aa r X i v : . [ q - b i o . N C ] F e b Measuring Consciousness
Siddhartha Sen Centre for Research in Adaptive Nanostructures and Nanodevices,Trinity College Dublin, Ireland.
Abstract
Abstract
In this paper a theoretical model for measuring consciousness based on experimental ob-servations is proposed. Consciousness, the awareness of one’s self and one’s immediate en-vironment, is defined, in this paper, in terms of the information about this awareness thatis contained in or being processed by the brain. This particular information content in thebrain is extracted from the correlation functions of brain waves observed in EEG measure-ments at N points. From these a time dependent probability function, P N ( t ) (AppendixB) is determined and then, Shannon’s information theory formula, P − P N ( t ) ln P N ( t ), isused to convert P N ( t ) to the information about awareness contained in the ensemble ofbrain waves (Appendix A). The sum, in the formula, is over the N points and the allowedrange of brain wave potentials measured. Consciousness is defined either directly by thisformula C ( t ), when it represents the information contained in brain waves at time t , orits time derivate D ( t ), which itself represents the rate at which this information is beingprocessed. These measures are not localized; they do not depend on a single, immutable,hardwired detail of the brain but they do reflect subjective experiences, encoded by anyone of a number of possible hardwired circuits. However, they are not clinical tools formeasuring consciousness but rather represent ways to extract the information content ofthe brain from experimental measurements. Justifications, based on observational evi-dence, are given for the formulas presented. keywords: consciousness formula, correlation functions, brain waves, memory Email: [email protected] ntroduction
Consciousness, our personal higher form of “self-awareness”, is time dependent and has a limitedfocus of attention. For human beings it defines who we are. The aim of this paper is to attemptto understand the nature of consciousness based on measurements made on the brain. Thereis convincing evidence linking consciousness to the brain see, for instance, Greenfield, 2001[1].We relate consciousness to the information available in the neocortex of the brain at anymoment of time, t , or to the rate at which this information is processed by the brain. Thesetwo related definitions give rise to two specific formulas for measuring consciousness. Therelevant information content of the brain can be determined from the measured brain wave EEGcorrelation functions by using ideas from information theory (Appendix A) and a mathematicalidentity (Appendix B).The first step required then is to justify the use of brain wave correlation functions to probebrain information. The second is to explain how the information content present in brain wavesis extracted. Thus we first discuss the nature of the information contained in brain waves thathave been established by experiment and then then describe the procedure for extracting thisbrain information from brain waves. Before we do this certain basic features of consciousnessmust be discussed.Consciousness can be separated into two classes: primary consciousness and higher con-sciousness (see for instance Edleman[2]). Primary consciousness is our basic awareness of theworld immediately around us and our knowledge of where our body ends and the externalworld begins as well as our ability to distinguish between our friends and enemies. This formof consciousness is necessary for all living creatures in order for them to survive and function.In contrast higher consciousness involves a thinking subject who is aware of his or her acts andalso has an awareness of mental constructions. For this higher form of consciousness to oper-ate requires the subject to have memory and the ability to respond to external environmentalchanges.Thus in our measurement based approach we require that the variables selected have ac-cess to memory, that they respond to external environmental signals and that they are timedependent. The requirement for access to stored memories is crucial as it makes the approachsensitive to personal subjective experiences, thoughts and experiences. The variables selected,the EEG correlation functions, are robust measurable time dependent features of the biologicalbrain that, as we show, have access to memory and are responsive to internal and externalsignals.Many approaches for understanding consciousness have been proposed with very differentstarting points and different objectives. An incomplete list of references of some approaches are:non-linear mathematics [Scott, 1995] [3], quantum theory [Penrose et al, 1995, 2011][4], quan-tum field theory [Vitiello 2001, Vitiello and Freeman, 2006, Stanford Encyclopedia of Philoso-phy, 2011][6], [Jibu et al., 1996] [5], [Chakraverty, 2014][7], holography [Pibram, 2004][8], evolu-tionary biology [Edelman, 1992][2], neuoroscience [Crick, 1994,Fingelkurts, 2010, Fingelkurts,2013][9], [46][47] philosophy [Chalmers, 1995][14] [Dennett, 1996; Putnam ,1988] [12][11], com-puter science [Churchland, 1986; Llyod, 2010] [10][15], cognitive science [Hobson,2000] [24],linguistics, psychology [James, 1977; Blackmore, 2002][20] [13], psychiatry [Hebb, 1980; Baars,1988] [18] [45], theoretical physics [Josephson, 1992] [16] and religion [Nikhilananda, 2005] [26].Further references can be found in the works of the authors we have listed.2here are a growing number of works in which the ways of measuring consciousness hasbecome the focus of attention. A recent review by Seth et al. [43] examines some of theseapproaches and can be consulted for an overview of the diverse methods used for this purpose.The review includes approaches based on measuring EEG brain signals.We briefly comment on two interesting approaches that use brain EEG data and eitherendeavor to measure consciousness using statistical methods or suggest a way in which thestructure of the data is related consciousness.In the first approach due to Casali et al. [44], the way in which brain waves are distributedand interact dynamically when probed by a transient magnetic field are used to define oper-ationally, a measure of consciousness. The method has been clinically tested and found to beeffective. It can differentiate vegetative states from minimally conscious states and can identifystates in which a subject is conscious but cannot communicate due to motor defects. However,the approach does not suggest a theoretical interpretation of what constitutes consciousness.The aim of the second approach, which has been studied by a number of authors, is to relateconsciousness to the presence of hierarchical, temporal, architectural structures identified bybrain waves. (See, for instance, Fingelkurts et al., 2001 [50]). These transient structures areshown to map onto structures and events within the outside world. It is suggested that bycapturing these hierarchical, temporal, architectures a conscious robot could be built. Theidea of consciousness proposed in these works is time dependent and global but no overall,conceptual understanding of consciousness is proposed and neither is there any attempt to linkconsciousness to memory.In a different direction Tononi [Tononi, 2008] [27] has proposed a formula for measuringconsciousness, based on an analysis of the structure and linkages between different operationalsubunits of the brain. In this work consciousness is related to the structure of the biologicalbrain by an explicit formula. The mathematical formula is constructed using the idea of inte-grated information, which is a rule for determining the information present in the entire brainthat is more than the information present in specially chosen subunits of the brain. Conscious-ness, C , is defined as the difference between the information content of the entire brain, E ,and that contained in the sum of a certain, prescribed set of brain subunits, P S I , that canbe regarded to be independent unconnected entities. Thus, C measures the degree of entan-glement present among brain subunits, which makes E different from P S i . The quantity ofintegrated information present in a system is taken to be a measure of its state of consciousness,while the quality of a conscious experience depends on a ”shape” in the space of qualia. Theprocess of discarding informations introduced by Tononi [Tononi, 2008][27] can be representedsymbolically as the difference, C → E − P S i . It would be zero if the information content of thesubunits, regarded as independent entities, determined the information content of the entirebrain.The measure for C introduced in this way is broad enough to be extended to discuss theconsciousness of all entities whether they are living or non-living as all that is involved isthe notions of units, subunits, entanglement and probability. Hence consciousness is a uni-versal property of the universe and levels of consciousness can be calculated. Evaluating theconsciousness value for a human being at a given moment is, however, not easy. It requiresassigning probabilities and calculating the extent that these brain subunits deviate from a stateof complete independence, based on a knowledge of how they are linked together. Nevertheless,conceptually the framework of Tononi et al. represents a significant step forward because it3ntroduces the idea of a complex system with subunits, all which are massively linked, as amodel for understanding consciousness. It also puts forward for the first time an operationallydefined formula for consciousness.However there is also a theoretical problem that Tononi’s approach faces. An insight ofcondensed matter theory is that knowledge of the structure of a complex system does notreveal its function.[6]. Consider a piece of matter. If we are given all of the atoms and theway they interact with one another within the system we would not be able to predict thatthe system behaves as if it contains phonons. Phonons, essential for understanding crystallinesystem, are not present as part of initial structure but, rather, only emerge once formation iscomplete. This observation means that identifying material brain structures with consciousnessmay not be possible.In this paper a very different approach is used to derive two formulae for consciousness.Unlike Tononi[27] our approach does not depend on the hard wiring details of the brain; neitherdoes it require identifying specialized subunits of the brain. Instead, the approach proposesthat consciousness for human beings, is always a time dependent feature that depends onmemory and responds to external signals. It is proposed that consciousness can be definedas either the information available in the brain at time t or as the rate of processing thisinformation. The key point of this paper is to describe and justify a procedure for extractingthe information present in the brain from EEG correlation measurements.The details of theprocedure are given in the section where the model proposed is described. Our starting point isthe conjecture that the brain waves contain brain information. Brain waves observed in the EEG[Hobson,2000] [24] represent the sum of all of the electrical pulses between masses of neuronscommunicating with each other within the brain (see Freeman[55], Tognoli [56], Fingelkurts[57],Fingelkurts[58]). Consequently, the dynamic state of the brain that can be measured at anypoint in time is represented by the total time-dependent information contained in the ensembleof brain waves at any given moment. This information includes that arising from emotions,facts, images, sounds, taste, memories and thoughts as well as information from the central,autonomic nervous system about the state of all our organs. This wide range of availableinformation is contained in brain waves as the elegant experimental results of Colgin et al[30]show that there is an ongoing dialog between brain waves and stored memory.Our memory has a crucial property: it seems to be invariant over time, while our cellularproteins constantly change. Thus, memory provides the continuity of our self that we accept asa feature of our existence. Our memory allows us to respond to changing situations, recognizefriends, recall past events and engage in abstract activities, such as music, art, mathematics andscience and define who we are. Thus, any theory of consciousness should include memory as anessential feature. This linkage is absent in the approach of Tononi[27]. The experimental studyof memory is currently undergoing a revolution see Tonegawa et al.[31], Queenan et al.[32], fora review of earlier work see Kandel et al[33].A basic observational feature of the brain is that it operates in three well defined states.These states are the waking state, the dreaming state and the state of deep sleep [Hobson,2000][24]. It has been found that associated with each of these states, there are specific,detectable, electrical brain waves ranging in frequency from less than 3 Hertz for deep sleep(delta waves), which are widespread, 4 to 8 Hertz for the dreaming state (theta waves) with aregional distribution that can involve many areas of the brain, to 8 to 12 Hertz for the normalawake state (alpha Waves), which usually involve the entire lobe with a strong concentration4n the occipital region when the eyes are closed. Frequencies above 13 Hertz to 40 Hertzrepresent a super alert state (beta and gamma waves) and these waves can be very localized.All of the brain waves referred to above are present at all times but, depending on our state ofwakefulness, one or other specific forms of these waves can be dominant. For example, when aperson opens his or her eyes, the alpha waves diminish and the beta waves increase. However,in both of these states gamma waves are also present (see Baars[45]). Recent research workhas also established that whenever a person begins a new activity, a unique brain wave pulsewith directionality is generated. If the same activity is then repeated, the pulse observed isdifferent from that observed during the first instance of the activity [Alexander, 2013] [25]. Ifbrain waves do represent the state of the brain, this observation would make sense because theperson themselves has changed between the two sessions of activity.There are no brain waves constantly present in the cerebellum. The ones that do at timesappear there are in response to inputs and are in the theta-range, the gamma-range or are in avery fast oscillation range (over 80 Hertz). Oscillatory behavior requires excitatory neurons. Inthe cerebellum there are a few such excitory neurons in the form of granule cells. Recent work[Knopfel, 2008][23] has shown that the gamma and the very fast oscillations are generated inthe cerebellum when external agents are introduced but these oscillations do not come fromthe excitatory granule cells themselves. Instead, they come from the inhibitory neurons thatare present. In addition the observed frequencies seem to correspond to ones observed in thecerebral cortex under similar conditions of excitation.The process of reconstruction of the external world and the constant monitoring of the stateof our internal organs are both essential for us to live successfully in the world. These brainactivities are reflected in the brain waves observed. (Fingelkurt et al[52]. Brain waves changewhen we open our eyes or hear sounds or when we faint. What molds our consciousness?
We start life with the history of our ancestors encoded in our DNA. This genetic informationcontains all of the mutations due to environmental mutagenesis and selection that our ancestorshave experienced. At the penultimate end of this descent we have our immediate ancestors,namely our parents and grandparents. This DNA history contains old data from the humanspecies and its wanderings [2, 9]. Thus, at birth we arrive with certain predetermined physicalcharacteristics and tendencies. From then on the environment in which we grow begins playinga significant role. By the environment we mean childhood upbringing, schooling, interactionwith friends, books, films, music, social media, family, sports and so on. There is also the wellknown effect of group and community behavior. Group behavior seems to be generated bysound, non-verbal clues and the presence of some catalysts, all of which results in members ofthe group reacting in an atypical fashion, while community behavior is decided by the normsand values of the community in which we live. This behavior sometimes transcends one’s owncommunity and in special situations one either rejoices or mourns together as a nation or as ahuman being.All of these observed effects have an effect on a person’s memory, sense of belonging, valuesystem and consciousness. This rich set of environmental effects listed does not pretend to becomplete but it underlines the fact that defining who we are is complex. Sometimes in this richtapestry the influence of one person or one event can determine the course of our life and sets5he goals that we seek [60].There are other important influences in our life that do not come from the environment orfrom interactions with others but, rather, from more abstract sources. For instance there arebooks and religion that tell us what are the aims of life and how it should be lived. Then,there are legends and histories of our country that very often suggest certain codes of conduct,certain aspirations and certain ways of regarding those not belonging to our own country, clanor community. They are, thus, of great importance for our perception of who we are [61][62][63].The changing nature of our consciousness with age is reflected in the distribution andnature of our brain waves [73]. As our consciousness is molded our brain waves change. Theseremarks suggest that consciousness is not determined simply by the hardwiring of the brain buton the ever changing coherent dynamics within an assembly of brain cells. Our awareness isinfluenced by our past experiences and our environment. It is a coming together of all our senseand emotional inputs including the state of our health. Conscious states are thus composed ofrepresentations of the world at the present moment and embedded within a representation ofwhat is present are the sensations, feelings and thoughts that represent the past [51].Let us now describe our model.
Model for Consciousness
We have proposed a measurement-based approach for the study of consciousness. A measureof a conscious experience is defined as the dynamic information contained in the brain at anygiven moment of time t and the measure of consciousness as the rate at which this information isprocessed at time t . These measures require time dependent brain wave observations. We havechosen EEG brain wave correlation functions as an example of an appropriate set of variablesto use and have justified this choice using experimental results. The ensemble of brain wavecorrelation functions have two essential features. They contain subjective memory information[30]and they reflect and respond to both the external world and our complex inner world [52].We also note that consciousness has different degrees. The lowest degree of consciousnessdistinguishes between the boundaries of living animals and their environment and allows ananimal to identify food and avoid predators. The higher degrees of consciousness lead to thecomplex notion of self awareness, necessary if a person is to have aspirations, to experience love,compassion, self sacrifice as well as a feeling of self worth. We have suggested that this higherlevel of consciousness crucially depends on memory, that in turn depends on many things,including our environment. Finally, we have suggested that besides the reasonable channels ofmemory formation, such as through reading, hearing, personal experiences and human contactsthere could be further, presently unknown sources, coming from our genetic history.We show (Appendix B) how a time dependent probability function P ( t ) can be constructedfrom the measurement of brain wave correlation functions.This function, P ( t ), has the propertythat the space average of brain potentials using it reproduces the measured brain wave corre-lation functions . Consciousness, C ( t ), as the information content of brain waves at time t , isthen, according to information theory, given by the formula C ( t ) = P − P N ( t ) ln P N ( t ). This isthe Shannon information formula (Appendix A) for brain waves and defines for us the dynami-cal brain. Alternatively, consciousness can be defined as the rate of processing this information D ( t ) given by D ( t ) = dC ( t ) dt . Thus, consciousness in the model represents the information con-6ent of or the rate at which information is processed by the dynamical brain at time t . It isrelatively easy to justify choosing EEG data for understanding consciousness because there isoverwhelming evidence establishing that brain waves reflect our interactions with the externalworld (see, for instance Freeman[48],Nunez et al[49],Fingelkurts[52]). Brain waves also reflectour conscious and even our subconscious thoughts as well as our personal, subjective experi-ences. This realization follows from the fact that brain waves interact with memory and hencehave access to our conscious and subconscious thoughts and our stored experiences [Colgin etal, 2009][30].We should note that the measures of consciousness proposed are based on extracting theinformation contained in the brain from brain wave measurements. They are not meant to beused as clinical tools as proposed by Casali[44]. It should also be stressed that the specificmeasures proposed certainly do not capture the full richness of conscious experience. They are,however, the start of a project to study subjective consciousness using brain measurements.We now give details of how to use measured brain waves to measure consciousness. Considerthe measured correlation functions, G = G ( V ( x , t ) V ( x , t )), for points ( x , x ) of the brain,at time, t , to represent the state of the dynamic brain at time, t , where, V a ( x , t ) , V b ( x , t )represent measured electric field values at two points for waves, a, b , that can represent anyone of the observed brain waves, i.e the alpha, beta, gamma, theta or delta waves. We willsuppress labels, a, b , present in V ( x, t ), from now on and use the notation, V i for V ( x i , t ) and G ij for G ( V i V j ). Each set, V V ..V N , represents a message of length, N .Using standard tools of mathematics we show, in Appendix B, that from the measured brainwave correlation functions, G ij = G ( V ( x i , t ) V ( x j , t )), a time dependent probability functioncan be constructed. It is: P N ( t ) = 1 Z e P Nm,n +2 [ V m ( G − ) mn V n ] Z = √ q | det ( G − ) mn ) | where, | det ( G − mn ) | , is the determinant. This is the key step of our approach. Once P ( t ) isconstructed from data we can immediately define the information content of brain waves attime t by the Shannon information theory formula as, C ( t ) = − X P N ( t ) ln P N ( t )Shannon’s formula is discussed briefly in Appendix A. The sum is over the N points measuredand the range of allowed values of the potentials V m is measured at time t . The range of thesevariables is − < V <
100 in units of millivolts. We identify C ( t ) as a measure of a consciousexperience and D ( t ) = dCdt , as a measure of consciousness. It represents the rate of processinginformation. The formulas proposed are theoretically well founded and grounded in data: theyare not an ad hoc constructions. Both C and D include subjective experiences.The measure is chosen to have two properties: C (0) = 0 and ( dC ( t ) dt ) t =0 > C (0) = 0. When timedependence is present consciousness increases from zero hence ( dC ( t ) dt ) t =0 >
0. Thus in ourapproach consciousness of a human being cannot be constant. It must change with time. An7mmediate consequence of these conditions is the result for t small: C ( t ) ≈ C (0) + t dCdt = t ΩThus for small times C ( t ) ≈ t Ω where Ω is a characteristic frequency associated with a brainwave. We have taken C (0) = 0. In general a response to an input signal corresponds to achange in t from t to t + t . Then we have C ( t + t ) − C ( t ) = t Ω. Thus C ( t ) can increase ordecrease depending on whether Ω is larger or smaller than it was at time t .Let us suppose we can introduce an effective probability function of the form, P ( t ) ≈ e − F ( tω ) , F ( ω ) >
0. Such a structure is reasonable from dimensional reasoning. The formulagives C ( t ) ≈ dF ( tω ) dt e − F ( tω ) where we have used the fact that the dominant contributions comefrom the region where F ( tω ) <
1. This simple example is not meant to be realistic as we haveused a single effective probability with just one frequency ω . Nevertheless, this example makesthe link between frequency and C ( t ) clear. In the next section we give a quantitative argumentlinking different states of awareness and frequencies.. Concluding Remarks and Comments
An approach to the study of consciousness, based on experimental measurements of brainwaves (neural oscillations) is proposed. In the approach a method for extracting the informationpresent in brain waves is suggested. This involves constructing a probability function P ( t ) fromthe measured brain wave correlation functions with the property that the average value of brainwave potentials calculated using it, namely, < V ( x, t ) V ( y, t ) > = R dV P ( t, V ) V ( x, t ) V ( y, t ), givethe measured correlation function between the chosen points x, y (Appendix B).Information theory tells us that if the probability, P , for a message of length N is knownthen the information contained in all possible messages of length N received is given by aformula due to Shannon [28]. Here we have taken a given set of measured brain wave potentials V V ..V N at time t to represent a message of length N . All possible messages of this lengththen correspond to the allowed range of values of the potentials V i , i = 1 , , ..N and on therange of values of N ≤ N m , where N m represents the total number of measured points. TheShannon formula, C ( t ) = P V − P ln P, i = 1 , , ...N , can be used to determine the informationcontained in all brain wave messages if we have a theoretical method for assigning a probabilityto a given brain wave message V , V , ..V N of length N . In Appendix B we explain how sucha probability function can be constructed from measured EEG correlation functions. Thesecorrelation functions contain the effect of all the complex interactions present between brainwaves as they are based on measurements, not theory. They are not expected to have anyuniversal structure but to have forms that reflect the complex interactions between brain wavesat the moment of time when observations were made. Thus the probability function obtainedis not a theoretical construct but based on data.A measure of consciousness D ( t ) = dCdt is then defined as the rate of change of the brainwave information at time t t. The definition it should be stressed is a specific measure ofconsciousness. We do not think a simple function of time can completely capture the richnessof experienced consciousness. Such a proposal is useful if clinical or neuroscience evidence isprovided to establish that brain waves have three important properties.8he first property is that brain waves provide an accesible means for exploring the dy-namical state of the brain. This is supported by neuroscience research [66][67]. A quote fromNorthoff[64] makes the point well. “In the same way as physical activity can be relationallydetermined, the brain can encode neural activity in a relationally determined way.”EEG measurements are one way to measure the brain’s neural activity. The method hasits technical limitations as scalp measurements cannot probe subcortical neural properties.However there are a variety of tools available to study neural oscillations and neural correlationfunctions such as fMRI, ERP, PET, MEG, etc [65].The second property is that brain waves constantly interact with the memory centers ofthe brain. It is well known that brain waves play an important role during memory formation[33, ? ], however, to establish the presence of a constant interaction between brain waves andmemory centers is important as it implies that brain waves contain in them personal subjectiveexperiences. Supported for such a feature comes from the observations of Colgin et al [30]and others [75, 76]who found that brain waves carrying incoming information, access memorycenters of the brain many times a second. This is done in order to interpret the nature of the incoming information . The process of comparison with memory creates “awareness” in a personregarding the nature of the incoming signal. As memories are subjective we can conclude thatbrain waves carry subjective information. It should be stressed that the brain wave patternsat any given moment of time, contain only a small fraction of the available information in thedynamic brain. The nature of this information is dependent on the areas of the brain that areprobed, the time and the environment.The third property is that there is strong clinical evidence linking memory and consciousness.There are numerous works on this topic[71, 69, 70, 68, 51, 72]. Tulving[69] provides empiricalobservational support for links between different memory systems(procedural, semantic, andepisodic) and corresponding varieties of consciousness ( anoetic, noetic, and autonoetic) theyare related to. In particular that episodic memory has autonoetic consciousness as its necessarycorrelate. Procedural memory is included in Tulving’s list, but this form of memory does notcontribute to consciousness in the sense of “awareness”. Thus the consciousness associated withthis form of memory Tulving calls, anoetic (not knowing) consciousness. Implicit memoriesthat do not contribute to awareness include the self regulatory centers of a living system thatregulate breathing, heart beats and body temperature [53]. In the absence of these memoriesthere would be no consciousness in a human being. Memory, as discussed by Tulving andothers cited, is thus necessary for consciousness. But consciousness and memory are not thesame. Consciousness is a moment-to-moment feature of living systems, while memory providesthe continuity of a person’s self, contributes to the content of conscious awareness, but it alsoprovides the information necessary for a person to survive in the world.We can conclude that the measure of consciousness proposed is useful and that it containssubjective information. The hard problem of consciousness for the model is thus to decode brainwave information, that is to understand, for instance, the way brain waves encode memoryinformation and information regarding our vital organs.The work of Fingelkurts et al.[52] is an important step in the direction of decoding brainwave information. They show how structural brain wave patterns can be mapped to events ofthe external world, but the imprint of memory present is not studied.In our brain wave picture the quality and meaning of a conscious experience is captured9ot just by C ( t ) but by the unfolding in time of a three dimensional surface representing thedistribution of V i , i = 1 , , ..N values as a result of an incoming signal interacting with memory.The unfolding time is expected to be a fraction of a second rather than milliseconds[30].Finally we briefly address a conceptual issue regarding the way consciousness and informa-tion are related in the model. The basic idea of the model is to construct a specific measure ofconsciousness in terms of the information content of the brain, extracted from measurements.We used measured brain wave information to to access the information content of the dynamicbrain and used this procedure to construct our measure of consciousness. Such a hypothesiswas made because of the link, supported by clinical research, between brain waves and memoryand between memory and consciousness [69]. Memories contain subjective information hencethe hypothesis that consciousness is related to the rate at which the brain processes informationis reasonable. The information relevant for human consciousness was associated with the brain,was time dependent, had the ability to constantly change in response to external input signalsand was embedded in an interactively generated memory system [51, 69]. Consciousness is afeature of a system. However the model can determine the degree of consciousness given anyinformation function C ( t ) by simply determining D ( t ) = dCdt but the value obtained will beinterpreted as the degree of consciousness of a system that has C ( t ) as its information function(Appendix C). It should be clear that a specific measure of an attribute is not the same as theattribute. Thus abstract information without further qualifications is not conscious [78].Our approach follows the standard practice of science, namely a system is specified (thebrain), the abstract idea of information contained in the system is determined from observation,using mathematical ideas, and then a specific hypothesis is made linking the rate of processingbrain wave information to human consciousness. This hypothesis can be tested. The test isto check that the degree of awareness of a person is related to the frequency of brain waveoscillations. We will discuss this result shortly. For modeling a physical system a similarsequence of steps are followed. A system of interest is identified, a suitable set of relevantabstract ideas like that of an electromagnetic field or of energy or of entropy are identified andextracted from measurements with the help of theoretical ideas and then the abstract ideasare used to draw testable conclusions regarding the system. For example the notion of entropylisted, underpins statistical mechanics, used to study the thermal properties of systems. Theabstract concept of entropy can be formulated using information theory [19]. For systemsin thermal equilibrium the information content is time independent and hence the system’sconsciousness is zero.The measure of consciousness proposed has testable consequences. We stated, for example,that the measure predicts that there should be a positive correlation between brain wave fre-quency and the degree of consciousness. This prediction follows from the formula proposed aswe will show. However at the observational level it is known that a person in deep sleep, ina coma or with a brain injury have, predominantly, very slow delta waves, leading to a smallvalue for D ( t ) = dCdt , while states with higher brain wave frequencies, representing higher levelsof awareness, will have larger values for D . This statement requires clarification. In REM sleepboth high frequency gamma waves and low frequency theta waves are present. However gammawaves are also present when alpha and or beta waves occur. Thus, D ( t ) for REM sleep is lowerin value than in those states where alpha or beta waves are present. But the REM sleep valuefor D ( t ) is higher than it is for a person undergoing an epileptic absence seizure even thoughin this state there is high EEG activity. This dicotonomy is observed because the brain wavesduring an epileptic absence seizure have high amplitudes but low frequencies (Seth et al.[43]).10e can take states with D ( t ) values lower than or equal to those obtained for REM sleep torepresent states of unconsciousness.Let us provide a quantitative version of these remarks. Suppose C ( t ) = P i =1 c i C i ( t ) wherethe sum represents the contributions to consciousness from an ensemble of brain waves thathave delta ( i = 1), theta (i=2), alpha (i=3), beta (i=4) and gamma (i=5) brain waves inthem, with probabilities P i , i = 1 , ...
5. In this expression the average over allowed potentialsis implimented directly by a single probability for each type of brain wave. We will call thisreplacement the mean field approximation. The numbers c i , i = 1 , .. c i ≥ , P i =1 c i = 1. In anygiven moment of time all the waves are present but the value of the weights depend on thestate of awareness. Thus in the state of deep sleep c dominates while in the awake state c dominates. In states i = 2 , , c i.e a gamma wave, component present. We nextnote that C i ( t ) and c i are dimensionless numbers as they are related to probability functions.For C i ( t ) to be dimensionless requires it to be a dimensionless function of t , namely ω i t . Fromthis it follows that D ( t ) = dCdt has the structure D ( t ) = P i =1 c i ω i dC i ( x ) dx , x = ω i t , where we use C i ( ω i t ) dt = ω i dC i ( x ) dx , i = 1 , .. c is roughly the same for these states whileit is absent for the epileptic absence seizures. Thus the level of consciousness for an epilepticabsent seizure is lower than it is in REM sleep although there is considerable neural activitypresent. The sketch given makes a number of simplifying assumptions but it clearly links D ( t )to brain wave frequencies.Another important consequence of our approach is that it explicitly notes that consciousnessand life depend on the presence of both external and internal time dependent sources that areresponsible for the observed time dependence of brain wave signals. This observation meansthat consciousness is not determined simply by the hard-wiring of a person’s brain but, ratheron many other factors.What is the self in the model? We have provided an operational definition, based onexperimental results, that the self initiates our thoughts and actions in a way we do not knowand that it provides us with our sense of being the same person over time. This notion ofcontinuity of the self comes from our memory since the individual copies of our basic cellularproteins are degraded and replaced over a period of a few weeks while our sense of self persistsfor all of our normal waking lives. There is also a second observational feature that we describeby the term, ”self”. This feature arises from the work of Libet[17], which shows that an actionwe initiate seems to start before we become aware of having initiating it. We describe this resultand our feeling of the continuity of our personality as a defining feature of our ”self”. This formof the term, ”self”, as we use it in this instance, is a convenient terminology. For a glimpse of themany dimensions of “Self” , the works of Eccles [37]and Ramachandran [54]maybe consulted.We end by saying that, although we have proposed a measurement based approach forconsciousness that includes subjective data, we still do not know what it is or where it islocated. We still do not know what seeing or hearing really means, nor do we know whatfriendship, love, anger, loyalty or beauty are. These are all words that represent experiencesand emotions. Perhaps the best we can do in our attempt to understand consciousness is totry to capture important aspects of its abstract core by testable measurements. The remarkregarding the absence of real understanding also holds for matter. We do not know for instancewhat an electron ”really” is. All that we can say is that it can be characterized by a set11f properties that can be measured and that we can predict the way it behaves in differentsituations. Acknowledgement
I would like to thank Paul Voorheis for discussions, useful comments, and for extensive editorialhelp, Mani Ramaswami and Mike Coey for many discussions, comments and encouragementand Jean-Pierre Gerbaulet for a careful reading of the paper, for comments and for drawingmy attention to the work of R.Kurzweil on thinking.
References [1] Greenfield, S (20010
The Human Brain , Science Masters, Phoenix ,[2] Edelman, G(1992)
Bright Air, Brilliant Fire:On Matter and Mind , Penguine.[3] Scott, A.C. (1995)
Stairways to the Mind , Springer-Verlag, New York.[4] Penrose, R(1995)
Shadows of the Mind , Vintage, R.Penrose and S.Hameroff, (2011)
Jour-nal of Cosmology , 14
Quantum Approaches to Consciousness , Stanford Encylopedia ofPhilosophy, (2011), J.Searle,(1997)
New York Review of Books
53, Koch, C and K. Hepp,(2006)
Nature
International Journal of Modern Physics
B,10,1735-1754[6] Vitiello, G(2001)
My Double Unveiled , John Benjamin (2001),Freeman, W. and G. Vitiello,(2006)
Physics of Life Research
3, 93-118[7] Chakraverty, B (2014)
Proc Interdisciplinary Perspectives On Consciousness and the Self (Bangalore), 279-294, Editors Menon, S et al, Springer[8] Pribram,K (2004)
Mind and Matter
The astonishing hypothesis:The scientific search for the soul , Charles Scrib-ner’ Sons.[10] Churchland,P.S (1986)
Neurophilosophy: Towards a Unified Science 0f the Mind-Brain ,MIT Press.[11] Putnam, H(1988)
Representations of Reality , Cambridge, MIT Press.[12] Dennett, D.C (1996)
The Conscious Mind , Oxford University Press.[13] Blackmore, S.J (2002)
Consciousness: An Introduction , Oxford University Press.[14] Chalmers, D (1995)
Facing Up to the Problem of Consciousness , Journal of ConsciousnessStudies, 2, 200-219[15] Lloyd, S (2010)
A Quantum Computer Scientist Takes On the Cosmos , Knopf, March 14.1216] Josephson, B and E.Rubik, (1992)
The challenge of Consciousness Research , Frontier Per-spective 3, 15-19[17] Libet, B (1985)
The Behavioral and Brain Sciences , 8, 529-566[18] Hebb,D (1980)
Essays on Mind , Lawrence Erlbaum Associates, Hillsdale, NJ.[19] Introduction to Theoretical Physics , Wiley (1975)[20] James, W (1977)
Writings of William James , ed J.J.McDermot, Chicago University Press,169[21] Baars, B (1988)
A Cognitive Theory of Consciousness. (Cambridge)[22] Endel Tulving,(1991)
J.Cognitive Neuroscience , 3 , 89-94[23] Knopfel, T et al, (2008)
Neuron
58, 763-774[24] Hobson, A (2000)
Beh.Brain Sc
23, 793-842[25] Alexander, D et al, (2013)
NeuroImage , 73, 95-112[26] Swami Nikhilananda, (2000)
Mandukya Upanishad , Advaita Ashram, Kolkata.[27] Tononi, G (2008)
Biol.Bullt , Vol 215, No. 3, 216-242[28] Shannon, C.E (1948)
A Mathematical Theory of Communication, The Bell System Techni-cal Journal , 27, 379-423, 623-656[29] Dirac, P (1930)
The Principles of Quantum Mechanics , Oxford University Press.[30] Colgin, L et al (2009)
Nature , 462, 353-357[31] Tonegawa,S et al, Memory Engrams Storage and Retrieval,
Current Opinions in Neurobi-ology
Ann.N.Y.Acad.SCi
Cell
The Brain , Oxford University Press[35] Kurzweil, R(2012)
How to Create the Mind , Viking Penguin.[36] Huth, A et al, (2016)
Nature , 532, 453-456[37] Popper, K and J.Eccles, (1977)
The Self and Its Brain , Routlage and Kegan Paul,[38] Eccles,J (1994)
How the Self Controls its Brain , Berlin Springer-Verlag[39] Van Essen, D.C et al, (1991)
Proc.SPIE , 1473[40] Jacobson, H (1991)
Science
Encyclopaedia Brittannica, Information Theory and Physiology [42] Landau, L.D and E. Lifshitz, (2005)
Statistical Physics , Elsevier[43] Seth,A Review of Measuring Consciousness, Cell (2017) (in press)[44] Casali, A et al A Theoretically Based Index of Consciousness independent of SensoryProcessing. doi:10.1126/scitraslmed.3006294[45] Baars,B.J, (2003)[46] Fingelkurts, A.A.; Fingelkurts, A.A.; Neves, C.F.H. Natural world physical, brain opera-tional, and mind phenomenal space-time.
Phys. Life Rev. (2010), 7, 195249.[47] Fingelkurts, A.A.; Fingelkurts, A.A.; Neves, C.F.H. Consciousness as a phenomenon inthe operational architectonics of brain organization: Criticality and self-organization con-siderations.
Chaos Solitons Fractals (2013), 55, 1331.[48] Freeman, W.J. Indirect biological measures of consciousness from field studies of brains asdynamical systems.
Neural Netw. (2007), 20, 10211031.[49] Nunez, P.L. Toward a quantitative description of large-scale neocortical dynamic functionand EEG.
Behav. Brain Sci. (2000), 23, 371398.[50] Fingelkurts, A.A.; Fingelkurts, A.A. Operational architectonics of the human brain biopo-tential field: towards solving the mind-brain problem.
Brain Mind (2001), 2, 261296.[51] Doege,P, The Mind-Brain Problem in Cognitive Neuroscience, Philosophia Scientiae, 17-2(2013)[52] Fingelkurts, A.A.; Fingelkurts, A.A. Mapping of the brain operational architectonics.In: Chen, F.J., editor. Focus on Brain Mapping Research.
Nova Science Publishers, Inc. ;(2005), p. 5998.[53] Le Doux, J, The Emotional Brain, Simon and Schuster,N.Y (1996)[54] Ramachandran, Phatoms of the Brain, Fourth Estate, London(1999)[55] Freeman, W.J. (1975).
Mass Action in the Nervous System.
New York: Academic Press.[56] Tognoli, E., Kelso, J.A.S. (2013). On the brains dynamical complexity: coupling and causalinfluences across spatiotemporal scales, In:
Advances in Cognitive Neurodynamics (III) , edY. Yamaguchi (Netherlands: Springer), 259265.[57] Fingelkurts, A.A.; Fingelkurts, A.A. Timing in cognition and EEG brain dynamics: dis-creteness versus continuity.
Cogn. Process.
Phys. Life Rev. (2010), 7, 195249.[59] Le Van Quyen et al, High Frequency oscillations in human and monkey neocortex duringwake-sleep cycles. doi:10.1073/
PNAS.
Phil.Trans.Royal Society,Lond B.Biol. Sc ,365 (1413),1351-1361, (2001)[69] Tulving, E, Memory and Consciousness, Canadian Psycology,26(1),1-12 (1985)[70] Ebbinghaus,H, Memoirs: A Contribution to experimental psychology (1895), Dover,N.Y(1964)[71] Franklin,S et al, The role of Consciousness in Memory,brain-mind-media.org urn:nbn:de0009-3-1505[72] Shevlin,H, Consciousness, Perception and Short-Term Memory. PhD Thesis, CUNY Aca-demic Work (2016)[73] Articles in:Craik et al, Handbook of Aging and Cognition, (3rd Edition), Mahwab,N.J.Lawrence Erbaum.(2011)[74] Hof,P.R et al, The aging Brain: morphomolecules and senescience of cortical circuits,Neuro.Sc 27(10)60713 (2001)[75] Miller,P et al Dynamic models of large-scale brain activity, Nature Neuroscience, 20, 340-352 (2017)[76] Amir,A et al, Vigilance-Associated Gamma Oscillations Coordinate the Ensemble Activityof Basolateralo Amygdala Neurons, Neuron 97, Feb 7 (2018)[77] Viahou et al, Nature: Scientific Reports 4, Article No 5101 (2014)[78] Pockett,S, Problems with theories that equate consciousness with information or informa-tion processing: Frontiers in neuroscience,8(2014)15 ppendix A: Basic Formula of Information Theory
Any device, system or process for generating messages is called an information source. Eachsource has an alphabet. A message containing information has regularities. It has statisticalstructure. A real source of information can be modeled, for example, as we do, by time depen-dent correlation functions, which contain a messages formed from the alphabet given by themeasured values of the electric field V i at large number of different points of the brain. Thesemessages contain information that are of interest. If a time dependent probability function P ( t ) can be assigned to such a message then A = − P P n ln P n is the average information permessage. For P ( V , ...V n ) the sum is over the location and range of values of all the V i presentin P i.e can take. The maximum value this sum A can take is called the capacity, K and isgiven by K = M ln N , where M is the range of values the variables V i can take and N thetotal number of source points possible. For the brain we can take N ≈ then K ≈ M × ≈ [40]. Appendix B: Assigning Probability to Correlation Functions
Consider correlation functions of electrical fields G ij = G ( V i , V j ) at any two brain points mea-sured at times t i .t j for measured potentials V i = V ( x i , t i ) , V j = V ( x j , t j ) , j = 1 , ...n . Wesuppose that measurements are made for a large number of point i , i , ...i N , and take the set ofthese measurements to represent a state of the dynamical brain at time t when t − t , ..t N = t .We also suppose G ij = G ji . The set of values V , V , ..V N at time t is a message of length N in the sense of information theory. The set of all messages then corresponds to all allowedvalues for this set for 1 ≤ N ≤ N max , where N max is the maximum number of points wheremeasurements have been made. We assume that the eigenvalues of the matrix G ij are real andpositive. This reflects the absence of strictly localised brain waves. However the model can beadjusted to deal with such excitations if EEG data reveals their presence.There is a simple procedure to extract a probability function from correlation functions.We start from the set of measured G ij values and use the following identity, G ij = 1 Z Z [ dV π dV π ... dV N π ] e − P Nm,n =1 [ V m ( G − ) mn V n ] V i V j Z = Z [ dV π dV π ... dV N π ] e − P Ni,j =1 [ V i ( G − ) ij V j ] where R [ dV π ... dV n π ] represent integrations over the measured set of numbers V ...V n . These num-bers all lie in a given range of values defined for the each type of brain wave considered.However for the identity to hold the range of any V m is −∞ < V m < + ∞ and det ( G ij ) = 0.This replacement of finite ranges by infinite ranges does not introduce a large error. . The timedependences present in V ( x, t ) is due to external and internal sources of information which arespace and time dependent.Let us consider the case of where only a single pair of measurements V = V ( x , t ) , V = V ( x , t ) is used to describe the brain state. The probability P of this brain state, in the model,16s given by (setting t = t = t , P ( t ) = 1 Z e − P [ V ( x i ,t )( G − ) ij V ( x j ,t )] Z = 1 q | det ( G − ( V i , V j ) | Here det | G | is the determinant function of the measured correlation function G and i, j cantake the two value, 1 ,
2. Then G = < V V >, G = < V V >, G = G = < V V > ,where < V i V j > is the two point correlator at time t . For the case when N different pointmeasurements are made for times t , we have the n point correlation function G ( i , i , ...i N )where V = V ( x , t ) , V = V ( x , t ) ..., V N = V ( x N , t ) can be similarly expressed in terms ofmeasurements. The corresponding probability function is P N ( t ) = 1 Z e − P Nm,n =1 [ V m ( G − ) mn V n ] Z = 1 q | det ( G − mn ) | In order for our analysis to apply the matrices G must have non zero determinant. Appendix C: Consciousness of Matter