01 s-matrix and feynman diagrams to quantum brain approach

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NeuroQuantology | March 2009 | Vol 7 | Issue 1| Page 30-45Başar E., S-matrix and Feynman diagrams to quantum brain approach

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ARTICLE—

S-Matrix and Feynman Space-Time Diagrams to

Quantum Brain ApproachAn Extended Proposal

Erol BaşarAbstract

This report describes the importance of oscillations in brain function andintroduces metaphors to quantum dynamics. In order to analyze scatteringprocesses at the level of elementary particles Werner Heisenberg proposed theuse of the so-called S-Matrix to understand nuclear interactions by studyingingoing at outgoing particles. Later, Richard Feynman developed useful schemesin order to visualize processes of elementary particle interactions. In the presentreport a metaphor to Feynman Diagrams is developed in order to model the“Ongoing Brain Activity and Event Related Oscillations”. The responsesusceptibility of the brain shows a probabilistic causality similar to uncertainprocesses in elementary particle physics. A new grammar called Brain FeynmanDiagrams is proposed in order to show brain oscillatory responses as a morevisible construct in comparison to conventional compound brain potentials.

Key Words: brain, brain oscillations, quantum brain, Feynman diagrams, s-matrix

NeuroQuantology 2009; 1: 30-45

1. Conceptual models in neuroscience1

The most complex system in the universe thatwe can observe and perform measurements isthe brain. Similar to the physicists whoestablished general frameworks in the last fourcenturies to explain the vast extent of physical orastrophysical phenomena, “Brain Dynamics” hasto integrate several conceptual frameworks,including the quantum dynamics concept. Forthose of us doing brain research, models arewords that refer to concepts, theories, orconclusions that purpose to explain or illustratehow the whole brain or some part of itfunctions. In a way, a model is a form of

Corresponding author: Erol Başar

Address: Prof. Dr.Erol Başar, Brain Dynamics, Cognition and

Complex Systems Research Center, Istanbul Kultur University,Istanbul Turkey

Phone: +90 212 498 43 92Fax: +90 212 498 45 46

e-mail: [email protected]

explanation where the unknown is explainedthrough the known.

All living systems are made up of physical parts and these directly determine thebiological processes. Physical processes areclosely associated with psychophysiologicalprocesses. Two such physical processes pertainto hemodynamics (e.g. Hagen-Poiseuille’s) andto the propagation of electrical activity.Accordingly, scientists that study the brainfrequently use metaphors of physical sciences.Examples are the use of Feynman diagrams(Başar, 1998, 1999), strategies of quantummechanics, principles of nonlinear dynamics,entropy and synergetics. The laser light and thesynchrony of neurons in cognitive processeshave a common theoretical framework,although, from the viewpoint of theirmechanism, they are completely different; one isa physical event and the other a phenomenon of cognition.





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Parallel to the developments inneuroscience, a magnificent breakthrough tookplace in physical sciences at the beginning of the20th century with the works of Henri Poincarré,Albert Einstein and the Copenhagen School with

Niels Bohr, Werner Heisenberg, Max Born, andErwin Schrödinger. In parallel, important areasemerged and new concepts were formulated ininterdisciplinary sciences. These includedmolecular biology which evolved with the worksof Jacques Monod, “Cybernetics” which wasdeveloped by Norbert Wiener, “Synergetics” byHermann Haken, “Dissipative Structures” by IlyaPrigogine (1980), and “Catastrophe Theory” byRené Thom.

Parallel to developments in

Neuroscience in the first half of the 20

th

century,Ramon ỳ Cajal, Hans Berger, and LordSherrington created new methodological trendsin neurological sciences Psychology experienceda magnificent breakthrough with the works of Karl Lashley 1929, Donald Hebb 1949, tomention only a few. Again in the first half of the20th century, Friedrich von Hayek launched avery important theoretical frame but being aneconomist and thus mainly a theoretician, he didnot perform experiments to provide empirical

support for his theory. The study of the cognitiveprocesses within the realm of these recentlydeveloped areas have been largely facilitatedwith the use of fast computers, functionalmagnetic resonance imaging (fMRG),magnetoencephalography (MEG), and positronemission tomography (PET).

2. Synchronization in neural assemblies of the

brain and “whole brain” approaches

Synchronization in neurons plays an importantrole in brain function. What doessynchronization refer to in the brain? There aretwo classes of synchronized clocks in the brain.(1) Synchronous neural oscillators in a givenspecial brain structure (Eckhorn et al., 1988;Singer, 1989) (2) Large scale synchrony betweendistant structures (Von Stein and Sarnthein,2000; Varela et al, 2001; Başar, 2004; Bresslerand Tognoli, 2006).

The EEG consists of the activity of anensemble of generators producing oscillatoryactivity in several frequency ranges. These “brain

oscillators” are active usually in a random way.However, with application of sensory-cognitive

stimulation, these generators become coupledand synchronized; they start acting in a coherentway. Synchronization and enhancement of EEGactivity produce the “evoked” or “event-related”oscillations that are phase-locked to the

stimulus. Or they may be nonphase-locked tothe stimulus and thus have an “induced”character.

The compound event-related potential(ERP), which includes the responses of ensembles of neural populations, represents atransition in the brain from a disordered state toan ordered one. The morphology of the ERPwaveform is an outcome of the superposition of evoked/event-related oscillations. The “naturalfrequencies” of the brain which compose these

oscillations range from the delta band (0.5-3.5Hz) to theta (3.5-7 Hz), alpha (8-13 Hz) andgamma (30-70 Hz) bands. That the oscillationsare the basic responses of the brain nowadaysfinds strong support from a large number of neuroscientist who endeavor to the understandthe brain and the way it functions in cognition(Yordanova and Kolev, 1998; Freeman 2006).

3. Causality in quantum mechanics and its

parallel in brain dynamics

In 1943 Werner Heisenberg (see Heisenberg,1961) formulated the so-called “S-matrixTheory” of particle interactions. In this theory,Heisenberg (1961) tried to use only thoseconcepts with clear operational significance. Thetheory is concerned only with the outcomes of scattering or collision processes and not with thedetailed sequence of events taking place duringthe process. The basic quantities of interest inhigh-energy physics, and more particularly in thestudy of strong interactions are the collisions orthe scattering, and the amplitudes between setsof initial and final particles, the collection of which is called the S-Matrix (Barut, 1967;Feynman, 1962; Heisenberg, 1961). The basicassumption of the S-matrix formalism is that,before the interactions, each physical system,considered with “all its evolution,” can berepresented by a well-determined way Øin (orcollection of vectors) in a Hilbert space (Ηin) of “incoming” or “initial” free-particle states. Afterthe interactions, it can be represented by a well-determined way Øout in a Hilbert (Ηout) of “outgoing” or “final” free-particle states. The S-matrix should determine the cross-section for



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the production or annihilation of particles. The S-matrix can also be considered as a pure functionthat transforms all the momenta before collisionto the momenta after the collision (Barut, 1967).

Accordingly, ⟨ | S | ⟩ = ⟨ out | in ⟩.

In 1983, Başar proposed to model thebrain using the S-matrix in quantum mechanicswhere cross-sections of production of elementary particles are predicted, as ametaphor. In neural mechanisms quantalprocesses are not as yet observed; thisrepresents a parallel to uncertainty dynamics.This proposal was further developed within aframework of super-synergy in the brain (Başar,2006). The laws of quantum physics are of astatistical character. This means that they are

valid for not a single system but an aggregationof identical system; accordingly, they cannot beconfirmed by measurements on one individualbut by a series of repeated measurements fromthat individual. In Einstein’s words “Quantumphysics formulates laws that govern crowds andnot individuals; not properties but probabilitiesare described. Laws do not disclose the future of systems but govern the temporal changes inthese probabilities. As in quantum physics, lawson the brain in specifically cognitive processing

are valid for a great congregations of individualunits. They are valid not for single neurons butfor neural populations. What applies to quantummechanics also applies to the dynamics of chaotic systems. In systems not properties butprobabilities are described, laws disclose thechange of the probabilities over time; and theyare valid for congregations of units.

In contrast to modern physics andquantum dynamics, the approach to the study of the brain/body-mind requires more thanknowledge on parameters and dimensions. Wehave to include in this analysis multipleuncertainties or uncertain causalities. Thesemultiple causalities originate from (1) nonlinearproperties of the vegetative system (e.g.irregularities in biochemical transmitters, cardiacoutput, turbulences in the vascular system,respiratory apnea, nonlinear oscillatoryinteractions in peristalsis); (2) nonlinear behaviorof neuronal electricity (e.g. chaotic behavior of EEG); (3) genetic modulations; and additionally(4) nonlinear properties of physical processes inthe body.

Conceptual work and experimentaldesigns lead to essential steps in brain research.When designing an experiment, the EEG shouldnot be considered as a non-dynamic or a passivebackground during a cognitive process.

According to this new type of experimentaldesign, it appears that for the comprehension of event-related potentials (ERPs), a new set of parameters in our work on the paramount EEGmust be considered, which is tentatively named"brain indicators". The following is a provisionallist of indicators,1) The nonlinear correlation dimension whichinfluences the degree of order in thespontaneous activity;2) Phase angle of the brain waves and their

amplitude modulation envelopes (Bullock andBaşar, 1988), rms3) Values of various EEG frequencies,4) Coherence in space and, coherence in time foreach frequency.

Using these indicators now it is possibleto move on to a new type of file, named the"brain state matrix". Earlier publications,attempted to create a picture of this matrix bystating that the brain state could be described byseveral measures of instantaneously defined EEG

properties, outlined above as indicators, during agiven short period of approx. 0.05-1 s (Başar,1983a, b). The knowledge of parameters in sucha matrix enables the experimenter to roughlypredict the shape, amplitude, and frequencycontent of the ERP. The amplitude of an evokedresponse (evoked potential, EP) often stronglydepends on the amplitude of the ongoingactivity (Rahn and Başar, 1993a, b). Theseexperiments showed that, if the subject's EEG isalready in a coherent state, the physical sensorystimulation does not create a new, morecoherent state. There is no EP to a physicalstimulus in such a coherent state of the brain.

The results can be extended withnonlinear descriptors by stating that, if thedimension of the EEG is low, the transition of theEEG to a lower dimension is not possible ordifficult. In other words, as explained earlier, if the brain's electrical activity shows a lowentropy state (high-order), the transition to alower entropy state is difficult (Başar, 1980). Theamplitude and the shape of the outgoingresponse or of the outgoing activity (evokedactivity) are inversely correlated with the





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ongoing activity. The outgoing response is afunction of the ongoing activity. The expressionof ongoing and outgoing activities is used here inreference to an important analogy in elementaryparticle physics. The S-matrix introduced by

Heisenberg was applied to elementary particlephysics and to the nuclear reactions byconsidering ongoing and outgoing waves.

This basic knowledge will be aprerequisite to build Feynman diagrams shownin figures 2-7.

Figure 1. A Feynman diagram showing the propagation of arenormalized electron from A to B. In this diagram, timeincreases to the right.)

4. Feynman Diagrams

The Feynman diagrams that are used inelementary particle physics have beendeveloped in order to describe and predict the

electromagnetic processes, whereby electronsand photons interact. This can give rise todrawings that appear complicated such as theone in Fig. 1. In this Feynman diagram, a singleelectron enters on the left at A, and then a singleelectron emerges on the right at B. To a non-physicist it looks as though one electron hasdirectly moved from A to B. The interactions are,indeed, complicated; there is a type of "grammar" to these diagrams, which allows onlycertain configurations to be realized in nature.

This grammar results from the basic laws of physics, such as conservation of energy andconservation of electric charge. Particlephysicists have found that this complexity shouldbe handled in a reduced form, and in order tounderstand the behavior of electrons andphotons, approximations are used which neglectall but simple Feynman diagrams. By consideringroughly the simple hundred diagrams for certainprocesses, physicists have been able to predictimportant relations precisely.

Our research group proposed (that byintroducing the Brain State Matrix which iscomposed of several EEG indicators, it would bepossible to predict several brain reactions whichare analyzed as sensory evoked and event-

related potentials Başar 1983, 1988, 1998; Başarand Güntekin 2007). In brain research we oftendescribe the evoked potentials as a transitionfrom an unexcited brain state to an excited one.However, the brain waves are often excited dueto as yet hidden sources. Thus, the EEG canoften be considered as superposition of internally evoked potentials stemming fromunknown sources within the CNS (Başar 1988).Accordingly, transitions of the brain waves whichoccur without defined external stimulation

should also be considered as an active transitionand approached with the method of Feynmandiagrams. For the time being, however, thesimpler case of transitions following definedsensory stimulation has been chosen.

As it was shown in several publications(Başar 1980, 1983, 1988b; Başar et al. 1987),there are several allowed and unallowedtransitions of the EEG following stimulation. Forexample, if a subject emits abundant highamplitude alpha waves prior to application of a

sensory stimulation, usually no enhancement of that frequency is seen in the encounteredresponse. On the contrary, we then observe analpha blocking. The same rule is true also for 40Hz activity (Başar et al. 1987)

Further, if the overall coherence betweenvarious structures of the brain is high, again theenhancement of EEG activity is low or vanishes.Additionally, there exist couplings betweenfrequency components and also betweenamplitudes of various EEG components amongdifferent brain structures - for example, there isimportant coupling or similarity between 10 Hzactivities of the reticular formation and thalamusas has been previously been described (Başar1983a,b; see also Fig.2). By starting with a brainstate matrix and developing new rules step bystep (which should be experimentally evidentand would allow the facilitation and prohibitionof several transitions of the brain rhythms) itcould be possible to predict a large number of brain reactions that we analyze as the brain'scompound response potentials.





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frequency components and also betweenamplitudes of various EEG components amongdifferent brain structures exists, for example,there is an important coupling or similaritybetween 10 Hz activities of the reticular

formation and the thalamus (Başar, 1983a, b).Starting with a brain state matrix and developingnew rules step by step (which should beexperimentally evident and allow the facilitationand prohibition of several transitions of thebrain rhythms) it could be possible to predict alarge number of brain reactions that areanalyzed as the brain's compound responsepotentials.

In accordance, this way of thinkingmaintains that the EEG is not only an activity

that reflects some brain state, but also anactivity that anticipates reactive mechanismsand controls the response to stimulation.Accordingly, the introduction of this new type of "grammar" may also serve to assist in the designof experiments that will contribute to theunderstanding of a large number of cognitiveprocesses. It is further suggested that the brainobeys the same dynamic laws or rules, whichgovern the control of the brain's excitability asdescribed in "Quantum Mechanics". If there is an

excited state in an atom it is very difficult toincrease the energy output of the same atom.The brain behaves similarly, if a neuronalpopulation is in an excited state, cognitive orsensory stimulation cannot excite thispopulation any further. Some rhythms orpatterns in natural phenomena can be explainedand/or predicted by the powerful Feynmandiagrams.

4.1 Brain-Body Feynman Diagrams

What will be analyzed with Brain-Body FeynmanDiagrams? The aim is to try to insert the entirehistory of the EEG activity combined withphysiological settings prior to stimulation. As ourmemory is strongly influenced by physiologicalsettings as blood pressure, respiratory cyclesalso with autonomous system. Since all functionsof the brain are mostly in concerted action, thesame chain of reasoning is also valid forintegrative brain functions. If theelectrophysiological responses of the braindepend on changes of cardiovascular input, i.e.blood pressure, respiratory cycles, the level of cholinergic or adrenalin secretion, the Feynman

diagrams that predict the brain responses mustalso incorporate these physiological parameters.These physiological parameters are extendedand/ or also influenced by emotional states. Theemotional states can directly influence brain

responses, however, emotional states can affectcardiovascular responsiveness, and this, in turn,may modify the electrical brain response. Figure3 illustrates several factors that will be evaluatedin order to build the Brain Feynman Diagrams.The most adequate way to start is to considerseparate simple “Feynman Diagrams” todescribe all these different psychophysiologicalevents. A partial Feynman diagram could bedeveloped to show the influence of emotionsdirectly on the brain or a Feynman diagram

developed to act on the cardiac output and alsoon the influences of the cardiac output to theBrain. Then the final Feynman diagram includingall histories or physiological settings will beconstituted from a chain of partial Feynmandiagrams as a large tree with several branches.

4.2 Factors Shaping the Computing of Brain-

Body Feynman Diagrams

A Feynman diagram is a bookkeeping device forperforming calculations in quantum field theory.

In physics, the interaction between two particlesis quantified by the cross section correspondingto their collision. This cross section, or moreprecisely the corresponding time evolutionoperator, propagator or S matrix, can beexplained as a sum of terms. What needs to beconsidered in the interaction of stimulationswith the neural populations in the Brain? As afirst step here is a short story in time.

A sensory or cognitive stimulation to thebrain evokes or induces oscillations. For thegeneral bookkeeping the following processes areto be considered; (1) Activation of a given brainarea with superposition of oscillations in alpha,beta, gamma theta, delta. (2) Phase re-orderingand phase-locking of the ongoing activity. (3)The oscillatory response is topology dependent.(4) In several frequencies there are blockings orenhancements depending on the level of pre-stimulus activity. (5) Coherences between thestudied structures have an influence on theresponse. (6) The age factor plays an importantrole (shifting of alpha frequency from occipital tofrontal areas. (7) Genetic factors play animportant role in oscillatory responses (Porjesz





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and Begleiter, 1996, 2003; Porjesz et al.1998,2002). (8) Neurological test scores (Doppelmayret al., 2005; Karakaş et al., 2003; Klimesch et al.,1997). (9) Health conditions, pathologies asAlzheimer’s disease or Multiple Sclerosis (Tass

and Hauptmann, 2007; Başar- Eroğlu et al.; 2007,Yener et al., 2007). (10) Sleep stages and statesof consciousness. (11) Factors of vegetativesystem related to high or low pressure levels andrespiratory cycles. (12) Emotional input to thebrain. (13) Anatomical information usingmagnetic resonance imaging (MRI). (14) Maleand Female gender differences.

Figure 3. Explanation of physiological settings andpathologies influencing brain responsiveness. The samefactors of which empirical weights are known will also beused in constructing Feynman Diagrams (Modified fromBaşar and Güntekin 2007).

These are some examples forbookkeeping or for describing the evolution of signals that need to be considered for theapplication of the Brain Feynman Diagrams.

There are several levels. The S-matrix is a matrixwith multiple dimensions considering theaccumulated rules depending on the parametersdescribed above. Furthermore, all these rulesdepend on the topology of brain structures

studied. Accordingly, weighting factors need tobe introduced for the responsiveness or thebrain response susceptibility.

4.3 How to develop a Grammar for Brain

Feynman Diagrams?

In this section, Brain Feynman diagrams will beorganized in order to show how to manifestBrain responses with diagrams including all timestories.

In Figure 4 alpha responses to light and

auditory stimulation are illustrated for fourtopologically different areas. Light stimulationdoes not evoke any significant alpha responsesat F4 and T4 locations, whereas light stimulationand auditory stimulation evoke alpha responsesat O2 and T4 locations. Similarly, the child brainneither shows spontaneous nor evoked alphaactivity until the age of three years (Fig 5). Thesefew simple analyzed diagrams can already giveimportant insight into a comparative analysis.These types of simple rules can be extended for

functional and comparative studies includingdiverse types of brain states, as well ascoherence measures as descriptors of connectivity or correlation dimensions asdescriptors of brain states. The building of morecomplex Brain Feynman diagrams will, mostprobably, facilitate the global analysis of electrophysiological events and enable researchscientists to gain insights into brain functionsthat are more difficult to understand usingdetailed analytic research.

In the following some more examples onBrain Feynman Diagrams for simple cases(figures 5, 6, 7). The physiological explanationsare described in the legends of the illustrations.In future, such diagram will evolve and presentmore complex neural processes.





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Figure 4. In the right temporal location the alpha responses in T4 location are high to the light stimulation and lower toauditory stimulation. In frontal location almost no alpha responses are recorded (Modified from Ba şar and Güntekin 2007).

Figure 5. In the child brain there are no alpha responses. This fact is reflected in the Feynman Diagrams. (According to theresults of Kolev et al. 1994 and Başar Eroğlu et al.1994)





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There are several reports related to eventrelated oscillations by using auditory oddballparadigm for middle aged and elder subjects.However we did not encounter any study relatedto event related oscillations of children below

the age of three years. We think that aconceptual preparation of Brain Feynmandiagrams for three years of children can providea god example for the utility of brain FeynmanDiagrams. In figure 5 an attempt is made for theprediction of Feynman diagrams of the threeyears of child brain. At the right side of theillustration two possibilities of event relatedoscillations upon target signals in auditoryoddball paradigm is hypothetically shown. Fromearlier studies (Başar et al. 1997) we know that

children that would not react with alphaoscillatory responses. We do not know whetherchildren are able to pay focused attention to

target signals. When we assume that childrencould learn the paradigm and perform increasedattention to target signals then most possiblyhigh amplitude delta and theta responses couldbe measured. However, in the Feynman diagram

“A” we did not present an alpha responsetogether with delta and theta responses. In thesecond possibility a Feynman diagram isillustrated by showing no delta, theta and alpharesponses. What will be the practicaladvantageous by trying to develop suchdiagrams? Before such an experiment is plannedthe analyzer should consider that no alpharesponses would be recorded and in search of interpretations, in search of pathologicaldeviations this main property of alpha

knowledge can be an important step to orientthe research scientist.

Figure 6A. In target signals higher delta and theta responses are recorded during the oddball paradigm. (According to theresults of Başar-Eroğlu et al., 2001)





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Figure 6B. Illustrates the responses to visual non-target stimulation during an oddball paradigm. The delta responses areless ample in comparison to target stimuli.

Figure 7. In healthy subjects high delta responses are recorded during an oddballparadigm. Alzheimer patients do not show high amplitude delta responses to visualresponses during an oddball paradigm. This fact is reflected in Feynmandiagram.(According to the results of Yener et al. 2008). Compare also with Figure 6.

Figure 7 illustrates Feynman diagramsfor Alzheimer patients that are stimulated withlight signal during an oddball paradigm. Note thechanges in healthy subjects (control) andmedicated Alzheimer patients. The comparison

of Figures 4 to Figure 7 clearly shows that thedifferences in brain responses can beschematized in a systematic and compact way,thus providing fast interpretations and planningof new measurements.





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4.4 How to compute Brain-Body Feynman

Diagrams

It is more appropriate to use the term "quantumcomputing" to refer to any use of the effectsconsidered "quantum mechanical" rather than

"classical." Nearly all of the interest, today, is in"quantum parallelism". As a metaphor in braintheory the term uncertainty of brain reactions isused instead of the expression “quantumparallelism”. According to David Deutsch (2003)(this “parallelism” can be understood as anextension of the Feynman path integralapproach to quantum mechanics, in which theprobability of a physical system for transitionfrom a state A to state B can be statisticallymodeled. In quantum computing, the computer

evolves along all possible paths from its initialstate, and the probability of any particular finalstate will be given by a sum of all paths that leadto that state. Another way of describing this is tosay that the computer evolves along anexponentially growing (multiplying with eachstep) number of paths, and in the final step allthese parallel computations interfere with eachother to determine the probabilities of variousoutcomes. Feynman suggested the possiblerelationship between quantum computing and

nanotechnology as early as 1959. He alsopointed out the fact that quantum computing ispotentially more powerful than classicalcomputing, since classical computers cannotsimulate quantum mechanics efficiently, whilequantum computers should be able to.

In the previous section the approximatesteps were described in order to put togetherseveral experimental facts to predict brainresponses by considering all histories and theevolution of processes in the whole brain priorto stimulation. However, the other relevantprocesses of vegetative and biochemicalprocesses in the whole body have beendescribed, that can or may strongly influence thebrain responsiveness (see Figure 4, 7 and 8). Aswill also be considered in the following sections,the computation or predictions of brainresponses with Feynman Diagrams is difficult.Therefore, powerful super computers (quantumcomputers) should be used to evaluate allpossible combinations and interactions in thebrain and CNS, and the following step isproposed; first, taking account of all possibleprocesses in the brain and attempt to roughly

predict the brain responses of a given subjectdepending on the age, pathological states andpossibly emotional behavior. After doing this thecorrections can be added to the computationsstemming from changes in vegetative

parameters; such as the effect of the increase ordecrease of the arterial pressure on the alpha,theta or gamma responses; how diseases in thegastrointestinal systems accompanied byincreased or decreased peristalsis effect themeasured responses; the influence of changes inthe balance in the lymphatic system on thebrain’s responsiveness? Most of the changes inbrain oscillatory responses upon thesephysiological changes cannot be found in theneurophysiological literature. However, by

continuing to use the brain oscillatoryapproaches it will only be a matter of timebefore sufficient empirical results are collectedto describe modifications of brain oscillatoryresponses in all these non-physiological orpathological changes. An illustration, which mayopen the way for a Feynman presentation ispresented in Figure 3.

4.5 Possible Advantages of “Brain-Body

Feynman” Diagrams

The simple brain Feynman diagrams that havebeen presented are easy to understand.However, in the study of brain responses it ispossible to progressively build hundreds of suchgrammar rules. Comparative studies and steps tocreate archives for all functions can be extremelycomplex and difficult. However, a simple visualanalysis of such simple Feynman Diagrams canallow the brain investigator to predict morecomplicated functions by an analysis of reduction. For example, the frontal brain alpharesponses usually have low amplitudes and showno phase locking. On the contrary frontal thetaresponses have large amplitudes and strongphase locking. If in a brain response a greatdeviation from the simpler Feynman Diagrams isobserved the new added values or differencescould make a fast understanding of brainfunction possible and help to interpret newresults.

The aim here, is not to survey a vastliterature on the computation of FeynmanDiagrams, however the aim is to indicate therelevance of Feynman Diagrams. Furthermore,Feynman Diagrams could also be considered as a





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schematic approach parallel to the Heisenberg S-Matrix. According to the literature theevaluation of Feynman diagrams can beperformed by Monte-Carlo calculations, which isa kind of experimental mathematics. If, in future,

it would be possible to use quantum computers,the probabilistic nature of quantum devices canalso be considered to solve brain-body FeynmanDiagrams. Then it would be appropriate toassess whether the Monte Carlo method wouldbe adequate for the modeling of brain-processes. When considering the schematicillustration of the Feynman diagrams, theproblem of multiple causalities appears (see alsoFigure 3). The prediction of the occurrence of abrain response would depend on various types

of initial conditions, meaning initial brain statesand a great number of factors from body andenvironment converging as multiple inputs tothe brain.

A great number of initial conditions haveto be considered for brain processes. Duringsignal processing of the brain, several hiddenvariables and/ or parameters influence the brainprocessing, and accordingly the manifestations

of oscillatory activity. This means that severalmain processes and sub-processes are in playand several links have to be considered. Thesemultiple processes, which occur in series and inparallel, can be computed as multiple trials byusing random trials generated by a computer,billions of times (see Figure 8). In this way, thebrain reactions could be described and orpredicted within limits of probabilistic windows.This is the essence of the Monte Carlo methodused mainly in order to describe life histories of

neutrons in nuclear reactions. Therefore, theMonte Carlo method seems to be a suitableapproach for modeling brain-processes.

Figure 8. For computation of brain Feynman diagrams several factorsinfluencing brain responsiveness will be embedded in fast computers inparallel or series. Evaluation of large statistics, also including the MonteCarlo method could be used for predictions of brain responses in subjects

(Modified from Başar and Güntekin 2007).





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This illustration provides above for developing of most complete Feynman Diagrams consideringall possible time stories and biological levels andstimulation condition.

5. Does the Language of “The Brain- Body-

Mind” Need the Evolution of a New Discipline?

Parallelism to “Quantum Theory”, “String

Theories” and Chaos?

In several sections of the present manuscriptand in various papers a number of experimentalapproaches for the analysis of experimentalresults were supported by main idea of frameworks initiated by Norbert Wiener, TheCopenhagen School, Hermann Haken, Donald

Hebb, Charles Darwin, and also of F.A. vonHayek. Much has been earned from the work of outstanding mathematicians, system scientists,and theoretical physicists; this has giving rise tothe multidisciplinary framework presented inthis book and to the development of theoscillatory brain dynamics. However, a higherorder way of thinking is that all these pathwayopening scientists were from a mathematicalbackground and tried to describe rules of thebrain and mechanisms of thinking. Although

enormous credit must be given to thedevelopments by Cybernetics, Dissipative

Structures, Catastrophe Theory, Synergetics,there is a strong argument for the necessity of direct knowledge from the brain (i.e. empiricalresults from the brain) in order to be able tounderstand the “principia” of brain working andthe “ principia of thinking” . This means, learningfrom experimental results of the brain and fromall that learning, establishing a theory containinga series of rules on brain functioning (Başar,2006). When trying to understand the brain andthe goal is to develop a physical-physiologicaland philosophical construct, the starting point isnot with mathematics to derive definitions; firstthe " principia mathematica" of the brain isdecoded. The hypothesis is that this way of

thinking is an adequate one. The human brain isthe most complex structure in the universeknown to us. Accordingly, a framework, whichcould enable an understanding of the brain,should be derived only from the language of thebrain. Considering the descriptions in thepresent essay three important features shouldbe underlined; (1) the brain is a learning system,its ability to react to external or internal inputschanges with time. The reactions of the learningbrain can be completely different compared to

the reactions of the emotional brain. (2) Thebrain’s reactions change during evolution of





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species. (3) In the maturing brain from the earlydays of childhood to the adult brain, responsesalso change. (4) Creativity and related states of intuition cannot be explained by the earlierframeworks developed by mathematicians and

theoretical physicists. By the application of oscillatory brain dynamics an area is approachedin which an attempt can be made to measureall the four features mentioned above. It isimportant to emphasize that “The Nebulous

Cartesian System” is a construct, a work inprogress; in turn, this work may open new waysto deepen the understanding of brain functionand possibly, the metaphysics of the brain. Thisis in keeping with the opinion of John vonNeumann (1966), who stated that: “[…] logics

and mathematics in the central nervous system,when viewed as languages, must be structurally

essentially different from those languages to

which our common experience refers”.

John Carew Eccles suggested in 1986that the synapses in the cortex may respond in aprobabilistic manner to neural excitation; aprobability that, given the small dimension of synapses, could be governed by quantumuncertainty. Further, Hameroff and Penrose(1996) developed elegant working hypotheses

that take into account the possible quantumnature of signal transmission at the micro-level,considering probable processes at the synaptic

level. Such hypotheses will probably be moreprofoundly examined in future and will needexperimental extensions. On the contrary,quantum like parallelisms of Başar that was firstinitiated in 1980 with quantum like resonances

and in 1983 with the s-matrix metaphor has lessambitious goals by describing quantum-likeprobabilistic behavior of brain wave responses inobserved brain reactions upon sensory-cognitiveexcitation. The quantum probabilistic behavior isnot only found at the micro-level (synaptic level)and or in single level, but also chaotic dynamicsresulting from multiple processes are also crucialentities. In pure physics, the dualism betweenwave and particles has a quasi-metaphysical rolehowever; the brain is much more complex: The

brain reaction susceptibility has multiplecausalities. This can simply be called “Brain’sMultiplicities” and these will have to be dealtwith in parallel.

It is hoped that the proposals in thiswork may motivate a number of youngneuroscientists to jointly evaluate results fromvarious types of measurements and toaccumulate them in the S-Matrix and in series of Feynman diagrams.

How far will this go?

Time will tell.





44

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01 s-matrix and feynman diagrams to quantum brain approach

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