The Soul/ Body Problem: A New Proposed Solution—Wave Interaction Dualism



 “To attain any assured knowledge about the soul is one of the most difficult things in the world.”


“….with what facts shall we begin the inquiry?”    Aristotle. On the Soul. Book 1, Chapter 1


 A new set of scientific facts for consideration in Philosophy of Mind and Neuroscience




Part 1:  Dualism and the Soul/ Body Problem

Part 2:  Wave/Particle Physics and Soul/Body Wave Interaction Dualism in Humans  

Part 3:  Wave Interactions and Compressible Flow  






A solution, expressed in scientific terminology, to the classic philosophic problem of the Dualism of Soul and Body  is offered by  the introduction of a physical wave behavior to the soul when it is embodied, so that a new unity  emerges.


The wave/particle example from quantum  physics is only partially dualistic  since it is the  unified interaction product of a physical wave speed  and a physical particle velocity. The new soul/body wave analogue is  the unified, and at the same time dualistic,  interaction product of an immaterial  soul’s wave speed c  and a bodily motion V.  


The proposition is explored that the spiritual, human soul, in its association with the body, obeys  the fundamental classical wave equation of physics exactly, whereas, in physics itself, only approximations to it are observed.


The new wave interaction approach is presented as  ‘a new set of facts’ for consideration in the Philosophy of Mind and Neuroscience





                       Dualism  and the Soul/ Body Problem






1.1 Introduction    


The philosophy of  human consciousness and intelligence, today involves an input of scientific facts from a large number of scientific disciplines, such as neuroscience, biophysics,  psychology, information theory and the like. 


In classical philosophy, the human or rational animal is described as a creature composed of the  union of a material body and a rational soul,  The question then arises as to how the two essentially different entities of body and of spirit  can  join to form an organic unity.  We shall attempt a scientifically based solution to this key problem. This is the well defined and well studied problem of dualism,  of which a classical example has been that of the philosophy of Descartes [1, 2].  He postulated that there were two entirely different substances involved in humans, namely matter and spirit; but then, the objection arose as to how  two entirely different entities could be joined to constitute a unity? How could they interact?


The theologian Karl Rahner,  S. J. [ 3,5 ] argued that body and soul cannot  be completely different, otherwise the two could not be joined to form an organic unity. Bernard Lonergan, S. J. makes the same point, from a different perspective, in his Insight: A Study of Human Understanding.[4]. These philosophers and theologians argue that the soul, in some aspects, must be similar to matter. What could these similarities be?


This question has led us to a search for material forms which an immaterial soul  could  emulate, or assume the role of, in order to function as a unity in a material body. In this search, the example of the  wave/ particle conundrum of early quantum physics was considered, and a dualistic, wave- interaction energy term 2cV in a flow energy equation was seen as offering a possible solution.


1.2  General Approach to the Dualism Problem


If the soul and body are to interact  in an intimate organic unity, then in human physical matters, the soul must participate in the physical activities of the body, and in those instances must be subject to the same physical and chemical laws as the body.


Therefore, some scientific laws must pertain even to an immaterial soul, not intrinsically, but  in those physical activities which the soul shares with the body.


Again, the material brain is flooded with the waves, electrical and electrochemical  in nature, which pertain to received sensory data and to the intelligibility they contain, transfer  and store. An entity which scans and interacts with this material intelligibility in  the brain and nervous system, even if  this scanning entity is  spiritual,  clearly  must possess,  or assume,  properties that relate to matter and to its laws of physical action.


We proceed to offer  a solution to this Dualism problem via a comparison with the laws of wave/ particle interactions  in quantum physics and in compressible fluid flow, with emphasis on the wave qualities. 



1.3   Physical Dualistic Wave Interactions  in Quantum Physics and in Compressible Flow ; A Unifying Concept


 Example 1: The physical wave/ particle dualism of quantum physics.    From its earliest days, a main feature of quantum physics was the question of how the quantum entity (wave function, Ψ) could  be, or could represent,  both a  wave and a particle. Waves and moving particles are dissimilar, but they are alike in both being physical motions. These quantum wave entities thus appear to be dualistic physical entities which are worth study.


In the case of quantum physics, the symbol Ψ, the ‘wave function’, represents,  in the Copenhagen interpretation, a wave amplitude, and  the square of this amplitude, Ψ2, , is the probability of the particular quantum action  taking place, or of the particle being in a particular place. For an  interaction of two quantum wave amplitudes, Ψ1 and Ψ2 , the ‘square of the sum’ rule applies in computing  the desired combined  probability, namely P = [  Ψ1 + Ψ2 ]2  = [  Ψ12  + Ψ22 + 2 Ψ1 Ψ2 ].  Here, a dualistic or mixed wave function ‘interaction’ term  appears as [2 Ψ1 Ψ2.].


Example 2:  Wave/ pulse Interaction Energy


Another example of wave particle interactions lies in compressible flow physics. Such flows have a wave speed c ( e.g. acoustic waves, acoustic  waves of compression or rarefaction, etc. ) and a local flow velocity V of fluid. If the particular  compressible fluid obeys the  classical wave equation, its wave pulses  then  travel at a pulse velocity (dx/dt)I, II  given by:


(dx/dt)I, II = c ± u 


where u is the component of flow velocity V in the x-direction.


Therefore, the wave pulse specific energy ( i.e. the energy per unit mass) in the x-direction is the square of the pulse velocity, that is 


Epulse =   (dx/dt)2 I, II = ( c ± u  )2 = c2 + u2 + 2cu,  and c2 + u2  − 2cu 


where 2cu is the interaction energy between wave speed c and flow u in the x direction, and in  the minus x-direction..


In three dimensions, we have ( c ± V)2 = c2 + V2 ± 2cV.


We see that these classical wave pulses travel at a velocity sum ( c + V), and that  the two c and V  speeds  also  interact to produce the  wave pulse energy containing the interaction energy 2cV term This wave speed plus flow speed  interaction in compressible flow  is the counterpart to the quantum wave/particle interaction; it is also  a unity of two dissimilar  entities, namely  c and V, yielding a ‘unity in duality’, 2cV, that we shall  put forward to support the validity of a Soul /body unity postulate.



1.4  Conclusions


We have outlined a solution to the Dualism Problem in the Philosophy of Mind.


Instead of Soul and Body being completely dissimilar, as with Descartes’ formulation, we, by an analogy with quantum physics, postulate that the human soul when embodied  is energetic and can (1)  assume an energetic form consistent with the classical wave equation and its unique linear equation of state, and can  (2)  interact with the various kinetic particulate and mass motions and fluid flows of the human body, so that it produces an interaction energy 2cV which constitutes an intimate “unity in duality”, thus resolving the soul/body duality problem.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          


More complete scientific details will be presented in Part 2:  Wave/Particle Physics and Soul/Body Wave Interaction Dualism in Humans  



References and Notes


1.  Descartes, Rene. Meditations on First Philosophy. U.of Chicago . The Great Books. No. 31. Encyclopedia Britannica, Inc. 1952.


2. Grim, Patrick.   Philosophy of Mind: Brains, Consciousness, and Thinking Machines. The Great Courses. Chantilly VA., 2008


3. Rahner, Karl, S.J. Hominisation: The Evolutionary Origin of Man as a Theological Problem.  Herder and Herder, New York, 1965.


4. Lonergan, Bernard J. F.,  S.J. Insight: A Study of Human Understanding. Philosophic Library, New York. 1956.


5. Rahner [3], as an  example of possible similarity between spirit and matter, wrote   “ matter ----  considered as  a sort of solidified spirit”. The science of today , however, points  to a position that  matter is, instead,  much more likely to be  ‘condensed energy’.  See  .


On this point also, Lonergan in  Insight, raises  the possibility that energy may relate  to the classical philosophic concept of ‘prime matter’.


6. In the case of Man, we take the position that we are dealing with an animal whose mental activity relates to, not only basic intelligibility in physical data as with all animals,  but also, uniquely,  to the  higher levels of consciousness and thought, that is  to such things as probability distributions of the basic data forms, their standard deviations , their correlations, and with  the myriad higher intellectual human activities involved in the fine arts, the practical arts, academic studies, theories, philosophies  and so on. In a word, to  human intelligence  as opposed to the simple basic detection of the  intelligibility in sensory physical environmental data.


This distinction between sensitive animals and man,  or between ability to grasp the intelligible versus the ability to be intelligent about the  intelligible,  is dealt with extensively by Lonergan in his Insight [4].  He writes, for example:


1) “ …. The distinction between the intelligible emergent probability of prehuman process and the intelligent emergent probability that arises, is the measure that man succeeds in understanding himself and in implementing that understanding.”


2) “…. in man there occurs the transition from the intelligible to the intelligent.”                  


3) “ ……and so in the limiting case of man, the intelligible yields to the intelligent …”


For Lonergan, intelligibility is the characteristic mark of material, physical reality, while intelligence or understanding and insight are the characteristic mark of man.


In Part 2 we go into details on our proposed soul embodiment model. These details will necessarily include some wave and flow physics; the full details on the technical aspect will be sequestered to Part 3, for reference as interest or need dictates.




End of Part 1












 Wave/particle Physics and Soul/Body Wave Interaction Dualism in Humans



2.1 Introduction


We have, in Part 1 above, countered, in scientific terms, the objections to the philosophic Dualism of  classical Soul/Body theories of human nature. This has been done by citing the ‘unity in duality’of a  wave interaction energy, 2cV, analogous to the wave/particle ‘unity in duality’  of quantum wave/particle  mechanics.


Here In Part 2, we give more detail on this soul/body wave interaction dualism.


The true nature of Man certainly has been  a matter of deep controversy and mystery.  On the one hand, there are the overwhelming facts of human intelligence, thought, theoretical solutions, academic and artistic activities, technologies,  social talents and civilized achievements which today reach out through space to encompass the entire universe and which must be accounted for. If these  realities are to be acknowledged and  explained, they require  a  mental or spiritual reality, incontrovertibly unique to Man, and more or less in line with the conclusions of the classical Philosophy of Mind.


On the other hand, there are the mounting facts of neuroscience which have demonstrated in great detail the role of physical  brain complexity in human mental processes. These appear to be purely  biological rather than dualistic.


What we propose here is that assigning a wave and compressible flow behaviour to an embodied  spiritual soul  in  man, converts a  disparate dualism into an intimate  unity, one in which the observed facts of both human mental reality  and human  intricate physicality are each fully acknowledged.  The new approach, which we propose to call wave interaction dualism, is also, in principle,  open to scientific verification, for example,  via the proposed wave behavior and its effects.



2.2  Dualism in Man  Let us first  look briefly back  at  the classical position that  man is a composite  of  soul and body, for example, a spiritual or non- material essence and a material, animal body. But then, on this position, while soul and body are similar in that both are energetic, the nature of their energies could be intrinsically different. And so the  objection of ‘dualism’ still arises to be overcome.


Now in the case of Man, we take the position that we are dealing with an animal whose mental activity relates to, not only basic intelligibility in physical data,  but also to the  higher levels of consciousness and thought, that is  to such things as probability distributions of the basic data forms, their standard deviations , their correlations, and with  the myriad higher intellectual human activities involved in the physical sciences both pure and applied, in fine arts, the practical arts, academic studies, theories, philosophies, religions   and so on.  We face  the astonishing, incontrovertible facts of   human intelligence,  as opposed to the simple basic detection of the  intelligibility inherent in the  sensory physical environmental,  and the repetitive stability that is the mark of sensitive, non-human animal behavior.


This distinction between other animals and man, or between ability to grasp the intelligible versus the ability to be intelligent about that which is intelligible , is dealt with extensively by Lonergan in his book   Insight:  A Study of Human Understanding [1 ].   He writes, for examples:


1) “ …. The distinction between the intelligible emergent probability of prehuman process and the intelligent emergent probability that arises, is the measure that man succeeds in understanding himself and in implementing that understanding.”


2) “ in man there occurs the transition from the intelligible to the intelligent.”                       


3) “ ……and so in the limiting case of man, the intelligible yields to the intelligent …”


For Lonergan, intelligibility is the characteristic mark of material, physical reality, while intelligence or understanding and insight are the characteristic mark of man.


A  Solution:  Our solution to furnishing a scientific explanation for the mental actions of the embodied human Soul, is that there is an energetic wave/flow interaction unity involved, and so we postulate that the embodied human soul exhibits an  energetic wave  behavior,  having wave speed c,  and relative flow speed V, which can  interact with the kinetic, material,  particulate motions  and flow  velocities V of the physical body. 


Since the flow speed V is relative, we can have wave speed c and bodily motion V,  or it can be the reverse with body wave c and soul flow V. In each case, the  interaction of  wave  speed c and flow speed V results in an interaction, one  yielding a real, dualistic unity  of body and soul/wave, with total wave- pulse energy  ETotal = [c+V]2 = c2 + V2 + 2cV, of which the unifying interaction energy is the term  2cV. 


2.3  A Soul/body Wave Interaction Dualism Suggested by  Quantum Wave/particle Dualism 


Since we have introduced a wave behavior into the embodied human soul, let us examine the  Classical Wave Equation and its linear wave  solution.  Although this equation is fundamental, we should note that in real physical systems ( gases, fluids, thin films, membranes, tissues, etc.) the waves that appear are never the exact classical waves, but are always  an approximation. This is because the equations of state of real physical systems are non-linear ( usually hyperbolic or hyperboloid) instead of being linear as required for exact classical wave  correspondence.


In the case of man, however, we now also  postulate that the human soul  supports the classical wave equation in  its exact form. This means that the soul  assumes the behavior of the linear equations of state p = ±av ±b . Thus, the soul supports waves of any amplitude large or small, and of either compression or rarefaction, and will  propagate them with unchanging  form,  instead of them growing to shocks or dissipating entirely. This postulate for unrestricted soul waves  is coupled with the known ability of the body to propagate in its tissues stable acoustic type waves, but only when they are restricted to being of very low amplitude.


Specifically then,  we  postulate  for man  a scientifically verifiable Wave Interaction  Dualism, consisting of (1)  a material body and a non-material soul,  where the latter interacts with the material body as an energetic (dynamic) wave motion  entity, which, being spirit, (2) can obey exactly the  fundamental classical wave equation and  its linear solutions.


2.1 Classical Wave Equation and Its Linear Equations of State


The classical wave equation  [2] ( for one- dimension x) is:


2 Ψ/∂x2 = 1/c2 ( ∂2 Ψ/∂t2 )



The general solution of this is Ψ = f(x − ct)  + F(x +ct) which gives a series of sloping straight lines on the x-t depiction of wave progress in space (x) and time (t).











2.2 Linear Equations of Stste for Hypotherical  Fluids  Which Support Classical Waves


Real gases, such as air and liquids such as water, have equations of state describing their behavior (changes in pressure, specific volume and temperature) under expansion, contraction  or wave motion , which are hyperboloid, whereas linear equations of state  are needed to exactly support classical waves.


A theoretical linear equation of state, known as the Tangent/Tsien/Chaplygin gas, which would support classical waves, is sometimes used in aeronautics and cosmology to get around the limitations and restrictions of the hyperboloid, real equations of state.  Fig. 2.
















2.3.1  Linear Equations of  State for a Postulated  Soul  Which Support Classical Waves



In its postulated embodiment,  the human soul  is  a wave entity Ψ, exhibiting the thermodynamic properties of  two  exact  linear equations of state:


p = −av +b and  p = +av +b


where p is pressure, v is specific volume (or volume of a unit mass ( v = 1/ρ) ) and a and b are constants.


 In the Tangent gas case ( Section 2.1 above) a linear equation of state for the hypothetical fluid called the Tsien/Tangent gas p = −Av +B), which is also a solution to the classical wave equation, is placed tangent to the hyperbolic equation of state for a real material fluid.  At the tangent point the pv energies of the two fluids are identical, so their behavior is also then  identical.


In the present soul/body case ( Fig. 3 ) a linear equation of state, which obeys the classical wave equation  and is assigned to the embodied  human soul ( p = −av +b),  is depicted as tangent  to some  averaged adiabatic equation of state pvk  for  human bodily tissue.  Another linear equation of state ( p = +av +b] also obeying the classical wave equation is orthogonal to the tangent case.





If the constant intercept (b) in the two equations of state p = ± av  ± b  isset to  zero, then  the equation lines pass through the origin of the pv coordinate system  (Fig 2 a) and reduce to:

 p =  ± av.


Fig. 2a.. Equations of State for linear solutions of the Classical Wave Equation (p  = ± av) passing through the origin  ( i.e. when the  intercept (b) is zero. ).






2.3.2 Wave/ pulse Interaction Energy (2cV)


In the classical wave equation, wave pulses travel, in the x-direction, at a total  speed of c, the wave velocity, plus a flow speed u [2]


(dx/dt)I, I = c + u 


where u is the component of  the flow speed V in the x-direction [2].


Therefore, the wave pulse specific energy in the x-direction is the square of the pulse velocity, that is 


                                                                 Epulse= (dx/dt)2 I, II = ( c+ u  )2 = c2 + u2 + 2cu


where 2cu is the interaction energy between wave speed c  and flow u in the x direction.


For three dimensional with velocity V, we have wave pulse energy  Epulse  = ( c + V)2 = c2 + V2  +2cV.


2.3.3 Wave Speed c


The wave speed c is given by

c2  = (dp/dρ);  c = ( dp/dρ)1/2



For  the equation of state  p = −Av + B =  = −Aρ-1 + B we  get, by differentiating for dp/ , 


dp =  −(−1) Aρ-2 , so that


c2 = dp/dρ = +A ρ-2 ; and  c = +A1/2 / ρ = + A1/2 v


 Thus, for the linear wave equation p = −Av+ B , and we see that the  wave speed c is positive and real .


For the orthogonal linear equation p = +Av +B, the wave speed c becomes  complex, namely (ic), and the interaction energy becomes 2icV.


This complexity indicates that the wave pulse may resonate. This resonant wave behavior could be important in the study of such soul properties as affection, sense of satisfaction accompanying  intellectual insight, etc.


In this model, the soul is postulated, when embodied, to supply a wave action of the exact classical wave kind, and to interact with bodily kinetic motions to produce an intimate dual energetic unity [ 2cV. 2icV].  This union  of soul with matter is described by the energy interaction. The soul- in- body is  now a unified seat of consciousness, intelligence, creativity  and affinity  directed towards the Greek triad of  desirables: ‘The Good, The True and The Beautiful’.


With the wave and wave interaction hypothesis or postulate, we have taken a first step towards describing the human dualistic interaction in scientific terminology. Other aspects of the soul/ body interaction remain to be studied and  described. For example,  let us look at  soul motions.



2.4   Human Dualistic Interactions and Wave Motion :    “ The Feast of Reason and the Flow of Soul”



Of the two motions  ( velocities  c and V  in the 2cV Dualistic  energy term) the bodily motions V are  more readily understood. Wave motions in fluid are also easily grasped.  But, for waves and flow  in spirit , we have to make some effort to properly grasp what is involved.


2.4.1 How does the soul move  the body?


We have started this inquiry into the Soul/Body interaction dualism by an analogy with quantum wave/particle dualism. The 2cV energy was  derived as  a concept from  fluid mechanics. Let us then try and continue by looking at the problem of soul and body motions from the standpoint of the formalism of the mechanics of motion.


2.4.2  Soul Motion and Force     We have characterized the motion of the soul as a wave motion of speed c. Now in mechanics, by Newton’s First Law,  force  arises from an acceleration.   Let us then continue our soul/body investigation  by defining  Soul Force as an acceleration in soul wave speed  c.  Then we have: 


Wave Acceleration = dc/dt ,

 Force =  ma = (‘density’ measure) x acceleration .


Force has physical dimensions of energy /distance, i.e. E/l.  Therefore, if we are dimensionally correct, we should also  have


2cV/l = E/l =   Force. 


But,  force is proportional to an acceleration ( F = ma), and so let us check our 2cV interaction energy term again


2c( l/t)/l = 2c/t =2 x  wave acceleration



Wave Force = EΨ /l = 2cV/l = 2c/t = 2 ( wave acceleration)  (unit ‘density’ parameter)


We tentatively conclude, therefore, that we can define Soul Force as Wave acceleration (dc/dt) multiplied by a unit ‘density’ parameter. (Here, the acceleration is a  ‘specific acceleration’)’ so that numerically its value is 1,  and it does not appear specifically in the equation for force.   i.e. F = dc/dt (1). )


Thus, we are dimensionally consistent with our soul assumptions, as formulated, and can now proceed to define soul motion in  relation to the human body in terms of wave speed c,  and Soul force in terms of wave acceleration dc/dt. .


Accelerated soul motions or impulses could conceivably pertain to such things as soul action, decision, attraction to,  affection for, love  of,   etc.  This soul wave/ acceleration,  dc/dt, recalls the Poet’s  ‘flow of soul’ .  This formalism  matches the  principles of classical mechanics that apply to the body and further  exemplifies a ‘unity in duality’ of soul and body.


Any ‘soul motion’ whatever thus interacts with the body via the force of an accelerated  wave pulse relationship 2cV, and a soul/body interaction occurs. In turn, any bodily motion whatever also interacts with the soul via an accelerated  wave action and again a force is generated.   In this way, soul and body would act  and move as  a unit at all times., but retaining their essential or intrinsic nature – the body being material and the soul intrinsically spiritual.


We should perhaps note that in this model,  even motions as spatially miniscule as atomic or molecular vibrations would interact to fundamentally knit the soul and body together into the dualistic  2cV unity.


2.4.3 The Problem of Consciousness: A Suggestion for Neuroscience and Philosophy of Mind


The problem of consciousness, or the sense of self awareness, remains one of the most perplexing in neuroscience and the Philosophy of Mind. We are suggesting a  role of wave interactions in the matter.


In our proposed model, any motion, whether of soul- wave acceleration or of bodily motion, generates a mutual  interaction, pulse energy linking soul and body in an intimate  continually renewed interaction energy, 2cV. In this all pervasive  interaction energy, we suggest,  may lie the source of the sense of ‘self awareness’, and the origin of consciousness.  .


2.2.4  Theory Validation and Further Relevant Questions


In the working out of valid insights [ 1] the ongoing steps  are, first, a searching, reasoned examination of the model which has emerged to solve the dualism problem. In the present case this would seem to include a scientific verification via the proposed wave interaction effect tand the unrestricted wave amplitude characteristic.


Following this, if the insight is reasonably supported, various further relevant questions automatically arise in the informed and inquiring mind to be investigated [4]. Among these, the nature and action  of love is undoubtedly foremost, an evaluation of which will welcome the attention and collaboration  of both ‘ saints and scholars’. 


One of these further relevant questions would also likely  be a new look at the differences and similarities between man and other animals. 


2.4.5 Differences between Man and Other Animals: Some General Considerations


This is of course a very large topic, which we shall only touch on here, and only in very general and illustrative  terms.


For our very general descriptive approach, let us  consider the case of the North American Beaver, sometimes considered as the ‘engineering animal’. It lives in domed hut, constructed of interwoven tree branches, in a lake; the hut has  a hidden  underwater entrance, and an inner, dry, earthen  floor built up above the lake water level. The water level in the lake, and so also inside the beaver  hut, is controlled by a dam at the lake outlet built of tree branches plastered with mud. In many cases, the little lake is actually formed by  the beavers having  constructing their dam across a small stream.


The combination of elements in this animal abode is astonishing, especially the lake-level-controlling dam. The ensemble of elements seems  to  show clear evidence of design. The impression that the animal is exhibiting ‘intelligent design’ is strong.


And yet, the ingenious beaver also exhibits the universal animal attribute of endless repetition. The habitation and dam construction is always the  same. This suggests social evolution rather than invention.  All animals have repetitious, extremely conservative behavior. Genetic control, plus parent- to- offspring rote learning seems the rule. Thus, the natural selection of a long chain of small, fortuitously favorable environmental occurrences, coupled with a drive to seek their own good, could perhaps account for the beaver’s apparent design originality. This, coupled with extreme animal stability of ‘design’, could  produce the behavior that is observed..


Turning to man, a striking difference from beaver behavior is that man’s interaction with his environment is marked by extreme variability and constant  innovation.  It is almost completely the opposite to the non-human animal pattern  of repetitive,  extreme stability. It is innovation versus conservation, and extroverted curiosity versus self -centered curiosity. It is the question : . ‘What is this to me?’ versus What is this and Why? Animals are curious and stable. Humans are curious and inventive, they are changeable socially, even  revolutionary, and their innovations are not at all limited to adopting chance occurring, useful environmental variations, but rather they spring from  insight into universal, immaterial, principles of a science.


The environmental sensory data are scanned and used in a brain whose scanning nature  is central. In animals, the result is  self centered. In man, the scanning is ‘insight- seeking’ or intelligent. Thus ,there is an  essential difference with humans. We have suggested that this essential difference includes the wave action of an  immaterial, intelligent, energetic  entity – the human  soul.


For a second example, let us consider, say, a watercolor painting of the aurora borealis. As a concrete material object, it is a combination of various colors and shapes on a paper base. As a human, artistic artifact it is an abstraction of sensory images, of memories of  aurora borealis events, the image areas show variations, shades, forms, paint brush marks, sharp color edges, blurred ones, colour mixings, composition, pleasing and unpleasing combinations, contrasts, etc. All concepts are clearly abstractions. It embodies both hope of artistic success and faults in technique, concept and finish.


If we were now to show this watercolour to our beaver, he will undoubtedly sniff it, touch it, and, since it is paper, he will probably try and eat it. He might possibly even use  it to patch a leak in his dam..   Clearly, its concrete material aspects or intelligibility are his only interest or comprehension. The artistic, mental and  human elements , which really make up the watercolour simply do not register with the beaver. It is not something for him to keep and ponder, or to enjoy. Such behaviour is not in his nature. The beaver is environmentally pretty successful, but he is definitely  not the ‘soulful type’.


Because of the hitherto unsolved problem of dualism, the vast ‘preponderance of evidence’ of the Philosophy of Mind that points to a  non-material human  essence  has, over the past century, gradually become negated in practice,  not by fact or reason, but by mere disregard, in favor of a vague expectation  of eventual explanation by massive, but logically irrelevant,  brain complexity.  The result has been a serious, debilitating confusion in human civil, religious,  intellectual and ethical  affairs.


The fact that a serious scientific solution can now be offered to solve the Dualism objection would  appear to reverse the situation at once. An interaction Dualism can no longer simply be rejected, since  other scientific reconciliations of the sort can always be proposed. Therefore, the position of  the Philosophy of Mind as central in the controversy appears  reestablished, it being  based on  the massive preponderance of unquestioned evidence as to human creative behavior requiring acceptance and explanation.  


Simply put, if science deals with the nature and functioning of the Body and  philosophy deals with the nature and functioning of Mind, then the proposed dualistic wave interaction union of Body and Mind would appear to constitute a new joint arena of interest and interactive research where science is now  required in Mind as it is in body.  


2.4.6 Fully Human Soul/ Body Dualism


We have proposed, and started to describe in scientific terminology, what we characterize as ‘fully human action’, which is an energetic, fully integrated, soul/body dualism. One has only to conjure up some human social gathering --- one  involving, say, some family, academic, political, sporting, artistic, or religious   ‘Feast of Reason and  Flow of Soul” event,  in order to make it clear at once  what this fully human experience is, and what is involved in a  postulated energetic, dualistic, body and soul human  nature. 


If as we contend, human reality is a composite, then it poses its peculiar dualistic challenge to being understood,  especially when the task  of integrating the physical and spiritual within a proper scientific formalism and  terminology is then required. 


The explanatory, interactive, dualistic, wave model proposed  can perhaps usefully be viewed as constituting  a ‘new set of facts’  for consideration by the Philosophy of Mind and  Neuroscience. 




2.5 Conclusions


(1) We have presented a new argument against rejecting all forms of soul/body dualism by adopting an approach  in which the spiritual is postulated to be able to configure itself so as to provide a soul/body wave interaction dualism.


At the same time, we have reiterated  our  view of the impossibility of explaining the overwhelming reality of the unique, abstract, mental, immaterial, insightful, intellectual, creative, original, artistic, and spiritual facts of human life by any conceivable complex  molecular materialism.


(2) Our  model requires  postulates (a) that  the   human spirit or soul be able to interact in an energetic,  wave-like, dualistic  manner  with the human  body and vice versa,   (b) that all  motions of either soul or body produce  energetic 2cV, 2icV, type interactions, and (c) that the wave motions of  the soul conform to the  exact classical wave equation.


(3) The dualism is with the soul’s ‘wave and flow’, c and V, on the one hand, and the body’s wave and flow .c and V, on the other. The unity is in a common, combined energy of interaction 2cV or 2icV  as described by the energy equation  Etotal = (c +V)2 = c2 + V2 + 2cV.


Since the human soul, as postulated, is spirit, its  wave action is contingent on the soul being embodied, and is not to be considered intrinsic, nor is the embodied soul to be identified with the physical materiality of the human tissue  with which the soul intimately  interacts in  dualistic wave pulses.


Clearly, such an interaction resulting in a  2cV ( 2icV) energy,  constitutes an intimate union, and the entity corresponding to it would necessarily act as an organic unity.  Both soul and bodily energies are  present, but in a new  interaction unity. It is believed that this approach solves the philosophic Dualism problem for soul/ body theories within  a valid scientific formalism.


This argument asserts that the human essence, while spiritual, has, in its action, the dynamic properties of a physical wave  so it can interact with the bodily flow energy. There is as yet  no experimental proof of the  wave interaction; and so, for the moment, it rests on its general reasonableness in fitting the known facts of human intellectual life. In principle, however, the soul/wave proposal would seem to be scientifically verifiable, for example through the asserted wave interaction. Verification must await the examination and assessment of neuroscience.


 The fact that it can be proposed at all, however,  may now philosophically negate any blanket objection to dualism, since  physical interactions other than wave action  may , in general, also be advanced, to be countered as they are put forward.


(4) We can now also put forward the presence of this interaction energy  of soul and body, [2cV, 2icV],  as a potential solution to the ‘hard problem of human consciousness ‘ in neuroscience and in the Philosophy of Mind.


(5) The main implications of the Wave Interaction Dualism appear to be twofold:  (1) it presents a solution to the Dualism Problem, and (2) it offers to  neuroscience  new possibilities, such as new sets of waves and wave interactions , e.g.  , waves of compression, of rarefaction, standing waves, group waves, resonant complex waves which may interact, for example,  with  electrochemical neurotransmitters.


We have presented these items as’ a new set of facts’  for evaluation by the Philosophy of Mind, and as a new` application of physical science to the realms of neuroscience.  Hopefully, this may help bring about an enriched awareness  and enjoyment of  “The  feast of reason and the flow of soul”  in human affairs.





1.  Lonergan, Bernard J. F.,  S.J.,  Insight: A Study of Human Understanding. Philosophic Library, New York. 1956.


2. Shapiro, A.H., The Dynamics and Thermodynamics of Compressible Fluid Flow. 2 Vols. John Wiley & Sons, New York, 1953.


3. Lonergan in Insight [1] writes : “ … material reality cannot perform the role or function of spiritual reality but spiritual reality can perform the role and function of material reality.”


4. In 2007, , a preliminary look into the properties of Quadrant II was undertaken. Shortly before that time, cosmologists had

extended the Chaplygin/tangent gas equation into Quadrant IV in order to get a negative  that would serve to explain the newly observed   acceleration in the  expansion of the universe.


The result of the 2007 investigation was the finding of a negative density and specific volume,  and a negative entropy in the Quadrant II  depiction of pressure-volume equations of state. This was interpreted in a preliminary fashion as in  the following excerpt:



Excerpt from ‘Science and the Soul/Body Problem “ 2007


[Posted in: in 2008 ]



“ The UF  :(Universal Field) forms in Quadrant II have negative temperature ( Item 3 above). Therefore, the entropy change dS is also negative  


dS = dQ/T = dQ/(−T) = −[dQ/T] 


While in Quadrant I, with its positive entropy change, the 2nd law of thermodynamics pushes inexorably towards disorder and random variability, in the  UFII  the stable forms are oriented towards order, design and pattern. This intrinsic orientation points towards the UFII being a seat of a sensitive, dynamic, capacity and drive towards information i.e. towards  intelligence and rationality.


 (6) The UF in Quadrant II is intrinsically non-quantified. That is to say it can assume any energy value from zero to infinity without change in basic properties.  [In Quadrant I, the energetic forms of ordinary matter are intrinsically quantified, since the p-v energy in real gases, for example, has a constant singular value, since pv = const. by definition.  Even the UF’s Tangent gas has limits set by the constant B].


(7) The UFII forms might be considered to be able associate naturally  with Quadrant I forms, in that  both have positive pressure and positive wave speeds. [Their specific densities, however, are opposite in sign].


Clearly, the UF in Quadrant II has properties that are remarkably similar to those listed in Section 3 for the human soul, namely, dynamic energy form, stability of form and  subsisting,  non-materiality since its energy is not a compressed energy of ordinary Physics or of any oddinary physical matter, intrinsically un-quantified,  intelligent since it always seeks order and design,  and rejects or resists  disorder or random meaningless variability..”


Currently, in  2015,  we would  be more inclined  to assign the Quadrant II peculiar and interesting  negative physical properties,  not primarily  to a soul embodiment,  but rather  to a physically  rarefied, exotic or  hypothetical scientific “ other world”   existence. 


This  Quadrant, rarefied, exotic, physical matter could, of course, also be assumed able to be taken into a soul/body  embodiment  by a spiritual essence or soul , just as we have Postulated for Quadrant I matter in order to explain the intellectual side of our present human existence.   Quadants II, III, and IV deserve  further careful examination, especially if the model proposed for Quadrant I is scientifically verified.


End of Part II






image002 Wave Interactions and Compressible Flow 



3.0 Introduction


Our proposed solution to the problem of Dualism in Part 2 involved a wave interaction energy 2cV. The waves we are interested in are compression pulses in a compressible fluid, i.e. in a fluid capable of experiencing density variations and having a finite and variable wave speed c, (as opposed to incompressible fluids where the wave speed is theoretically infinite).  Specifically, these compression  waves are called  acoustic or ‘sound’ waves and are described by what is called the Classical Wave Equation.


This equation will be derived below. It is the description of all stable propagating waves of compression or rarefaction and of any amplitude, large or small. In compressible flow physics, the two equations of state for theoretical gases that support exact classical waves are called the Tangent/Tsien/Chaplygin Gas and the Orthogonal Gas


3.1 Compressible Flow


The physics of compressible flow [1,2]  embraces many fields, such as, hydromechanics, aeronautics, meteorology, jet flow, rocket propulsion, astrophysics and cosmology. Compressible flow is intimately linked to fluid wave motions. 


Its equations of state,  describing known, physically  real gases, are usually plotted in Cartesian coordinates on a pressure- volume or pv-energy  diagram in Quadrant  I, where the thermodynamic variables of pressure p, density or specific volume ρ=1/v , temperature T and pv-energy are all positive quantities. With one exception, the equations of state of gases linking pressure and specific volume  ( i.e. of a volume of a unit mass of gas  v = 1/ρ ) are hyperbolic curves on the pressure-volume diagram, for example the  Ideal Gas, atmospheric air, oxygen etc.



The exception is a hypothetical, or exotic compressible fluid called the Tangent Gas [3].   Its linear equation of state (p =  −Av +B)  was formulated in 1939 by H.S. Tsien in Quadrant I on the Cartesian pressure-volume  energy diagram  for aeronauticPs and rocket propulsion, and, in a slightly different form ( p =  −Av ) had already been formulated in 1904  by S.A. Chaplygin [4] for application to aeronautical  problems of jet flow and lift.


Figure 1. Equations of


An  extension of this linear Chaplygin gas equation [ p = −Av] was made in 2001 from Quadrant I into Quadrant IV  in order to  obtain a cosmic flow with the negative pressure needed  to explain  the  observed acceleration in the rate of expansion of the  Universe  [5,6,7] .   


This Part 3  will outline the pertinent background  physics of compressible fluid flow and its equations of state. 



3.2  Compressible Fluid Flow

Compressible fluids change their shape and their density more or less readily. Those which are very compressible are called gases. Since they are subject to density changes as their pressure varies, they exhibit pressure waves of various sorts.  Their  physics  [1,2] embraces compressible  fluid mechanics, aeronautics, meteorology, jet flow, rocket propulsion, astrophysics, shock waves, supersonic flow,  cosmology, etc.

The quality of compressibility makes possible a wide variety of behavior in gases. Because of it, pressure waves are possible;, for example,  acoustic or sound waves, shock waves , etc.. The same physical principles also extend to quantum waves.

In known, or real gases, only compression waves are persistent,  rarefaction waves simply attenuate and die out. However, no known real gases will support waves of a finite amplitude --- such waves grow to compression shocks instead.  Only  very low amplitude waves, known as acoustic or sound waves, can travel unchanged for any length of time in real gases. One theoretical gas, however, known as the Tsien/Chaplygin gas or Tangent gas, is unique in that it can support finite amplitude  waves of either compression or rarefaction which remain stable. Expressed another way, we say that ‘these two linear gases ( p = −Av +B) obey, or support, the classical wave equation’.

The equations of state of most real gases ( linking pressure, volume, density and temperature)  are hyperbolic, ( e.g. pv = RT) and are depicted on the Cartesian pv-energy diagram in Quadrant I.

 The two principal hypothetical or exotic gases--- Tsien’s Tangent Gas  and Chaplygin’s negative pressure, cosmological gas----  actually have the same linear equation of state,  [p = −Av +B].


2.3  Equations of State of Gases

 A.  REAL GASES  ( Compressible fluid systems)

1. The Ideal Gas: Isothermal expansion  pv =constant =  RT   (Hyperbolic curve)            

                       2. Adiabatic expansion:  pvk = constant  (Hyperbolic curves)




The p-v plots of both of these real gas types are hyperbolic curves.


Figure 2. Cartesian plot of pressure –volume equations of state

in Quadrant I for the real Ideal gas and its adiabatic expansion


In the adiabatic expansion equation,  pvk = constant,  k  is the  ratio of the specific heats [k = cp/cp.].   For ordinary  atmospheric air,  k has the value  of 1.4.

The equation of state  variables are pressure (p) and volume per unit mass ( v = 1/ρ, where ρ is the fluid  density).





1. Tangent Gas / Tsien’s Tangent Gas :            p = −Av +  B  ( Linear; wave  speed c is real and positive). k = −1


2. Chaplygin’s Gas :      p =  − Av+  B  (Linear; wave speed c is real and positive).  k = −1


3. Orthogonal Gas ( Isothermal):  p = +Av +B  (Linear; wave speed is complex ic). k = +1


As we shall see, the plots of the equations of state of these three  exotic or hypothetical gases, linking pressure  p and specific volume,  v= 1/ρ ,  are linear, i.e. are all  simple straight lines on the pv-energy diagram.


3.4  The Tangent Gas Equation of State;  Unique Linear Fit  to the Classical Wave Equation

This  relationship in aeronautics  was formulated  in 1939 by Prof.  H.S. Tsien, co-founder  of the  Jet Propulsion Laboratory at Cal Tech, who is  also  known today as the Father of Chinese Rocketry. His equation is  called the tangent  gas” [1] (Figure 2). 

This tangent gas describes the behavior  of  a  theoretical fluid  whose linear equation of state [ p = −Av + B]  is placed on the pv-energy diagram so as  to lie  tangent to an ideal gas equation of state , or to an  adiabatic expansion equation [Fig.2].

Since  hyperbolic curves are somewhat difficult for manual computation,  Tsien in 1939, in the age of slide rule calculation for engineering work, well before the general use of computers, introduced this  simple approximate method consisting of drawing a tangent  line [p = −Av + B] to the hyperbolic curves at any desired point.  At or near  such a  tangent point on the ideal gas or the adiabatic expansion  curve,  his ‘tangent gas’ straight line   gives results very close to those of the hyperbolic real gas curve.

 The Tangent gas  approximation is unique (1) in that its equation of state describes the only known fluid, real or theoretical,  which  supports stable compression waves of any  amplitude  [1,8],  that is to say, it will theoretically propagate finite amplitude waves of expansion and compression  without them becoming unstable and growing to shock waves.  This is in contrast to known or real  gases,  such as the ideal gas or the adiabatic expansion gas, in which  waves of finite amplitude either die out, or grow unstably to become  compression shocks.  The tangent gas  (Tsien/Chaplygin gas) is also  unique in (2) satisfying the classical wave equation exactly,  without the approximations required for real gases.


3.5 The Tangent Gas and Quantum Physics Wave Equations


Quantum physics describes the world of the very small, namely that of the atom and elementary particles of matter at a space  dimension of around 10-9 m.


Atoms and elementary particles are described, not as point particles of matter, but instead as wave packets having a finite dispersion in space. An atom for example is at once a particle and a wave.


The wave equations describing the nature and behavior of the atomic and sub-atomic quantum world  are  derived from  the classical wave equation as a base,

 nd her relevant questions rom Part 2, Section ctualitye geersted in and move through bulk animal tissue  rarefaction ans of any

In quantum physics, various wave/particle equations are then added to the classical wave equation to obtain probabilistic  wave/particle equations describing the probable location of the particle in space and its various quantized` energy levels. For example:


as shown above, the classical wave equation is ( for one dimension x):


2 Ψ/∂x2 = 1/c2 ( ∂2 Ψ/∂t2 )


The Klein-Gordon equation for a spin-less particle is:


1/c2 ( ∂2 Ψ/∂t2 ) =  2 Ψ/∂x2  −( mc2 /h2 ) Ψ,


so that,  if the mass m is set to zero, the Klein-Gordon wave/particle equation  reduces to the classical wave equation.


In a similar manner,  the other quantum wave/particle equations, such as the Schrödinger equation, are derived.


Our point here is that a basic, starting wave equation for quantum physics is the classical wave equation.


The wave interactions that go on in quantum physics lead to interaction energy terms 2cV in the energy equations of quantum physics. We have then used this quantum physics example of wave energy  unity 2cV emerging from an interaction duality,  to clarify and  focus the argument in the Dualism debate in the Philosophy of Mind.


3.5.1  Wave/ pulse Interaction Energy 2cV


In the case of the classical wave equation, the wave pulses travel at the sum of the wave speed  c plus the flow speed u ( or V)


(dx/dt)I, I = c + u 

where u is the component of V in the x-direction.


Therefore, the wave pulse energy in the x-direction is the square of this pulse velocity, that is 


EΨ =  (dx/dt)2 I, II = ( c+ u  )2 = c2 + u2 + 2cu


and 2cu is the interaction energy between wave and flow in the x direction.


In three dimensional flow we have then,  ( c + V)2 = c2 + V2  +2cV.




3.6  The Orthogonal Gas: (Isothermal):


This is a new formulation of a theoretical gas, orthogonal to the Tangent Gas and with much the same properties,  which has a complex wave speed (ic)  and may have special pertinence to the theory of the functioning of the human Mind, since it involves resonance.