Phase precession, geometric phase, synchronization and consciousness

Consciousness as the last stronghold

Some days ago I read a short passage by Geidar Dzhemal on the difference between knowledge and information. In it, the Russian author invoked the inviolability that the consciousness of the workers still had in Dickens’ time, when they “went home to sleep and in the night found the way back to their hearts”.

For Dzhemal, as for so many others, the information society, which tends to abolish the difference between the internal and the external, destroys the last defensive bulwarks of our “inner fortress”. It is not easy to dismiss this type of lament, which is becoming increasingly common, since the invasion of consciousness by the new technologies, with their unstoppable deluge of triviality, is not a minor aspect, but perhaps the most notorious of our times.

However, one can be sure that, as long as we reach the state of deep sleep every night, we have not yet forgotten the way back home; only waking tends to move away from that fundamental state, and that already by its very nature, regardless of how invasive our technologies are.

And what is most characteristic of the deep sleep state, as essential for life as taken for granted? The balance or indistinction between the internal and the external, precisely. We have then a double paradox, if that is what we want to call it: the waking and dreaming states exist because of a sort of imbalance or dynamic equilibrium, and the fact that this dynamic equilibrium is not consciously perceived while waking makes the return to unconsciousness all the more necessary as the only way to experience a certain state of rest.

Dzhemal opposes knowledge as “understanding of the I” to information as recognition, just as he opposes an “authentic” inner truth to a merely operative external truth; and this also seems admissible and accesible. However, if we do not want that not only our idea of truth, but even the very sensation of reality to be beaten in retreat, it is our recognition that must advance: recognition of our projection in the world, and recognition of the action of the world in oneself prior to that understanding of the self that authors like Dzhemal claim.

Conscience understood as the last stronghold always has to lose, it is made for heroic defeats. This may give it its charm in a world where unthinking facts prevail, but that is not enough; the prospects of success or defeat should be completely secondary to our appreciation of reality.

Consciousness as a navigation system

Few things more curious than the attempt of the analytical sciences to delimit consciousness, or, faced with the prohibitive nature of the task, the neural correlates of the various activities with a “cognitive” component. The problem is that all sorts of neural correlates can be found that fit a cognitive model without the activity under study requiring cognition to take place at all, except in the most trivial way: we catch a fly ball not by some kind of prediction or trajectory calculation, but by simply moving in such a way that the same angle is maintained —without even thinking about it. Not surprisingly, the simplest explanation is the one that always has the most implications, even for the very nature of differential calculus.

One of the recent revelations in neurocognitive sciences is the phenomenon known as phase precession: a progressive advance in the firing of the hippocampal neurons related to spatial memory. This phenomenon was first seen in laboratory rats and bats, and only recently has been verified in humans. Today there is speculation as to whether it may be the key to a “universal code” of the human brain beyond specific tasks, since it has also been detected in other brain areas and in relation not only to self-localization in space but also to the processing of sounds and smells, learning and the organization of long-term memory —entering fully into what are considered higher functions of the brain.

In a recent article, these processes are referred to as a “human negotiation of their environment”. Pending confirmation of the universality of the phenomenon, Josh Jacobs tries to figure out applications: “Then we can begin to better understand how this neuronal coding mechanism can be used for brain-machine interfaces, and manipulated by therapeutic brain stimulation”.

Nothing less could be expected. Looking for some theoretical depth, it is worth noting that if phase precession happens to be of great relevance, it is not so much because it might provide us with some specific “universal code”, but because it is one more expression of a very general but insufficiently appreciated problem: the need for local asynchrony in information processing.

What the phase precession precisely indicates to us is the importance of synchronization in the brain’s activities: but were not this synchronization a truly active matter, there would be no activity as such. For example, in ordinary CPUs, operations are subject to a clock cycle that already implies a global synchronization by design, an organizing principle that governs the results of the parts; this is passive synchronization, designed from above.

There is no “global synchronizer” in the brain, nor in molecules, nor in Nature in general. However, as Koichiro Matsuno noted long ago, the laws of physics do imply a global synchronization, by virtue of Newton’s third principle of motion, which takes for granted the simultaneity of action and reaction. Thus the transmission of signals, and therefore of information, loses all connection with local time and its contribution to an internal global time.

In other words, Newtonian absolute time is external and metaphysical, but neither relativity, nor quantum mechanics, nor entropy as interpreted in statistical mechanics and information theory, modify the timeless concept of interaction. Thus the active role that local asynchrony may have in constructing a global internal time evaporates, and can never be properly recovered if it does not find a place at the level of principles.

Of course, one cannot expect very recent and derivative disciplines such as neurosciences to correct the situation of other much more general and older branches of knowledge such as physics, as that is not how things work. And yet the elementary fact remains: there can only be synchronization if there is local asynchrony in the first place.

Derived disciplines are content to speak of critical action or stimulus times; for example, for Arthur Winfree, the great pioneer in the study of resonance and synchronization in biology, a “phase singularity” was the stimulus time during which it is not possible to assign phase to a process.

To find another perspective we should fit the critical times of the descriptive sciences into the fundamental principles of physics. In “Quaternary Spirit” we already discussed the subject, but phase precession allows us to look at it from a different angle. Of course, we will never find a way to give physical “substance” to the passage of time because it cannot be dissociated from the subjective sensation internal to consciousness.

Indeed, if phase precession seems so important in memory sequencing, it may well be because it itself contributes in a key way to creating our notions of space, time and causality —causality being synonymous with spatiotemporal ordering. This is not merely to say that our ideas in this regard are reduced to particular neurological processes, for these ideas are already the more specific internal manifestation of a temporal profile explicitly and implicitly posited as external, but at the level of measurement or mediation.

But from the most immediately external point of view, if we aspire to a more rounded perspective, we should never lose sight of James Gibson’s post-cognitive, environmental approach: it makes no sense to speculate about what is in our head without pondering where our head is in. But although Gibson was a radical empiricist, he did not fail to insist that the most directly relevant aspect from the environment is not shapes or colors but invariants, which do not operate at an abstract mathematical level but with irreducible effectiveness. The aforementioned angle invariance or “optical cancellation” proposed by McBeath for the outfielder problem, that sort of “calculus without calculus” that we all have without knowing it, is clearly inspired by Gibson’s post-cognitive psychology.

This example shows that even radical empiricism can connect directly with mathematics, and what is even more important, it does so in a way opposed to the computational approach that tries to reduce any process to calculus within a metric and its algebra. This allows us to “invert” the perspective without actually forcing anything, since it is human calculus that has forced the data into its own Procrustean bed.

It seems evident that a phase precession such as that produced in neuronal firing in the hippocampus or other areas has nothing to do with the so-called “geometric phase” that occurs in many physical systems, except for the mere fact of affecting phases and potentials; moreover, the former shows an anticipation, while the latter usually implies a delayed potential. However, both phenomena, still of problematic status, share as a common denominator the problem of local asynchrony prior to the external requirements of global synchronous time.

Besides that, the geometric phase is not limited to giving a “supplementary curvature” to cyclic, adiabatic and conservative systems such as those of optics, the area in which it was discovered, but can also occur in non-cyclic and dissipative systems, such as biological ones, and in animal locomotion itself —its universality has made it an important aspect of robotics and the more recent control theory. And although physicists themselves erroneously present it as exclusive to the interference phenomena of quantum mechanics, it is clear that it can occur at any scale being an element of continuity in the transition between different scales and physical domains.

Although it does not seem to have been the subject of specific studies, phase memory should be studied in perception-action cycles in coordinated rhythmic movements, such as the famous Haken-Kelso-Bunz model or other similar models specifically adapted for this purpose. The geometric phase is so called because it reflects the geometry of the environment and the incidence of non-dynamic aspects (often described as “information”) in the global dynamic evolution —“global change without local change”. Needless to recall that dynamics refers to motion and forces, while potentials refer to position.

But what the geometric phase exhibits, already since the first cases with polarized particles, is the global or “internal” orientation of the system, which however has been left out of its “external”, necessarily closed, dynamic description. And the fact that this question arises at any scale and in all types of systems only adds to its interest.

The geometric phase is today conceived as a supplement to the dynamics, but in reality it also makes it possible to modify the very laws of motion and their meaning; and so we have spoken of a “fourth principle” and even of “three and a half principles”, although three consistently articulated principles suffice.

Mechanics have cut out the natural substratum basically through the first and third principles. The principle of inertia, which in order not to be purely ideal can only be conceived as a rolling ball, demands “an isolated system with the property of not being isolated”; and the principle of action and reaction, a simultaneity of interactions in dynamics that is at best metaphysical. In a relational mechanics, such as that introduced by Wilhelm Weber or the one proposed by Assis, the principle of dynamic equilibrium replaces the principle of inertia, while the third principle acquires a completely different meaning by depending on potential.

The principle of dynamic equilibrium as formulated by Assis says that the sum of all forces of any nature acting on any body is always zero in all frames of reference. On the other hand, the fulfillment of the third principle in relational mechanics implies the so-called “retarded potentials” similar to a geometric phase —but it is understood that they are only retarded with respect to the global synchronization implicit in Newtonian mechanics and its heirs. It is perfectly licit to think that it would have to be the other way around: if global synchronization exists, it should be alien to dynamics, since all interaction requires time. Geometric phase or retarded potential are thought to be passive with respect to forces, but a simultaneous correlation can never be reactive with respect to something that takes time to change, quite the contrary.

This has a myriad of implications that we have not even begun to draw out. To begin with, there are no blind forces in Nature, because there are not even forces of a constant nature: feedback is built in “by default” even in the orbits of electrons, in any extension of the old Kepler problem. To say that Newton explained the elliptical trajectories of the planets is a didactic device at best.

Retarded potentials are never a “trivial loop”, even if they do not seem to add anything to the known solution of a differential equation as in Kepler’s problem. In reality these equations, from a purely descriptive point of view, are not really differential nor do they strictly define local conservation, but always discount it from the given global conservation, so that the local passage of time follows from the general condition and not the other way around as is assumed. We have already spoken repeatedly of this radical inversion that the standard calculus involves and of some of the possible alternatives. But calculus itself, no less than the principles of motion, veils the problem of synchronization and the relation between global and local time, from which we have derived our present idea of universality.

Returning to the three principles of motion, without this modification of the first and third principles, and indirectly of the second principle, any synchronization process rotates like a tractionless wheel in a vacuum. This is precisely what physics has tried to reduce Nature to. It is now noted that the brain has a much more “sophisticated” “navigation system” than those created by man, but what does this “sophistication” consist of? Is there not something more fundamental than the complexity of neuronal connections?

Current state of the sciences

Talking about the relationship between science and power is in bad taste, a bit like talking about money or politics at the dinner table; but in today’s ultra-bureaucratized science there are no other relations than those. What sounds ridiculous today is to raise the relation between technoscience and truth.

Another issue that is hardly talked about is secrecy. Even pure mathematics suffers deeply from it, in order to prevent giving any advantage to “colleagues” who in fact are seen as competitors. It is true that this is not a recent development, since back in the days of the “invisible colleges”, and even much earlier, people played riddles and information was revealed in dribs and drabs; but now, giving it all for the applications, everything has taken on a different dimension.

Probably even a plausible demonstration of the Riemann hypothesis would today encounter obstacles to its dissemination for fear that it might serve to break security codes, even if no one has shown how it might lead to faster factorization methods. And while there is not much to worry about that possibility, the fact remains that today the consequences of knowledge matter much more than knowledge itself. This, in turn, has more consequences than the very consequences of knowledge. However, the more ominous the consequences may be, as in biotechnology for example, the less the research is publicly questioned.

Evidently, if concealment pervades even pure mathematics, one need not imagine the levels of opacity in sciences with much more defined interests, from physics to biology, economics, sociology, applied mathematics, statistics and data analysis, behavioral sciences, and so on and so forth.

One can only laugh in the face of those who still present science as an independent and daring exploration of the world; and yet it is true that the West seeks to exhaust its possibilities in a very specific sense, to the exclusion of all others. In this it is undoubtedly coherent.

This sense is the project of domination of Nature and its complete substitution or elimination. And it is in such a sense that it cannot be allowed to triumph, for its triumph entails the destruction of us all. Which does not mean that “Science” seeks to destroy us, for the greatest triumph of power and the greatest defeat of thought is to believe that there can be no other science than the present one.

The present sciences, and the point made about phase precession is merely an example, cannot fail to combine a high degree of technicality and formal sophistication with an empiricism which in reality is only opportunism, and where understanding is spoken of in a purely instrumental sense. Their presumed technical superiority of means only hides an unavoidable theoretical incompetence, since the meaning of theory is limited to its predictive capacity.

It has been discussed, for example, whether “the problem of consciousness” might involve exotic aspects like quantum coherence. Most physicists and neuroscientists consider this a remote possibility, if not pure charlatanism. Of course, quantum mechanics is not universal, but neither is classical mechanics. On the other hand, the geometric phase is universal, and is present at all scales, since all potentials are entangled regardless of the kind of mechanics in which they are embedded.

Western logos still does not get out of the impasse created between Descartes and Newton, and it does not get out of it, first of all, because it does not want to, because the disposition that drives it is the radical opposition between the infinite inertia of the material world and a consciousness as an independent hole or singularity. Without this opposition it would never have gotten this far in the first place, so it will not stop claiming its rights.

The modification of the principles of mechanics that we have pointed out ends radically with the separation of Nature, no less than of consciousness. The sum of forces at any point is always zero, but in addition the sum of any number of zeros is also zero. It makes no sense to think that consciousness can be localized: what is unreachable inside oneself, cannot be reached outside; and yet relational mechanics allows us to make the same or similar predictions that modern physics arrived at from a very different start point.

It is very likely that a physics based on dynamic equilibrium would never give rise to the hypertrophy of today’s technoscience, which has come so far only by dint of great tensions and imbalances. But at this point, it is still true that it is capable of transferring the whole mass of accumulated knowledge to a new language and a new disposition, without even having to make abrupt transformations that never make sense in science.

Fish or not fish

In a very important sense, the antithesis of modern control theory is biofeedback, since it applies to internal rather than external government and involves a range of control that is not instrumentally voluntary.

Several questions of extreme interest and intimately related appear, which can only be outlined here. It remains for researchers to properly illuminate the relationship between phase shifts, positive and negative, and brain synchronization or motor coordination. On the other hand, possible biological phase memories, which may also affect the brain to some extent, such as that of the bilateral nasal cycle, and their connection with respiratory volumetry or sleep stages, have yet to be clearly identified. In addition, the connection between geometric phases in biological systems, their relevant signals, and biofeedback should be studied.

But first of all, it would be necessary to design experiments in which the geometric phase acquires prominence within perception-action cycles. It is a matter of studying whether the presence of this phase memory can emerge in consciousness itself, and the conditions for consciousness to detect it.

Dynamic equilibrium, as a zero balance, is everywhere and nowhere. Therefore, even if its presence can be admitted in any motion, there is nothing specific that allows us to identify or recognize it directly. Is the geometric phase recognizable by consciousness, if it takes place in the movements of our body? Does it evidence any property, beyond quantitative relations? These are questions that may seem very strange, if one forgets the irreducible ambiguity that has accompanied this phenomenon in physics since its detection.

Dynamic equilibrium is indiscernible by definition, but such a well-studied exponent of the geometric phase as the Aharonov-Bohm effect clearly shows us how a charged particle “feels” or reflects the potential even where the electric and magnetic fields are zero. Can an electron accurately perceive this circumstance and yet be inaccessible to my consciousness? Of course, we are not talking about microscopic scales, but of the parallel transport itself.

Depending on the physical case, its description and interpretation, a geometric phase can be seen as a parallel transport, as a self-induction, as a curvature or flow of the symplectic form, as a conical intersection of potential energy surfaces, as a transition between dimensions, as a torsion or a change in density, as a phase transition, as a point of degeneracy, as a retarded potential, as a resonance, as a loop, as an enslaving principle, as a hole or singularity of the topology of motion, or other ways that need not be mutually exclusive. The better the balance between prediction and description, without one taking precedence over the other, the more credit the interpretation of this or any other phenomenon will deserve.

The geometric phase usually has a smaller contribution to the global phase that than that of the dynamic phase. This, together with the fact of its late recognition, has almost inevitably led to its subordination to already built mechanical ideas. However, we have seen some cases, even in the realm of living beings, in which the non-dynamic contribution —at least in the usual sense- can be many times greater than the standard dynamic contribution. It would be interesting to see whether there is also room for this large amplifications in the human organism, and if the answer is positive, what may be concluded from them.

Is there something non-mechanical within mechanics? But what could it mean that something is non-mechanical? This may have many answers that have nothing to do with the usual discussions about determinism and indeterminism. If we can eliminate the principle of inertia and replace it with the principle of dynamic equilibrium, a good part of what we understand by “mechanics” disappears at a stroke, and it is even possible to interpret that bodies move by their own impulse without incurring in contradiction. Let us not forget that this last principle is much more economical and frees us once and for all from the scholastic arbitrations of inertial reference frames and related conventions.

However, the essence of mechanics is not inertia, but the constitution of a closed system or circuit; and there are no closed systems without the third principle. In the fields what is fulfilled is not the third principle but the conservation of momentum or quantity of motion.

In a relational approach such as Weber’s mechanics the third principle is automatically fulfilled by definition. Weber’s law does not describe a field but is easily transformed into a field by integrating over the volume. It is obvious that in the ellipses of electrons or planets the third principle cannot be verified, so the question always remains why stable and closed orbits are observed. The answer, as Nikolay Noskov saw it, would be in resonance, but resonance does not exclude interaction —emission and absorption- but rather defines its conditions. Correlation is the mother of interaction, and resonance coupling is the effective principle of synchronization in the absence of global synchronization imposed from above.

The analogy between a physical field and the field of consciousness is not entirely gratuitous. But by physical field we mean a portion of space in which a certain evolution in time takes place; whereas consciousness, as we have understood it in our writings, implies a contrast with the undifferentiated background —the homogeneous medium, with unit density, from which all momentary modifications result. This could lead us to other different aspects of equilibrium and its formulation.

In any case, and in the present state of things, it is not necessary to carry the analogy very far nor to try to close it, since, for consciousness, the whole point is whether it is capable of perceiving phase memories, directly, indirectly or whatever. When we have a certain answer to that, other questions may or may not be raised. The subject may question our ideas about causality and its representation. It is also a challenge to find its relation to sound and music.

There are countless forms of equilibrium and to summarize we have been referring to the zero-sum equilibrium, to a unit product equilibrium, and to the equilibrium that can exist between the minimum variation of energy and the maximum production of entropy. The first concerns the motion itself, the second the density with respect to the homogeneous medium, the third an alternative mode to the Lagrangian for the general equations of mechanics. The connections between these three types of equilibrium may be infinite but finding their common axis does not depend so much on algebraic equalities or equivalences as on the intangible methodological balance between description and prediction. Needless to say, none of these four modes of equilibrium receives much consideration in modern physics and mathematics.

Mechanics, as the study of motion in closed systems, is a genuinely mercurial science, that is to say, it supposes a virtual reflection of something that neither moves nor is extensive. Were it not for this, it would not be of inexhaustible interest. And it is mercurial not by a vague analogy, but entirely and by the deepest necessity. Motion is already unnoticed spirit, which as a closed system has separated itself from something prior to measurement: this is the path of descent. And the opposite path of ascent is what was once called the work of the Sun, but in fact this operation embrace one and the other.

The true work of the Sun, the most illuminating and recondite of all, is consciousness itself, and if this is not even suspected it has not been possible to adjust much its ascent and descent.


At this point, mean secrecy in science seems almost the least of its problems, which we will not pretend to solve. But, for me at least, science as a whole is worthless if it does not have an intimate, genuine connection with our inner world; nor does prediction alone have any value for what is meant here by knowledge. Yet it is not a question of making the sciences more subjective, since our very idea of mechanics already has in us an excess of subjectivity, of compulsion and civilizing zeal only compensated with an increasing dullness.

It has already been said, to directly contemplate that there is no inertia in the world, to verify that it is basically an overdetermination, is as deep a meditation as it might be, which does not otherwise require any support or instrument, nor any special knowledge.

One may ask what make us feel that we exist if there is always a zero balance of forces. But one may also ask: does one need to be pushed in order to feel that one exists? Evidently not; however, the zero balance exists whether we are pushed or not.

We speak of “Nature” in the singular, but we could just as well speak of infinite natures. Our principles tend to reduce that infinitude to a single plane, just as they try to make that plane a new infinitude “according to the measure of man”; but man already contains within himself all those natures without the need to reduce them. The control of Nature as something external enslaves us and results in a permanent descent with no limit in sight; only its harmonization within us elevates us and gives us our true measure.

The problem outlined should be studied with exquisite care. The fact that the geometric phase is seen in physics as an ancillary phenomenon sets a clear precedent of misunderstanding on the subject. The new is subordinated to the old even when it presents the best opportunity to restate the whole question. The theory of electromagnetism itself shows us in an exemplary way that a fundamental force can be used with the greatest technical virtuosity not only without understanding half of its subject, but without even being interested in what may have been left out.

The same is true for our biology, our engineering or our mechanology. It is clear that modern technoscience does not work for the emancipation of the human, but for its integration with machines within an already defined scheme; and why should it have to do so if those of us who are outside its interests do not care about it either, nor do we succeed in finding the root of the matter.

Both thought and the principle of instrumentation from which technique arises can be seen under a ternary scheme well before the birth of modern mechanics; however, the latter defines a horizon in which the attempt to fill its gaps and contradictions, not even consciously, closes the circle of compulsion in which we move. To dissolve that encirclement today cannot depend more on theory than on practice.

Nor should it be forgotten that simple human behavior and its conscious observance is superior to any technology, which alone does not have the power to undermine it. But in the absence of consciousness, technologies are used both to plug holes in behavior and to enlarge them.

The agent-environment unity is prior to the “interaction” between one and the other conceived as separate aspects. There is a great distance between the I that appears in the child of 4 or 5 years of age and the Cartesian self ready to measure the world, but both mark different stages of an opposition between the I and the other that feeds back on itself. To rediscover the non-I that does not need to assert itself against anything in the middle of a logic that seems designed to eliminate it opens a perspective that only those determined to triumph over this material civilization can appreciate.

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