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The Eurhythmy Principle[edit]

Explanation of the name - ethymology and meaning[edit]

Since Nature, i.e., Physis, is One, it follows that one of the fundamental objectives of Science is the search for basic principles, sufficiently general, that will allow us to derive particular laws enabling us to apprehend physical reality in different scales of observation and description. One of these basic principles is the Eurhythmy Principle (1). The name Eurhythmy (2) comes from the Greek word Εὐρυθμία (eurhythmía), which results from the composition of the root eu (éu) with ῤυθμός (rhytmós), where eu means "good","as it should be" and ndῤυθμός means cadency, measure, movement which is harmonic and rhythmical according to some rule. The composed word thus means the good cadency, the adequate course, that follows the right measure, that is to say, the “good path" defined by given surrounding conditions.

Conceptual characterization of eurhythmy[edit]

The eurhythmy principle was born in the domain of non-linear physics (3) but it can be extended, with the appropriate reformulations, to other scales and dimensions of reality. The new physics of complex systems, in which it is assumed that, in general, action is not proportional to reaction, and also that the cartesian principle of linear superposition is also not appropriate, is therefore called Eurhythmic Physics (4). Naturally, as would be to expectable, this new physics contains in itself traditional physics, i.e., classical physics, relativistic physics and electromagnetism as particular instances. In this point of view towards Nature, one assumes the existence of a basic, underlying, chaotic and undetermined physical medium, the subquantum medium. This primordial medium was, in a way, anticipated by Anaximander's ἄäπειρον (apeiron), meaning the absence of limits, of an end, or of a determination (πέρας). Like in the past with Anaximander, this new physics does not take reality as stemming from a fundamental form or even matter, neither from Nothingness, as in some religious traditions, but rather from an underlying medium capable of taking elementary configuration s and forms, which give rise to the emergence of organized structures. Thence, a physical being is to be understood as a very complex relational system, in a permanent state of becoming. The (physical?) dimension of this complex physical being is assessed above all by its capacity to interact with other beings, that is to say, with its surroundings. The principle that describes this genetic process of becoming, of reciprocal interdependence in which the physical being suffers modification but also modifies its surroundings, is precisely the Eurhythmy Principle. In general, Eurhythmic Physics does not start from the abstract presupposition of isolated systems, introducing their interactions with the surroundings in an ad hoc way, as simple perturbations" which should be discarded or reduced to a minimum. On the contrary, the root conception is that reality constitutes a rather complex system of relations, in which connections with the surrounding medium determine the very existence of physical entities themselves. In this way, two assertions become valid in Eurhythmic Physics: 1. The evolution of any system S from state S1 to state S2 can not be described by the simple elements of S, but rather by the interconnection of system S with the surrounding medium; 2. Systems S', S, etc, that co-determine the transition from S1 to S2 are said to be neighbor systems of S, in which this neighborhood is not a spatial concept (two systems can be spatially neighbors but not physical neighbors and vice versa). From this general outlook of Eurhythmic Physics also results the denial of any sort of atomism. “Elements”, or elementary parts, are defined from systems and systems are determined through their connections with neighboring systems. To know the “elements” of some system depends on knowing the type of interactions one is studying. In last resort, the fundamental “atomic” element would be the entity emerging from the subquantum medium. But this entity is, in itself, already a system and not an “element”. The Eurhythmy Principle tells us that physical entities that at some observation scale and of description are being apprehended are those that, in their becoming, follow, on average, a stochastic, non-deterministic, adaptive path which leads them to interact with the medium so as to maintain themselves and persist. Naturally, those physical entities that do not follow this evolutionary and adaptability basic principle will de-emerge, suffer a transformation a cease to exist as such. Therefore, from a practical viewpoint, one can say that this principle establishes a sort of natural propensity for complex physical entities to adapt themselves to the surrounding medium, and thus to evolve in a dynamical way leading to their persistence. This signifies, in the main, an organizational principle that opens the way for the mathematization of natural processes of mutual interactions – thus the name Eurhythmic Physics for the non-linear physics of complex systems. Since the Principle of Eurhythmy aims at describing mutual interactions between complex systems, it can be applied to diverse objects and scales of the description of reality. Thus, its domain of applications covers in a natural way from physics to the other sciences, namely social sciences and humanities (5).


One of the first formulations of the Eurhythmy Principle came to light in the beginnings of our era, in the School of Alexandria. In his explanation of the phenomenon of the reflection of light, Heron of Alexandria proposed the Principle of the Shortest Path. This principle allowed him to derive, for the first time, the law describing the reflection of light. About a millennium and a half later, in 1600, Pierre de Fermat was able to explain the phenomenon of light propagation in different optical media, applying the Principle of the Least Time, which tells us that light, in propagating from some point to another through several optical media, follows the particular path such that the time spent in the whole way is as small as possible. One can naturally say that Heron’s Principle of the Shortest Path is but a simple particular instance of Fermat’s Principle of the Least Time because, in the phenomenon of reflection, light stays in the same optical medium so that the least time corresponds to the shortest path. Following Fermat, Maupertius, in 1744, proposed the Principle of the Simplest Path for light. This principle was later extended to mechanics by Euler, Lagrange, Hamilton, and others. These principles were then designated variational, extremum, or least action principles. One can show that classical mechanics can be derived from these extremum principles. One should naturally understand that all these extrema principles are but particular instances of the Principle of Eurhythmy. In the first quarter of the XXth Century Louis de Broglie (6), in an attempt to explain in causal terms the particle-wave dualism stemming from the domain of microphysics, proposed the Guidance (Guidage) Principle. This quantum mechanical principle of de Broglie’s constitutes the first version of the Principle of Eurhythmy. Initially, the Principle of Eurhythmy was, in fact, a generalization of the Guidage Principle, but now extended from quantum physics to all of physics.


In the conceptual framework of Eurhythmic Physics, which contains Quantum Physics as a particular case, a particle is formed by a complex region with a very high concentration of energy but also highly localized, dubbed acron (7), together with a relatively extended region almost devoid of energy, the theta wave. The reciprocal interaction acron – theta wave is described by the Principle of Eurhythmy. One can metaphorically think of the theta wave as a kind of sensorium through which the acron “feels” the surrounding medium. On the other hand, the theta wave also plays an essential role in the stability of the acron. If the acron moves over to a region of low intensity of the theta wave, its average lifespan decreases because there the acron loses energy in regenerating its theta wave. Under these conditions, those acra which are observed are those that survive, those whose lifespan is measurable, those that avoid low-intensity regions, that is to say, those whose becoming is described by the Principle of Eurhythmy. One gathers that the Principle of Eurhythmy takes on its intrinsic meaning in the context of complex systems since acra, corresponding to so-called elementary particles, constitute rather complex and highly organized structures from the subquantum medium. The becoming, i.e., the transition of a given acron from a state to another occurs in a non-deterministic way in the sense that, due the complex interactions with the medium, it results impossible to predict its future states. In spite of the impossibility of predicting the future state of an acron, it is nevertheless possible to to establish a global statistical tendency for an acron to evolve to a given state. In an explicit way, the Principle of Eurhythmy tells, then, that the acron moves inside its theta wave following a stochastic trajectory that leads it, on average, to the regions where the theta field is most intense.

General characterization[edit]

Even though it originates from Physics and, specifically, from the mathematical and conceptual problems of Quantum Physics, the Principle of Eurhythmy is nevertheless generalizable so that its quantic and eurhytmic formulation is but a particular case. Expressed in an independent way, it tells us that: Any entity embodies a complex system of interactions such that, in general, this entity is defined as the emergence of an organized structure (i.e., of a form) in which the system of interactions tends, under given circumstances, to a maximal stabilization. The Principle of Eurhythmy is thus understood as a genetic principle. Beyond stability and persistence, it captures becoming and the genesis of entities, understanding these as organized systems that persist only in constant interaction with the surrounding medium and in constant reshaping. The opposite of the Principle of Eurhythmy would be then a cacotropy, that is to say, the evolution of a given system towards a zone of destructive interactions where the organizational form would de-emerge and would be annihilated. This event occurs everywhere but it so happens that the de-emergence of forms is always flowed by the emergence of new forms. In this way, the study of what there is, i.e., Science, has to face, in general, this genetic dimension without which there would be no Reality.

Taken in this independent formulation, eurhytmy becomes a constitutive principle, and not just a reflexive principle. It is not a dictum regarding our reflections on Nature. Regarding the existence of structures and organization, we won´t say it is “as if” Nature “tends to” or “chooses” those situations in which organization emerges, “avoiding” or “rejecting” all other possible situations. We don’t project on Nature teleonomic elements resulting from our reflections. We don’t interpret Nature as if it had intentionality since only highly organized systems, like human minds, do have it. Hence, we affirm that eurhythmy is a constitutive principle of Nature itself, so that we have to formulate it not by analogy with minds (which are a very particular case), but rather forging the concepts and the mathematical apparatus from which the emergence of organization and the becoming of systems can be understood by themselves, from the structures that, in each case, are under study.


1 - J.R. Croca, The principle of eurhythmy a key to the unity of physics, in Special Sciences and the Unity of Sciences, Eds. Pombo, O.; Torres, J.M.; Symons, J.; Rahman, S. (Eds.), Springer, 2012. J.R. Croca, Hyperphysis – the Unification of Physics, in A New Vision on Physis, Eds. JR Croca and J. Araújo, Centro de Filosofia das Ciências da Universidade de Lisboa, Lisboa 2010. 2 - The Greek name Eurhythmy for the basic principle of Nature was suggested by Professor Gildo Magalhães Santos. 3 - J.R. Croca, Eurhythmic Physics or Hyperphysis – the Unification of Physics, to be published. 4 - The Greek name HyperPhysics for the new global physics, permitting a true unification of physics was suggested by Dr. Maria Manuela Silva, collaborator of our Lisbon research team. Later, Prof. Mario Gatta, suggested the name Eurhythmic Physics due to the key role the Principle of Eurhythmy plays in the conceptual and mathematical formulation of the theory. 5 - R. N. Moreira The crisis in theoretical physics science, philosophy and metaphysics, in A New Vision on Physis, p. 255, Eds. J.R. Croca and J. Araújo, Centro de Filosofia das Ciências da Universidade de Lisboa, Lisboa 2010; G. Magalhães, On eurhythmy as a principle for growing order and complexity in the natural world, p. 313, Eds. J.R. Croca and J. Araújo, Centro de Filosofia das Ciências da Universidade de Lisboa, Lisboa 2010; G. C. Santos, Between two worlds. Nonlinearity and a new mechanistic approach, , p. 331, Eds. J.R. Croca and J. Araújo, Centro de Filosofia das Ciências da Universidade de Lisboa, Lisboa 2010; P. Alves, Theses towards a new natural philosophy, , p. 359, Eds. J.R. Croca and J. Araújo, Centro de Filosofia das Ciências da Universidade de Lisboa, Lisboa 2010. 6 - L. de Broglie, Ondes et quanta. Comptes Rendus de l’Académie des Sciences de Paris, v. 177, p. 507-510, 1923; L. de Broglie, Quanta de lumière, diffraction et interférences. Comptes Rendus de l’Académie des Sciences de Paris, v. 177, p. 548-550, 1923. 3); L. de Broglie, Les quanta, la théorie cinétique des gaz et le principe de Fermat. Comptes Rendus de l’Académie des Sciences de Paris, v. 177, p. 630-632, 1923; L. de Broglie, Non-linear wave mechanics: a causal interpretation. Amsterdam: Elsevier, 1960; L. de Broglie, The Current Interpretation of Wave Mechanics: A Critical Study, (Elsevier, Amsterdam, 1969); G.M. Santos, The principle of eurhythmy in physics, biology and economics, private communication. 7 - The Greek word acron was suggested by the late Portuguese philosopher Professor Eduardo Chitas.

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