Follow up on Summary and Conclusions left out.

o Along the same lines as the ‘real’ versus ‘ideal’ justifiable arguments we now add additional evidence in behalf of the anticipated eventual transition from the abstract ‘ideal’ to the measurable ‘real’ paradigms explaining existential reality:

The report “Breakthrough Study Reveals Biological Basis for Sensory Processing Disorders in Kids.” constitutes the general explanation of the specific sensory processing disorders we clinically see in autism and the attention deficit hyperactivity disease (ADHD). It also underlines the importance of the human brain’s right hemisphere first impact with sensory input from ‘real’ environmental (external or body proper) input sources of new or familiar information before an adaptive response is either subconsciously implemented reflexly or after further analytical processing especially when processing unfamiliar sensory inputs. The master control nerve networks of frontal brain neocortex is continually processing information input arising from right hemisphere initial effort to coordinate ongoing activity from multiple sources such as Left temporal and parietal lobe multisensory input and Left frontal language processing Broca’s area. The frontal neocortex brain is continually assessed of the ongoing ‘real’ environmental biopsychosocial circumstances, from passive meditation to active social partying. When the new or familiar input is received at the Right hemisphere the master frontal neocortex analytical sorting of available response alternatives present in the neocortical pre motor attractor phase space. This is subsequently followed by a conscious activation of the adaptive motor choice neurohumoral response, all things considered. What is important to notice is how the brain synaptic ‘real’ time processing precedes in time the ‘ideal’ adaptive motor response especially in the presence of new/unfamiliar information sense-phenomenal input arrives in Right brain hemisphere. All of this complex analytical sorting immediately follows after a subconscious reflex motor response is released for the overall biological preservation of the human species priority as previously published and discussed by me in various HiQ listings and fora. This detailed explanation hopefully supports my biased view about the importance of the ‘real’ preceding the ‘ideal’ solution.

The Unexpected Transition from Idealism to Realism.

The information explosion we have witnessed in the last two decades has unexpectedly accelerated the relentless, forward evolutionary process of complexity as experienced and narrated by human language semantic accounts in our communications. There is an insurmountable amount of verifiable evidence sustaining the ‘real’ demonstrable fact that only the human brain and that of our primate relatives have the ability to pay attention to objects/events in the audio-visual scene without always looking or listening at them directly. This is done by recreating an internal map of the previous sense phenomenal world we experience by mapping our sensory field onto specific brain cells. The mapping includes local and non-local verifiable observables. This is the existentially real case whether the ‘wave’ or ‘field’ mass particle carrier we conveniently derive as an ideal notion fits the previous consistent falsifiable experience or not. Thus, the local quantum physics interpretation implies being bounded within a finite space-time region where an observable object/event exhibits a ‘real’ behavior conditioned to the relevant environmental circumstances properly belonging to the space-time region itself. This is the classical Copenhagen Interpretation (CI). It is along these lines that the linear algebraic approach focuses on ‘real’ physical local and ‘ideal’ metaphysical non-local representations (symbolic or sentential logic) on a probability basis emphasizing that the notion of a field or wave is only a convenient derivative notion from the ‘real’ local actual measurements that preceded the ‘ideal’ non-local explanation.

The competing model-poems that ‘ideally’ explain the same ‘real’ phenomenological description of the object/event sensory reality that preceded it is called the Transactional Interpretation of Quantum Mechanics TIQM. The advantage of the transactional interpretation is, in my opinion, that it incorporates probable interpretations of ongoing verifiable existential experiences that are irreducible to linguistic coding in symbolic or sentential logic representations. It’s emphasis on sense-phenomenal empirical ‘reality’ descriptions are more reliable especially when the Transactional Interpretation (TI) predictions are confirmed. Consequently the Lagrangian Quantum Field Theory (QFT) is our most empirically well-confirmed physical theory where the ‘ideal’ explanation of the metaphysical component of ‘real’ empirical object/events descriptions harmonize. The reliance on verifiable sensory facts excels in the expediency of calculations and their intuitive understanding because it is closer to phenomenological experimental manipulation in the physics lab. That makes the derived metaphysical ‘ideal’ model poem more credible when applying the theory to make predictions. Anytime that a pragmatic empirical ‘reality’ description of the occurrence of an object/event and an ‘ideal’ metaphysical logic sophistication explanation (i.e., there is an isomorphic mapping of the elements of a C*-algebra into the set of bounded operators of the Dirac/Hilbert space.) lead to the same existential reality conclusion, then pragmatic ‘realism’ trumps mathematical rigor due to the resulting simplicity, efficiency, and ease in understanding. When the TIQM model is mathematically modified further to incorporate the speculative probability of identifying the n-1 dimension space coordinates of probable sources of cosmological information input located beyond our local 4-dimensional space-time, the TIQM becomes a superior ‘ideal’ model when also explaining non-local sources of information input (e.g., measurable cosmic radiation) causally efficient in influencing the human evolving complex ‘reality’. This emphasis has made possible to grasp the seemingly conflicting multidisciplinary aspects of the same human reality in a real mesoscopic biosphere vital environment. This has been my personal experience.

The TIQM model superiority is best illustrated by adopting the Dirac notation analytical tool, an empirically based ‘ideal’ representation where the ‘entanglement’ coupling is based on the complementary pairing/coupling of opposite spin unit particulate matter. The mechanism needs to be at the subatomic micro level but two macromolecules like DNA or RNA can be functionally coupled iff their micro components are spin-coupled first. I am not even sure that experimentally our sources are actually separating spin couples at random, it may be separating in opposite directions larger photon components already coupled that remain so even at cosmological dimensional units, as explained in the introduction above. We may never know. That way local or ‘non-local transfinite information’ input can gain empirical ‘de facto’ codon control of the transduction/translation genetic genotype machinery resulting in verifiable empirical phenotype results as observed in experimental labs as an induced re-arranging of the corresponding polynucleotide DNA helical structure and the subsequent RNA translation of environmental alterations in the corresponding functional enzyme production controlling phenotype expressions as briefly explained below in tracking the phenotype results from environmentally induced genotype alterations, e.g., ‘optogenetic’ tests.

It should be noted that the sophisticated mathematical axiomatic (logic) ‘ideal’ representation of the verifiable ‘real’ fact observation of an object/event in a derived wave or field conveyance regards the conveyance conceptualization as the fundamental notion for no convincing reason other than the symbolic/sentential representational elegance. The ‘ideal’ elegant map sophistication has unjustifiably become thereby more important than the ‘real’ empirical observable territory! Thus, the Wightman axiomatic quantum field theory (QFT) becomes thereby superior to the linear algebraic QFT even when both are abstract explanations of an ‘ideal’ field with infinite degrees of freedom for putative sub-Planckian quantum particles that appear in special circumstances.

As noted earlier, the less mathematically elaborated algebraic QFT abstraction originated from observables in the measurable local and the probable non-local environments whereas the more mathematically sophisticated axiomatic approach is limited to a conceptual elaboration of the field, a derived carrier model notion from classical local quantum physics. Furthermore, in the classical local quantum physics interpretation an observable is regarded as a property belonging to space-time region itself, i.e., Higgs Bosons ‘creating’ something out of a nothing vacuum? Is this a new mathematical ‘Genesis’ criticizing the ‘Delta Function’ as improper and laden with self derived contradictions as Von Neumann opined?

Fortunately, as it turns out, von Neumann was the proponent of a new ‘ideal’ framework based on Hilbert’s theory of operators and Dirac was the proponent of a ‘real’ framework of reference amenable to the rigors of testing of the local phenomenal events in the biophysical chemistry labs (e.g., optogenetic testing to cover the micro invisibilities) and the non-local events in the astronomy observatories covering the cosmological transfinite n-1 dimensional invisibilities.

Mathematically, the Dirac Delta Function is limited in scope when defined over the ‘real’ line, is zero everywhere except for one point at which it is infinite, and yields unity when integrated over the real line. Von Neumann promotes an alternative framework, which he characterizes as being “just as clear and unified, but without derived mathematical objections.” He emphasizes that his framework is not merely a refinement of Dirac’s; rather, it is a radically different framework that is based on Hilbert’s theory of operators-valued distributions. When objectively, dispassionately analyzed both arguments have their own merits but would be incomplete if either one claims exclusivity. If we had to choose only one it is clear that when pragmatics and rigor lead to the same conclusion, then, as I said above, pragmatics trumps rigor due to the resulting simplicity, efficiency, and increase in understanding made possible. Most important, however, is that it allows for unexpected new environmental circumstances as they get empirically detected. In other words, the TIQM model approach adopts the pragmatic orientation in the Lagrangian QFT (based on perturbation theory, Feynman’s path integrals and renormalization techniques). The “axiomatic” QFT refers specifically to the ‘ideal’ derived component of existential reality based on operator-valued mathematical distributions.

The undersigned author is not that familiar with the Weinberg ‘real’ pragmatic formulation that allegedly zeroes in human physical intuition and provides heuristics that are important when performing calculations; however, the mathematical theorists do not consider it mathematically rigorous enough and pay little attention to the fact that their proposed mathematical structure does not provide any techniques for connecting with familiar or new experimentally determined quantities. It is clear that these two approaches to QFT, the rigorous axiomatic and the Lagrangian pragmatic are rival research programs. I think we can get the best of both propositions that harmonizes with ongoing complex phenomenal reality as it evolves and I satisfy my curiosity as to their philosophical foundations. Then, because of my neurophilosophical interests in using the best available strategic tool when analyzing the mysterious struggle of our human species trans-generational survival against odds I compare the competing mathematical strategies and wonder why use the infinitesimals of classical quantum physics when you can use n-1 dimension transfinite parameters, more meaningful in the analysis of current existential reality.

Who, when leisurely meditating on the issues of life and human consciousness upon retirement, has not immediately reckon the relevance of particulate brain matter in reciprocal motion inside and outside a physical brain and the force(s) fueling the physical mass unit particles to exhibit dynamic reciprocal motion according to the well established laws of physics? It was all about analytically speculating how such motion carrying the invisible micro unit dimensional particle in a putative field (electric, magnetic or both) or wave conveyance can be explained best using the available mathematical logic metaphysics tools. Dirac’s pragmatic approach proposed the equivalence of matrix mechanics and wave or field mechanics by using the Delta Function, an improvement on the original Hilbert Space use by incorporating scalar metrics definable in terms of the mathematical scalar’s complex conjugate (a coupling/conjugation of a ‘real’ number + an ‘ideal’ imaginary number). That strike of genius makes possible to analogize such coupling with the still mysterious experimental non-local coupling of opposite spin particles (Φ is the topological anti-dual of Φx) at a distance when the source allegedly fired them in opposite space-time directions. The double slit experiments show their remaining entangled connectedness even when miles apart. As mentioned above, the stochastic nature of the physical particles as they travel in opposite directions until one of them ‘randomly’ selects one of various spin orientations available in the instrument after which the other particle mysteriously selects only the opposite complementary orientation, a ‘spooky’ action at a distance as relativity considers the result. I personally think they remained coupled when they left the source. Our human brain limits in both the perceptual and conceptual resolution capacities makes my speculation impossible to measure but neither is it justified to assume their original randomness. How else can we simultaneously measure the position of a unit mass particle ‘m’ being accelerated ‘a’ by a causally efficient force ‘f’ according to f=ma when the ‘ideal’ operators have no eigen values or eigen vectors? Here is the opportunity to calibrate the adequacy of competing mathematical physics ‘ideal’ algebras, one based on ‘real’ experimental observables related to bounded space-time locations like the finite double cone ‘twistor’ model where light traveling in opposite directions intersect at the vortex of the light cone or an ‘ideal’ algebra based on ‘real’ relativistic QFT interpretations? You be the judge, stay with the ‘ideal’ axiomatic version about how things should be (a la von Neumann) or transition to the ‘reality’ based version about how things probably are or predictably will be (a la Dirac), all things existentially relevant to human beings reality limitations being considered. Dirac’s Hilbert space assigns generalized eigen functions to unit particle mass ‘m’ position and their instantaneous velocity ‘v’ from measurable F= mv momentum operators resulting in the nuclear spectral theorem where Φ and Φx remain connected as mathematically derived by an algebraic QFT of observables in our ‘real’ 4-dimensional Minkowski space-time.

Another instance for comparing the axiomatic or Dirac models is found in the recently reported “Breakthrough Study Reveals Biological Basis for Sensory Processing Disorders in Kids.” As narrated, it constitutes the general explanation of the specific sensory processing disorders we clinically see in autism and the attention deficit hyperactivity disease (ADHD). It also underlines the importance of the human brain’s right hemisphere first impact with sensory input from a ‘real’ phenomenological environmental (external or body proper) input sources of new or familiar information before an adaptive response is either subconsciously implemented reflexly or after further analytical processing especially when processing unfamiliar sensory inputs. It has been observed in the brain clinical lab how the master control nerve networks of the frontal brain neocortex is continually processing information input arising originally from the right ® hemisphere initial effort to coordinate ongoing ‘real’ phenomenological activity from multiple sources such as Left (L) temporal and parietal lobe convergence of multisensory input and Left (L) frontal language semantic processing Broca’s area. The frontal neocortex brain is continually assessed of the whole spectrum of ongoing ‘real’ environmental biopsychosocial (BPS) relevant circumstances, from passive meditation to active social partying. When the new or familiar input is received at the Right hemisphere the master frontal neocortex analytical sorting of available response alternatives present in the neocortical pre motor attractor phase space working memory. This subconscious effort is subsequently followed by a conscious activation of the best adaptive motor choice neurohumoral response, all things considered. What is important to notice is how the brain synaptic ‘real’ time processing of information input precedes in time the freely conscious choice of the ‘ideal’ adaptive motor response. This choice is especially important in the presence of new/unfamiliar information sense-phenomenal input arrives in Right brain hemisphere. All of this complex analytical sorting immediately follows after a subconscious reflex motor response is released with priority for the overall biological preservation of the human species priority as previously published and discussed by me in various HiQ listings and fora. This detailed explanation hopefully supports my biased view about the importance of the ‘real’ preceding the ‘ideal’ solution. For more details see my Blog at:

When defending the human biological survival priority (BPS) premises as argued before the objections of some professional mathematical physics theorists, I state that by conditioning the sophistications of the axiomatic mathematical operations to conform the standard ‘real’ locality axioms e.g., isotony, locality, covariance, additivity, positive spectrum, etc., Dirac’s original model theory can be extended to reach the cosmologic invisibilities of transfinite non-local space-time manifolds beyond our local Minkowsky 4-dimensional manifold. For the reasons stated above about the human species brain perceptual and conceptual resolution limitations, I am not including an unjustifiable inclusion of a mysterious and unique invariant vacuum state as already noted. This is the basis on which I am still working on an all encompassing TOE model poem of human mesoscopic existential reality incorporating and modifying the original Cramer’s TIQM model and proposing the measurable details for the corroboration of a ‘Transactional dark baryonic reciprocal receptor DNA/RNA mediating a two way information transfer between unidentified transfinite space-time coordinates and a premotor cortical acceptor in the human brain neocortical attractor phase space as published.

The resulting set of algebras on Minkowski space-time that satisfy these axioms is referred to as the net of local algebras. It has been shown that special subsets of the net of local algebras — those corresponding to various types of unbounded space-time regions such as tubes, monotones (a tube that extends infinitely in one direction only), and wedges — are type-III factors.

The classical N-dimensional complex vector space representation of a complete human brain dynamics of mesoscopic existential reality as the linear algebraic combination of the observable ‘real’ plus the logically inferred ‘ideal’ components waits for experimental corroboration of the putative ‘reciprocal dark baryonic receptor’ in human brain networks.

There is nothing new when we focus on our complex, evolving ‘real’ lives with the objects and events in our quotidian 4-dimensional Minkowsky space-time physical environment. A reliable simplification can be achieved if the ‘ideal’ component is dimensionally considered a vector A in an N dimensional vector space over the field of complex numbers , symbolically stated as . The vector A is still conventionally represented by a linear combination or sum (from n=1 to infinity N) of basis vectors as represented in a column matrix from A1 to AN:

even though the coordinates and vectors are all complex-valued by including putative negative dimensions to explain the ‘transactions’ between local and non-local cosmological coordinates.

We can improve on the reliability of such model if we avoid immeasurable infinities (N) and settle for probable transfinite n-1d approximations. This way, A can be a vector in a complex Hilbert space. Some Dirac/Hilbert spaces, like , have local finite dimension (d), while others have a non-local infinite dimension (n) adjustable to a transfinite (n-1 d) dimension so it becomes related to local sensory objects/events. In an infinite-dimensional space, the column-vector representation of A above would be a list of infinitely many complex numbers from A1 to An as shown above. The symbol to the left, above, indicates that all n-dimensions are summed/integrated and may be represented as a row as seen below if represented as a ‘ket’ B. Finite dimensions are experimentally testable for local observable/environmental ‘real’ conditions while transfinite coordinate locations are more adequate for probable testable non-local ‘ideal’ environmental situations especially for their predictable potential of future catastrophic events threatening the human species transgenerational biological survival against ‘real’ adaptive odds.

or in a more easily generalized notation,

where the left ‘bra’ member is a ‘row’ and the right ‘ket’ member is a ‘column’ equivalent functionally linked. A bra next to a ket implies a linked/coupled matrix multiplication. (n x n). x

The bra row may be written in short as a ket row equivalent or in any convenient symbol, letter or word inside the ‘ket’ column space. By common practice ket columns are used for labeling energy eigenkets in quantum mechanics with a list of their quantum numbers. In quantum mechanics, a stationary state is an eigenvector of the Hamiltonian, implying the probability density associated with the wavefunction is independent of time.[1] and thus the assumed invariant bra component in my ‘ideal’ 9-dimensional model of a ‘complete’ TOE model of human reality. The ket corresponds to a quantum state with a single definite energy (instead of a quantum superposition of different energies). The quantum states are rays of vectors in the Dirac/Hilbert space, as c|ψ⟩ corresponds to the same state for any nonzero complex number c. It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket. It is very similar and equivalent to the concept of atomic orbital and molecular orbital in chemistry, with some slight differences as briefly explained below..

We use ‘quantum numbers’ to describe the micro spin values of conserved unit dimensional particulate matter quantities in the brain dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities, since quantum numbers are discrete sets of integers or half-integers. This is distinguished from classical mechanics where the values are time-dependent variables and can range continuously. While quantum numbers often describe specifically the energies of electrons in atoms, they can also apply to angular momentum, spin, etc. as variables. Any quantum system can have one or more quantum numbers; it is thus difficult to list all possible quantum numbers.[1]

An inner product (n x n) is a generalization of the dot product. The inner product of two vectors is a complex number because it contains values in both the ‘real’ number positive and an ‘ideal’ virtual number negative vector directional domain. A bra–ket notation x uses a specific notation for inner products. A bra next to a ket implies matrix multiplication. We can also use Dirac notation to represent inner or dot products.

One can also use the bra-ket notation to isolate different but related individualized sets of information content inside (brackets). . If we analyze ‘real’ local verifiable environmental conditions inside our three-dimensional (3-d coordinate axes x,y,z at right angles from each other), a complex 9-dimensional Euclidean space is represented, the bra for a static, time-independent invariant situation and the ket portion representing the variable portion of the same reality represented in a linear metrics. The bra-ket representation takes the general form where denotes the complex conjugate of . We can easily see the 9-dimensional ‘ideal’ space come to life as published in more detail before.

Another important special case to notice is the inner product of a vector with itself, which is the square of its norm (magnitude) the bra-ket symbolic notation takes the row form

The real importance of the bra–ket notation is allowing the formation of sets confined inside (brackets) as when multiplying two sets of either stationary or variable quantities. . This way both the bra and the ket are meaningful on their own, and can be used in other local or non-local contexts other than an inner or dot product representation. There is an obvious advantage about this ingenious way of representing the invariables and the variables, the local and the non-local, the ‘real’ and the ‘ideal’, the present as it verifiably is in the ‘real’ world and the probable future as it may be or the ‘ideal’ world should be as a goal, the immediate from the transcendental, the journey and the destination, the map and the territory. This clear distinction in the ongoing complex evolution of the human existential reality, confuses the lay and the experts, with subconscious or consciously deliberate results, but ultimately to protect human lives from eventual extinction after completing their life cycles.

Whatever the good, bad or indifferent intention to maintain our human biopsychosocial (BPS) integrity and keep track of the continuous relentless challenges in our environmental biosphere may be, we need an appropriate analytical logic tool allowing a continuous scrutiny of the present that is and the probable future that may or should be. The Dirac ‘real’ approach of focusing on the specific physical, verifiable observables using linear metrics represents to me the necessary frame of reference to metaphysically predict the probability of dangerous occurrences ultimately threatening human lives. The transactional interpretation of the quantum mechanics (TIQM) model, as modified, can accommodate relevant unsuspected occurrences. To follow is a brief account of the related sentential/symbolic linguistic representations in a linear algebra approach to vector calculus theory models.

The use of a scalar quantity metrics allows for the rigorous representation of intuitive geometrical notions such as the length of a vector or the angle between two vectors. They also provide the means of defining orthogonality between vectors of local environments, a scalar product of zero inner or dot product by generalizing our 3-d ‘real’ Euclidean spaces and also the probable ‘ideal’ vector spaces of any (possibly infinite) dimension, as are studied in functional analysis. Thus, there are finite-dimensional Dirac/Hilbert ‘real’ local spaces as fully elaborated in linear algebra, and there are n-infinite-dimensional separable ‘ideal’ non-local Dirac/Hilbert spaces that can be made structurally and functionally into n-1 dimensional isomorphic/equivalent to transfinite space . Modified Hilbert spaces are Dirac space equivalents and there is a unique Dirac space up to isomorphism for every cardinality of the orthonormal basis. See below the vector notation for the xy plane

Dirac’s bra-ket notation reliably makes possible a separation of the ‘real’ 4-d Minkowsky space-time describing what happens in the ‘real’ local dynamic human brain (as measured by fMRI and other techniques) from the ‘ideal’ non-local but probable and predictable n-1d transfinite space conditioned to the elusive proof that every bounded linear operator on a Dirac/Hilbert space has a proper invariant subspace. In my biased opinion some cases of this invariant subspace problem have already been proposed along with my own published speculative arguments. A reconciliation of quantum and relativistic aspects of human existential reality has proven to be insurmountable, especially the mathematical conundrum of describing the sizes of infinite sets using the transfinite cardinal numbers as briefly summarized now..

. The notion of using (brackets) is predicated on their ability to isolate as ‘sets’ related aspects of one same human existential ’reality’ some of which may be functionally linked (entangled) in the local or non-local environment. The cardinality concept was intuitively developed by Georg Cantor, also the originator of set theory, in 1874–1884. Cardinality can be used to compare two or more different finite sets such as e.g. the two sets {1,2,3} and {4,5,6} as having the same cardinality if combined and arranged to have a one-to-one correspondence reciprocal link between them {1->4, 2->5, 3->6}). When applied to infinite sets;[1] e.g. the set of natural numbers n = {0, 1, 2, 3, …}. now becoming denumerable (countably infinite) sets and this cardinal number is called , aleph-null also called transfinite cardinal numbers.

The magic of the TIQM Dirac’s genius when handling the ‘ideal’ non-local environmental coordinates in n-1 dimensional transfinite space is to be able to ‘see the unseen’ objects/events by humans and make probable predictions and preparation strategies to protect against their potentially harmful future causal effects on human lives on earth. As mentioned above, the notation demonstrates how a bra can become an equivalent ket by way of a conjugate transpose (Hermitian conjugate) of a bra into the corresponding ket and vice-versa: because if one starts with the bra row representation: and then perform a complex conjugation followed by a matrix transpose, one ends up with the equivalent ket column or vice verse as seen below:

Bras can become the linear operators on kets such as states whose wavefunctions are Dirac delta functions or infinite 2-d plane waves, pretty much like modified Hilbert spaces but more flexible in that it doesn’t require normalization of wave functions in quantum states that assigns a strictly positive length or size to each vector in a vector space, a goal for the possible future. Measurements are associated with linear operators called observables on the Dirac/Hilbert space of quantum states.

The dynamic environmentally induced interactive variations in the unit-dimensional aggregates, like time independent static invariants of the unit dimensional physical particule are also be described by linear operators on the Dirac/Hilbert space. It should be noted that ‘real’ sense-phenomenal ‘local’ and describable information input is taken care of by the classic Hilbert space but verifiable ‘non-local’ objects/events beyond human threshold of resolution capabilities can still be ‘ideally’ explained as probable by the inner product which by definition is linear in the first argument and bounded as derived comes from the Cauchy-Schwartz inequality. The functional integration of the ‘local’ and ‘non-local’ elements provides a much more complete description of human existential reality as argued.

In the specific case of our speculative arguments on how the human brain dynamically analyzes and processes reciprocal information inputs from environmental local (including body proper) and non-local transfinite sources we conveniently normalize or scale the quantum wave function to = +1 when involving vectors or linear operators. We find how bra-ket notations best explains the causal link between verifiable observables and the predictable micro spin coupling, as amply discussed elsewhere. The local (albeit of an infinite scope) verifiable objects/events are discrete and countable (quantized). The non-local (infinite) are continuous and non countable but may become verifiable on a quantum probability basis. ‘Real’ & local discrete with an infinite scope. ’Ideal’ & non-local continuous with an infinite scope.

At the risk of being repetitious, we need to emphasize that any ket |Ψ⟩ can define a complex scalar function of r, i.e., a wavefunction as where Ψ(r) on left is a mathematical function mapping any point in space acting on kets, by , e.g., the momentum operator p in space r relates to wave function as .The Dirac/Hilbert notation may just as well explain the evolution of the complex brain dynamics when adjusting to ongoing familiar or new objects/events representing a potential threat to the human species biological survival as it causally affects its biopsychosocial (BPS) parameters.

One may conveniently consider a time independent unit dimensional discrete, invariant physical mass particle at a given moment in real time, mesoscopic existential reality as simultaneously coexisting with the corresponding time dependent continuous variations of their particulate characteristics as they aggregate in the same moment in time. The invariant infinite is countable by definition and the variant infinite is uncountable beyond the threshold of phenomenological resolution. They represent the entire spectrum of infinite reality from the micro sub-Planckian to the macro cosmological manifolds. Since infinite (N dimensional) objects/events are not phenomenological measurable in principle, we have to invent a putative countable transfinite (n-1 dimensional) manifold of discourse. The rest of the arguments will focus on the evolutionary component of the unit whole complex aggregate structure and function as anticipated and hopefully predicted and confirmed as causally related by their justifiable and consistent verification as probable. A transition from the unreliable indeterminate invisibility domain to the probable and more reliable determinate invisibility now able to be tracked in its evolutionary path with the mathematical logic tool of linear metrics that has proven so successful in science, technology and philosophy. We need to define the causally efficient force (f) behind acceleration (a) of the unit dimensional mass (m) particle responsible for their physical aggregates variations in structure and function (f=ma) affecting our existential human reality in our 9-dimensional biosphere environment as published elsewhere