Giovagnoli, R., Lowe, R. (eds) The Logic of Social Practices II. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 68., 2023
For ancient pre-Socratic societies the living pattern of the Universe was— according to Plato—als... more For ancient pre-Socratic societies the living pattern of the Universe was— according to Plato—also the blueprint for the organizational structures within a society. Divine order and equilibrium were the universal principles and the theoretical construct governing nature around us and the entire cosmos.
The old Theory of Everything (ToE) as it was mathematically conceptualized by Pythagoras and visualized by Plato—in the 5 synonymous regular forms—epitomized the principle of harmony. With the recent rediscovery of Plato’s 5th element we are able to under-stand that it was a higher dimensional world view based upon a geometrical living pattern of the world.
This metaphysical superstructure was allegedly strongly linked to high ethical standards Plato discussed an ideal society in his “Republic.” Meanwhile, according to theoretical physics, the Universe is expanding at an accelerating pace and governed by ‘dark energy’ and ‘dark matter’ where ‘black holes’ are gaining more and more significance. How does the loss of ancient superstructures and new concepts of theoretical physics affect our society, and which rites and habits are left from antiquity?
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named epitahedron {E±) which turned out to be Plato’s „5th element“ followed intuitively from the question: “If the Penrose Pattern is a 2D slice of 5-dimensional space, what would it’s 3-dimensional space cell look like?” Origami seemed the best way to explore this question. Enfolding the kites and darts to obtuse and acute triangles from the Robinson decomposition lead to the finding of two irregular heptahedra. Further research lead to hermeneutic interpretations of the Isis & Osiris myth as story which conveyed a detailed origami instruction for the unit cells of 5-dimensional space: therein the pentagonal grid and its 3-dimensional shape is symbolized by two brother gods Osiris and Seth & the sister goddess Isis. Was paper enfolding already a game in ancient Egypt that still survived until millenia later in Japan ?— Here the“Origami“technique and the "Katachi" concept shall be highlighted in regard to higher dimensional models of the word.
elements, fire, water, earth and air, the dodecahedron, as fifth element, — usually denoted as symbol for the world itself — the dodecahedron itself is not mentioned. The cover images of this issue provide an answer to this eminent almost two and a half millennia old riddle: Two simplices, the 3D representation of the Penrose Kites & darts tiling, (epitahedra E+), the unit cells of 5-dimensional space are forming the dodecahedron in a Boolean intersection.
Thus the 5th element synonymous the "quintessence" and the "aether" regains shape.
the explicit notches on a so-called ritual bread (Vrbjanska Čuka, ca. 5500 BC) can be identified as construction of both, the acute and obtuse golden triangles. These geometrical elements found in spiritual and erotic contexts often interpreted as symbols of trascendence will be examined in reference to Euclidean and hyper-Euclidean geometry. The further evolution of geometrical thinking can be recognized on highly elaborated geometrical decorations on the bottoms of Chalcolithic figurines from the Šuplevec-Bakarno Gumno culture (5th millennium BC). They reveal together with underwear designs in the shape of equilateral triangles preliminary studies
for Euclidean Geometry and simple construction methods of the golden mean.
Furthermore the fundamental role of female artistic research in the development of an epistemic language on the ‘dark grounds‘ of mathematics and science as well as possible metaphysical
concepts shall be examined. This assumption may initiate a re-evaluation of Chalcolithic artistic research and its relevance for the development of science and art in antiquity and open speculations supported by the current attempts for the reconstruction of a female ontology in philosophy.
Keywords: Chalcolithic figurines, cult bread, golden section, vesica pisces, pygēometry, Pelagonia
Brilliant mathematical concepts describe physical realities on all different levels, but classical mechanics, relativity, electrodynamics and quantum mechanics are epistemologically separated by different mathe- matical notations and space concepts: while ART resides in 4-dimensional curved Minkowski space-time, QM requires at least 6 dimensions for one particle in phase space.
— Let’s assume, the diverging concepts do not require another formula but rather an epistemic reset which enables reinterpretations of physical phenomena from an unifying point of view:
In this regard visualizations of symmetries of physical phenomena in a higher-dimensional geometrical framework shall be useful.
The here suggested visualization model aims to unite features of different concepts such as Riemannian manifolds and Hilbert spaces, as a discrete dynamic hyper-Euclidean vector space.
It is derived from the geometry of the 5-dimensional space based on the 3D representations of the Penrose kites and darts tiling, which exhibits the principles of the Poincaré homology sphere. This is the space which works like a machine as required by group theory and may serve as a toy model for the universe as suggested by H. Poincaré.
The poster presents some cosmological structures therein such as Lorentzian symmetries in the 4D Kepler model on the large sale as well as for the depiction of ‘time‘. On the other hand it shows on the quan- tum level how the same 4-simplices which are constituting the higher-dimensional space, are serving as unitary representation of the Lorentz group in spin foam models for quantum gravity.
— Maybe finally only the assumption of a higher dimensional space-time reality is need?
The visualization suggests a unified world view by means of a five-dimensional geometry that renders Kaluza-Klein’s theories—as confirmed by Louis de Broglie in 1927—visually accessible. Moreover, this unification between the GRT-cosmology and QM derived from the 3D representation of the Penrose Kites and darts tiling provides fundamental structures used in quantum information, as well as in Kepler’s planetary motions as comprised in the Poincaré homology sphere as a model for the universe.
https://www.mdpi.com/journal/entropy/announcements
The old Theory of Everything (ToE) as it was mathematically conceptualized by Pythagoras and visualized by Plato—in the 5 synonymous regular forms—epitomized the principle of harmony. With the recent rediscovery of Plato’s 5th element we are able to under-stand that it was a higher dimensional world view based upon a geometrical living pattern of the world.
This metaphysical superstructure was allegedly strongly linked to high ethical standards Plato discussed an ideal society in his “Republic.” Meanwhile, according to theoretical physics, the Universe is expanding at an accelerating pace and governed by ‘dark energy’ and ‘dark matter’ where ‘black holes’ are gaining more and more significance. How does the loss of ancient superstructures and new concepts of theoretical physics affect our society, and which rites and habits are left from antiquity?
named epitahedron {E±) which turned out to be Plato’s „5th element“ followed intuitively from the question: “If the Penrose Pattern is a 2D slice of 5-dimensional space, what would it’s 3-dimensional space cell look like?” Origami seemed the best way to explore this question. Enfolding the kites and darts to obtuse and acute triangles from the Robinson decomposition lead to the finding of two irregular heptahedra. Further research lead to hermeneutic interpretations of the Isis & Osiris myth as story which conveyed a detailed origami instruction for the unit cells of 5-dimensional space: therein the pentagonal grid and its 3-dimensional shape is symbolized by two brother gods Osiris and Seth & the sister goddess Isis. Was paper enfolding already a game in ancient Egypt that still survived until millenia later in Japan ?— Here the“Origami“technique and the "Katachi" concept shall be highlighted in regard to higher dimensional models of the word.
elements, fire, water, earth and air, the dodecahedron, as fifth element, — usually denoted as symbol for the world itself — the dodecahedron itself is not mentioned. The cover images of this issue provide an answer to this eminent almost two and a half millennia old riddle: Two simplices, the 3D representation of the Penrose Kites & darts tiling, (epitahedra E+), the unit cells of 5-dimensional space are forming the dodecahedron in a Boolean intersection.
Thus the 5th element synonymous the "quintessence" and the "aether" regains shape.
the explicit notches on a so-called ritual bread (Vrbjanska Čuka, ca. 5500 BC) can be identified as construction of both, the acute and obtuse golden triangles. These geometrical elements found in spiritual and erotic contexts often interpreted as symbols of trascendence will be examined in reference to Euclidean and hyper-Euclidean geometry. The further evolution of geometrical thinking can be recognized on highly elaborated geometrical decorations on the bottoms of Chalcolithic figurines from the Šuplevec-Bakarno Gumno culture (5th millennium BC). They reveal together with underwear designs in the shape of equilateral triangles preliminary studies
for Euclidean Geometry and simple construction methods of the golden mean.
Furthermore the fundamental role of female artistic research in the development of an epistemic language on the ‘dark grounds‘ of mathematics and science as well as possible metaphysical
concepts shall be examined. This assumption may initiate a re-evaluation of Chalcolithic artistic research and its relevance for the development of science and art in antiquity and open speculations supported by the current attempts for the reconstruction of a female ontology in philosophy.
Keywords: Chalcolithic figurines, cult bread, golden section, vesica pisces, pygēometry, Pelagonia
Brilliant mathematical concepts describe physical realities on all different levels, but classical mechanics, relativity, electrodynamics and quantum mechanics are epistemologically separated by different mathe- matical notations and space concepts: while ART resides in 4-dimensional curved Minkowski space-time, QM requires at least 6 dimensions for one particle in phase space.
— Let’s assume, the diverging concepts do not require another formula but rather an epistemic reset which enables reinterpretations of physical phenomena from an unifying point of view:
In this regard visualizations of symmetries of physical phenomena in a higher-dimensional geometrical framework shall be useful.
The here suggested visualization model aims to unite features of different concepts such as Riemannian manifolds and Hilbert spaces, as a discrete dynamic hyper-Euclidean vector space.
It is derived from the geometry of the 5-dimensional space based on the 3D representations of the Penrose kites and darts tiling, which exhibits the principles of the Poincaré homology sphere. This is the space which works like a machine as required by group theory and may serve as a toy model for the universe as suggested by H. Poincaré.
The poster presents some cosmological structures therein such as Lorentzian symmetries in the 4D Kepler model on the large sale as well as for the depiction of ‘time‘. On the other hand it shows on the quan- tum level how the same 4-simplices which are constituting the higher-dimensional space, are serving as unitary representation of the Lorentz group in spin foam models for quantum gravity.
— Maybe finally only the assumption of a higher dimensional space-time reality is need?
The visualization suggests a unified world view by means of a five-dimensional geometry that renders Kaluza-Klein’s theories—as confirmed by Louis de Broglie in 1927—visually accessible. Moreover, this unification between the GRT-cosmology and QM derived from the 3D representation of the Penrose Kites and darts tiling provides fundamental structures used in quantum information, as well as in Kepler’s planetary motions as comprised in the Poincaré homology sphere as a model for the universe.
https://www.mdpi.com/journal/entropy/announcements
The old Theory of Everything (ToE) as it was mathematically conceptualized by Pythagoras and visualized by Plato—in the 5 synonymous regular forms—epitomized the principle of harmony. With the recent rediscovery of Plato’s 5th element we are able to under-stand that it was a higher dimensional world view based upon a geometrical living pattern of the world.
This metaphysical superstructure was allegedly strongly linked to high ethical standards Plato discussed an ideal society in his “Republic.” Meanwhile, according to theoretical physics, the Universe is expanding at an accelerating pace and governed by ‘dark energy’ and ‘dark matter’ where ‘black holes’ are gaining more and more significance. How does the loss of ancient superstructures and new concepts of theoretical physics affect our society, and which rites and habits are left from antiquity?