Gianfranco Basti • Pontifical Lateran University, Italy • basti@pul.it
Upshot: The “Info-Computational Constructivism” or “Info-Computationalism” (IC) of
Dodig-Crnkovic, as based on the notion of “Natural Information” and “Natural
Computation”, is able to embrace the whole domain of natural sciences, from fundamental physics, to biology, to cognitive and social neurosciences, the artificial simulations of such systems included. At the same time, IC, as an essential part of a constructivist approach, needs an integration with the logical, mathematical and physical evidences coming from the Quantum Field Theory (QFT), as fundamental physics of the emergence of “complex systems” in all the realms of natural sciences.
«1». For illustrating the main thesis of this commentary, I follow the two main lines of
Dodig-Crnkovic paper: the notions of natural information and computation , and their applications to natural and artificial cognitive systems. At the same time, I try to suggest how QFT, with its logic and its epistemology as well, can support, integrate, or even correct some IC notions, always clarifying them at the fundamental levels – logical, mathematical and physical.
A change of paradigm: from mathematical physics to physical mathematics
«2». After the first, introductory chapter, the second chapter (§§ 7-27) of the paper
“expounds the two basic concepts of IC” (§6), i.e., the notions of “natural information” and of “natural computation”, as far as they are based on the information approach to quantum physics, and hence distinguished from their usual notions, respectively, of symbol transmission (information), and of symbol manipulation (computation).
«3». There are several theoretical versions of the information theoretic approach to quantum physics. It is not important to discuss all of them here (for an updated list in
Quantum Mechanics (QM), see, for instance (Fields, 2012)), even though all can be reduced to essentially two.
«4». The first one is related to a classical “infinitistic” approach to the mathematical physics of information in QM. Typical of this approach is the notion of the unitary evolution of the wave function, with the connected, supposed infinite amount of information it “contains”, “made available” in different spatio-temporal cells via the mechanism of the “decoherence” of the wave function. Finally, essential for this approach is the necessity of supposing an external observer
(“information for whom?”
(Fields, 2012)) for the foundation of the notion and of the measure of information, reduced to the only Shannon’s, purely syntactic , measure and notion of information in
QM (Rovelli, 1996). Among the most prominent representatives of such an approach,
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we can quote the German physicist H. D. Zeh (Zeh, 2004; 2010) and the Swedish physicist at the Boston MIT, M. Tegmark (Tegmark, 2011).
«5». Dodig-Crnkovic refers essentially to QM, when she speaks about natural information/computation, intending at the same time with “natural computation” and/or with “nature as computation” (Zenil, 2013), “the morphological computing , i.e. computation governed by underlying physical laws, leading to change and growth of form” (§9). That is, physical/chemical/biological processes related to the progressive emergence of ever more complex natural structures of matter (from adrons and leptons to atoms, to molecules, to cells, tissues, organs, organisms, until social groups. See
§11).
«6». Now it is contradictory with the “constructivist” approach to suppose that the mathematical laws of nature “produce” the ever more complex structures characterizing our evolving universe. «Effects» are produced by «causes» not by «laws», which at last rule, and hence make pre-(retro-)dictable as to observers, the causal processes they rule.
Hence, it is not «kinetics», as defining the geometrical laws of mechanics, but
«dynamics», as defining the different types of forces, and of force fields, «causally» acting on material things (processes, particles, systems…), that produces the different form of «orders». They can be “quantified” through their proper “order parameters”, characterizing the emergence of ever more complex systems, in nature, at all the levels of matter organization – and self-organization. This holds also in quantum physics and explains epistemologically the difference between QM and QFT, this latter justifying the evolutionary emergence of the same mathematical laws of nature with the processes they rule. This is against the «eternity» of such laws, according to the dualistic Platonic ontology underlying the Newtonian paradigm of the beginning of modern science. To sum up, the change of paradigm related to the constructivist approach must be from the mathematical physics of the Newtonian approach, to the physical mathematics of contemporary constructivism.
«7». Indeed, the second approach, the emergent one today in quantum physics, is related to a “finitistic” approach to the physical mathematics of information, taken as a fundamental physical magnitude together with energy. It is related to the Quantum Field
Theory (QFT), because of the possibility it gives of spanning the microphysical, macrophysical, and even the cosmological realms, within one only quantum theoretical framework, differently from QM (Blasone, Jizba, & Vitiello, 2011). This is directly related to the fundamental role in quantum physics of the “third principle of thermodynamics”, on which the notion of “quantum vacuum” as a dynamic fundamental reality “containing causally” everything that exists, and might exist in the universe(s).
«8». The theoretical, core difference between QM and QFT can be thus essentially reduced to the criticism of the classical interpretation of the QFT as a “second quantization” as to the QM. In QFT, indeed, the classical Stone-Von Neumann theorem
(Von Neumann, 1955) does not hold. This theorem states that, for system with a finite number of degrees of freedom, which is always the case in QM, the representations of the canonical commutation relations are all unitarily equivalent to each other , so to justify the exclusive use of the syntactic notion and measure of information in QM.
«9». On the contrary, in QFT systems, the number of the degrees of freedom is not finite, “so that infinitely many unitarily inequivalent representations of the canonical commutation (bosons) and anti-commutation (fermions) relations exist”. Indeed, through the principle of the Spontaneous Symmetry Breaking (SSB) in the ground state, infinitely (not denumerable) many, quantum vacua conditions, compatible with the
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ground state, there exist. Moreover, this holds not only in the relativistic (microscopic) domain , but also it applies to non-relativistic many-body systems in condensed matter physics, i.e., in the macroscopic domain, and even on the cosmological scale (Blasone,
Jizba, & Vitiello, 2011, p. 18. 53-96).
«10». Indeed, starting from the discovery, during the 60’s of the last century, of the dynamically generated long-range correlations mediated by the Nambu-Goldstone bosons (Goldstone J. , 1961; Goldstone, Salam, & Weinberg, 1962), and hence of their role in the local gauge theory by the Higgs field, the discovery of these collective modes changed deeply the fundamental physics. Before all, it appears as an effective, alternative method to the classically Newtonian paradigm of the perturbation theory, and hence to its postulate of the asymptotic condition. Several phenomena related to what Dodig-Crnkovic, names as “morphological computing” can find in QFT, and in the SSB of quantum vacuum their fundamental explanatory, dynamic,framework. For instance, the thermal field theory; the phase transitions in a variety of problems at any scale; the process of defect formation during the process of non-equilibrium symmetry breaking in the phase transitions, characterized by an order parameter. All these phenomena and many others are fruitfully approachable by using the same principle of the “inequivalent representations” in QFT. For the same reason, and for recovering
Turing’s early suggestion, even though on a different basis (see below), I prefer to speak in IC about morphogenetic computing.
«11». The emerging picture for the naturalistic ontology is thus deeply different from the atomism of the Newtonian one, as much as the notion of mechanical vacuum is different from the notion of quantum vacuum. The ontological paradigm of physical system in QFT, indeed, is no longer the isolated particle in the mechanical vacuum (= atomism), of which Carnap’s Logical Atomism (LA) constitutes its formal ontology counterpart. In QFT no microscopic physical system is conceivable as completely isolated (closed), since it is always in interaction with the background fluctuations
(quantum vacuum condition, including in itself all the universes). In this sense, “QFT can be recognized as an intrinsically thermal quantum theory” (Blasone, Jizba, &
Vitiello, 2011, p. ix).
«12». Of course, because of the intrinsic character of the thermal bath, the whole QFT system can recover the classical Hamiltonian character, for the necessity of anyway satisfying the energy balance condition of each QFT (sub-)system with its thermal bath
(

E = 0). A condition mathematically formalized in QFT by the “algebra doubling” principle between an algebra and its co-algebra (Hopf algebras) (Vitiello, 2007).
«13». In this way, another fundamental character of IC, that since the beginning of
Dodig-Crnkovic paper (§1) is emphasized as a key-notion, has its proper fundamental dynamic explanation by QFT approach. It is, the IC principle, inspired by G. Bateson’s seminal idea of the “necessary unity between a biological (and hence cognitive) system and nature” (Bateson, 2002), according to which,
“for different type of agents, the same data input (…) will result in different information. (…) The same world for different agents appears differently” (§2)
This principle has in the QFT formalism of the “algebra doubling” for justifying the intrinsic character of the thermal bath in QFT systems its proper causal and mathematical explanation. It satisfies, however, a realistic approach in epistemology, when applied in cognitive neuroscience, as I explained elsewhere (Basti, 2013a; 2013b;
2014) and we see more briefly below.
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«14». In QFT context, the notion of non-symbolic, “morphogenetic computation”, having in A. M. Turing’s pioneering work on “morphogenesis” its proper ancestor
(Turing, 1952) (see §9), has the deepest justification at level of fundamental physics. In fact, it concerns the different physical interpretation of the Heisenberg uncertainty principle and of the related particle-wave duality. It is thus not casual that QFT can offers a much more effective dynamic explanation of the causal mechanism of
“morphogenesis” than the diffusive processes suggested by Turing and inspired to QM, that actually constitute the paradigm of the “molecular kinetics” in bio-chemistry (Basti,
2013a).
«15». Indeed, while in QM the Heisenberg uncertainty reads: h
2
Where x is the position p the momentum of the particle and h is the normalized Planck constant, in QFT the same relation reads:
   h
Where n is the number of quanta of the force field, and
 is the field phase. If (
 n = 0),

is undefined so that it makes sense to neglect the waveform aspect in favor of the individual, particle-like behavior. On the contrary if (
 
= 0), n is undefined because an extremely high number of quanta are oscillating together according to a well-defined phase, i.e., within a given coherence domain. In this way, it would be nonsensical to describe the phenomenon in terms of individual particle behavior, since the collective modes of the force field prevails.
«16». To sum up, in QM the uncertainty and hence the wave-particle duality relationship is between two representations, particle-like and wave-like, and accordingly the uncertainty is, respectively, on the momentum or on the position of the particle. In any case, the Schrödinger wave function in QM is not the expression of some dynamic entity like a force field, but simply the expression of different ways of measuring/representing the quantum phenomenon.
«17». On the contrary, in QFT the duality is between two dynamic entities : the fundamental force field and the associated quantum particles that are simply the quanta of the associated field, different for different types of particles. In such a way, the quantum entanglement does not imply any odd relationship between particles like in
QM, but simply it is an expression of the unitary character of a force field. In other terms, Schrödinger wave function of QM is only a rough statistical coverage of a finest structure of the dynamic, constructive nature of reality .
Wigner functions, quasi-probabilities and the notion of “natural information”
«18». Finally, QFT can offer a rigorous pathway for a quantitative definition of the IC notion and measurement of “natural information” (§7), as distinct from the syntactic notion and measurement of Shannon information used in QM, and that cannot justify in principle any constructive, causal approach to complexity.
«19». Indeed, because of the intrinsic openness to the quantum vacuum fluctuations of any QFT system, and because of the associated thermal bath, it is possible to define in
QFT, thermodynamic operators such as “entropy” and “free energy”, as well as the dynamic role they play in the different QFT systems. From the fundamental standpoint,
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the notion of dynamically generated long-range correlations, and the related notion of phase transition in terms of the dynamic constitution of different phase coherence domains, like as many SSB conditions of the quantum vacuum ground state, gives a new light to the Schrödinger notion of information as neghentropy in fundamental physics. “Neghentropy” is indeed “ free energy”, that is energy “properly channeled” toward the “right places” where it can perform “work”. The “free energy” is thus
“ ordered energy”. The notion of “coherence domain” and of Goldstone bosons of QFT gives at last a rigorous dynamic explanation to such a notion that both classical thermodynamics and QM are unable to offer!
«20». Indeed, at the relativistic microscopic level, a phase coherence propagate with a phase velocity of the order c
2
/ v, where c is the light velocity
1
, and v  c is the velocity of propagation of the (energy) signal. Therefore, the dynamic constitution of a coherence domain, by the SSB of the quantum vacuum (=long-distance correlations) in the ground state, corresponds to the definition of an optimal dynamic channeling for the successive propagation of the energy added to the system from the thermal bath. This is traveling only with velocity v  c, so that no violation of c is allowed, bringing the system out of the ground state (out of the equilibrium stability condition).
«21». All this emphasizes the logical and ontological relevance of the following passage, synthesizing the widespread applicability of QFT in the whole domain of fundamental physics, from cosmology, to the physics of condensed matter, living and neural systems included. This is particularly true nowadays, after that the empirical confirmation of the so-called “Higgs mechanism” in QFT, and hence of the Standard
Model in quantum physics, awarded with the Nobel Prize to P. Higgs and F. Englert.
Quantum dynamics underlies macroscopic systems exhibiting some kind of ordering, such as superconductors, ferromagnets or crystals. Even the large-scale structures in the Universe, as well as the ordering in the biological systems, appear to be the manifestation of the microscopic dynamics ruling the elementary components of these systems. Therefore, in our discussion of the spontaneous breakdown of symmetry and collective modes, we stress that one crucial achievement has been recognizing that quantum field dynamics is not confined to the microscopic world: crystals, ferromagnets, superconductors, etc. are macroscopic quantum systems. They are quantum systems not in the trivial sense that they are made by quantum components (like any physical system), but in the sense that their macroscopic properties, accounted for by the order parameter field, cannot be explained without recourse to the underlying quantum dynamics (Blasone, Jizba,
& Vitiello, 2011, p. ix).
«22». What is here to be emphasized is that in QFT the Wigner function (WF), on which the probabilities of the physical states are calculated, are deeply different from the Schrödinger wave function of QM, not only because the former, differently from the latter, is defined on the phase space of the system. Indeed, WF characterizes a physical entity – the force field – and not a conceptual representation of a physical particle uncertain behavior , related to a measure operation, like the wave function in QM. What is much more fundamental, for defining the notion and the measure of “natural information”, is that the WF uses the notion of quasi-probability (Cahill & Glauber,
1969), and not the notion of classical probability of the Kolomogorov axiomatic theory of probability (Kolmogorov, 1956).
«23». Indeed, the notion of quasi-probability, not only violates the third axiom of the classical theory, because negative probabilities are allowed. It also violates the fifth axiom, because regions integrated under given expectation values do not represent
1 The velocity of “morphogenesis” or “form (ordering) propagation” is thus instantaneous as the phenomenon of quantum entanglements makes evident. This gives new fundamental evidence to Wiener statement – recalled in the paper (§20) that “information is information, not matter or energy”. The velocity of propagation of energy is indeed v  c, as we see immediately.
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mutually exclusive states
– i.e., the separation of variables in such distributions is not fixed, but, as it is evident in all the phenomena of phase transition, can evolve dynamically . The number and the properties of the elements of the distribution are not the same at the beginning and at the end of the measured process!
«24». From the computability theory standpoint , this means that a physical system in
QFT, against the Turing Machine(TM) paradigm, is able to change dynamically “the basic symbols” of its computations
, since – according to the QFT uncertainty principle
– new collective behaviors can emerge from individual ones, or vice versa. In this way, this justifies the definition of the information associated with a Wigner distribution as a semantic (non-syntactic) information content , since the system is able to change dynamically the codes of its computations, so to suggest a new, semantic sense, of the term and of the notion of “computational dynamics” 2 .
«25» As I demonstrated elsewhere (Basti, 2014), in formal logic, an inference process , based on such a probability calculus, in which the basic symbols – and hence “truth”! – between the antecedent and the consequent are not conserved , cannot satisfy the logical connective of the material implication ( p
 q (1011)). On the contrary, it satisfies the logical connective of the converse implication ( p
 q (1101)), i.e., the connective of all the “form generation” or morphogenetic processes. However, it is also the logic of an inductive inference, not as a logic of the (empirical) corroboration of true propositions already given, as usual after Hume, Stuart-Mill and Carnap induction theory, but as the logic of the Aristotelian ( ontological) constitution of new true propositions. This means that the IC notion of “morphogenetic computation” is non-symbolic in the syntactic TM sense (see §32), because it is the computational dynamics process of new symbol dynamic generation, and not of the syntactic symbol manipulation.
«26».The semantic information in QFT computations – i.e., the operational counterpart of IC natural information - hence satisfies, the notion of “ contingent (not logical) truth
”, so to escape the Bar-Hillel & Carnap paradoxes (Carnap & Bar-Hillel, 1964), just like the “Strong Semantic Information” does in Floridi’s theory, with which a QFT computation shares the same Wigner probability distribution (Floridi, 2011). This suggests a more rigorous and effective way, from the physical, logical and computational standpoints, for deepening the relationship between the IC “natural information” notion and Floridi’s “structural information” notion (see §§1-19).
“Coherent states and coherent domains in the physics of the living matter”
«27». The title of this sub-session is between quotation marks because effectively is the title of a recent review paper of the Italian physicist, Giuseppe Vitiello, from the
University of Salerno (Vitiello, 2010).
“The great challenge that modern molecular biology is not yet able to answer, consists in the emerging of complex, macroscopic functional properties of the microscopic biochemical activity, ruled by the probabilistic laws of the molecular kinetics” (Vitiello, 2010, p. 14).
2 To avoid misunderstandings, the notion of “semantic” information and computation allowed by the QFT notion of “coherence domain constitution” has nothing to do with Traski’s T (Truth) function in sentential meta-logic: [( T ( p )=1):= (“ p ”  p )] (that is: <“the snow is white” is true, iff the snow is white>). In other terms, it is meaningless to interpret in quantum computability theory, a “coherence domain” in QFT as a sort of “meta-language” for deciding about the “truth” of quantum computations based on the QM principle of “decoherence”, as recently suggested by P. Zizzi (Zizzi, 2013). A “quantum coherence domain” and a “quantum decoherence” are two non-commensurable notions. The first one, is defined on a dynamic entity – the WF on the phase space of the dynamics –, the second one is defined on a statistical representation of the result of a measurement operation – the Schrödinger wave function.
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«28». The fourth chapter of Dodig-Crnkovic paper (§§ 39-51) is devoted to the study of the IC notion of “structural coupling” between the system and its environment, before all in living systems. Now, for using an expressive metaphor of another Italian physicist, E. Del Giudice, researcher in bio-physics and unfortunately recently deceased, the tremendous effort of the actual bio-molecular research of individuating, at cellular and sub-cellular level, all the microscopic structures of living matter is like to pretend to understand the social structure of a city by completing its phone directory.
From molecular kinetics to molecular dynamics and the notion of “emergence”
«29». So, the first successful step toward the comprehension of the self-organizing dynamic mechanisms of living systems, consisted in the extension of the formalism of
QFT in the study of coherent states of the condensed matter, also to the living matter.
For such an extension, scholars are following, before all, the original intuitions of H.
Frölich model (Frölich, 1968; Frölich, 1988), developed by the researches of another pioneer in this field, F. A. Popp, who first coined the evocative term of “biophotons” for denoting the electromagnetic emissions of the living matter oscillating molecules (Popp
& Yan, 2002; Yan, et al., 2005). In QFT, the elementary biological system corresponds to a macroscopic variable , identified with the density of electric polarization of the biomolecules and of the water molecules. The most interesting aspect of the Frölich model consists thus in the possibility that long-range coherence phenomena emerge as dynamic effects in the biological matter.
“This means that quantum dynamics generates among the elementary components (the electric dipoles of water and of biomolecules controlling the inter-molecular binding) large-scale correlations (“large” as to the characteristic dimensions of the components, and hence till some hundreds of micron): in such a way we have “in-phase”, i.e., coherent, motions and oscillations .
The elementary components are thus correlated, and assume a “collective” behavior characterizing their “whole” as such. We are faced, in such a way, with a transition from the microscopic scale of the elementary components and of their properties to the macroscopic scale characterized by coherence properties that can be no longer attributed to the single components, but to the system itself” (Vitiello, 2010, p. 14).
«30». To sum up, the basic hypothesis of QFT applied to living matter is that “at the dynamic fundamental level, the living matter can be considered as a set of electrical dipoles whose rotational symmetry is broken down ” (See (Vitiello, 2010, p. 16). For the mathematical apparatus of the theory, see (Del Giudice, Doglia, Milani, & Vitiello,
1983; Del Giudice, Doglia, Milani, & Vitiello, 1985; Del Giudice, Doglia, Milani, &
Vitiello, 1986; Del Giudice, Preparata, & Vitiello, 1988; Del Giudice & Vitiello,
2006)). In such a way, the ambiguous, qualitative notion of emergence has, in the context of QFT, a precise connotation, and it is quantitatively well defined. Namely, the emergence of macroscopic properties is given by the dynamic process determining the system ordering – i.e., the dynamic channeling of free energy for performing a suitable work, for which Maxwell invented his famous “demon”, definitely exorcized by QFT!
.
Of course, any emergence process is related also to a scale change, then, because the dynamic regime responsible of this change is of a quantum nature — since the elementary components have a quantum nature —, the resultant system, with its macroscopic properties, is thus a quantum macroscopic system (Vedral, 2010; 2012)
(see §19)
.
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Doubling of the Degrees of Freedom (DDF) in cognitive neuroscience 3
«31». Finally, the third chapter of Dodig-Crnkovic paper (§§ 28-38) is devoted to the application of IC main principles to the comprehension of natural and artificial cognitive systems. As Perrone and myself emphasized in several papers during the last twenty years (see (Basti & Perrone, 1995; 2001; 2002; Basti, 2009), and more recently
(Basti, 2013a; 2013b; 2014)), only the long-range correlations , which propagate in realtime along wide areas of the brain, and manifest themselves as “chaotic” complex oscillations, with their intrinsic fractal structure, can offer a valid dynamical explanation of an intentional mind act. They always involve, indeed, the simultaneous correlation among emotional, sensory and motor components, located in very far areas of the brain, as well as the entanglement with the outer environment (the thermal bath)
4
.
Such a coordination, that constitutes also the dynamic “texture” of long-term memory phenomena, cannot be explained in terms of the usual axon-synaptic networking, too slow and too limited in space and time, for giving a suitable explanation of this phenomenon.
«32». On the other hand, Walter J. Freeman and his collaborators, during more than forty years of experimental research by the Neurophysiology Lab at the Dept. of
Molecular and Cell Biology of the University of California at Berkeley, shared our same theoretical convictions. Moreover, they observed, measured and modeled this type of dynamic phenomena, in mammalian and human brains during intentional acts.
«33». The huge amount of such an experimental evidence found, during the last ten years, its proper physical-mathematical modeling in the dissipative QFT “algebra doubling” of Vitiello and his collaborators. In this way, this convergence justified the publication, during the last years, of several joint papers on these topics (see, for a synthesis, (Freeman & Vitiello, 2006; Freeman & Vitiello, 2008; Capolupo, et al., 2013;
Basti, 2013b)).
«34». Very recently, the amazing results – for execution velocity and storing capacity –, of the implementation in nanotechnology of a similar approach has been published in a large review paper (Subrata & Al., 2014), summarizing ten years of hard work. This paper does not quote the QFT approach to quantum computation, but it uses the same notions of “phase coherence domains” and of “frequency-fractal computing”, explicitly for simulating the underlying quantum dynamics of natural brains. This paper, kindly suggested to me by the same Dr. Dodig-Crnkovic, thus completes, from the artificial system standpoint, the work on real brains performed by Freeman and his collaborators.
Even more recently. M. Piattelli-Palmarini defined, like me, such an approach as a new paradigm in computer science and computer technology (Piattelli-Palmarini, 2014).
«35» To sum up (Vitiello, 2009), Freeman and his group used several advanced brain imaging techniques such as multi-electrode EEG, electro-corticograms (ECoG), and magneto-encephalogram (MEG) for studying what neurophysiologist generally consider as the background activity of the brain, often filtering it as “noise” with respect to the synaptic activity of neurons they are exclusively interested in. By studying these data
3 This part has been developed in other two my recent papers (Basti, 2013a; 2013b) and in a book, actually in print (Basti, 2014) to which I refer for further studies.
44 If such a “doubling” is the physical basis of consciousness, both in animals and humans, this means that this is no-longer the solipsistic “self-consciousness” of Descartes, Kant and of all the phenomenological tradition. “Consciousness” is the instantaneous “doubling” or “quantum entanglement” with such a limited “part” (effectively a “slice”) of reality with which my brain is in interaction, according to a realistic epistemology. If the “same world appears different for different agents” (§2) is because the difference slices their brains “cut”, but they are all “real”, just as different slices of the same cake.
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with computational tools of signal analysis to which physicists, differently from neurophysiologists, are acquainted, they discovered the massive presence of patterns of
AM/FM phase-locked oscillations . They are intermittently present in resting and/or awake subjects, as well as in the same subject actively engaged in cognitive tasks requiring interaction with the environment. In this way, we can describe them as features of the background activity of brains, modulated in amplitude and/or in frequency by the “active engagement” of a brain with its surround. These “wave packets” extend over coherence domains covering much of the hemisphere in rabbits and cats (Freeman W. J., 2004; Freeman W. J., 2004; Freeman W. J., 2005; Freeman W.
J., 2006), and regions of linear size of about 19 cm in human cortex (Freeman, Burke,
Holmes, & Vanhatalo, 2003), with near zero phase-dispersion (Freeman , Ga'al, &
Jornten, 2003). Synchronized oscillations of large scale neuron arrays in the

and
 ranges are observed by MEG imaging in the resting state and in the motor-task related states of the human brain (Freeman & Rogers, 2003).
Conclusion: toward a constructionist change of paradigm in modern science
«36». The novelty of the constructivist approach, with the support of IC and QFT approaches, in the contemporary epistemology and ontology of natural sciences, already synthesized in my slogan “from mathematical physics to physical mathematics”, has been described by P. Davies, in the following way:
“In a universe limited in resources and time – for example, in a universe subject to the Lloyd’s cosmic information bound - concepts such as real numbers, infinitely precise parameter values, differentiable functions and the unitary evolution of the wave function are a fiction: a useful fiction to be sure, but a fiction nevertheless” (Davies, 2010, p. 82).
In other terms, the change of paradigm consists in the turnaround of the dualistic
“Platonic” relationship, characterizing the Galilean-Newtonian beginning of the modern science:
Mathematics

Physical Laws

Information
Into the QFT one, much more powerful for its heuristic power:
Information

Mathematics

Physical Laws
The key-problems for a further research along this direction, as we have anticipated, but we cannot develop here, are all about the notion and measure of “natural information” in QFT, as far as it supposes:

The notion and measure of natural information, based on the notion and measure of
“quasi-probability”, typical of WF, and of a QFT approach to quantum computing like Subrata’s one, and hence,

The morphogenetic computational paradigm with its proper logic, and mathematics
– set theory (meta-mathematics) included.
This is an amazing, huge, constructivist, research project for several future works.
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