December 2006

Introductory Note: A revised, expanded, and hyperlinked version of the 1997 paper, “Time-Logics of the Quantal Base State in Homeopathic Potentization” -- published by the JOURNAL OF THE AMERICAN INSTITUTE OF HOMEOPATHY (90:2) -- is hereupon posted under a new title because many questions have arisen due in significant measure to the fact that, unfortunately, the JAIH printed the paper without employing a symbol font, which made the mathematical explications difficult to decipher (the fact that the JAIH printed the article at all is, of course, rather surprising and deeply appreciated). Adaptation of Sanskrit and Tibetan terminology is well warranted by the precedent-setting activity engaged in by Erwin Schrödinger during the period he formulated his famous linear-time-independent canonical wave equation for quantum mechanics: practice of Tantric sexual yoga in ménage à trois as Traigunyasiddhi leading to Trigunatita (unification of the forms of the form by spontaneous fusion at superposition), for which he received the Nobel Prize in '33. It can be noted that dyadic yoga practice leaves projective-identification at transference intact, whereas concentration in triadic yoga smears the framework determining conditions prerequisite to transference and its associated regressions. Intercalated Sanskrit and Tibetan terminologies, now employed, are adapted from definitions provided in Sir John Woodroffe's THE WORLD AS POWER and Kumar Kishore Mandal's A COMPARATIVE STUDY OF THE CONCEPTS OF SPACE AND TIME IN INDIAN THOUGHT and the GLOSSARY to Sri Aurobindo's RECORD OF YOGA and UNBOUNDED WHOLENESS: DZOGCHEN, BON, AND THE LOGIC OF THE NONCONCEPTUAL by Anne Carolyn Klein and Geshe Tenzin Wangyal Rinpoche. The latter two of these four have become available to me only late this year (autumn, 2006) and the information they provide adds considerably to my conviction that at some far removed, likely pre-last-ice-age memetime, the basis of pre-Vedic thought lay in detailed physical theory, not the mere cosmological and numerological and musicological metaphors we suppose to have come down to us (as a corruption of words). Considerable support for this conviction is provided by the work of Giorgio de Santillana and Hertha von Dechend (HAMLET'S MILL) and William Sullivan (THE SECRET OF THE INCA: Myth, Astronomy, and the War Against Time). Santillana's and Dechend's account of the origin of the notion of invariance and Sullivan's thesis on precessional time and several quotations from the ancient Aymara language (recently demonstrated to be based on a 3-valued logic, and the implications of that demonstration relative to our understanding of brain function and questionable on/off properties of neurons and genes) strongly suggest the notion of ringlet time as a rheostatic topological operator having “come down” (by corruption of words) to Andean civilization from a globalized precursor, the LAST of some FIRST MEN who lived in a state of Nature no all-against-all lawless Melvillean riotocracy. A truly high-tech society, with its chemistry based not in atomistic concepts but acoustically-modified gravity-wave modes (i.e., acoustic black hole computer analogues Klein-bottled across all layered scale-level nesting-foams, as permitted by m-valued universal physical constants) would likely leave environmental footprints (a notion itself rooted upon inappropriate tacit assumption of validity of passive linear-time and absence of propositional calculi embodied in languages speakable and/or unspeakable of higher order-type than 2-logically-valued) undetectable with present-day technologies, based on completely different notions as they are (which is to offer some support for the underlying thesis of Olaf Stappleton's LAST AND FIRST MEN at the present critical juncture, human species, planet Earth). Given the enormity of what has been perpetrated, as institutionalization of the long-dead Cartesian-Newtonian-Wesphalian paradigm shifts into incendiary collapse, that Fall will take with it science-as-we-have-known-it -- as well as oh-so-much more. No institutionalization has long survived the death of its informing paradigm. These Sanskrit and Tibetan terminological intercalations are made by way of indicating AUTHENTICITY of the terms relative to the MATHEMATICAL concepts employed in explication of a special case, i.e., homeopathic potentization, as that process may indirectly reflect upon mechanisms of action in treatment with Ayurvedic herbs and the Tibetan Rinchen rilpo medicinals. It is to be noted that stereochemical studies of conductivity properties of DNA sugar-phosphate backbone, by metallic intercalation or pendent donors, have only remote import for the present thesis (a circumstance several critical observers have failed to notice). Content of this paper is most easily appreciated in light of the related earlier paper, also developed over a temporal-curl-based mathematical model of superconductivity of p-electron gas core (not hard-wired backbone) of DNA in critical-state helix-coil transition, “A New Theoretical Approach to the Homeopathic Law of Similars” (JAIH, Autumn 1995, 88:3) the abstract to which is as follows: A new notion of fundamental mechanisms in immune system and biological clock activity is presented as underlying the means by which homeopathic substances effect cures. These mechanisms are not an expression of molecular biology, but transpire on the submolecular quantum frequency level of biological organization. The healthy state of the organism is dependent upon these frequency parameters functioning within specific ranges (essential base, snying po'i gzhi). Any factor that shifts these frequencies outside their normal range (deluded base, khrul gzhi) is disease inducing. Chronic shifts of this nature eventually produce tissue pathology. Homeopathic substances are described as effecting cures by returning the quantum frequencies to their normal range.

What does your exclusion (Apoha, gzhan sel) exclude (bali, gtor ma)? What does your Gödel number number? Your Adhikara? Your marker for immunologic self-identity? Selfsame or non-simple? Reverse transcribed? Inversion of the retrograde transcription of the non-simple identity? Attend to the interface. Temporal interface. Why was popular rejection of the semantic dimensions of pre-WWI avant-garde art, art music, and metalogic prefigurative of the post-WWI dissimulation of quantum physics? And are we hard upon entry over cusp catastrophe as consequence of this gtor ma?

Abstract to the present paper: Potentizing homeopathic substances beyond the Avogadro limit is a critical-state coherent process, wherein an element of active information cannot be considered identical to itself (i.e., cannot be selfsame, the same as itself). Temporal ordering is paramount in transferring such non-simple information to and from the quantal base state and requires m-valued Lukasiewicz logics -- order-types numbered by numbered Gödel numbers -- and skew-parallel pencils, figures, geometries to represent the dynamic identity-transparent Zietgeber display (gzhi'i rtsal) from the ground state (Adhisthana) produced by the active temporal operators (emerging into dynamic display rtsal gyi rig pa as Trikaladrsti). In order to model the turbulent dynamics of dilution-succussion, the Hilbert space of quantum theory must be modified under extensions of aleph-null-valued Lukasiewicz propositional logics, interpreted not in terms of truth-value, but non-simple identity states, such that an m-logically-valued reference space becomes the informational ground (Alaya-adhikarana, gzhi gnas), or quantal base (Adhara, gzhi) state, decomposed (as Samantabhadra) and recomposed (Adhyaropita-samaropa, sgro 'dogs to Alaya, kun gzhi) by operator-time. Such temporal operations inherently involve complex angular momentum exchange via complex and hypercomplex “imaginary time”. This temporal-spin is a generalization of Dirac's “spin coordinate” and offers insight into how homeotherapeutic potency sustains itself indefinitely.

Non-Technical Synopsis, “Transliteration”

Investigations of core concepts in energy medicine, and the increasing number of studies of the electromagnetic properties of biological organisms, have led Christopher Johannes to the hypothesis that an information process underlies and encodes energy fields associated with living systems. Interaction between the non-energetic information process and the energetic fields is proposed to be an essential feature of homeopathic potentization and therapeutic action.

Understanding of this information process or ground (Brahman denoting: ground principle), may be enhanced by studies of radiation exchange associated with DNA, the molecule which stores, processes, and otherwise handles the information of biological inheritance. The Paine-Pensinger model of this radiation exchange treats DNA as being enveloped in a cloud of free electrons. When environmental radiation of a specific frequency impinges upon the molecule, it begins the twisting behavior which communicates its stored information to other molecules by means of chemical actions. At the same time, however, processes transpiring in the cloud of free electrons generate a wave phenomenon with acoustic properties, which radiates out from the molecule carrying with it the stored information. Analysis of the equations descriptive of the acoustic-wave phenomenon reveals several levels of information processing engaged in by these waves, levels that couple internal information with environmental information -- thus suggesting that the genetic information unit, and its corresponding wave signature, is multi-leveled like a stack of acetate overlays. The operators -- in the descriptive equations -- which characterize stacking and unstacking of the information overlays are time-like rather than space-like, and this has implications for the properties of the informational ground proposed by Johannes.

Cubist time-pattern superimpositions and multi-leveled logic
The information imprinted on the transparent “acetate overlays” is time-pattern related; it is clock-type information. And the “acetate overlays” are themselves clocks: a time-pattern is superimposed upon a less complex time-pattern to yield a second-order time pattern, and so on. What imprints the time-pattern on the time-pattern? The hypothesis of the Paine-Pensinger model is that time-itself is the imprinter. Time as imprinter is called “operator-time” and is written directly into the descriptive equations. When time imprints itself, the resultant imprint is a new imprinter -- rather as the hand drawing itself, around and around like a tiger turning to butter, swirls into a Picasso-ish Cubist superimposition of time-patterns (“concretion of time” and “haptification of space” in the interpretation of Jean Gebser's The Ever-Present Origin). The registration of this self-forming activity upon (a fractalizing) space involves the appearance of spin or angular momentum, like the onset of twisting in the DNA molecule. This hypothesis can be experimentally tested by studying the described radiation exchange process. It can also be applied to modeling homeopathic potentization in a manner similar to that described by Fritz-Albert Popp (1990).

One of the characteristic properties of the Cubist time-pattern superimposition is that it is multi-leveled. In order to understand the information content of this superimposition a new kind of logic is required, a logic which, too, is multi-leveled. Time-itself, apparently, speaks a language wherein any given statement has stacked themes, like Messiaen's Turangalila Symphony. If we are unaware that half a dozen themes are being played simultaneously, we hear only noise or chaos. But if we learn to musically comprehend instant by instant on multiple levels, then the simultaneity of the stacked themes becomes gloriously enchanting cosmic love play (of quantal action or Kriya), as the translated title of the symphony suggests. This is a very abstract form of program music. Time, also, it appears, has a program, a program which invokes a peculiar sort of identity wherein it is impossible to absolutely distinguish one part of the system from another, or the part from the whole which contains it. Operator-time, then, can be treated as a logical operator. Which is to suggest that the operator actively stacks and unstacks the “acetate” clock-sheets which compose the informational ground proposed by Johannes. Time is its own instrument, orchestra, notation, and composer.

Multi-leveled logic and the layered transparent
But in order to understand in detail the effects of this multi-leveled time-action upon spatially-referenced events, we need as tools not only a new kind of logic, but also a new notion of representation spaces and the types of geometrical figures that can exist within them. Having been unaware of the self-forming actions of time, our mathematical investigations of material systems have led us only to a vacuum state, not also to Johannes' informational ground. The second- and third-order self-forming actions of time have been transparent to us, mathematically invisible. Application of multi-level logic to consideration of the geometrical properties of representation spaces gives us, however, a densely stacked “reference space” that, by operations of time-logic, keeps a composite (stacked themes) accounting of all events that transpire on each of its unstacked transparent “acetate” clock-sheets.

Kandinsky's book, On the Spiritual in Art, maintains that given geometrical shapes can only be certain colors; a triangle, say, must be yellow. Mondrian came to declare that in representing reality a painter must use only perpendicular relations and panes of pure color. The shapes of Ellsworth Kelly, once saturated with color, define their own spaces. Did these artists somehow intuit (via Goethe-like properties of light) that the time-logics of self-forming are color-coded? Cognitive paths described in Rice Pereira's book, The Nature of Space, A Metaphysical and Aesthetic Inquiry (into “The Transcendental Formal Logic of the Infinite”), led her to paint in what she called “the layered-transparent”. Joe Goode “looks through” in most everything he paints. Frantisek Kupka, by 1913, had painted a spontaneous LOCALIZATION. No wonder Marcel Duchamp asked himself something like: Of what use is mere painting to a mind attempting comprehension of a multi-leveled universe READYMADE as if single-leveled by enculturation, where every “constant object“ found and every “other” is a phenomenologically-constructed LARGE GLASS reflecting a peculiar identity into Mallarmé's “anterior sky” via his “windowpane”, or even the WINDOWS of Delaunay which open onto a “new reality” of discrete action in “uneven measures”?

The layered transparent of the informational ground is a reference space containing stacked information possessing a peculiar holographic identity. Homeopathic miasmatic (diatheses) types (Vasana, bag chags: latencies) can be understood as manifesting an inherited tendency to lose certain “color-coded” time-logic shapes from this layered transparent. The potentized homeopathic substance, via the energetic-field dynamic, acts to return the lost “colors” to the informational ground of the biological organism. If this is so, then, it seems, the molecular aspects of homeopathic potentization should in some way reveal this fact.

Indeed, this does seem likely to be the case. It's too bad that Picasso and Braque did not persist with their Analytic Cubism and carry its practice of phenomenological reduction into the field of molecular chemistry. Had they done so, we likely would have gathered much insight into homeopathic mechanisms of action. Surely, they would not have painted the stick-and-ball figures of molecules as single-level geometries. They would have painted a molecule as a multiple, a composite, a superimposition (Samaropa-adhyaropa, sgro 'dogs) of time-patterns. They would have imaged the geometrical relations underlying molecular chemistry as not being absolutely definable from the perspective of single-valued logic. And had they pursued the implications of this, their images would increasingly have become multi-faceted, because these painters would have intuitively known that spacetime is modular: limited spacetime domains (Adhikara: jurisdiction or competence of Tantra, the principle of control) nested one inside the next. “Acetate” clock-sheets within “acetate” clock-sheets within “acetate” clock-sheets. And had these images of “molecular Cubism” been analyzed for their implications in biophysics, it would have become apparent that the multiplicity of limiting values (such as a limiting velocity) implicit in Einstein's Special Theory of Relativity are responsible for this stacked compartmentalization -- just as were the “simultaneous contrasts” of Chevreul's color theory studied in Delaunay's and Kupka's Orphism. Clearly, each limited spacetime domain has its own complement of limiting values.

Time operates on space to generate form
Time (Kala = operation making time possible [i.e., a possible-world logic]) operates (Dik = operation making spatial position possible; Srsti = first primary logical operation on the ground state {Adhisthana = ground state [part grounded in whole; particular in general]}) on space (Akasa = representative of Brahman, the Ground Principle) to generate form (Yantra = disposition of Tantra [i.e., matrix of the operators in decomposition]; Mantra = coherency of Tantra [i.e., coherent phase relationship of the operators]). The notion “generate” is a misnomer derivative of the exclusion your exclusion (Apoha, gzhan sel) excludes (Bali, gtor ma), crossing the G. Spencer Brown cross not crossed being a cross: the requisite algorithm is Lukasiewicz-Gödel encoding by Schrödinger-Samaropa (superposition) over kun gzhi (allbase); the inversion, decomposition of the ground state principle (Brahman) by m-logically-valued mathematical involutes. In Boccioni-Severini-Russolo's Futurism, the sense of duration was equal to memory crossed into percept. Speed… and its limits. Alfred Jarry (who wrote Ubu Roi) was focused on reaching the limit, any limit, wherever he could find it. Time imprinting itself over into an imprinter does its imprinting only “in the limit” of any given limited spacetime domain (Adhikara, such as that of a living unit, or cell). Velocity, acceleration, time-rate-of-change of acceleration (sequence inverted in cascade by decompositional involutes). Each have their limits at which time operates, imparting a twist. At each type of limit, a different type of twist. Shape and its topological properties. Time operates on space to generate (decompose) form. Three types of time: three-fold operator-time. Each depositing and retrieving their own class of time-logic shapes from the layered transparent of the informational ground. Music-sculpture: Musculpt.

A water-borne stack of crisis states
In homeopathic potentization the dilution-succussion process, from the perspective of the above-described notions, becomes a water-borne stack of crisis states that cascade highly organized (i.e., coherent) time-pattern shapes through the nested collection of “acetate” clock-sheets constituting the transparent informational ground. Turbulence viewed simultaneously on many levels with a many-leveled logic. In its abstract general form, this turbulent process occurs widely in nature, in the Earth's atmosphere and its oceans, for instance; and these may be profitably compared with the homeopathic case. The clock-sheets in homeopathic dilution-succussion are a spectrum of wave motions existing on smaller and smaller scale levels: the characteristic wave lengths become shorter and shorter as concentration of the solution becomes less and less. Material potential decreases as second- and third-order time-patterns elaborate themselves, through twisting, during the crisis that comes when limiting values (established by the Adhikara [jurisdiction or competence of Tantra, the principle of control] of the given limited spacetime domain) are reached. These patterns in higher-order time require for their description number systems more complex, more “imaginary”, than the natural counting numbers, and hence these patterns are relatively “transparent” to us. Ultimately, a material substance vacuum state (beyond the Avogadro limit) is reached, which corresponds to a hyper-stacked time-logic configuration. Time unfolds itself upon the topology of space as emergence of material structure; the disappearance of material structure enfolds quantum action-potential (Kriya) stored in higher-order “imaginary” time-logic configurations. One can speculate that “appearance” occurs in every limited spacetime domain and every class (non-denumerably transfinite, denumerably transfinite, finite: distinct topological transforms over each order-type transition by Dasyalipsa [D³: bearing the triple-yoke of decomposition by mathematical involutes] of Isvara to Prakrti) of limited spacetime domains permitted by m-valued universal constants (each such value under Adhikara or jurisdiction of Tantra, control, of the corresponding m-valued Lukasiewiczian logic order-type, propositions of which are codified by numbered Gödel numbers) constituting this one-and-only universe of unbounded wholeness -- such that the connectivity of events is not carried by external event knocking into external event, but by the quantum potential acting from inner to outer, implicate to explicate. During homeopathic potentization, a special case of “disappearance”, time-pattern shapes carried by the energetic field, in conjunction with the dilution-succussion procedure, impart spin as a peculiar kind of twist (in the limit of the various classes of limits) at each sheet-to-sheet transition crisis, such imparting transpiring explicate to implicate, in reverse D³-transcription. The imparted spin is time (as logical operator) imprinting itself as the imprinter upon the layered-transparent of the Abelian-transcendental formal logic of the informational ground (visualized by Rice Pereira, among others -- including Yayoi Kusama, however much to her chagrin).

Lukasiewiczian Time-Logics, by Three-fold Temporal Curl
(Trikaladrsti-tapassiddhi: T¹, T², T³), superposed (Adhyaropita)
over the Quantal Base State (Alaya, kun gzhi)
in Homeopathic Potentization

Informational Ground and Temporal Operators
Johannes (1996) has postulated a “non-energetic, meaningfully ordering, informational ground” as primary to any energy field dynamic in homeopathic mechanism of action beyond the Avogadro limit. Properties of this informational ground may be deduced from Paine's and Pensinger's (Paine and Pensinger, 1979; Cong Huyen Ton Nu Nha Trang and Pensinger, 1994; Jus, Pensinger, and Paine 1995) model of radiation exchange by superconductant DNA, and these deductions may be experimentally investigated by dynamical studies of the genetic molecule. This should not be surprising, because any submolecular informational ground associated with living systems or organic substances unconnected with nature's premiere information repository on the molecular level would be either purely redundant or counterproductive.

Whitmont, quoted by Johannes (p. 154), says, “Cells interpret nucleotide sequences that themselves are more like unconscious sounds than somatic units.” (Emphasis added by Johannes.) This sentence captures well the sense of the Paine-Pensinger model. Their mathematical treatment describes superconductant DNA as generating coherent quadripolar waves which carry all the information contained in the nucleotide-pair sequences into the molecule's environment. The sets of acoustic wave equations derived in the model are written in Maxwellian form, as this relates more directly to the solenoidal dynamics (Mudra, where a scalar becomes a vector) of DNA's helix-coil transitions than does the time-dependent Dirac refashioning of the Schrödinger form of the quantum wave equation. These Paine-Pensinger equation sets are unique, however, in that the notion of orders of active temporal operators (Trikaladrsti-tapassiddhi: T¹, T², T³) is introduced and written directly into the equations. Analysis of the properties of these topologically active temporal operators will generate insight into characteristics of the submolecular informational ground, or quantal base state (Alaya, kun gzhi), and suggest that the genetic language may not only be composed of codons that are single-level ciphers. Indeed, the orders of non-linear wave (non-simple-identity “beam me up according to Hoyle” phase-digibio) signatures (Mantra) of the nucleotide-pair sequences hypothesized to coherently pulse from the molecule at helix-coil transition suggest a much more complex multivalued language (of non-simple animistic identity transparency, not truth-valued existential separatism) which couples single-valued codon sequences with environmental variables via coherent-wave dynamics. The Regge calculus (which transcribes spacetime curvature configurations into n-dimensional lattices [Yantra]), Karpenko functionals (Tanmatra) of Lukasiewicz m-valued logics over the primes (Bindu), the implications of this in terms of the Riemann hypothesis for prime number distribution, and numbered Gödel numbers (Paramanu, the propositions Gödel numbers codify by prime-number factors raised to Lukasiewicz order-types) will be required to decode the multi-leveled ciphers of the genetic language. Both Sanskrit and Tibetan vocabularies will be found of considerable utility in explicating the mathematics involved. This should not be surprising if a “universal grammar” is encoded into the DNA molecule (and its quantum wave properties) as metalinguistic theorist Noam Chomsky has for long maintained (even if it turns out that “aspects” of this “grammar” are not recursively generative over a linear-time reference frame [therefore, by “Church's hypothesis”, i.e., calculable iff recursive, not calculable by employment of ₁T₂-logic Turing machines], but calculable based upon quantum-phase-digit linear-time-independent Schrödinger decomposition [Samaropa in Schoenberg retrograde-inversion] by mathematical involutes of the _µT_m-logical Lukasiewiczian informational ground [Adhisthana]).

Operator-Time, Multivalued Wave Function, and M-Valued Logics
The temporal operators written into the superconductant DNA wave equation sets are a species of operator-time in a field-theoretic context. Were these equation sets to be transposed into Schrödinger form, the first inclination of the physicist would be to conjugate the temporal operators to the Hamiltonian, H, the total energy operator. (In classical particle mechanics, H is a function of generalized coordinates and momenta minus the Lagrangian function L. If time is not explicit in L, then H represents the total energy of the system. In quantum mechanics, H is an operator which provides the equation of motion for the wave function.) Indeed, conjugating operator-time to the Hamiltonian was considered and rejected as early as the 1920s by Pauli. More recently, Misra, Prigogine, and Courbage (preprint, no date given) have reconsidered this proposition and reached the conclusion that operator-time is incompatible with the standard interpretation of quantum mechanics. They say, “…the generator of the time evolution group is also the operator representing the energy observable and hence is required to be bounded from below.” Which is to conclude that operator-time would generate negative values of the energy, and this is regarded a meaningless. But conjugating operator-time to the Hamiltonian is to treat it simply as a measurable, not an active topological operator. Authentic operator-time would have to enter the Schrödinger format in a much more complex manner involving a related reinterpretation of the wave function on physical considerations alone.

When Dirac revised the initial time-dependent Schrödinger wave equation (which was unbalanced in regards to time reference), the resultant quadratic invoked a spin coordinate used to explain the observed split in spectral lines. No one quite knows, even yet, what this spin coordinate is whose value, according to Dirac's formulation, must be either plus or minus 1/2. Spin 1/2 is agreed not to be simple physical spin upon an axis, because the spin value cannot vary over a range as h (Planck's constant, normally treated as single-valued, not m-valued) tends to zero. Such continuous variation (tantamount to giving the “constant” m-values) would be required to yield a classical rotational analogy. It is the property of remaining either plus or minus 1/2 (whatever m-value hypothetically given h, Planck's “constant”) that identifies Dirac's spin coordinate as a shadow of topologically-active operator-time. This notion -- involving actual m-values to h and continued Dirac spin of plus and minus 1/2 -- can be applied to analysis of the homeopathic potentizing process (involving dilution and succession) in a manner similar to that suggested by Popp (1990), but reinterpretation of the wave function, which is connected to the Hamiltonian operator, is first required.

One of the primary distinctions between Newtonian and post-Newtonian physics is that the variables in Newton's laws of motion are single-valued, whereas the quantum wave function (connected to the Hamiltonian operator of the quantum wave equation which replaced Newton's laws of motion) is multivalued. Simplifying for clarity of illustration, in a single-valued function, for every given value of x there is a unique value for y. Multivalued functions, however, specify many values of y for every given value of x. Again to simply for clarity, in the wave function, if x is a temporal variable and y a spatial variable, at any given time x, the entity being represented will appear to be located in many different positions y. In order to avoid the apparent violation of common sense multiple values for y suggest (i.e., that an entity can be in many different places at a given time), in 1926 Max Born proposed that these values be understood as probability amplitudes: that is, as indications of the likelihood only that the entity should be found in the designated locations. This probability interpretation became the standard approach (never embraced by Schrödinger) to dealing with the question of quantum nonlocality. However, for our purpose of understanding spin 1/2 as a shadow of operator-time, another interpretation is more useful.

Four years before Schrödinger wrote his time-independent quantum wave equation, Emil Post (1921) and Jan Lukasiewicz (who was the actual originator and whose personal history with the involved notions went back to the turn of the century, but whose work was published in Polish) each produced rigorous accounts of _µT_m-valued logics. {No copy of Jan Lukasiewicz's book, Aristotle's Syllogistic, which I had seen referred to in the notes to several mathematics papers, was indexed in the Cornell Library system or the Library of Congress during the mid-1970s when I was most actively pursuing access to this area of thought.} Post demonstrated that logics can be constructed, without contradiction, such that a proposition can have one of any number, m (later generalized to Cantor's orders of infinity), of possible logical-values. This was not applied to the multivalued wave function of quantum mechanics surely for many reasons, plausibly the most explicit of which was because, even though Post had demonstrated that there can be any number of logical-values to a given proposition, that proposition, according to the interpretation provided in Post's 1921 paper, can still be ascertained to be tantamount to single-valued (what can be understood as a disclaimer enabling publication, and possibly peace of mind, introduced toward the end of the paper made this appear possible). Since then, however, fuzzy logic has shown there can be a fuzziness between true and false, 1 and 0, and this logical property -- here legitimately violating the ₁T₂-logic law of distributed middle -- can be used to make machines like refrigerators more self-regulative. Moreover, G. Spencer Brown, in his book, Laws of Form (1969), while elaborating proofs of Sheffer's postulates for Boolean algebras, demonstrated that the notion of “distinction” is more fundamental than that of “truth-value”. A highly unwelcome demonstration which has largely been ignored by logicians of the Academy who have preferred to fret over the so-called threat to mathematics posed by Gödel's theorems, theorems in actual fact no threat at all to mathematics (only to these logicians' habituated thought processes and preferred states of consciousness) but existence demonstrations for _µT_m-valued logics (which do include, at the most-reduced case, ₁T₂-valued logic) in transcendence of truth-value semantics. The painter Rice Pereira, in my judgment, correctly read implications of Gödel in visualizing a “transcendental formal logical of the infinite” and in numerous ways anticipated the thought of G. Spencer Brown concerning form dynamics: indeed, with her notion of a “layered-transparent”, she in many ways moved beyond the thoughts of each logician. If we consider that the notion of “identity” is more fundamental, yet, than that of “distinction” -- for there must be a preceding notion of identity if that notion is to be bifurcated into separate identities by the drawing of a distinction -- we may arrive at an expanded understanding of Lukasiewicz-Post order-types of logical-value and entertain full-blown _µT_m-valued logics wherein a given proposition may legitimately -- but, additionally to that of fuzzy logic, in violation of the ₁T₂-logic law of non-contradiction -- simultaneously embrace any permitted number, µ, of the any available number, m, of the logical-values to the proposition. Normative utilization of such propositions is holotropic; whereas, in the fully hologramic case of _CT_C-valued propositions, given the properties of C, self-reentrant, self-referential, open awareness of unbounded wholeness would be reciprocally maintained, state and case under such logic being immeasurable, undiminishable, and linear-time-independent (like the active “ingredient” in a fully potentized homeopathic medicinal substance).

A reinterpretation of the significance and meaning of orders of logical-value is encouraged by recent developments in the field of mesoscopic physics, where it has clearly been demonstrated that some atomic entities (not only elementary particles) are multivalued and can exist in more than one place at a given time (Browne, 1995 and 1996; Gribbin, 1995). The identity of such entities cannot be “simple”, cannot be absolutely self-identical, selfsame, a matter of itself-and-only-itself. Such entities possess “complex” identity: that is, distinction between the given entity and other entities cannot be absolute, an opaque wall, but must be a matter of degree, state, or case, must exhibit one or another order-type of identity transparency. This means that an order of logical-value (the multiple values of which a proposition can simultaneously and validly express, even if there is a ₁T₂-logic contradiction involved) represents an order of identity transparency: one of the non-denumerable transfinite set of states between “no A is not-A” and “A is absolutely not-A”. The unbounded logical domain, implied by multiple orders of logical-value to a given proposition, contextualizes the multivaluedness of the quantum wave function such that transposing the temporal operators of the superconductant DNA wave equation sets from Maxwellian to Schrödinger form necessarily involves the hypothesis that operator-time is the logical operator which determines the order of logical-value configuring the reference frames (or informational grounds, Alaya-adhikarana, gzhi gnas) of given system dynamics. Active operator-time (Trikaladrsti-tapassiddhi: T¹, T², T³), as authentic topological operator (not merely a measurable), would decompose (as mathematical involutes) and recompose an m-logically-valued reference space (particularly in the biological case, syning po'i gzhi, essential base).

M-Logically-Valued Reference Space (not a Vacuum)
as Quantal Base State -- and Molecular Indeterminacy
A point in Hilbert space (the multi-dimensional function space used in quantum theory), even though it has many degrees of freedom representing the intersection of many spatial dimensions, is still logically single-valued. Hilbert space was constructed with a calculus of propositions wherein each proposition must be either true or false. This same function space, however, can repeatedly be reconstructed with each order-type of logical value permitted by an m-valued calculus of propositions interpreted in relation to the notion of identity transparency, not truth-value -- thus yielding a Pereira “layered transparent”. A given point, then, would not only have many degrees of freedom, but, being logically m-valued, would also have many shadow selves holographically peppered throughout the space (phase-valued logics, i.e., Lukasiewiczian _µT_m-valued propositional algebras of sets of states of quantal non-simple identity -- not truth-value -- over phase spaces, only the ₁T₂ order-type of which is a Boolean-valued universe). Simple-locality and simple-identity would not be inherent properties of entities mapped onto sheaves of this densely-stacked function space, which may be called an m-logically-valued reference space (MVRS). Gödel's (1931) discoveries concerning the limitations of mathematical systems constructed with a single-valued logic can be viewed as opening a window upon m-valued logics, identity transparency, and nonlocality. Fuzzy sets/logics in the real interval [0, 1], as interesting and useful as they may be, must be understood as deeply involved in the continuing dissimulation of Schrödinger's wave-function. It is not permissible, for instance, to construct a _µT_m-valued or _CT_C-valued Hilbertian phase/function space by employment of a ₁T₂-valued logic; nor is its permissible to axiomitize such hyperspaces by employment of Tarskian ₁T₂-valued logical semantics and derivative notions: they must be constructed and axiomitized by employment of the same order-types they exhibit -- otherwise, they could have no semantic authenticity at exhibiting the order-types they purport to exhibit. Such order-type exhibitions would be merely the given order-type as “viewed” through the “lens” of the ₁T₂ order-type. Accomplishing “authenticity” here requires development of holographic Musculpt as mathematical notation.

Orders of operator-time written into the Maxwellian form of the Paine-Pensinger DNA wave equation sets would logically decompose and recompose the MVRS of the biological organism. In the realm of biology, at least, the MVRS, not a vacuum, would be regarded as the quantal base state or informational ground. The function of this ground (Alaya-adhikarana, gzhi gnas) would be to keep a running m-logically-valued composite accounting of all single-valued information exchanges transacted on other scale levels. The primary mechanism of action of potentized homeopathic substances would be to return multivalued information to the MVRS which was lost during disease pathogenesis. Miasmatic types (diatheses) would relate to inherited predispositions (congenital frequency anomalies in the quantum wave processes of superconductant DNA: see our 1995 paper entitled “A New Theoretical Approach to the Homeopathic Law of Similars” noted in the references) for given patterns of information loss on the MVRS. Emergence of allopathic symptoms and tissue pathology would transpire as the effects of m-logically-valued-information loss, on the MVRS, cascade via quantum wave interactions through the logical-value hierarchy, ultimately affecting single-valued information exchange processes on the molecular and cellular levels.

When, however, atomic entities (nowadays, i.e., December 2006, even small molecules have been so experimentally demonstrated, making molecular indeterminacy almost a moot point) can be in more than one place at a given time -- as recent experiments in mesoscopic physics have demonstrated (Browne, 1995 and 1996) -- the single-valued geometrical relations underlying molecular chemistry cannot have absolute definability. From the perspective of a single-valued binary logic, they are definable only in an indeterminate fashion. Traditional Aristotelian-Baconian logic is both single-valued and binary, i.e., a ₁T₂ logic, in that 2-values to a given proposition are available (true-false), only one of which is permitted at a given time (either true or false). A relation seen as parallel from the perspective of a single-valued logic would also manifest infinite degrees of skewness when viewed from the perspectives of the various order-types of m-valued logics (i.e., _µT_m logics, wherein any number of values are available and simultaneously permitted). Indeed, skew-parallel figures and “diversely identical skew-cubes” have been constructed with the use of null-vectors in developing a geometrical representation of the “identity-in-diversity” explicitly characterized by m-valued logics (Bennett, 1956). The implied molecular indeterminacy is the subject of a book written by Isaacs and Lamb (1969) on the basis of research conducted at The Johns Hopkins University School of Medicine.

The primary thesis of this unjustly neglected monograph is that Heisenberg's indeterminacy principle applies to the variables describing molecular motion in living systems at normal pressures and temperatures. This hypothesis is justified, in the main, by arguing that the actual conditions in biological organisms do not fulfill the minimum prerequisites for assuming applicability of the central limit theorem of probability theory or a Gaussian (normal) distribution of the variables of molecular dynamics involved in an indeterminacy relation. This challenge to the statistical thermodynamics of molecular biology necessitates recourse to quantum principles in explaining emergent phenomena of organisms. Many properties of living systems poorly explained with deterministic notions of molecular motion, it is argued, become elegantly comprehensible by following through the implications of molecular indeterminacy.

Notwithstanding the enormous amount of data Isaacs and Lamb marshal in support of their thesis, it appears they conflate two independent arguments in accounting for the origins of molecular indeterminacy. This does not negate the value of their analysis or conclusions, but does call for some clarification and expansion of theory. The two conflated arguments are given as follows:

(1) This argument is stated explicitly and clearly, thus:

1. in physical systems at atomic spacetime scales, distribution of conjugate variables of motion involved in an uncertainty relation is Gaussian, thereby yielding an equality relation with the uncertainty product;
   
2. in living systems at molecular spacetime scales, distribution of conjugate variables of motion involved in an uncertainty relation is non-Gaussian, thereby yielding a inequality relation with the uncertainty product;
   
3. since the conjugate variables of motion involved in an uncertainty relation cannot, by definition, be handled in a deterministic fashion, and since in living systems such variables of molecular motion cannot be assumed to be in Gaussian distribution, the molecular motion in living systems must be an expression of an enlarged indeterminacy;
   
4. to reestablish equality of the uncertainty relation under non-Gaussian conditions, the uncertainty product must be multiplied by a factor of Î;
   
5. absent knowledge of the value of factor Î for living systems, a plausibility argument, based on the conditions in living systems, is made to the effect that the value of factor Î is large enough to encompass in uncertainty molecular motions of living systems.
   

(2) This argument is tacitly embedded in the first. The lack of infinite divisibility of spacetime is sufficiently all encompassing as to be significant for instrumental intervention at molecular spacetime scales, thus making measurements of conjugate variables of motion, involved in an uncertainty relation at those scales, indeterminate.

The second argument is not made with sufficient explicitness or clarity. It is partly hidden in the concluding “then-must” predicate of point [c], above, and partly hidden in the attempt of the plausibility argument of point [e], above, to establish a sense of the magnitude of factor Î. Argument (2) must be made fully explicit and completely independent of argument (1), because, after all, the raison d' être of indeterminacy is instrumental intervention having effects of sufficient magnitude on the system being measured such that the measured system is consequentially disturbed. Multiplying the uncertainty product by a factor of Î is equivalent to scaling Planck's constant, h, to the spacetime scale of molecular motion. This is the reverse of seeking a classical analogy for Dirac's spin coordinate by allowing h to tend to zero; here the value of h jumps by a step-function (determined by relativistic limits associated with each limited spacetime domain, as described below) to a maximal value. Justification for this scaling of h must be given independently in argument (2); then, and only then, can argument (1) validly be used to establish a theoretical context for experimental determination of the value of Î.

The breakaway notion of Planck's radiation law for blackbodies was realization that prediction does not require a description of the spatial field; characterization of the properties of an elemental oscillator is sufficient. This shifts the emphasis decisively from analysis of spatial ordering to that of temporal ordering. Quantum mechanics is a theory of “clocks within clocks within clocks” (Bohm, 1983). Isaacs and Lamb touch upon this notion in their discussion of what they call “retroversion”, the fact that temporal and spatial limitations occur in interconnections between units forming subassemblies of a process. This issue of modular spacetime, or the formation limited spacetime domains, is intimately involved with that of subsystem-system-supersystem partitioning in dynamical systems. The Paine-Pensinger model of the quantum wave properties of the DNA molecule addresses this subject by allowing limiting values of dynamical variables (relativity theory) to dictate quantization (quantum mechanics). Three orders of active temporal operators (“clocks within clocks within clocks”) in the canonical equation of the superconductant DNA model (descriptive of dynamics of the p-electron gas core of the molecule) operate only at limiting values established by the phase velocity of those waves accomplishing energy and momentum transfer with perfect efficiency. This phase velocity is a limiting velocity relative to its given limited spacetime domain (no waves within the given domain may exceed this speed limit), just as the much faster velocity of light is a limiting velocity relative to its much larger limited spacetime domain, the universe at large. The brief exposition offered here is the independent argument (2) spoken of above as being required to fully justify the conclusions of Isaacs and Lamb -- which is detailed in the mathematics of the Paine-Pensinger model (also as regards a “general theory of process” and a computerized multi-scale numerical model of tornado genesis).

The value of Î, for a given spacetime scale of living units, is derivable from the phase velocities of the coherent waves generated by the involved types of DNA (each histological type of DNA having its unique set of quantum markers-tags, e.g., frequency-response window). The limit of these phase velocities is a limiting velocity scaled to the limited spacetime domain of the living unit; the similarly appropriately scaled value of Planck's constant, h, can be deduced from this limited velocity. In this manner, Î and similar factors will disappear from the equations descriptive of the system and be replaced by appropriately scaled values of fundamental constants. (This scaling of universal physical constants is altogether different from the scaling of value ranges permitted to dynamical variables; the former treats universals as m-logically-valued, while that latter truncates the range of numerical values permitted to particulars, thus filtering numerical models.) The phase velocities of the coherent waves emitted by various histological types of DNA molecules can be derived from experimental observations of changing transition temperatures in response to changing ambient electromagnetic field parameters, as given in the equations of Paine's and Pensinger's superconductant DNA model. The reader will note that the resultant notion of Heisenberg uncertainty does not rely upon probabilities, but m-valued logics; and that this casts the Heisenberg uncertainty relations into a completely different light, with implications distinct from those considered in the standard theory, implications more akin to the work of Gödel than that of Bohr.

Three-Fold Operator-Time (Trikaladrsti-tapassiddhi: T¹, T², T³)
During correspondence between physicist David Bohm and British philosopher J. G. Bennett (1962-63), Bohm elaborated a notion of “the three kinds of time”. Quoting Bohm (letter dated 3rd February, 1962):

So now there are two kinds of time, which I denote by t and t respectively. The time parameter, t, refers to the wave function and therefore to the continuously changing potentialities.

But we now need a third kind of time. For if a certain quantum state, h, dies out exponentially, the system will disappear from existence unless another quantum state, h, surges up and takes its place. This is the time of repetition or hyparxis, which shall denote by T.

Evidently, the three kinds of time must be related. The movement will take place in the following way:

1. The potentialities are prepared (this is detailed by the parameter t);
2. The present actuality dies out, while another actuality arises within the new potentialities to take its place (this is described by the parameter t);
3. The repetition of time, T, is the parameter of hyparxis. It represents roughly the number of periods, t , of exponential decay of actuality that are needed before the new (or repeated) actuality arises again. (Emphasis added.)

Evidently, the ratio t/T represents the “ability to be”. For if the ratio is small, the system finds it difficult to repeat its existence after it dies out, so that its existence is relatively “tenuous” and weak. On the other hand, if t/T is of the order of unity, it is a really “solid” kind of existence.

The canonical equation of the Paine-Pensinger model of superconductant DNA has three terms, each with its own class of temporal operator. These temporal operators are formalizations of the three kinds of time Bohm refers to. Compare the following statement (Cong Huyen Ton Nu Nha Trang and Pensinger, 1994, Vol. II, p. 331) describing this canonical equation with Bohm's statement given above:

In term #3, the quantum of information to be exchanged is defined by the linear time taken by a parcel of p-electrons in transiting T_o Û T_c. [T here designates temperature.] The inverse of this period establishes the fundamental frequency of this quantum. The number of such transits establishes the number of quanta to be read. (Emphasis added.) Term #2 evaluates the time taken to receive these quanta -- which themselves exist as a sinusoidal function of time -- within the structure of the DNA molecule [it's p-electron gas core]… Term #1 evaluates the time taken by the embedding environment to receive the signal represented by term #2.

Three-fold operator-time acting (at limiting velocities, limiting accelerations, and limiting time rates of change of acceleration of given limited spacetime domains) as a composite logical operator, decomposing and recomposing an MVRS, is a generalization of the above described “three kinds of time” and an extension of Bohm's notion of “active information”. It can be noted that Bohm used the term “hyparxis” (ability to be) for “repetition” because he was discussing with Bennett Bennett's notion of three framework conditions designated “Time, Eternity, and Hyparxis” as explicated in Bennett's four-volume magnum opus The Dramatic Universe. Sri Aurobindo's notion of “Trikala” (Trikaladrsti-tapassiddhi: T¹, T², T³), Bennett's notion of “three framework conditions”, Bohm's notion of “the three kinds of time”, and Paine's and Pensinger's notion of “three-fold operator-time” are related but subtly different. Aurobindo's conception-perception is of an active-time regarded wholly linear in nature, where the three aspects are understood as past, present, and future transformable by yogic application of consciousness-force: clearly, a partial understanding only (likely the result of commitment to Darwinian evolutionary theory and the psychological consequences of a suborning to Hindu nationalism and consequent impulse to demonstrate compensatory power). Bennett's three framework conditions can be regarded as an “image” of three-fold operator-time as “viewed” through the lens of Aristotelian-Baconian ₁T₂-valued logic (Bennett, in helping to develop a theory of “skew-parallels” and “diversely-identical skew cubes” as an extension and application of “Clifford parallels”, made no link to the m-valued logics of Lukasiewicz and Post, a link essential to rigorous understanding of the “diversely-identical” in animistic identity-transparency and “to set our ontology free from the limitation of single-valued existence”, to quote Bennett's appendix on the subject). Bohm's three kinds of time can be regarded as three-fold operator-time seen in terms of quantum theory divorced from relativity theory. Paine's and Pensinger's three-fold operator-time can be regarded a quantum-relativistic notion where the “image” as “viewed” through the lens of Lukasiewicz-Post _µT_m-valued logics is not drawn. J. W. Dunne (1934) has argued that linear time requires another kind of time to measure its rate of flow, and that this other kind requires another, and so on to infinity. Dunne's argument does not apply to temporal operators. That three order-types of operator time are necessary and sufficient to decompose and recompose an infinite set of orders of logical value on the MVRS can be demonstrated in the context of G. Spencer Brown's calculus of distinctions or indications (Cong Huyen Ton Nu Nha Trang and Pensinger, 1994, Vol. II, pp. 343-4).

Complex Angular Momentum Cascade and Temporal-Spin
Fritz-Albert Popp's (1990) notion “that the introduction of a momentum operator into the Hamiltonian of the dilution describing the succession procedure favors considerably the creation of coherent states” is tantamount to treating the total framework of the dilution-succussion procedure in homeopathic potentization as equivalent to a turbulent multi-scale dynamical system. Each higher level of dilution-succussion-potency would correspond to a smaller and smaller scale level of such a system. A direct analogy in turbulent hydrothermodynamics is the energy-momentum cascade leading to the formation of severe storms in the Earth's atmosphere (Paine, Zack, Moore, and Posner, 1975). Energy-momentum cascades from larger scales of wave motion to smaller until it becomes trapped, until, ever more concentrated, it runs out of sufficient flat Newtonian space and time. In the crisis state of this turbulent event, the storm radiates coherent information (“Hawking radiation” from this “acoustic black hole computer analogue” which serves the function of providing a way of escape from a condition of infinite collapse -- as acoustically-modified gravity-wave modes, or, in other words, infrasound -- which is deposited upon, and/or pokes holes in, various boundary layers (e.g., tropopause boundary). See recent EOS and Science News reports of experimental verification of this computer-modeled prediction (repeatedly made during the early-to-mid 1970s) of the generation of Hawking radiation by tornadoes (Scentman and Wescott, 1996; Science News, 1996). One can regard the tornado, not only as an geomantic-geospatial analogue of an acupuncture needle, but regard the superconductant plasma its electromagnetic-hydrothermodynamic “bottle” contains as a geo-analogue to a potentized homeopathic substance. If passing the Avogadro limit in homeopathic potentization is regarded as analogous to transiting the crisis state in the atmospheric energy-momentum cascade, then numerical modeling details of this cascade process may shed light upon how Bohmian “active information” is deposited upon the MVRS during dilution-succussion. Pursuit of such an analogy would not involve departure from our initial thesis regarding the Paine-Pensinger model of superconductant p-electron gas core of DNA, because that model describes the molecule as receiving energy and angular momentum through radiation exchange, reaching a critical state in helix-coil transition, and radiating coherent waves during this process.

In the atmospheric case, when an imbalance develops between the mass and momentum fields within a large-scale motion field, energy and momentum cascade to a smaller-scale field of flow. During this cascade event, angular momentum is transferred from one limited spacetime domain to another such that the horizontal component of velocity is twisted into an imaginary dimension. This 90-degree twist (mediated by an operator with the square-root of minus-1, or an imaginary number, as a coefficient) in the spatial axis of rotation can be regarded either as the emergence of complex angular momentum or, alternatively, as the temporal curl of horizontal velocity. An account of this has been given as “the atmospheric analogue to Maxwell's equations” (Paine, Zack, Moore, and Posner, 1975, pp. 133-4). This analogue is not as surprising as it might at first appear. Maxwell developed his electromagnetic field equations on a hydrodynamic analogy. Paine, et al., reversed the analogy and adopted Maxwell's mode of thought. A further development was a portrait of the tornadic superconductant plasma as a transducer of electromagnetic field fluctuations into acoustically-modified gravity-wave mode signatures emanating as what has become known as Hawking radiation. As the cascade ensues from one scale level to the next, the spatial axis of spin undergoes repeated 90-degree twists into and out of imaginary dimensions. Temporal curl (which performs a function similar to Maxwell's “demon”) is time actively imparting an imaginary spin moment to the system.

That time can accomplish this feat of imparting spin to a system was first suggested by Russian physicist Nicolai Kozyrev (1968) during the 1950s; Stephen Hawking (1988), with his notion of “imaginary time”, has recently suggested something similar. As in Dirac's spin 1/2, the imaginary spin moments imparted during severe storm genesis occur only by 90-degree jumps; there is no continuous variation over a range. Transposition from Maxwellian to Schrödinger format of the temporal curl involved in energy-momentum cascade would involve the appearance of operator-time as a generalization of Dirac's spin coordinate. In the larger context developed above, this temporal-spin (quantized as Roger Penrose's “twistor”) would be responsible for depositing and removing Bohmian “active information” from the MVRS of the involved system, be it atmospheric, genetic, or homeopathic. One can speculate that the “indefinite therapeutic durability” (Johannes, p. 153) of potentized homeopathic substances is an expression of the fact that the m-logically-valued information actively deposited on the MVRS by imaginary operator-time is not measurable in the familiar terms of real linear-time -- “imaginary” and “real” being used here in the sense of the types of number systems required for development of the time-logics involved.

Physical Embodiment of the M-Logically-Valued Reference Space
Superconductant DNA's p-electron parcel temperature oscillations -- as intracellular Zeitgeber -- govern DNA-generated coherent waves which structure water inside the protein cylinder of cellular microtubules. These microtubules act as wave guides by selecting for wave trace velocities. This quasi-superradiance -- thermal energy transformed to coherent “light” pulses, the transformation involving intermolecular electron transport (Foster, 1969 and Slifkin, 1971) and a process at the submolecular level analogous to the functioning of a screen grid in a radio beam power tube -- mediates a self-induced transparency (microtubules conduct coherent pulses like fibre-optic cable) necessary for the aggregate cytoskeleton to function as an “optical” computer (Hammeroff, 1987 and Hammeroff, Rasmussen, and Mansson, 1988 and Penrose, 1994). The cellular automata engaged in mutual “switching” to induce self-organized activity patterns perform pure multivalued wave-effect processing: no binary switches are involved. These factors underlie collective behaviors of neuronal, perineural, and somatic cell aggregates -- as well as the deterministic genetic adaptation of bacterial cell colonies (Lipkin, 1995). Why is this quantum level explanation required? Because thermodynamically-driven stereochemical lock-and-key-device processes do not, and, in principle, cannot, explain functional integration. What evidence do we have of this? The whole realm of degenerative disease is not understood, which means that growth-and-repair processes in organic systems are not adequately understood. Moreover, genetic variability of disease vectors is not merely a matter of misuse of antibiotics and random mutations; highly self-organized quantum exchange processes are at the root of it, implicating electromagnetic pollution (Becker, 1974 and 1990), an ozone-depletion-driven changing UV environment, and response of flora and fauna to the radiational impacts of recombinant DNA technologies.

Homeopathic Mechanism of Action
The homeopathic substance acts on the m-logically-valued reference space, not the single-valued frequency correlates of stereochemical information. The MVRS -- sometimes referred to as “Chi” (Hammeroff, 1974) and often misconstrued as energy -- has properties similar to a holographic plate with a superposition of standing wave patterns registered upon it. This is recorded in the structured water aspect of cellular cytoplasm-cytoskeleton. The superconductant DNA-generated coherent waves project through, and structure, the cytoplasmic-cytoskeletal hologram in conveying integrative information (i.e., the multilevel codes contained in the nucleotide-pair sequences and their associated superposed quantum waveforms transmitted by a quadripolar-wave transpose as the frequency signifier for immunological self-identity and as the clock signals generated by the ensemble of p-electron parcels in the DNA free-electron gas environment) to the cell membrane -- thus rate-limiting, via a bias control and Bosè-Einstein condensation, the “active transport system” governing osmotic nutrient transfer across the membranic phase boundary. Shifted DNA frequency parameters must become chronic to cause modification of the MVRS. The dilute succussed homeopathic substance “imprints” its solvent (Becker, 1990) via the structured-water hydration shells of its molecules’ active atomic groups. Dilution plus succussion, by imprinting the solvent, converts the frequency information of the active substance into a form (₁T₂-logically-valued into _µT_m-logically-valued) that is readable by the Lukasiewiczian time-logic operators over the MVRS. Both “imprinting the solvent” and the “cytoplasmic-cytoskeletal hologram” partake of the reduced Brownian motion which structured water is an expression of. Hand-held succussion is known to be much more effective than machine succussion. Succussion progressively structures the water of the solvent via oscillatory processes of attraction and repulsion at very short distances (Israelachvili and McGuiggan, 1988 and Becker, 1990; for discussion of the role of structured water relative to inter-molecular charge transfer processes see Szent-Györgyi, 1957, 1960, and much more comprehensively in Gilbert N. Ling, n.d.) in the bioelectromagnetic environment established by the hand-holder. Repeated dilution potentizes by imprinting the evermore structured (with repeated succussion) hydration shells of the active atomic groups. Imprinting is patterned reduction of Brownian motion. The less there is to pattern, the more easily is the pattern imposed, i.e., imprinted. Hence, the necessity of dilution for potentizing. Experimental studies of this can be done by machine potentizing various substances with varied environmental electromagnetic field parameters. What is being patterned is the free-electron clouds of the hydration shells. The pattern imposed is as much a temporal ordering, as a spatial one, i.e., not only constraining Brownian motion into minimized and regular spatial movement patterns, but also imposing regular time patterns on fluctuations. It is in passing the Avogadro limit that _µT_m-logically-valued Bohmian “active information” as complex angular momentum is deposited upon the MVRS by temporal curl as Lukasiewiczian logical-operator.

Symptom-Complexes
The symptom-complex tied to a given homeopathic substance gives expression to a loss of frequency information on the m-logically-valued reference space -- which information the active homeopathic substance returns to the MVRS. Homeopathic symptom-complexes are asymptomatic as far as allopathic medicine is concerned. Allopathic symptoms occur with tissue pathology. The homeopathic symptom-complex occurs before tissue pathology exists -- as a result of frequency shifts out of normative range becoming more and more chronic.

Autogenic Discharges
Autogenic Therapy's (Luthe and Schultz, 1969-73, and Pensinger and Paine, 1977-78) medical model is required to fully understand the onset of homeopathic symptom-complexes. Chronic frequency-regime shifts manifest as homeopathic symptom-complexes in large measure as a result of patterned suppression of sub-clinical autogenic discharges characteristic of a given TYPE (physical type, temperamental type, psychological type, homeopathic substance type: “guna” in the Sanskrit). TYPE has to do not only with stereochemical genetic inheritance, but also with inherited wave properties of the quantum structure of the genome, miasmatic (i.e., inherited DNA frequency anomalies or diatheses) components, and persistent quantum states of neuronal cell aggregates manifest via long-range phase correlation and the consequent cellular “automata” self-organization. The quantum mechanics of spontaneous neuronal discharge (and its interaction with the MVRS) mediates the two-way psycho-somatic transposition. That is why homeopathic materia medica reads like accounts of psychological-temperamental types, rather than allopathic signs and symptoms.

Homeopathic Effect in Ozone Therapy
and the M-Logically-Valued Reference Space
The wide-ranging biological effects of therapeutic ozone, particularly those associated with a homeopathic-like healing crisis, are on the same order of magnitude as those associated with autogenic brain discharges, suggesting that ozone’s mechanisms of action must include direct engagement with those factors responsible for functional integration (Pensinger and Paine, 1980 and Pensinger, Oliphant, and Paine, 1981). Electron acceptors (like ozone) and electron donors (like glutathione, vitamins A, C, and E), be they oxidizing or anti-oxidizing, participate in intermolecular electron transport, if the subsystem-system-supersystem composite is so organized as to be in Szent-Györgyi’s “beta state” (Szent-Györgyi, 1957, 1968, 1972). Intermolecular electron transport is instrumental in establishing the physical substrate of the MVRS via quasi-superradiance: much of Szent-Györgyi’s laboratory experimentation in relation to intermolecular electron transport involved study of processes underlying bioluminescence (Szent-Györgyi, 1960). One mechanism of action of the triatomic molecule, ozone, may be via enhancement of a compromised quasi-superradiance, and thereby a restoration of the information carrying capacity of the MVRS. Three levels of temporal ordering characterize processes associated with the reference space; a carrier function, a function mapping intrasystemic information exchange, a function mapping intersystemic flows (Paine and Pensinger, 1979). Processes in the Earth’s atmosphere involving ozone metabolism can be described in these same general terms (Paine and Pensinger, 1977). This correspondence suggests the notion that processes occurring in the biological organism involving the MVRS have analogues in equivalent processes performing similar functions in the Earth’s atmosphere -- and that the underlying logic of this equivalency is central to explaining the full range of ozone’s therapeutic effects on the biological organism. General principles of self-organization apply to multi-scale processes wherever they might be found.

Ozone a Fourier-Transform Operator
What is not explained is how ozone oxidizes pathogens and antibodies non-specifically, but does not disrupt those structures required for normal function. This is a recognition issue: the essence of immune system function, most basically rooted in the quantum frequency properties of the MVRS. The atmospheric analogue of these processes involves wave-trace-velocity recognition in (coherent) accoustically-modified gravity-wave organization of ozone metabolism and transport across the tropopause boundary. Molecular biology would say equivalent wide-ranging recognition is impossible in organic systems because the multitude of lock-and-key recognition devices required would be too enormously complex. Lock-and-key recognition is specific recognition, not only in fit, but in location: binding sites. How do you get classes of non-specificity out of this specificity? But m-valued wave-functions simplify the identity tag business very greatly. Systemic integration has to do with the general properties of systems, which are non-specific and can be represented by invariants of permissible transformations (transformation is the geometrical way of saying algebraic function). The nest of non-specific invariants prerequisite to systemic integration in a given class of organic systems can be physically embodied as a class of superposed frequencies. By decomposition, the frequency-tagged structures participating in the given class can be identified. Therefore, again by decomposition, those frequency-tagged structures not participating in the given class can also be identified. Ozone may be a Fourier-transform operator on a frequency space, an operator with a composite wave-function embodying invariants prerequisite to systemic integration in a wide class of organic (and inorganic) systems. Were this the case, then ozone would target for oxidation any frequency-tagged structure which is not a decomposition element of its own wave-function. How would this frequency recognition relate to the process of oxidation? The stereochemical “fit” of a given lock-and-key device (largely a matter of the geometry of bond angles) is only the first “step” in a chemical transformation involving the interacting atomic groups. This transformation is geometrical in nature, as much as electromagnetic. But function is an algebraic way of saying geometrical transformation! So the total given transformation (not just the lock-and-key device) may have a wave-functional analogue physically embodied as a frequency tag. And likewise for the total transformational prerequisites of systemic integration in a given class of systems. The invariants of the frequency space itself define the regime by which specific stereochemical processes are integrated spatially and temporally! Clearly, ozone directly interacts with this frequency aspect of the organism and thereby distinguishes between cytoskeleton-possessing eukaryotic cells and non-cytoskeleton-possessing prokaryotic cells to oxidize only prokaryotes (bacteria, blue-green algae, and viruses).

Frequency Tags (Mantra) and Numbered Gödel Numbers
(Tanmatra) over Lukasiewicz Order-Types (Prana)
According to the Paine-Pensinger model of superconductant DNA, each histological type of DNA (collagen cell DNA, muscle cell DNA, et cetera) has a unique frequency response window to ambient radiation beat down to it through a frequency cone (rather in the manner of a superheterodyne radio receiver, particularly were it equipped to receive pulse codes). This “window” -- and its superposed (Samaropa-adhyaropa, sgro 'dogs) m-valued “overtone series” -- is part of the immunological tag for self-recognition. The impinging radiation is beat down so as to be receivable by the p-electron parcels (temperature oscillations of which function as biological clocks, i.e., intracellular Zeitgeber, responsive to environmental signals) composing the free-electron gas core of the molecule, about which the sugar-phosphate backbones helix-coil transit during replication of nucleotide sequences and their radiating coherent quadripolar-wave analogs. The DNA free-electron gas core is the functional equivalent of the “tank” of the superheterodyne radio receiver. Even after beat reception (production of a series of beats below that of the transmitted signal) by the radio receiver, it must rectify and amplify the current to make it audible. The functional equivalent of this rectification and amplification by superconductant DNA is transduction of the Bohmian “active information” content of the radiation between Lukasiewicz order-types (Prana). “Prana” is translated by Sir John Woodroffe in The World as Power as “radix of a particular stress system over the ground state”, i.e., the informational ground (Alaya-adhikarana, gzhi gnas), or quantal base (Adhara, gzhi) state. A “particular stress system” refers to the notion of a physical field, and the implication considered here is that different fields correspond to different logical-value order-types with distinct associated numbering systems (which relates to basic ideas in superstring theory and M-theory). “Radix” is Latin for “root”. Alexander Karpenko has recently demonstrated that m-valued Lukasiewicz logics and their order-types correspond, by functionals, to “rooted trees” over the primes, which are factors of Gödel numbers. So, one considers that the Schrödinger-Samaropa (superposition) of frequencies -- ELF, VF, VLF, LF, MF, HF, VHF, UHF, SHF, EHF -- constituting the “frequency domain” of the organism by wave-interaction nodes, standing-wave fronts, sources and sinks, et cetera exhibits liquid-crystal-like structure. As regards cellular function, this likely transpires over coacervate phase, the structured intracellular water considered in detail most expertly by Gilbert N. Ling with his “polarized multilayer theory of cell water” (which has many features similar to Andrei Sakharov's “multi-sheet model of the universe” composed of collapse/anti-collapse sheets of Novikov dust; a self-similarity-type comparison not at all incidental if superconductant DNA radiates acoustically-modified gravity-wave modes through Ling's colloidal Schwellungswasser [suggested not only by our model, but also by the work of Freeman Cope (1971) on biological superconductivity and Herbert Fröhlich on long-range coherence (1968) and Bosè condensation (1975)], for, in that case, the n-dimensional lattices of the Regge calculus would be applicable to Ling's multilayer theory). The frequency domain may be treated as a closest-packing, super-dense, transfinite point-set topology-manifold, with the points or nodes connected by superstrings. Compacted, points of the topology-manifold are _CT_C-logically-valued; decomposed into a “layered transparent” Riemann-surface map, the points are _µT_m-logically-valued. The MVRS is equivalent to the compacted topology-manifold. Decomposing (as Samantabhadra) and recomposing (Adhyaropita-samaropa, sgro 'dogs to Alaya, kun gzhi) by operator-time (Trikaladrsti-tapassiddhi: T¹, T², T³) the MVRS involves un-numbering (frequency un-tagging by spontaneous localization) and numbering (frequency tagging by spontaneous fusion). A numbered Gödel number (gal mdo) spanning the superstring distance (Regge “bone”) between Lal Ded “dots” (Bindu, gtan tshigs) is “an uninterrupted continuum of the word” (_CT_C-logically-valued Lukasiewicz proposition). Bindu = metaphysical point (“without localized position” in Woodroffe's words; a Laya center being a point-center-of-action, Kriya). Lesser-logically-valued order-types over decomposed sheets of the compacted topology-manifold have lattices, points, and connecting lines differentially named in Sanskrit and Tibetan. Paramanu = class of minima (i.e., physical-region singularities). Tanmatra = arrangement (logical lattice) of Paramanu. Mudra = posture and gesture of Tanmatra (at discharge: “a scalar becomes a vector” in Woodroffe's words). Guna = leg of Tanmatra logical lattice (“translated as 'quality', but also means 'strand' or 'thread'” in Woodroffe's words, i.e., superstring or Regge “bone”).

Severe-Storm Genesis: Earth's Homeotherapeutic Strategy
Severe storms in general, tornadoes in particular, generate acoustically-modified gravity-wave modes capable of poking holes in the tropopause boundary and thus allowing drawdown of stratospheric ozone into the troposphere. The best hope the biosphere has to avoid an abrupt climate-shift of major proportions due to anthropogenic greenhouse warming is adequate healing crisis by severe-storm genesis to: [1] pump into the troposphere quantities of ozone adequate to neutralize the human carbon footprint and excess greenhouse gases with their modification of the frequency-response characteristics of the global atmosphere; [2] generate enough homeotherapeutic superconductant plasma to return to the Earth's MVRS the m-logically-valued information destroyed by the various forms of pollution (including microwave pollution) the planet has been subjected to; [3] provide a sufficient number of penetrations by geomantic-geospatial analogues of an acupuncture needle to inject the m-logically-valued homeotherapeutic information conveyed by the superconductant plasma.

Atmospheric Self-Medication and M-Logically-Valued Monetary Units
An intelligent humanity would seek to deeply comprehend the quantum substrate of planetary autopoiesis, self-organization, and self-repair. It would then analogically embody the involved principles in its social, political, and economic interfaces with natural processes, and by so doing attempt to positively reinforce the planet's self-homeotherapeutics. One strategic move in this direction would involve implementation of m-logically-valued monetary units so as to internalize market externalities in the fashion required to encourage by incentive and sanction the full spectrum of collective human behaviors currently prescribed by the planet.

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