Following is a letter to Dr. Gilbert N. Ling ( www.gilbertling.org/ ) of the Damadian Foundation for Basic and Cancer Research, which, in due course, discusses the Riemann surface model in relation to integration of cellular functions.

Dear Professor Ling:

Reading discussions of your polarized multilayer cell water hypothesis, particularly concerning translational and rotational restriction of motion of intracellular water molecules, I could not escape the thought that the coherent (i.e., acoustically-modified) pressure waves we hypothesize are generated by superconductant DNA, and which would propagate through the cytoplasm, would modulate primarily the time-patterning of the spatial movements of polarized multilayer intracellular water molecules (i.e., the rhythms by which the “geese” change location in their “translation structure” : the flying geese not only shift location in formation, unlike particles of an elastic medium, but their translation structure undulates a waveform, which is riding on a long-wave guide of atmospheric infrasound the geese use as a navigational aid). The dynamic properties of the coherent waves hypothesized to be generated by DNA exhibit three levels of temporal ordering related to intrasystemic, intersystemic, and non-orientable information processes. As I understand it, NMR spectroscopy is primarily focused on the rotational component of motion and reads, through relaxation time, the instantaneous spin moment. Time patterning (velocity, acceleration, and time rate of change of acceleration) of spin-up and spin-down of the proton “top” would carry the three types of information mentioned above, the coherent waves imparting angular momentum quanta to the water molecules. It is our thesis that these three orders of temporal information are intimately involved in integration of cell functions and immune self-recognition. One would think that first, second, and third-order derivatives of NMR absorption spectra sequences could provide a window on these temporal-information processes in polarized multilayer cell water.

Your discussions of the temperature rise and energy gain involved in the autocooperative transition to a coacervate phase suggest that the coherent waves hypothesized to be generated by DNA, which would propagate through the intracellular water, could provide a component of the energy-temperature signal required to initiate Bose-Einstein condensation underlying the autocooperative phase transition. We believe the coherent waves generated by DNA would fall within the microwave spectrum. According to our notion, the critical piece of temporal-order information relative to Bose-Einstein condensation is the third-order temporal derivative involved in non-orientable information processes. One way to isolate components of the energy-temperature signal would involve performing the experiments on extrovert models at different temperatures within a Faraday cage, and later within a Faraday cage with ambient fields of differing properties, and comparing the results.

At mention of your reluctant use of the terms “cell” and “membrane”, I had to laugh because, in consideration of the non-orientability and identity transparency associated with third-order temporal patterning in autocooperative phenomena, I adopted the term “autopoy” (from “autopoiesis” ) for the basic unit of a self-organizing process. As fractal entrapment may be involved in selective permeability of the “Plasmahaut” (a term for “membrane” I find very congenial), I have regarded it as the skin of a fractal drum, i.e., the autopoy’s tympanum, which is beat by DNA-generated coherent waves (the tympanum being the “moon” of Hoa Binh, hoa binh meaning “peace” in Vietnamese). A fractal boundary is a borderless border: the closer you look at it, the more it is not there, the more it becomes “Cantor dust”, holes nested inside of holes. It is a border that is a correlation, rather than a mere severance. When such a boundary is configured according to variations of an m-valued function, that boundary is imbued with attributes of the area bounded. (This is one reason for not interpreting Schrödinger’s wave equation in terms of probability amplitudes, but in terms of
m-valued Postian logics.) Koch curves based on fractal dimensions have this property of assuming the attributes of the area bounded. Such curves are scale-level nests within scale-level nests, one-dimensional “sheets” within one-dimensional “sheets”. A Koch curve is a one-dimensional Riemann surface: the m-valued Abelian functions behind the multi-sheeted Riemann surface are also behind the Koch curve with its fractal properties. Cantor dust is sheet after sheet of nested hole patterns, which patterns model -- in the geometry of the superposed numerical grids forming the selectivity network of fractal entrapment -- the attributes of the area bounded by the curve. The differentially permeable vibrating tympanum-Plasmahaut should be a functional map of the polarized multilayer cell water it enfolds. At the end of the article entitled “VirFut Q-Pro” (http://members.brandx.net/user/autopoy/sgpapers/virfut.html) displayed in the Saigon Papers on our website, there is a discussion of exchange processes at borderless borders in Bronze Age Southeast Asia and China relative to the tradition of placing bronze drums under waterfalls.

While reading your discussions of the correspondence between bulk-phase and cell-surface protoplasm, it seemed to me that this correspondence may be central to treatment of three-dimensional autocooperative transition to coacervation phase. The two-dimensional NP-NP system array on cell surface may be an algebraic-function map of the (NP-NP-NP)n three- dimensional multilayer bulk phase in the following manner:

My suggestion is that the first, second, and third-order derivatives of changing NMR absorption spectra sequence patterns on NP-NP checkerboard cell surface (as time-differentiated sequences of instantaneous spin moment maps) correspond to sequences of point-set topologies (covering surfaces) representing the functions of enzymes subject to differential permeability of the Plasmahaut, and that these fractally-nested sequences, when projectively superposed as composites, collectively correspond to the first, second, and third-order changing NMR absorption patterns of the
(NP-NP-NP)n three-dimensional multilayer bulk phase, which, in turn, correspond to point-set topologies (universal covering surfaces), which, when projectively superposed as composites, represent, as a multi-sheeted algebraic Riemann-surface map, the multiply-connected m-valued functions of enzymes in the autopoietic ecosystem which the cell constitutes.

But function is an algebraic way of saying geometric transformation! So the molecular conformational transformations associated with the metabolic activities of enzymes subject to differential permeability of Plasmahaut would be implicit in changing NMR patterns of the (NP-NP-NP)n three-dimensional multilayer bulk phase which are superposed composite of the NMR absorption patterns on NP-NP checkerboard cell surface.

The DNA-generated coherent waves, carrying by phase-angle encoding all the information in the nucleotide pairs and propagating through the bulk-phase protoplasm to beat upon the Plasmahaut drum tympanum, would impart angular momentum quanta to the spinning proton “tops” according to the changing nucleotide pair sequences. In this way, the transformational pre-requisites and temporal-order requirements of systemic integration would be represented in a superposed wave-functional analogue and communicated to the discrete entities disposed to carry them out. In this context, the Schrödinger wave-function would not be interpreted relative to probability amplitudes, but in terms of Postian m-valued logics.

Recognition issues are simplified in this context. Systemic functional integration has to do with the general properties of systems, which are non-specific (disturbances of which initiate the non-specific stress reaction) and can be represented by invariants of permissible transformations. Functional specificity and immunological memory require simple-identity and simple-location: the binding site and lock-and-key-fit recognition. But how do you get classes of non-specificity out of this specificity? The non-specific invariants pre-requisite to systemic integration in given classes of organic subsystems, systems, and supersystems can be physically embodied as a class of superposed frequencies. By Fourier-transform decomposition, the frequency-tagged structures participating in the given class can be identified. An enzyme, for instance, would not recognize a frequency-tagged binding site which is not a decomposition element of its own wave-function. Given that function is an algebraic way of saying geometric transformation, the total stereochemical conformational transformation associated with a given lock-and-key device may have a wave-functional analogue physically embodied as a frequency regime signature. And likewise for the total transformational pre-requisites of systemic integration in given classes of organic subsystems, systems, and supersystems. The invariants of the frequency space itself define the regime by which specific stereochemical processes are integrated spatially and temporally. The DNA-generated coherent waves, carrying by phase-angle encoding all the information in the nucleotide pairs and propagating through the bulk-phase protoplasm to beat upon the Plasmahaut drum tympanum, thus imparting angular momentum quanta to the spinning proton “tops” of the NP-NP checkerboard cell surface and (NP-NP-NP)n three-dimensional multilayer bulk phase according to the changing nucleotide pair sequences, would be imposing -- click, click, click -- a discrete sequence of frequency-tag sheets (corresponding to stereochemical conformational transformations) constituting the actual differential permeability “filters”.

In THE MOON OF HOA BINH, we applied the general ideas behind those given above to the functions of roles in strategic contingency theory of organizational adaptation through resource exchange across boundaries, which involves altered sub-unit relations. (I began developing these thoughts in studying the animistic [i.e., identity transparent and cooperative] properties informing dynamic transformations of the cellular underground Viet Cong [political] Infrastructure [bureaucracy] in response to a changing battlefield environment.) Subsequently, in "M-Valuation in a Generalized Currency Basket" displayed in the Saigon Papers on our website (http://members.brandx.net/user/autopoy/sgpapers/m-valuation.html), elaborations of these ideas were applied to m-valued monetary exchange units defined on fractal boundaries, instead of the simply-closed national borders single-valued monetary units are presently defined on. From the beginning of my engagement with these general ideas, back in the mid-Sixties, I have ruminated on properties of a holographic medium, called Musculpt (music-sculpture), which would be capable of displaying a synaesthetic (e.g., colored-hearing) analog of the processes being contemplated.

The Riemann surface is an algebraic (not geometric) entity, which maps the march of an m-valued function, the array of its branch points, and the connectivity of its
m-branches. This multi-sheeted surface is the appropriate algebraic understanding of Schrödinger’s wave-function, just as Emil Post’s m-valued truth systems are the appropriate logics of that wave-function, and J. G. Bennett’s “skew-parallel geometries” which describe “diversely identical skew-cubes” are the basis of the appropriate geometry, and non-self-identical numbers (which eventually will emerge from the set of zeros and transfinites) will enumerate the appropriate fiber bundle arithmetics. Probability amplitudes are simply a way of escaping the consequences of Schrödinger’s discovery. It appears to me that your c-value, c'-value, and their charge density analogues, are m-valued functions in just the sense intended in the above discussion, and that they and other such functions would be appropriately contextualized relative to Riemann surface mappings. But this is not simply a mere representational scheme. Though the Riemann surface is algebraic, the Riemann manifold is, of course, geometric, and an expression of the fact that Riemann was first and foremost a geometer. He may actually not have realized how relevant his algebraic surface was to the “enfolded” and “implicate” (to use David Bohm’s terms) order of his geometric manifold. A. D. Sakharov’s multi-sheet model of the universe, an outgrowth of his theories of the metric elasticity of space, sheds considerable light on this relevancy. The explicit connection with your c-values is Riemann’s famous statement that charge is “lines of force trapped in the topology of space”. Hidden in this notion is an “implicate order”-level explanation of why parallel protein chains yield maximal water polarization.

During your discussion of the fact that maximal water polarization occurs only when there is parallel orientation of the protein chains, and of the assistance provided by unidirectional stirring, I immediately thought that the coherent waves hypothesized to be generated by DNA, which would propagate through the intracellular water, could provide, not only a component of the energy-temperature signal, but also the functional equivalent of unidirectional stirring. Succussion in “potentization” of homeopathic substances involves pendulum-swing oscillations which similarly could impart the functional equivalent of unidirectional stirring in process of “ imprinting” the hydration shells of the substance undergoing dilution in water. Hand-held succussion is clinically known to be more effective than machine succussion, which suggests involvement of a field phenomenon, which, according to Riemann’s notion, would have its source in lines of force trapped in the topology of space, trapped in, as it were, Sakharov’s metric elasticity of space (the “protoplasm” of the universe, perhaps).

But I would like to enter the discussion about parallelism and skew-parallelism, not via bulk phase intracellular protoplasmic structured water, but via the normal water of the intercellular space. Your demonstrations of correspondence between Plasmahaut and bulk phase in significant measure dissolve the traditional notion of boundedness, leaving no longer a cell wall with various sorts of fingers plugging holes, but at best a mere phase boundary between structured water and normal water, two such watered-down phase boundaries and the intervening normal water being the only thing separating one cell from the next. In my experience, most people find the very idea of such identity transparency extremely frightening. Worse yet, Victor P. Starr has taken great strides in demonstrating that normal water simply does not exist. This was done initially in his extraordinary paper entitled “The Hydrodynamic Analogy to
E = mc2” (Tellus, 9:1, 1959) and later in his book, The Physics Of Negative Viscosity Phenomena (McGraw-Hill, 1968). He shows that Lorentz-Fitzgerald contraction relates to gravity wave modes within a fluid medium, meaning that each such fluid medium has its own unique limiting phase velocity subscribing to all the rules of Special Relativity. Elements of the fluid wave contract according to the Lorentz-Fitzgerald formula. Now, the DNA-generated coherent waves, which we hypothesize to propagate through the protoplasm and set the Plasmahaut to vibrating upon the water in the intercellular space, have a gravity wave mode component (designated b in the equations, and referred to in that 1979 paper on superconductant DNA as “the counterforce to the pressure gradient term”) which would subscribe to Starr’s formulations. Starr’s idea is of the utmost importance to Riemann’s idea concerning the origin of charge, which your c-value “distance functions” (i.e., fundamentals of metric geometry, and which likely are measures of the metric elasticity of the protoplasm of various histological types, in direct analogy to Sakharov’s multi-sheet model of the metric elasticity of space of the universe at large) parameterize. A comparison of the role of your c-values in characterizing protoplasmic elasticity (involved in conformational transformation) with the role of distance functions in Sakharov’s theory of elasticity may be edifying.

Starr’s formulations indicate that each and every limited spacetime domain has its own unique limiting phase velocity which subscribes to all the rules of Special Relativity. The speed of light, therefore, is m-valued (the recent speed of light experiment, apparently demonstrating that light travels faster than light, which has received so much publicity, has gone some distance in demonstrating this thesis). It could be said that each nested relativistic limited spacetime domain has its own “light”. Lorentz-Fitzgerald contraction is an indication that as time slows down as the speed of light is approached, the length of the moving entity shortens in the direction of movement. The metric geometry distance function (i.e., the “c-value” ) describing the march of this contraction characterizes the involved space. Space itself, a relative “somewhat”, loses a FRACTION of a dimension in the direction of movement as the limiting phase velocity of the given relativistic limited spacetime domain is approached. Thus, by implication of Starr’s formulation, the speed of light is m-valued (i.e., it needs contextualization on the Riemann surface) and this m-valuedness is related to fractal dimensions. In 1977, we wrote a paper entitled “Toward a General Theory of Process” which propounded on the implications of this. We believe that space undergoes topological transformations at limiting velocities, limiting accelerations, and limiting time rates of change of acceleration. Axes of rotation (which NMR spectroscopy measures) are tilted evermore into imaginary fractal dimensions as first, second, and third-order limiting values of dynamic variables are reached relative to the given relativistic limited spacetime domain.

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