A breakthrough in neuroscience needs a “Nebulous Cartesian System

siology 64 (2007) 108–122www.elsevier.com/locate/ijpsycho

International Journal of Psychophy

A breakthrough in neuroscience needs a “Nebulous Cartesian System”Oscillations, quantum dynamics and chaos in the brain and

vegetative system

Erol Başar a,⁎, Bahar Güntekin a,b

a Istanbul Kültür University, Faculty of Science and Letters, Turkeyb TÜBITAK BAYG, Ankara, Turkey

Received 20 May 2006; received in revised form 24 June 2006; accepted 13 July 2006Available online 17 October 2006

Abstract

The Cartesian System is a fundamental conceptual and analytical framework related and interwoven with the concept and applications ofNewtonian Dynamics. In order to analyze quantum processes physicist moved to a Probabilistic Cartesian System in which the causalityprinciple became a probabilistic one. This means the trajectories of particles (obeying quantum rules) can be described only with the concept ofcloudy wave packets.

The approach to the brain–body–mind problem requires more than the prerequisite of modern physics and quantum dynamics. In the analysis ofthe brain–body–mind construct we have to include uncertain causalities and consequently multiple uncertain causalities. These multiplecausalities originate from (1) nonlinear properties of the vegetative system (e.g. irregularities in biochemical transmitters, cardiac output, turbulencesin the vascular system, respiratory apnea, nonlinear oscillatory interactions in peristalsis); (2) nonlinear behavior of the neuronal electricity (e.g.chaotic behavior measured by EEG), (3) genetic modulations, and (4) additional to these physiological entities nonlinear properties of physicalprocesses in the body. The brain shows deterministic chaos with a correlation dimension of approx. D2=6, the smooth muscles approx. D2=3.

According to these facts we propose a hyper-probabilistic approach or a hyper-probabilistic Cartesian System to describe and analyze theprocesses in the brain–body–mind system.

If we add aspects as our sentiments, emotions and creativity to this construct, better said to this already hyper-probabilistic construct, this “NewCartesian System” is more than hyper-probabilistic, it is a nebulous system, we can predict the future only in a nebulous way; however, despite thischain of reasoning we can still provide predictions on brain–body–mind incorporations. We tentatively assume that the processes or mechanismsof the brain–body–mind system can be analyzed and predicted similar to the metaphor of “finding the walking path in a cloudy or foggy day”.This is meant by stating “The Nebulous Cartesian System” (NCS).

Descartes, at his time undertaking his genius step, did not possess the knowledge of today's physiology and modern physics; we think that thetime has come to consider such a New Cartesian System. To deal with this, we propose the utilization of the Heisenberg S-Matrix and a modifiedversion of the Feynman Diagrams which we call “Brain Feynman Diagrams”. Another metaphor to consider within the oscillatory approach of theNCS is the “string theory”. We also emphasize that fundamental steps should be undertaken in order to create the own dynamical framework of thebrain–body–mind incorporation; suggestions or metaphors from physics and mathematics are useful; however, the grammar of the brains intrinsiclanguage must be understood with the help of a new biologically founded, adaptive-probabilistic Cartesian system. This new Cartesian Systemwill undergo mutations and transcend to the philosophy of Henri Bergson in parallel to the Evolution theory of Charles Darwin to open gatewaysfor approaching the brain–body–mind problem.© 2006 Published by Elsevier B.V.

Keywords: Brain–body–mind; Quantum brain model; Chaos; Brain oscillations; Alpha; String theory; Feynman Diagrams; Heisenberg S-Matrix; Darwin; Evolution

⁎ Corresponding author.E-mail address: [email protected] (E. Başar).

0167-8760/$ - see front matter © 2006 Published by Elsevier B.V.doi:10.1016/j.ijpsycho.2006.07.012

In a previous essay related to models and new concepts tostudy brain functionswe indicated that neurosciences need to seeka breakthrough, inwhichmultidisciplinary approaches combiningphysiology, physics, psychophysiology, and philosophy should

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http://dx.doi.org/10.1016/j.ijpsycho.2006.07.012

109E. Başar, B. Güntekin / International Journal of Psychophysiology 64 (2007) 108–122

be interwoven, and we also shortly mentioned the frame for theabove stated nebulous system (Başar and Karakaş, 2006). In thepresent survey, which is written following the evaluation ofpapers within the present special issue, this newly proposedCartesian System will be described in more detail: The coreidea is based on the invincible spirit of René Descartes.Founding on contemporary trends computer approaches andstatistical analyzes now take the place of the glorious “CartesianAnalytic Geometry of 1600s” and the rigid Newtonian trajec-tories are replaced with hyper-dimensional probabilistic and/orquasi-deterministic pathways to describe brain–body–mindincorporation.

1. Why is a new “unified framework” needed to explain thebrain–body–mind relationship?

The expression “mind” is an abstract and invisible notion ofphysicists and even the biological scientists. Currently,physicists and biologists are somewhat tackled to touch theboundaries of the processes related to the mind–brainincorporation. They study cognitive processes as “attention”and “remembering”; they measure the electrophysiologicalactivity at the absolute threshold of perception, they can predictdream onset; they can differentiate the electrical responses ofthe brain upon known and unknown faces. Accumulatingknowledge, progress and refinements in science and technologyhave helped to make the processes that were in the realm ofphilosophy (for the physicists in the realm of metaphysics)“observable, measurable and testable”. Mind and cognition arebeing studied by the positivistic sciences for over a century now,first in psychology and later in the physical/biological sciences.

The coordinate system and the analytical geometry createdby Renée Descartes enormously contributed to the develop-ment of natural science, the concept and research work basingon the “Cartesian System” governed the positive sciences untilthe beginning of the twentieth century. The physicists havechanged their working frame by introducing Einstein's movingcoordinate system and Heisenberg's uncertainty framework. Inthe second half of the twentieth century highly brilliant pro-posals have been achieved by Norbert Wiener (1948), RenéThom (1975), Prigogine (1980), Herman Haken (1977), andlast but not least nonlinear mathematics and chaos theoryintroduced by e.g. Abraham and Shaw (1983), Grassberger andProcaccia (1983) and Lorenz (1963). However, in spite of theusefulness of these new trends, none of the contemporarymultidisciplinary approaches could reach the glory of “Des-cartes Cartesian System”. What are the reasons for this greatlack? We think that in the twentieth century most of the scien-tists initiating trends to unify sciences have been mathemati-cians, physicists and theoretical scientists; they did not havedirect empirical experience in the realm of biology. AlthoughN. Wiener conducted experiments with the frog, he could notthoroughly study the outcome of biological processes. Anotherimportant critic to the unifying trends is the fact that none ofthese relevant scientists made a major step to incorporate theconcepts of other contemporary pioneers to achieve a morecomprehensive scope.

Besides “Cybernetics”, “Dissipative Structures”, “Catastro-phe Theory” and “Synergetics”, in the world of theoreticalphysics a highly influential trend is based on the so-called“string theory”. Although this theory is very popular forphysicists trying to unify the existent theories, brain scientistsdid not yet consider this theory as an important metaphor foroscillatory brain dynamics and cognitive processes. This trendwill be shortly treated in Sections 1.4 and 8.

1.1. Does the “Cartesian System” need a major revolution?

According to Capra (1984) the Cartesian model needs amajor revolution. In his words: “Transcending the Cartesianmodel will amount to a major revolution in medical science, andsince current medical research is closely linked to research inbiology–both conceptually and in its organization–such arevolution is bound to have a strong impact on furtherdevelopment of biology. To see where this development maylead, it is useful to review the evolution of the Cartesian modelin the history of biology. Such a historical perspective alsoshows that the association of biology with medicine is notsomething new but goes back to ancient times and has been animportant factor throughout its history.”

What could a major revolution in the description of brain–body–mind incorporation imply? By taking the advantage ofthe accumulated data on oscillatory brain dynamics, ondynamics of the circulatory system and on dynamics of overallmyogenic systems, we propose a major change in the classicalCartesian system considering vaster needs in medicine andbiology. Can the approach with this new Cartesian system,which we name “The Nebulous Cartesian System”, have areasonable chance to be more efficient than other earlierproposals? In the time period of the evolution of “BrainDynamics” we applied concepts and methods derived from thedisciplines of Cybernetics, Quantum Dynamics, ChaoticDynamics, Catastrophe theory; and we were involved with ahuge number of experiments in conventional physiology andbrain research. We used all relevant concepts of these importanttrends trying to grasp relevant parts of these trends (Başar, 1980,1998, 1999). The theory of oscillatory brain dynamics is nowcompletely recognized by a great number of neuroscientists;and this field is enormously growing as the reports of thisspecial issue points out.

1.2. Quantum dynamics and brain oscillations

The “uncertainty principle in quantum physics” wasformulated by Werner Heisenberg, who developed the follow-ing model of thought: If one day a microscope with very highresolution could be used, the experimenter would be able toobserve the interaction of a gamma ray with an electron, whichis in the aperture of the microscope. Heisenberg assumed thatthe gamma ray, which is used for illumination of the electrode,would undergo an interaction with the electron (Fig. 1). Thismeans: By supplying energy to the electron the position of theelectron should be changed according to the physical motionlaws. When the observer has the aim to localize the position of

Fig. 2. Filtered spontaneous activity-event-related oscillation epochs to appliedtarget tones during a P300 experiment. Filter limits are 8–13 Hz. Groups ofsweeps (3–13 and 65–79) are separately illustrated to show the relevant changesin 10 Hz spontaneous activity and in event-related oscillations. This illustrationclearly shows that the stimulation induces change in the spontaneous activity,which, in turn, modifies the brain responsiveness. (Modified from Basar andStampfer, 1985.)

Fig. 1. The microscope of W. Heisenberg. A model of “thought”.

110 E. Başar, B. Güntekin / International Journal of Psychophysiology 64 (2007) 108–122

the electrode, this aim will certainly fail. He would then observenot the exact position of the electron at the moment of collisionwith X-ray light. The observer would see only the position ofthe electron following the displacement. This model of thoughtwas subject of discussions already after the development ofquantum mechanics. Finally, the experimental requirements ofWerner Heisenberg were fulfilled and the microscope theorywas supported by new experiments (Cassidy, 1999). In this waythe prediction of Heisenberg was realized.

Can we translate the uncertainty principle manifested by themicroscope thought experiment to brain research? Attemptingthis translation we consider an experimental electroencephalo-graphic (EEG)-recording as illustrated in Fig. 2.

When we stimulate the brain with a sequence of cognitiveworking memory inputs the spontaneous activity of the brainincessantly changes. The development of alpha activity, i.e.increases in amplitude, has, in turn, an important influence onthe alpha responses. The brain is learning and goes from a“preliminary state” to a “learnt state”. We have mentioned thesame situation in the microscope analogy; at the moment ofapplication of the cognitive input the state of the brain changes,and accordingly we cannot determine the exact cognitive re-sponse to cognitive inputs or to cognitive inputs with emotionalcomponents.

1.3. How may the brain show chaotic behavior and quantumtype of uncertainty?

In a prominent and popular book on chaos, Gleick (1987)advocates that new science goes so far as to say that twentieth-century science will be remembered for just three things: “rela-tivity”, “quantum mechanisms”, and “chaos.” In other words,chaos has become the century's third great revolution in thephysical sciences. Like the first two revolutions, chaos cutsaway at the tenets of Newtonian physics. Can this developmentalso be useful and of such great importance in brain research?

The brain is a nonlinear system par excellence. Accordingly, inthe last two decades, the concepts of chaotic dynamics havefound an important application in research on compound elec-trical activity of the brain.

Why does the brain behave as a chaotic system? We canexplain this process at least within three fundamental levels. Inseveral structures of the brain there are several groups of neuraloscillators in at least five frequency channels. Therefore, thebrain has a large number of degrees of freedom related to thoseactivities. Accordingly, the dimension of possible states ofsubstructures within the brain or of the whole brain is high. In achaotic system, small changes in initial conditions may giveraise to large changes in the trajectory of the system.

On the contrary, the quantum like “uncertain” behavior of abrain structure can be observed even by few neurons behavingsimilarly. However, the dimension of the studied brain structure,which consists of only few neurons, does not show chaoticbehavior. But upon excitation, such a structure can behave alsoin a probabilistic manner or behave in an indeterministic way:The neuron (neurons) may fire or not fire. Once a neuron isfiring the experimenter is no more able to excite the neuron as atthe beginning. A good example can be given by describing asession using light stimulations on a human subject. Already,only a unique stimulation may cause higher alpha activity andthe second stimulation will not find the neuron or neuron groupsat the same functional level.

In Fig. 3 a hypothetic neural network consisting of neuronpopulations is presented. The probability of firing single

Fig. 3. Three different steps describing various possibilities of responsiveness inneural populations and their indeterministic and/or chaotic behavior.


neurons is similar in Fig. 3A–C. However, the large amount ofneurons in the network of Fig. 3B increases the incertitude ofthe system. Upon an excitation (sensory or cognitive) theindividual neurons can react separately with different degrees ofprobability; they can also react as an ensemble. Some neuronsmay be already excited by hidden sources within the centralnervous system (CNS) and therefore, not able to react duringtheir refractory periods. This type of reaction of the ensemble of

neurons can be compared to Boltzman's statistical mechanics orthe population of atoms in a target under the bombardment of abeam in an accelerator.

In Einstein's words “Quantum physics formulates laws thatgovern crowds and not individuals; not properties butprobabilities are described”. Laws do not disclose the futureof systems but govern the temporal changes in these proba-bilities. Similar to quantum physics, in cognitive processinglaws of the brain are valid for large populations of individualunits. Rules for excitation are not valid only for single neuronsbut also for neural populations. What applies to quantummechanics also applies to the dynamics of chaotic systems. Inboth systems, not properties, but probabilities are described,laws disclose the change of the probabilities over time; and theyare valid for congregations of units.

A given substructure of the brain or a brain tissue, in fact,shows that both properties can be observed together. Singleneurons may behave with uncertainties originating from thenature of neurons similar to quantum systems and “chaoticuncertainty” resulting from the existence of high dimensional-ity. This can be interpreted as a result of the existence of severaloscillatory frequencies that give rise to higher degrees offreedom (Fig. 3C). We would also like to emphasize the funda-mental physiological findings of Hughes and Crunelli (2007),who described the alternation of theta and alpha oscillations ortransition from one type to another type of oscillatory behaviorin neural populations.

1.4. The string theory as a unifying concept

In string theory the basic objects are not particles, whichoccupy a single point in space, but one-dimensional strings.These strings may have ends or they may join up with them-selves in closed loops. According to Hawking (2001), “just likethe strings on a violin, the strings in string theory supportcertain oscillation patterns, or resonant frequencies, whosewavelengths fit precisely between the two ends. But while thedifferent resonant frequencies of a violin's strings give rise todifferent musical notes, the different oscillations of a string giverise to different masses and force charges, which are interpretedas fundamental particles. Roughly speaking, the shorter thewavelength of the oscillation on the string, the greater is themass of the particle.”

2. A unifying step in brain function: most general transferfunctions in the brain according to Fessard (1961)

Fessard (1961) emphasized that the brain must not beconsidered simply as a juxtaposition of private lines, leading toa mosaic of independent cortical territories, one for each sensemodality, with internal subdivisions corresponding to topicaldifferentiations.What are principles dominating the operations ofhetero-sensory communications in the brain? This question needsan extensive use of multiple microelectrode recordings, togetherwith a systematic treatment of data by computers (Gray andSinger, 1989; Eckhorn et al., 1988). Fessard (1961) indicated thenecessity of discovering principles that govern the most general


or transfer functions of multiunit homogeneous messagesthrough neuronal networks. The transfer function describes theability of a network to increase or impede transmission of signalsin given frequency channels. The transfer function, representedmathematically by frequency characteristics or wavelets (Başar,1980; Başar-Eroglu et al., 1992), constitute the main frameworkfor signal processing and communication. The existence ofgeneral transfer functions would then be interpreted as theexistence of networks distributed in the brain having similarfrequency characteristics facilitating or optimizing the signaltransmission in resonant frequency channels (Başar, 1998). Inan electric system an optimal transmission of signals isreached when subsystems are tuned to the same frequencyrange. Does the brain have such subsystems tuned in similarfrequency ranges, or do common frequency modes exist inthe brain?

The empirical results reviewed here imply a positive answerand provide a satisfactory framework to Fessard's question.Frequency selectivity's in all brain tissues containing selective-ly distributed oscillatory networks (delta, theta, alpha, beta,and gamma) constitute and govern mathematically the generaltransfer functions of the brain. According to Fessard's predic-tion all brain tissues, both mammalian and invertebrates, wouldhave to react to sensory and cognitive inputs with oscillatoryactivity or with similar transfer functions. The degree of syn-chrony, amplitudes, locations and durations or phase lags iscontinuously varying, but similar oscillations are most oftenpresent in the activated brain tissues (Başar, 1999). As to theprocess of coding explained in the previous section the generaltransfer functions of the brain manifested in oscillationsstrongly indicates that frequency coding is one of the majorcandidates to govern brain functioning.

3. Generalization of questions by Descartes and Fessardconcerning the brain–body interaction

As we stated above, Alfred Fessard (1961) posed a questionsimilar to Descartes, who mentioned the possibility of theexistence of some common principles and rules governing thenature. In other words are there some general principles thatgovern the transmission of the signals in the brain? The questionof Alfred Fessard related to electrical signals in the brain can beextended and generalized to the brain–body incorporation. “Arethere also some general transfer functions in functional inter-actions of the brain with the vegetative system and biochemicalpathways? Do cranial nerves and the brain stem link thevegetative system to cortex and provide also cognitive/memoryintegration”.

The autonomic nervous system, which regulates what weusually call our innards, is the part of the body linked with thebrain. The autonomic nervous system regulates our vital func-tions without our conscious control. We breathe, our heart beats,our stomach digests and our bladder muscles contract. Furtherwe secrete saliva, insulin, and digestive enzymes. Our skeletalmuscles are able to show vasodilatation and vasoconstrictionwithout our conscious control of them. These functions areoperating mainly on structures hidden from view. The auto-

nomic system acts on smooth muscle (in the blood vessels andintestines, cardiac muscles and glands). The autonomic systemalso has afferent pathways carrying signals from our innards tothe brain and spinal cord. Başar and Weiss (1981) after studyingcommon features of contractility of the organs that are undercontrol of the autonomous nervous system have proposedgeneral classifications of those organs with the expression of theoverall myogenic system, which will be explained in thefollowing sections.

3.1. The sympathetic system and EEG-oscillations

Living system settings are ensembles of detectors and alltypes of mechanisms that serve living systems to maintainsurvival functions such as normative values of blood pressure,respiratory rhythms, cardiac pacemakers, and body temperature.Such mechanisms that are important to maintain the bodywithin the limits of healthy life qualities should be also cate-gorized into the level of persistent memory since damage tothese settings strongly affects higher levels of nervous activityand all levels of memory activation. Gebber et al. (1995) re-viewed a series of articles from their laboratory on the 10-Hzrhythmic sympathetic nerve discharges of cats and offered ahypothesis on its functional significance.

The rhythm is ubiquitous to the discharges of sympatheticnerves with different cardiovascular targets and it arises from asystem of coupled nonlinear brain stem oscillators, each ofwhich has a selective relationship with a different portion of thespinal sympathetic outflow. The 10-Hz rhythmic discharges ofsets of sympathetic nerves are differentially related and thepattern of relationships in one experiment can be the reverse ofthat in the next. The authors hypothesize that nonuniform anddynamic coupling of the central circuits controlling differentsympathetic nerves is the basis for the formulation of complexcardiovascular response patterns that include differentialchanges in regional blood flows.

Are they tuning and matching effects between cognitive 10-Hz oscillations and sympathetic discharges? This question maybe answered in the future. However, the fundamental findings ofGebber's group indicate that the physiological settings of thecirculatory system and of phyletic memory characteristics arein the 10-Hz frequency range. A link between cognitive andvegetative processes may possibly be supplied with general 10-Hz oscillations.

Başar and Weiss (1981) measured and reviewed mechanismsof control, auto-oscillations of blood flow, contractility of thevasculature, forced oscillations in the peripheral circulatorysystem, spectral activity of peristaltic organs, dynamics of thelymph nodes and the lymphatic system and found that all thesesubsystems showed spectral properties (oscillatory activity) inthe ultraslow frequency range of 0.01 Hz, 0.04–0.06 Hz, and0.1 Hz. These authors introduced the concept of the overallmyogenic system after quantifying and treating the performanceof smooth muscle dynamics, by considering this as the dynamicsof an overall and coordinated dynamic system. The smoothmuscle cells are building blocks and basic effectors of the overallmyogenic system (see Fig. 4 showing the organization of

Fig. 4. Schematic illustration of the overall myogenic system, which comprehends the vasculature, peristalsis organs and the lymphatic system.


the overall myogenic system). The overall myogenic systemincorporates:

(1) The “vascular system”, with all the arteries, arterioles,etc., in the systemic circulation.

(2) The “lymphatic system”with lymphatic vessels and nodes.(3) The “visceral system”, which performs the visceral func-

tions of the vegetative system and peristalsis in vegetativefunction.

Aladjalova (1957) demonstrated ultraslow periodicities inthe brain as early as 1957. In the meantime there are a numberof publications indicating the existence of these ultraslowoscillations and the possible links with the EEG (Ruskin et al.,

Fig. 5. Spontaneous mechanical contractions of the portal vein. Left: time series; rigperiod in which the smooth muscle presents a mixed contractile activity. Compare c

1999; Allers et al., 2002). Multi-second oscillations in firingrate with periods in the range of 2–60 s (mean, 20–35 s) arepresent in 50–90% of the spike trains in basal ganglia neuronsrecorded from locally anesthetized, immobilized rats. Todetermine whether these periodic oscillations are associatedwith similar periodicities in cortical activity, transcorticalelectroencephalographic activity was recorded in conjunctionwith single- or dual-unit neuronal activity in the subthalamicnucleus or the globus pallidus, and the data were analyzed withspectral and wavelet analyses (Allers et al., 2002). Multi-second oscillations in firing rates of 31% of the STN neuronsand 46% of the GP neurons with periodicities significantlycorrelated with bursts of theta (4–7 Hz) activity in transcorticalEEG. These are concrete examples showing the possibility of

ht: phase portrait. (A) Example of the so-called “minute rhythm” activity. (B) Ahanges in the dimensionalities in (A) and (B). (Modified from Başar, 1990).


ultraslow wave oscillatory coordination between myogenicorgans and the brain.

4. Mutual excitation and overall tuning in the brain and inthe “overall myogenic system”

The approach to the brain–body–mind problem requires alarger account of “multiple causalities” in comparison to theprerequisites of modern physics and quantum dynamics. In theanalysis of the brain–body–mind construct we have to includemultiple uncertainties or uncertain causalities. These multiplecausalities are originated from (1) nonlinear properties of thevegetative system (irregularities in biochemical transmitters,cardiac output, turbulences in the vascular system, respiratoryapnea, nonlinear oscillatory interactions in peristalsis, seeFig. 5) (2) nonlinear behavior of the neuronal electricity (forexample chaotic behavior of EEG) (see Fig. 6), (3) geneticmodulations and (4) additional to these physiological entities,the nonlinear proprieties of physical processes in the body.

5. What are multiple causalities? What is a“hyper-probabilistic Cartesian System”?

Newton's concept fits excellently with the “Cartesian Sys-tem”. The establishment of a more efficient new “Cartesiansystem in the brain–body–mind incorporation” is a most funda-mental and difficult step. In search of probabilistic causalfactors, similar to the task of C. F. vonWeizsäcker, such a task inbrain research is more difficult in comparison to physicalsciences. In the 1930s Heisenberg's theory was classified inthe realm of Metaphysics (Popper, 1935). Today, Heisenberg's

Fig. 6. A comparative presentation of power spectra (compressed spectral arrays) acalculated from the same EEG segments (simultaneous recordings from the same su

quantum mechanics is a dominating branch of physics. Ourconcept of “probabilistic causality in the brain–body–mindincorporation” differs from the quantum theoretical causality.This difference results from multiple causalities as consequenceof the richness of interacting biological components in pheno-mena or processes of psychophysiology. Accordingly, we try toformulate a concept of “probabilistic causalities in biology”.This is yet partly a metaphysical question.

According to the coordination and/or tuning of oscillatoryactivity in communication within the brain and its link to thevegetative system and spinal cord, the most general transferfunctions of the brain–body–mind incorporation seems to be inconcert (see Fig. 7). However, the multiple uncertainties andnonlinear interactions have probabilistic reactions. Thesegeneral transfer functions are also influenced by activation ofbiochemical pathways (see the Alzheimer study by Yener et al.,2007).

According to the developments of the positive sciences wetentatively formulate four steps to generate the new proposal orthe new Cartesian system.

5.1. The first step

The Cartesian System formulated by Descartes was the firstfundamental concept and analytical framework related andinterwoven with the concept and applications of NewtonianDynamics. Although the conventional and classical Cartesiansystem has created gigantic steps till the beginning of the 20thcentury in physics, this Cartesian system could not respond tonew developments because of the probabilistic nature ofquantum dynamics and the moving reference systems of the

nd the correlation dimension D2. Each D2 value and the adjacent spectra werebject in frontal, central, parietal, and occipital locations; from Basar, 1990).

Fig. 7. Schematic illustration of the autonomous nervous system and biochemical pathways that are interconnected and interactive in functioning.


theory of relativity. F. Capra (Capra, 1984) describes that al-ready during the twentieth century this reference system was faraway to respond to the needs of progresses in biology.

5.2. The second step

The second step includes the developments in quantumdynamics at the beginning of the 20th century. In order toanalyze quantum processes, physicist moved to a ProbabilisticCartesian System in which the causality principle becamea probabilistic one. This means the trajectories of particles(obeying to quantum rules) can be described only with theconcept of cloudy wave packets. Although the processes ofquantum dynamics were not classified under the title of theProbabilistic Cartesian System, this step has been mentionedfrom the viewpoint of historical development.

5.3. The third step

As the third step, we propose aHyper-probabilistic CartesianSystem in order to describe the processes in the brain–bodysystem, i.e. a framework with a nonlinear linking of the CNSand the autonomous control system performing the vegetativefunctions (see Fig. 7). We name this reference system as a hyper-probabilistic since subsystems of the brain–body incorporationdepict all probabilistic causalities as described in the paragraphabove.

5.4. The fourth step

Descartes, at his time undertaking his genius step, did notpossess today's knowledge on physiology and modern physics.We think that time has come to consider such a New CartesianSystem for understanding of brain–body–mind incorporation.In the description of the brain–body–mind incorporation it isnecessary to include some processes that belong to studies ofmetaphysics of the brain: “dreams,” “intuition”, “creativity”,

“unconscious states” including “unconscious learning” and“problem solving” that belong to the domain of brain meta-physics. This means that the hyper-probabilistic Cartesiansystem is not sufficient as a complete framework or referencesystem. Accordingly, we have to add to this hyper-probabilisticCartesian system our “sentiments”, “emotions” and “creativity”in order to complete the spectrum of processes including bothconscious and unconscious domains. Therefore, we have to adda fourth step and after that step the hyper-probabilistic systemwill be transformed to a “nebulous system”, because we canpredict the future only in a nebulous way, according to difficultyof predictions in dreams, in unconscious states and creativity.The intuitions that are necessary for creativity according toHenri Bergson (1907) take place in an inhomogeneous timespace, which is called durations and which is not measurablewith conventional physical clocks. Accordingly, as the fourthstep we tentatively assume that the processes or mechanisms ofthe brain–body–mind system can be analyzed and predictedsimilar to the metaphor of “finding the walking path in a cloudyor foggy day”. This is what we call “The new NebulousCartesian System”, which is illustrated in Fig. 8.

6. Possible ways to approach functioning of the brain–body–mind incorporation in the framework of a “NebulousCartesian System”

By proposing the Nebulous Cartesian System it was evidentthat we have to accumulate knowledge on electrophysiology,anatomy, learning processes and all physiological settings andstore them at several levels of a multiple coordinate system ofthe Nebulous Cartesian System. When the brain works severalparameters and entities related to brain functioning are mostlyworking in parallel being linked with all parameters of sub-systems of a brain–body–mind incorporation. When we con-sider the brain as a probabilistic (nebulous) working andadaptive machine one would expect to be able to approximatelypredict the next steps of this machine. It is possible to say that

Fig. 8. The Nebulous Cartesian System is described here in a hypothetical way. There are several sub-coordinate systems with multidimensional spaces. The axes arenot rigid, since all elements of subsystems of the autonomous system and of the brain show high degrees of plasticity and indeterministic behavior. These coordinatesystems are nebulously described since there are no conventional coordinate systems with absolute origins and absolute time space. In reality, this sub-coordinatesystem and the general one will be described with the help of matrices with embedded information in a multidimensional space.


we try to describe working principles and walking pathways ofthese machines by starting with the initial conditions. From thisconstruct taking account all the histories. Then we have theproblem of determining the integral overall histories. This is thepath-integral. And with this view, we point out the need of usingFeynman Diagrams and/or Heisenberg's S-Matrix. Both thesemethods are interrelated. In earlier publications, we havealready mentioned the possibility of using this method in brainresearch.

6.1. S-Matrix formulation of Heisenberg, brain dynamics andphysical causality

In 1943 Werner Heisenberg formulated the so-called S-matrix theory of particle interactions. In this theory, Heisenberg(1961) tried to admit only those concepts into the theory thathave a clear operational significance. The theory is concernedonly with the outcomes of scattering or collision processes andnot with the detailed sequence of events taking place during theprocess as in the earlier approach of quantum mechanics. Thebasic quantities of interest in high-energy physics, and moreparticularly in the study of strong interactions, are the collision,or scattering, amplitudes between sets of initial and final par-ticles, the collection of which is the S-Matrix (Barut, 1967;Feynman, 1962; Heisenberg, 1961; Iagolnitzer and Barut,1967). The basic assumption of the S-matrix formalism is thateach physical system, considered with “all its evolution,” can berepresented before interactions by a well-determined ray Ion (orcollection of vectors) in a Hilbert space (In) of “incoming” or“initial” free-particle states and after interactions, by a well-determined ray Øout in a Hilbert (Hout) of “outgoing” of “final”free-particle states. The S-matrix should determine the crosssection for the production or annihilation of particles. The S-

matrix can also be considered as a pure function that transformsall the momenta before collision to the momenta after thecollision (Iagolnitzer and Barut, 1967); accordingly

h jSj i ¼ h out j in iIn 1983 Başar (1983a) proposed to present the brain response

with the same formalism that introduces matrices alreadydenoted as brain matrices. This formalism should again presenta metaphor to the S-matrix that predicts cross sections of pro-duction of elementary particles. Currently, our tentativeassumption is that we may approach the task of understandingthe brain function and may predict responses by using a largenumber of indicators.

Conceptual work and experimental designs lead to essentialsteps in brain research. When designing an experiment, theEEG should not be considered as a non-dynamic or a passivebackground during a cognitive process. According to this newtype of experimental design, it appears that for the comprehen-sion of event-related potentials (ERPs), a new set of parametersin our work on the paramount EEG must be considered, whichwill be tentatively named “brain indicators”. The following is aprovisional list of indicators: the nonlinear correlation dimen-sion influences the degree of order in the spontaneous activity,(1) phase angle of the brain waves and their amplitude modu-lation envelopes (Bullock and Başar, 1988), rms (2) values ofvarious EEG frequencies, (3) coherence in space and coherencein time for each frequency.

Using these indicators we can now go on to a new type offile, which is called the “brain state matrix”. What is the brainstate matrix? In earlier publications, we have tried to create apicture of this matrix by stating that the brain state could bedescribed by several measures of instantaneously defined EEGproperties, outlined above as indicators, during a given short


period of approx. 0.05–1 s (Başar, 1983a,b). The knowledge ofparameters in such a matrix enables the experimenter to predictroughly the shape, amplitude, and frequency content of the ERP.The amplitude of an evoked response (evoked potential, EP)often depends strongly on the amplitude of the ongoing activity(Rahn and Başar, 1993a,b). These experiments showed that, ifthe subject's EEG is already in a coherent state, the physicalsensory stimulation does not create a new, more coherent state.There is no EP to a physical stimulus in such a coherent state ofthe brain.

One can extend the results with nonlinear descriptors bystating that, if the dimension of the EEG is low, the transition ofthe EEG to a lower dimension is not possible or difficult. Inother words, as explained earlier, if the brain's electrical activityshows a low entropy state (high-order), the transition to a lowerentropy state is difficult (Başar, 1980; see chapter 11, inparticular Fig. 11-7). The amplitude and the shape of theoutgoing response or of the outgoing activity (evoked activity)are inversely correlated with the ongoing activity. The outgoingresponse is a function of the ongoing activity. The expression ofongoing and outgoing activities is used here in reference to animportant analogy in elementary particle physics. The S-matrixintroduced by Heisenberg to elementary particle physicsdescribed the nuclear reactions by considering ongoing andoutgoing waves.

6.2. Feynman diagrams

We already proposed to develop an ensemble of rules,similar to those of the so-called Feynman diagrams forinteraction of elementary particles, and use these as a tool forunderstanding the reaction function of the brain. This should beconsidered as a tentative step for combining several simulta-neous measurements of brain processes and approach thequestion of “How brains may work” in a global manner. Therules will be completely different from the physical Feynmandiagrams. Nevertheless, we may use a similar way of thinking,in the hope that this step can be enhanced by developing a“brain dynamics study program” including the characterizationof the brain's pathological states, the brains of lower vertebratesand of invertebrates. The Feynman diagrams which are used inelementary particle physics have been developed in order todescribe and predict the electromagnetic processes, wherebyelectrons and photons interact. The interactions are, indeed,complicated; there is a type of “grammar” to these diagrams,which allows only certain configurations to be realized innature. This grammar results from the basic laws of physics,such as conservation of energy and conservation of electriccharge.

Particle physicists have found that this complexity should behandled in a reduced form, and in order to understand thebehavior of electrons and photons, approximations are usedwhich neglect all but simple Feynman diagrams. By consideringroughly the simple hundred diagrams for certain processes,physicists have been able to predict important relationsprecisely. As the Başar and co-workers have shown (Başar,1980, 1983b, 1988; Başar et al., 1987), there are several alloyed

and unalloyed transitions of the EEG following stimulation. Forexample, if a subject emits abundant high amplitude alphawaves prior to application of a sensory stimulation, usually noenhancement of that frequency is seen in the encounteredresponse. On the contrary, we then observe an alpha blocking.The same rule is true also for 40 Hz activity (Başar et al., 1987).

Further, if the overall coherence between various structuresof the brain is high, again the enhancement of EEG activity islow or vanishes. Additionally, a coupling between frequencycomponents and also between amplitudes of various EEGcomponents among different brain structures exists—e.g., thereis an important coupling or similarity between 10 Hz activitiesof the reticular formation and the thalamus (Başar, 1983a,b). Bystarting with a brain state matrix and developing new rules stepby step (which should be experimentally evident and wouldallow the facilitation and prohibition of several transitions of thebrain rhythms) it could be possible to predict a large number ofbrain reactions that we analyze as the brain's compoundresponse potentials.

In accordance our way of thinking comprises that the EEG isnot only an activity that reflects some brain state, but also anactivity that anticipates reactive mechanisms and controls theoutput to stimulation. Accordingly, the introduction of this newtype of “grammar”may also serve to design experiments for theunderstanding of a large number of cognitive processes. Wefurther suggest that the brain obeys the same dynamic laws orrules, which govern the control of the brain's excitability asalready described in the “Quantum Mechanics”. If there is anexcited state in an atom it is very difficult to increase the energyoutput of the same atom. The brain behaves similarly. If aneuronal population is in an excited state, cognitive or sensorystimulation cannot excite this population any further. Somerhythms or patterns between phenomena of nature can beexplained and/or predicted by the powerful Feynman diagrams.

6.2.1. Brain–body Feynman diagramsWhat do we intend to analyze with Brain–Body Feynman

Diagrams? We try to insert the entire history of the EEG activitycombined with physiological settings prior to stimulation. InSection 4 we have described that the memory is stronglyinfluenced by physiological settings as blood pressure,respiratory states (cycles, etc.). In Fig. 7 we illustrated theinteraction of the CNS with subsystems of the vegetativesystem. Since all functions of the brain are mostly in concertedaction, the same chain of reasoning is also valid for integrativebrain functions. If the electrophysiological responses of thebrain do depend on changes of cardiovascular input, i.e. bloodpressure, respiratory cycles, the level of cholinergic or adren-aline secretion, the Feynman diagrams that predict the brainresponses must incorporate also these physiological parameters.

These physiological parameters are extended and/or influ-enced also by our emotional states. The emotional states candirectly influence the brain responses, however, the emotionalstates can affect the cardiovascular responsiveness, and the lastone, in turn may modify the electrical brain response. Fig. 9illustrates several factors that will be evaluated in order to buildBrain Feynman Diagrams. The most adequate way to start is to

Fig. 9. Explanation of several factors influencing the brain responsiveness. Thesame factors from which we know the empirical weights will also be used inconstructing Feynman Diagrams.


consider separate simple “Feynman Diagrams” to describe allthese different psychophysiological events. We can develop apartial Feynman diagram to show the influence of emotionsdirectly on the brain or we can develop a Feynman diagram toact to the cardiac output and also at the influences of the cardiacoutput to the brain. Then the final Feynman diagram includingall histories or physiological settings will be constituted from achain of partial Feynman diagrams as a large tree with severalbranches.

6.2.2. Factors shaping brain–body Feynman diagramsA Feynman diagram is a bookkeeping device for performing

calculations in quantum field theory. In physics, the interactionbetween two particles is quantified by the cross section corre-sponding to their collision. This cross section (or more preciselythe corresponding time evolution operator, propagator or S-matrix) can be explained as a sum of terms. What do we haveto consider the interaction of stimulations with the neuralpopulations in the brain? As a first step we try to describe theshort story in time.

A sensory or cognitive stimulation to the brain evokes orinduces oscillations. For the general bookkeeping the followingprocesses are to be considered: (1) Activation of a given areawith superposition of oscillations in alpha, beta, gamma, theta,delta. (2) Phase re-ordering and phase-locking of the ongoingactivity. (3) The oscillatory response is topology depended. (4)In several frequencies there are blockings or enhancements

depending on the level of prestimulus activity. (5) Coherencesbetween the studied structures have an influence on theresponse. (6) The age factor plays an important role (shift ofalpha frequency from occipital to frontal areas). (7) Geneticfactors play an important role in oscillatory responses (Porjeszand Begleiter, 1996, 2003; Porjesz et al., 1998, 2002). (8)Neurological test scores (Doppelmayr et al., 2005; Karakaset al., 2003; Klimesch et al., 1997). (9) Health conditions,pathologies as Alzheimer's disease or Multiple Sclerosis (Tassand Hauptmann, 2007; Başar-Eroglu et al., 2007; Yener et al.,2007). (10) Sleep stages and states of consciousness. (11)Factors of vegetative system related to high or low pressurelevels and respiratory cycles. (12) Emotional input to the brain.(13) Anatomical information by using magnetic resonanceimaging (MRI). (14) Gender differences (male, female).

These are some examples for bookkeeping or for describingthe evolution of signals that need to be considered for theapplication of Brain Feynman Diagrams. We will proceed atseveral levels. The S-matrix is a matrix with multiple dimen-sions considering the accumulated rules depending on theparameters described above. Further, all these rules depend onthe topology of studied brain structures. Accordingly, we haveto introduce weighting factors for the responsiveness or thebrain response susceptibility (see Fig. 10).

6.2.3. The grammar of brain Feynman diagramsIn Fig. 10 alpha responses to light and auditory stimulation

are illustrated for four topologically different areas. Lightstimulation does not evoke any significant alpha responses at F4and T4 locations, whereas light stimulation and auditory stimu-lation evoke alpha responses at O2 and T4 locations. From thissimple model, we go to another simple model to compare alpha,gamma, theta and beta responses to light stimulation at occipitalareas. The occipital cortex responds with 10 Hz, 4 Hz, 40 Hz,20 Hz responses to visual stimulations. In future, we willconsider responses of cerebral ganglia in Aplysia. The alpharesponses are missing and spontaneous 10 Hz activity is scarce-ly present. Similar to this, the child brain neither shows spon-taneous nor evoked alpha activity until the age of 3 years. Thesefew simple analyzed diagrams can already give importantinsight to a comparative analysis. These types of simple rulescan be extended for functional and comparative studies in-cluding diverse types of brain states as well as coherencemeasures as descriptors of connectivity or correlation dimen-sions as descriptors of brain states. The building of more com-plex Brain Feynman diagrams can, most probably, facilitate theglobal analysis of electrophysiological events and enable re-search scientists to discover insights to brain functions that aremore difficult to understand by using detailed analytic research.

6.3. Computing of brain–body Feynman diagrams

It is more appropriate to use the term “quantum computing”to refer to any use of effects considered “quantum mechanical”rather than “classical”. Nearly all of the interest today is in“quantum parallelism”. As a metaphor in brain theory we usethe term uncertainty of brain reactions instead of the expression

Fig. 10. Partial Feynman Diagrams for visual and auditory stimulation. For explanation see text.


“quantum parallelism”. According to David Deutsch (2003) this“parallelism” can be understood as an extension of the Feynmanpath integral approach to quantum mechanics, in which theprobability of a physical system for transition from a state A tostate B can be statistically modeled. In quantum computing, thecomputer evolves along all possible paths from its initial state,and the probability of any particular final state will be given bya sum of all paths that lead to that state. Another way ofdescribing this is to say that the computer evolves along anexponentially growing (multiplying with each step) number ofpaths, and in the final step all these parallel computationsinterfere with each other to determine the probabilities ofvarious outcomes. Feynman suggested the possible relationshipbetween quantum computing and nanotechnology as early as1959. He also pointed out the fact that quantum computingis potentially more powerful than classical computing, sinceclassical computers cannot simulate quantum mechanics effi-ciently, while quantum computers should be able to do so.

In the previous section we described approximate steps inorder to put together several experimental facts in order topredict brain responses by considering all histories and theevolution of processes in the whole brain prior to a stimulation.However, we already described other relevant processes ofvegetative and biochemical processes in the whole body thatcan or may strongly influence the brain responsiveness (seeFigs. 4 and 7). As we will also consider in the followingsections, the computation or predictions of brain responses withFeynman Diagrams is difficult enough. To find a solution to thisproblem, for which high powerful super computers (quantumcomputers) should be used to evaluate all possible combinationsand interactions in the brain and CNS, we propose the followingstep: First, we take account of all possible processes in thebrain and try to roughly predict the brain responses of a givensubject depending on the age, pathological states and possiblyemotional behavior. After doing this we can add corrections tothe computations stemming from changes in vegetative para-meters, e.g. how would the increase or decrease of the arterialpressure affect the alpha, theta or gamma responses? Howwould diseases in the gastrointestinal systems that are accom-

panied by increased or decreased peristalsis effect the measuredresponses? How may the balance change in the lymphaticsystem influence the brain's responsiveness? Most of thechanges in brain oscillatory responses upon these mentionedphysiological changes cannot be encountered in the neurophys-iological literature. However, by using the brain oscillatoryapproaches it will only be a question of time to collect enoughempirical results to describe modifications of brain oscillatoryresponses in all these non-physiological or pathologicalchanges. An illustration, which may open the way for aFeynman presentation is presented in Fig. 9.

6.3.1. Possible advantages of “brain–body” Feynmandiagrams

The simple brain Feynman diagrams that we have presentedare easy to understand. However, in the study of brain responsesit is possible to progressively build hundred of such grammarrules. Comparative studies and steps to achieve archives for allfunctions can be extremely complex and difficult. However,simple visual analysis of such simple Feynman Diagrams canenable the brain investigator to predict more complicated func-tions by analysis of reduction. For example, the frontal brainalpha responses have usually low amplitudes and show nophase locking. On the contrary frontal theta responses havelarge amplitudes and strong phase locking. If in a brain responsewe observe a great deviation from the simpler Feynman Dia-grams, the new added values or differences could make a fastunderstanding of brain function possible and help to interpretnew results.

We do not aim to survey vast literature on the computation ofFeynman Diagrams. Further, Feynman Diagrams could also bea schematic approach parallel to Heisenberg S-Matrix. Accord-ing to the literature the evaluation of Feynman diagrams can beperformed by Monte Carlo calculations, that is a kind ofexperimental mathematics. If in future it can be possible to usequantum computers, the probabilistic nature of quantum devicescan also be considered to solve brain–body Feynman Diagrams.Why would the Monte Carlo method be adequate for modelingbrain processes? When we consider the schematic illustration of


the Feynman diagrams, we are confronted with a problem ofmultiple causalities (see also Fig. 9 and Section 5). The pre-diction of the occurrence of a brain response would depend onvarious types of initial conditions; it means initial brain statesand a great number of factors from body and environmentconverged as multiple inputs to the brain. A great number ofinitial conditions have to be considered for brain processes;during signal processing of the brain, several hidden variablesand/or parameters influence the brain processing, and accord-ingly the manifestations of oscillatory activity. This means thatseveral main processes and sub-processes are in play andseveral links have to be considered. These multiple processes,which occur in series and in parallel, can be computed asmultiple trials by using random trials generated by the com-puter, billions of times (see Fig. 11). In this way the brainreactions could be described and/or predicted within limits ofprobabilistic windows. This is the essence of Monte Carlomethod used mainly in order to describe life stories of neutronsin nuclear reactions. Therefore, Monte Carlo seems to besuitable to achieve such an approach.

7. Gateway to metaphysics of the brain

There are several ways to transcend the gateway to brainmetaphysics: As a prominent example we mentioned the work

Fig. 11. For computation of brain Feynman diagrams several factors influencingbrain responsiveness will be embedded in speedy computers in parallel or series.Evaluation of large statistics, also including the Monte Carlo method, could beused for predictions of brain responses in subjects.

of Henri Bergson (1907) and the “Evolution of Species” byCharles Darwin in the light of statistical mechanics and devel-opment of the entropy during high level cognitive processes.

7.1. Does a Maxwell's demon trigger the creative evolution?“Bergson's intuition” revisited with the concept of probabilisticoscillators in the brain

The work of the genius French philosopher Henri Bergsondiscusses the work of Charles Darwin, and he comes to theconclusion that the superiority of the human brain in com-parison to lower species is its ability of “intuitive and creativethinking”.

Henri Bergson emphasized three types of mental abilitiesduring evolution of species: instinct, intelligence and intuition(Bergson, 1907). Instincts are observed in low living beings asinvertebrates, intelligent behavior also belongs to functionalproperties of lower vertebrates and mammalians. However, onlyhuman beings have the ability of intuition. The “intuition” isalso, according to René Descartes and John Locke, what makesthe human being different from other species. At the beginningof 20th century the proposal of Bergson could not be analyzedby means of electric recordings. Since two decades we haveanalyzed the electrophysiology of species using recordings ofspontaneous electrical activity and evoked potentials, incollaboration with the laboratory of T.H. Bullock in SanDiego (Başar et al., 1999; Bullock and Başar, 1988). In additionto the conventional electrophysiological recordings we madeuse of the efficient method of oscillatory brain dynamics toanalyze the electrical activity of isolated ganglia of Aplysia,Helix Pomatia and brains of low vertebrates as goldfish and ray.We also analyzed cortical and sub-cortical structures of the catbrain and the scalp recordings from the human brain. Ouranalysis of brain oscillations included delta, theta, alpha, betaand gamma oscillations.

Our findings revealed that the alpha oscillations (10 Hz)can be interpreted as a key indicator in evolution of species. Inthe ganglia of Aplysia and Helix Pomatia 10 Hz oscillationswere only scarcely recorded. Further, the 10 Hz activity showedincreasing amplitudes in low vertebrates and in the cat brain incomparison to invertebrates. In the human brain the alphaactivity shows high level wavelet entropy. Earlier studies of T.H.Bullock have also showed that the alpha coherency in in-vertebrate ganglia is totally absent and reaches higher valuesfrom low vertebrates to the human brain.

According to the mentioned empirically grounded results,we tentatively propose that the changes in coherence, amplitudeand entropy of alpha oscillations are key indicators for thedevelopment of mental activity during evolution of species. Isthe superiority of the human brain manifested by intuition andcreativity correlated with lower entropy alpha activity incomparison to lower species? Is the second law of thermody-namics loses its validity in developing intelligent systemsby evolution of intuitions (Maxwell Demon?). Although thisquestion stays yet partially answered, it is clear that theevolution of alpha activity is a prominent candidate as “sign ofintuitive behavior in human beings”.


8. Does the own language of the “brain–body–mind” needthe evolution of a new discipline? Parallelism to “quantumtheory”, “string theories” and chaos?

In several sections of the present essay and in papers of bothspecial issues a number of experimental approaches for theanalysis of experimental results were supported by main ideasof frameworks initiated by Norbert Wiener, CopenhagenSchool, Hermann Haken, Donald Hebb, Charles Darwin, andalso of F.A. von Hayek. We learned enormously from the workof outstanding mathematicians, system scientists, and theoret-ical physicists. This is the crucial point, giving rise to thepresented multidisciplinary framework and to the developmentof the oscillatory brain dynamics. But, a higher order way ofthinking is the following: All these pathway opening scientistscame from the mathematical logic and tried to describe rulesof the brain and mechanisms of thinking. Although we giveenormous credit to the developments by Cybernetics, Dissipa-tive Structures, Catastrophe Theory and Synergetics, westrongly argue for the necessity of direct knowledge from thebrain (i.e. empirical results from the brain) in order to be able tounderstand “principia” of brain working and the “principia ofthinking”. This means: we learn from experimental results of thebrain and from what we learned we try to establish a theorycontaining a series of rules on brain functioning (Başar andKarakaş, 2006). When we try to understand the brain and wehave the goal of developing a physical–physiological andphilosophical construct, we do not start with mathematics toderive definitions; first we decode the “principia-mathematica”of the brain. We hypothesize that our way of thinking is anadequate one. The human brain is the most complex structure inthe universe visible to us. Accordingly, a framework, whichcould enable us to understand the brain, should be derivedonly from the language of the brain. Certainly the search of aframework or description of the dynamics of the brain cannotsolve all the problems related to brain–body–mind incorpora-tion. However, the developed framework may help for recurrentmeasurements and computations to further understand brain–body–mind functioning.

Considering the descriptions in this essay we try to underlinefour important features: (1) the brain is a learning system, itsability to react to external or internal inputs changes with time.The reactions of the learning brain can be completely differentcompared to the reaction of the emotional brain (Güntekin andBaşar, 2007). (2) The brains' reactions change during evolutionof species. (3) In the maturating brain from early days ofchildhood to the adult brain, brain responses also change. (4)Creativity and related states of intuition cannot be explained byearlier frameworks developed by mathematicians and theoret-ical physicists. By application of oscillatory brain dynamics weapproach an area in which we try to be able to measure allthe four features mentioned above. We emphasize that “TheNebulous Cartesian System” is a construct and/or workingbench; in turn, this working bench may open new ways todeepen the understanding of brain function and possibly meta-physics of the brain. We also share the opinion of John vonNeumann and Burks (1966), who stated: “[…] logics and

mathematics in the central nervous system, when viewed aslanguages, must be structurally essentially different from thoselanguages to which our common experience refers”.

We believe that our proposal to establish the “NebulousCartesian System” is in the sense of F. Capra (1984, see alsoSection 1 of the present survey) and that such a proposal isneeded to initiate a breakthrough in neuroscience after heavyaccumulation of data is derived from the evolution of species, thelearning brain, and creative brains. The present survey was basedon the evaluation of papers in the frontier of the new emergingbranch of oscillatory dynamics in neuroscience as presented bythe authors of the present special issue. The brain oscillations aretuned as the strings of a violin during cognitive processes;accordingly, we mentioned the string theory of quantum physicsas a metaphor to describe functional processes in the brain.“Natural Frequencies” of the brain are the EEG oscillations, andthe essence of the oscillatory brain dynamics is based on EEGresonances, as the resonances of strings that make the groundtones in music are similar to the ground mechanisms of the brain.

John Carew Eccles suggested in 1986 that the synapses inthe cortex may respond in a probabilistic manner to neuralexcitation; a probability that, given the small dimension ofsynapses, could be governed by quantum uncertainty. Further,Hameroff and Penrose (1996) and Penrose (1990) developedelegant working hypotheses that take in account the possiblequantum nature of signal transmission at the micro-level, con-sidering probable processes at the synaptic level. Such hypo-theses will probably be more profoundly treated in the futureand will need experimental extensions. On the contrary, quan-tum like parallelisms of Başar that was first initiated in 1980with quantum like resonances and in 1983 with S-Matrix meta-phor has less ambitious goals by describing quantum-like pro-babilistic behavior of brain wave responses in observed brainreactions upon sensory-cognitive excitation. In such processeshidden variables can be originated also from the vegetativesystem as described in previous sections. The quantum proba-bilistic behavior is not only to search at the micro-level(synaptic level) and/or in single level, but chaotic dynamicsresulting from multiple processes are also crucial entities asdescribed in Section 5. In pure physics, the dualism betweenwave and particles has a quasi-metaphysical role; the brain ismuch more complex: the brain reaction susceptibility has mul-tiple causalities. We will call this simply “Brain's Multiplici-ties”. We have to deal with all multiplicities in parallel.

We hope that the proposals in our essay may motivate anumber of young neuroscientist to jointly evaluate results fromvarious types of measurements and to accumulate them in the S-Matrix and in series of Feynman diagrams.

How far we will go? Time will tell.

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A breakthrough in neuroscience needs a “Nebulous Cartesian System

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