Nature never breaks her own laws
O marvelous and stupendous necessity! thou dost compel by
thy law, and by the most direct path, every effect to proceed
from its cause.
Leonardo Da Vinci
Abstract
This essay is written in the form of a mosaic. It intersperses simple language, primary and secondary quotes within text, footnotes and epigraphs from classical thinkers and cutting-edge researchers. It invites readers, be they casual or experienced, to a certain play of irony and fantasy in their reflection on the main thrust of the argument. The essay is divided into two parts. The first seeks to introduce the readers to some of the main concerns of frontier science and the Philosophy of Science at the beginning of this millennium: the Universe Models proposed by scientists from fields related to Physics and Mathematics in their eagerness to explain more and more discoveries and to lay out a solid new scientific paradigm. We are convinced that the leap between sidelines and insides—when confronting straightforward style with systematic contrast—does not lessen the rigor of research, and serves to lighten the density of the topic by projecting nuances and resonance onto the logos and its concatenation. It may also serve to vivify field and figure, in order to recreate the fertile delight that generally comes from a good reading of deep intertext. In the second part, we attempt to subtly demonstrate a fortunate discovery: the validity and solidity of the laws of Nature, upheld on the basis of their abstract mathematical expression (the Number Phi (φ), the golden number or golden section), which despite having faded into oblivion, buried under centuries of disuse in the fields of Aesthetics and Art, has proven to be useful as a critical instrument and a template for concrete solutions that we wish to share. We believe that this Model may serve not only to answer some of the scientific issues that we have referred to, but to redirect the discussion itself, and break the logjam of many frontier forums that place conditions on the application of the Models produced over the last century. Having glimpsed those realms where analysis and common sense come together for addressing one of the most salient issues of our time, we chose to close the essay by offering practical, concrete findings on the topic of Models, which not only specialists in the field may find useful, but also any reader, especially educators, who are charged with sharing these findings with the present and future generations.
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Notes
Pfr. Gillies (1993, pp. 21–46).
"Consciousness, Brain and the Physical World," in Philosophical Psychology, 1990, quoted by Harman (1994, p. 141).
See Quine, W.V., "Two Dogmas of empirism," 1951, quoted by Gillies, op.cit. p. 112.
Einstein, quoted by Asimov, c1959, (1991, p. 125).
Karl R. Popper, 6th ed., c.1934, (1959, p. 111), quoted by Gillies, op.cit., p. 131.
Cfr. Ibid., p. 149.
Dickson, c1968, (1975, p. 302).
Einstein, quoted by Asimov, op.cit., p. 125.
Asimov, ibidem.
Ibid., p. 126.
Dickson, op.cit., p. 322.
Pfr. Oliver (1992, pp. 212, 220 y 224).
Ibid., pp 200 y 224.
Ibid., pp. XX and 224. See also Grégoire Nicolis and Ilya Prigonine in Exploring Complexity, 1989 (quoted by Oliver, p. 190 “Reversible and deterministic laws that describe elemental interactions are probably not telling the whole story. This leads us toward a new vision of matter, one that is not passive like the matter described in the mechanical worldview, but rather associated with spontaneous <SIC> activity” … “This change is so profound that we believe we are truly justified in speaking of a new dialogue between Man and Nature”.
Rein (1998, p. 22). As McLuhan explains (op.cit., p. 55), “Max Planck, Werner Heisenberg and Louis de Broglie introduced new components of acoustic space into physics with the notions of quanta, indetermination, resonance, and wave mechanics. Heisenberg simplified the general presentation of quantum mechanics, jettisoning the principle of continuity in Riemannian or Euclidian geometry and introducing the suggestion of the shortest length to overcome certain difficulties of quantum electrodynamics”.
Jammer, Concepts of Space, 186, quoted by McLuhan E., op.cit. p.55. Granew wonders, “How should we understand time expansion? How is it possible that protons that are separated from each other can correlate their actions maintaining the arbitrary observer’s communication speed limits?” (see Granew 1998, p. 50).
Dickinson, op.cit., pp. 323 y 324.
Ibidem.
Ibid., p. 325.
To corroborate this it is worth consulting the exceptional diagnosis made by the Indian researcher A.K. Mukhopadhyay on the state of the art in the field of Quantum Physics. “Quantum mechanics is the most successful theory of the 20th century. By itself, however, it is incapable of responding to the paradox of the probabilities and determinism of nature. This theory urgently needs “windows” to keep it from suffocating, because as Heisenberg himself admitted, as a theory it is too closed (…) The superficial problem consists of determining how microscopic quantum phenomena are related to the emergence of the macroscopic reality. And, how microscopic reality emerges from sub-quantum or sub-microscopic realities. The most profound problems are somehow linked to the opening of this domain or field to deeper realities (2006, p. 12)”.
“Consciousness is not only neurocentric; it is also independent of neurons. Consciousness dwells where neurons cannot be detected. Consciousness might very well be something that is beyond the brain. Evidence of this can be found in neurophenomenology (e.g., out-of-body experiences, autoscopy, etc.) and in neuronal behavior (e.g., love, altruism, disinterested search for truth). Supracortical consciousness as consciousness of being is the keystone of a stable consciousness independent of the brain through a cerebral consciousness that is trapped by the means of consciousness itself (…) The existence of supracortical consciousness voids any consideration that there is nothing outside or beyond the cerebral cortex (Mukhopadhyay, ibid., p. 17).
Mario Bunge explains it as follows: “The Aristotelian teaching of causes persisted in official Western culture until the Renaissance. When modern science was born, it set aside formal and final causes because it considered them beyond the scope of experimentation, and material causes were taken for granted with respect to all natural phenomena, although with a decidedly non-Aristotelian meaning” (quoted by Eric McLuhan, op.cit., p. 62).
Plato, La República, Book VII, p 54., quoted by McLuhan, Eric., op.cit., p. 97.
The Temple in Man; Sacred Architecture and The Perfect Man, Inner Traditions International, New York, c1949, (1977, pp. 108 and 132).
Consult the first chapters of Volume I of Spengler (1976).
Consult Book III about Hermes in Los Grandes Iniciados, by Edward Schure, 6th ed., Editores Mexicanos Unidos, Mexico City, (1982, pp. 137–181).
Moses, quoted by Schure in Book V, op.cit. p. 212.
Moses, ibidem.
Heraclitus posited the logos as the informing principle of cosmology, of the Cosmos. In Heraclitus’ view, God’s primary name is Supreme Reason, Logos; and in a different invocation, the “Wise Being” or even the “Only Wise Being.” As F.M. Cleve explains, the Divine Body surrounding the world is that part of the resulting logos that never “changes.” (McLuhan and McLuhan, c1990, p. 48).
Pythagoras as analyzed by Schure, op.cit., pp. 354–355. Following this same line of reflection, Plato would rigorously synthesize his vision of Genesis as follows: “Wherefore God resolved to have a moving image of eternity, and when he set in order the heaven, he made this image eternal but moving according to number, while eternity itself rests in unity; and this image we call time. For there were no days and nights and months and years before the heaven was created, but when he constructed the heaven he created them also. They are all parts of time, and the past and future are created species of time, which we unconsciously but wrongly transfer to the eternal essence; for we say that he "was," he "is," he "will be," but the truth is that "is" alone is properly attributed to him, and that "was" and "will be" only to be spoken of becoming in time, for they are motions” (Plato 1996, p. 677).
Cfr. Ghyka (1953, p. 234).
Plato, Timaeus…op.cit., pp. 672–673.
Ratio that Luca Pacioli called divine proportion; Kepler called it the precious jewel of Geometry or divine section; Leonardo da Vinci gave it the name of golden section, or number of gold.
Plato, op.cit., p. 673.
Ghyka, op.cit., pp. 237–238. “An invariant is a thing that when other related things are modified, remains unchanged: and the change… is represented in Logic (and also in Mathematics, of course) by means of relations that, mathematicians call transformations. As C.J. Keyser puts it in his Mathematical Philosophy, ‘each step of the way of progress in the arts, sciences or philosophy consists virtually of discovering the invariants of a certain field of transformations, or the group of transformations that leave certain things unchanged…’.”
Ibid., p. 55.
“The golden section is imposed when the attempt is made -through a new subdivision- to get two equal consecutive positions to form part of a geometric progression and thus bring together the triple effect of equal parts, succession and continuous proposition” (ibid., p. 38) “Inorganic crystals increase by agglutination (addition to identical elements), while a living organism grows by a kind of expansion from the inside outward, which has been called intussusception.” (ibid., pp. 124–125). “The constituent elements of living tissue are continually renewed by combustion and elimination” … “and present a single plane of symmetry (in the direction of their movement) and are notably asymmetrical with respect to the perpendicular plane at the average beginning of their section by the previous one.” “Living things grow while keeping the general contour of their shape” (ibid., pp. 125 and 126).
Ghyka, ibid., p. 239.
As Einstein himself put it, “becoming” in three-dimensional space has been transformed into “being” in the four-dimensional world. According to Herman Weyl, the “objective world is; it does not become; it only appears to become to our blind consciousness,” (quoted by Capek 1961, pp. 158–159).
“We discovered that everything that people make, every procedure, every style, every artifact, every poem, cannon, device, tool, theory, technology- every product of human effort- displays the same four dimensions… I would go so far as to say that confirming and detailing this link between speech and artifacts represents the biggest intellectual discovery not only of our time, but of the last two centuries at least. And yet, the four laws are astonishingly simple. They must have the deepest significance for the arts and sciences and not just because they erase the distinctions that existed between them. They also offer a common set of tools for moving forward or backward—which are practically the same thing—for making use of and constantly renewing the tradition that everyone has and for exploiting each other as resources…” (McLuhan Eric and Marshall, op.cit., p. 11).
McLuhan speaks of four essential elements instead of three in his contribution (which are the ones proposed by the golden section formula). McLuhan bases his premise on a critique of the Hegelian dialectical structure: in his view “for some mysterious inherent reason, the shape of triad eliminates the field. But when a fourth term is added to the triad, forming a tetrad, the shape becomes a new shape: resonant, appositional and metamorphic (McLuhan, op.cit., p. 33).
In simple, classic terms, the rules found by McLuhan are none other than the Theory of Relativity and the Golden Section applied to problems that human beings face in maintaining their body and moving on with their life at a given moment. Like the use of warm-clothing technology, with which humans cover their body against the cold. The season changes and people are forced to stop using this technology. A change in conditions leads to a change in needs and behavior. This function is today known as the Theory of Relativity, previously, the Phi number.
If we decide to substantiate this using the Pythagorean scheme, we realize that this scheme is based on the mathematical tertiary law, which is the keystone of Pythagorean theogony and science. Schure explains the tertiary law as follows: this law is fundamental to the sciences. “It is the constitutive law of life. The Monad represents the essence of God; the Dyad, his generative and reproductive light. This generates the world, God’s visible flowering in space and time. But this real world is triple. Just as man is made up of three distinct elements that are fused to each other—body, soul and spirit—so the Universe is divided into three concentric spheres: the natural world, the human world and the divine world. The Triad, as if by charm, opens the internal structure of the Universe to the delighted spirit. It shows the endless correspondences between the macrocosmos and the microcosmos… Lifting veil after veil, and probing the powers of the divinity itself, you will see the Triad and the Dyad wrapping themselves in the shadowy depth of the Monad like an outpouring of stars in the abyss of immensity” … “This living conception of the forces of the Universe, penetrating from high to low, has nothing to do with the empty speculations of pure meta-physicians, such as, for example, Hegel’s thesis, antithesis and synthesis” (Schure, op.cit. pp. 360–362).
“A theory is all the more impressive the simpler its premises are, the more types of things it describes, and the more applications it allows,” Albert Einstein, quoted by Asimov Isaac, El Libro de Citas sobre Ciencia y Naturaleza, Asimov and Shulman eds., Lasser Press Mexicana, Mexico City, D.F., c1988, (1989, p. 160).
Plato held the same opinion: all phenomena of nature are merely shadows of eternal forms or ideas. Nevertheless, most human beings by far are perfectly satisfied with their life among the shadows. They never think that there must be something that casts the shadows. They think that shadows are everything, shadows are lived as shadows. With this, they also forget about the immortality of their own soul (See Gaardner, c1994–1995, p. 108).
“Taoists assert that the comedy of life could be more interesting if each person conserved the unities. Maintaining the proportion of things and giving a place to others without losing one’s own place was the secret of success in the worldly drama. We must know the entire work in order to play our roles properly; the conception of the whole must never be lost in the conception of the individual.” (Okakuro Kakuzo, The Book of Tea, quoted by McLuhan, op.cit., pp. 90–91).
“In the flow of sensations there are invariants that provide the only fixed points in the variation of the sensations in time functions, or in reciprocal functions of the ones on the others. They are the functional invariants that are none other than the laws of nature” (Rougier, quoted by Ghyka, op.cit., p. 238).
See Ghyka, ibid., p. 140. In the living world, the principle of minimum action and its earlier variants (Hamilton, Curie, Gibbs, Boltzmann, Mie) do not impose an absolute dictatorship as in inorganic systems. “The static equilibrium that converges in lovely crystalline nets is the least of the living organ’s concerns. There are two other desiderata with which the principles of symmetry and equilibrium must eventually agree: growth and reproduction regulated by a law of economy, not economy of action or of energy but of substance… And not in an arbitrary sense, but for the purpose of allowing life, once incarnated, to build its morphological receptacle, to adapt and perpetuate itself” Ibid., p. 121.
Zeysing, quoted by Ghyka, ibid., p. 38.
The axiom that is derived from this law states that the only difference between two indistinct objects is the degree of evolutionary development in time–space. In the language of modern physics, this corresponds to the level of order. For examples we can look to the work of two cutting-edge researchers. “Degrees of freedom reflect the evolutionary development of a system or its level of order. In this regard, another esoteric law comes to mind, the law of identity, which refers to the unifying principle that underlies all known phenomena—precisely what complexity science has been looking into (Semetsky 1998, p. 64). The field of atomic experimentation has given rise to these approximations: “…the new conditions of Physics often involve space–time modification in itself. One of these space–time modifications is the extension of four-dimensional conditions to higher dimensions. Fields of energy related to higher dimensions also show unusual properties (e.g., superluminal speeds, negative energy and elements that are not local). These fields of energy and their corresponding potentials have been characterized as complex inasmuch as they possess imaginary and real components.” (Work by Rauscher, quoted by Rein Glen, "Biological Effects of Quantum Fields and Their Role in the Natural Healing Process," also in Frontier Perspectives, Vol. 7, No 1, pp. 21–22).
See Mc Clain (1978).
As McLuhan observes, op.cit. p. 54.
"Some Educational Implications of Hemispherical Specialization," in The Human Brain, comp. by M.C. Wittrock, Prentice-Hall, New Jersey (1977, p. 138).
Apud. Rosen (1970, pp. 14–15 y 113–114).
McLuhan, op.cit., p. 65.
The introduction of the telephone had a similar effect on older people. Our parents or grandparents resisted this model of communication, just as we distrusted automatic teller machines years later. When a new model arises, people take a while to learn to use it and to get used to it.
“Heidegger observed, quite rightly, that modern technologies, electrical informational media, are responsible for the return of acoustical, Eastern-style forms of consciousness that make our legacy more disembodied” (quoted by McLuhan, op.cit., p. 74).
McLuhan, ibid., p. 75.
Quoted by McLuhan, ibid., pp. 90–91.
Pfr. McLuhan, ibid., p. 43.
Cfr. Graneau (1998, p. 50).
See Castaneda (1984).
Mc Luhan, op.cit., p. 80.
Martin (c1992, 1993, p. 53).
Cfr. Gaarder, op.cit. p. 101–103.
“Precisely because the soul is immaterial, it can see the word of ideas,” Gaarder, ibid., p. 106.
Gaarder interpreting Plato, ibid. p. 107.
Silberstein-Sorfer Muriel and Jones Mablen, Doing Art Together, Simon and Schuster, N.Y., c1982, p. 94.
“It is odd to see the degree to which modern Mathematics, the Physics of Relativity and Quanta, the infra-atomic Chemistry of Bohr, Rutherford, Braggs, agree with this conception. On a purely abstract basis—Cantor’s set theory—a new theory of numbers has been formulated. This theory, thanks to the calculation of classes and the calculation of relations by Peano, Frege, Couturat, Russell (which under the name of Logistics make up a branch of knowledge that is common to Logic and Mathematics), enables the general reconstruction of Arithmetic, Algebra and Analysis exclusively with the identity principle; and these cantorian numbers, cardinal or ordinal, defined as classes, classes of classes, or types of order, revived the concept of the Platonic number”(Ghyka, op.cit. pp. 234–235).
In McLuhan’s view, “a great deal of the confusion of our time arises naturally from the divergent experience of literate Western man, on the one hand, and his new environment of simultaneous or acoustic knowledge, on the other. Western man is torn between the demands of visual and auditory cultures or structures.” (McLuhan, op.cit., p. 122).
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In recent years, Humberto Ortega-Villaseñor and Genaro Quiñones Trujillo have published the results of their research in several scholarly journals of South America, Europe, the USA and China.
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Ortega-Villaseñor, H., Quiñones Trujillo, G. The Abbreviated Symbol of Living Forms, Unit and Growth. Fudan J. Hum. Soc. Sci. 9, 465–491 (2016). https://doi.org/10.1007/s40647-016-0127-x
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DOI: https://doi.org/10.1007/s40647-016-0127-x