TOWARDS A SCIENCE OF HEALTH? BIOPHYSICS AND BIOMECHANICS

Miguel Ángel Martínez Iradier

HOLISM AND REDUCTIONISM IN THE LIFE SCIENCES

Physics, so solidly supported by mathematics, continues to be considered the queen mother of experimental sciences and therefore a model for all the others, including modern biology and biomedicine. It is also common to assume that physics is a reductionist science capable of explaining things by its mechanisms, although this is far from being true and in fact, as Poincaré recalled, the principles of action on which it is based by its very nature do not admit univocal mechanisms but mathematically precise analogies.

This underlying ambiguity of Physics is the cause of all sorts of confusion, all the more so when she comes to help other disciplines inextricably related to complexity trying to sketch its simplest aspects.

Surely one of these misunderstandings is that physics can only be relevant to living systems at the level of their constituent blocks —ions, molecules, cells, etc.- through their corresponding disciplines, such as chemical physics or molecular biology. However, we have just noticed that the atoms, particles and their associated fields are calibrated by their respective principles of action, which are their authentic invariant elements. These action principles are integral by definition, no matter how much physics, in its predictive aims, continuously uses them as a mere excuse to derive local solutions.

As always, it is what we do which determines what we think, just as it is the application what determines the interpretation.

The origin of biophysics, and even of psychophysics, can be traced back to the Leipzig and Berlin schools in Helmholtz's days. Already in the first half of the twentieth century, and long before the blossoming of this vast field, there were pioneers such as Lotka the mathematician and the great promoter of theoretical biology Nicolas Rashevsky. A lot has happened in the meantime, but we can still take these two names as opposing ways of understanding the discipline: either clinging to biometric data or speculating on the mathematical relationships one can develop from them.

Where are we today? The fact that today's biophysics is more reminiscent of the Schrödinger of What's Life? than of this two mentioned authors is already quite eloquent. It speaks to us, independently of the merits of the great Austrian physicist, of the predominance of molecular biology and the constructivist ideas of building blocks.

In spite of the present hegemony of molecular biology, biophysics resists to be reduced to a single perspective, it's too vast and multiform for that. And now that computer science and artificial intelligence are expanding their power of statistical correlation exponentially, many theoretical physicists are moving into this field in the hope of giving it a universality it now lacks. They would be called to save the great fault that already separated Rashevsky from Lotka and that has not stopped getting bigger, as it requires more than computing or statistics to close it.

Faced with this arrival of fresh air and young talents, little can an old spectator like me say except to greet them. However, I cannot resist making some totally extemporaneous observations at this interesting junction; and it is clear that only as extemporaneous could contribute something, even if only the distance.

As much as it may surprise many, the idea held here is that for biophysics to be more holistic or global what it needs is not principles with increasing degrees of abstraction but, on the contrary, to be more faithful to what the foundations of biomechanics or even plain mechanics, understood as continuum mechanics, imply. There's almost nothing trivial about this last one, to the point that we can suppose that it has almost everything that biophysics can need and then some.

And since at present it is so advisable to proceed by contrast, we are going to touch on a case that is completely secondary in modern biology but that in another era had great significance.

A HIDDEN SYMMETRY

Discovered for science by Richard Kayser in 1895, the nasal cycle alternating the respiratory flow remains an enigma despite the abundant literature on the subject. Long before that, various ancient yoga texts implicitly assumed its importance for the general regulation of organic and mental functions. The basic idea held by yoga, of a hidden axis of symmetry in the organism that gives rise to a "sun/moon" alternating current of activation/relaxation even admits an updated version in consonance with our present knowledge of the dual organization of our organism and the autonomic nervous system (ANS) in particular with its sympathetic and parasympathetic subsystems, sensory and motor signals, anabolism and catabolism, and even the two cerebral hemispheres.

Since there are already many studies devoted to the physiology and biochemistry of this unexplained phenomenon, and despite their extensive data collection work they do not provide conclusive evidence or shed any clear light on its nature, I would like to briefly propose here a more basic approach to the subject, which nevertheless connects better with the physical and mathematical treatment of biological signals.

Circulation —or alternation- exists when two conditions cannot be satisfied simultaneously. This elementary truth seems equally valid for all types of systems, whether physical, chemical, biological, or socioeconomic. Life is a situation out of equilibrium, an imbalance that anyway has to find some partial equilibrium with its environment to have some sort of stability. Without imbalance there would be no differentiation, and without some kind of equilibrium there would be no persistence or duration.

But this equilibrium cannot be based only on the boundary conditions between the interior and exterior of a system, on its bordering surface, since in such a case the very limit would be the attractor and would prevent the development and differentiation of a relatively autonomous internal territory. Thus, the balance between the interior and the exterior tends to reproduce itself in the interior as a "center", even when in reality it supposes the virtual cancellation of both.

A good example of this dynamics is the organization of the cell itself, which has had to begin with a lipid membrane or filter that divides an inner enclosure from the outside —the "basic language" - to gradually allow the folding, aggregation and recombination of more complex molecules that would eventually lead to globular proteins, enzymes and nucleic acids capable of replication thanks to the action of the former ones —these macromolecules being the "high-level language".

Seen in this elementary way, the imbalance needs to rest in order to survive. And in reality, if we stop to think about it, the DNA or biological inheritance corresponds to a passive phase of stability or rest that would be useless without the enzymes that activate and modulate them in very variable ways depending on the medium in each occasion of expression.

In a very different order of things, something similar has to happen with the alternation of the flow of air through the two nostrils, no matter how much this cycle varies from individual to individual and even in the same subject over time —without that variability it would be difficult to act as a buffer in the midst of changing circumstances. The suspicion that the predominance by one or the other nostril has to correspond to a predominance of the sympathetic or parasympathetic, of active response or of rest in the ANS, seems simply reasonable and is to a large extent supported by numerous studies.

This, however, is still a relatively trivial alternation, although not for us in the most ordinary circumstances —just as we don't find trivial, either biologically or psychologically, the difference between whether something is inside or outside our body. In phase shifts or in dreamless sleep the flow has been balanced and in such circumstances the powerful inertia of involuntary biology would be somewhat suspended. It is a pity that we cannot realize these privileged moments of our daily agenda and our biological calendar, because if there were really some kind of biorhythm, it could not be based on fixed numbers but on verifiable and measurable real time fluctuations.

Ironically, the originator of the rightly forgotten theory of biorhythms was the famous Berlin otolaryngologist Wilhelm Fliess, praised by his friend Freud as "the Kepler of biology", who , just a few years before Kayser made his little-publicized discovery, recommended the extraction of the nasal turbinates through which this respiratory cycle manifests itself.

What this virtual axis of symmetry, this shushumna or invariable middle between both phases would designate, is a center that is center because it is neither in the interior nor the exterior, but is rather a measure of reference for both ends.

And what is implicitly stated for the autonomic nervous system could also be applied, via analogy, to the central nervous system and its afferent and efferent impulses, the pathways of perception and action. Also here we tend to counterpose a thinking subject and a thought object, when it is obvious that the thinking subject does not cease to be one more object of thought interposed by the general activity of thinking, which would be the immanent logos from which our logic would have fallen apart.

BIOPHYSICS AND BIOMECHANICS

Biophysics is currently experiencing a great moment as its branches are constantly dividing and connecting; no two researchers have exactly the same perception of the discipline, but few doubt that the light that physics can shed on complex biological systems must be at the level of applied physics rather than fundamental physics. However, the same basic physics is inseparable from statistics, an essential signature of what is understood by applied physics. We would like to show here how basic physics, duly considered, has important things to say about the most global aspects of life.

Returning to the nasal cycle, since Kayser it falls by his own weight that the whole question is a matter of tone, and vital tone we could say, since he himself defined it as "the alternation of the vasomotor tone throughout the periphery on both sides of the body". The local mechanism involves changes in the sympathetic tone of the erectile venous tissue of the nasal mucosa.

Tone is something characteristic of the vascular system, muscles, skin and vagus nerve, so important in its overall regulatory effect that it has even been called the "nerve of life". This vagus nerve in turn influences vasomotor tone and blood pressure, musculature and skin —in addition to many other aspects such as breathing, the heartbeat, the functioning of the abdominal viscera, emotions, and a long etcetera.

The same vagus nerve is double and bilateral and transmits sensory and motor signals; although classified within the parasympathetic system, it can be said to act as a mediator between the sympathetic and parasympathetic phases, and is as fundamental to the autonomic system as the spinal cord is to the central nervous system. However, there is no direct and unequivocal way to measure vagal tone, only indirect methods derived from cardiac variability and the arrhythmia of the elemental respiratory cycle.

The most reliable and tangible way to measure a signature as eminently global as the vital tone of the organism is through the blood pulse in the radial artery, as has been done in different physicians and cultures for thousands of years. This previously involved an empirical semiology and a medium, the touch, with a strong subjective component, although modern techniques such as applanation tonometry make a precise and automated measurement perfectly accessible. Naturally we are not talking here about the pulse as just an index of the circulatory system, but about the individual physiology as a whole.

A drop maintains its particularity thanks to its surface tension that marks the physical condition of the boundary with its environment, and in the same way can be characterized the individual tone of a cell and even a higher organism such as the human being. The whole difference lies in the great complexity of the exchange with the medium of an organism, but, even so, breathing and its continuation in circulation should be sufficient to define this tone in what's most characteristic.

There is a tendency to think that when passing from the tension of a drop to the biological signals of the human body the increase in complexity is such that the most fundamental mechanical aspects become too diluted, but the facts and equations disprove this prejudice. On the other hand, one also tends to think that physics deals with purely local or reductionist aspects when all gauge theories since Maxwell have arisen from an integral approach from which local aspects are later deduced.

The case of the classical Maxwell equations for electromagnetism is paradigmatic, because initially it was a theory expressed in integral equations and entirely based on the notions of flow and circulation, with the Faraday flow tube as the basic element. It describes a system in a phenomenological and organic way, from outside to inside, including the constitutive relations that define permittivity and permeability, the respective tension and deformation of the electric and magnetic field that refer us directly to the mechanical properties of materials. There is therefore a set of basic symmetries and a metric that limits them through material properties attributed to the space in which they transform.

In short, Maxwell's electrodynamics is but a continuation of the hydrodynamics initiated by Daniel Bernoulli by studying precisely the mechanical values of blood circulation and later by Euler; in its formal aspects hydrodynamics was indeed the first "field theory" ever, and from it we can pass to Laplace's equation, Poisson's equation, Maxwell's second equation, Poiseuille's equation for laminar flow and Ohm's law, which still is used as the base for hemodynamics.

The fall of the laminar flow in the Poiseuille equation gives rise to a first-kind Bessel function that, just as it can be observed in the membrane of a drum, reflects the cross-section vibration modes. Here, the acoustic and tone elements, never lost in the logic of continuity ("with tangential tension, the solid deforms, and the liquid flows"), clearly emerge again.

The pulsology of some traditions, such as Chinese medicine, tried to represent this cross section in its classification of characteristic pulses. If we consider the cycle of nasal alternation in terms of gradient or quantity of flow, it is worth asking if this variation is also translated into quantitative terms to the pulse in the radial artery of the right and left wrist, and even if it is permissible to superimpose them in an interference pattern or to get an average. The function can also be extrapolated to spherical coordinates if we look for a three-dimensional expression.

A traditional representation of the three axes of the human body contemplates a continuous polarity and a correspondence between the left and right sides, the lower and upper part, and the anterior and posterior face; the ends of the three axes being an unfolding in the space of a fundamental duality activity/receptivity or activation/rest. In mechanical terms we can generalize them as tension/deformation or force/adaptation. Can we move from qualitative correspondence to statistical correlation?

THE GEOMETRIC PHASE AND THE BILATERAL RESPIRATORY CYCLE

The geometrical phase is better known as the Berry phase in quantum mechanics but it exists equally in classical electrodynamics and even has exact analogues in waves on the surface of water.

This forces one to think that there is nothing special about quantum potentials, and only by separating the particle from the field could one think otherwise. The geometrical phase, "global change without local change", can only be conceived in terms of the continuum; only the interference patterns of wave systems show this kind of displacement.

After Berry showed the simplest case for cyclic adiabatic processes, there have been generalizations for non-adiabatic, non-cyclic, dissipative or non-conservative processes. Independent of the dynamic aspects of the systems, the geometric phase has demonstrated a profound universality which in spite of everything, and precisely because it's not linked to the forces, always remains in the background.

This "anholonomy" is also not alien to living beings and their locomotion. Inevitable the example of the revolving falling cat —the "Maxwell cat"- surely the happiest example of how a living being protects its invariance against the contrary efforts; or the no less universal figure of the movement of the snakes. Shapere and Wilczek showed their relevance in cellular self-propulsion in viscous fluids by describing a circuit of forms with arbitrary infinitesimal deformations in cylinders and spheres.

We could call this "Maxwell cat", the global contortion of the system, "the fifth equation of electromagnetism" —Maxwell's fifth, of course- although it is understood that this additional curvature does not add anything to its dynamic profile, but only to its global configuration. The status of the geometric phase is ambiguous and it is not surprising that physicists do not miss the chance to affirm that it does not alter quantum mechanics or classical electromagnetism in any way. That's as far as it goes!

The only problem is if these other "fundamental laws" are only emerging ones, the local application of an intrinsically global theory —which is certainly already the case with the first gauge theory, precisely Maxwell's one. Then the geometric phase would be a slipknot with which the continuum holds the system. The anholonomy from the point of view of calculation and integrability would be an holonomy from the point of view of mere continuity.

There has also been an abuse of the "non-local" word for quantum potentials in Bohm's interpretation. In the cases of geometric phase in classical electrodynamics and hydrodynamics the only thing we have is the definite restriction of the global configuration of the system. This is something very different from the total vagueness of the expression "non-local". In such cases, ignoring classical precedents, those advocating non-local interpretations put things too easy to dismiss for the vast majority always inclined towards local application.

Shapere's and Wilczek's demonstration rests entirely on the application of the arguments of the gauge fields of fundamental physics —fields in which the Lagrangian is the invariant calibre- to the deformation of bodies. This approach of a circuit of forms or deformations is suitable to follow the evolution of the volumetry and mechanical forces in the expansion and contraction of the lungs. The analogy is established between electrodynamics and the theory of elasticity, which is known to overlap easily. Let us explain this a little.

Anyone who observes his breathing can see in the most direct way that there is a correspondence between the depth of breathing and the clearing of the nasal passages. Deep abdominal breathing sustained for a time tends to eliminate bilateral alternation; on the other hand, higher or shallower breathing accentuates the alternation and blockage of one of the pathways.

Since increased voluntary activity tends to accentuate high or shallow breathing, it can be assumed that the ANS tends to compensate for these imbalances; which in turn means that lateral alternation also compensates in some way for the height and depth of breathing considered on the vertical axis. As for the anterior-posterior axis, apart from the difference in the filling of the lung volume when done from the base, we have already mentioned the polarity between the spinal cord and the vagus nerve in terms of the two central and autonomous nervous systems.

Naturally, all this takes place in a context of continuous transformations of which there can only be degrees of statistical evidence. However, the idea of calibre or gauge as already presented in classical electrodynamics is perfectly adapted to describe this, including of course the connection with acoustics.

In the variations of respiration and lungs movement, from deeper to shallower, we not only have changes in volume and shape, but also in the filling of that volume, i.e. air pressure and surface tension of the lungs. There is a correlation and possibly also a pressure-tension/deformation/volume circuit. All these are eminently mechanical issues.

We also have this primary presence of mechanics at the level of cells and even macromolecules such as DNA, without there being any need here to raise hierarchical mechanisms of subordination between different levels, since we are talking about problems inherent to the very continuum mechanics and therefore, to continuity. Let's take a closer look at this.

The problem of the chain of command and control in biology is far from being solved because it is supposed to act fundamentally by nerve and chemical signals when what happens is that these emerge from the mechanical conditions of the environment to a much greater extent than we suppose. It also happens, of course, that the relationship between these conditions and particular elements, such as molecules, are very difficult to calculate. But there is also the geometric phase, which after all shows how the propagation path depends of the properties of the medium, and it is in this sense that it is more revealing.

The geometric phase can also be measured in polymers such as DNA, and in fact without their contribution an exact solution to the mechanical problems of twisting and elasticity cannot be reached. Now, the same elastodynamics rationale can be extended to the parameter space of the lungs in a sufficiently long breathing time sequence.

The geometric phase can be seen as a torsion in the same way that torsion can be seen as a change in density. If in an originally homogeneous medium we imagine the appearance of a denser clot and a less dense bubble, both could not just arise without a torsion or vorticity to connect them. This may extend to other types of inhomogeneity.

Truly, the shallow, gasping and altered breath that nearly all of us have supposes a full-fledged contortion of a homogeneous respiratory cycle. But it does not help to characterize it as pathological, since in reality it's only an internal reflex or adaptation to the activity that the external environment and the same subject demands of the organism. As we said, bilateral alternation should also reflect how the ANS compensates for imbalances caused by voluntary activity.

The geometrical phase has also been called phase memory or system memory, since the properties of the medium or its potential provide an additional restriction on the evolution of the dynamic parameters that makes them not return to their original state. In fact, the most basic way to describe it is as the evolution of those wave parameters near some hole or singularity in the topology. Fortunately, we do not have to deal with infinite quantities here.

The change of sign is a typical feature of the geometric phase revealed in the clearest way in the exterior differential forms which in passing are also the most compact and elegant way of representing the integral aspects of electromagnetism. They also find a graphical translation that brings us back to acoustics: the circuit of forms of the modes of vibration of a membrane whose limits also vary within a circuit, discovered by Arnold in 1978. This naturally connects with the Bessel functions that we notice in the pulse cross-section.

The geometric phase is also present at the conical intersection of potential energy surfaces that define global landscapes for chemical reactions. In any case, a strong enough correlation between the modes of the pulse and the gauged circuit of forms of pulmonary mechanics would not be surprising, if we bear in mind not only that the circulatory and respiratory systems are intimately associated —something already sufficiently recognized- but that the respiratory system itself contributes greatly to the total impulse responsible for the blood circulation.

In this total impulse we must of course take into account the measurement of the return of the venous circulation, which is much greater with abdominal or deep breathing and much less with high or superficial breathing; a factor that also has a very direct influence, through capillary congestion, on the blood pressure index —and this being in turn connected in a loop with the cardiac response.

We must not lose sight of the fact that the immediate cause of the alternation in the passage of air through the nose is congestion by vasodilatation and decongestion by vasoconstriction of the venous tissue by the modification of the sympathetic tone with chemical mediators such as noradrenaline, which also affects the heart and is also considered a stress hormone. So the whole phenomenon makes sense as a process.

All the results obtained in electromagnetic theory have analogues in the theory of potential flow. In the simplest hydrodynamic case of geometric phase for waves in a moving medium, the parameters are the velocity of flow and its torsion or vorticity; it should be seen if this can be applied to the thread of respiration, to its ideal continuity so continuously disturbed.

In short, in biological systems the geometric phase is or should be a measure of the degree of (forced) contortion of the system with respect to an unforced fundamental state, and as such it should be robust against various types of noise. On the other hand, it remains to be seen whether both the dynamic elements and the phase shift have a continuous, and therefore immediate, acoustic translation in terms of tension, tone or timbre.

This calibration model of a complex motion inspired by gauge fields should have multiple uses in biology and biomechanics; to give just one example, it could be used to determine, gauge on gauge, the degree of stress, in the short term and with cumulative effects, suffered by cells exposed to different intensities and frequencies of electromagnetic radiation.

TWO PRINCIPLES

It may seem incredible that no one before Arnold Ehret defined vitality —and with it health- as Power minus Obstruction (V = P - O); but it is even more unbelievable that neither medicine nor theoretical biology have made later use of such a basic approach, the same one that a yogi or a Taoist could have subscribed two thousand years before Ehret.

Unbelievable, since after all Ehret's definition is the only one elementally mechanical ever given, science and the times still being supposed to be mechanistic at the beginning of the twentieth century. Nothing could be further from the truth, if we judge by the success of his formula, which is but the most direct possible application of the idea of a machine performance. "The principle for the construction of the ideal engine is to make it work with the smallest amount of friction". It's hard to find where the problem is in understanding this. Nor does it have such a great difficulty when applied to the human body.

Ehret's law may remind us the later Lotka's law, known as the "maximum power principle", but both arise from a very different context; their interpretations, moreover, point in very divergent, if not diametrically opposite directions.

Lotka wanted to bring a physical principle to the Darwinian ghost "mechanism" of natural selection, something that many others have tried with little luck if any. But Lotka's principle maximizes energy consumption and flow, not efficiency like Ehret's, in which the flow caliber is maximized only when the elimination of obstruction is maximized. The section or caliber of entry into the airways and the caliber of the thoracic cylinder in spontaneous or not voluntarily forced respiration also run in parallel. On the other hand, Lotka's principle seems to ask for the exercise of force whenever possible.

Leaving aside its completely different meaning, Ehret's principle, although so general, can be measured quite locally and directly, while Lotka's, like everything that appeals to natural selection, only admits global statistics in population dynamics. The first is really mechanical and easy to verify, the second is neither one nor the other.

There are certainly immediate ways of appreciating power and obstruction in different physiological signals, such as the pulse, where they are practically synonymous with pressure and tension, or resistance to pressure. The inclusion of the other basic constituent factor, deformation, allows to delve deeper into the analysis.

In addition to that it's not difficult to directly connect the Ehret principle with the problem of the nasal cycle. As a general rule, the total air flow, and the inlet section or calibre, tend to remain constant throughout the cycle, both when one side or the other predominates and when both are momentarily balanced.

However, first-person experience seems to indicate that the overall calibre tends to increase if the balance is not transitory and persists for increasing intervals of time. This is accompanied, also to an increasing degree, by a deeper breathing but with a decreasing flow of air that eventually becomes imperceptible. Such circumstance manifests itself in the dreamless sleep phases, as well as in periods of great absorption or concentration within the wakefulness, provided that both have a sufficient duration.

What can be seen in such cases is an increase in energy efficiency, and a general, and not merely nasal, effect of cleansing or decongestion. It can therefore be assumed that if these periods were long enough, they would have a profound effect on the overall balance of the organism. And this is the main reason, in accordance with others, why prolonged meditation was always considered to have an equally profound effect on health.

We can dismiss this idea if we want, but the truth is that, duly considered, it's the only one based on an entirely mechanical principle from top to bottom: Ehret's efficiency principle.

Already during the hours of sleep, even with dreams, a change of patterns in the respiratory flow and nasal cycle can be observed; this is something that the sleep sciences can sufficiently document. If during vigil we are forced to act in a world that we perceive as external to us, in dreams, on the contrary, it is the world that enters us. In the dreamless sleep, both tropisms are cancelled and the consciousness is empty of contents, although, it goes without saying, what we understand by consciousness is precisely that which does not depend on any content.

According to this, ideally all the cerebral/mental activity as well as the same breathing would tend to cease in the bottom of the dreamless sleep, which would act as a fundamental state. We would have a sort of asymptotic spectrum for the fluctuations of the breath and the mind traditionally seen as closely linked.

On the other hand, the fact that the body enters into more intense degrees of physical elimination, which is an energy-demanding work, when physical and mental activity is reduced to a minimum, raises the interesting question of how to define here the work done, the energy available, and the potential energy.

Even when it seems that the breath is about to cease, it's always assumed that this does not take place, but only that it has become so deep that it leaves hardly any marks on the surface; nothing indicates that the body has oxygen supply problems.

This brings us back to the issue of the potential already implicit in the geometric phase. But one does not have to look too far for the reasons. The body at rest is doing as much work as during its activity —the difference is that it now invests its energy in doing that work inside, cleaning and removing obstructions, rather than outside. This necessarily has to find a translation into the fundamental tone of the organism, whether we interpret it through the pulse, the breath or any other signal.

Lotka's maximum power principle is generally applied to external resistance, but could also be applied to internal resistance. Similarly, the Ehret principle of efficiency should have an external translation, even if we are not always in a position to follow it.

In the wake of Lotka, T. Odum has sometimes stretched the maximum power principle in terms of production and efficiency, but in this way it loses its restrictive power. For J. DeLong, what the principle says in its purity is that "biological systems are organized to increase their power whenever restrictions permit". In the context of natural selection it is always assumed that these restrictions are external.

The efficiency principle cannot ignore internal aspects, and while its simplicity is as sure a guide as there may be for these kinds of factors, it can also be too limited. It seems evident that any such general formula has to admit an expansion of terms if we want to deal more in detail with the untold complexities of life.

Although the formula (V = P - O) unequivocally invites to simply identify the power P with life and O, the obstruction, with the negative element that opposes it, it's clear, to give the most elementary example, that the same foods that sustain life can act successively as a source of power and obstruction. P tends to be identified with pressure and energy, O with tension and matter, and between them, at the constitutive level, we have the whole dividing line of deformation. But this deformation does not affect both parts equally, in the same way that in electromagnetism we have tensions without deformation and deformations without tension.

Probably the principle of maximum efficiency should be understood as easiness and could be written as maximum (internal) pressure with minimum stress and minimum deformation.

As matter and energy, O and P, are continent and content; since we know of no life that can exist without continent, here we have the egg and the hen, or the egg and the snake. But the same energy can be exerted outwards or inwards, and also and in parallel, towards the formation of structures or towards the creation of space and inner freedom.

As we have already pointed out, there is surely no more faithful and mechanical way to identify the state of O and P, continent and content, than the acoustic analysis of vital signs. Both acoustics and our organic arrangement, as well as hydrodynamics and electrodynamics, are naturally modeled around the idea of a tube of flow. It goes without saying that an empty tube doesn't sound as a full tube, and a thick one does not sound as a thin one. The potential theory refers us to this same context and circumstances. Metabolism can give us a biological measure of power, but much more indirect and problematic.

A quantum potential is also a potential of the wave field, and in this sense should not be different from the classical potential. This quantum potential looks the same as the pressure tensor of the Madelung equation, the hydrodynamic equivalent of the Schrödinger wave function. Here, too, continent and content can be distinguished.

Take the so-called tunnel effect, which is originally linked to de Broglie's wave mechanics; if we think in terms of point particles, we are obliged to think of an effect exclusive to the quantum domain. In a wave with real dimensions it is not difficult to explain it as a classical effect, which is equivalent even with an elastic rubber inside a container, as Paul Marmet liked to show. The classic model even offers the same pattern of dispersion as that revealed by quantum mechanics.

In the classical equivalent, it counts not only the thickness of the walls of the potential well, but its height also. A pixel animation shows in detail how the entire mass of a liquid can jump over a much higher barrier and get completely out of its confinement keeping the height of its center of gravity —and its potential- invariant. Although the process requires absolutely no discrete steps, these animations inevitably recall the associations between quantum mechanics and cellular automata, no less than the interpretation of quantum potentials by Bohm and Hiley as information potentials.

The maximum power principle and the efficiency principle should have something to say about the general orientation of the economy and society. Indeed, in modern societies the principle of efficiency is reduced to local economies of costs and production, totally subordinated to the hegemony of the maximum power principle, which also maximizes consumption, profit, accumulation and imbalance rather than circulation and homogeneous distribution. It's not hard to see either that the maximum power principle by itself tends towards the fastest possible depletion of resources and the global collapse of the system.

This also explains why in our societies the Darwinian external evolutionary model based on competition is promoted, in the face of all evidence and the plausibility of the internal development model; in such a way that even when the latter is considered, it's only to better subordinate it to the former.

The efficiency principle always prevails, while maximum power is only optional for systems that, in the absence of restrictions, tend to expand and self-destruct as quickly as possible.

TOWARDS A HEALTH SCIENCE?

Ehret's efficiency law plays no role in the health sciences, but this is no surprise since, as we all know, modern biomedicine is not at all concerned with health, but with innumerable diseases and ailments. If there really was a science of health, the principle of efficiency would have to be not only the most solid starting point but also the point of return and reflexion.

It is truly remarkable that modern science has been obsessed for more than four centuries with finding mechanical patterns in the external world and in our anatomy and yet has been unable to attend to such a purely functional argument. In fact, one can bet that this omission has a profound meaning in the general economy of things and in the government of the human.

Naturally we are aware that in the human body, which is an open dissipative system and not a conservative one, the categories of mechanics must be applied with particular care and discernment; but even so it cannot be denied that many aspects of conservative systems are still valid and relevant. A particularly crucial point, especially if we consider issues such as efficiency in the body, is how to move from closed, frictionless systems to open, frictional systems operating with external forces. This also has great significance in our global understanding of mechanics.

In classical mechanics it is the Third Principle of action-reaction that defines what is a closed system and therefore a mechanical system itself. The situation is very curious because Newton conceived his three principles to safeguard his theory of gravity and celestial mechanics but it is in the very orbits of the planets where the Third Principle can be least verified. Since then the application domain of this third principle has not ceased to be controversial, also in the case of the Lorentz force and other aspects of electrodynamics, as well as in Quantum Mechanics itself and General Relativity.

As Mario Pinheiro reminds us, by Noether's theorem, the conservation of momentum must always be valid in modern physics, but the law of action and reaction does not always holds. Surely this is a way of admitting that in practice and at the most fundamental level we cannot explicitly characterize systems as closed, and they must have varying degrees of interaction with the continuum or physical vacuum.

Pinheiro, developing further an idea from Landau and Lifshitz, considers a simple set of equations for out-of-equilibrium rotating systems with a balance between minimum energy variation and maximum entropy production that would have to be of great interest for the general appreciation of the mechanical-thermodynamic interface; these equations, which also describe a topological component of torsion with a mechanism of conversion of angular motion into linear motion, show a different momentum than that of Newtonian mechanics and predict "mutual interaction between systems and a self-regulating energy exchange", something that in living systems seems simply indispensable. Free energy is an essential term for the mechanical behavior of the continuum.

However, in a biological organism we find restrictions and circumstances that can still be very different. A distinction should be made between the internal entropy of the organism and that which exports to the environment, not to mention the maximum power principle, which seems to openly contradict the principle of minimum energy variation.

If we look within modern science for an equivalent for the three principles of Newton's mechanics in open systems such as biological organisms, we are not going to find it. To find something similar we have to look back way further, and then look for a quantitative and mathematical translation.

Actually, the triguna of the Indian Samkya system —the philosophy from which the yoga is derived- and its application to the three reactive modes of human body known as tridosha in Ayurveda brings a strong similarity for the case. The Triguna, as if we said, is the system of coordinates for modalities of the material world in qualitative terms. The three basic qualities, Tamas, Rajas and Satwa, and their reactive forms in the organism, Kapha, Pitta and Vata correspond very well with mass or inertia, force or energy, and balance by transmission of motion. But it is evident that in this case we are talking about qualities and open systems without further definition.

Here the third law of mechanics should give way to the conservation of the moment, implicitly admitting a variable degree of interaction with the medium. In harmony with this, Ayurveda considers Vata to be the guiding principle of the three as it has autonomy to move on its own as well as to move the other two principles. Vata defines the sensitivity of the system in relation to the environment, its degree of susceptibility in relation to it. In other words, the state of Vata is itself an index of the extent to which a system is effectively open.

In the human body the most explicit and continuous form of interaction with the medium is breathing, and therefore it is in the order of things that Vata governs this function most directly. Although doshas are modes or qualities, in the pulse they find their faithful translation in terms of dynamic values and the mechanics of the continuum that is our driving motif —as long as we conform to very modest degrees of precision, but in any case enough to give us an idea of the basic dynamics and patterns.

And since the other two modes reduce to what moves and what is moved, and the three as a whole are never in the same plane, the basic dynamic can only be an ascending or descending scale in which certain relationships remain invariant. Only with the coexistence of the three modes can compound beings occur; what varies is the proportion and degree of activity of each of them. This ascending or descending scale is also a scale of wider sensitivity or progressive dullness, of subtler restrictions or of increasingly material restrictions.

It wouldn't have to be too difficult to find the common ground that the Indian and Chinese semiologies of the pulse have beyond the differences of terminology and categories, and to pass from this common ground to the quantitative, but extremely fluid, language of continuum mechanics. Thus we would have a consistent method for moving from qualitative to quantitative aspects, and vice versa. Our world and our culture would welcome this.

We would then be able to conceive dynamics and patterns that right now go unnoticed as inherent, just as many global aspects of our biomechanics go unnoticed.

The health of the organism tends to maximum internal pressure and minimum internal tension. Outside the activity required by the environment, and even in that activity, it also seeks the least possible deformation that adaptation to an effort demands. All these are problems of optimization within a given domain, and can be applied to states of rest as well as physiological activity. What we propose here is that the pulse as a signature already has enough information to give us a global model of the flow and circulation that we call life; we only have to put its different aspects in order.

In the pulse signal it can also be evaluated impulse response functions quite similar to the Green's functions that already appear in hydrodynamics, electrodynamics or aeroacoustics and that incorporate the already commented Bessel functions. These functions provide a clear approach full of physical meaning, but we would still need to adequately define the impulse in different circumstances, as well as the degree of openness of the system in line with equations such as those of Pinheiro or similar.

In fact these or related functions, such as linear response functions, have long been used in information theory or to study the synaptic response of neurons. Naturally, stress tests are the order of the day in medical check-ups, in which the recovering function of rest values is also relevant. Now it is a question of translating these well-known techniques in terms of efficiency and quality.

It may be assumed that the acupuncture system with its twelve meridians or channels, which after all also rests on the ideas of flow and circulation, is a projection at skin level, taking into account the asymmetry in the arrangement of organs and other anatomical circumstances, of an elemental symmetry group based on the three axes of space. In this respect we must never forget that the meridians only form one level among those contemplated by Chinese medicine, and not precisely the deepest.

All palliative medicines, whether Eastern or Western, "holistic" or "reductionist", manage to find a compromise between an uncomfortable truth and the capacity of the client/patient. Even if Ehret were absolutely right, we would barely find one person in a thousand able to follow his recommendations to the letter. Much more than positive health, which in our present circumstances requires drastic measures more than at odds with our ways of living, people simply want relief for their ailments. However, there is no doubt that the old medicines were more concerned with health and the current ones with disease. It is not only that disease gives more money —at least within the modern "disease system", but that our circumstance as well as our relationship with the environment is increasingly pathogenic, if not pathological in itself.

However, on a theoretical level the simplest truths such as the efficiency principle are an invaluable guide to unravel the more than complex casuistry of diseases and sick people in their irreducible individuality. Since we live in the world in which we live, it is clear that we cannot ignore one extreme or the other: we cannot renounce the simplicity of truth just as we cannot ignore the complexity of facts.

The canonical texts of Chinese or Indian medicine, not to mention others such as those of the ancient Greeks or Avicenna, explicitly show guidelines for the classification of individuals according to qualitative typologies; these typologies were also reflected in a very significant way in the semiology or interpretation of the pulses, their types and their evolution over time in health and illness. These typologies, revealing an elemental combinatorics, were useful although naturally their scope was very limited by the subjective and phenomenological aspects of the evaluation. If we can bridge here the gap between qualitative aspects and continuous measurement, we would have access to a continuous combinatorial domain of incomparably greater scope within which to subsume increasing amounts of data, whether from one type of medicine or another. This as to "the path of complexity" towards which our overabundance of means compulsively pushes us.

From this point of view of complexity, everything we can obtain through molecular biology, whether at the level of genes or any other type of chemical markers, still has very limited value because it cannot be naturally framed in a macroscopic picture observable in real time. This means that modern biomedicine can hardly fulfill its promises of a "personalized medicine" that makes sense for the doctor himself; and without this, rather than medicine, we would have to speak of an electronic oracle. The role of the physician in this situation, if not increasingly accessory, would resemble that of a troubled interpreter.

In addition to checking the main structures and organs, it is essential that we have a dynamic reference at macroscopic level to guide us on the possible evolution of the organism over time. This has always been entrusted to the tacit knowledge of the doctor, to his appreciation of individual differences and to what we call his "clinical eye"; but this type of knowledge cannot be transferred naturally to any expert/AI system. On the other hand, the parameters of the pulse as a general signature of the vitality phenomenon can be transferred integrally and naturally because they are quantities that still can be translated into nuances.

But what's more, we believe that the pulse is already giving extremely valuable average information about the state of the internal environment in which all biochemical and biological interactions take place, and this is really decisive in the internal landscape that defines health. Going on with the analogy of continuum mechanics, we would thus speak of an approximation to the constitutive properties of that medium —much as we now speak of permeability, permittivity and susceptibility.

If precious information can be lost in the Maxwell equations by moving from the global to the local with the standard vector analysis, this should also be considered in the mechanical analysis of blood circulation, which should always maintain the holistic approach as much as possible. This integral approach allows us to see aspects free of metrics or orientability-dependent.

E. J. Post insists on how cyclic integrals, classical or not, have by themselves exact quantum-counting properties independent of metrics —both the Ampere-Gauss cyclic integral and the very Aharonov-Bohm's integral which serves as a model of geometric phase. In fact the determination of e or h is much less reproducible using only the Scrhödinger-Dirac theory or the QED. This counting ability can also be relevant to both measurement references and continuous combinatorics aspects that may arise in typologies, profiles and configurations of pulse analysis and biological data analysis.

Examples like this one mentioned by Post, basically ignored by most physicists, should convince us of the power of resolution of integral methods if we know what to look for, whether in physics or in any other case that presents analogous conditions like the one we are dealing with. All this agrees with our vision that there are no fundamental levels or systems, but rather the emergence of statistical ensembles, and that physical laws, understood as fields, have always had an integral character but a differential application and interpretation.

In biology, medicine or physiology we always have to deal with the weak consistency of data and measurements, all the more reason to look at physics as the reference standard. And if biology or medicine have been modeled by physics bottom-up, the only thing we are advocating for is its downright use from top to bottom, to find out to what degree it can improve that consistency. None of this would be strange to us if it weren't for the inveterate habits of thinking and a bias towards the idea of constituent blocks.

Thus, the most direct way of offering consistency to the growing constellations of medical or physiological data is under the coverage of the same global/macroscopic aspects of physics, in the sense we have described. The point is that by adopting this downward direction we have to develop new categories, categories that until now have been atrophied by the predominance of the constructive or ascending approach. This article is only an introduction to that problem.

Entropy itself is a macroscopic measure, often defined as the number of microstates consistent with the constitutive or state macroscopic quantities that characterize a system; although it should not be forgotten that only by metrics we are authorized to speak of macro and micro levels, and some very important aspects are independent of metrics. Since the terms entropy and information are interchangeable to almost all effects, even from the perspective of information theory the consistency of the data will depend crucially on the macroscopic characterization of the system —so much more in open systems that maintain a self-regulating loop with directly observable values. In the ongoing race for massive use of data in medicine, this is not only fully relevant, but almost the only thing that makes sense. A medicine without phenomenology is neither possible nor desirable.

The history of medicine shows that it is much easier to propose therapies than consistent theories about health and how the body works. Again, with the mechanical and acoustic properties of the pulse, it is easy to conceive extremely simple therapeutic strategies but with a wide range of degrees of sophistication and adaptation to individual constitutions; it would then remain to be seen whether these strategies that assume a global biomechanical perspective are also effective.

Here we cannot even begin to raise the complex relationships between entropy, increasing restrictions in organisms, elimination deficit, aging, maximum power and efficiency. These may be exciting topics for theoretical biology. But to get to the bottom of these issues, an additional thread is also needed to serve as a guide. Also in medicine, the most important thing of all, even more than how the doctor perceives the individual organism, is how this organism perceives itself. While this may seem the most intangible factor, it's also something that leaves traces at all levels.

Also the nasal cycle of which we spoke earlier would be a footprint at a certain level of how an organized being feels about itself; moreover, it would indicate a balance between perception and action that still leaves a variable gap for self-perception. Francois Chollet says that "when you have access to both perception and action, you are looking at an AI problem", so that you can start looking for an optimization loop. Truly, the Natural Intelligence of the organism already makes a balance between perception and action, but it is the self-perception that obstructs the path or determines in any case the level at which such equilibrium or imbalance can take place; and at the same time the self-perception is limited and unbalanced because the intelligence, and the organism following it, are more occupied with the activity in the environment than with its perception.

References
A. L. Pendolino, V. J. Lund, E. Nardello, G. Ottaviano, The nasal cycle: a comprehensive review
M. Berry, Anticipations of the Geometric Phase
V. I. Arnold, Methods of Classical Dynamics
A. Shapere, F. Wilczek, Self-Propulsion at Low Reynolds Number
J. Samuel, S. Sinha, Molecular Elasticity and the Geometric Phase
A. Ershkovich, Electromagnetic potentials and Aharonov-Bohm effect
P. Marmet, Reality of Waves in Particles
M. J. Pinheiro, On Newton’s Third Law and its Symmetry-Breaking Effects
M. J. Pinheiro, A reformulation of mechanics and electrodynamics
E. J. Post, A history of Physics as an exercise in Philosophy
F. Chollet, What worries me about AI, Medium Magazine
M. A. M. Iradier, Health, Life, Aging, Evolution