Noncommutative Geometry

We have been lied to about what real Pythagorean harmonics alchemy is. The lie started with Philolaus who wrote a book, even though he was not a real practitioner of the Pythagorean training, requiring five years of silence meditation as incubation. The lies in this book were then spread by Plato and Archytas and powerful lies they were! They created Western civilization which has enabled very fancy materialistic technology, at great expense to ecology and social justice around the world. Aristotle critiqued the lies spread by Plato but Aristotle did not know the real truth of Pythagorean philosophy. By then, as Dr. Peter Kingsley has pointed out, it was too late.

In fact the secret of Pythagorean alchemy was known in ancient Egypt since 2/3 was the sacred fraction there, as well as in ancient Sumeria and ancient Dravidian culture and ancient Chinese culture – going back to the original human culture, the San Bushmen from at least 70,000 years ago! Just as Pythagoras means "snake-master" so too did the San Bushmen teach that N/om as snake energy is sacred and the ancient Greeks knew this was the reproductive life force energy that is ionized into the cerebrospinal fluid. For example ejaculation is mainly lecithin and lecithin is what myelinates the neurons so that more electromagnetic charge can be stored up in the body.

And so the One was also known as the Counter-Fire that exists in the Underworld and as the pan pipes blow this creates the One as the Fire and light of the Universe. So the Pan Pipes were the original Harmonia "breathing" that feeds the spirit light energy. Or in other words the secret, as Empedocles taught, is to visualize the fire underneath the water in the body – to reverse the Tetraktys based on the complementary opposites of the Perfect Fifth and Perfect Fourth – so that more Air or Aion energy (ionized Snake kundalini) energy is created, called Qi or Prana by the ancients in China and India.

AbstractThe work extends the A. Connes’ noncommutative geometry to spaces withgeneric local anisotropy. We apply the E. Cartan’s anholonomic frame approachto geometry models and physical theories and develop the nonlinear connectionformalism for projective modulespaces. Examples of noncommutative generationof anholonomic Riemann, Finsler and Lagrange spaces are analyzed. We alsopresent a research on noncommutative Finsler–gauge theories, generalized Finslergravity and anholonomic (pseudo) Riemann geometry which appear naturally ifanholonomic frames (vierbeins) are defined in the context of string/M–theoryand extra dimension Riemann gravity..Pacs: 02.40.Gh, 02.40.-k, 04.50.+hMSC numbers: 83D05, 46L87, 58B34, 58B20, 53B40, 53C07 Contents 1 Introduction 22 Commutative and Noncommutative Spaces 42.1 Algebras of functions and (non) commutative spaces . . . . . . . . . . . 52.2 Commutative spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Noncommutative spaces . . . . . ....

We give examples of spectral triples, in the sense of A. Connes, constructed using the algebra of Toeplitz operators on smoothly bounded strictly pseudoconvex domains in C^n , or the star product for the Berezin–Toeplitz quantization. Our main tool is the theory of
generalized Toeplitz operators on the boundary of such domains, due to Boutet de Monvel and Guillemin.

Now we know from history that the training has been done by rote, the explanations mired in alchemical secrecy, and then if someone does achieve the rare status of qigong master it's only because they've been able to store up their energy sufficiently. In which case for real qigong masters they then need to protect their energy, dole it out carefully, build up a base of students, etc. It's obviously not easy especially considering this shamanic training goes against the grain of the modern world. "Your language-focused mind is an idiot; only spirit has wisdom. No matter how much book knowledge or street smarts you have, it won't help with spiritual affairs. Spiritual wisdom is only voiced by spirit. You may be its instrument, but you don't know jack squat. Get over yourself and allow spirit to take over. Easier said than done. And it's never done." Dr. Bradford Keeney So then the basic principle of enlightenment training is to visualize, with the eyes closed, spirit-light or shen, beneath the life force or jing energy (see the first image above). Spirit or shen turns generative force (jing) into yuan qi. "Since it is the undivided yin-yang it is called the One vitality." p. 122, Taoist Yoga: Alchemy and Immortality. As the Tao Te Ching states on alchemy (works link):, "empty the mind and fill the belly" which are reminiscent of later Daoist inner alchemy breathing practices meant to tonify the energy center in the lower abdomen. Chapter 40's passage "the movement of Dao is reversal" Alchemically this means we visualize and focus our fire or spirit qi underneath our water or life force qi, in order to bring out the qi hidden within spirit and life force. Professor William Clarke Hudson II, University of Virginia provides the Neidan alchemy commentaries on the Tao Te Ching:

Only Alain Connes, the Fields Medal (harder to get than Nobel Prize) math professor, has recovered the secret noncommutative phase logic of music theory. Because he is the only source doing this, below I provide a compilation of quotes that I have transcribed from Connes, culled from various sources (His Music of the Quantum Sphere spectral lectures mainly plus Connes published papers and books). Connes sums up this theory as (2, 3, infinity) or 2, 3,∞ . Time emerges from noncommutativity: Such that 3 is now to the 12th and the 19th root of 3 while 2 is to the 19th and and the 12th root of 2. The spectral musical shape is noncommutative with a geometric dimension of zero and yet positive volume!

In Permaculture the TLUD stove is a well-known documented energy saving cooking and heating device also called the "Chinese gasifier" and it appears to have originated from the ancient Kang bed-stove design, documented to at least 5200 years ago in China. Neidan Daoist alchemy can also be traced to similar ancient origins in China and amazingly it relies on the SAME mechanical principles as a transduction of physical energy into heat and light and force. The ancient Kang bed-stove energy is called "Dragon's Breath" which is also another name for the alchemical Neidan Qi energy of the Universe in Daoism.

This article reveals how the Kang bed-stove using a Bellows TLUD design and driven by the ancient water wheel power - is a direct parallel explanation for Daoist Neidan alchemy training.

Western science usually assumes the paranormal and spiritual are "woo woo" claims of weak-minded individuals - with no real "off the shelf" repeatable results. Yet Noncommutativity destroys the claim. Noncommutativity is the most advanced science concept and is lurking behind relativistic quantum physics as biology - as this book documents. Finally it is through simple music as meditation that the secret of noncommutativity is experienced as paranormal spiritual nondualism explained by noncommutative relativistic quantum nonlocality.
To order the book as a book format see
https://www.lulu.com/en/us/shop/voidis-yinyang/music-as-meditation-noncommutativity-paranormal-occult-supernatural-spiritual-psychic-science/paperback/product-8gw7m2.html?page=1&pageSize=4
thanks
This book is comprised of my previously published articles on the interwebs spanning a 20 year period.

We present an exposition on the geometrization of the electromagnetic force. We show that, in
noncommutative (NC) spacetime, there always exists a coordinate transformation to locally eliminate
the electromagnetic force, which is precisely the Darboux theorem in symplectic geometry. As a consequence,
the electromagnetism can be realized as a geometrical property of spacetime like gravity.
We show that the geometrization of the electromagnetic force in NC spacetime is the origin of gravity,
dubbed as the emergent gravity. We discuss how the emergent gravity reveals a novel, radically
different picture about the origin of spacetime. In particular, the emergent gravity naturally explains
the dynamical origin of flat spacetime, which is absent in Einstein gravity. This spacetime picture
turns out to be crucial for a tenable solution of the cosmological constant problem.

Recently John H. Schwarz put forward a conjecture that the world-volume action of a probe D3-brane in an AdS5 x S5 background of type IIB superstring theory can be reinterpreted as the highly effective action (HEA) of four-dimensional N=4 superconformal field theory on the Coulomb branch. We argue that the HEA can be derived from the noncommutative (NC) field theory representation of the AdS/CFT correspondence and the Seiberg-Witten (SW) map defining a spacetime field redefinition between ordinary and NC gauge fields. It is based only on the well-known facts that the master fields of large N matrices are higher-dimensional NC U(1) gauge fields and the SW map is a local coordinate transformation eliminating U(1) gauge fields known as the Darboux theorem in symplectic geometry.

We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of symplectic geometry rather than Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence
principle which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory and so gravity can emerge from the noncommutative electromagnetism, which is also
an interacting theory. As a consequence, it is feasible to formulate a background independent quatum gravity where the prior existence of any spacetime structure is not a priori assumed but defined by fundamental ingredients in quantum gravity theory. This scheme for quantum gravity resolves many notorious problems in theoretical physics, for example, to resolve the cosmological constant problem, to understand the nature of dark energy and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture for what matter is. A matter field such as leptons and quarks simply arises as a stable localized geometry, which is a topological object in the defining
algebra (noncommutative ⋆-algebra) of quantum gravity.

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.

We combine aspects of the theory of motives in algebraic geometry with noncommutative geometry and the classification of factors to obtain a cohomological interpretation of the spectral realization of zeros of $L$-functions. The analogue in characteristic zero of the action of the Frobenius on l-adic cohomology is the action of the scaling group on the cyclic homology of the cokernel (in a suitable category of motives) of a restriction map of noncommutative spaces. The latter is obtained through the thermodynamics of the quantum statistical system associated to an endomotive (a noncommutative generalization of Artin motives). Semigroups of endomorphisms of algebraic varieties give rise canonically to such endomotives, with an action of the absolute Galois group. The semigroup of endomorphisms of the multiplicative group yields the Bost-Connes system, from which one obtains, through the above procedure, the desired cohomological interpretation of the zeros of the Riemann zeta function. In the last section we also give a Lefschetz formula for the archimedean local L-factors of arithmetic varieties.

This work contains among the results of this PhD, an introduction to noncommutative geometry, an introduction to epsilon-graded algebras, and an introduction to renormalization of scalar (wilsonian and BPHZ point of view) and gauge quantum field theories.

After an introduction to some basic issues in non-commutative geometry (Gel'fand duality, spectral triples), we present a "panoramic view" of the status of our current research program on the use of categorical methods in the setting of A.Connes' non-commutative geometry: morphisms/categories of spectral triples, categorification of Gel'fand duality. We conclude with a summary of the expected applications of "categorical non-commutative geometry" to structural questions in relativistic quantum physics: (hyper)covariance, quantum space-time, (algebraic) quantum gravity.

We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index

Eddie Oshins documented his noncommutative discovery of Neigong training through his "Quantum Psychology" website. Alain Connes has argued that music theory provides the "formal language" for noncommutative phase science, as Connes summarizes with the equation: 2, 3, infinity. I realized that music theory underlies the explanation and efficacy of nonwestern healing modalities since all human cultures use the natural harmonics of the Octave, Perfect Fifth and Perfect Fourth as 1:2:3:4 (through noncommutative phase logic). Only Connes has also emphasized this noncommutative phase secret of music theory.

Professor Noam Chomsky recently gave a youtube interview, at age 91, mentioning how, when asked, he does not have the time to meditate. The irony of his life as longevity and his lack of time presented itself as proof of what he called the focus of his career in cognitive studies: the study of the Inner Mind. And so just as Chomsky refers to the Pre-Socratic Heraclitus, then science needs to consider that possibly its logic thus far, based on symmetric commutative logic, has been wrong.

So now going back to Dr. Andrija Puharich's work, for life as ecology we need left-handed asymmetric resonance via the hidden momentum of light or as Puharich emphasizes – the delocalized proton magnetic moment with the electron (when water is split by ultrasound, creating a backwards precessional ELF subharmonic that is greatly amplified as anti-matter energy). So Dr. Bandyopadhyay has verified Puharich's claim about ultrasound as the "common frequency point" of resonating proteins in the body such that a quantum coherence occurs. But as the quantum biology founder, Professor Johnjoe McFadden, emphasizes, for quantum coherence to be amplified to a macroquantum level then some sort of secret [noncommutative] resonance of vibrations is the key.

Restoring the Lost Logos as the name for a section of my University of Minnesota Master's Thesis in 2000. I was approached to have the Master's Thesis published as a book by Charles Madden, a physicist focused on music theory. Only Madden did not understand my physics and as I studied his work I realized my error. I had confused the Taiji symbol of Daoism with "logistic" symmetric math and Madden points out that the Taiji can NOT be a fractal since it's not symmetric math.

So then I began discovering the noncommutative phase math or quantum algebra of Fields Medal math professor Alain Connes. Not till I saw his posted youtube lecture on music theory did I realize that indeed my own music theory philosophy of science as "restoring the Lost Logos" has been corroborated. This noncommutative definition of music theory is ONLY understood by Alain Connes because the music-math training by Western education is a deep psycho-physiological indoctrination in what math professor Luigi Borzacchini calls a "deep, pre-established disharmony" as a "cognitive bias" towards symmetric geometry.
So this new essay on "Restoring the Lost Logos" is based on my life long research into music as a meditation healing practice. Thanks

The theory of general Galois-type extensions is presented, including the interrelations between coalgebra extensions and algebra (co)extensions, properties of corresponding (co)translation maps, and rudiments of entwinings and factorisations. To achieve broad perspective, this theory is placed in the context of far reaching generalisations of the Galois condition to the setting of corings. At the same time, to bring together K-theory and general Galois theory, the equivariant projectivity of extensions is assumed resulting in the centrepiece concept of a principal extension. Motivated by noncommutative geometry, we employ such extensions as replacements of principal bundles. This brings about the notion of a strong connection and yields finitely generated projective associated modules, which play the role of noncommutative vector bundles. Subsequently, the theory of strong connections is developed. It is purported as a basic ingredient in the construction of the Chern character for ...

Since the first optical instruments were invented, the idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope Env Ω Φ A in a given class of morphisms (a class of representations) Ω with respect to a given class of morphisms (a class of observation tools) Φ. It turns out that if we take a sufficiently wide category of topological algebras as K, then each choice of the classes Ω and Φ defines a "projection of functional analysis into geometry," and the standard "geometric disciplines," like complex geometry, differential geometry, and topology, become special cases of this construction. This gives a formal scheme of "categorical construction of geometries" with many interesting applications, in particular, "geometric generalizations of the Pontryagin duality" (to the classes of noncommutative groups). In this paper we describe this scheme in topology and in differential geometry.

We present the solution of a longstanding internal problem of noncommutative geometry, namely the computation of the index of a transversally elliptic operator on an arbitrary foliation. The new and crucial ingredient is a certain Hopf algebra associated to the transverse frame bundle. Its cyclic cohomology is defined and shown to be canonically isomorphic to the Gelfand-Fuks cohomology.

Cyclic cohomology has been recently adapted to the treatment of Hopf symmetry in noncommutative geometry. The resulting theory of characteristic classes for Hopf algebras and their actions on algebras allows to expand the range of applications of cyclic cohomology. It is the goal of the present paper to illustrate these recent developments, with special emphasis on the application to transverse index theory, and point towards future directions. In particular, we highlight the remarkable accord between our framework for cyclic cohomology of Hopf algebras on one hand and both the algebraic as well as the analytic theory of quantum groups on the other, manifest in the construction of the modular square.

The Gelfand - Na\u{i}mark theorem supplies the one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological space.  Generalizations of several topological invariants can be defined by algebraical methods. This article contains a pure algebraical construction of inverse limits in the category of (noncommutative) covering projections. It is proven that Moyal planes are  inverse limits of covering projections of noncommutative tori.

In this talk, motivated by the need to address foundational problems in relativistic quantum physics, we first historically introduce some basic elements of non-commutative geometry (Gel’fand-Naimark duality and Connes’ spectral triples); then (following arXiv:1007.4094) we speculatively suggest that, when coupled with Tomita-Takesaki modular theory and suitable notions of categorical covariance (higher C*-categories), non-commutative geometry provides a possible way for a formulation of a theory of quantum relativity, where non-commutative relational space-time might be spectrally reconstructed from an operational formalism of categories of observable algebras.
Part of this work is a joint collaboration with:
Dr.Roberto Conti (Sapienza Universita' di Roma),
Dr.Matti Raasakka (Paris 13 University).

Since the first optical instruments were invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope Env Ω Φ A in a given class of morphisms (a class of representations) Ω with respect to a given class of morphisms (a class of observation tools) Φ. It turns out that if we take a sufficiently wide category of topological algebras as K, then each choice of the classes Ω and Φ defines a "projection of functional analysis into geometry," and the standard "geometric disciplines," like complex geometry, differential geometry, and topology, become special cases of this construction. This gives a formal scheme of "categorical construction of geometries" with many interesting applications, in particular, "geometric generalizations of the Pontryagin duality" (to the classes of noncommutative groups). In this paper we describe this scheme in topology and in differential geometry.

Starting with a brief review of our prior construction of n-ary algebras, based on the relation among the n-ary commutators of noncommuting spacetime coordinates [X 1 , X 2 , ......, X n ] with the polyvector valued coordinates X 123...n in noncommutative Clifford spaces, [X 1 , X 2 , ......, X n ] = n! X 123...n , we proceed to construct generalized brane actions in noncommutative matrix coordinates backgrounds in Clifford-spaces (C-spaces). An instrumental role is played by the Clifford-valued scalar field Φ(σ A) which provides the functional form of the noncommutative matrix coordinates in C-space, X M ≡ Φ −1 (σ A)Γ M Φ(σ A), and that is given in terms of the world manifold's σ A polyvector-valued coordinates of the generalized brane, and which by construction, satisf y the n-ary algebra. We finalize with an extension of coherent states in C-spaces and provide a preliminary study of strings in target C-space backgrounds.