Grothendieckian Construction of K-Theory with a Bundle that is Topologically Trivial and Class that is Torsion.


All relativistic quantum theories contain “antiparticles,” and allow the process of particle-antiparticle annihilation. This inspires a physical version of the Grothendieck construction of K-theory. Physics uses topological K-theory of manifolds, whose motivation is to organize vector bundles over a space into an algebraic invariant, that turns out to be useful. Algebraic K-theory started from Ki defined for i, with relations to classical constructions in algebra and number theory, followed by Quillen’s homotopy-theoretic definition ∀ i. The connections to algebra and number theory often persist for larger values of i, but in ways that are subtle and conjectural, such as special values of zeta- and L-functions.

One could also use the conserved charges of a configuration which can be measured at asymptotic infinity. By definition, these are left invariant by any physical process. Furthermore, they satisfy quantization conditions, of which the prototype is the Dirac condition on allowed electric and magnetic charges in Maxwell theory.

There is an elementary construction which, given a physical theory T, produces an abelian group of conserved charges K(T). Rather than considering the microscopic dynamics of the theory, all that is needed to be known is a set S of “particles” described by T, and a set of “bound state formation/decay processes” by which the particles combine or split to form other particles. These are called “binding processes.” Two sets of particles are “physically equivalent” if some sequence of binding processes convert the one to the other. We then define the group K(T) as the abelian group ZS of formal linear combinations of particles, quotiented by this equivalence relation.

Suppose T contains the particles S = {A,B,C}.

If these are completely stable, we could clearly define three integral conserved charges, their individual numbers, so K(T) ≅ Z3.

Introducing a binding process

A + B ↔ C —– (1)

with the bidirectional arrow to remind us that the process can go in either direction. Clearly K(T) ≅ Z2 in this case.

One might criticize this proposal on the grounds that we have assumed that configurations with a negative number of particles can exist. However, in all physical theories which satisfy the constraints of special relativity, charged particles in physical theories come with “antiparticles,” with the same mass but opposite charge. A particle and antiparticle can annihilate (combine) into a set of zero charge particles. While first discovered as a prediction of the Dirac equation, this follows from general axioms of quantum field theory, which also hold in string theory.

Thus, there are binding processes

B + B̄ ↔ Z1 + Z2 + · · · .

where B̄ is the antiparticle to a particle B, and Zi are zero charge particles, which must appear by energy conservation. To define the K-theory, we identify any such set of zero charge particles with the identity, so that

B + B̄ ↔ 0

Thus the antiparticles provide the negative elements of K(T).

Granting the existence of antiparticles, this construction of K-theory can be more simply rephrased as the Grothendieck construction. We can define K(T) as the group of pairs (E, F) ∈ (ZS, ZS), subject to the relations (E, F) ≅ (E+B, F +B) ≅ (E+L, F +R) ≅ (E+R, F +L), where (L, R) are the left and right hand side of a binding process (1).

Thinking of these as particles, each brane B must have an antibrane, which we denote by B̄. If B wraps a submanifold L, one expects that B̄ is a brane which wraps a submanifold L of opposite orientation. A potential problem is that it is not a priori obvious that the orientation of L actually matters physically, especially in degenerate cases such as L a point.

Now, let us take X as a Calabi-Yau threefold for definiteness. A physical A-brane, which are branes of the A-model topological string and thereby a TQFT shadow of the D-branes of the superstring, is specified by a pair (L, E) of a special Lagrangian submanifold L with a flat bundle E. The obvious question could be: When are (L1, E1) and (L2, E2) related by a binding process? A simple heuristic answer to this question is given by the Feynman path integral. Two configurations are connected, if they are connected by a continuous path through the configuration space; any such path (or a small deformation of it) will appear in the functional integral with some non-zero weight. Thus, the question is essentially topological. Ignoring the flat bundles for a moment, this tells us that the K-theory group for A-branes is H3(Y, Z), and the class of a brane is simply (rank E)·[L] ∈ H3(Y, Z). This is also clear if the moduli space of flat connections on L is connected.

But suppose it is not, say π1(L) is torsion. In this case, we need deeper physical arguments to decide whether the K-theory of these D-branes is H3(Y, Z), or some larger group. But a natural conjecture is that it will be K1(Y), which classifies bundles on odd-dimensional submanifolds. Two branes which differ only in the choice of flat connection are in fact connected in string theory, consistent with the K-group being H3(Y, Z). For Y a simply connected Calabi-Yau threefold, K1(Y) ≅ H3(Y, Z), so the general conjecture is borne out in this case

There is a natural bilinear form on H3(Y, Z) given by the oriented intersection number

I(L1, L2) = #([L1] ∩ [L2]) —– (2)

It has symmetry (−1)n. In particular, it is symplectic for n = 3. Furthermore, by Poincaré duality, it is unimodular, at least in our topological definition of K-theory.

D-branes, which are extended objects defined by mixed Dirichlet-Neumann boundary conditions in string theory, break half of the supersymmetries of the type II superstring and carry a complete set of electric and magnetic Ramond-Ramond charges. The product of the electric and magnetic charges is a single Dirac unit, and that the quantum of charge takes the value required by string duality. Saying that a D-brane has RR-charge means that it is a source for an “RR potential,” a generalized (p + 1)-form gauge potential in ten-dimensional space-time, which can be verified from its world-volume action that contains a minimal coupling term,

∫C(p + 1) —–(3)

where C(p + 1) denotes the gauge potential, and the integral is taken over the (p+1)-dimensional world-volume of the brane. For p = 0, C(1) is a one-form or “vector” potential (as in Maxwell theory), and thus the D0-brane is an electrically charged particle with respect to this 10d Maxwell theory. Upon further compactification, by which, the ten dimensions are R4 × X, and a Dp-brane which wraps a p-dimensional cycle L; in other words its world-volume is R × L where R is a time-like world-line in R4. Using the Poincaré dual class ωL ∈ H2n−p(X, R) to L in X, to rewrite (3) as an integral

R × X C(p + 1) ∧ ωL —– (4)

We can then do the integral over X to turn this into the integral of a one-form over a world-line in R4, which is the right form for the minimal electric coupling of a particle in four dimensions. Thus, such a wrapped brane carries a particular electric charge which can be detected at asymptotic infinity. Summarizing the RR-charge more formally,

LC = ∫XC ∧ ωL —– (5)

where C ∈ H∗(X, R). In other words, it is a class in Hp(X, R).

In particular, an A-brane (for n = 3) carries a conserved charge in H3(X, R). Of course, this is weaker than [L] ∈ H3(X, Z). To see this physically, we would need to see that some of these “electric” charges are actually “magnetic” charges, and study the Dirac-Schwinger-Zwanziger quantization condition between these charges. This amounts to showing that the angular momentum J of the electromagnetic field satisfies the quantization condition J = ħn/2 for n ∈ Z. Using an expression from electromagnetism, J⃗ = E⃗ × B⃗ , this is precisely the condition that (2) must take an integer value. Thus the physical and mathematical consistency conditions agree. Similar considerations apply for coisotropic A-branes. If X is a genuine Calabi-Yau 3-fold (i.e., with strict SU(3) holonomy), then a coisotropic A-brane which is not a special Lagrangian must be five-dimensional, and the corresponding submanifold L is rationally homologically trivial, since H5(X, Q) = 0. Thus, if the bundle E is topologically trivial, the homology class of L and thus its K-theory class is torsion.

If X is a torus, or a K3 surface, the situation is more complicated. In that case, even rationally the charge of a coisotropic A-brane need not lie in the middle-dimensional cohomology of X. Instead, it takes its value in a certain subspace of ⊕p Hp(X, Q), where the summation is over even or odd p depending on whether the complex dimension of X is even or odd. At the semiclassical level, the subspace is determined by the condition

(L − Λ)α = 0, α ∈ ⊕p Hp(X, Q)

where L and Λ are generators of the Lefschetz SL(2, C) action, i.e., L is the cup product with the cohomology class of the Kähler form, and Λ is its dual.


Being Mediatized: How 3 Realms and 8 Dimensions Explain ‘Being’ by Peter Blank.


Experience of Reflection: ‘Self itself is an empty word’
Leary – The neuroatomic winner: “In the province of the mind, what is believed true is true, or becomes true within limits to be learned by experience and experiment.” (Dr. John Lilly)

Media theory had noted the shoring up or even annihilation of the subject due to technologies that were used to reconfigure oneself and to see oneself as what one was: pictures, screens. Depersonalization was an often observed, reflective state of being that stood for the experience of anxiety dueto watching a ‘movie of one’s own life’ or experiencing a malfunction or anomaly in one’s self-awareness.

To look at one’s scaffolded media identity meant in some ways to look at the redactionary product of an extreme introspective process. Questioning what one interpreted oneself to be doing in shaping one’s media identities enhanced endogenous viewpoints and experience, similar to focusing on what made a car move instead of deciding whether it should stay on the paved road or drive across a field. This enabled the individual to see the formation of identity from the ‘engine perspective’.

Experience of the Hyperreal: ‘I am (my own) God’
Leary – The metaprogramming winner: “I make my own coincidences, synchronities, luck, and Destiny.”

Meta-analysis of distinctions – seeing a bird fly by, then seeing oneself seeing a bird fly by, then thinking the self that thought that – becomes routine in hyperreality. Media represent the opposite: a humongous distraction from Heidegger’s goal of the search for ‘Thinking’: capturing at present the most alarming of what occupies the mind. Hyperreal experiences could not be traced back to a person’s ‘real’ identities behind their aliases. The most questionable therefore related to dismantled privacy: a privacy that only existed because all aliases were constituting a false privacy realm. There was nothing personal about the conversations, no facts that led back to any person, no real change achieved, no political influence asserted.

From there it led to the difference between networked relations and other relations, call these other relations ‘single’ relations, or relations that remained solemnly silent. They were relations that could not be disclosed against their will because they were either too vague, absent, depressing, shifty, or dangerous to make the effort worthwhile to outsiders.

The privacy of hyperreal being became the ability to hide itself from being sensed by others through channels of information (sight, touch, hearing), but also to hide more private other selves, stored away in different, more private networks from others in more open social networks.

Choosing ‘true’ privacy, then, was throwing away distinctions one experienced between several identities. As identities were space the meaning of time became the capacity for introspection. The hyperreal being’s overall identity to the inside as lived history attained an extra meaning – indeed: as alter- or hyper-ego. With Nietzsche, the physical body within its materiality occasioned a performance that subjected its own subjectivity. Then and only then could it become its own freedom.

With Foucault one could say that the body was not so much subjected but still there functioning on its own premises. Therefore the sensitory systems lived the body’s life in connection with (not separated from) a language based in a mediated faraway from the body. If language and our sensitory systems were inseparable, beings and God may as well be.

Being Mediatized

Without Explosions, WE Would NOT Exist!


The matter and radiation in the universe gets hotter and hotter as we go back in time towards the initial quantum state, because it was compressed into a smaller volume. In this Hot Big Bang epoch in the early universe, we can use standard physical laws to examine the processes going on in the expanding mixture of matter and radiation. A key feature is that about 300,000 years after the start of the Hot Big Bang epoch, nuclei and electrons combined to form atoms. At earlier times when the temperature was higher, atoms could not exist, as the radiation then had so much energy it disrupted any atoms that tried to form into their constituent parts (nuclei and electrons). Thus at earlier times matter was ionized, consisting of negatively charged electrons moving independently of positively charged atomic nuclei. Under these conditions, the free electrons interact strongly with radiation by Thomson scattering. Consequently matter and radiation were tightly coupled in equilibrium at those times, and the Universe was opaque to radiation. When the temperature dropped through the ionization temperature of about 4000K, atoms formed from the nuclei and electrons, and this scattering ceased: the Universe became very transparent. The time when this transition took place is known as the time of decoupling – it was the time when matter and radiation ceased to be tightly coupled to each other, at a redshift zdec ≃ 1100 (Scott Dodelson (Auth.)-Modern Cosmology-Academic Press). By

μbar ∝ S−3, μrad ∝ S−4, Trad ∝ S−1 —– (1)

The scale factor S(t) obeys the Raychaudhuri equation

3S ̈/S = -1/2 κ(μ +3p/c2) + Λ —– (2)

where κ is the gravitational constant and Λ the cosmological constant.

, the universe was radiation dominated (μrad ≫ μmat) at early times and matter dominated (μrad ≪ μmat) at late times; matter-radiation density equality occurred significantly before decoupling (the temperature Teq when this equality occurred was Teq ≃ 104K; at that time the scale factor was Seq ≃ 104S0, where S0 is the present-day value). The dynamics of both the background model and of perturbations about that model differ significantly before and after Seq.

Radiation was emitted by matter at the time of decoupling, thereafter travelling freely to us through the intervening space. When it was emitted, it had the form of blackbody radiation, because this is a consequence of matter and radiation being in thermodynamic equilibrium at earlier times. Thus the matter at z = zdec forms the Last Scattering Surface (LSS) in the early universe, emitting Cosmic Blackbody Background Radiation (‘CBR’) at 4000K, that since then has travelled freely with its temperature T scaling inversely with the scale function of the universe. As the radiation travelled towards us, the universe expanded by a factor of about 1100; consequently by the time it reaches us, it has cooled to 2.75 K (that is, about 3 degrees above absolute zero, with a spectrum peaking in the microwave region), and so is extremely hard to observe. It was however detected in 1965, and its spectrum has since been intensively investigated, its blackbody nature being confirmed to high accuracy (R. B. Partridge-3K_ The Cosmic Microwave Background Radiation). Its existence is now taken as solid proof both that the Universe has indeed expanded from a hot early phase, and that standard physics applied unchanged at that era in the early universe.

The thermal capacity of the radiation is hugely greater than that of the matter. At very early times before decoupling, the temperatures of the matter and radiation were the same (because they were in equilibrium with each other), scaling as 1/S(t) (Equation 1 above). The early universe exceeded any temperature that can ever be attained on Earth or even in the centre of the Sun; as it dropped towards its present value of 3 K, successive physical reactions took place that determined the nature of the matter we see around us today. At very early times and high temperatures, only elementary particles can survive and even neutrinos had a very small mean free path; as the universe cooled down, neutrinos decoupled from the matter and streamed freely through space. At these times the expansion of the universe was radiation dominated, and we can approximate the universe then by models with {k = 0, w = 1/3, Λ = 0}, the resulting simple solution of

3S ̇2/S2 = A/S3 + B/S4 + Λ/3 – 3k/S2 —– (3)

uniquely relating time to temperature:

S(t)=S0t1/2 , t=1.92sec [T/1010K]−2 —– (4)

(There are no free constants in the latter equation).

At very early times, even neutrinos were tightly coupled and in equilibrium with the radiation; they decoupled at about 1010K, resulting in a relic neutrino background density in the universe today of about Ων0 ≃ 10−5 if they are massless (but it could be higher depending on their masses). Key events in the early universe are associated with out of equilibrium phenomena. An important event was the era of nucleosynthesis, the time when the light elements were formed. Above about 109K, nuclei could not exist because the radiation was so energetic that as fast as they formed, they were disrupted into their constituent parts (protons and neutrons). However below this temperature, if particles collided with each other with sufficient energy for nuclear reactions to take place, the resultant nuclei remained intact (the radiation being less energetic than their binding energy and hence unable to disrupt them). Thus the nuclei of the light elements  – deuterium, tritium, helium, and lithium – were created by neutron capture. This process ceased when the temperature dropped below about 108K (the nuclear reaction threshold). In this way, the proportions of these light elements at the end of nucleosynthesis were determined; they have remained virtually unchanged since. The rate of reaction was extremely high; all this took place within the first three minutes of the expansion of the Universe. One of the major triumphs of Big Bang theory is that theory and observation are in excellent agreement provided the density of baryons is low: Ωbar0 ≃ 0.044. Then the predicted abundances of these elements (25% Helium by weight, 75% Hydrogen, the others being less than 1%) agrees very closely with the observed abundances. Thus the standard model explains the origin of the light elements in terms of known nuclear reactions taking place in the early Universe. However heavier elements cannot form in the time available (about 3 minutes).

In a similar way, physical processes in the very early Universe (before nucleosynthesis) can be invoked to explain the ratio of matter to anti-matter in the present-day Universe: a small excess of matter over anti-matter must be created then in the process of baryosynthesis, without which we could not exist today (if there were no such excess, matter and antimatter would have all annihilated to give just radiation). However other quantities (such as electric charge) are believed to have been conserved even in the extreme conditions of the early Universe, so their present values result from given initial conditions at the origin of the Universe, rather than from physical processes taking place as it evolved. In the case of electric charge, the total conserved quantity appears to be zero: after quarks form protons and neutrons at the time of baryosynthesis, there are equal numbers of positively charged protons and negatively charged electrons, so that at the time of decoupling there were just enough electrons to combine with the nuclei and form uncharged atoms (it seems there is no net electrical charge on astronomical bodies such as our galaxy; were this not true, electromagnetic forces would dominate cosmology, rather than gravity).

After decoupling, matter formed large scale structures through gravitational instability which eventually led to the formation of the first generation of stars and is probably associated with the re-ionization of matter. However at that time planets could not form for a very important reason: there were no heavy elements present in the Universe. The first stars aggregated matter together by gravitational attraction, the matter heating up as it became more and more concentrated, until its temperature exceeded the thermonuclear ignition point and nuclear reactions started burning hydrogen to form helium. Eventually more complex nuclear reactions started in concentric spheres around the centre, leading to a build-up of heavy elements (carbon, nitrogen, oxygen for example), up to iron. These elements can form in stars because there is a long time available (millions of years) for the reactions to take place. Massive stars burn relatively rapidly, and eventually run out of nuclear fuel. The star becomes unstable, and its core rapidly collapses because of gravitational attraction. The consequent rise in temperature blows it apart in a giant explosion, during which time new reactions take place that generate elements heavier than iron; this explosion is seen by us as a Supernova (“New Star”) suddenly blazing in the sky, where previously there was just an ordinary star. Such explosions blow into space the heavy elements that had been accumulating in the star’s interior, forming vast filaments of dust around the remnant of the star. It is this material that can later be accumulated, during the formation of second generation stars, to form planetary systems around those stars. Thus the elements of which we are made (the carbon, nitrogen, oxygen and iron nuclei for example) were created in the extreme heat of stellar interiors, and made available for our use by supernova explosions. Without these explosions, we could not exist.

Yantra + Yi-Globe = Yi-Yantra. Note Quote.

The lower and the upper semicircles of the Yi-globe,



where the hexagrams are shown in plane, best serve for direct comparison. There, the structural features common with the yantras are clearly visible: the arrangement of the hexagrams around the center, the concentric circles embedded into one another, and the perfect balance and symmetry.

The analogy between the Yi-globe and the yantras can be recognized in almost every formal detail, if the Chamunda-yantra (Yantra literally means “support” and “instrument”. A Yantra is a geometric design acting as a highly efficient tool for contemplation, concentration and meditation carrying spiritual significance) is taken as an example


The similarity between the two symbols is still more complete with respect to the metaphysical contents. Yantras are the symbols of deities, whereby one part represents a god (generally, a goddess) itself, while the other part stands for the cosmic activity (function) attributed to the deity and the power manifested in the latter; thus actually, a yantra symbolizes the whole universe as well. The power of the yantras lies in the concentrated visualization – completed with the vibration of the associated mantras – capable even in itself of raising and directing cosmic energies into the human psyche, whereby man merges into the deity in his mind and, at last, becomes one with the universe, the cosmic wholeness.

When the properties of the two symbols are analyzed, the following cosmological analogies between the Yi-globe and the yantras are found


The comparison clearly reveals that the Yi-globe and the yantras represent the same spiritual content and that most of their formal elements are identical as well. Accordingly, it is fully justified to take the Yi-globe as a special yantra.

Figure below demonstrates how easily the Yi-globe transforms into the form of a yantra. Since this yantra perfectly reflects all the connotations of the Yi-globe, its name is Yi-yantra.


On the petals (or other geometrical elements) of the yantras, mantras are written. On the Yi-yantra, the hexagrams replace the mantras at the corresponding places. (This replacement is merely formal here, since the function of the mantras manifests only when they are expressed in words.)

Based on the exposed analysis, the connotations of the individual geometrical elements in the Yi-yantra are as follows:

  • The two circlets in the center stand for the two signs of Completion, representing the Center of the World, the starting point of creation, and at the same time the place of final dissolution.
  • The creative forces, which are to give birth to the macrocosm and microcosm, emanate from the center. This process is represented by the hexagon.
  • The eight double trigrams surrounding the hexagon represent the differentiated primal powers arranged according to the Earlier Heaven. The two squares show that they already embrace the created world, but only in inherent (i.e., not manifested) form.
  • The red circle around the squares unites the ten hexagrams on the axis of the Yi-globe. The parallel blue circle is level I of the Yi-globe, whereto the powers of the Receptive extend, and wherefrom changes (forces) direct outwards in the direction of level II. The six orange petals of the lotus (the six hexagrams) show these directions.
  • The next pair of the orange and blue circles, and the twelve orange petals with the twelve hexagrams stand for levels II.
  • The next circle contains eighteen orange petals, representing level III. At its outer circle, the development (evolution) ends. On level III, the golden petals show the opposite direction of the movement.
  • From here, the development is directed inwards (involution). The way goes through levels IV and V, to the final dissolution in the Creative in the Center.
  • The square surrounding the Yi-globe represents the external existence; its gates provide access towards the inward world. The square area stands for the created world, shown by the trigrams indicated therein and arranged according to the Later Heaven.

Spirit is Matter on the Seventh Plane; Matter is Spirit – on the Lowest Point of its Cyclic Activity; and Both — are MAYA. Note Quote.


In the 1930s the scientist Sir James Jeans wrote:

the tendency of modem physics is to resolve the whole material universe into waves, and nothing but waves. These waves are of two kinds: bottled-up waves, which we call matter, and unbottled waves, which we call radiation or light. If annihilation of matter occurs, the process is merely that of unbottling imprisoned wave-energy and setting it free to travel through space. These concepts reduce the whole universe to a world of light, potential or existent . . . . — The Mysterious Universe

The idea of matter being crystallized light echoes what H. P. Blavatsky wrote half a century earlier in The Secret Doctrine, where she speaks of “that infinite Ocean of Light, whose one pole is pure Spirit lost in the absoluteness of Non-Being, and the other, the matter in which it condenses, crystallizing into a more and more gross type as it descends into manifestation” (The Secret Doctrine). Material particles, she said, were infinitely divisible centers of force, and matter could therefore exist in infinitely varying degrees of density. Our physical senses have been evolved to perceive only one particular plane of matter, which is interpenetrated by countless other worlds or planes invisible to us because composed of ranges of energy-substance both finer and grosser than our own.

Modern science has analyzed matter down to the point where it vanishes into wisps of energy. Energy is said to be a measure of motion or activity. But motion of what? It is a truism that there can be no motion without something that moves. Scientists in the last century believed that wave-motion took place in a universal medium called the ether. This hypothesis was abandoned because the ether proved to be chemically and physically undetectable, and science was left with the unlikely idea that waves are transmitted through “empty space.”

Modern physicists believe that underlying the material world there is a quantum field, also called the quantum void or vacuum. The quantum field is said to be “a continuous medium which is present everywhere in space” (The Tao of Physics) and matter is said to be constituted by regions of space in which the field is extremely intense. Scientists assert that the quantum field is non-material, but deny that it is mere nothingness. Paul Davies states that the quantum void is not inert and featureless but throbbing with energy and vitality, a seething ferment of “Virtual” particles and “ghost” particles. (Superforce) It therefore seems to be actually a form of ether, which is non-material only in the sense that it is not composed of physical matter. Rather than material particles being “knots of nothingness,” as Davies calls them, they may therefore be seen as vibrations in an etheric medium composed of a subtler, superphysical grade of substance. The same reasoning applies to all the other “non-material” fields and forces postulated by science.

Everything is relative. Physical matter is condensed energy, but what for us is energy would be matter for beings on a higher plane than ours, as is suggested by the fact that energy does not exist in a continuous flow but is composed of discrete units or quanta. Likewise, the energy on the next plane would be matter to an even higher plane. The loftiest form of energy in any particular hierarchy of worlds is what we call spirit or consciousness. As H. P. Blavatsky put it: “Spirit is matter on the seventh plane; matter is Spirit – on the lowest point of its cyclic activity; and both — are MAYA.” (The Secret Doctrine). To say that spirit and matter are “maya” or illusion does not mean that they do not exist, but that we do not understand them as they really are. Any particular plane of energy-substance can be understood only with reference to superior, causal planes. Everything — from atom to human, from star to universe — is the expression of something higher.

Throughout the ages, sages and seers have suggested that hidden within the phenomenal world in which we live there are inner worlds of reality — astral, mental, and spiritual — and that the physical world is but a pale shadow of the spiritual world. These inner worlds cannot be investigated with physical instruments, but only by delving into the depths of our own minds and consciousness, and this requires many lives of self-purification and self-conquest. Scientists using only materialistic methods are in no position to deny point-blank the possibility of such higher planes.

Most scientists, in fact, now believe that some 90% of the matter in the universe exists in a state unknown to them; it is called “dark matter” because it is physically unobservable, and its existence is known of only by its gravitational effects. Such matter is suggestive of the higher subplanes and planes postulated by theosophy, which are composed of matter of increasingly slower rates of vibration and are therefore beyond our range of perception. Given scientists’ confessed ignorance of most of the matter in the universe and their inability to explain satisfactorily the evolution of life and consciousness and the “laws of nature” along materialistic lines, any suggestion that they are on the verge of discovering the innermost secrets of nature or of reducing the mystery of existence to a single equation is premature to say the least!

In theosophical philosophy, the physical universe is regarded as no more than a cross section through infinitude. Universal nature is composed of worlds within worlds within worlds, filled full of conscious, living beings at infinitely varying stages of their evolutionary awakenment. Our finite minds cannot embrace the infinite. As G. de Purucker says in his Fundamentals of the Esoteric Philosophy, we can do no more than to try and form a simple conception of the Boundless All: never-ending life and consciousness in unceasing motion everywhere. The ancients, he says, were never so foolish as to try to fathom infinitude. They recognized the reality of being and let it go at that, knowing that an ever-expanding consciousness and an ever-growing understanding of existence is all that we can ever attain to during our eternal evolutionary journey through the fields of infinitude.

Third Space Theory of Postcoloniality. Note Quote.


Writers, such as Homi Bhabha and Salman Rushdie, who proceed from a consideration of the nature of postcolonial societies and the types of hybridization these various cultures have produced, proposed a radical rethinking—an appropriation of the European thinking by a different discourse. Whereas in European thinking, history and the past are the reference point for epistemology, in postcolonial thought space annihilates time. History is rewritten and realigned from the standpoint of the victims of the destructive progress.  Hybridity replaces a temporal linearity with a spatial plurality. Salman Rushdie  makes this obvious when commenting on the message of his controversial novel, The Satanic Verses, in an essay called “In Good Faith” as follows:

The Satanic Verses celebrates hybridity, impurity, intermingling, the transformation that comes of new and unexpected combinations of human beings, cultures, ideas, politics, movies, songs. It rejoices in mongrelization and fears the absolutism of the Pure. Melange, hotchpotch, a bit of this and a bit of that is how newness enters the world. It is the great possibility that mass migration gives the world, and I have tried to embrace it. The Satanic Verses is for change-by-fusion, change-by-conjoining. It is a love-song to our mongrel selves.

Even though on the surface postcolonial texts may contain race divisions and cultural differences, they all contain germs of community which, as they grow in the mind of the reader, they detach from the apparently inescapable dialectic of history. Thus, postcolonial literatures have begun to deal  with problems of transmuting time into space and of attempting to construct a future. It highlights the acceptance of difference on equal terms. Now both literary critics and historians are recognizing cross-culturality as the possible ending point of an apparent endless human history of conquest and occupations.  They recognize that the myth of purity or essence, the Eurocentric viewpoint must be challenged. The recent approaches show that the power of postcolonial theory lies in its comparative methodology and the hybridized and syncretic view of the modern world which it implies.

Of the various points in which postcolonial texts intersect, place has a paramount importance. In his dialogism thesis, Mikhail Bakhtin emphasizes a space of enunciation where negotiation of discursive doubleness gives birth to a new speech act:

The  hybrid is not only double-voiced and double-accented . . . but is also double-languaged; for in it there are not only (and not even so much) two individual consciounesses, two voices, two accents, as there are [doublings of] socio-linguistic consciousnesses, two epochs . . . that come together and consciously fight it out on the territory of the utterance.

Also, Homi Bhabha talks about a third space of enunciation, a hybrid space or a new position in which communication is possible. Third Space theory emerges from the sociocultural tradition in psychology identified with Lev Vygotsky. Sociocultural approaches are concerned with the “… constitutive role of culture in mind, i.e., on how mind develops by incorporating the community’s shared artifacts accumulated over generations”. Bhabha applies socioculturalism directly to the postcolonial condition, where there are, “… unequal and uneven forces of cultural representation”. For Bhabha, such negotiation is neither assimilation nor collaboration as it makes possible the emergence of an “interstitial” agency that refuses the binary representation of social antagonism. The “interstitial perspective” as Bhabha calls it replaces the “polarity of a prefigurative self-generating nation ‘in-itself’ and extrinsic other nations” with the notion of cultural liminality within the nation. the liminal figure of the nation-space would ensure that no political ideologies could claim transcendent or metaphysical authority for themselves. this is because the subject of cultural discourse – the agency of a people – is spilt in the discursive ambivalence that emerges in the contest of narrative authority between the pedagogical and the performative, which is to say, between the peoples’ status as historical objects of a nationalist pedagogy and their ability to perform themselves as subjects of a process of signification that must erase any prior or originally national presence. Hybrid agencies find their voice in a dialectic that does not seek cultural supremacy or sovereignty. They deploy the partial culture from which they emerge to construct visions of community, and versions of historic memory, that give narrative form to the minority positions they occupy: “the outside of the inside; the part in the whole”.

This “new position” Bhabha proposes is closely related to the “homeless” existence of post-colonial persons. It certainly cannot be assumed to be an independent third space already there, a “no-man’s-land” between the nations. Instead, a way of cultural syncretization, i.e. a medium of negotiating cultural antagonisms, has to be created. Cultural difference has to be acknowledged: “Culture does imply difference, but the differences now are no longer, if you wish, taxonomical; they are interactive and refractive”. This position emphasizes, contrary to the too facile assumption of world literature and world culture as the stages of a multicultural cosmopolitanism already in existence, that the “intellectual trade” takes place mostly on the borders and in the border crossings between cultures where meanings and values are not codified but misunderstood, misrepresented, even falsely adopted. Bhabha explains how beyond fixed cultural (ethnic, gender- and class-related) identities, so-called “hybrid” identities are formed by discontinuous translation and negotiation. Hybridity, liminality, “interrogatory, interstitial space” – these are the positive values Bhabha opposes to a retrograde historicism that continues to dominate Western critical thinking, a “linear narrative of the nation,” with its claims for the “holism of culture and community” and a “fixed horizontal nation-space”. We must, he argues eloquently, undo such thinking with its facile binary oppositions. Rather than emphasizing the opposition between First World and Third World nations, between colonizer and colonized, men and women, black and white, straight and gay, Bhabha would have it, we might more profitably focus on the faultlines themselves, on border situations and thresholds as the sites where identities are performed and contested. Bhabha says, “hybridity to me is the ‘third space’ which enables other positions to emerge”.

Matter-Antimatter ऋग्वेद (ṛgveda)

शयुः परस्तादध नु दविमाताबन्धनश्चरति वत्स एकः |
śayuḥ parastādadha nu dvimātābandhanaścarati vatsa ekaḥ |

“Two female twins manifest in various forms. Out of them, one is white and other is black. The black and white females are sisters. This is one of the great deeds of gods.”

The Vedas describe matter and anti-matter as twins. This is indeed a perfect description, as particle and its anti-particle are born me same womb (energy). Sometimes these twins are described as both sisters and sometimes as one brother and other sister. As these descriptions are not of human beings, these analogies are valid. The Vedas describe matter as white and anti-matter as black. Universe consists of matter and anti-matter. A verse from the ऋग्वेद (ṛgveda) describes this.

स सुष्टुभा स सतुभा सप्त विप्रैः सवरेणाद्रिं सवर्यो नवग्वैः |

sa suṣṭubhā sa stubhā sapta vipraiḥ svareṇādriṃ svaryo navaghvaiḥ |

“Those born together were divided in two forms.”

Opposite forms can have two meanings, matter and antimatter, or positive and negative electric charge. A positively charged particle attracts a negatively charged particle. Following verse describes this phenomenon:

दवे वीरूपे चरतः सवर्थे अन्यान्या वत्समुप धापयेते |

dve vīrūpe carataḥ svarthe anyānyā vatsamupa dhāpayete |
Our universe is matter dominated. If matter and anti-matter are created together in same amount, then we should find equal amount of anti-matter. Why is it that we don’t find much evidence of anti-matter as far as we can observe. Are remote parts of the universe anti-matter dominated? Did matter and anti-matter somehow get segregated in different corners of the universe. Scientists do not think so. Scientists believe that when universe was very young, for some reason a small excess of matter over anti-matter was generated. As matter and anti-matter annihilated each other, this small excess remained, and that small excess is our universe. The Vedas take a different view. According to the Vedas matter and energy are constantly being created at the surface of the universe, and there is an imbalance in their creation. Matter and anti-matter continually annihilate each-other and the small excess of matter has accumulated over the age of the universe. Following verses describe the annihilation of anti-matter.
जग्मिर्युवा नर्षदनमवोभिस्त्राता न इन्द्र एनसो महश्चित ||
jaghmiryuvā nṛṣadanamavobhistrātā na indra enaso mahaścit ||

Indra is considered responsible for killing of black people in the ऋग्वेद (ṛgveda). As matter and anti-matter are attracted towards each other due to opposite nature of electric charge resulting in annihilation, electric force is indeed responsible for this phenomenon.

यमस्य मा यम्यं काम आगन समाने योनौ सहशेय्याय |
yamasya mā yamyaṃ kāma āghan samāne yonau sahaśeyyāya |
जायेव पत्ये तन्वं रिरिच्यां वि चिद वर्हेव रथ्येव चक्रा ||
jāyeva patye tanvaṃ riricyāṃ vi cid vṛheva rathyeva cakrā ||
न तिष्ठन्ति न नि मिषन्त्येते देवानां सपश इह येचरन्ति |
na tiṣṭhanti na ni miṣantyete devānāṃ spaśa iha yecaranti |
अन्येन मदाहनो याहि तुयं तेन वि वर्ह रथ्येवचक्रा ||
anyena madāhano yāhi tuyaṃ tena vi vṛha rathyevacakrā ||
रात्रीभिरस्मा अहभिर्दशस्येत सूर्यस्य चक्षुर्मुहुरुन्मिमीयात |
rātrībhirasmā ahabhirdaśasyet sūryasya cakṣurmuhurunmimīyāt |
दिवा पर्थिव्या मिथुना सबन्धू यमीर्यमस्यबिभ्र्यादजामि ||
divā pṛthivyā mithunā sabandhū yamīryamasyabibhṛyādajāmi ||

Yama means twin, and here one of the twins is called Yama and other his sister Yami. This dialogue, which is cited as prohibiting the union of siblings, is not about the illegitimate relationship at all. This is a dialogue between a particle and its anti-particle. If they join together, they will change into radiation and material universe will not evolve. The Vedas are written from the viewpoint of an existing universe, and sages celebrate the important physical processes leading to the present state of the universe. The stress here is that the material universe has evolved due to one particle combining with another particle to generate a third particle and so on. This is why Yami is told to join with someone else, not her own anti-particle. In the Vedas Varuna is often called Asura. Varuna has earlier been identified as electron. Spies of Varuna are often mentioned in the Vedas, and “Nobody can deceive the spies of Varuna.”

बळ इत्था देव निष्क्र्तम आदित्या यजतम बर्हत |
वरुण मित्रार्यमन वर्षिष्ठं कषत्रम आशाथे ||
आ यद योनिं हिरण्ययं वरुण मित्र सदथः |
धर्तारा चर्षणीनां यन्तं सुम्नं रिशादसा ||
विश्वे हि विश्ववेदसो वरुणो मित्रो अर्यमा |
वरता पदेव सश्चिरे पान्ति मर्त्यं रिषः ||
ते हि सत्या रतस्प्र्श रतावानो जने-जने |
सुनीथासः सुदानवो ऽंहोश चिद उरुचक्रयः ||
को नु वाम मित्रास्तुतो वरुणो वा तनूनाम |
तत सु वाम एषते मतिर अत्रिभ्य एषते मतिः ||
baḷ itthā deva niṣkṛtam ādityā yajatam bṛhat |
varuṇa mitrāryaman varṣiṣṭhaṃ kṣatram āśāthe ||
ā yad yoniṃ hiraṇyayaṃ varuṇa mitra sadathaḥ |
dhartārā carṣaṇīnāṃ yantaṃ sumnaṃ riśādasā ||
viśve hi viśvavedaso varuṇo mitro aryamā |
vratā padeva saścire pānti martyaṃ riṣaḥ ||
te hi satyā ṛtaspṛśa ṛtāvāno jane-jane |
sunīthāsaḥ sudānavo ‘ṃhoś cid urucakrayaḥ ||
ko nu vām mitrāstuto varuṇo vā tanūnām |
tat su vām eṣate matir atribhya eṣate matiḥ ||

Rupture…Another Drunken Risibility


How is rupture important to any discourse? Is it the waning of a line of discourse in that the impulsive impact is debilitating over temporality and even spatially or is it a sudden change of the direction altogether hitherto unknown or never before comprehended, a kind of digital break, a sudden change of phase or a sudden phase transition. The latter are called by me ‘ruptures’. But, why do I call it only debilitating to begin with, it could very well be the accelerated impact that could be thought out. a complete dislocation from one discourse to another, bridged by only a kind of conscious memory of the shift. the important factor to be taken into consideration is the determination of the ‘threshold’, where the rupture occurs. This could be cataclysmic as in the case of the extinction of dinosaurs. What is cataclysmic is the eventality of this threshold, a cross over of which is the rupture that is being thought about.


These deliberations are indeed painful. When I was caught up in a paradox in logic (Goodman’s paradox), I could comprehend only to land up in this soup, the thoughts collapse into thinking as if there is a flattening out of the hierarchy between the thought and thinking. Elevation is possible when there is a pre-ordained depression.

For me, suddenly, philosophically, rupture has gained prominence. I am very convinced, if it could be achieved, majority of the philosophical systems in vogue would just annihilate themselves.

I was wondering about the assistance that could come from the field of chaos theory. but then I dismissed it as soon as it had sprung. Chaos Theory is so damn dependent of the sensitivity to initial conditions that it becomes well nigh possible to simulate the results: it becomes deterministic, predictable and thereby, a continuity in what would come about in the future if there is at all a rupture in the sense I mentioned about. This dismisses the notion of a hitherto unthought of break with the past and the present. Knowing the infinitely unknown future based on the finitely known past!!!

Another thing that I thought about was the idea of Clinamen by Lucretius. if I am in a position to link up his idea with the Deleuzean one of the former’s notion of a slight movement in the angle of declination with the latter’s initiation of ‘turbulence’ in the laminar flow, I somehow see this as converging towards the Chaos (read Chaos Theory). This ‘Turbulence’ is still accounted for in that it is still deterministic and predictable. Therefore, a dismissal of Lucretius’ position is validated.

Phaneroscopy/Phanerology de-agentify

Yes, it is a limitation to break the world/universe, or what have you into the binaries. A resolution of the same ain’t possible, until one either exercises an asymptotic progression/regression machine on it, and thus relegating the whole into an aporetic point of philosophical frustration that goes by the name of dialectics, or, one somehow experiences an event of binaries morphing into one another. Such a collapse of the one into the other gravitates the defining points of differences into identities, and this goes by the name of Laruellean “decisionism-in-the-last-instance”. So, dialectics with the second method goes on a honeymoon where minds of the left spend countless nights trying to get it back to the realistic domain (pun intended!!!).


I’d be sorry to be getting into territories that speak the language of failed poets/prose writers, for otherwise, I’d not be able to justify how bad a writer I really am!!! The lightened poetry of non-sense and/of Being: Even if such a poetry did exist (for me, at least it never did), then it was probably the romantic ideal of the by-gone philosophical ages, and we seem to have come a long way out of it, but still cling on to the symptoms of such an era. Pity!! It is not conjoining the obscure with the nothingness, or the Other World. It is rather the tunnelling of the lyrical aspect with the nothingness, a Schellingian approach to when he says that without confrontation, there is nothing of the creation possible. Dialectical, yes, in a way, but also the underside of it, which is considered a pariah, an outcast, an avoided and avoidable theory of creativity, or what I understand as Leper Creativity. Yes, losing identity could be viewed as relative here. But as I said, “could be”, and I refuse to truck with it imposed-consciously. And hereby, I also answer a subsequent point: “it” is uncharacteristic of holding true to the pillars of what constitutes it. Far-fetchedly, “it” is like what Wittgenstein would say: rise up the rung of the ladder and then discard it. But, a difference is to be spotted here. For Wittgenstein, the climber discards the ladder, whereas in this the present context, with each rising up on the rung of the ladder, a sort of dehumanization takes place in terms of awe/sublime/incapacitation. In other words, a sense of belonging to the “it” is bred in the “we” (agents/agencies) undoubtedly, but is lost sight of due to the intense flows of the “it” in time. A sort of exponential hypertrophy of the “it” due to “we”, or loosely saying emergentism in which node/nodes of “we” are simply sucked in. So, “we” build up the “it”, and lose it identity-wise in the process.

On similar lines, the knowledge of surplus is bluntly replaced by the awareness of it, an excess that is wasted more than it is used, and a kind of “solar anus” in the Bataillean sense, truly. Philosophical aesthetics falling in the hands of terrorizing hermeneutics: yes, I concur on this. This is one of the reasons, why I have started advocating phaneroscopy/phanerology over phenomenology, and it comes close to your recent studies on the quantum physics. But, then do we have a choice? We are yet to be defeated by the exploding solar anus, even though we are well on our way to a crushing defeat. Analogically, when someone says that “a world without capitalism is possible”, I tell of such Occupy/World Social Forum pundits that it is, but in a way that is stripped of agencies, and not otherwise. Sorry for the hubris here on my part, but my way of looking into these aspects could either mean that I am going a bit too far in my analysis, or getting really cracked brain now. On the point of polarity between order and disorder becomes unidentifiable when I say of lemniscate obscuring the horizon. Why do I say this? For me, order is nothing but an echo of a disordered anarchy that still reverberates. With this, I quash ethics, and I have no qualms in doing so, for a whole new set of rules need to be rewritten/rethought in this very darkness, which incidentally is on the avoidable radar still, but is making a stealthy invasion upon us, and before time will annihilate us, and de-anthropocentrize. Can’t help feeling sorry for Kant now for sure.

“It” is the cosmic “capitalism”.

Conjectures of Capitalism and Organic Necrocracy, RN


Following a reading of Freud and Deleuze in their use of death drive, Reza Negarestani tells us that capitalism forges an inhuman model that “weds the concrete economy of human life to a cosmos where neither being nor thinking enjoys any privilege.” Taking his trajectory from the investigation of Nick Land in his “The Thirst for Annihilation“, he tells us that “what brings about this weird marriage between human praxis and inhuman emancipation is the tortuous economy of dissipation inherent to capitalism as its partially repressed desire for meltdown.” According to a quote from Land, “What appears to humanity as the history of capitalism is an invasion from the future by an artificially intelligent space that must assemble itself from an enemy’s resources.” Negarestani compares this emancipatory capitalism with HP Lovecraft‘s fantastic concept of ‘holocaust of freedom’, which celebrates the consummation of human doom with human emancipation.