)(S,T) = K(b,S,T) gives the result with magnetic induction k(b) and electric intensity (S,T) giving the gauge specialization K (of an echelon-module). [cf. A11. The Arrow of Fusion (The General Standard): section fifteen, "Echelon-Module"]

A ring-module is an echelon-module together with a metric system, giving the echelon its scalars. A ring is the scalar system gotten from a ring-module; it is the evaluation of the metric system attaching to the echelon within a ring-module. A protoring-module is an echelon-module together with a gauge specialization K, whereby the echelon is restricted to a modular system of co-type beta in P'; it is written (S,T)beta = k(beta)(S,T) = K(beta,-,-)(S,T) = K(beta,S,T), and it is sometimes called the gauge homogeneity, or the alpha-protoring, with reciprocity beta = †(alpha).

Section 16. Second Division,Pre-Existence III

The density of locale is a system of correspondence between the contact lemma P and the localization P'L = loc(P,L) of the noumenal realm L over P: It is a parametrized arrow (afilament) rhob from P to P'L, and it is given by a rule of correspondence that passes a noumenalalpha to the metric homogeneity delb evaluated at the localization F'H = loc(F,H) of the alpha-covering H over the alpha-field F; it is written

rhob: P --> P'L; alpha |--> delb(F'H).[A Dictionary for The Random Element Machine: "Density of Locale", p.73]

We can get an easy feel for the behavior of the density of locale if 1.) we suppress the parameter b (writing rho in place of rhob), and 2.) we deconstruct our use of the logistic density

rho-bar(theta) = 1/[1+exp(theta)] to model rho. The idea, here, is that we can describe an excitation tau: rho-bar --> rho (epic), so that rho = tau(rho-bar), giving the isomorphism rho ~ rho-bar. The terminology is the following: quiescent condition of density, rho-bar; excitation isomorphism, tau; and excited condition of density, rho.

Section 17. Third Division,Existence

The matter of this section is arranged in a fashion which gives best emphasis to the procedural distinctions which arise in the handling of those decidable and undecidable bits of whatnot. We give a formalism within which a full spectrum of ontological analysis may be conducted with perfect ease and rigor. And, because the whole matter revolves around a special sort of correspondence (the one called consideration), we now investigate the necessary means of consideration as follows.

A consideration is a correspondence through which the parts of a whole are seen in relation to one another, and in relation to the whole; it is a vital correspondence whose strength is conveyed (or transacted) by means of volition, and its terms are understood as follows. An act of consideration is an act of volition through which the parts of a whole are seen in relation

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to one another, and in relation to the whole. And if the correspondence theory of consideration holds any validity, then too does our notion of consideration reduce as follows. A consideration is a simple theory between an entity and a system: It is a theory of the form e::S, with fixed entity e, with fixed system S, and with variable term ::. We now have the means to evaluate, on a rigorous footing, a broad swathe of ontological whatnot: It is the capacity to deem with precision the specific nature of that which experience and reflection bring into the realm of consideration. The definitions follow.

An entity is that which may be considered: It may or may not exist, and we say that its ontological value is a matter of discovery; an entity must be weighed in the balance of experience to know whether its ontological status is positive or negative. An existent is that whose ontological value is positive. A non-existent is that whose ontological value is not positive.

Here, we may accept as valid the argument that an object is an existent whose assertion negates the contrary assertion that nothingness may replace the entire realm of existence. And, because existence is a self-perpetuating process of displacing nothingness, we may say that an object is that whose existence displaces the notion of an absolute and entire void called nothingness. In fact, we may use the criteria of definedness as a means of starting the proof of an all-embracing existence theorem. The definitions follow.

An entity is well-defined if its construction is unique and complete on its domain of defintion. An object is a well-defined entity. An entity is ill-defined if it is not well-defined; its existence is not asserted with validity. An entity is decidable if its existence can be determined through a consideration of its definability (either for or against a positive ontological status).

We often deal with multiple entities of diverse ontological value, and with diverse sorts of aggregation. The language of class algebra is helpful here: It enables the assertion of a useful proposition ("Existence exists!"), and it enables a logical demonstration of its validity. The definitions follow.

A class is zero or more entities considered together. A set is a class that does not include itself; it lacks Bertrand Russell's property -- the one called 'self-inclusion'. A class is proper if it is not a set. We now give the existence theorem, followed by a useful corollary.

Proposition. Existence exists.Proof. Let e be the class of things which exist; and let e' be the class of things which

do not exist. Suppose that e is empty. Then e does not exist; it lies in e', which is thus nonempty and exists. This gives that e' lies in e, contradicting nonexistence (and affirming the contrary hypothesis that existence exists). This affirmation completes the proof.

Corollary. Differences exist.Proof. Put e–e' into e' and argue that the contradiction gives e–e' into e.

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Chapter D. Ontological Extension

Section 18. Fourth Division,Existential Immediacy

The fourth division expands the criteria for existence into ideas on those special ontologies which exist with immediacy; it introduces the doctrine of ontological necessity -- a modern variation on "the ontological argument".

0. Introduction (object). This section relies (for understanding) on a simple demonstration of natural magic: It relies on the capacity of a psyche to affirm, and to interact with, an object (that which exists) formed abstractly by the powers of imagination reposed within us all.

1. Experiment (magic box). This subsection describes an experiment in which the reader(as subject) participates with a brief sequence of mental operations aimed at the discovery of aprocess through which an anxiety is produced in connection with a basic principle ofpsychology: It is the first fundamental principle of psychology; it is sometimes called theprinciple of "object permanence"; it is used to illustrate the behavior of a generalized anxietyabout existence (and about pre-existence); and, it is sometimes used to explain the secondfundamental principle of psychology -- the so-called principle of "existential anxiety".

The principle of existential anxiety is concerned with a species of tension experienced (either in our conscious waking mind, or in the subliminal department of personal and transpersonal experience) as a sense of uncertainty, anticipation, or trepidation for things beyond our present capacity to know: It involves feelings related to "moral inability", and to prospects of immortality!

To start the experiment, I will give an instruction which you may choose to follow. I should caveat this experiment by noting that the intended effect will register better within you if you actively participate: It is a "thought experiment" of the sort that Einstein called a gendanken experiment, and its success depends critically on the level of your own personal involvement.

I want you to form a vivid mental image in the front of your mind: Picture a box with something in it (a picture in a box). I say the magic word and, Presto.. a box with nothing in it! Now I explain. Your mind is very like this box: First you have ideas; then ideas bear their fruit; then the picker's knife sets in, and the bounty is withdrawn!

2. Example (appetite). Here, in a slightly more expansive sense, a vivid bit of imagery isabstractly provided: The reader (as participant) is invited to pass through an open door ofancient make, and to enter a great hall of assembly -- a great hall of feasting! Within the wallsof stone and timber erected now about you, you may see a strong table set for grand repast.And, as you approach the table bearing more curiousity than actual appetite, you realize thatinducement lines the table: Fire draws the eye!

The eye perceives the site; the ear receives the sound; and the hand commits the plan: An object is produced! You may desire to possess it -- to possess it perfectly. There is real psychic danger here, and it is carnal...

3. Mechanism (complex anxiety). There is by now an object within your mind. You havealready given it some consideration: You may wish to give it more! Give consideration the waythat you would give water to the plants bearing leaf and bloom within your garden. That garden

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could be a planter box, either within or without the window opening from a favorite room to the world beyond your door. That garden could be a bit of median soil placed between your front door and the street beyond it. Or, that garden could be an abstract place of many hopes taking root within the horizon which you know to be your future.

Give it more consideration, and notice the way that the object puts down roots within the psychic ground of your inner experience. You may notice the early appearance of a small bud, and you may notice its growth into full bloom -- a fruit-bearing bloom which we call anxiety. That anxiety is a special breed of tension, and it is used to sustain within sensorium a useful bit of stress: It is a stress with certain features including, but not limited to the following devices: a trigger, a switch, a complex mechanism, or a system of vaguely imaged events hovering about a horizon not entirely present within this particular moment of your conscious awareness.

You may desire that a description be given, but this is just more anxiety... And, so we retreat from the matter in all respects except to warn that a diabolical bit of machinery has been activated; it has been left running in a more or less idle mode since the time of your first social awareness. It is a machine driven by many little anxiety modules, most of them subliminal, and this machine is called the Jones machine.

4. Application (peaking). A Jones machine is a complex system of many anxieties, tensions, and realizable stresses at work within our every waking moment. And though a special "Jones for this" (or a particular "Jones for that") may or may not evoke within the waking mind any sense of sudden peaking experience (Maslow's little Aha!), we nonetheless perceive within the current of our conscious awareness a sense of rhythm -- a flow of events: Life is for us a continual series of moments compounding moments, gentle subliminals slipping in and out of range of other subliminals (not all of them entirely gentle).

Our work in this area builds primarily on the following system of observations concerning the behavior of an arbitrarily given stressor (the anxiety), and it builds derivatively on the mechanism through which a realizable stress becomes itself imminent in the never-ending flow of ideas, thoughts, and feelings. Specifically, a fluxion is a processive extension; a tension is an impeded fluxion; and, an anxiety is a prime of tension (resolved under noumenality): It is expressed as an individual 'echelon-module' induced by the noumenal primes (r in Q) associated with a noumenality M: alpha --> S (monic, w/ host S).

Thus, to each stressor used to prime a trigger event, there corresponds an echelon (formed by its own echelon-module), and this echelon is a minute (and probably subliminal) effect developed within a background tension given little notice (our background tension is merely a ground condition, or zero, against which suprathreshold events may register their activity, putatively in order of occurrence). In fact, more often than not, our sense of the Jonesing mechanism carries with it an altogether curious implication: It is our ability to perceive within sensorium those sudden changes to the rate at which new information is presented for consideration; it is the swiftness (celeritas) with which the world impresses its immediacy upon the capacity of psyche which we call mind.

Section 19. Fifth Division,Multiplex Contingency

The fifth division postulates the matter of things which exist on multiple planes of contingent reality -- multiple planes of anxiety, with the anxiety ranging in intensity from negligible to mild, from mild to strong, and from strong to overwhelming...

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The essence of our problem is that we are given a system of unknown character -- a system of countless little bits of whatnot slipping and mixing (one preposing another), and we are asked to fit the unspecified system into a larger (more comprehensive) framework in such a way that the inherent slip and mix of the unknown contributes (with or without its own awareness) to the overall working of our life-giving framework: It is our model of viability in action.

An easy sort of comparison to consider is the systematic projection of each system against each of the several planes of existence relative to which its ontological stasis is representable (with or without the anxiety). The idea is that each plane of existence will give a different image of the system under consideration, and that these several images may be combined to reconstruct a tolerably good image of the whole system given: We get a contingency! (It is specific tension related to a desire for permanence.)

In this way, and for this reason, we arrive at a pronounced need for a piece of technology which we might call the 'contingency chip': It is a chip, or a chip set, whose primary function is asserted by a statement of effect, where the effect is itself taken as a variable contingent upon the noumenality M: alpha --> S (monic, w/ host S). Therefore, our contingency is considered to multiplex a system across each individual plane of existence, whether or not the given system is pre-manifest (say, as an object) or not. It is a matter of "existential instantiation", and we feel that this sort of gadget must be very clever!

Section 20. Sixth Division,Vertical Interaction

The sixth division combines the prior five divisions into a system of vertical interaction (think of "angels ascending and descending" a musical scale) across their constituent potentials to exist -- their ontological potentials. The problem here is to give a useful characterization of each ontological potential, together with a recipe for each respective deployment in the construction of our over-riding system of instantial loci: It is a matter of progression from the primordial zero division, to the ponderable first division, to the pre-existential second division, to the existential third division (with all four divisions charted in Chapter C - The Four Divisions); it is a launch protocol from the existential immediacy of the fourth division, to the multiplex contingency of the fifth division, to the vertical interaction of the sixth division, to the ontological combination of the seventh division, to the transcendental expression of the eighth division (with a rapid succession of all five divisions in Chapter D - Ontological Extension, which chapter this is); and, it is a paired system of two considerations (source of becoming, and periphery of becoming), giving the echelon of becoming.

With this game plan clearly established, we now turn to the sequel: The sequel passes through ontological combination (§21), and transcendental expression (§22), prior to considering the echelon of becoming (§§23-24).

Section 21. Seventh Division,Ontological Combination

The seventh division arranges categories and classes of ontological combination discovered within the sixth division.

Throughout this work, the key to ontological combination lies within each abstract genius loci -- each specific instance of the abstract tool of instantial locus, written @. An easy way to

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see this tool in action is to consider the structure of @, given the data on an arbitrarily given interpretation via the interpreter tool, written #.

The setup supposes a binomial arrow A: Echelon --> Sys; (S,T) |--> A(S,T) be a binomial arrow of indeterminate structure. The problem is to interpret a structure for A, and the interpretation # is resolved by the following recipe for 'complete factorization':

1. #A ; given (to do) 2. (@!)A ; substitution (vague) 3. @(!A) ; associativity 4. @[A(-,-)] ; apperception 5. A(@,@) ; realization 6. A(S,T) ; instance 7. A((S,T)) ; nesting 8. A(z) ; point 9. A((x,y)) ; co-ordinates10. A(x,y) ; stripping11. A(H,H) ; covering (entailed)12. A(S'H,T'H) ; inversions of systems S and T (to get a covering density)13. A(locSH,locTH) ; localization14. A(locS,locT)(H) ; factorization

Here, we should conclude that our complete factorization is 'complete' in the noumenal sense given (arbitrarily) by the accepted convention of the noumenal parameter 'alpha' which, on account of its acceptance, does persist a bit into its own noumenal realm of semantic consequence: It is the realm perfected as the (semantic) transitum X -- a temporal fabric.

Section 22. Eighth Division,Transcendental Expression

The eighth division is a transcendental meta-division governing the expression of life among the first seven divisions. The preceding division (§21) hints that, 'Interpretation is local.'

The primary attribute of interpretation is not so much the vague substitution expressed by the condition # = @!, rather it is the recurring sense of localization which it engenders: The above derivation entails of a covering H through which the localizations S'H = locSH and T'H = locTH are expressed. Thus it happens, in the most ordinary way, that (if H satisfies a right-cancellation law, with H' the inverse of H) we get the following string of equalities (upto an accepted convention on resolving power):

S' = S'(idH) = S'(HH') = (S'H)H' = (locSH)H' = locS(HH') = locS(idH) = locS.A similar demonstration holds for T', giving the most curious identities S' = locS and T' = locT.

Now it happens, that the term S'(idH) expresses a purely transcendental feature of the covering density S'H. Namely, the energy of covering (associated with an inhomogeneity in its density) is expressed (or should I say hidden) by the simple expedient of an identity operation idH, which may or may not hold (to arbitrary precision) under the above mentioned right-cancellation law. And, because the right-cancellation law is algebraically equivalent (alpha-isomorphic, with noumenal alpha) to a corresponding assertion of monicity with respect to the (domain restricted) localization

(locS|Coverings): (Sys|Coverings) --> Densities; H |--> S'H,where

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locS: Sys --> Densities; T |--> S'T,is domain restricted from Sys to Sys|Coverings (and where Sys|Coverings may or may not give Coverings, in respect of the particular construction given the restriction operator for a general system). In consequence of this open matter, we have our bridge from ordinary monicity to its transcendental entailment using absolutely nothing more than a one-to-one correspondence.

Section 23. Ninth Consideration,Source of Becoming

The ninth consideration forms no proper division, and its concern runs chiefly into the source of becoming within each division (zero through eight).

From the center of all becoming (the source of every procession), to the periphery of all entelechy (the periphery of every manifestation), we consider the operation of a pair receptor (-,-) together with two systems (the source S, and the periphery T) arranged to accommodate a "field of opposition" in such a way that the Hausdorff representation of becoming is described (in the sense of Kolmogorov) as the secular reduction S*/alpha of the entirety S*=d(S), d: d --> d, with alpha a subsystem of d. That is, the echelon (S,T) formed by an echelon-module A, is developed consonant with the random element machine (rem) generated by the specific noumenality M: alpha --> S (monic, w/ host S). Here, the center of becoming is written C(S,T) = S/alpha, and the periphery of becoming is written C*(S,T) = T/C(S,T). Thus, we get that the center C and periphery C* split T (the periphery of all entelechy), giving the final result

T = C + C*,where the operation + is used to denote the direct sum of two systems (C and its entirety C*).

Section 24. Tenth Consideration,Periphery of Becoming

A tenth consideration does not properly exist, except inasmuch as there might be a periphery to the ninth consideration.

An obvious approach, here, is to consider the co-grid associated with a given grid, and to let the co-grid (the dual of a grid) be used to generalize the direct sum C+C*. We can then ask under which conditions this generalization (the co-grid duality) would be measurably distinct from the ground condition specified by the direct sum C+C*.

A partial answer is strongly indicated by the phenomena discovered, and by the formalism invented, by Vladimir I. Arnold -- a leading Soviet mathematician at work in the area of Kolmogorov dynamics (and in more general sorts of entropy, such as those presciently anticipated by the ergodic theory of measurable dynamics). Arnold's unique contribution to the work advertised here (the ubiquitous tongues of diffusion) consisted in a multi-layered, constructive proof of the existence of the sort of pre-stochastic process which I myself dissertated in the closing chapter of my paper on Alpha Measure Theory (1993) or, more completely, (1994). [cf. Hans Jenny, Kymatics; Ref. Ralph Abraham, On Morphodynamics]

The apparently shared insight, which seems to grow out of both schools of work, concerns the matter of stochastic broadening through which an otherwise brittle bit of speculative legerdemain becomes itself robust, adaptive, intelligent, viable and (in many other respects) entirely life-like.

Thus, as each periphery of becoming retreats from an encroaching sphere of understanding, we begin to realize the overwhelming futility of this, our fleeting and necessary endeavor to the contrary: It is the single greatest challenge afforded us, and we are grateful.

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Part 2~ ~



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Appendices: The Echelon Protocol

The echelon protocol is a general protocol for navigating an (arbitrary) echelon system, and we use it for interactive devicing: It is a formal procedure drawn corollary to ontological analysis; it is a devicing procedure drawn out of pure abstraction -- pure ontology.

Our protocol is developed (in sequence) through the following eight appendices (A through H): A.) Specify conditions of use, via parametric similitude; B.) Entify conditions of operation, via noumenal similitude; C.) Concretize conditions, via noumenal embedding (a species of encryption); D.) Rectify noumenal implication, via grid setup (a special pullback grid); E.) Transmit grid, via quiver; F.) Co-ordinate echelon validity, via zero condition; G.) Fuzzy wiggle the zero condition, via zero gauge; and, H.) Protoring the gauge condition, via gauge homogeneity (a control factor).

Appendix A.Specify conditions of use, via parametric similitude

The logistic module is the real-valued kinematic process given by a rule of correspondence defined by the logistic density rho-bar. A alpha-logistic module (type alpha) is a real-valued kinematic process given by a rule of correspondence defined by an alpha-logistic density alpha-rho-bar. Because of this definition we may say that the logistic module is a hyperbolic instance of the alpha-logistic module.

A b-module (with metric b) is a structural perturbation of rho-bar, and it is written rhob. Here, the metric b lives in the gauge beta given by a reciprocity of the noumenal parameter alpha; it is written beta = †(alpha).

Appendix B.Entify conditions of operation, via noumenal similitude

An easy condition of operation U may be entified (abstractly) by imposing upon its parametric similitude (above) a noumenal condition. We simply require that the parameter alpha (above) be a subsystem of the contact engine d: d --> d, so that our typing parameter alpha is a contact (i.e., a contact system). To obtain a noumenal of alpha, we merely embed alpha in the host system S; it is written under the noumenality M: alpha --> S (monic).

The entified U is a system S/alpha that is well-defined by alpha (under secular reduction). The attributes and features associated with the reference system S (the primary) will show up as an attribute system T (the adjunct), and the two are related by the special correspondence S::T;U, with entified(U) = S/alpha.

Appendix C.Concretize conditions, via noumenal embedding (a species of encryption)

An arbitrarily given system S is, by nature, abstract. It is a cohesive whole of no particular type (no alpha has been induced) and, as it lacks an entified condition of operation U,

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its identifiers slip and mix is unpredicable fashion: The whole of it is just another garden variety slippy mix.

Thus, within the scope of this appendix, and for the sake of (realtime) dynamic encryption, we concretize U via S/alpha: We consider the spectrum Q consisting of each prime subsystem of the object S/alpha (which is well-defined and exists). Here, a noumenal prime of S (type alpha) is a subsystem r of S whose alpha-reducts are alpha-trivial; here, an alpha-reduct of S (type alpha) is a subsystem r/alpha; here, a subsystem T of S is alpha-trivial if each reduct of T lives in the alpha-null system of S; and, here, the alpha-null of S is a subsystem 0 of S (type alpha) which satisfies the following conditions: 1.) An arrow A: S' --> S is monic if, and only if, the short sequence 0 --> S' --> S is exact; and, 2.) An arrow A: S --> S" is epic if, and only if, the short sequence S --> S" --> 0 is exact.

Therefore, an identifier for the correspondence alpha::S;U is a prime r of S/alpha (it is a system within Q): Its effect upon a would-be similitude S::T;U passes between S and T through U, where entified(U)=S/alpha, and it is said that r binds S and T via the noumenal condition U. Moreover, the relatedness of these two correspondences under the shared condition U is written as the following hyperchannel:

(alpha::S;U) :: (S::T;U),which simplifies to

alpha : S :: S : T.Notice that our simplification of the hyperchannel to a formal analogy is pronounced, "alpha corresponds to S in the way that S corresponds to T." It is also pronounced, more succinctly, "alpha is to S as S is to T". And, in closing this appendix, it should be noticed that our simplification describes a golden ratio (by normalizing the channels alpha::S and S::T relative to U): It states that a U-normalized hyperchannel will convey the identifiers in alpha::S;U to a would-be similitude S::T;U through a process known to the literature as "empathy". In other words, the noumenal hypothesis on T is identified by empathy.

Appendix D. Rectify noumenal implication, via grid setup (an a fortiori pullback grid)

The rectified implication (of noumenal import alpha), given a system S and some would-be similitude T, is described as the total effective consequence of (alpha::S;U)/U: It is used to describe the exactly similar consequence of (S::T;U)/U. We may see this illustrated by the example of a noumenal grid Gamma(Q,X) for a temporal fabric X with spectrum Q, provided that the display scheme Y gives at least one universe Z (the zero condition Z is a translocation of Y), whose reduct Z/U is an observable spacetime continuum.

Appendix E. Transmit grid, via quiver

The ability to convey into a display the capacity dithered into a grid is predicated on the processive extension, which we call a fluxion 'phi'. This ability is a system of correspondence between a grid Gamma(X0,X1) and a display system X2: It is a quiver psi from Gamma(X0,X1) to X2, and its rule of correspondence passes each conditioned-argument (r,x(r);C(r)) [the condition C: X0 --> X2 occurs as an artifact of the systems, and of their pathologies under graphing] to its corresponding element y in X2; it is written

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psi: Gamma(X0,X1) --> X2; (r,x(r);C(r)) |--> y.The evaluation of psi at r is C-conditioned to a value y = psi(r,x(r);C(r)).

In order to get a realistic estimate on the innate behavior of C, we want to describe the qualitative features of C in terms of the susceptibility 'chi' and capacity 'c' [section two]. A basic approach to the proper relationship is indicated by the following correspondence identity:

V(c,chi;C) = c :: chi; C,where V denotes the fusion of its argument, the echelon (c,chi;C). In other words, this echelon gives a reference capacity c (the primary) its attribute susceptibility chi (the adjunct), under the grid condition C. And, if our grid should happen to be noumenal, then our grid condition is given by the noumenal 'alpha', so that C = Ualpha. It is helpful to remember that Ualpha is the universe of discourse indicated by the noumenality M: alpha --> S (monic), with S the encryption host. Notice, also, that the primary c is equal to S (type alpha); i.e., c is the typed version of S.

Seeing that our correspondence is the fusion of an echelon, we may build our transmission directly through the echelon system, without further recourse to the correspondence induced by the echelon (c,chi;C). The trick, at this point, is to coordinate this echelon with the eleven ideas (of noumenal entelechy) described in section zero. And, as a shortcut to this elaboration, we run a co-ordination as follows.

Appendix F. Co-ordinate echelon validity, via zero condition

The total specific effect produced by an echelon (S,T;U) is rendered here via the 'echelon-substitution instance' (c,chi;C) <--| (S,T;U), which asserts the capacity/susceptibility echelon to be the "presenting issue" for the standard/normal echelon which it entails. [A19. Noumenal Similitude (direct method), final section]

A system of noumenal coordinates is gotten [section nine] under a condition of comprehension, and it gives a co-ordinate range of validity within the noumenal plane.

Appendix G. Fuzzy wiggle the zero condition, via zero gauge

The zero condition Z is expressed by the gauge beta, given an arrow E: Z --> beta (epic) placed at the bottom of the second tope within a random element machine (rem) Xi: This epic is sometimes called the zero gauge, because it expresses each zero condition Z (a universe) as a gauge beta (a bunch of measures).

The more colorful designation of E as a fuzzy wiggle derives from the special case in which the zero condition Z is given by the zero weight Z = S'Phi, with tension Phi: alpha --> Y, and with S' the inverse of our host S. In other words, Z = locS(Phi) = loc(S,Phi), with S'=locS. Thus, we may assert (with a modicum of sobriety) the following definition:

A fuzzy wiggle is a system of correspondence between a zero weight S'Phi = locS(Phi) and a gauge beta = †(alpha): It is an arrow E (which is epic) from S'Phi to beta, and it is given by a rule of correspondence that passes each subsystem in S'Phi to a corresponding metric b in beta (a metric is a measure of proximity); it is written

E: S'Phi --> beta (epic).

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Appendix H. Protoring the gauge condition, via gauge homogeneity(a control factor)

The control factor is expressed as a gauge-homogeneity whose application, it seems, is well-suited to the demands placed on high-energy particle physicists. The matter of it all seems to depend principally on the phenomena associated with some low-lying sort of diffusion process at work beneath our presumptive spacetime continuum. And though the expression of such process is admittedly abstract, there are nonetheless a number of useful features whose parametrization may reduce the whole to a viable measurement model -- a programmable system of parameters amenable to estimation. Of particular interest are the models whose idealization may be locally approximated by a Fick type homogeneity.

We may be concrete, here, and I would like to suggest my favorite particle field of Quantum Field Theory (QFT) as the neutrino field with application: The application is bio-medical, and it points to a much needed cure of cancer. I call our application Neutrino Therapy, and it runs as follows.

An otherwise healthy tissue sample is subjected to irradiation by a reliable neutrino source passing its emission through a suitably arranged control module [the module is controlled by a factor k, where k: beta --> P', given a protoring P' = zeta(P), with secular inversion zeta of noumenal type alpha, and with the reciprocity beta = †(alpha)]. The desired effect is arranged by embedding an EPR-switch within k(beta) = {k(b), metric b in gauge beta}. The EPR-switch toggles our neutrino field back and forth between the passive and active states (and back again). The protocol is called "Gone In Sixty Seconds!", and it runs as follows.

A passive neutrino field is scanned into the cancer-bearing tissue, giving total penetration of the tissue by our field. The EPR-switch is thrown, putting our passive neutrino field into the active state: Our active field binds itself to the time continuum of cancer-bearing cells within the tissue sample. The active field is scanned right back out of the sample, removing time continuum from unwanted cancerous cells, which promptly lose interest in their prior activity, which was growth. The body's own process rapidly breaks down the offending cells (which no longer have time continuum, and which are no longer malignant). The overgrown cells either return to normalcy, or their material substrate may itself be removed (either by scalpel, by laser, or by a novel transport mechanism related to the EPR-device).

The interesting details are given precise expression through the Klein-Nishina formula (relating impedance to refraction, via scattering cross-sections). Simpler versions of this powerful formula are introduced by the Breit-Wigner resonance, and by the Cauchy-Lorentz dispersion. Not surprisingly, the whole formalism is known to reduce itself to the easy case studied in undergraduate quantum physics courses as the Compton Scattering of electrons: The neutrino fields are implied (I suspect) through the dual problem of noumenal aperture; it is a fascinating application of the Nyquist effect (aliased power) to the subject-matter of device-windowing!

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RCMP, Applied DevicesFrom: June the 11th, AD 2016 (Saturday)

To: June the 12th, AD 2016 (Sunday)

Advanced Operating System

0. Introduction. We have three primary options from which to evaluate an echelon (S,T). In all three cases, we apply some process A to the systems denoted S and T, but the machinery invoked by each of the three cases is dramatically distinct. We also have a fourth (adjunct) option, which seems to introduce an element of totally unpredictable behavior, and it is constrained in relatively vague ways. They are given as follows. In the first case, we work with a general domain Gamma(Sys,Sys). In the second case, we use an event ! against an arrow A. In the third case, we have an instantiator @ against a pair receptor (-,-). And, in the fourth case, we have an interpreter # which may or may not relate directly to the prior three cases.

1. Module Sys. We are given two systems S and T, together with an instruction that a pair be formed of them. We can imagine that our pair is formed within a general domain Gamma(Sys, Sys) of unspecified condition U.

In keeping with accepted notation, we indicate each special domain with a subscripted parameter U (the above condition) by writing GammaU(Sys,Sys) = Gamma(Sys,Sys;U). In other words, a special domain is a general domain together with a condition U whose expression is used by the protogrid Gamma to modify handling of arguments S and T taken from two identical copies of Sys; they are written Sys and Sys.

2. Module !. We are given a piece of information about the occurrence of an event. This information is passed to an arrow A through a mechanism which we will not describe, except to say that we may indicate the passing of this information as an awareness; it is written !A. What is more, a resulting apperception occurs, and it is expressed by equating the awareness !A to the anticipation A(-,-); it is written !A = A(-,-).

In other words, an apperception is an occurrence of identicality between an awareness !A and some corresponding anticipation A(-,-).

3. Module @. A tool of particular interest for me is indicated by the symbol @; it gives instance to an argument, but not necessarily to a parameter (which may or may not be presented as argument). The idea here is that arguments (say S and T) may be called, while parameters (U) must be passed. Thus, an argument is a system called by an arrow, and a parameter is a system passed to an arrow. Also, an instantial locus is a special tool that calls an argument into reception (at a slot within a receptor); it is written @, and its use is shown by the following paradigm: @A(-,-) = A(@,@) = A(S,T), some S and T in Sys.

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4. Module #. The 'interpreter' # is, perhaps, the most problematic of our four options: Itmay assume one identity after another, passing through a series of betrayal upon betrayal enroute to some other identity -- an identity which too will (in time) be betrayed to unknownpurpose. Thus, we include # explicitly as a means of keeping track of the sort of intermittencywhich seems to mar our best efforts to the contrary. By intermittency I mean the seeminglysporadic behavior which allows an identity to hold (on again, and off again) at more or lessrandom intervals of frequency and duration. A favorite identity, which is by no means absolute,is given by the condition # = @! = @(!) = instantial locus (of event) = local event.

The self-evident assertion here is that each local event is itself the interpreter of an intermittency whose precise form is by nature indefinite. It is used to show where an interpretive system (say, the noumenal alpha) becomes itself entwined with the filaments of an interpreted system (say, the host S).

5. Hybridization. In any given problem drawn (we may say) from the real world, we want touse the finest machinery available from each of the above four worlds: We want to say withgreat precision how best to combine these worlds to the get the best fit to any problem whichmight be framed within the object language used to pre-process the input system, say S. And,in similarly addressing T as an output system, we also want to use our several options to give abest description of the solution (an output) for our little problem.

6. Parenthesis. A receptor is a delimited bit of whatnot into which an argument may be called. An indicative is a delimited bit of whatnot into which a parameter may be passed.

7. Special Operations. An echelon is a pair of systems S and T written as a single entity(S,T) -- a system. The system of all echelons is a system written Echelon, and its description isformally identical to the direct product Sys x Sys. The difference between Echelon and Sys xSys consists not in their describable effect, but rather in the behavior of their rule systems.Specifically, an echelon differs from an ordinary pair in that an echelon may include anindicative, but a pair may not. An echelon is more susceptible to parametrization than is anordinary pair.

Here, Gamma(Sys,Sys) < Echelon < Sys x Sys.An arrow of fusion is a system of correspondence between Echelon and the system C of

all correspondences: It is an arrow V from Echelon to C, and it is given by a rule (ofcorrespondence) that passes each echelon (S,T) in Echelon to its underlying correspondence S::T; it is written V: Echelon --> C; (S,T) |--> S::T.

A device is an arrow of fusion with a condition, say U; it is writtenVU = V(U): Echelon --> C; (S,T) |--> S::T;U.

An arrow A is presented (in practice) through a process ALambda, where ALambda = {Alambda: Dom A --> Cod A, lambda in Lambda}.

8. Examples. 1.) The arrow of time is presented by noise. 2.) A bundle of arrows is presented by its filaments. 3.) An echelon process is a process

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ALambda: Echelon --> C; (S,T) |--> S::T.Each lambda in Lambda contributes Alambda(S,T) to ALambda(S,T) = S::T in C.

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RCMP, Applied DevicesFrom: June the 13th, AD 2016

To: June the 14th, AD 2016

Echelon Pair Receptor (EPR)

Preface. If we put two systems into a pair receptor, then we get ourselves a pair (of systems). But if we consider the pair receptor in abstraction (without its component systems), then something out of the ordinary occurs to us. We get ourselves a glimpse of a supernatural world -- a world beyond all natural consideration, a world of divine and princely things at work upon creation.

Definitions. An echelon is a pair of systems S and T written as a single entity (S,T); it is a system of two systems -- a base for the unfolding of an open process. An open process is a structure phi over an echelon (S,T): It is a system of arrows, with each constituent arrow in phi a process from S to T; it is written phi: S --> T (open phi). An unfolding is an echelon (S,T) together with an open process phi from S to T; it is written (S,T;phi).

Remark. The unfolding may be written as a special correspondence S :: T; phi. Here, the open process phi is a system (and thus a condition); it is a condition of diverse procession.

Definitions. The consequence of a system S (under an arrow A) is the image of A over S; it is written A(S) in the codomain (i.e., the range) Cod(A). The noumenal consequence of a system S is its entirety S* = d(S), where d: d --> d. The extended consequence of a system S is a consequence S-tilde extended beyond its noumenal consequence S* (the entirety); it is written

S-tilde = unfolding(S*) = unfolding[entirety(S)].

Example. Let (S,T) be an echelon unfolded by an open process phi: S --> T (open phi). Let S-tilde be the unfolding of the (noumenal) entirety S*. Let epsilon be a transducer of the form

epsilon: S-tilde --> T,where epsilon(tilde(S)) = phi(S) in T. And, since S is arbitrary in Sys, we get the identity

epsilon(tilde) = phi.The corresponding tope (a would-be commutative square whose bottom arrow has been reversed) is written with initus S --> S* (entirety), with pivot S* --> S-tilde (unfolding), with terminus S-tilde --> T (transducer), and with resultant S --> T (open phi).

Note. The transducer epsilon: S-tilde --> T is solved by the formula epsilon = phi(tilde'), where tilde' denotes the arrow inverse to tilde. This transducer is used to shape the open process phi: S --> T; its parameter induces each specific wormhole within the open phi.

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RCMP, Applied DevicesFrom: June the 14th, AD 2016

To: June the 15th, AD 2016

Device Realization

Introduction. Starting with the awareness !A (where the application ! passes the binomial arrow A to the anticipation A(-,-), we get an identity under !; it is called the apperception, and it is written !A = A(-,-). Here, we have invoked the pair receptor (-,-).

Construction. The realization is a system of correspondence between the grid Gamma(Awarenesses, Anticipations), with Awarenesses being the system of all awarenesses and with Anticipations being the system of all anticipations, and the system of all apperceptions (which is written Apperceptions): It is an arrow realization from Gamma(Awarenesses, Anticipations) to Apperceptions, and it is given by the rule of correspondence that passes each echelon [!A,A(-,-)] in Gamma(Awarenesses,Anticipations) to its corresponding apperception !A = A(-,-); it is written

realization: Gamma(Awarenesses,Anticipations) --> Apperceptions;[!A,A(-,-)] |--> !A = A(-,-).

Example. A device-level structure is a system of arrows (the structure) whose level of abstraction is that of a device: It is a structure L used to condition a process ALambda, and it is written

ALambda,L(-,-) = ALambda(L)(-,-) = ALambda(-,-;L).In fact, the device (of which L is the condition) is precisely the L-th filament of the process ALambda, and our device is written ALambda,L. Here, our realization gives the result

!ALambda,L = ALambda(-,-;L).

Remark. The echelon pair receptor (EPR) is a device ALambda = phi [cf. Item K] whose (device-level) structure is L = epsilon. In other words, the device-level structure associated with a wormhole device ALambda is precisely the transducer epsilon. That is, our epsilon [op.cit., sections 5-6] is a wormhole transducer for the EPR device given by the open process phi.

Application. A good application in the matter of device realization occurs in the design of a wormhole switch. The switch is used to gate a wormhole under very stringent control, and it is modeled (to device precision) by the same sort of gating system found within the elastic-voltaic control of ionic channels in a bilipid nervous membrane. Here, the switch is described as a Poincare-Bendixson type effect associated with a bimodal dispersion relation, such as the one predicted by the Van der Pol system (or by a parametric amplifier). [cf. A23.2. Permission Key: Generic Wormhole Device]

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RCMP, Adaptive DevicesFrom: June the 14th, AD 2016

To: June the 15th, AD 2016

Diffusion Across A Heterogeneous Substrate

TimeTime is an ocean of many dimensions; it is a sea of chaos tossing measureless bits of whatnot through the several planes of existence -- through diverse worlds of noumenal character, and through never ending successions of wave upon wave crashing in among one another.

The tiny threads of random correlation (within our busy little chaos engine) do gather unto their length a mighty filament of noise -- a prickly strand of complex information bearing into a greater noise-bundle, and it is the bundle which we call time.

A cross-foliation of many wave systems does weave the warp and woof of a temporal fabric X, and its study reverts (layer by layer) through dynamical systems, to kinematic processes, to abstract arrows, to simple correspondences, and to the individual echelons of which each simple correspondence is the fusion.

ErrorThe ability of an experimental apparatus to instrue within its own localized fabric (of time) a species of error, and the capacity of its environment to conduct error orthogonally away from an otherwise ideal bit of time: These are the determinative factors in the rate of propagation for an error signal generated in response to the lag and drift of an otherwise tame system (of temporal character).

From the view of a systematic theory of the echelon, we may dissect the above scenario relative to a single unit of propagation; it is a unit set up prior to the introduction of a propagator, and its unfolding will give rise to as much of the virtual propagation as is needed (on a dynamical basis of a demand-driven system of logistic supply).

Let a system S and its cosystem T be given to a pair receptor (-,-), so that we get an echelon (S,T). The unfolding, which we denote phi of (S,T), is a binomial arrow argued over our echelon. The unfolding is modeled by a parametric system of diffusions, where each diffusion filament resolves itself into its centralizing and decentralizing components, respectively.

The centralizing component S' of a diffusion filament tends to concentrate error signal 'theta' into the immediate vicinity of each temporal strand. The decentralizing component S" of a diffusion

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filament tends to diffuse error signal into the extreme hinterlands of each temporal strand. And in the middle ground, where space and time do conspire to the support of life (and of life's purpose), we discover a naturally occurring heterogeneity about the distribution of covering elements over the low-lying chaotic substrate.

Therefore, in the construction of a diffusion across a heterogeneous substrate, we allow our formalism to adapt itself to a nontrivial range of fluctuation (up and down the ladder of abstraction) whereby the underlying chaos within our continuum may interact remotely with certain of the overarching structures built almost entirely with reference to a right true continuum (a complete transitive system).

Density of Error over TimeThe standard normal form of an error density (over time) is described (to good qualitative fit) as a logistic density, and it is written rho-bar: Error --> Capacity; theta |--> 1/[1+exp(theta)]. If this density is expressed over the real number system (the one constructed by Dedekind), then we may calculate the continuum line-derivative of rho-bar (our dependent variable) relative to theta (our independent variable), to obtain the result

d(rho-bar)/d(theta) = rho-bar(1– rho-bar).To this logistic equation we may introduce a parameter b reflective of the perturbation

perturbation: rho-bar --> rhob.Moreover, should we prosecute the matter to any further consequence, we arrive at the

natural discovery that each scalar parameter b expresses the scalar behavior of a metric within the gauge beta. Thus, to each density of locale rhob, we have a linking parameter to the metric homogeneity delb (within the protoring P').

Finally, each density of locale contributes a value of the dispersion relation which, in turn, gives the density of states within a distribution of energy over a physical system configured within a spacetime continuum. And, because each density of states corresponds to a covering density (presumed inhomogeneous), it follows that fluctuations within the span of dark energy across each universe will give rise to very small temporal anomalies -- anomalies whose propagation may vary broadly from one universe to another universe.

And, should we suppress (for simplicity) the non-essential data and parameters attaching to a "mechanical universe", we may attack the matter abstractly through the notion of instantial locus. An instantial locus is a tool denoted by the symbolic term @, and it is characterized by the 'realization' @A(-,-) = A(@,@): The definition is completed by requiring that the arguments be generated (by each @), or formed (by basing each @, say by a condition U). Here, the assumption is that AU(@,@) ≠ AU'(@,@), showing that U≠U' gives different basing; it is a difference expressed as a density, a distribution, and a dispersion.

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RCMP, Applied DevicesFrom: June the 15th, AD 2016

To: June the 17th, AD 2016

The Zero Diffusion

Introduction. A cosmos is a system of 10^504 universes, where each universe is configured through a translocation ji: Y --> Zi of a cosmic display scheme Y into a corresponding zero condition Zi.

Detail. Here, the figure 10^504 denotes a one followed by five hundred four zeroes: The figure arises from an assumption of four spacetime dimensions in a cosmos of four hundred eighteen Planck cells, giving 2^(418x4) = (2^418)^4 = (10^126)^4 = 10^(126x4) = 10^504.

Remark. The carrying capacity of a universe operating in the ground state is expressed by a mild (parametric) deformation of the logistic density rho-bar(theta) = 1/[1+exp(theta)].

Definition. A density of locale is a metric perturbation of the logistic density rho-bar, away from the time-averaged ground state (indicated by the overbar), and it is written

rhob(theta) = {1/[1+exp(theta)]}b.

Note. The development of our density of locale follows out of the article Item Q: Early Alpha Measure Theory (focus on example four). The notation there must be adapted to the current form: I suggest that the old 'beta' be rendered into a new b0, and that the old 'b' be rendered into a new b1. Thus, we might use the convention b = (b0,b1) without confusion.

Example. The Glauber functions are rendered here to readg(s;b0,b1) = 1/{1+exp[-2b0(s-b1)]},

where the notation x = g(s;b0,b1) allows us to solve the inverse as s = g'(x;b0,b1) = ix+b1, givenix := 2b0ln[x/(1-x)].

With this notation, the induced operations of Item Q are writtenx +' y = 1/{1+exp[-2b0(ix+iy+b1)]},

andx ' y = 1/(1+exp{-2b0[ixiy+b1(ix+iy+b1-1)]}).

The supporting development of Item Q can be read to some advantage. I recommend that the reader pick up at proposition two (whose proof is helpful), and then skip forward to example one and the sequel.

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RCMP, Applied DevicesFrom: June the 15th, AD 2016

To: June the 16th, AD 2016

Wormhole Perturbation

Introduction. My first experience with the art and science of wormhole design befell me as an honest matter of serendipity. Having never heard the term wormhole, and never having considered wormhole theory, I was positively astounded when my exposure to the paradigm of wormhole duality first presented itself to my awareness fully forty-nine years ago.

The basic arrangement involved a sturdy yellow truck (by Tonka), a reliable scooping mechanism (a serving spoon from my foster parent's kitchen), and a healthy measure of latitude within which to experiment with the uses of my apparatae within the confines of an available ground system (a patch of dirt in the back yard).

The whole procedure began innocently enough as I began to dig down into the hard dirt beneath my hands and feet. But, I did not get very far down before I realized that a second hole prepared at a near remove would enable the formation of a subficial structure -- a connection between the two holes at a distance of eight inches (give or take one or two, more or less). And, as that connection began to form, and as my breakthrough began to deepen, I realized that if I were both careful and thorough in my completion of the project, then I would have at my disposal the means of running through the very depth of it all my sturdy yellow truck.

Before deploying the truck, I did make specific recourse to open, and to expose, the cab -- it was a driver's compartment without a driver. I did apply the scoop (still dirty from digging) to loosen and pry each flange across the undercarriage, thereby allowing the top of the truck to be completely separated from its underlying chassis. And were my suspicions confirmed: There was no driver in the truck. There were fingers like you would not believe, but no driver! I did therefore reattach the assembly (in its entirety) and recrimp each flange until the vehicle was tunnel ready.

I pushed the truck down the sloping entry to the tunnel (on my left); I pushed the truck down and across the low point of that U-shaped tunnel; and, I did also pull the truck back up through the other side (on my right). I retrieved the vehicle safely and securely, and I did verify that despite the sinister (left-handed) method of approach, the vehicle had been nevertheless retrieved intact: The hull had not been damaged (it remained properly attached); the vehicle integrity had not been compromised (my seal had held through the uncertain transit); and, as before, there was still no driver in the truck!

I further realized that the top section of my tunnel bore itself the strange resemblance to a land bridge over the void beneath. And though I did not immediately realize the significance of this bridge, I did nonetheless test its integrity with yet another transit of the vehicle which I now call Tonka-One. Only after I had demonstrated the effect to my own personal satisfaction did I realize the serendipity: I had discovered (with Tonka-One) that a duality was built into the tunnel/bridge, and that, should I choose the direction of approach with care, I could as easily go over or under the duality to arrive in time for lunch on the other side (of transit).

Having convinced myself very thoroughly of the effect, I did bury and conceal the whole system, using only the dirt -- the dirt which I had previously extracted using only the mechanism

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supplied by my foster parent's kitchen (the serving spoon repurposed to a scoop). And thus it is, to this very day that I wonder: How did all that driver get into the truck? I wonder: What will become of Tonka-Two?

Tonka-Two. Fully twenty-six years had lapsed before I gave the matter of Tonka-One a proper write-up. Having made my breakthrough in the year 1967, it was not until the year 1993 that I attempted a theoretical explanation of my little duality theorem using a sophistication no more protracted than had already been found meet within Albert Einstein's theory of Special Relativity. And though the matter was set into a context of great generality, the actual explication was surprisingly concise. A private circulation of my paper on Alpha Measure Theory made known the inner workings of this theory of measure, and it too was buried (and forgotten) until I realized this day its significance to the work with which I continue to find myself inextricably interwoven, intermingled, and otherwise intertwined.

The year is now 2016, and fully twenty-three years have passed since I did the write-up: This is a sum of forty-nine years since I discovered the effect of duality against an otherwise homogeneous system of transit: I discovered that despite best efforts at the sealing of Tonka-One, that the world of us does conspire to the inclusion of a driver in the truck -- lots and lots of driver!

Liberty One. Today, I feel as though a burden of circumstance and of misunderstanding has been lifted from my immediate horizon: I feel as though the world of possibility has been restored (at least partially restored) to my good name -- to my good intention, and to my good fortune. Accordingly, this is Liberty One, signing all good wishes!

The Business at Hand. The following insert [Item Q] is a j-peg bitmap of the opening excerpt of my original paper on the relativistic topic of wormhole duality, dated December 1993.

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RCMP, Applied DevicesJune the 17th, AD 2016

Review of Contents

In the design of a generic wormhole device [cf. Permission Key, page 2 (following title page)], we attempt a metaphor borrowed from transpersonal analysis. We suppose with Socrates, Plato, and Aristotle; we suppose with India, Persia, and Egypt; we suppose with daring, vigor, and candor, that to any arbitrary entelechy unfolding within the world of men (and of ideas), there corresponds a process which answers very nearly to a description of the given entelechy itself. In fact, we suppose that to any systematic difference 'delta' which might subtend our process of unfolding entelechy, that we may describe this systematic difference as an arrow of the form delta: S --> Gamma(X0,X1); a |--> (x0,x1). This delta is sometimes called the dither of its host S into the grid Gamma(X0,X1), and it is taken to be a subjective bit of play giving life to an otherwise mechanical system -- the random element machine Xi.

Accordingly, we take an interest in the echelon process as a special fusion (with condition), giving a device -- a device which we back-solve (down to its essentials) as a generic wormhole device: It is the thrust of this entire document. Moreover, we take as a grounding principle the idea of locality as either of the following notions (prior to their shared fusion with one another as a tunable device of the sort advertised): a.) the instantial locus @ gives the instantial capacity (of distribution, i.e., realization); and, b.) the local event @! = # gives an enticing link to the density of locale rhob. Thus, the fusion of a.) and b.) gives precisely the sort of grounding principle we need (in respect of locality).

Here, the echelon process is studied in respect of an echelon pair receptor (EPR), with the result of an EPR-switch (a wormhole switch) drawn out of a wormhole transducer, where the transducer is written epsilon: S-tilde --> T through a process of device realization, where S-tilde (the host system S with an overhead tilde sign) is the result of opening a system S; it is written

open: S --> S-tilde.The key link between this echelon process and ordinary diffusion physics consists in an

identification between the underlying mechanics of diffusion and the echelon process out of which they seem to derive. Specifically, we are able to show that the temporal fabric X (preceding the spacetime continuum model of a universe Zi = ji(Y) = ji[f(X)] ) gives rise to a diffusion variable 'theta' through a process of verticulation, written verticulation: X --> theta.Thus, by coding our fabric X into the convenient meso-syntax of an accessible diffusion variable (such as theta), we obtain a significant leverage against some otherwise very musty equations concerning the general behavior of a fabric under transformation. We also get direct access to a canonical diffusion system using no more sophistication than is required to understand the logistic density rho-bar(theta) = 1/[1+exp(theta)].

Finally, by relating the opening of a host S to S-tilde, to a process of 'fusion and diffusion' , we get a very nice bridge to diffusions across a heterogeneous substrate: It includes access to time, error, propagator, and a useful density argument. Also, we gain direct access to the zero diffusion derived out of rho-bar, and this formalism finds direct application in the 'early alpha measure theory' of a wormhole. It remains for the experiment to confirm my early investigation of the paradigm for 'wormhole duality'.

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Part 3~ ~ ~


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Dielectric Capacity In MylarField-Theoretic InteractionRC Mann-Price, MA/PhDExternal AdjunctHarvey Mudd LaboratoryMidas Energy GroupFebruary 16, 2016

0. IntroductionExcitable media

This report is a study of conduction in excitable media; it is a study of the asymmetric interactions throughwhich a population of individual systems propagate signal. We assume that such systems are character-ized by transitions occurring between two states of conduction: high and low.We find that the (quasi-critical) behavior of individual systems, such as dipoles and ion channels, evokespatterns (of activation) that support the spontaneous emergence of an organic intelligence -- an intelli-gence easily trained to the facile acquisition of diverse modes of productive decision-making, and ofcreative discovery, within an unknown training environment.This line of investigation distinguishes three types of dynamical regime: 1.) a purely spatial distribution,2.) a purely temporal procession, and 3.) the hybrid spacetime transponder. In each case, we have theessential growth (and persistence) of structure on all scales of the spacetime evolution. The correspond-ing paradigms are: 1.) a social polymer system, 2.) a random membrane system, and 3.) a mixed dielec-tric transponder.Throughout this report, the level of rigor and precision grows increasingly acute, resolving each individualsystem into its scheme of tension -- its pattern of support for a coalition of many little modules (of action)evolving real-time feedback intelligence.

1. The essential paradigmsA polymer system

Our first inquiry treats conduction in mylar. It describes the growth of current across a dielectric substratepressed between two fields -- one perturbed, the other quiescent. The displacement is measured undera voltage-controlled excitation which is hoped to produce an elastic response. The response should bemediated by the electrostatic compression and relaxation of polymer density (dipoles) within our device.The following image depicts a plate of gold (Au), a plate of silver (Ag), and between them a dielectric

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substrate (mylar), which is populated by randomly oriented dipoles:

The polymer system (spatial) is ‘social’ in the sense that patterns of activation unfold within the hostdevice through the sharing of a local distribution -- a distribution of energy concentrated over the space ofmany constituent dipoles.

A membrane systemOur second inquiry treats the biological membrane, consisting of a phospholipid bilayer; it is the dielectricsubstrate used to construct the cellular enclosures for each neuron (nerve cell). The capacitance of thissubstrate has been studied by Curtis and Cole, who pioneered the study of electrical fields in tissue.A schematic is given for the elasto-voltaic control of a biological membrane penetrated by a single-species ionic channel, together with the plates of a battery (in purple) used to indicate the voltaic pileequivalent of charge separated across the inner and outer walls of the membrane.

The membrane system (temporal) is ‘random’ in the sense that each individual ion channel across thebilayer opens and closes according to a rule given by a stochastic process -- a process whose variablesare random.

A dielectric transponderOur third (and final) inquiry treats the basic model for a generic transponder, which is asserted through ablend of the social polymer and the random membrane. The result is a complex system with the capacityto ‘channel entropy and field structure’ -- a spacetime fabric growing uniformly in the large, heteroge-neously in the small, and discretely in the very fine scales of cosmic expression. Because of this, eachuniverse within our cosmos is a randomly biased transponder; it is a transponder whose activity is sharedthrough a social dispersion, and it is sensitive.The dielectric transponder (spatio-temporal) is ‘mixed’ in the sense that a combination of random andsocial techniques is invoked to articulate the propagation of signal -- a signal of intelligent behavior within“ ”

2 Dielectric Capacity In Mylar (Field-Theoretic Interaction).nb

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a “complex adaptive system”.

2. Parametric amplifierTo capitalize on the sensitivity of a dielectric transponder, and to expand on its adaptive behavior, somebasic features of the parametric amplifier are observed of its synthesis (within a complex adaptivesystem).

Experimental gainOur basic device develops an electrostatic potential across the terminals of a parallel plate capacitor.This potential describes a voltaic load across the plates, compressing the density of polymer within thecapacitor substrate -- a dielectric substrate of mylar.An applied field charges the device through a reorientation (and distribution) of individual molecules (thepolymers). These molecules become excited at a rate measured by their empirical rate constant A,which specifies the strength of interaction between each local field and the applied (perturbation) field.Once the applied field is removed, these molecules return to their quiescent state at a rate measured bytheir empirical rate constant B, which specifies the strength of interaction between each local field and thequiescent (ground) field.The cyclic process, governed by the rate constants A and B, is subjected to a symmetric decompositionagainst each of several contact parameters α. A similar experiment with ion channels in nerve cell hasshown the existence of a bimodal recurrence within the coupled rate equations. This is thought to giverise to a parametric gain with respect to the applied (input) field. The resulting amplifier is, therefore, a‘parametric amplifier’ embedded within a relaxation oscillator of parametric type.

Carrying capacityThe symmetric decomposition of a cyclic process amounts to a normal mode decomposition of an oscilla-tor skewed by the contact parameter α; it is the so-called ‘bias parameter’, and it specifies the range andscope of deformation applied to a normal mode decomposition. The standard normal form underlyingthis process is given by the logistic map

dx /dt = rx(1 - x),with 0⩽r⩽4 and 0⩽x⩽1.

Medial loadThe dielectric capacity of a mylar system S is studied relative to the polymer contact α used to estimateeach structural element r in S/α -- each (putative) load element and its connectedness within S. Thiscapacity is measured by a system of currents drawn through S. Thus, to each local measure of capacitythere corresponds an arrow within the medial process M : α→ S (monic), giving the noumenal capacityM /α : α→ S /α. [cf. Graph/Id, §Remark; February 8, 2016] This noumenal capacity is sometimescalled the medial load, and its diagram is the following:

Dielectric Capacity In Mylar (Field-Theoretic Interaction).nb 3

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Specific entropyBetween a central value and some peripheral spread, a specific entropy takes hold. If im(M) =M(α) in S,then the central tendency (or value) is im(M) and the peripheral spread in S is

S / im(M) = cod(M) / im(M) = coker(M).The secular reduction of peripheral spread by central value gives the correct qualitative behavior for anentropy; it is written

coker(M) /α = [S / im(M)] /α ≃ [S /dom(M)] /α ; monic M= [S /α] /α ≃ Sα2 ; consecutive reductions

General entropyMore abstractly, the specific entropy es of an arrow A is written

es(A) = (coker/dom) (A).The general entropy e of a process A = {Aλ : dom A → cod A; λ inΛ} is written

e(A) = {es(Aλ), Aλ in A}.

3. Special factorsImplicit parameter

An implicit parameter occurs within each filament of the displacement current. This current is renderedas a process (of many constituent currents, many individual arrows). Each value of this parameterindicates the influence of a partial pressure upon the device, and the process may be said to show anelasto-voltaic response.

Kelvin parameterThe Kelvin parameter τ of absolute temperature is a measure of kinetic activity. It is used to indicatethose levels of activity through which a thermodynamic system may pass, especially those at whichstability becomes critical.For instance, the specific entropy as a function of energy for a two state system is depicted as a unimodalcurve:

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The temperature as a function of energy for the two state system depicted above is given by a pair ofhyperbolas:

[Kittel & Kroemer, Thermal Physics (2000): pp.460-461]The negative reciprocal of the absolute temperature is given by a rotated sigmoid (the ninety degreerotation of a bounded monotone function):

4. The experimentApparatus

Between two plates of silver and gold, a thin film of blue mylar is pressed. A sensitive clamp is arrangedto obtain, for each measurement of current across the plates, a precise estimate of pressure across thefilm. Each degree of partial pressure imposed by the clamp is recorded as a filament (an arrow) in thekinematic process -- the process resolving an applied kinematic field of force.Similarly, the kinematic field may be substituted by an electrostatic field setup with a special effect ateach boundary layer near the interface of a conducting plate and the insulating mylar. Here, the electro-

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static pressure will vary as a function of penetration depth within dielectric substrate, so that a precisespecification of the test medium (blue mylar) must be given.

ProtocolThe experiment is conducted under a system of guidelines aimed at the elucidation of three overlappingclasses of phenomena: the field-theoretic interaction between the perturbation field and the quiescentfield; the boundary layer interaction; and, the general dipole interaction. The following interactionschematic shows three overlapping regions of interaction:

The guiding theme throughout each propagation of signal across our device is three-fold. First, we wantour mylar device to emulate the behavior of a full-blown, wide-open dielectric transponder. Second, wewant to tease into its component layers the detailed exchange (of one signal event for another), wherethe value of a deviced event is estimated under the transactional analysis of the cost-benefit index foreach event in the signal. Third, we want to see the explicit evidence of the echelon criteria (for activeuse): the device ‘gives more than it takes’. That is, the effective use of our dielectric technology shouldfully engage each opportunity presented within the operation of a quiescent field. This includes coupledinteractions within each ‘subficial’ structure concealed by the remote sharing of quiescent field technology.Accordingly, some special tools are developed for the handling of our several implicated technologies.The tool set is organized by a novel technique invented for the propagation of error signal within theoperating environment for a complex system. Indeed, the system and its environment are seen to inter-act in the manner of a random element machine whose construction is delineated below.

5. Data reduction and errorTerminology

A system is a cohesive whole. An arrow is a system A that points a system B to a system C; it is writtenA : B →C. A structure is a system of arrows. A process is an indexed structure; it is written

A = {Aλ : dom A → cod A; λ inΛ},given an index system Λ.

Random element machineThe following diagram gives a random element machine used for the reduction of an experimental sys-

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tem S to a manageable data structure:

The systems used to define the above random element machine are the following:contact lemma ℘ = {α in d, d : d → d};contact system α in℘;host system S;noumenal grid Γ(Q, X);scheme of action Y;zero condition Z =S-1 Φ;gauge β = α†; and,protoring ℘-1.

The arrows used to relate these systems are the following:selection σ :℘→α;noumenal M : α→S (monic);dither δ : S → Γ(Q, X);quiver ψ : Γ(Q, X) →Y;translocation j : Y → Z;fuzzy wiggle E : Z→β (epic);control k : β →℘-1;tension Φ : α→ Y;zero noise W : S → Z;reciprocity † : α→ β; and,secular inversion ζ :℘→℘-1.

Error signalWithin each tension Φ : α→Y, we get a species of error whose image in the scheme Y gives rise to thesupport of a translocation j : Y → Z. The image of translocation is called the zero weight, and it is asubsystem of the zero condition Z = S-1 Φ, which is the localization of tension over the host system. Eachsubsystem of Z is measured in a gauge β under an arrow E which expresses the amount of wiggle roomassociated with the subsystem. And, because this expression is given by a fuzzy number, the epicE : Z→β is called the fuzzy wiggle. In particular, the wiggle room associated with the zero weight is givenby a fuzzy number in the gauge β, and its result is called the error signal θ; it is written

E(zero weight) = error signal in β,where

im(j) = zero weight in Z.

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The support diagram (a tope) is the following:

6. Numerical techniquesThe continuum of time

A constructive use of noise (and of noise-like systems) assigns to each noise bundle (a bundle of noisefilaments) a measure group whose average over the bundle converges to an ordinary time continuum;the work is done by the measure group. Thus, two bundles are continuum-equivalent if their measuregroups give the same continuum. Note, however, that an equivalence class may distribute its bundlesnonuniformly relative to a zero condition, say the zero weight (of signal propagation through continuum).

The constructed bundleA noise bundle B is constructed from the spectrum Q populated by noise parameters r, giving the noisefilament as a preimage (B →Q, epic)-1 (r), which is the fiber in B (over r in Q), so that the construction isdescribed by the behavior of the local monic Γ(Q, X) → B. The following illustration gives the right idea:

Here, the bundle B is the pivot of a short exact sequence (of arrows).

The reconstructed scheme of actionThe commutative diagram

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is identified by the following arrows: dither δ; idempotents p0,p1; indicial i; geometry g; spectral extensionγ = gi-1; transit f; action h = fγ; quiver ψ. Here, the dither δ : S →Γ(Q, X) is given under the quiverψ : Γ(Q, X) →Y of a noumenal grid Γ(Q,X), so that the pullback condition

fg = hiis satisfied identically by the composition ψδ. That is, the identity ψδ = fg = hi holds at each argumentincluding, in particular, at the noumenal M : α→ S (monic), giving

(ψδ) (M) = ψ(δM) = Φ.Here, the tension Φ : α→Y is the fluxion ψ impeded by the noumenal dither δM. In other words, theimpedance associated with the scheme Y resolves under Φ to a system of preimages, with one preimageto each module of action within Y. Here, the typical preimage is written Φ-1(h(r)), with r in Q. Thus, thescheme of action Y is reconstructed, module by module, within the impedance δM.This reconstruction can be tested in the laboratory by calculating the preimage of each module, and thenanalyzing the spectrum Q as the codomain of a composite arrow p0(δM) : α→ Q. The individual filamentsover Q are measured upto the resolving power of Q within the host impedance δM, and the scheme Y isrebuilt using the estimates on each module.

Modular resolutionThe modular resolution of a scheme Y is a family of modules

Mod(Y) = {h(r), r in Q}driven by an action h : Q→Y, with spectrum Q and scheme Y, and indexed by a transit f : X →Y. Here, hpicks a module and f gives it index. Thus, each module in Y bases a system within the impedance δM,and each such system is said to be an element of impedance. In other words, h resolves the impedanceinto elements δM a, where a in α expresses the component of δM whose module in Y is given by thebehavior of S/a under a domain restricted dither δ S/a composed with hp0. This construction is illustratedby the commutative diagram for ‘the reconstructed scheme of action’. Also, we sometimes want to knowwhich of these elements of impedance is representable; we want to know when, and to what extent, eachelement will contribute to the base Y.

The representable quiverA quiver is a grid-theoretic fluxion, where a fluxion is a processive extension; this quiver is written

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ψ : Γ(X0, X1) →X2,with systems X0,X1,X2 and grid Γ(X0,X1). A quiver is representable if its action is transitive. A scheme isthe codomain of a representable quiver. Therefore, the base of a noumenal grid (which is a pullbackgrid) resolves into modules if, and only if, its quiver is representable.

7. A correspondence conditionThe kinematic process

The kinematic process resolved by the above experiment may be described as an α-transitive system,where the contact α is given as the domain of a tension Φ : α→Y (the tension being an impeded fluxion,and the fluxion being a processive extension). Thus, if each arrow within that process can be written as arandom variable, the resulting process is stochastic. Now, a dynamical system is a stochastic processwhose filaments (the random variables) are transitive. Therefore, an α-transitive kinematic process A isan α-dynamical system, so that A/α is a dynamical system (if the filaments are random variables).

Dynamical systemsTechnically speaking, the definition (tangent bundle) for a “dynamical system” is actually the definition fora kinematic process. To avoid confusion, we may say that a ‘kinematic process’ is a section of sometangent bundle (this is correct), and that a ‘dynamical system’ is a section of the corresponding cotangentbundle (also correct).Thus, the correspondence between a kinematic process and some dynamical system must be articulatedby a revised definition of the tangent and cotangent bundles, but not necessarily along the lines laid outby N. Steenrod’s fibre bundle. Rather, we retain the bundle as the pivot of a short exact sequencebetween a grid Γ(X0, X1) and its first argument X0. [cf. noise bundle below] Also, our bundle must rest onthe operative notion of a system, rather than on set theory.

ReferenceN. Steenrod, The Topology of Fibre Bundles; Princeton University Press (1951)

8. The noise termThe zero noise is written W : S →S-1 Φ, with tension Φ, and with quiescent field F0, cover H0.

Quiescent and applied fieldsA field is an arithmetic cover. The noumenal field F associated with a tension Φ : α→ Y is given in termsof the gauge-homogeneity, giving a cover

H = ∇βΦ,

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where the gauge β = α† is a modular system of metrics (a metric is a measure of proximity), so that weget the secular reduction

F = H /α.In other words, the α-arithmetic reduction F of the cover H is a subcover of H. Also, there is the notionthat a potential U is an arithmetic tension Φ/α, together with the idea that a field F can be written as agauge-homogeneity over a potential, giving F = ∇βU. The corresponding commutative diagram is

ConnectionHere, in connection with the numerical techniques based in each continuum of time [Section 6], and inresponse to our findings on the noise term associated with a tension Φ, we assert a notion of continuum-equivalence that reduces the theory of fields (in a deformed continuum) to a study of ‘the bending prob-lem’, which is asserted by the following recipe for a study of abstract albegra:

The number line is used to introduce the basic operations of arithmetic, so that if the line is bent to a curve,

the operations get transformed and ordinary arithmetic becomes abstract.

InterpretationThese are our findings, and they point to a novel interpretation of statistical mechanics -- an interpretationof depth and significant realignment. Thus, if our findings are valid, and if our interpretation holds underfurther testing, then we would have to reexamine some major constructs associated with the basic opera-tion of a continuum. In particular, we would have to reconsider the species of continuum that is currentlyused to model events unfolding within the spacetime fabric. We would discover that a continuum is acomplete transitum (of some type α). Thus, to each continuum X over a transitum X, we get X = X /α; thisis called a load-bearing continuum, and α is the load carried.

9. PolarizationThe problem of establishing an electrostatic field in matter is simplified by an assumption on the behaviorof the charge-carriers within a given body of known substance. Our assumption is that each individualcharge is bound to a specific molecule within a polymer density, and that the charge is free to moveabout its molecule, so long as it does not stray.


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As to the molecule itself, however, we are dealing with a chain (the polymer) whose orientation within aknown substance is sensitive to the presence of one or more fields of impressed force. We are dealingwith the tendency of a known chain to rotate into a position of alignment with an imposed field E, which isdescribed (for the moment) as an electrostatic field. And because E exerts upon our molecule thistendency to align (against the randomizing influence of various types of noise), we begin with the assump-tion of a weak field into which a system of randomly oriented dipoles will proceed to bias each jitteringdegree of alignment (without significant loss of background noise). This procedure is called polarization,and it is gradual to the extent that our applied field is reasonably weak. Accordingly, a mechanism ofalignment is expressed through the combined action of many individual dipoles contributing to a net bias.This bias is described as a field called the polarization P, which is the “dipole moment per unit volume”.[DJ Griffiths, Introduction To Electrodynamics (1981): p.144]

PermittivityA gentle augmentation occurs through the electrostatic generation of a field D = ϵ0 E + P; this is called theelectric displacement, and it describes the superposition of the electric field E (free charge) and its polar-ization P (bound charge). The multiplicative scalar ϵ0 is called the permittivity of free space, and itdescribes the unperturbed permittivity of a vacuum (in the absence of matter).The displacement may also be written D = ϵE, where the permittivity ϵ is an empirical constant associatedwith the effect of passing an electric field through matter. Also, a dielectric constant is defined by theratio κ = ϵ/ϵ0, and this is sometimes called the “specific inductive capacity”. [Slater and Frank, Electro-magnetism (1947): p.43] Further, the ratio of polarization P to ϵ0 E is called the “susceptibility,” and isdenoted by χ. Thus we have P = χϵ0 E, with κ = 1 + χ. [op. cit., p.44]Hecht [Optics (1987): p.36] puts it nicely when he describes the electric permittivity of a medium for thecase of the parallel plate capacitor, where it is “the medium-dependent proportionality constant betweenthe device’s capacitance and its geometric characteristics.” He adds that, “the permittivity embodies theelectrical behavior of the medium: in a sense, it is a measure of the degree to which the material ispermeated by the electric field in which it is immersed.”

Load parameterThe arrow of selection, written σ :℘→α, draws a contact system α from the contact lemma℘ = {α in d, d : d → d}, given a contact engine d : d → d. The contact α is sometimes called a load parame-ter for the continuum X formed by completing the transitum X, where X is the codomain of the geometryg : S →X, with host system S. Here, it is seen that X is a ‘load-bearing continuum’ -- a geometric contin-uum of type α. This α is also the noumenal domain for the embedding M : α→S (monic, type α). Here,an economy of notation occurs because each monic of type α is, by construction, an embedding (type α);it is an α-embedding.A general embedding theory falls out of this formalism as a straightforward corollary of the ‘sublogisticcontinuum’, which I now construct.

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10. Application: ‘egg-catcher’Noumenal permittivity

The permittivity ϵ is the coupling parameter between the electric field E and its medial displacement fieldD; they are written

D = ϵ0 E + P = ϵ0 E + χ ϵ0 E = (1 + χ) ϵ0 E = κϵ0 E = ϵE,where P is the polarization, ϵ0 is the polarizability of free space, and ϵ is the polarizability of the medialhost (dielectric substrate S/α) for E.This polarizability may be expressed as the image im(M) of the noumenal M : α→ S (monic) from acontact α in the lemma ℘ to the host system S; it is written ϵ ≈ im(M). Also, we may understand thenoumenal as embedding a permittivity ϵ of type α; it works because the monic M gives α = dom M ≃ im M.In other words, the displacement arises out of direct consequence of the noumenal M, and its correspond-ing phenomena are manifest in both the field and current (of displacement). Accordingly, we need toknow something about the ways in which subficial structure may creep up to the level of manifestationexpressed as fluctuation within the total effective action. That is, we need to know something very tellingabout the behavior of noise buried low beneath each logistic continuum.

Sublogistic continuumThe logistic continuum is the continuum generated by the logistic density function x(θ) = 11 + eθ. Thisdensity function may vary with far-reaching effect given any change to the parameter values. Thus, if wecode with a parameter value that is only approximately correct, we may inadvertently confuse eachmatter of entailment associated with two distinct (but similar) signals. To keep track of this type of confu-sion, and of its surprising consequences, we use a density argument to isolate each carrier of subficialstructure; we use a model of the sublogistic continuum.The sublogistic continuum is a continuum whose density over the logistic continuum is under unity; it isan ‘egg-catcher’, and it finds broad use in the world of real-time encryption. In other words, our workneed not suffer the classical tradeoff between stability and efficiency; it is a matter of direct import tosecure communications.

11. Simulation: A biological reaction-diffusion systemThe cubing relation

Let an error signal θ map into the open unit interval 0 < x < 1 with logistic densityx(θ) = 1

1+eθ .The θ-derivative x’=x(1-x) distributes signal with dispersion x”=x(1-x)(1-2x). The sigmoid x is amodal; the

’ ”

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θ ’ ”logistic x’ is unimodal; and, the dispersion x” is bimodal.The sigmoid x(θ) gives an asymmetric pair of diffusion potentials whose polarization V looks voltaic. Thecharacteristic force is F = -dU /dV, where U = pw(1 -w) is the kinetic potential arising from a work functionw = V2 2; it is the work needed to charge up a dielectric with unit capacitance C=1. In a reaction-diffu-sion system, the force F is given by the Laplacian ∇2 V, which expresses curvature. Substituting the workfunction w into the kinetic potential U gives the result

F = ∇2 V = -2 μ2 V1 - V2.Here, ∇2 = ∂2 ∂x2 and μ = mobility of charge in the dielectric substrate.A normalized Laplacian is given by setting ∇ = 1 2 μ ∇, so that we get ∇2 V = -2 μ2 V + 2 μ2 V3 ⇒2 μ2 V3 = ∇2 V + 2 μ2 V ⇒ V3 =V + 1

2 μ2 V =1 + 12 μ2 V = 1 + ∇2V. Notice that the factorization

1 + ∇2 = 1 - i ∇ 1 + i ∇ , where i = -1 , indicates a product of feedforward and feedbackward forces ofpropagation. Thus V3 - ∇2 V = V, so that the cubing arrow cu : V →V3 gives the constitutive relation

cu - ∇2 = id .

Diffusion mechanismsThe transmembrane current (across nerve cell) is a voltage-controlled diffusion of charge (isospin) carri-ers. The diffusion mechanisms are voltage-gated ion channels, together with ionic tunneling and a smallcontribution from osmotic back-transport through not too tightly closed channels. The channel mecha-nism permits charge carriers to flow from regions of high ionic concentration to regions of low ionicconcentration as established by Hodgkin & Huxley (1952). The ionic tunneling hypothesis explains themembrane capacitance measured in the squid giant axon by Curtis & Cole (1938). Osmotic back-trans-port (back-propagation) is an adaptation of Brucke’s theory of osmosis through aqueous pores (1843);this adaptation explains small ionic transient currents against the concentration gradient ∇ρ across aclosed membrane channel.

Convective and diffusive current densitiesThe convective derivative

_dtdρ = _∂t

∂ρ + x ·∇ρ,with x ·∇ρ = ∇ ·(ρ x ) = div jconvective, has current density jconvective = ρ x , where x = dx /dt. Also, Fick’s law

_∂t∂ρ = -D ∇2ρ,

with -D ∇2ρ = ∇ ·(-D ∇ρ) = div jdiffusive, has current density jdiffusive = -D ∇ρ. Here, Fick’s law holds for apassive diffusion near the equilibrium concentration ρ∞.Finally, notice that the difference between these two current densities is a vector field. And, if this vector

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field is divergence-free, then two current densities have identical divergence, givingρ = f (ρ) + D ∇2ρ .

Here, the kinetic term ∂ρ/∂ t is time-like, taking the form ∂ρ/∂ t = f (ρ). And, the diffusion term x ·∇ρ isspace-like, taking the form x ·∇ρ =D ∇2ρ.

A vector identityThe time-derivative of a quantity n is written

_dtdn = _∂t

∂n +_∂x∂n._dt

dx,giving ∂n /∂ t = -x ·∇n if dn /dt = 0 (a condition of stasis). A Fickian diffusion is characterized by the condi-tion ∂n /∂ t = -D ∇2 n. A non-Fickian condition is the divergence of a current density j(t, x), so that n is ascalar density n(t, x) satisfying j = -D ∇n, so that x ·n = div j = ∇ ·(-D ∇n). Using the vector identity∇ ·(DA) = ∇D ·A +D ∇ ·A, with A = -∇n, we get the separation ∇ ·(-D ∇n) = -∇D ·∇n - D ∇2 n. Combiningthis separation with the equation div j = ∇ ·(-D ∇n) yields the heterogeneous diffusion system

div j = -∇D ·∇n - D ∇2 n ,where the inhomogeneity ∇D ≠ 0 corrrects the homogeneity (∇D = 0) assumed in the Fickian idealization.

RemarkHere again, the relative admixture of kinetic and diffusive parts in the non-Fickian correction -∇D ·∇ngives rise to the polarization V0 = VspreadVcenter, where the space-like (diffusion) terms is given byVspread = (V+ -V-) /2, and the time-like (kinetic) term is given by Vcenter = (V+ + V-) /2. Thus the voltagefluxion is given schematically by the following figure:

12. Asymmetric membrane physicsThe biological membrane

A cellular membrane is a semi-permeable barrier between two distinct concentrations of a given ionspecies. The control mechanism is a population of asymmetric channels sensitive to differences ofelectro-static potential. Activation is described by letting n denote the fraction of channels open to thetransit of ions, and letting n∞ denote the steady-state value of n.

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∞The rate equation

_dtdn = ___τn∞-n

is used to solve the relaxation time τ in terms of the (forward) energy E+(V) required to open a channelthat has a transmembrane potential V, and of the (reverse) energy E-(V) required to close a channel thathas a transmembrane potential V.

Normal mode decompositionThe activation energies E+ and E- resolve, through a normal mode decomposition, into a (center) symmet-ric component Ec and a (spread) anti-symmetric component Es. The normal modes are written

Ec ≡ 2E++E-, Es ≡ 2

E+-E-.The activation energies are recovered from their normal modes by writing

E+ = Ec +Es, E- =Ec - Es.

Asymmetric rate constantsThe principle of detailed balance asserts that individual channels will open and close with rate constantsα and β satisfying the condition

_βα = ___1-n∞n∞ .

This formula holds because the principle of detailed balance states that equilibrium is maintained if, andonly if, the rate at which channels open, given by the product of α and 1-n∞ (denoting the rate constantand the steady-state number of closed channels), is balanced by the rate at which channels close, givenby the product of β and n∞ (denoting the rate constant and the steady-state number of open channels),so that α(1 - n∞) = βn∞. The result is given by collecting rate constants to one side of this equation.

Relaxation timeA standard estimate of the relaxation time is obtained from the expression

τ ≡ ___α+β1 .This expression is deduced from an open dwell time τo defined as the average duration of a channel inthe open state, and similarly for the closed dwell time τc. If the process of opening and closing channelsis decoupled as two distinct Poisson processes, the expected dwell times are calculated by the followingLaplace transforms

τo ≡ < t >β = ∫0∞te-βt dt∫0

∞e-βt dt =0!β11!β2 = _β1,

τc ≡ < t >α = ∫0∞te-αt dt∫0

∞e-αt dt =0!α11!α2 = _α1.

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From electrical circuit theory we know that serial (time-like) parameters add reciprocally1 /τ = 1 /τo + 1 /τc, so that the intended relaxation time (given above) is the harmonic mean of theexpected dwell times, τc = 1 /α and τo = 1 /β.

The Boltzmann conditionThe opening and closing of a channel involves forward E+(V) and reverse E-(V) activation energiesspecified by the Boltzmann condition for equilibrium

___1-n∞n∞ = e-E-(V)/kT


The rate constants are obtained by combining this condition with the asymmetric rate constants formula(above), giving

α(V) = λe-E+(V)/kT, β(V) = λe-E-(V)/kT,where λ ≡ α(V0) = β(V0) is the zero-point constant of proportionality. With these rate constants, therelaxation time τ (above) becomes

τ = λ-1e-E+(V)/kT + e-E-(V)/kT-1.Using the energies E+ and E- recovered from the normal modes (above), this relaxation time τ takes theform

τ = τ0 e-Es/kT sech(Ec /kT) ,where τ0 ≡ τ(V0) = 1 /2 λ denotes the zero-point relaxation time. Since Ec and sech are both symmetric,the asymmetry of τ is born entirely by the exponential factor e-Es/kT. We have thus characterized the timewithout assuming symmetric energies. This is crucial because, as I show in section 12, symmetricenergies would violate the second law of thermodynamics.

Morris-Lecar modelThe Morris-Lecar form of the relaxation time is written

2 τλ = sech[a(V - V0) /kT],with a ≡ dE+(V0) /dV by neglecting the anti-symmetric component (setting E+ = E-) and linearizingE+(V) = a(V -V0). Thus, our correction to the Morris-Lecar model is contained entirely in the exponentialfactor (the anti-symmetry) to reconcile the relaxation time with the second law of thermodynamics.

13. Channel entropy and field structureThe hyperbolic scalar field

The exponential factor e-Es/kT gives rise to a hyperbolic scalar field. The key is provided by solving theBoltzmann condition (above) to isolate the sigmoid

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n∞(V) = 1+e-(E+-E-)/kT1 .

This sigmoid is the Gibbs density (1878); it determines the fraction of time a single channel is open, aswell as the fraction of channels open. In either case (serial time-like, or parallel space-like), we get thesame activation equations, so that we can multiplex the membrane.Solving the above sigmoid for the structural factor

σ ≡ kTE+-E-

gives rise to the identityσ = ln n∞

1-n∞,where σ is the energy difference between the forward and reverse activations (the work per cycle) perthermal energy kT. This ratio of internal energy to thermal energy is a measure of hysteresis per activa-tion cycle. In terms of the spread energy Es, σ measures the anti-symmetric energy per thermal degreeof freedom

σ(V) = kT/2Es(V).Integrating the structural factor, we obtain Boltzmann’s H function for the channel entropy∫σdn∞ = -n∞ ln n∞ - (1 - n∞) ln(1 - n∞) ≡ H. In other words, each cycle generates entropy at a rate propor-tional to the anti-symmetric (spread) energy

dn∞dH = kT/2Es .

We now see the problem created by assuming symmetric energies E+ = E-: the anti-symmetric energywould vanish, taking dH /dn∞ with it, and the activation cycle would amount to a perpetual motionmachine whose continuation is uninhibited by entropy (a violation of the second law of thermodynamics(in a closed system operating near equilibrium)).

The hyperbolic field axiomsThe Gibbs density generates a scalar field under the structural identity σx ≡ ln x

1-x. The induced opera-tions of addition x + y ≡ 1(1 + eσx+σy) and multiplication x ·y ≡ 1(1 + eσx σy) have identities e+ ≡ 1 /2,e· ≡ 1 / (1 + e) and inverses x- ≡ 1 - x, x ' ≡ 11 + e1/σx, all of which satisfy the following system of fieldaxioms. [cf. Appendix A]The additive axioms are given by the following system of equations: associativity - x + y + z = 1+eσx+(σy+σz)

1 = 1+e(σx+σy)+σz1 = x + y + z

identity - x + e+ = 1+eσx+σ+1 = 1+eσx+0

1 = x inverse - x + x- = x + (1 - x) = 1+eσx+σ1-x

1 = 1+eσx eσ1-x1 = 1+( x

1-x) (1-xx )1 =_21 = e+

commutativity - x + y = 1+eσx+σy1 = 1+eσy+σx

1 = y + x

18 Dielectric Capacity In Mylar (Field-Theoretic Interaction).nb

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The multiplicative axioms are given by the following equations: associativity - x ·(y ·z) = 1+eσx(σy σz)

1 = 1+e(σx σy) σz1 = (x ·y) ·z

identity - x ·e· = 1+eσx σ·1 = 1+eσx 1

1 = x inverse - x ·x ' = 1+eσx σx'

1 = 1+eσx/σx1 = 1+e

1 = e· commutativity - x ·y = 1+eσx σy

1 = 1+eσy σx1 = y ·x

And, the distributive axiom is given by the following: distributivity - x ·y + z = 1+eσx(σy+σz)

1 = 1+eσx σy+σx σz1 = (x ·y) + (x ·z)

The preceding field axioms hold as long as Es ≠ 0. The field collapses wherever Es = 0.

References1.) J.W. Gibbs, “On the equilibrium of heterogeneous substances,” Transactions of the ConnecticutAcademy 3:108(1876), 343(1878).2.) Paul and Tatiana Ehrenfest, The Conceptual Foundations of the Statistical Approach in Mechanics(1990); Dover: Mineola, N.Y..3.) C. Morris & H. Lecar, “Voltage oscillations in the barnacle giant muscle fiber,” Biophysical Journal35:193(1981).

Dielectric Capacity In Mylar (Field-Theoretic Interaction).nb 19

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Appendix A. The general field transformProposition

If (A,*) is an abelian group, if B is a set, and if g:A-->B is a bijection, then * induces an operation (underthe transform g)

x*g y := gg-1(x)*g-1(y)which forms an abelian group (B, *g ) having identity

e*g ≡ g(e*)and typical inverse

x ' = gg-1 (x)-1.Proof

Let g:A-->B be a bijection of an abelian group A onto a set B. If 0<x<1, thengg-1(x)*g-1(e*g) = x

⟺ g-1(x)*g-1(e*g) = g-1(x)⟺ g-1(e*g) = e*.

Now,x*g x ' = e*g

⟺ g-1(x)*g-1(x ') = g-1(x*g x ') = g-1(e*g) = e*⟺ g-1(x ') = g-1(x)-1 *e* = g-1(x)-1

⟺ x ' = gg-1(x)-1.Source

Robert C. Price, Alpha Measure Theory (1993); First Dissertation, Berkeley

Appendix B. The chaos engineNegative entropy

Entropy always increases (Clausius) in equilibrium systems (Tatiana Ehrenfest). Negative entropy ispermissible in far from equilibrium systems. Strange attractors guarantee that the system will stay farfrom equilibrium. The strange attractor drives a non-equilibrium system into a chaotic regime of dynami-cal behavior, so that the underlying group of a chaotic dynamical system is a chaos engine. The chaosengine transforms entropy into useful information about the actual phenomena associated with a dynami-

20 Dielectric Capacity In Mylar (Field-Theoretic Interaction).nb

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cal system.

SourceRobert C. Price, Analysis of the Logistic Equation (1989); Term Paper, BerkeleyRobert C. Price, Perpsectives In Non-Linear Dynamics (1990); Term Paper, BerkeleyRobert C. Price, Chaos in Population Dynamics and Electronic Oscillations (1992); Master’s Thesis,BerkeleyRobert C. Price, Stability Of Large Random Matrices (1993); Term Paper, BerkeleyRobert C. Price, Pythagoras To Grassmann: An Orientation (1993); Term Paper, BerkeleyRobert C. Price, Vision From Chaos: A Neural Odyssey (1996); Second Dissertation, BerkeleyRobert C. Price, A Universal Retina And Its Prototype (2003); Third Dissertation, Berkeley

Appendix C. The direct method of fluxionUniverse of discourse

There exists a universe of discourse (I) whose identity (II) we approximate (III).Axiom I: Science is concerned with the repeatable measurement of things that exist. This presumes,of course, that something exists to be measured. This is the fundamental axiom of science: “Existenceexists” -- the axiom of existence.Axiom II: We discern what we can, or believe what we will, but the nature of existence is indifferent toour conceptions of it. Existence has a specific, reproducible character whose identity it is the task ofscience to discern, articulate and simplify. This is the second fundamental axiom of science: “Existencehas identity” -- the axiom of identity.Axiom III: On the conviction that identity lends to natural law a measure of regularity, or repeatability,we formulate models that codify reproducible results. If we are cognizant of our models and their limita-tions, we also recognize that the task of science is never ended. We continually refine our methods tobetter approximate natural law. Whatever may be the ultimate identity of existence, we remain somewhatignorant. Thus, our evolving models reflect a grasp of existence which, to be fair, is somewhat indefinite.This is the third fundamental axiom of science: “Models are indefinite” -- the axiom of indefinite models.

Foundation hierarchyTier Zero (Axioms): Three fundamental axioms (existence, identity and indefinite models) define theuniverse of discourse U.Tier One (AEons): The axioms imply the existence of a many-to-one mapping Ψ : U→ Q whose inver-sions determine a quotient space U /Ψ from which the semigroup property is deduced on Q.Tier Two (Fluxions): A unique identity element e is obtained on Q by application of a kernel


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Φ : Q×X →X. The kernel-domain interaction Φ:Q generates fluxions that are correlated by inductioncurrents in Φ:Q by calibrating their respective AEons in U with the eth aeon on Q.Tier Three (Duality): Q is a current on Φ, and Φ is a Q-action on X. Q is the current that turns thewheel Φ. Together they generate a semigroup with identity.

My propagatorThe datum provides a stationary vertical from Q to U, a lag-free state e to which the r th filament ϕr can bepulled back, and from which the sth filament ϕs can be pushed forward. If correlation currents are estab-lished between the datum at e and the r th and sth fluxions, then the r th and sth aeons are correlated intheir fluxions. This correlation is represented by a propagator K : Q×Q→Φ : Q; (r, x) ↦K(r, s) from ther th to the sth fluxions in Φ:Q.The problem is to construct the propagator K(r,s) from r to s. An obvious guess is to pull conditions backfrom r with the inverse ϕr-1, to push them forward to s with ϕs, and to form the propagator by the composi-tion K (r, s) = ϕsϕr-1.

However, the inverse ϕr-1 fails to isolate the point of origin. A second guess is to pull conditions backfrom r with the reverse ϕ-r and to form the propagator by the composition K(r, s) = ϕs ϕ-r.

However, the reverse map misses the point of origin entirely -- warped by phase drift. A phase compen-sator θ : Q→Q is needed to fix the drift. I construct K by the composition K (r, s) = ϕs ϕ-θ(r), providedsuch a θ can be found; it is probably the error signal.

K(r, s) = ϕs ϕ-θ(r)

22 Dielectric Capacity In Mylar (Field-Theoretic Interaction).nb

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Composition rule for propagators

K(s, t)K(r, s) = K(r, t)

My proofK(s, t )K(r, s) = [ϕt ϕ-θ(s)][ϕs ϕ-θ(r)] ; definition of K

= ϕt[ϕ-θ(s) ϕs] ϕ-θ(r) ; associativity= ϕt[ϕ-θ(s)+s] ϕ-θ(r) ; additivity= ϕt ϕe ϕ-θ(r) ; definition of θ (compensator)= ϕt ϕ-θ(r) ; definition of e (datum)= K(r, t) ; definition of K

SourceRobert C. Price, Eine kleine Lehrbuch auf dem Fluxion Methoden (2000); Handbook, Berkeley

Dielectric Capacity In Mylar (Field-Theoretic Interaction).nb 23

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0.  Revised Allocation Schedule

"Love American Style"

RC Mann‐Price, MA/PhD

Los Angeles

December 25, 2015

' I found the plane of human endeavor

a dry and barren ground;

I watered it with the sweat of my brow

and brought forth fruitful things. '


This schedule is an investment plan aimed at a worldwide system of infrastructure 

spending at a projected cost of $600 trillion.  The plan is intended to support a 

permanent erasure of Freemasonry, and it will be sponsored by the following three 

underwriters:  China ($300 trillion); Midas ($100 trillion); and, @ ($200 trillion).

The actual cost per allocation unit is $1.1001 trillion, and the recipients are Asia (300 

units), Europe (50 units), Africa (50 units), North America (50 units), South America (50 

units), and a remaining scatter (100 units).

Example.    The $300 trillion allocation to Asia will support the following areas:  Russia 

($100 trillion); India ($100 trillion); Central and Southeast Asia ($100 trillion).  Russia and 

India will each contribute $50 trillion to China.

The stockholders share ownership at the following rates:  1% host/liaison/manager; 24% 

the money (4 Midas, 8@, 12 China); 8% general congress (of managers); and, 67% 

target/site.  The initial value is projected at $2.5 quadrillion.

The allocation unit ($1.1001 trillion) will be divided to the following purposes:  an 

unscum echelon ($100 million) will float a bug zapper; the bug zapper ($100 billion) will 


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raise an infrastructure; the infrastructure ($1 trillion) will support an economy; and, the 

economy will support many colonies on deep space planets, where deep space is 

accessed through a wormhole grid.

Remark.    Midas will be owned by the following interests:  Rand 25% (articulation); 

Caltech 25% (help desk); Pentagon 25% (security); and, Bungalow 25% (map room).

Centers of administration

The six hundred units of infrastructure allocation will be arranged within a system of 

three divisions.  There will be centers of administration (100), areas of interest (200), 

and centers of need (300).  The centers of administration are enumerated as follows.

1.    Minsk, Belarus  (East meets West)

2.    Perth, Scotland

3.    Perth, Australia

4.    Saint Petersburg, Russia

5.    Moscow, Russia  (Kremlin)

6.    Berlin, Germany  (Brandenburg Gate)

7.    Paris, France  (City of Lights)

8.    The Hague  (International Criminal Court)

9.    Armagh, Northern Ireland

10.    Limerick, Southern Ireland

11.    Cardiff, Wales

12.    Colchester, England  (Camulod)

13.    La Paz, Bolivia  (Lake Titicaca)

14.    Caracas, Venezuela  (Angel Falls)


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15.    Los Angeles, California  (Hub and Rail, High‐Speed Cross Country Service)

16.    Sacramento, California  (Waterworks)

17.    Baltimore, Maryland  (Hub and Rail, Northeast Corridor)

18. "

19. "

20. "

21.    Boston, Massachusetts  (Cambridge)

22.    Manhattan, New York  (The Bronx)

23.    Charleston, South Carolina  (Sunday in the Park)

24.    Athens, Greece  (Acropolis)

25.    Cairo, Egypt  (Al Kahira)

26.    Tunis, Tunisia  (A Day At The Races)

27.    Soweto, South Africa  (Four Chairs)

28.    Nanjing, China  (City of Heaven)

29.    Urumqi, China  (Center of Asia)

30. "

31. "

32. "

33. "

34. "

35.    Kaohsiung, Taiwan  (Red Hair Beach)

36.    Tokyo, Japan


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37.    Kaesong, North Korea

38.    Incheon, South Korea

39.    Phnom Penh, Cambodia

40.    Nouakchott, Mauritania  (Sahel Pipe And Rail)

41.    Timbuktu, Mali  (Sahel Pipe And Rail)

42.    Gilgit, Kashmir  ("Elders of a Gentle Race")

43.    Almaty, Kazakhstan  (Father of the Apple)

44.    Baku, Azerbaijan  (Prince Caspian)

45.    The National Park System (Yellowstone, Buffalo Trust)

46.    Kabul, Afghanistan

47.    Detroit, Michigan  (Motor City)

48.    Gnome, Alaska

49.    New Qoms, Poland  (Southeast)

50.    New Damascus, Poland  (Southeast)

51.    New Aleppo, Poland  (Southeast)

52.    Al Khalil, Palestine  (Hebron)

53.    Ghazzah, Palestine  (Gaza City)

54.    El Arish, Sinai  (Rhinocolura)

55.    Bayt Lahm, Palestine  (Bethlehem)

56.    Nazarat, Palestine  (Nazareth)

57.    Capernaum, Palestine  (Sea of Galilee)

58.    Afiq, Palestine  (Golan Heights)


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59.    Rafah, Palestine  (Gaza Strip)

60.    Elat, Sinai  (Gulf of Aqaba)

61.    Agri Dagi, Turkey  (Mount Ararat, Center of the World ‐‐ Yezidi)

62.    Vilnius, Lithuania

63.    Nicosia, Cyprus  (Lefkosia)

64.    Istanbul, Turkey  (Hagia Sophia)

65.    Ephesus, Turkey  (Temple of Artemis)

66.    Al Basrah, Iraq  (Basra)

67.    Sharm el Sheikh, Sinai  (Red Sea)

68.    Diamond Head, O'ahu  (Hawaii)

69.    Vancouver, British Columbia  (Thank You)

70.    Chicago, Illinois  (The Windy City)

71.    Ensenada, Mexico  (Baja Fish)

72.    Naples, Florida  (Thomas More, Ave Maria School of Law)

73.    Havana, Cuba

74.    Rio de Janeiro, Brazil

75.    Casablanca, Morocco

76.    Abidjan, Cote D'Ivoire

77.    Jakarta, Indonesia

78.    Ho Chi Minh City, Vietnam  (Saigon)

79.    Panama City, Panama  (The Canal Zone)

80.    Manila, Philippines  (Ali)


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81.    Christchurch, New Zealand

82.    Sidney, Australia

83.    Guam, Northern Mariana Islands

84.    Guadal Canal, Solomon Islands

85.    Papeete, Tahiti

86.    Jerusalem, Palestine  (Garden of Gethsemane)

87.    Munich, Germany

88.    Al Madinah, Saudi Arabia  (Medina)

89.    Al Dawhah, Qatar  (Doha)

90.    Abu Dhabi, United Arab Emirates  (Financial Services)

91.    Asmara, Eritrea

92.    Djibouti, Djibouti

93.    Shiraz, Iran

94.    Waterloo, Iowa  (Corn on the Cob)

95.    Santa Fe, New Mexico  (The Santa Fe Institute)

96.    Coeur d'Alene, Idaho

97.    Allentown, Pennsylvania

98.    Ljubljana, Slovenia

99.    Moon Base Alpha, The Moon  (Tranquility Basin)

100.    Pristina, Kosovo

Areas of interest

Two hundred areas of interest will be decided among the cities of Europe, Africa, North 


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America, South America, and Oceania.  Midas will decide the matter.

Centers of need

Three hundred centers of need will be decided among the cities of Asia.  Midas will 

coordinate the matter.


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1.  North America

1.    Honolulu, Hawaii

2.    Juneau, Alaska

3.    Ottawa, Canada

4.    Nuuk (Godthab), Greenland

5.    Montgomery, Alabama

6.    Phoenix, Arizona

7.    Denver, Colorado

8.    Hartford, Connecticut

9.    Dover, Delaware

10.    Tallahassee, Florida

11.    Atlanta, Georgia

12.    Boise, Idaho

13.    Springfield, Illinois

14.    Indianapolis, Indiana

15.    Des Moines, Iowa

16.    Topeka, Kansas

17.    Frankfort, Kentucky

18.    Baton Rouge, Lousiana

19.    Augusta, Maine

20.    Annapolis, Maryland

21.    Washington, DC


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22.    Lansing, Michigan

23.    St. Paul, Minnesota

24.    Jackson, Mississippi

25.    Jefferson City, Missouri

26.    Helena, Montana

27.    Lincoln, Nebraska

28.    Carson City, Nevada

29.    Concord, New Hampshire

30.    Trenton, New Jersey

31.    Santa Fe, New Mexico

32.    Albany, New Jersey

33.    Raleigh, North Carolina

34.    Bismarck, North Dakota

35.    Columbus, Ohio

36.    Oklahoma City, Oklahoma

37.    Salem, Oregon

38.    Harrisburg, Pennsylvania

39.    Providence, Rhode Island

40.    Columbia, South Carolina

41.    Pierre, South Dakota

42.    Nashville, Tennessee

43.    Austin, Texas

44.    Salt Lake City, Utah

45.    Montpelier, Vermont


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46.    Richmond, Virginia

47.    Olympia, Washington

48.    Charleston, West Virginia

49.    Madison, Wisconsin

50.    Cheyenne, Wyoming

51.    Rockford, Illinois (share with Europe)


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2.  Latin America

1.    Chihuahua, Mexico

2.    Guadalajara, Mexico

3.    Mexico City, Mexico

4.    Lesser Caribbean Islands

5.    Kingston, Jamaica

6.    Port‐au‐Prince, Haiti

7.    Santiago, Dominican Republic

8.    San Juan, Puerto Rico

9.    Belmopan, Belize

10.    Guatemala, Guatemala

11.    San Salvador, El Salvador

12.    Tegucigalpa, Honduras

13.    Managua, Nicaragua

14.    San Jose, Costa Rica

15.    Panama City, Panama

16.    Cartagena, Columbia

17.    Bogota, Columbia

18.    Quito, Ecuador

19.    Georgetown, Guyana

20.    Paramaribo, Suriname

21.    Cayenne, French Guiana


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22.    Lima, Peru

23.    Brasilia, Brazil

24.    Belo Horizonte, Brazil

25.    Sao Paulo, Brazil

26.    Porto Alegre, Brazil

27.    Asuncion, Paraguay

28.    Santiago, Chile

29.    Concepcion, Chile

30.    Montevideo, Uruguay

31.    Buenos Aires, Argentina

32.    Cordoba, Argentina

33.    Rosario, Argentina

34.    Bahia, Blanca

35. ‐ 50.    (As Needed)


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3.  Europe

1.    Oslo, Norway

2.    Stockholm, Sweden

3.    Helsinki, Finland

4.    Tallinn, Estonia

5.    Riga, Latvia

6.    Warsaw, Poland

7.    Bratislava, Slovakia

8.    Budapest, Hungary

9.    Kiev, Ukraine

10.    Kharkiv, Ukraine

11.    Odessa, Ukraine

12.    Kishinev, Moldova

13.    Bucharest, Romania

14.    Sofia, Bulgaria

15.    Skopje, Macedonia

16.    Tirana, Albania

17.    Valleta, Malta

18.    Thessaloniki, Greece

19.    Rhodes, Greece

20.    Trieste, Italy

21.    Podgorica, Montenegro


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22.    Sarajevo, Bosnia and Herzegovina

23.    Zagreb, Croatia

24.    Vienna, Austria

25.    Prague, Czech Republic

26.    Ingolstadt, Germany

27.    Rome, Italy

28.    Copenhagen, Denmark

29.    Amsterdam, Netherlands

30.    Barcelona, Spain

31.    Brussels, Belgium

32.    Luxembourg, Luxembourg

33.    Schaan, Liechenstein

34.    Bern, Switzerland

35.    Milan, Italy

36.    Bologna, Italy

37.    Florence, Italy

38.    Naples, Italy

39.    Madrid, Spain

40.    Bilbao, Spain

41.    Lisbon, Portugal

42.    Andorra, Andorra

43.    Monaco

44.    Aachen, Germany

45.    Strasbourg, France


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46.    Reykjavik, Iceland

47.    Dublin, Ireland

48.    London, England

49.    The Vatican, Vatican City

50.    share with Rockford, Illinois (North America)


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4.  Africa

1.    Rabat, Morocco

2.    Casablana, Morocco

3.    Marakech, Morocco

4.    Algiers, Algeria

5.    Tripoli, Libya

6.    Alexandria, Egypt

7.    Khartoum, Sudan

8.    N'Djamena, Chad

9.    Niamey, Niger

10.    Ouagadougou, Burkina Faso

11.    Bamako, Mali

12.    Dakar, Senegal

13.    Banjul, Gambia

14.    Bissau, Guinea‐Bissau

15.    Conakry, Guinea

16.    Freetown, Sierra Leone

17.    Monrovia, Liberia

18.    Yamoussoukro, Ivory Coast

19.    Accra, Ghana

20.    Lome', Togo

21.    Porto‐Novo, Benin


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22.    Abuja, Nigeria

23.    Yaounde, Cameroon

24.    Bangui, Central African Republic

25.    Malabo, Equatorial Guinea

26.    Libreville, Gabon

27.    Brazzaville, Congo

28.    Kinshasa, Democratic Republic of the Congo

29.    Kigal, Rwanda

30.    Bujumbura, Burundi

31.    Kampala, Uganda

32.    Nairobi, Kenya

33.    Dodoma, United Republic of Tanzania

34.    Juba, South Sudan

35.    Addis Ababa, Ethiopia

36.    Djibouti, Djibouti

37.    Mogadishu, Somalia

38.    Lilongwe, Malawi

39.    City of Maputo, Mozambique

40.    Antananarivo, Madagascar

41.    Harare, Zimbabwe

42.    Luanda, Angola

43.    Lusaka, Zambia

44.    Windhoek, Namibia

45.    Gaborone, Botswana


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46.    Pretoria, South Africa

47.    Mbabane, Swaziland

48.    Maseru, Lesotho

49.    (Reserve)

50.    (Reserve)


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5.  Russia

1.    Vladivostok

2.    Khabarovsk

3.    Irkutsk

4.    Krasnojarsk

5.    Novosibirsk

6.    Omsk

7.    Chelyabinsk

8.    Yekaterinburg

9.    Ufa

10.    Samara

11.    Kazan

12.    Nizhny Novgorod

13.    Volgograd

14.    Rostov‐on‐Don

15.    Makhachala

16.    Vladimir

17.    Yaroslavl

18.    Tver

19.    Kaluga

20.    St. Petersburg

21.    Murmansk


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22.    Smolensk

23.    Bryansk

24.    Kursk

25.    Belgorod

26.    Keliningrad

27. ‐ 50.    (As Needed)


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6.  China (from Russia) + Mongolia

1.    Tianjing

2.    Fuzhou

3.    Nancheng

4.    Wuhan

5.    Jinan

6.    Hefei

7.    Shanghai

8.    Zhengzhou

9.    Lanzhou

10.    Xining

11.    Yinchuan

12.    Taiyuan

13.    Shijiazhuang

14.    Hohhot

15.    Beijing

16.    Shenyang

17.    Changchun

18.    Herbin

19.    Ulaanbaatar, Mongolia

20. ‐ 50.    (As Needed)


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7.  China (from India)

1.    Lhasa

2.    Kunming

3.    Nanning

4.    Xl'an

5.    Macao

6.    Guangzhou

7.    Changsha

8.    Taipei, Taiwan

9.    Guiyang

10.    Guanzhou

11.    Chongqing

12.    Chengdu

13. ‐ 50.    (As Needed)


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8.  India

1.    New Delhi

2.    Himachal Pradesh

3.    Punjab

4.    Uttarakhand

5.    Haryana

6.    Uttar Pradesh

7.    Rajasthan

8.    Bihar

9.    Jharkhand

10.    Chhattisgarh

11.    Odisha

12.    Madhya Pradesh

13.    Gujarat

14.    Telengana

15.    Andhra Pradesh

16.    Goa Karnataka

17.    Tamil Nadu

18.    Kerala

19.    Sikkim

20.    Meghalaya

21.    Assam


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22.    Manipur

23.    Tripura

24.    Mizoram

25. ‐ 50.    (As Needed)


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9.  Western Asia, Middle East

1.    Ankara, Turkey

2.    Yerevan, Armenia

3.    Tbilisi, Georgia

4.    Tabriz, Iran

5.    Tehran, Iran

6.    Esfehan, Iran

7.    Mosul, Iraq

8.    Kirkuk, Iraq

9.    Baghdad, Iraq

10.    Karbala, Iraq

11.    Al Basrah, Iraq

12.    Kuwait City, Kuwait

13.    Amman, Jordan

14.    Doha, Qatar

15.    Abu Dhabi, United Arab Emirates

16.    Riyadh, Saudi Arabia

17.    Muscat, Oman

18.    Sana'A, Yemen

19.    Astana, Kazakhstan

20.    Bishkek, Kyrgyzstan

21.    Tashkent, Uzbekistan


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22.    Dushanbe, Tajikistan

23.    Islamabad, Pakistan

24.    Kathmandu, Nepal

25. ‐ 50.    (As Needed)


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10.  Eastern Asia, Oceania, and such

1.    Thimphu, Bhutan

2.    Dhaka, Bangladesh

3.    Nay Pyi Taw, Myanmar

4.    Bangkok, Thailand

5.    Kuala Lumpur, Malaysia

6.    Singapore

7.    Vientiane, Laos

8.    Hanoi, Viet Nam

9.    Bandar Seri Begawan, Brunei

10.    Palembang, Indonesia

11.    Bintulu, Malaysia

12.    Dili, Timor‐Leste

13.    Port Moresby, Papua New Guinea

14.    Canberra, Australia

15.    Wellington, New Zealand

16.    Pyongyang, North Korea

17.    Seoul, South Korea

18.    Kagoshima, Japan

19.    Sapporo, Japan

20. ‐ 50.    As Needed


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11.  Appendix:  Affiliate Operations


Los Angeles

June the 21st, AD 2016

The basic operating condition imposed by the preceding allocation schedule is that each affiliate 

give more than it takes.  The means of building a new economy of abundance (to replace an old 

economy of scarcity) will be taught by men and women dispatched from a team developed by 

the Rand Corporation with help from Harvard University.

The Midas Energy Group should be owned and operated by the following established interests:

1 %  Brain Trust; U.C. Berkeley (Pallas Athena & King Midas)

4 %  Central Liaison; Urumqi

10 %  Yezidi; rulership

10 %  Human Resources; Harvard University (Loeb Editions) 9.9, NSI 0.1

14 %  Planning Commission; Rand Corporation (COSRIMS) 11, NSI 3

20 %  Help Desk; Caltech 19.5, GIS 0.5

19 %  Security; caballero 8, police chief 8, external (I.A.I) 1, NSI 2

5 %  Sea Watch; Samoa, Hawaii, Etc. (NOAA)

4 %  External Operations; The Chronicle of Philanthropy 0.1, Ave Maria Law School 3.9

2 %  Internal Operations; Harvey Mudd College, Pitzer College

5 %  Director (w/ Harvey Mudd support)

5 %  Co‐director (w/ Pitzer support)

1 %  Bungalow; map room 0.5, GIS 0.5

The basic operations are the following:

caballero  ::  grounds keeper / power glove / liaison

Africa  ::  police chief

Asia  ::  operations (big center)

Europe  ::  office (a little off center)

Oceania  ::  sea watch (ecosystem)

Harvard‐Rand  ::  manager training

Chronicle : Ave Maria  ::  consortial relations : advocacy

NOTE.    Harvard‐Rand will recruit and train six hundred (600) managers, from which eight (8) 

regional directors will be appointed.  Reference Applied Devices, Echelon Systems.  Also, NSI is 


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National Standards Institute.


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National Standards Institute

National Standards Institute in an interplanetary consortiumorganized for the draft and proliferation of a terse, lucidstatement of effect:  It is the effect of science, weights,and measures upon the progress of humanity as an anthropologicalentity at work upon the planet Earth, and within the deepeningreaches of Intergalactic Space.

The National Standards Institute will administer a 5.1% sharein the Midas Energy Group.  The allocation attaches to existingmembers as follows.

0.1% Harvard University 3.0% Rand Corporation 2.0% Security

Page 1

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Reference Applied Devices, Echelon Systems, Charity Garden

Applied Devices  (This is the money!)

70% Midas10% Me10% Wife10% NGO :: Dominican Foundation (Izzo) 5; Clear Creek Abbey 3; and, Sisters of St. Cecilia 2.

Echelon Systems  (This is the science!)

20% Midas35% Director35% Co‐director10% Charity :: "Food Not Bombs"

Charity Garden  (This is everything!)

10% Cathedral of Our Lady of the Angels:  Los Angeles, CA10% Columban Fathers:  St. Columbans, NE10% Dominican Foundation:  New York, NY10% Dominican Sisters of St. Cecilia:  Nashville, TN10% Clear Creek Abbey:  Hulbert, OK10% First Things (ecumenical review):  Rockford, IL10% The Cardinal Newman Society:  Manassas, VA10% Echelon Systems:  Los Angeles, CA10% Applied Devices:  Pasadena, CA10% Midas Energy Group:  Pasadena, CA

Page 1

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RCMP, Applied DevicesJune the 18th, AD 2016

ParenthesisIntroduction. This article is concerned with interjection; it is concerned with various methods and modes of laying into a construction some qualifying or explanatory bit of rhythm, substance or prose: It typically occurs within an otherwise complete section of the matter under consideration, and it occurs (more often than not) as an interval within the flux and flow of subject matter.

Definitions. An interval is a delimited bit of whatnot. A receptor is an interval into which an argument may be called. An indicative is an interval into which a parameter may be passed.

Remark. These definitions satisfy the pattern U: "The term A is an interval into which the event B occurs." One definition uses a code C given by "A = receptor" and "B = argument called"; and, the other definition uses a code C' given by "A' = indicative" and "B' = parameter passed". The U-correspondence between code C and code C' is written

C :: C'; U,and it resolves into a similitude of terms and events; they are written (A::B;C and A'::B';C'); and, they are abbreviated to read (A:B;C and A':B';C'). By combining the abbreviated forms with the patterned correspondence above, we get a compound formula: It is a correspondence between two correspondences, and its standard form is written without explicit reference to the codes which bind them (or to the pattern which relates the codes); that is, it is written by a rule of analogy

A : B :: A' : B'.This rule is asserted by the utterance, " A is to B as A' is to B' ". The matter now comes full circle, as we realize that our rule of analogy is used to assert the substitution instance

(receptor : argument called) :: (indicative : parameter passed).The utterance, " receptor is to argument called as indicative is to parameter passed " asserts the expression given.

Definition. The notion of parenthesis is an abstract species of interjection: It is an interval J into which an event K occurs.

Example. A propagator K(r,s) [see A23. Planes of Existence, part 3: page second to last] is used to describe the effect of an event K unfolding within an interval J.

Note. An EPR-switch is a bimodal switch the effect of which is the flip-transposition of an ordered pair. The underlying pair is given within a pair receptor (-,-) together within an echelon condition (the indicative), and its invariance under the EPR-switch is written (-,-)EPR/switch.

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RCMP, Applied DevicesJune the 18th, AD 2016


Introduction. We draw a distinction between two sorts of transposition: First, we have the ordinary transposition of two entities, such as might occur were the two entities presented as an ordered pair -- a pair whose order might be reversed. Second, we have the special transposition of two entities given as a juxtaposition of two expressions read symbolically from left to right (and again, from right to left). The first case is a general transposition, and its articulation occupies the bulk of our present effort. The second case is a special instance of the flip-transposition, and its use will occupy the place of privilege accorded its significance in our theory of the EPR-switch -- the wormhole diode. [see A23. Planes of Existence et al.]

The steps of a flip-transposition are exposed to a degree of precision necessary to identify, and to exploit, a number of opportunities present within a procedure which I devised (May 16, 2015) for the expression of a flip-transposition. The point of repeating that precision here is that we may use the opportunity to code several bits of 'procedural anomaly': They may be read as simple abrogations (taken one by one, into a bizarre type of event calculus) from my procedure, which is given as follows.

Procedure. The general transposition is constructed as a system of individual syntactical maneuvers expressed as a short sequence of the form

precursor --> pivot --> successor,where the precursor system gives a unary setup (ten steps, 0-9), where the pivot expresses a dominance procedure (seven steps, 10-16), and where the successor gives a specialization to the flip-transposition (five steps, 17-21). The resulting instruction set is given in three sections as follows.

precursor :: unary setup0. ; environment (the unknown)1. u ; unary operator2. x ; entity3. (u,x) ; pairing 1,24. . ; radix5. (u,x). ; juxtaposition 3,46. u.x ; operational form of 57. ux ; simplification8. u(x) ; evaluation9. x^u ; co-evaluation/effect

pivot :: dominance procedure10. (x0+x1)^u ; u splits x11. [+(x0,x1)]^u ; relational form of +

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12. u[+(x0,x1)] ; relational form of u13. (u+)(x0,x1) ; associativity14. (uo+)(x0,x1) ; composition u+ = uo+15. u(+)(x0,x1) ; evaluation16. +^u(x0,x1) ; co-evaluation/effect

successor :: flip specialization17. $ := x^u ; declaration18. u := T ; concrete (transpose) instance19. +^T(x0,x1 ) ; substitution 16,1820. +(x1^T,x0^T) ; application (includes exterior flip)21. +($1,$0) ; substitution 17,1822. +($1,x0) ; flip-invariant x0 (effect of interior flip)23. $1+x0 ; operational form

Remark. The rate of procession in the implementation of these twenty-three (or so) steps would depend on the quality of machine used to evaluate each step of this procedure. For instance, a spacetime machine (such as the photo-neutrino interaction, which may or may not be lepton mediated), the time constant would differ markedly from the dilly dally effort to run one step per hour (or per day).

Note. To complete the above algorithm (as a constructive proof), it would be necessary to give a detailed account of step 0., which indicates the formation of an arbitrary (possibly featureless environment). And though such an algorithm is known to me (I wrote it on May the 19th, AD 2015), its articulation is presently deferred to another article under the title, Environment (say B3.).

Example. Do a restriction.

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RCMP, Applied DevicesFrom: June the 18th, AD 2016

To: June the 24th, AD 2106

EnvironmentHold on to your algorithms!

Introduction. In the matter of constructing an unknown (but fully functional) environment for the operation of an arbitrarily complex assemblage of applied devices, we have occasion to review the introductory notes to volume four of my journal (Biophysical REM: An Easy Guide to Hyperbolic Geometry; From: November the 29th, AD 2014). This occasion is presented by a construction (dated May the 19th, AD 2015): It is a REM-based construction (in the language of my journal), and it shows precisely the manner of passing from step zero (an inviat being that through which nothing may pass) to step thirty-two (a name being that by which a thing is invoked, i.e., properly called).

Procedure. The whole construction is drawn through five sections of thirty-two (or so) steps, and they are given as follows. A.) setup (steps 0-5); B.) consideration (steps 6-12); C.) contact lemma (steps 13-19); D.) operating lemma (steps 20-27); and, E.) operating environment (steps 28-32). The sequence of five sections is then written A --> B --> C --> D--> E, and we take the view that A ~ 0B, and that E ~ 0D, so that the sequence 0 --> B --> C --> D --> 0 gives the easy result [ B | C | D ], which (if exact) would give B --> C (monic) and C --> D (epic), and the sequence [ B | C | D ] (exact at B, C and D) would give the standard sequence

< B | C | D >.

A. setup :: command relation0. Omega0 ; inviat (impassable)1. Omega ; inchoacy (impredicable)2. ~: Omega0 --> Omega ; compliance 0,1 (wiggle)3. Xi = ~/Omega0 ; operating system1 2,0 (REM)4. xi in Xi ; subsystem 3 (control factor, gauged k)5. xi: Omega0 --> Omega/Omega0 ; relation 2,3,4 (it is command)

B. consideration :: noumenal command6. alpha ; noumenal (subsystem of contact engine)7. Omegaalpha ; noumenal filament 6,1 (cipitat)8. Xi | Omegaalpha ; restriction 3,7 (le piece de resistance)9. xi(alpha) ; evaluation 5,6 (noumenal operation)10. eval(alpha,xi) ; relational form of xi (pivot)11. co-eval(xi,alpha) ; flip (echelon pair transpose)12. C(xi,alpha) ; consideration (xi in Xi | Omegaalpha)

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C. contact lemma :: noumenal power13. system ; cohesive whole (a notion)14. arrow ; relation between systems (a notion)15. A: B --> C ; notation (an arrow)16. d: d --> d ; special arrow (contact engine)17. alpha in d ; subsystem (contact)18. {alpha in d, d: d --> d} ; power system 17,1619. P0 ; name (contact lemma)

D. operating lemma :: range of consideration20. alpha in P0 ; element 17,19 (setup)21. d.alpha ; juxtaposition 16,17 (entirety of alpha)22. {d.alpha, alpha in P0} ; system 21,20 (entirety of power system)23. P ; name (ranging lemma)24. C(xi,alpha) in P ; subsystem 12,23 (range within lemma)25. alpha in Ent ; entity 6 (beyond entirety 20,23)26. {alpha in Ent, C(xi,alpha) in P} ; system 25,24 (transcendental induction)27. Pxi ; name (pixie)

E. operating environment :: entirety of consideration28. Cxi: Pxi --> P0 ; consideration 27,19 (contact reduction)29. Cxi(alpha) ; filament 12 (contact environment)30. xi in Xi ; subsystem 5,3 (control factor, k)31. {Cxi, xi in Xi} ; command system 28,30 (system2) [3]32. C/Xi ; name (seeksee, co-operating)

Explication. A step by step explication would be helpful here, but it could easily be very boring (almost tedious..). Nonetheless, there are a few fundamental matters in real need of fuller treatment. In fact, most of the construction would benefit from a good going over. Let us see how far we can make this puppy run..

Step 0. The inviat is impassable. The inviat Omega0 is that through which nothing may pass: There is only one; it precurs every measure (every alpha-theoretic abrogation, and every null); it is neither well-defined nor systematic; it is the root of every entity -- the standard of every consideration, every factor, and every protoring homogeneity (within reach of an arbitrarily given, but otherwise fixed, gauge beta); and, it is excepted in no respect save the omnipresent wiggle drawn off of its, otherwise inaccessible, pretext -- its each (and every) instance (via hypercode ... ) as a pre-tension Omegaalpha, which is sometimes called the cipitat at alpha.Step 1. An inchoacy is impredicable. An inchoacy Omega is that of which nothing may be predicated: Nothing may be proposed; nothing may be stated; nothing may be uttered; nothing may be asserted, gesticulated, or otherwise signed to prevail against first nature (inchoate and primordial of all feature, attribute, or discernible linkage). In short, our inchoate Omega is as supremely distant from distinctive character as any entity (that which may be considered) may be without rising into the realm of cohesive things (the indicative systems; where a thing is that which may be indicated, and a system is a cohesive whole) -- the parametric entirety beyond all noumenal specificity, beyond each (and every) cipitat filament [7].

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Step 2. The impassable wiggle is impredicable. Here, the impassable (inchoacy Omega0) is used to evaluate the full unqualified wiggle (the wiggle waggle precursor to every arrow; it is a pointed little correspondence between two entities, the impassable Omega0 and the impredicable Omega). The unsounded depths of this badly defined bit of wiggle waggle virtue do swell into each peak and prime of inchoacy impeding and, it wells into all inchoacy with such perduring fullness as to call very nearly into the diverse planes of existence a pleroma of untold cause and circumgrading, as though to confute inchoacy into mere substance primordial and resplending. But, it is checked neither by force, nor by tensing, nor by any specific agency of fluxion: Rather, the whole of it persists in an insufferable state of dynamic imbalance, writhing and splining after every cause (noumenal, and extra-noumenal) into each specific cipitat filament [7].Step 3. The inviat reduces wiggle. It is the nature of a rogue to deceive, and to play upon the unspent hope of a soul gone short of purpose well-vested. It is the nature of a scoundrel to pick, and to part of remnant means the slip and mix of fortune failing. It is the nature of a fiend to fet upon the shanting carcass of a body once vital and full of vigor. And, it is the nature of a devil to care of it all. But, should all doubt and redoubt rise to the contrary, be it known to you that it is also the nature of Royalty to sound its call of Victory over the tribulation of its thrall! Here, in the Royal prerogative gone shant of failing, gone wye of distal count, we do feel and know that not all is well in a Land burdened by loss of mettle, hope, and memory! We do further see, at the extreme extremity (of every conceivable extremity), that all things diverge to an Absolute Horizon -- the projective point at Infinity (true transcardinal infinity). We do also see and affirm that to this projective matter there is a discernible pattern -- an essential pattern whose virtue is clear to the heart that knows no bound -- no earthen limit, and no reason to negate the obvious: The ambiguity of our time is a sure and certain sign of the distance we have travelled -- the length which we have traversed in the service of Deity, and of God's own chosen blood, that to this day of making we are found necessary, and worthy, of further work upon this plan. Our shared service is known already to them who govern, and we are soon in praise for the hearing of it. And, because the whole of it is known only through its combined effect (not necessarily cohesive), we do obtain of wiggle waggle persistence the inchoate form we know as Omega, and we obtain it (in secular fashion) as an indefinite species of reduct, written (for convenience of expression) ~/Omega0, where Omega0 is (as always) the one impassable inviat at the absolute bottom of each (and every) entity -- each and every bit of preponderable whatnot (that which may be considered).

Therefore, should we seek within (or without) the derived mechanism, expressing our two principals (the entity Omega0, and the entity Omega), the means of predicting the indecipherable code beneath all possible (and impossible) existence, then would we have within (or without) our actual understanding the veritable basis for a full-blown wide-open, unthrottled expression of the paradigm developed (in my journal) as a Random Element Machine (rem) chosen (at random, or at concealed purpose) to be the paradigmatic instance Xi, which we write in the mundane way as the secular reduct Xi = ~/Omega0. And, should the matter afford confusion, we might further add that Xi need not form a proper object (a well-defined system, such as the very attractive prototype planned in the material substrate group marked early in its evolution as rhodopsin), but merely that Xi is in some respect (elaborated as follows) an operating system. In other words, each (and every) conceivable operation within (or without) any particular plane of existence reduces in strictly natural fashion to a subsystem xi in Xi. Because of this, we have the following step:Step 4. Our control factor k lives in the given operating system Xi. Every little metric b gives gauge (gives beta), and beta gauges k. This process, which we loosely call gauge (a modular system of metrics, with each metric an alpha-measure of raw proximity, with proximity being

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the distal expression of linealized semantic transit, with the distal being a hyperbolized form of the semantic entailment of a noumenal prime (given noumenal alpha), with each hyperbolization being the density of locale relative to metric b, and with the semantic entailment being the primitive Xr in transitum X corresponding to a prime r in Q as specified by an implicit arrow gamma: Q --> X; r |--> Xr (where gamma is implicit in a noumenal grid Gamma(Q,X)), determines (if anything does) the precising system of estimates (bounded only in density of locale rhob) out of which a species of homogeneity (call it delbeta) is itself equated (identically, rather than indiscernibly) with our control factor k evaluated precisely at beta. In other words, we routinely find it written (without comment, hint, or due explanation) that

k: beta --> P'; b |--> delb.Here, in passing, we close note four by saying that P' is the protoring (as rendered by the alpha-th secular inversion of the contact lemma P); it is written P' = zeta(P). And, by choosing the definite article, we are saying that the arrow zeta: P --> P'; alpha --> k(beta) is defined for all alpha in P', but this does not mean that P' is well-defined; it merely asserts an invariant nature which transcends any particular choice of alpha (in P) with which to render the secular inversion zeta. (I presume the matter to be obvious.)Step 5. Each choice of control factor gives a command. Here, the command is expressed, not as an arrow between systems, but merely as a system of correspondence between the inviat Omega0 and an indefinite sort of entity Omega/Omega0 comprised of the secular reduct of an (almost) arbitrary Omega (relative to Omega0).

Bear in mind, here, that the secular reduct of an entity bears only the most superficial resemblance to that of a system: In fact, the commonality of notation might be entirely done away with. Yet, as the matter does reflect convention, we shall continue by asserting the secular reduct of an entity e (relative to a presumably unrelated entity e') to be an entity e/e' characterized by the condition that to each part of e there are parts e' and e" such that e splits (under a direct sum-type correspondence, written e = e'+e") into an explicit part e' followed by an implicit remnant e" (which may or may not have discernible feature or attribute). And, despite this degree of indefinite measure (concerning the range of vagueness, uncertainty, and existential ambiguity) we nonetheless get adequate use from the conventional formula e" = e/e'. Therefore, to the notion of secular reduct we shall let answer the entity e/e', it being the secular reduct e/e' of an entity e (relative to an entity e').

An obvious line of inquiry, here, is to consider under what conditions the above correspondence gives rise to an actual rule of analogy -- a rule which, if it held, would (to say the least) utterly decimate the problem of incommensurables (without loss of notation). And herein lies our justification for preserving the reductive (modular) notation!

entity comprised of the secular reduct of an indefinite sort of inchoacy Omega relative to Omega0

some indefinite sort of inchoacy OmegaStep 6. Step 7. Each cipitat is a filament of an inchoacy. The filaments of inchoacy Omega which give a proper cipitat Omegaalpha are the filaments of noumenality -- the noumenal filaments (with noumenal alpha).

The matter of it all is within its awesome entirety, nothing more (and nothing less) than pure unadulterated noumenal virtue: It is the quintessential virtue known throughout the surviving world of Natural Philosophy as pre-tension!

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Step 8. Step 9. Step 10. Step 11. Step 12. Step 13. Step 14. Step 15. Step 16. Step 17. Step 18. Step 19. Step 20. Hooray for P0!Step 21. Step 22. Step 23. Step 24. Step 25. Step 26. Step 27. Step 28. Step 29. Step 30. Step 31. Step 32.