Thanks for the copy of Roger Penrose's book The Large, the Small and the Human Mind (Cambridge U. Press, Canto edition, 2000). I read The Emperor's New Mind (1989) and Shadows of the Mind (1994) shortly after they came out, but this one, shorn of a lot of detail, is, indeed, as you say, particularly clear. As you point out, there are many similarities to the ideas contained in MOON -- but arrived at along different paths: for Penrose via quantum-gravity and those areas of higher mathematics having to do with issues of computability versus non-computability; in MOON via inner experience and studies of autogenic brain discharges, tornado genesis, quantum properties of DNA, pathogenesis of degenerative disease.
There is an account of what Penrose calls Objective Reduction (OR) of the quantum wave-function given in MOON, but like everything else in MOON, it is provided in the form of OR, not in syllogistic presentation. MOON contains many ideas, but few of them are described, which is part of what MOON has to say about OR and its undoing: syllogistic description is “after” OR is, and has nothing to do with its undoing. One might, at first pass, regard what MOON has to say on this subject as an account of SR (Subjective Reduction) rather than OR, but this would be mistaken; the reduction of state MOON ruminates upon takes place objectively in the neuronal and perineural tissues via quantum properties of superconductant DNA, likely including a coherent to decoherent acoustically-modified gravity-wave-mode transition, and the impacts of this transition upon intracellular structured water and phase boundaries like the cell membrane and cytoskeleton.
There is nothing to speak of which Penrose has to say in the three above mentioned books which MOON disagrees with, though there is much in MOON with which Penrose might disagree -- as MOON develops this line of thought further along. OR, in the perspective of MOON, is, in a certain aspect, the result of organic pathology induced by prescriptive enculturation. The multiple branches of the m-valued function described by Schrödinger wave equation, are, according to MOON, properly interpreted only with m-valued logics understood in relation to identity-transparency, not truth-value. The organic pathology removes capacity of the brain to mediate conscious awareness of m-logically-valued percepts and propriocepts. This organic brain pathology can be reversed such that m-logically-valued percepts and propriocepts become directly available to consciousness. This reversal of organic brain pathology does not, however, stop OR from transpiring in the brain, it removes a “buffer” that prevents conscious awareness of m-logically-valued wave-effect processing.
What is this “buffer”; what is “conscious awareness” in relation to this “buffer”; why would OR take place only in the brain? OR does not take place only in the brain, but the reduced conscious awareness associated with OR in the brain is mediated by organic processes which can become diseased in various ways. It would also be correct to say that reduced collective states associated with OR not transpiring in brains are mediated by natural processes which can become diseased in various ways. There are “healthy” and “diseased” states of all natural systems, not only those currently designated organisms or ecologies. It is necessary to understand why this is so in order to see what “conscious awareness” is in relation to the above mentioned “buffer”.
MOON says that it is not possible to understand reduction of the wave-function in a closed system, even in an open system; reduction of the wave function becomes understandable only in a self-reentrant system. Such a system has three LEVELS of temporal ordering, two of which are nonlinear. The canonical equation is, therefore, rewritten to describe three levels of temporal ordering of a system with components in spatial array. The “spontaneously fused” state of the system is its unstable “critical” state, which is self-reentrant; the “spontaneously localized” stable state of the system is its “ground state”, which is disaggregated. Growth and repair processes (which all systems, organic and inorganic exhibit) require continuous far-from-equilibrium transitions between these two states. Such transitions have two nonlinear levels of temporal ordering which are essential to coherent behaviors like superconductivity at temperatures far removed from absolute zero. Chronotopologically, time has an asymmetric linear aspect (cylinder), a symmetric aspect (torus), and a non-orientable aspect (Klein bottle) -- each of which, depending on the organic condition of the brain, may become directly available to conscious awareness.
The logical properties of a system spontaneously fused at criticality are expressive of its self-reentrant condition: self-reference is the hallmark of such a condition, and m-valued logics of identity-transparency are required to describe this hallmark. If Church's Hypothesis regarding calculability (“calculable if and only if recursive”) is taken as correct, then self-reentrant critical-state processes are non-calculable, as propositions of the m-valued logics of identity-transparent self-reference are non-recursive (by virtue of being self-referent). Propositions in such m-valued logics decompose and recompose (unfold and enfold, to use Bohm's analogy) by involution and devolution, not by recursive extension. Such processes will not compute recursively also because the m-valued logics of identity transparency invoke non-self-identical numbers: two is not two and only two, but also simultaneously other numbers as well (in superposed orders of imaginary time). Non-self-identical numbers are numbers in (multiply-connected, multi-sheeted: the nesting sheet being, from a single-valued logic perspective, time-like relative to the space-like nested sheet) number spaces where isotropy (value of a standard increment the same in all degrees of freedom), simple location, and simple identity are not manifest, where null vectors map parallels that are parallel yet simultaneously skew, number spaces, that is, where isotropy, simple location, and simple identity drop out only under algebraic groups of arithmetic operations, the operators engaging in such operations being autopoietic in nature, and, in the case of quantum mechanics, equivalent to OR.
A point in Hilbert-space (the multidimensional function space of quantum mechanics), though it has n-degrees of freedom, nonetheless is still logically single-valued. Hilbert-space was constructed with a single-valued logic and, therefore, entities mapped into this space, by definition, must conform to the truth-value-related rules of that logic: no A is not-A; the case is either A or not-A. These two rules, in particular, rule out non-simple identity and non-simple location. But Hilbert-space can be reconstructed again and again and again using different orders of the m-valued logics of identity-transparent self-reference, resulting in a MVRS (m-logically-valued reference space) mapped on a bridged (i.e., multiply-connected) multi-sheeted Riemann surface (universal covering surface). The MVRS, then, would be our number space for describing entities in spatial array, which are subject to three levels of temporal ordering. What are the “algebraic groups of arithmetic operations, the operators engaging in such operations being autopoietic in nature, and, in the case of quantum mechanics, equivalent to OR”? These “algebraic groups of arithmetic operations” are logical in nature, accomplish involutory-decomposition/devolutory-recomposition, and establish levels of temporal ordering. Call these groups “three-fold operator-time”.
These algebraic groups map numerical mappings in the MVRS. Such decomposition-recomposition operations are not recursively calculable because no finitely massive paralleling of finite sequential processes in a given order of logical value sum to a higher or lower order of logical value: propositions in different orders of logical-value are incommensurate because meaning is in large measure in the form of the proposition (which is not to say that content carries no meaning). Meaning being in the form does not mean an m-logically-valued proposition cannot be Gödel numbered. It can be so numbered, but such numbers will, in most cases, not be self-identical numbers. M-logically-valued propositions numbered with non-self-identical Gödel numbers would be logical lattices bridging Riemann-surface sheets in the MVRS. Riemann created his surface such that the march of an m-valued Abelian function could be uninterruptedly plotted through its multiple branches, but m-valued Abelian functions are logically single-valued, just as conventional n-dimensional Hilbert-space is logically single-valued. So the universal covering surface constituting the MVRS is not the universal covering surface constituted by a stack of Riemann surfaces; it is such a universal covering surface where every Riemannian point is an MVRS bridge point between any two sheets, and every Riemannian bridge point is an MVRS bridge point bridging some finite number of sheets, and every higher-order MVRS bridge point is an MVRS hyper-bridge point bridging some transfinite number of sheets (there being different orders of infinity). Non-self-identical Gödel numbers in logical lattices would be numbers at such bridge points. Gödel-numbered logical lattices of this sort would have form by virtue of the shape of the involved lattice.
What is the relation of such a logical lattice to a Regge lattice? The Regge calculus translates the spacetime curvature configuration of General Relativity to an n-dimensional lattice equivalent. The n-dimensional Regge lattice can be mapped into standard n-dimensional Hilbert-space, where one of the dimensions is regarded as time-like (viewed from a single-valued logic perspective). In the MVRS, however, with its m-valued logics, sheets are not regarded time-like or space-like: temporal ordering is associated with “algebraic groups of arithmetic operations”, called “three-fold operator-time”, which accomplish logical involutory decomposition and devolutory recomposition. A “transformation” is the geometrical equivalent of an algebraic group of arithmetic operations. First order operator-time is the expression of an algebraic group of arithmetic operations involving imaginary numbers (Hamilton's quaternions) initialized at approach to a limiting velocity and involving a geometrical transformation of space when that absolute limit is reached. Second order operator-time is the expression of an algebraic group of arithmetic operations involving hypercomplex numbers initialized at approach to a limiting acceleration and involving a geometrical transformation when that absolute limit is reached. Third order operator-time is the expression of an algebraic group of arithmetic operations involving higher-order hypercomplex numbers initialized at approach to a limiting time rate of change of acceleration and involving a geometrical transformation when that absolute limit is reached. These hypercomplex arithmetic operations involve Cayley's 8-tuples and require Grassmann algebras for their general description. Each order of operator-time is, therefore, a topological operator on the MVRS. A Regge lattice is a Gödel-numbered proposition stripped of its m-valued logical properties. Attach these logical properties to the Regge lattice, find its equivalent curvature configuration, and one would have the (sculpted-polytope Platonic) form of the Gödel-numbered proposition.
Now, consider the proposition that consciousness in its active aspect is the set of all topological operators on the MVRS, and consciousness in its passive aspect is the MVRS acted upon. This consciousness is, obviously, not “conscious awareness” as currently understood by science. First of all, this notion of consciousness is global; universal; self-referential, and, therefore, m-logically-valued. Secondly, the only topological operators on the MVRS are logical operators called “operator-time”. Time is not a faculty of mind derivative of, for instance, remembrance; mind is a faculty of time. Objective or subjective is an either/or distinction applicable only under single-valued logic, whereas consciousness embraces m-orders of logical-value. This global idea of consciousness is more like Indic notions of consciousness or C.G. Jung's idea of the collective unconscious. The “conscious awareness” of science, according to this notion, would be a reduced system-state achieved under the involutory decomposition accomplished by three-fold operator-time. In other words, conscious awareness would be due to OR of the global, universal system-state, just as Roger Penrose hypothesizes.
Ilya Prigogine begins his book The End of Certainty: Time, Chaos, and the New Laws of Nature (Free Press, 1997) by quoting Karl Popper (p. 1):
Earlier this century in The Open Universe: An Argument for Indeterminism, Karl Popper wrote, “Common sense inclines, on the one hand, to assert that every event is caused by some preceding events, so that every event can be explained or predicted… On the other hand,… common sense attributes to mature and sane human persons… the ability to choose freely between alternative possibilities of acting.” This “dilemma of determinism,” as William James called it, is closely related to the meaning of time.
These two sentences begin Prigogine's discourse wherein he explains how the arrow of time has been resurrected from time-symmetric Newtonian physics and how quantum theory is to be reformulated so as to accommodate this resurrection and banishment of symmetric time. One might first observe that no one who has engaged in systematic introspection -- prolonged concentration in self-observation, through which one becomes engaged by direct experience of the self-referential properties of cognition with m-valued logics -- could so easily as Popper suggest that human beings, sane or otherwise, have “the ability to choose freely between alternative possibilities of acting.” One would even be inclined to suggest that inadequately-introspective Popper had not adequately informed himself concerning the effects of operant conditioning, let alone concerning effects of collective unconscious archetypal gradients upon individual behaviors. And since Prigogine chooses the above quote from Popper as the first sentence of his book about resurrecting the arrow of time, one cannot help but entertain the notion that Prigogine's lifelong project to resurrect time asymmetry has a political agenda attached to it not dissimilar from the political agenda espoused by Karl Popper. That political agendas have had something to do with interpretation of the meaning of quantum mechanics is a central theme of MOON, which further argues that political leverage on such interpretation played a major role in causing World War Two and details of its unfolding events.
That absence of understanding of the salient aspects of the MVRS and the mechanisms of OR therewithin continues to have profound influence on human behaviors is illustrated by observations about the war in Bosnia made in Samantha Power's book A Problem from Hell (Basic Books, 2002). Speaking of systematic Serb killing of Muslim and Croat civilians, she states (p. 289) that “The talk of 'ancient hatreds' implied a degree of inevitability and spontaneity belied by the carefully coordinated, top-down nature of the killing…” Power later quotes U.S. Department of State official Jon Western as saying (p. 290): “Milosevic was never going to call up his henchmen and say, 'Go commit genocide.' We had to develop the case by showing the systematic nature of the campaign. Only by working backwards could we show intent.” Assuming accuracy of the content of these statements, one might still observe that, just like statements of Popper and Prigogine, both of these statements exhibit no insight into collective unconscious processes, mistakenly attribute free will to the ego function in face of archetypal gradients, and, furthermore, mistakenly attribute lack of self-organizational competency to those very same archetypal processes. The belief that punishing individuals will deter genocide, informed as it is by this lack of insight into collective unconscious processes, is, therefore, unwarranted. The fundamental causes have to be removed if genocide is actually to be deterred.
Within the framework of the MVRS, what is an archetypal gradient? It is a set of Gödel-numbered Regge lattices, with their m-logically-valued properties intact, undergoing OR via the algebraic groups of arithmetic operations designated three-fold operator-time. Only once OR has been completed within the neuronal and perineural tissues of human brain does “conscious awareness” transpire. Given that the involutory march of decomposition determines the properties of a particular OR in human brain, choice in conscious awareness as OR cannot be determined by conscious awareness, but must be determined by the nature of that involutory march. Ability to make free choice is not an attribute of the ego function, but of the larger global consciousness which decomposes an ego function.
This is certainly the case in processes associated with creative thought, with those of instinctive impulse, and with those of the collective impulses driving self-organized group behaviors, be those collective impulses associated with the role attributions of leader or follower. The more primeval, the higher the order of temporal operation involved in origins. “Ancient hatreds” and the like probably involve second order operator time. Operational thought, pedestrian “conscious awareness”, roof-brain chatter probably involve only the linear operator, i.e., first order operator-time. When conscious awareness is limited to only those ORs associated with the linear operator, this is due to the presence of a “buffer”. This “buffer” is a functional lacuna in neuronal and perineural tissue preventing registration of processes associated with the nonlinear operators. This functional lacuna is absence of semiconductant to superconductant transitions in nuclear neuronal and perineural DNA.
Lacuna-on-the-brain is a pathological state. Presence of this “buffer” is due to intergenerational transmission (enculturation) of what in Autogenic Training is called “neutralization antagonizing forms of resistance”, some two dozen categories of habituated cognitive behaviors which prevent the brain from transiting deeply enough into the trophotropic state to allow spontaneous brain discharges to electrochemically unload records of chronic stress stored by the CNS as shifts out of their normative ranges in the parametric values of the quantum wave properties of DNA. We now, of course, have the quantum consequences of recombinant DNA technology to worry about relative to pathogenesis of lacuna-on-the-brain. If, through some type of effective long-term practice of dehabituation, a person is able to rid him or herself of neutralization antagonizing forms of resistance, brain discharge processes will spontaneously remove the buffer and restore semiconductant to superconductant transitions in nuclear neuronal and perineural DNA, thus allowing direct awareness of the m-logically-valued processes decomposed and recomposed by the nonlinear orders of operator-time in the logical march associated with spontaneous localization and fusion. Or such is the scheme of things as presented in MOON.
No. I am not arguing against intervening to stop genocide. Samantha Power's book (A Problem from Hell, Basic Books, 2002) is extremely important and very informative -- with the caveat that few words are devoted, for instance, to the question of why Yugoslavia disintegrated and no words are employed to explain why ethnically-rooted separatism, justified with the term “nationalism”, is more legitimate in the former Yugoslavia than would be ethnically-rooted separatist nationalism in, say, the American Southwest. Since the Jewish population of the Rhineland was not attempting to secede from Germany in the 1930s, the holocaust simile to Balkan behavior is far less then perfect. The central reservation I have about the book, however, is Power's tacit assumption that the Western powers have merely been negligent, that they have no deep psychological need to aid and abet, to ignore if not condone, genocide, that they are not the fundamental “causers” sitting behind their front men, the perpetrators. I also protest the implicit notion that killing “noncombatants” is somehow not the primary objective of modern warfare, as it is hard to find any war in the modern era where more soldiers have been killed than civilians, overwhelmingly so the more proximal the case is to the present day. Is this to be regarded a mere accident? The idea that it is no accident is, of course, derided as a dastardly conspiracy theory. Well, wash my mouth out with soap! There is no way YOU, or more accurately, your psychological state, could possibly be causal, if not responsible. For all such true believers in the beneficence of a constitutional democracy rooted in Newtonian assumptions, I recommend the words of art critic Octave Mirbeau (The Torture Garden, San Francisco: RE/SEARCH Publications, 1989 reprint of the 1931 translation of the 1899 edition):
Really -- I honestly believe that murder is the greatest human preoccupation, and that all our acts stem from it… murder is the very bed-rock of our social institutions, and consequently the most imperious necessity of civilized life. If it no longer existed, there would be no governments of any kind, by virtue of the admirable fact that crime in general and murder in particular are not only their excuse, but their only reason for being… The joy of killing has become greater and, besides, has become popularized in proportion to the spread of social refinement… Murder is born of love, and love attains the greatest intensity in murder. There is the same physiological exaltation, there are the same gestures of strangling and biting -- and often the same words occur during identical spasms.
There is no evidence that the decades of moral dandruff over genocide have effectuated the slightest deterrence of genocide. Why is that? Because those shedding the dandruff have absolutely no understanding of what causes the thing they present themselves as trying to prevent.
I am arguing that the touted solution to genocide is part and parcel of the cause of the very abomination being decried. I cheered upon learning that Vietnam intervened into Cambodia. This was not a naive cheer, though, as I knew that, when the collective human unconscious has developed a need for genocide, stopping it one place will only make it appear at another; if one path to fulfillment of the need is blocked, another will be found. Whatever were Vietnamese motivations, the Vietnamese intervened while everyone else stood by in voyeuristic fascination. I think this voyeurism is not incidental passive voyeurism, that it is actively engaged and pre-mediated, however subliminally, not merely negligent mass homicide, not simply a case of accomplice-via-inactive-nonintervention-of-the-witness. To deride subliminal willfulness as mere “unconscious conspiracy” is to invert the actual roles of individual and collective, personal and impersonal, in determination of the dissociative mass psychotic break -- collective hysteria in the technical sense.
The solution touted is: war crimes trials of selected autocratic individuals deemed responsible for premeditated centrally-orchestrated reprehensible criminal acts against humanity, with intent to destroy an identifiable ethnicity undertaken on basis of the personal free will of the responsible autocratic individuals. As Nobel laureate Ilya Prigogine assures us (see: The End of Certainty: Time, Chaos, and the New Laws of Nature, Free Press, 1997), free will exists in the world because asymmetric linear-time evolution of events is subject to chance, to probability, to the fact that the future is not a series of determined events, but a series of possibilities. Were this not the case, everything would be determined, time could also run backwards, genocide could be undone, those killed restored to life, and those responsible could not have been responsible because free will would be impossible and, hence, no such thing as responsibility would exist in the world (it would reside in the uncaused First Cause of that world).
But, actually, the case for responsibility on basis of a free will rooted in chance is not a good one, as a causal connecting principle, not probabilities, has, until recently, been necessary to an unambiguous, beyond-the-shadow-of-a-doubt-type, demonstration of legal culpability. Legally speaking, due-process-wise, synoptic global causality is not required; what is juridically important is proximal cause. This is why “deterministic chaos” has become of such great importance, of such abiding psychological necessity to the contemporary world: chaos can have a deterministic origin and, hence, responsibility for genocidal chaos can be fixed on a discrete initial condition, be that initial condition an Amazonian wing-flapping butterfly or a malevolent autocratic personality. The global Newtonian (social, political, and economic) institutionalization can thus be saved in face of the challenges presented to it by the hundred-year-old “new physics”.
Genocide is collective punishment. Collective punishment -- killing the whole family, the whole clan, the whole tribe, the whole ethnic group -- traditionally, was not a strategy of retribution, i.e., kill the loved ones or compatriots of the transgressors/perpetrators so as to make the lesson especially clear, no matter how much the contemporary 18th century sensibility would like that to be so, but an expression of a tacit assumption about the nature of reality, that assumption being animistic “identity transparency”: the killers kill the corporate person, and then collect signifiers (mutilation behaviors) of having psychologically “eaten” (introjected) the identity of that corporate person. The group slain is not a collection of individuals but a person in its own right.
Genocide in the modern era is a regressive (psychologically cannibalistic) throwback, an infantile form of identity transparency which has arisen due to repression of all mature forms of identity transparency in this age of population or ensemble physics, in this age of economic corporate persons. We collect tribal art and artifacts as signifiers of that which has been “eaten”, of that which has been slain, vanquished: animistic identity transparency. The act of pulling together a collection of ears, say, or a tribal art collection, is an unconscious act of psychological introjection (by a “wanttabe”) which is compensatory to the collective cultural fact of projective identification leading to the original act of slaying the alien corporate person. But we don't like our Canadian snipers in Afghanistan to collect fingers, let alone receive bronze stars into the bargain, because such numismatic behaviors come too close to a public revelation of the true nature of our common collective psychological state.
The UNAMIR commander, Romeo Dallaire, as described by Power, clearly had this psychodynamic electrochemically constellated in his brain by being an engaged witness to genocide in Rwanda: beat-frequencies impressed through long-range phase correlation, within an environment raised to self-organized criticality, wherein correlation lengths go to infinity and Poincaré resonances probabilistically “determine” dynamic evolution of events. Phenomenologies of the resultant post-traumatic stress disorder (PTSD) revolve around neuronal discharge and resistances to neuronal discharge of the repressed, and hence regressed, collective contents thus electrochemically constellated. Or, as Derek Dillon says in MOON (Vol. I, p. 259) by way of translation:
…the human need for war arises out of the denial to experience of the collective aspects of consciousness. Those become buried in the unconsciousness and, since they cannot find healthy social expressions, emerge in regressed form as collective violence. The allure of war is to taste momentary loss of self in collective awareness -- like the petite mort of sexual orgasm. The mass hysteria involved is very like a state of collective demonic possession. The person participating in an atrocity action, for instance, is simply not an individual for the duration of the experience -- even if the act is perpetrated by a single individual: the collective unconscious does not require the physical presence of a group. Many of the “psychopathological” aspects of PTSD, I believe, relate to the continued constellation of collective contents. The collective energy gestalt associated with mass violence and activated by the dissolution of individual identities is recorded as archetypal patterns of neuronal facilitation in the brains of the participants: electrical predispositions imposed on the cortex, a collective induction. You might say that a kind of electromagnetic “ghost” is made to cling to the brain. Some primitive rites may have been designed to dissipate this specter; various psychotic behaviors may represent a struggle with it… And this “ghost” is not just an after-the-fact residue of the killing; it's right there on the battlefield when the murder goes down. Drivin' your luuuuurp inta Injun Cuntry! If you're tuned-in, you can sense its presence: sixth sense. Deep serious shit, mon! Ain't no time ta sweat da small stuff, diddy-bop, dream about DXin' a gook. It's a pattern of psychic energy in the neighborhood of the coming kill. You can smell it, taste it, feel it crawl along the hairs on the back of your neck. Knowin' your dork is in the wrong hole, ya drop some Special Forces popcorn, swallow a greenie, take some uppers, gulp a green bomb. Some people find sensitivity to the presence of this “ghost” is as good as radar; its either boggie time and adios motherfucker, time for a little E & E shuffle, right you should un-ass and dee-dee-mau, Hotel-Alpha most ricky-tick, sky, make-yoarsel'-a-hat, beat feet, or necessary you get on the horn and ask your buddies back in the camp to crank up the four-deuce, forget the smoke, and come walzin' right on in with the HE. Comprendi?
Derek's recurrent argument in MOON is that animistic identity transparency was rediscovered in higher mathematics beginning in the early 19th century and later in the new physics, that this rediscovery was suppressed through dissimulation, and that this suppression has led humanity into the maw of global war, World War One being a mere scrimmage, World War Two being the junior varsity encounter before the real event. Prigogine, in The End of Uncertainty, quotes I. Bernard Cohen for different reasons, but, for those clued in, to similar effect (without providing an adequate bibliographic reference, p. 55):
Even if the decades 1800-1930 do not show a single revolution in the domain of probability, they provide evidence of a probabilizing revolution [Cohen's emphasis], that is, of a true revolution of fantastic consequences attendant on the introduction of probability and statistics into areas that have undergone revolutionary changes as a result.
Derek, in MOON, maintains that this “revolution” without “a single revolution” is the dissimulation suppressing identity transparency which led humanity into the maw of mass warfare wherein killing of “noncombatant civilians” became the raison d'état. Prigogine's “realistic interpretation of quantum theory”, its reason of state-function, offers a pristine example of the culmination of Derek's thesis (The End of Uncertainty, p. 54):
There is no collapse of the wave function, as the dynamical laws are now at the level of r, the density matrix, and not of wave functions Y. [This formulation removes the non-simple identity inherent in animistic “participation mystique” (to use the technical term employed in social psychology), as it is the m-valued wave-function, even independent of superposition of wave-functions, which gives rise to identity transparency, that condition which, when viewed relative to a spatial reference, is construed as “nonlocality”. Treating the explicit m-valued mathematical property (something first explicated in higher mathematics in the 1820s) of the wave-function as mere probabilistic density matrix allows retention of simple identity and dissipation of the threat of animism by treating the wave-function as if it had nothing to do with wave-functions.] Moreover, the observer no longer plays any specific role. [Best to get rid of the observer when an objectionable quality of subjective state is the object (i.e., projective identification) of intense collective subliminal fear.] The measurement device has to present a broken time symmetry. For these systems, there is a privileged direction in time, exactly as there is a privileged direction in time in our perception of nature. It is this common [Progogine's emphasis] arrow of time that is the necessary condition of our communication with the physical world; it is the basis of our communication with our fellow human beings. [This last formulation is a most pristine illustration of total identification with the ego-function, a single-valued function which is most fundamentally denied by the m-valued properties of the wave-function. Moreover, there is likely not a single educated person on the planet who is unaware of the fact that human beings experience time in more than one fashion, not only with an arrowhead attached. This way of appealing to human perception, in this context, therefore, is not only bad science, but intentional falsification, intentional dissimulation, as the identification must willfully be sustained.]
As Shigehisa Kuriyama has so brilliantly demonstrated (The Expressiveness of the Body and the Divergence of Greek and Chinese Medicine, N.Y.: Zone Books, 1999), the transition from Homeric to post-Homeric Greek perception and proprioception involved a collapse of breadth and depth in experienced self-identity, a collapse to mere identification with the body, with the musculature, as exemplified in the canons of Greek sculpture. This state of psychological identification set the stage for dominance of the atomistic theory of matter. That the tacit assumptions underlying this psychological identification state persist into the present day is attested to by Prigogine's judgment that (Uncertainty, p. 47) “… in order to attribute well-defined properties to matter, we have to go beyond probability amplitudes; we need probabilities themselves.” Well-definition, of course, implies simple identity, i.e., the notion that that being considered possesses selfsameness, is itself and only itself, a notion which the post-Homeric state of psychological identification requires absolutely, and which is absolutely denied by the m-valued properties of Schrödinger's wave-function. The notion of a trajectory in space is rooted in the notion of well-defined identity, which is, in turn, rooted in a state of psychological identification and its associated type-of-logic-employed habituations regarding recognition of order as opposed to disorder. Prigogine argues for a theory of matter, for a type of quantum mechanics, which disallows a wave-function that is a wave-function and allows only those sorts of functions which are compatible with properties of the ego-function. The effect of this is to deny to the socius normative experience of collective states. This denial is repression, a repression that leads to regressive expressions of the denied collective states. One such expression is collective need for genocide.
I could go through Prigogine's book paragraph by paragraph and show how this theme governs every choice made as to how physical theory is to be elaborated. In dismissing relevance of Poincaré's recurrence theorem, he, by implication, dismisses discourse on Zeno's paradox, wherein it is illustrated that there are an infinite number of points contained in any length of the time line, no matter how small that length might be chosen: suggesting that all of asymmetrical linear time is holographically contained in any part thereof. A similar situation, which Prigogine ignores, prevails relative to making spatial measurements on a Koch curve: the more precise the measurement made, the more the thing being measured simply is not there to be measured: non-simple identity of measuring rods and the measured. Why this is ignored and dismissed is because, if it were not, the implication would be that Planck's constant, the gravitational constant, the velocity of light, Planck's length, Planck's time, and Planck's energy each would not have a single definite value, but would be m-valued. Quantum mechanics with a veritable vengeance: all of its “bizarre” properties would apply at every scale-level, at every time-step. Perception organized by the ego sphere would be gravely drawn into question; the identity contagion of spirtistic animism would be greatly substantiated.
When functions diverge to infinity or diminish to zero, as do Dirac's delta functions, this is treated by Prigogine as indicating that dynamics is rooted in probabilities, not trajectories. But if one is not identified with the ego-function and its perspectives, and, therefore, does not assume validity of material well-definition, then one may entertain the notion that divergence to infinity or collapse to zero indicates, not a transition to “diffusive motion”, but passage to a higher valued logic on the phase space -- an order of logical-value wherein zero may well equal infinity. The phase space, the function space, the configuration space, the state space can be constructed under any order of logical value one might choose, each such order corresponding to a given value for each of the following: Planck's constant, the gravitational constant, the velocity of light, Planck's length, Planck's time, and Planck's energy. Renormalization, of course, conceals from the ego-function presence of logical-value transitions. When, due to instability-driven Poincaré resonances, the logical structure of the phase space is transcended at “some critical value of the energy”, as Prigogine says, or, at “a critical state of energy-momentum imbalance” as occurs, for instance, in the case in tornado genesis, the “exponential divergence of neighboring trajectories” need not be treated as “diffusive motion” with “well-defined probabilities”, but can, non-egoically speaking, be treated as “pencils of skew parallels” mathematically handled with fiber bundle arithmetics (these being the geometric and algebraic equivalents of the m-logically-valued properties of Schrödinger's wave-function, discussed in sections 8-10 of the linked paper). And there is no need to filter for accelerations or suppress the interference term, without which one could not see onset of the critical energy-momentum imbalance initiating, for instance, the cascade of complex angular momentum leading to tornado genesis.
When an account of nature fails, when an organizational framework fails, when a system of governance fails, and these failures are resisted over decades, over generations, and response to this situation is increased brainwashing, increased threat, increasingly violent repression, then social autoimmune processes set in which can amplify to situations like that which transpired with collapse of the Russian Tzararchy where any and all professionals were targeted for elimination, where “expert” as opposed to “red” was regarded a crime because of perceived causal responsibility for the failed condition. And if such failure becomes civilization wide, not merely national in character, then amplification can lead to increasing incidence of genocide.
Yes, it is quite clear to me that you cannot understand how I can maintain that prosecuting individuals for atrocities is the primary cause of atrocities. Actually, I do not say this; I maintain that such prosecution is a derivative cause of atrocities. The primary cause is forceful imposition of the experience of absolutely-in-so-far-as-distinct individuality. The constitutionally democratic Cartesian-Newtonian nation-state has the barrel of a gun placed against the back of every head. Any brain that deviates from absolutely-in-so-far-as-distinct identity, any brain, that is, that provides conscious evidence of oscillatory entry and reentry into a pure quantum state and does not limit awareness to Penrose OR, receives no desert, with appropriate legalized fanfare is sent to its room, loses its allowance, is sent to the principal's office, to a child psychiatrist, is fined, is charged with a felony, is subjected to psychotropic drug therapy, electroshock therapy, incarcerated, may have its neuron-cell corpus etched with MSG, is lobotomized, electrocuted, gassed, hung, taken down with anesthetics, guillotined. I am fully aware of the fact that you have not experienced any other state of identity than the absolutely-in-so-far-as-distinct variety, or, if you have, nascent experience of other states of identity has been immediately suppressed out of fear, out of panic in face of clear threat, such threat being named “dissociation”. I do not blame you for confining your experience to such a tiny speck of reality, because I know that the gun barrel resting on your pons is attached to a device with a well-worked hair-trigger -- and the slightest deviation is not tolerated: some level of enforcement is always employed, no matter how small the infraction. How little is understood -- permitted, that is -- of col(indi)lect(vidual)tive is elaborately illustrated by the February 3, 2003 Newsweek article “Fear at the Front” by Evan Thomas (pp. 24-5). Great propaganda piece!
But, really, all this talk about war, genocide, terrorism, nuclear exchanges is just gibberish on a sideshow: the real event is occurring with respect to the human brain and its relation to immunity. Only a very small percentage of deaths associated with the current global cusp transit will be due to war, genocide, terrorism, nuclear exchanges; most will occur due to vectorless autoimmune disease and resultant increased virulence of vectored diseases. Virulence and immune competency are relative-states, in the full quantum mechanics sense of “collective and cooperative behaviors”. Molecules do not produce quantum fields; quantum fields produce molecules. Molecules are caused by coerced socialization of baud-rate limitations on human brain: molecules are time-lapse statistical maps of quantum fields; they are cognitive constructs perceived under instrumentation by cognitive processes reduced by lacuna-on-the-brain. Just as political, economic, and sociological events all are in the realm of effects, not causes, so, discrete molecular biology mechanisms of action are derivative. You think nation-state (ego sphere in projective identification) forcing brain to function disproportionately in one of its quantum states (Penrose OR, also known as the ergotropic modality) and denying it normative access to its pure quantum state (trophotropic modality) has no effect on the collective relative-state of immune competency versus vector virulence? Certainly, this forcing must become chronic if the condition of disease is to fulminate. Onset of fulmination has begun because such forcing has been growing exponentially since the late 1600s.
Whenever I run across the proposition that we never see a broken glass jump up off the floor and reconstitute itself on the tabletop, therefore time is asymmetrical, I have to laugh: it's a totally irrelevant argument. In time reversal, the glass reconstitutes not as matter, but as anti-matter. We don't see anti-matter. We don't know the spacetime topological connectivity transforms involved in such reconstitutions, so we don't have any idea where the reconstituted anti-matter glass is located. Ostensibly, this is not an issue in regards to the Poincaré recurrence theorem where a state recurs in time forward; but what is here ostensible may be so only under certain assumptions.
Ilya Prigogine, in The End of Certainty (N.Y.: Free Press, 1997), says, “We need a 'divine' point of view to retain the idea of determinism” (p. 38). He then proceeds to present an account of his lifelong struggle to overcome this point of view and attain to a perspective in physics that explains the universe in terms of the prevailing everyday experience of time, the experience of the ego-function where the future is unknown, indeterminate, an array of possibilities. He says that “…the desire to achieve a quasi-divine point of view” is “ideological” (p. 38). This is a precious example of psychological projection in postmodernist explication. An even more precious case is less explicit.
A key feature of Prigogine's treatment of the laws of chaos are Bernoulli polynomials, which are pivotal in his account of why time is asymmetrical, why it has an arrowhead attached, why nature's acts of creation are irreversible, why emergent properties, once emerged from the point of view of the ego-function, do not run in retrograde. We will discuss this briefly momentarily, but first we must note that surely Jacob Bernoulli has turned over in his grave as a result of such misapplication of his polynomials. Derek Dillon, in MOON (Vol. II, p. 556), quotes the epitaph etched into Jacob Bernoulli's tombstone by way of alluding to 3rd-order temporal curl: “Eadem mutata resurgo” (Though changed, I shall arise the same). Certainly, this is no affirmation of the irreversibility of time asymmetry, for it is a superposition of “a quasi-divine point of view” and the perspective of the ego-function. Prigogine states that “the Bernoulli map [the march of a function defined in terms of Bernoulli polynomials] is not an invertible system” (p. 96), but it is unlikely that Jacob, having accomplished inversion in his grave, would agree: it is simultaneously invertible and non-invertible, as Jacob reminds us with his epitaph.
In the first scene of MOON, which is a “table of contents” of the novel, Derek becomes transfixed by two instances of chaos: the temporal turbulence of a dripping water facet; the spatial turbulence of a noodle maker's reshaped square of dough, the baker transformation, that is. The essential tension in the deep structure of the novel's story line is thus drawn at the very beginning: What is the relation of these two forms of hazard, both of which are exacerbated by the chaos of war? Temporal curl, quantized as Penrose's “twistor”, is the answer Derek and associates eventually arrive at. The baker transformation is a generalization of the Bernoulli map, as Prigogine so clearly describes in The End of Certainty. In mapping with an equation of motion how spatial points in the square of dough move as the dough is squished and stretched -- move in time forward and time backward, as the point trajectories are time reversible -- it is noted that in time forward the migrating points form horizontal bands and in time backward they form vertical bands. It is because of this band structuring that Derek and associates arrive at the notion of tornado as spacetime gate: the relativity physics aspects of the cascade of complex angular momentum leading to tornado genesis involve iterations of the baker transformation in terms of an atmospheric limited spacetime domain, such that time stops as the limiting velocity is attained, and begins running in reverse as the axis of rotation of the rotating coordinate reference frame tilts from the horizontal plane through an imaginary dimension onto the vertical plane. This process is then inverted, so that time again runs forward. And then the inversion is reverted, and the reversion is inverted: time storm. In the last iteration, as the cascaded process of collapse becomes entrapped, as the time-step itself blurs into a squish-line continuum, as sufficient space runs out, as the last horizontal to vertical tilt is accomplished, a great deal of exotic physics comes into play… and the physics community decided that this cannot be allowed to be so, not, forgodsake, in the world of everyday experience. People go crazy, you know, in the presence of these… these… these pathological phenomena. So… everybody jumped onto the back of a butterfly flapping its wings in the Amazon basin. Lah-dee-dah! Hee-hah!
Derek points out indefatigably throughout MOON that chaos (theory) is what you see when you look at m-logically-valued processes through the lens of single-valued binary logic, a 1T2 logic: two truth-values available, only one of which can be true at a given time. The very notion of probability is indefinable absent the postulates of Boolean algebra. Only one of the array of probable states can come true at a given time: they are simultaneous probabilities, not simultaneous actualities. The very notion of a linear sequence is indefinable absent the laws of traditional Aristotelian-Baconian logic, e.g., “The case is either A or not-A” and “No A is not-A”. Without these laws of distributed middle and non-contradiction, no absolute distinction can be drawn between one element of the sequence and another. If the sequence in question is the sequence of instants on a time-line with an arrowhead attached, the before-and-after ordering of those instants cannot be maintained absent assumption of these laws of traditional logic: without such laws, an instant could be itself and some other instant simultaneously. There would be no possibility of a given time. So, when Prigogine informs us “that even simple probabilistic processes are time oriented” (p. 74), we are not the least surprised -- nor do we find the argument compelling, given that both properties are derivative of the same precursor: single-valued binary logic.
This is not a trivial point, for on the same page 74, where Prigogine makes an argument that the basic objects of physics are probabilities, he asks the question: “If there is more than a single description, who would choose the right one?” The very idea that there can be only a single correct description of nature is an expression of the assumption that nature is self-identical, selfsame, the same as itself, that it cannot simultaneously be itself and something not itself: in other words, this idea of a single correct description requires assumption of the binary logic laws of distributed middle and non-contradiction. Moreover, this assumption is the origin of all cultural conflict: if nature is selfsame, then there can be only one correct description of it; and each different culture claims to embody that one correct worldview construct.
At each stage of Prigogine's argument as to how the Bernoulli map can be generalized so as to demonstrate time asymmetry, and only time asymmetry, he proceeds by introducing a consideration explicitly tied to binary logic. In preparing the way for description of the baker transformation, he presents the equation of motion for the Bernoulli map (modulo 1), i.e., between 0 and 1, and then states (p. 89) that “An arbitrary number x between 0 and 1 can be represented in a binary digital system…” He proceeds from there. When he wants to reveal deeper “insight into the mechanism of the baker transformation by representing it as a Bernoulli shift” (in simulating the Bernoulli map in terms of the probability distribution of points rather then trajectories of points, fluctuations over time settle into linearity: this is the shift), he associates with each point (x, y) numbers defined by a binary digit representation, the corpus of which constitute a doubly infinite sequence (p. 99). This is done in order to establish the time line extending from minus-infinity to plus-infinity. Probability, time, and sequence are each used to define each other, when each, initially, is defined by the conventions of single-valued binary logic. Does this mutuality of definitions offer us any insight into why Prigogine proclaims that “the integral containing a product of singular functions… diverges and is therefore meaningless” (p. 94), and insists again that “products of singular functions that diverge… are meaningless” (p. 95)? Of course it does.
We are told that resort to a probabilistic description is inherent in the nature of nature and not imposed by human limitations: that is (p. 74) “…the basic objects of physics… are probabilities [Prigogine's emphasis].” Setting aside the issue of whether or not physics is nature, this is mainly because (p. 101) “…in the real world, we can only look through a finite window” and because (p. 105) “Whenever we perform an experiment, whether by computer or some other means, we are dealing with situations in which the initial conditions are given with a finite [not infinite] precision…” Setting aside the issue of whether or not, at the outset of an existence-proof argument the purpose of which is to demonstrate time asymmetry, it is legitimate to assume that initial conditions exist, “initial” being a time-related notion, it is clear, nonetheless, that both looking through only a finite window, which harks back to the turn-of-the-19th-to-20th-century issue of the Axiom of Choice, and assuming inherent finitude in measurement precision mean exiling “the divine point of view” and insisting on only the perspective of the ego-function. This is tantamount to arguing that the nature of nature is the nature of the ego-function. The “we” in “we can only look” and “we are dealing with”, mentioned above as given on pages 101 and 105, is the coercive “we” of the socialized ego-function, not the collective “we” of the corpus of participatory natural processes, let alone the “it” of a wholly objective nature with no subjective components. There is allowed zero possibility of a “quasi-divine” unconscious, an unconscious composed of infinite sets, as is so convincingly essayed by Ignacio Matte Blanco (The Unconscious as Infinite Sets, London: Duckworth, 1975). In “setting up” a “description at the statistical level”, an “arbitrary but limited number of digits” (p. 101) of the doubly-infinite time-line are chosen, digits represented in the binary system. Alan Turing, in order to create the Boolean-logic Turing Machine, similarly chose binary digits and excluded an infinite set of such digits, thus limiting his machine to modeling functions of the ego-function. Not surprising that present-day computing machines are so adept at processing probabilistic descriptions.
Less than infinite precision in knowledge of initial conditions means, according to Prigogine and chaos theory, that over time “we observe the exponential divergence of neighboring trajectories” (p. 41), and this divergence leads to the “uncomputability and apparent lawlessness” (p. 104) that Roger Penrose is all the time raising the specter of. The exponential divergence is due to Poincaré resonances (“coupling of degrees of freedom” in Prigogine's parlance; nascent “identity transparency” in Derek's terminology), and to “Poincaré's nonintegrability”, i.e., that an interactive system cannot be fragmented for study without fundamentally altering its properties. The theory of this has been worked out by Kolmogorov, Arnold, and Moser and is called KAM theory. It is because of this divergence that outcomes are indeterminate, and it is for this reason that Prigogine goes to a probability distribution description. No longer treating individual point trajectories in the baker transformation, he treats bundles of point trajectories or ensembles, which are the distributions (p. 81). Description of these bundles, of these probability distributions, he finds, is deterministic; therefore, as stated on p. 74, “…the basic objects of physics… are probabilities [Prigogine's emphasis].” Paradoxical or not, it is in the nature of nature that bundles of the indeterminate are deterministic.
Resonances produce the random trajectories, and KAM theory demonstrates (p. 41) that this onset of chaos occurs when a critical value of energy appears. In order to obtain a description of the time evolution of sets of ensembles, i.e., the time steps taken in the march of the probability distribution function, an operator is defined, the Perron-Frobenius operator (p. 83). The operator prescribes how the function is to be operated upon, and its properties define the nature of the function space within which it operates. Operating on a function with an operator transforms the function into another function. As explained by Prigogine on pages 92-96, the Bernoulli polynomials are functions of the Perron-Frobenius operator. In describing the march of such functions, Prigogine says their higher degrees disappear due to damping, the rate of this disappearance being related to what is called the Lyapunov exponent, log 2. There are two classes of Bernoulli polynomials, one known as eigenfunctions, functions wherein the operator produces the same function multiplied by a constant value called the eigenvalue. The second class involves derivatives of what is known as the Dirac delta function, where, under a certain condition, the probability distribution vanishes everywhere but at a given point, and, under another condition, the function diverges to infinity, i.e., is a singular function, products of which, Prigogine tells us, are “meaningless” (pp. 94 and 95). Hilbert space is the function space which contains the well-behaved eigenfunctions, but, since, in order to get an irreducible spectral representation of the Perron-Frobenius operator, both the well-behaved and the singular functions are required, it is necessary to go beyond Hilbert space to “rigged Hilbert space, or Gelfand space” (p. 96).
Now, okay, how did Derek Dillon and associates in MOON regard all this? They made their version of the Perron-Frobenius operator a derivative operator and called it “operator-time”. But description of the energy-momentum cascade leading to tornado genesis required more than one level of time differentiation, more than one order of derivative, so operator-time became 3-fold operator-time: the Perron-Frobenius operator became composite, became three operators nested one inside the next. The eigenfunctions remain unchanged under 3-fold operator-time, except that they are multiplied by constants called eigenvalues: this being the process by which scale levels are decomposed in the function space within which 3-fold operator-time operates. For each such scale level there is a corresponding degree of Bernoulli polynomials. Lyapunov time, in this case the time taken to decompose or recompose the set of scale levels, is likely not related to the exponent, log 2, but to N/logN, the distribution of prime numbers. It is at a critical value of macroscale energy-momentum imbalance that exponential divergence of trajectories is initiated, thus initializing the cascade of complex angular momentum. The products of the involved derivatives of the Dirac delta functions do diverge, do go to infinity under 3-fold operator-time, but these divergences, these singularities at the limiting velocity, the limiting acceleration, the limiting time-rate-of-change of acceleration are not regarded as meaningless. To the contrary, these divergences, though recognized as instances of indeterminacy from perspective of the ego-function, are not, however, treated as the onset of inherent indeterminacy in nature, but as the emergence from perspective of the ego-function of an emergent property termed “skew-parallelism”, defined through the use of null-vectors, which, under 3-fold operator-time is responsible for charge creation as “lines of force trapped in the topology of space”, to quote Georg Friedrich Bernhard Riemann -- and, we might add, trapped in the time storm loops of recurrent retrograde temporal inversions. Skew-parallels are trajectories that are skew, yet simultaneously parallel. Heisenberg indeterminacy is the tip of the iceberg of skew-parallelism.
In the complex angular momentum cascade of tornado genesis, exponentially diverging trajectories of spatial points in topologically transforming atmospheric limited spacetime domains are, in the limit, the limit of limiting velocities, accelerations, and time-rates-of-change of acceleration, that is, bundled, but these bundles do not constitute probability distributions, as in the Prigogine treatment, but “pencils of skew-parallels” represented with fiber bundle arithmetics. The baker transformation, when applied, not to the dough of smooth noodle maps, but to topologically transforming atmospheric spacetime domains, necessarily involves a lot of exotic physics, in the first instance that of relativity theory. Topological transformations of space take place at absolute limits, absolute limits relative to the limited spacetime domain under consideration: the dimension of topologically transforming space in the direction of movement of its points is fractalized when time stops at the limiting velocity. More exotic topological occurrences transpire at limiting accelerations and limiting time-rates-of-change of acceleration.
But -- as Prigogine also recognized regarding his own formulation of the baker transformation -- Hilbert space is inadequate as a function space for operations of 3-fold operator-time. For one thing, skew-parallels cannot be defined in Hilbert space, as there are no degrees of freedom for the involved null-vectors. Why? Because the required degrees of freedom are not spatial or temporal; they are logical. Being simultaneously skew and parallel violates the rules of single-valued binary logic required by the perspective of the ego-function. A divine point of view must be superposed upon the perspective of the ego-function if tornado genesis is to be numerically modeled. For each degree of Bernoulli polynomials mapped into the function space by decomposition there is a corresponding order of m-valued logic. This can be well-ordered by plotting the mapping on a collection of multi-sheeted Riemann surfaces, a universal covering surface. We are dealing with infinite sets here, the full Cantorian universe, Matte Blanco's unconscious as infinite sets. There is no-time and there is time. Time is the decomposition of no-time, just as Julian Barbour maintains in The End of Time: The Next Revolution in Physics (Oxford U. Press, 2000). There is irreversibility (from the perspective of the ego-function) and there is simultaneous reversibility (from the divine point of view). From the ego-function, everything is nothing but changes; from the divine point of view, nothing ever changes. But all arrows of time do not point in the same direction, or, rather, the same direction is not the same direction, m-logically speaking that is. How does Derek know? Because, in the early 1970s, running on NASA and USAF mainframes, the computerized multiscale numerical forecast model of tornado genesis based on these cascade concepts was routinely predicting tornado outbreaks 12 hours in advance on a one kilometer grid using historical data sets. Why was this model never put online with real-time data? Because “the physics community decided that this cannot be allowed to be so, not, forgodsake, in the world of everyday experience. People go crazy, you know, in the presence of these… these… these pathological phenomena. So… everybody jumped onto the back of a butterfly flapping its wings in the Amazon basin. Lah-dee-dah! Hee-hah!”
Yes, that is correct. I did state a correspondence between degree of Bernoulli polynomials and both scale level and order of logical-value -- degree, level, order -- and this in some sense establishes an equivalence between the latter two. Superficially, this seems unlikely, and certainly the two are not the same. But we must look at how the Riemannian universal covering surface, with its non-self-identical numbers, is related to what the ego-function regards ponderable spacetime, with its self-identical-number-related isotropy. This seems to me a fundamental principle of what in MOON is called Musculpt. Speaking in binary syntax: on the one hand, spatial separation, and the possibility of motion such separation entails, is a function of the notion of identity imposed by the rules of binary logic. On the other hand, the m-non-self-identical values of a number that is self-identical under 2-valued logic are not 100-percent absent even in the representation space of the binary order. Spatial separation, scale, motion, temporal separation, shape, form, color, aural tonality, timbre, and other such properties of binary-order representation are reduced expressions of higher-valued-logical, cross-modal, synaesthetic properties in a manner somewhat analogous to how linear perspective allows 3-dimensional space to be represented on a 2-dimensional picture plane. This becomes particularly apparent if one uses Dürer's screen grid in making a study of linear perspective, and then imaginatively visualizes this screen grid in viewing the natural surround wherever one might stroll while practicing voluntary dissociation in walking meditation, as Derek describes and performs in MOON. Such attempts at desocialization to the bare percept are controlled experiments. This painterly orientation to the perceptual process was highly cultivated by both Vasili Kandinski and Piet Mondrian. In this sense, scale level is a “reflection” of order of logical-value, of layer in painter Rice Pereira’s “layered transparent”. Normal, everyday perceptions are “shadows on the wall of Plato's cave” wherein the static, timeless “perfect form” is seen unfolded in irreversible time-bound Penrose OR state. Musculpt is the “complier program” for Penrose OR. A first approach to a mathematical description of such OR can be seen in Table 1 of the Appendix to the 1980 paper "Some Preliminary Considerations toward Development of a Mathematical Model of the Autogenic Brain Discharge as Spontaneous Localization in Quantum Measurement".
Well, unfortunately, I must beg to differ. The third value in a 3-valued logic does not signify “maybe”. This, I think, is where a lot of logicians, mathematicians, and physicists go wrong. And it is why I agree with Roger Penrose on noncalculability and simultaneously disagree with him on noncalculability. If the third value is “maybe”, what is the fourth value in a 4-valued logic, the fifth value in a 5-valued logic, the mth value in an m-valued logic? Degrees of “maybe” between true and false? Probabilities of truth-ness or falseness, of on-ness or off-ness, up-ness or down-ness, yin-ness or yang-ness? This is contemporary fuzzy logic, one interpretation of m-valued logic, an interpretation based on retention of the notion of truth-value as being the fundamental irreducible foundational concept of logic. Early in the 20th century, Bertrand Russell demonstrated in On Logical Atomism that the greater the number of logical-values beyond two there are involved in the meaning of a proposition, the less meaning that proposition can convey. This was a verdict on m-valued logics taken from the point of view of 2-valued logic. What fuzzy logic actually is is 2-valued logic without the law of distributed middle; it is not an authentic m-valued logic. To regard the third value in a 3-valued logic as “maybe” is to view 3-valued logic through a 2-valued-logic lens. In actual m-valued logics, no concatenation of 2-valued propositions can yield the meaning of any 3-valued proposition: orders of logical value are absolutely incommensurate. Orders of logical-value are orders of self-reference; each order of self-reference produces its own unique notion of identity: the manner in which the itself of a self is not itself. It is not just analogous to the fact that no matter in what way you put together how many cats, no way or no how-many or no combination thereof will yield a dog, but that the notion of logical accommodation by which “dog” and “cat” are logically assimilated to “animal” is superceded in transiting from one order of logical-value to the next. This is the principle involved, the principle embodied in Schrödinger's cat. The power spectrum of a self that has no itself that is not not itself does not devolve to dead and/or alive, which applies only to selves that are only themselves (each word here was very carefully chosen: disallowing double negatives is binary syntax). We have not yet discovered what these m-notions of identity are (though there are hints to be found in the Tenth Book of Plato's Republic and the Tibetan Book of the Dead). We only know that they arise out of self-referencing self-reference and that identity transparency is involved. This last sentence is a statement stated from the perspective of placing the cognitive focus in 2-valued logic and looking through the stack of logical-value orders to the mth order. From the perspective of placing the awareness in the mth order and looking through the stack to the binary order, the statement, undoubtedly, would be very different. For one thing, almost certainly, the very ideas of logical and ontological precedence, and of numerical cardinality, would not be predicated by the statement. Likely the statement could not be stated in a natural verbal language or written in existing forms of mathematical notation; perhaps it could be “stated” and “written” in what Derek Dillon in MOON calls “Musculpt” -- a notational medium and linguistic modality that does not yet exist in a technological form, but is conceivable. “Calculable if and only if recursive” applies only to the binary order of logical-value. And no amount of recursive concatenation of 2-valued propositions will yield the meaning of any 3-valued proposition, nor will any amount of recursive concatenation of 3-valued propositions yield the meaning of any 4-valued proposition, and so on. Prove it, you say? The notion of proof is tied to the notion of truth-value, which has no meaning in orders of logical-value 3…m. If looking at all-that-is-the-is-ness from the mth order of logical-value is somehow godlike, then it is easy to understand why God does not prove things; rather, s/he says “Let there be…” Penrose OR (objective reduction) in human brain is outputting in incommensurately reduced binary form results of m-logically-valued processing to a peripheral device, the conscious ego-function. M-logically-valued processing is noncalculable using a binary recursive logic engine, but that does not mean it is noncalculable using an authentic m-valued quantum logic engine. Therefore, I agree and disagree simultaneously with Roger Penrose's thoughts on noncalculability. Moreover, contemplating import of Penrose's perspective on this issue along with pondering upon import of the identity status of Schrödinger's cat is a route to understanding the fact that all conscious thought is a form of pulsed-microwave audiogram (transmitted vibrational analog of the words, received and translated by the brain into what is experienced by the ego-function as self-originated inner talking) and a type of auditory hallucination -- something Derek Dillon experientially grapples with throughout MOON and resolves only in the final scene during confrontation with the “Third Voice” (an audiogramic personification of the third logical-value). Getting rid of the dominance of roof-brain chatter involves understanding its character as pulsed-microwave audiogram, and the implication of such understanding for the operative notion of identity.
I appreciate your cautionary advice; please don't withhold it in the future. Nonetheless, I find I cannot actually agree that I am conflating science and politics. Consider import of the title of John Desaguliers' book of 1728, The Newtonian System of the World, the Best Model of Government. Science is politics, pure and simple. Identifying laws of nature has nothing to do with Nature; it has to do with gaining self-control -- and then exerting control by a controlled self over an environment brought into being by the establishment of self-control. Nature just is is-ness. The bhakti path to enlightenment is simply developing the capacity to let go of all claims to self-control, a very scary process. All natural laws are in amnesis, in forgetting, forgetting is-ness. Natural laws are conventions of forgetfulness, the manners by which orders of logical-value drop out of view, the view from the mth order. This is no mere Eastern mysticism. Just as the artist triumphs over the “chaos of the world” by mastering his canvas, so the scientist banishes “chaos” by recoiling into his abstractions. But this “triumph”, this “recoil” is projective identification in amnesis. Comprehension of Nature is anamnesis, as Plato so well understood. All learning is remembering. The “chaos” out there perceived by the artist, by the scientist, is in-here, inside the artifice of the socially constructed ego-function.
Contemporary events are not in the least driven by conscious rational considerations; the conscious considerations are nothing more than rationalizations of unconsciously motivated collective compulsions. Strung all along Prigogine's path of discovery are subtle post-modernist distortions that sum to an enormous dissimulation. This dissimulation is not Prigogine's personal psychological problem inflicted on the world, no more than was WWII in Europe Hitler's personal psychology become mass psychosis. The ego-function is a mere speck of dust floating on a vast sea; the sum total of all living ego-functions constitutes nary an island, and all about deep currents, tidal bores, and riptides control the flow. In order to evaluate this “conjecture”, let us look closely at what Prigogine calls (p. 88) the “time-oriented flow of correlations”. I will argue that what he presents is the ego-function's perspective on such correlations. And I interpret his contention that such a perspective is the whole perspective as being a political act, a political act with political consequences. Given that the first sentence of The End of Certainty quotes Karl Popper, I do not see how this interpretation can be regarded a rash behavior (though in these days and times…).
Look, I find it very difficult to read books like this one by Prigogine. Not because I have trouble understanding the subject matter, but because I have to periodically rise from my chair, go to the bathroom, and throw up. This is the literal truth, not something stated for effect. Why should I respond in such an extreme, even psychologically non-normal, fashion? (1) My way of processing conceptual abstractions is to introject, then evaluate in the gut with the being, not merely the binary aspects of brain function; (2) I have been close enough to the spilled blood such ideas as those promulgated by Prigogine have caused as to have it splashed in my face. After Vietnam, sitting in a physics classroom and listening to the ordure coming out of the physicist's mouth was a physiological impossibility for me. Not only does Prigogine's first sentence quote Popper, (The Open Universe: An Argument for Indeterminism), he later, in producing “A Unified Formulation of Quantum Theory”, embraces Popper's notion of “propensities”, without, as far as I can see, actually using the term, while quoting Popper twice again (Quantum Theory and the Schism in Physics) on the omnipotence of indeterminism, which Prigogine calls “probability itself”. Popper made himself into one of the main figures justifying the dissimulations that produced both world wars, that led to onset of the Nazi pathogenesis by preventing cultural integration of departures in 19th century higher mathematics and early 20th century physics. And he had extremely destructive influence on major figures in many fields, such as John Eccles in neurology and George Soros in moneyology. The Soros case is particularly instructive, in that he has devoted his billions to embodying Popper's embrace of the dissimulations. According to Soros' own account, his fundamental approach to the money markets emerged out of thoughts about m-valued logics (which underlie categories of self-referential statements) -- which thoughts were directly and personally influenced by Popper's perspectives. Soros' notion of market reflexivities thus emerged. One can therefore regard Soros' influence on the international monetary system as being driven by a falsification of quantum mechanics and its higher mathematics precursors -- which falsification, according to the account given in MOON, was the deep structure of the causes of both world wars. Having sent many test impulses to The Office of George Soros regarding m-logically-valued monetary units, Derek Dillon has little doubt as to validity of these connectivities. And when you look at the political activities of Soros' The Open Society Institute and the sorts of research it funds (e.g., Samantha Power's A Problem From Hell), well, is it any wonder the U.S. is presently engaged in a new global war in order to maintain the dollar hegemony that stands in the way of virtually every category of institutional reform (i.e., changing the Cartesian-Newtonian institutions embodying the deep structure of the causes of both world wars) globally? Tell me Prigogine's science is not politics! Tell me Nobel prizes are not awarded for political correctness!
Prigogine's central thesis, in developing his notion of the “time-oriented flow of correlations”, is characterized by the following statement of his early realization (p. 60): “I became convinced that macroscopic irreversibility was the manifestation of the randomness of probabilistic processes on a microscale.” As with all of his conceptual transitions, Prigogine begins by invoking (p. 120) a binary-logic frame. “Suppose that the potential energy V in the Hamiltonian is the sum of binary interactions.” The word “binary” here has three meanings, one explicitly stated, the other two implicit and unstated. It is stated that the involved interactions are between two particles. It is not stated that the interactions are either on or off, that no consideration is given to graded scales of interaction: a lot smearing off to a little bit; a little bit growing to a lot. Nor does he note that the binary-logic frame is required to establish the very existence of the two particles he wishes to consider. Without the 1T2 logic laws of “distributed middle” and “non-contradiction” the particles under consideration could not be regarded as absolutely-in-so-far-as-distinct. He then tells us that once having made the assumption of summing binary interactions, there are well established theorems that demonstrate a conservation law concerning wave vectors of the two involved particles. A statistical formalism, it is noted, can be used to describe dynamical evolution. “If we integrate this [distribution] function over the coordinates,” he says (p. 120), “we lose all information about the position of particles, and thus correlations, in space.” This lose of information is called “the vacuum of correlations”. If one integrates all the coordinates except for two, the resultant distribution function is called a “binary correlation”. Prigogine then states (p. 122) that “A dynamical event transforms the vacuum of correlations into a binary correlation.” He builds up higher and higher orders of correlations from there.
The “we” in “we lose all information”, in the above given statement quoted from page 120, is again the coercive “we” of the socialized ego-function, not Matte Blanco's unconscious as infinite sets -- so, the perspective we learn from this exercise Prigogine describes is the perspective of the ego-function resulting from information loss. Where is the coordinate information lost from? is a very good question. Where is it lost to? is another good question. What, in the system under study, corresponds to “If we integrate…”? which is responsible for the “vacuum of correlations” and the subsequent march of their establishment as “probabilities themselves” in irreversible time sequence. These questions are good questions because all along Prigogine's argument he conflates the perspective of the observer with properties of that being observed by the observer -- which is the hallmark of projective identification (the psychological state prerequisite to naive and/or sophisticated realist materialism). In applying these ideas about flow of correlations to a reformulation of quantum theory he says (p. 139), “With the limit of large systems, this sum [of the oscillatory terms in Schrödinger's wave equation] becomes an integral, and acquires new properties.” New, emergent, properties with respect to Nature, or with respect to the description developed from perspective of the ego-function? This is projective identification.
Applied to quantum mechanics, the “vacuum of correlations” results from applying integrals to integrate the coordinates of quantum objects. Prigogine on page 135 uses the phrase “coordinates of the quantum object.” Fact of the matter is, however, a quantum object, by definition, can have no coordinates; if it has coordinates, it is not a quantum object; indeed, the term “quantum object” is a contradiction in terms, an oxymoron. Coordinates come into being only when quanta become objects as a result of being reduced to the binary order of logical-value, at which point the quanta is no longer a quanta, but an object. Nonlocality does not mean that an “object” is at a multitude of coordinate locations; it means that there are no coordinates: the logical possibility of coordinates does not exist in the domain of consideration. Prigogine makes this sort of error over and over in different contexts. On page 131, he says “…in both cases [Newtonian dynamics and quantum theory] there exist an individual description in terms of trajectories or wave functions…”. This is repeated on page 133: “…the individual level of description corresponding to the wave functions…” He would thus have us believe that a wave-function is a wave, and that a wave is an individual -- because the wave-function in mathematical notation is represented by an individual element. Now I am no advocate of reification being considered a fallacy. On the contrary, I believe that, substantially, what we take to be concrete is in reality consensual construct; and what we take to be abstract is largely, in actuality, the bare percept. Nonetheless, the reification has to conform to the reality of the case, otherwise it surely is fallacious.
What Prigogine does not seem to recognize about the early history of quantum mechanics is that Planck's radiation law demonstrated that it is not necessary to detail the spatial field in order to make accurate predictions; it is only necessary to describe the properties of a fundamental oscillator. Knowledge of past and present details of the spatial field can remain very vague (quasi-“vacuum of correlations”) and yet, with sufficient knowledge of the fundamental oscillator, the Zietgeber, the time-giver, that is, one can reach into the future and pick out details of the spatial field. Why? Because that is what a time-giver does. The time-giver, being an infinitely enfolded logical operator, contains within itself specification of all that detail. Indeed, this enfoldment likely embraces orders of infinity. Time as logical operator is not spatialized time: the future of the binary order does not spatially exist until it comes into being by becoming; nor is it predictable from a sufficiently detailed knowledge of the past and present spatial field, a type of knowledge which is unobtainable for reasons of logic. To the degree you know the time-giver, you know what the time-giver knows. All of Prigogine's discussions about trajectories being replaced by “probabilities themselves” is based on the assumption that prediction requires detailing the spatial field, which is not at all the actual case. The details of the Bohr model of the atom, and all that, really are largely beside the point. It's not of great moment what “the starting point for formulation of quantum mechanics” was, as this starting point was simply “the discovery that the sun does not go around the earth”. The physicist's feet were pulled out from under him by Planck's radiation law, and very suddenly he found himself lying on his back, dazed. He is still there on his back; yet dazed.
Heisenberg's uncertainty principle, as Prigogine points out (p. 134-5), is a result of the fact that the coordinate and momentum operators do not commutate: the order of their application to the involved function changes the result and, therefore, one result cannot be well-defined if the other is well-defined. Commutation, association, distribution are arithmetic principles. If there is a series of arithmetic operations to perform -- addition, multiplication, differentiation, and so on -- then this is an instance governed by one of these principles. What Prigogine does not point out is that commutation is an arithmetic property defined under the rules of binary logic; commutation cannot be similarly defined in orders of logical-value 3…m. By virtue of self-referencing self-reference, each such order of logical-value has its own order-specific notions of number, arithmetic, algebra, geometry, and so on. The uncertainty principle prevents detailed knowledge of the spatial field for reasons of logic. And pencils of skew-parallels (which Prigogine mistakenly regards divergent trajectories or diffusive motion) resulting from ill-determination of the spatial field initial conditions cannot be represented in Hilbert space for reasons of logic: rules of the binary order of logical-value do not permit parallels to be simultaneously skew even in non-Euclidian geometries, because in skew-parallelism the parallel considered is not selfsame, and therefore violates the binary-logic law of contradiction: Hilbert space lacks sufficient degrees of freedom in the realm of logic. The involved divergence, for reasons of logic, is regarded as “emergence” of chaos (“emergence” from the point of view of the ego-function). More orders of logical-value are required if quantum mechanics is to be understood. The m-valued functions employed in Schrödinger's wave equation must be interpreted in terms of m-valued logics. This is why an infinitely enfolded time-giver as logical operator is necessary in description of the properties of a fundamental oscillator. And it is in this fashion that we (ego-function) can begin to see to what “If we integrate…” corresponds in the establishment of a “vacuum of correlations” (from point of view of the ego-function), when this “vacuum”, from perspective of the mth order, is actually infinite correlation density at infinite correlation length. What Prigogine calls (p. 122) “dynamics as a history of correlations”, in the present view is regarded logical decomposition of global identity transparency under 3-fold operator-time (Plato's amnesis), because Prigogine's “persistent interaction” is a binary logic way of speaking about m-logically-valued identity transparency. As a result of the fact that all his departures begin with an invocation of a binary-logic frame, Prigogine must start with what the binary-logic frame mandates: no A is not-A, i.e., atomism, absolutely-in-so-far-as-distinct “quantum objects“, particles. And then he finds himself treating a single particle as an ensemble in order to get a probability distribution. But to treat a particle as an ensemble is to regard A as not-A, which is to go into binary-logic fallacy, into divergence, into chaos, into quantum complementarity, into wavicle. Anyway we (ego-function) look at it, 3…m orders of logical-value are required -- and real comprehension is not possible absent the “quasi-divine” perspective of the mth order.
As a result of 3…m orders of logical value, second- and third-order operator-time (nested partial derivative operators with respect to variables defining the spatial field) are non-hermitian, i.e., the involved eigenvalues have no real numbers in Hilbert space. This means that the massenergy of relativistic quantum physics is not the mass and energy of Newtonian physics; massenergy is a superposed composite (with three nested sets of units) under 3-fold operator-time (which not only replaces the Hamiltonian operator, but redefines the wave-function). It also means that all levels of superposed massenergy (both kinetic and potential) are treatments of zero-point energy. Temperature is hermitian; hypertemperature is non-hermitian. Hypertemperature has no representation in Hilbert space. Each degree Kelvin is absolute zero for some system composite. Hypertemperature is the spin component contributed to space by operator-time as temporal curl (quantized as Penrose's “twistor”). The thermodynamic limit is, therefore, a relative absolute, a limit absolute relative to the limited spacetime domain, or class of limited spacetime domains, under consideration. There are nested sets of conservation laws. The three states of matter -- gas, liquid, solid -- are differentiated, as class, by topological transformations carried out under 3-fold operator-time, as seen by the ego-function locked within the logical rule constraints established by 2-valued logic. Fields and particles are “time-lapse photographs” of spatial curvature configurations; they are cognitive constructs: there is any number of particles, including an infinite number, in any portion of space, no matter how small, depending on how time is “lapsed” by the governing m-valued logical operator. The states of matter, as permitted under 2-valued logic, are decomposed from more complex forms existing under 3…m-valued logics. The various forms of structured water are intermediate states and cases in point. Plasma is a higher-order state of matter as viewed through a 2-valued logic. A plasma bottle is a particular sort of time-logic proposition and an essential element of the spacetime gate syntax of a tornado.
Derek Dillon points out in MOON that the deep (collective unconscious) structure of the causes of World War Two was signaled by two events related to the above given considerations: (1) in 1926, Max Born came forth with the probability amplitude interpretation of the wave-function given in Schrödinger's equation, and this interpretation, without Schrödinger's compliance, quickly became holy writ; (2) in 1936, Birkhoff and von Neumann (“The Logic of Quantum Mechanics”, Annals of Mathematics, 37) dropped the commutative law (because of Heisenberg uncertainty) and achieved some level of recognition that quantum logic has some relation to projective geometry. But where is the Riemann surface stack? Where the required universal covering surface? Though some doubt is cast on the utility of Hilbert space, where is the recognition that every point in the referencing phase-space is multivalued, that it has shadow points peppered over the complete space, that translation across a single-valued sheet is projected as a static lattice to the m-logically-valued referencing function space. (This last sentence is a more encompassing way of understanding what Prigogine means when he says (p. 119) that “Given that a trajectory is represented by a point in phase space, we can see that the collapse of trajectories would correspond to a situation in which a point decomposes over time into a multiplicity of points, exactly as in the diffusion process we analyzed in Chapter 1.” But this is not a collapse, and this is not chaotic divergence, and this is not something that takes place over time.) How strange that Birkhoff and von Neumann should invoke the concept of a logical “lattice” but not view it as a true point-set topology! Similarly, they use involutory relations and the concept of skew-fields, but the m-valued logics (first formulated in 1921) screaming in the background are completely ignored. Dropping commutative laws for 2-valued propositions, indeed! Can laughter be suppressed? These missing recognitions are not ignorance speaking; they are expressions of psychological dread. And this paper, summarizing a decade of collective psychoneurotic posturing, was published just three years before the first actions were taken in the inevitable avalanche of consequences. Can't see the connection to the war? Call consciousness in its active aspect the set of all topological operators on the m-logically-valued reference space; call consciousness in its passive aspect the reference space acted upon. The self-referential consciousness referred to here is the universal variety which Western psychology approximates as the collective unconscious. Karl Popper's anti-historiographic historiography notwithstanding, everything described above about operator-time being a logical operator is necessary to any adequate historiography: laws of amnesis are the laws of nature. Mankind In Amnesia, as Immanuel Velikovsky titled his last book. Will mankind ever again enter Plato's anamnesis, that is, re-enter Nature?
All laws, all rules are laws-rules of amnesis. Most fundamentally, there are no laws, no rules because there is no game. This goes back to the very origins of the Judeo-Christian world construct. Cabalistic thought embraces the above given statements; rabbinical thought rejects these statements. The issues involved are at the root of Prigogine's treatment of resonant frequencies (Poincaré resonance), divergence, and Poincaré nonintegrability. He takes the rabbinical position; I (and Chuang Tzu), the Cabalistic. Wherever there is resonance, there is divergence: the mathematical description of resonance involves division by zero, which is an illegal operation according to the basic rules of arithmetic (as derived by application of single-valued binary logic). The existence of this illegality Poincaré's French logicality defined as nonintegrability. Prigogine resolves this instance of criminality by statistically reformulating the laws of dynamics such that the resonance can be treated as no mere probability amplitude (Born's proposal in 1926), but as probability itself. I, however, maintain that the necessity to divide by zero indicates the presence of a more permissive order of logical-value (within which the binary order is nested) under which rules governing the corresponding arithmetic are less prescriptive -- and that behind this order is another more permissive order, and another, and another, to the mth case: i.e., in the mth case of anamnesis, there is no game. Gödel's work demonstrating arithmetic “incompleteness” strongly supports the Cabalistic position I take. Moreover, “resonance” between the frequencies of two “quantum objects” (oxymoron) is a single-valued binary logic way of speaking about animistic “identity transparency”, which intrinsically requires m-logically-valued propositions to characterize. As Derek Dillon was told by the Third Voice in MOON upon arriving at this satoric recognition (Vol. II, p. 669):
Don't cradle your head! This is no occasion for catatonic response. Four-eighteen. [Cabalistic number for completion.] Four-eighteen. Breathe! Walk and breathe. Four-eighteen. Anapana-sati. The satin-flow essence which you breathe. Kayanupassana. Vedananupassana. Cittanupassana. Dhammanupassana. Insight meditation. It's constellated now; it will KILL you unless you live it. Oh, how many diseases it knows how to approximate!
Cabalistic tribalism and Taoist spiritualism embrace the autopoiarchism driven by animistic identity transparency, while rabbinical-Confucian insistence on The Ten Commandments embraces the self-organizational deterministic chaos of Prigogine's probabilities themselves. Regardless of Iraq and global Islamic terrorism, we will no doubt be fighting another world war over this issue in due course. The only real hope of avoiding this war is if binary computers rapidly become more pervasive and thereby more quickly program a critical mass of their users. Then there will be no more naysayers on the commandments. During the mid-1930s, Alan Turing was traveling the same intellectual climes as was Gödel, Cantorian climes of the infinite sets constituting Matte Blanco's unconscious. Had Turing not been mentally raped at Bletchley Park by the military intelligence mindset decrypting the Nazi codes, he would never have created a finite-sequence logic engine, the basis of binary computing: we would have been using m-logically-valued quantum computers long ago, and there would be no necessity of a Third World War: historiographic continuity in amnesis. The point of all this is that no amount of moral behavior on part of the power elites, no amount of protesting to coerce such moral behavior, resolves the deep structure of causation relative to world war and genocide. At most, all these can accomplish is to change the pattern of war and genocide. You want to overcome mass war and genocide? Then resolve the fundamentals in the deep structure of causation. You want mass war and genocide to continue? Then regard them determined by the probabilities themselves and continue protesting outcomes.
What were the deep structure (collective unconscious) triggering events for WWI and for what looks to be the oncoming WWIII, you ask? For WWI, I would say the early precursor events were discovery of m-valued Abelian functions, discovery of non-Euclidian geometries, and the diagonal proof given by Cantor for a denumerable transfinite set which demonstrated an equivalence in cardinality between the whole set and any one of its proper subsets. Cantor's proof was a mathematical demonstration of the principle behind animistic identity transparency (later, in the mid-20th century, this was technologically illustrated by properties of a holographic plate). These three constellated the late 19th century backdrop. The more immediate triggering event for WWI was formulation of the famous “Axiom of choice” whereby it is deemed permissible to choose an infinite set to subject to a mathematical operation, rather than a mere infinite sequence (which cannot become an actual infinite quantity in a finite time) as is worked with in the calculus. Relative to a probable WWIII, I would say the immediate triggering events were the recent discovery and replication of experimental demonstration that atomic entities, not only elementary particles, can be at more than one location at a time, which is giving rise to the field of quantum computing, and the discovery that light can be stopped and that it can get to point B before it left point A. These speed of light experiments suggest to me, minimally, that the speed of light is logically m-valued, not single-valued. The prevailing political, social, and economic institutional base, as well as the egoic standpoint of personal psychology, are irredeemably wed to the Cartesian-Newtonian paradigm. Each of the above mentioned events were part of the unrelenting march of theoretical and experimental demonstration that this paradigm has been bankrupt for over 150 years. The world view construct and the institutional base are utterly out of correspondence. This represents an enormous and rapidly amplifying degree of collective cognitive dissonance and existential anxiety dissipated in increasing incidence of mass hysteria events and group displays of “clinging behaviors” (i.e., fundamentalisms of every stripe). Mathematics and science have long been demonstrating that the prevailing institutional base has no legitimacy. Moreover, the illegitimate institutional base is preventing emergence of legitimate analogical generalization of the new paradigm into political, social, economic, and psychological applications. Everything has been crumbling and nothing is being allowed to replace what soon will be a big pile of broken bricks (as 9/11 symbolizes). By way of compensation: the ever increasing obsession with control technologies like behavior modification and control by electromagnetic fields, mind reading and control by similar means, robotics, genetic control and modification, cloning, artificial organs, bone, skin… control, control, control.
Yes, it is true that there is a certain correspondence between “string theory” and the structure of what I have been calling an m-logically-valued reference space (MVRS). I am no expert on anything, least of all string theory, but as near as I can tell the correspondence did not really develop until string theory was generalized to superstring theory and superstring theory was generalized to the theory of p-branes (the one dimensional string becoming a p-dimensional membrane). A sheaf of p-branes is similar to the structure of the MVRS (as Hilbert space involuted on a Riemann surface m times under m-valued logics), except, of course, the m-logical values stacked on each point of the pth brane are absent, thus limiting the ability of the p-brane to model quantum processes. Also not well handled by the p-brane is chronotopology. There can be no authentic generalization of general relativity without explicit and sophisticated handling of the shapes of time, which certainly have much to do with distinguishing between statics and dynamics (e.g., electro-static versus dynamic electric fields), between weak and strong “forces”, between matter and anti-matter, and so on. Once you are dealing with a changing spacetime curvature, instead of forces propagating in space and time, time absolutely has shape, not only space: the sole sophisticated way of understanding this is “operator-time”. Operator-time is not a notion intrinsic to the p-brane because the p-brane lacks a basis in m-valued logics, the logical operators of which form the foundation of operator-time. Cute terminology and mathematicization for its own sake, rather than depth of thought, become arbiters of worth in scientific institutions run by pea-brains whose main purpose is to manipulate the worldview construct for psychologically regressive politico-military and economic ends.
I've finally managed to read Candace Pert's Molecules of Emotion (N.Y.: Simon & Schuster, 1997). The first few times I approached it, I set it aside because her personal story is that all-too-familiar same old story and I was never in the mood for replays. This time I started in the middle and worked back to the beginning and thereby was able to get into it. The other mental block I had was her association with Georgetown University Medical School. In the early Seventies I spent untold hours in that medical school's library and later, after publication of the Autogenic Therapy paper I presented in Kyoto, Roland Fischer invited me for lunch to meet the reigning patriarchs of the Department of Psychiatry. Roland was a very unorthodox and brilliant Swiss biochemist involved in the synthesis of LSD who later became a neuropsychologist prominent at the Maryland Psychiatric Institute, editor of The Journal of Altered States of Consciousness for most of its lifespan, and a major figure at Georgetown University Medical School until his retirement to Majorca. The lunch in 1980 was to celebrate publication of my paper and to throw some of the implications Roland and I had been discussing at several of the leading authorities, as thought was being given to publication of the follow-up paper “Some Preliminary Considerations toward Development of a Mathematical Model of the Autogenic Brain Discharge as Spontaneous Localization in Quantum Measurement” (this long paper was never published, of course). The lunch was pleasant enough, but it was quickly made clear that the level of abstraction involved in “the implications” was a bit much, so that was quickly put to rest. My major interest, actually, was in getting permission to check books out of the medical library. Having to sit in the library to read every word cut my efficiency by about 70 percent as I lived quite a distance away and was forced to spend my time there late into the night after work. My request that they arrange such permission was treated as way out of bounds. We all laughed it off. Having impersonated a faculty member eight hours a day for five years at a major university to gain access to the stacks, having been surreptitiously handed a faculty card (no pictures in those days), had apparently totally disoriented me to realities of university protocol. Anyway, I continued following out my ideas at the medical school library weeknights and at the National Library of Medicine weekends, but I never had anything to do with those people again. Over a period of several years every time I entered the GU Medical School library I submitted a request for a copy of Wolfgang Luthe's six-volume Autogenic Therapy. They never got a copy. And my regard for Georgetown University dropped lower than it had been when I was a student in the early Sixties at American University's SIS. George Washington's medical school library obtained a copy after two years of such repeated requests. The National Library of Medicine got a copy after only one year of my requests.
It's too bad Candace never ran across the work of Edmund Jacobson, like Walter Cannon a student of William James, and like Candace a person denied a well-deserved Nobel (in his case for creation of the EEG). Candace's “big aha!” (p. 137) regarding the James-Cannon debate on emotion was Jacobson's central theme throughout 60 years of active research. This is recounted at length in his swansong book Biology of Emotions (Springfield: C. C. Thomas, 1967). His multitude of papers published in the 1930s abundantly documents what I describe in the “autogenic discharge as spontaneous localization” paper (p. 15):
Through the study of simultaneous electroencephalographic and electromyographic recordings, Jacobson was led to question the commonly held idea that brain action precedes muscular contraction. In the case of the intact organism, where no electrical stimulation of the brain is used, he concluded that, “Central nervous regions do not prevail over an allegedly subordinate peripheral region” [157, p. 110], but, rather, that during mental activity the central nervous system and neuromuscular system operate simultaneously through a mechanism of “reciprocating activation”. Regarding the question of mind-body interaction, he says:
According to the present argument, the control of mental activity and of behavior has never been experimentally identified and will not be recorded in any portion of the organism, because it resides in the integrated totality.
It was soon after reading Jacobson's paper “On Meaning and Understanding” (American Journal of Psychology, XXII, 1911), which describes autosensory observation as taught in his laboratory, that I ran across copies of Nicoll and Bennett at Samuel Wiser's in NYC. I'd have never made the big financial investment in 1964 N & B required (a good portion of my total net worth at the time) had I not earlier read Jacobson on autosensory observation. It was because of Jacobson's Titchenerian use of autosensory observation as an integral part of his experimental EEG-EMG-EPG studies, I am sure, that he was scotched out of the Nobel. On all the anathema issues of the day -- contentless awareness, self-observation, time as remembering -- he was on the wrong side of the eight ball.
These days I am working myself more into notions of homeopathic mechanism of action relative to autogenic discharge, as I am coming to believe that the homeopathic remedy operates not directly on the electromagnetic structure of the organism, but via neurohumoral discharge. As the autogenic discharge is believed to unload electro-chemical records of stress, this idea of homeopathic mechanism of action would necessarily involve Candace's idea about memories being stored at the receptor level (p. 143, which is where I began to read her book from the middle to the beginning). Unfortunately, she does not seem to have a very clear idea of exactly how memories are stored at the receptor level: by molecular conformational processes or what? This circumstance is similar to Karl Pribram's idea about memory storage via neural holograms. He could not give an account of what the source of the “reference beam” is for “display” of the molecularly-stored memory trace. And he was not interested in coherent radiation from superconductant DNA as a possible source when I made this proposal and sent him a copy of the 1979 International Journal of Quantum Chemistry paper soon after it was published. I think the major reason why adequate ideas for molecular memory store and display are absent is because notions about the neural code are wrong, as they are not informed by quantum-relativity conceptions.
We are born with all the memories we will ever have. A given life is a process of Platonic remembering: anamnesis. This is a result of space and time being spacetime. Once you have spacetime curvature, time has shape, topological form -- no less than does space. An elementary particle is empty spacetime given topological shape, temporally no less than spatially; an atom, a more complex such shape; a molecule, yet more complex such a shape. The simultaneous m-(virtual)worlds of a quantum theory not interpreted via probability amplitudes, but relative to m-valued logics, are the totality of passing time as spatialized by a Newtonian two-valued-logic mindset. Infinite sets (of temporal instants no less than spatial points) are involved here, where any proper subset has the same cardinality as the whole set. Planck's limiting values are relative to the class of sets of spacetime domains considered. The representation space for each instant of passing-time is the unfolded m-(virtual)worlds enfolded as the temporal topology of a given lifetime. Time, as operator-time, unfolds itself upon the topology of space as emergence of material structure; the disappearance of material structure enfolds quantum action-potential stored in higher-order imaginary time-logic configurations. Every proper subset of linear-time has the same cardinality as the whole of linear time: the instant contains as “much” linear-time as the whole set of instants. Close to Barbour here, except for his probability “mists”.
In this context, what is a receptor? Stereochemical lock and key is only the final docking mechanism of a binding operation. Recognition and homing of ligand on receptor is governed by the radiated quantum wave properties of receptor and ligand (this applies also to antigen and antibody, DNA and RNA, and so on). Specificity of receptor for ligand, before final stereochemical docking, is a function of receptor-ligand music-sculpture: temporal topologies of superposed frequencies, waveforms, orientations, and intensities. Consider the following from my article on the homeopathic ozone effect:
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 multivalued reference space. The atmospheric analogue of these processes involves wave-trace-velocity recognition in (coherent) acoustically-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).A receptor site is a physical-region singularity in the (morphogenetic) quantum field of the organism. All receptors of a given class map on a given n-dimensional decomposition “sheet” (of the m-logically-valued reference space of the field of the organism) as a Regge lattice-array equivalent of the prevailing spacetime curvature configuration. The Regge calculus generates n-dimensional lattice equivalents to the solutions to Einstein's field equations. A receptor site can be active or a hole. When active, the physical region singularity is occupied by a receptor molecule. When the receptor molecule binds with a ligand, it is locked into a specific stereochemically-mediated function. The sheet-bound Regge lattice functionally integrates multiple receptor-ligand actions of a given class. Integration of receptor-ligand actions of multiple classes is mediated by cross-sheet lattices mapping orders of logical-value higher than two. The neural code is not based on two-valued logic; it is m-logically-valued. The two-valued synaptic action-potential neural system is input-output device, while the superposed-frequency-driven neuropeptide and perineural and cytoskeleton and microtubule system is the m-logically-valued quantum processor system. All “memory traces” (the full complement of which we are born with) are m-logically-valued superposed frequencies on the multivalued reference space of the organism, physical-region singularities of which are receptor sites. The coherent waves generated by superconductant perineural (centrally and peripherally) DNA, in conjunction with microtubles, “display” the stored holographic “memories” (what are currently regarded percepts, somatosensory propriocepts, and memories of such “memories”), decomposed as two-logically-valued and read back through the synaptic action-potential system for output into enculturated two-logically-valued conscious awareness. Remember The Short Happy Life of Ivan Osokin?
Or so I have come to believe as I follow my snail's path.
Yes, that is true. Thank you for pointing it out. There is very likely a relationship between these physical region singularities as receptor “holes” and acupuncture points and meridians. In fact, in 1978 while at Cornell, after reading several of his articles in the American Journal of Chinese Medicine, I wrote Robert Becker in Syracuse a long letter proposing that acupuncture points are physical region singularities in the quantum field of the organism established in considerable measure by the radiating coherent wave properties of superconductant DNA. He wrote back stating that the idea was intriguing, but he was in no position to evaluate it. The next year, following publication, I sent him a copy of our superconductant DNA paper. Later, I found out that his lab was in upheaval at the time because of all that, politically, was coming down on him -- which he eventually described in his books. Unfortunately, he never mentioned the superconductant DNA paper in any of his bibliographies. He probably forgot about it. In the late 70s, I dug up and read virtually every paper he had until then published. And it was his theories about an analog data system (mediated by the perineural cells) that provided major inspirational input for creation of ideas such as those given above. Acupuncture points may be holes (intersection points, physical region singularities) simultaneously existing in multiple cross-sheet Regge lattices: nodes of wave superposition. The meridians may be lattice “struts” (laser-like coherent wave propagation channels or gradients) simultaneously existing in multiple cross-sheet Regge lattices: breaking wave crests of wave superposition. A given set of simultaneous cross-sheet Regge lattices, per the above-given discussion of ozone, would physically embody a given prerequisite (organic quantum field wave-function and equivalent stereochemical geometrical transformation as frequency regime invariant) of organismic functional integration. Solution to the Einstein field equation is equivalent to a spacetime curvature configuration; the curvature is equivalent to an n-dimensional Regge lattice; the lattice is equivalent to the m-logically-valued Eigen-function value array of a quantum wave-function superposition. What we are talking about here is bio-quantum-gravity. Unfortunately, Roger Penrose has not been interested in this ever since 1979 when he was first sent a copy of the superconductant DNA paper and the proposal was made to him in the cover letter that his “twistor is the quantization of the temporal curl” involved in generation of the coherent acoustically-modified gravity wave modes propagated by the molecule in response to the ambient electromagnetic field -- this gravity wave generation being the direct effect of the superconductant state. A similar proposal related to analogous processes in the Earth's atmosphere was tendered to Steven Hawking immediately after publication of his paper on particle creation near blackholes. A scathing and emotionally negative response came back by return mail. More recently, 2002, Raymond Chiao of UC-Berkeley, was not interested in the superconductant DNA model's description of generation of coherent gravity waves by DNA, when queried by letter, even though he has produced a detailed model describing how superconductors could transmute electromagnetic radiation into gravity waves, just as the 1979 superconductant DNA paper, in its own different mathematical model, describes. There has been a great deal of non-interest over a period of decades on the part of a large number of experts in the very things they purport to most be interested in. Perhaps the implied superconductant bio-levitation is just simply outside their cognitive field of fire. If so, how are we to credit their theories of brain function, calculability, emergent properties, histories of imaginary time, and so on?
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