Biogrammatic Vir(Ac)tuality. Note Quote.

In Foucault’s most famous example, the prison acts as the confluence of content (prisoners) and expression (law, penal code) (Gilles Deleuze, Sean Hand-Foucault). Informal Diagrams are proliferate. As abstract machines they contain the transversal vectors that cut across a panoply of features (such as institutions, classes, persons, economic formation, etc), mapping from point to relational point, the generalized features of power economies. The disciplinary diagram explored by Foucault, imposes “a particular conduct upon a particular human multiplicity”. The imposition of force upon force affects and effectuates the felt experience of a life, a living. Deleuze has called the abstract machine “pure matter/function” in which relations between forces are nonetheless very real.

[…] the diagram acts as a non-unifying immanent cause that is co-extensive with the whole social field: the abstract machine is like the cause of the concrete assemblages that execute its relations; and these relations between forces take place ‘not above’ but within the very tissue of the assemblages they produce.

The processual conjunction of content and expression; the cutting edge of deterritorialization:

The relations of power and resistance between theory and practice resonate – becoming-form; diagrammatics as praxis, integrates and differentiates the immanent cause and quasi-cause of the actualized occasions of research/creation. What do we mean by immanent cause? It is a cause which is realized, integrated and distinguished in its effect. Or rather, the immanent cause is realized, integrated and distinguished by its effect. In this way there is a correlation or mutual presupposition between cause and effect, between abstract machine and concrete assemblages

Memory is the real name of the relation to oneself, or the affect of self by self […] Time becomes a subject because it is the folding of the outside…forces every present into forgetting but preserves the whole of the past within memory: forgetting is the impossibiltiy of return and memory is the necessity of renewal.


The figure on the left is Henri Bergson’s diagram of an infinitely contracted past that directly intersects with the body at point S – a mobile, sensorimotor present where memory is closest to action. Plane P represents the actual present; plane of contact with objects. The AB segments represent repetitive compressions of memory. As memory contracts it gets closer to action. In it’s more expanded forms it is closer to dreams. The figure on the right extrapolates from Bergson’s memory model to describe the Biogrammatic ontological vector of the Diagram as it moves from abstract (informal) machine in the most expanded form “A” through the cone “tissue” to the phase-shifting (formal), arriving at the Strata of the P plane to become artefact. The ontological vector passes through the stratified, through the interval of difference created in the phase shift (the same phase shift that separates and folds content and expression to move vertically, transversally, back through to the abstract diagram.)

A spatio-temporal-material contracting-expanding of the abstract machine is the processual thinking-feeling-articulating of the diagram becoming-cartographic; synaesthetic conceptual mapping. A play of forces, a series of relays, affecting a tendency toward an inflection of the informal diagram becoming-form. The inflected diagram/biogram folds and unfolds perception, appearances; rides in the gap of becoming between content and expression; intuitively transduces the actualizing (thinking, drawing, marking, erasing) of matter-movement, of expressivity-movement. “To follow the flow of matter… is intuition in action.” A processual stage that prehends the process of the virtual actualizing;

the creative construction of a new reality. The biogrammatic stage of the diagrammatic is paradoxically double in that it is both the actualizing of the abstract machine (contraction) and the recursive counter-actualization of the formal diagram (détournement); virtual and actual.

It is the event-dimension of potential – that is the effective dimension of the interrelating of elements, of their belonging to each other. That belonging is a dynamic corporeal “abstraction” – the “drawing off” (transductive conversion) of the corporeal into its dynamism (yielding the event) […] In direct channeling. That is, in a directional channeling: ontological vector. The transductive conversion is an ontological vector that in-gathers a heterogeneity of substantial elements along with the already-constituted abstractions of language (“meaning”) and delivers them together to change. (Brian Massumi Parables for the Virtual Movement, Affect, Sensation)

Skin is the space of the body the BwO that is interior and exterior. Interstitial matter of the space of the body.


The material markings and traces of a diagrammatic process, a ‘capturing’ becoming-form. A diagrammatic capturing involves a transductive process between a biogrammatic form of content and a form of expression. The formal diagram is thus an individuating phase-shift as Simondon would have it, always out-of-phase with itself. A becoming-form that inhabits the gap, the difference, between the wave phase of the biogrammatic that synaesthetically draws off the intermix of substance and language in the event-dimension and the drawing of wave phase in which partial capture is formalized. The phase shift difference never acquires a vectorial intention. A pre-decisive, pre-emptive drawing of phase-shifting with a “drawing off” the biogram.


If effects realize something this is because the relations between forces or power relations, are merely virtual, potential, unstable vanishing and molecular, and define only possibilities of interaction so long as they do not enter a macroscopic whole capable of giving form to their fluid manner and diffuse function. But realization is equally an integration, a collection of progressive integrations that are initially local and then become or tend to become global, aligning, homogenizing and summarizing relations between forces: here law is the integration of illegalisms.


Knowledge Within and Without: The Upanishadic Tradition (1)

All perceptible matter comes from a primary substance, or tenuity beyond conception, filling all space, the akasha or luminiferous ether, which is acted upon by the life giving Prana or creative force, calling into existence, in never-ending cycles all things and phenomena – Nikola Tesla

Teilhard de Chardin:

In the eyes of the physicist, nothing exists legitimately, at least up to now, except the without of things. The same intellectual attitude is still permissible in the bacteriologist, whose cultures (apart from substantial difficulties) are treated as laboratory reagents. But it is still more difficult in the realm of plants. It tends to become a gamble in the case of a biologist studying the behavior of insects or coelenterates. It seems merely futile with regard to the vertebrates. Finally, it breaks down completely with man, in whom the existence of a within can no longer be evaded, because it is a subject of a direct intuition and the substance of all knowledge. It is impossible to deny that, deep within ourselves, “an interior” appears at the heart of beings, as it were seen through a rent. This is enough to ensure that, in one degree or another, this “interior” should obtrude itself as existing everywhere in nature from all time. Since the stuff of the universe has an inner aspect at one point of itself, there is necessarily a double to its structure, that is to say in every region of space and time-in the same way for instance, as it is granular: co-extensive with their Without, there is a Within to things.

Both Indian thought and modern scientific thought accept a fundamental unity behind the world of variety. That basic unitary reality evolves into all that we see around us in the world. This view is a few thousand years old in India; We find it in the Samkhyan and Vedantic schools of Indian thought; and they expound it very much on the lines followed by modern thought. In his address to the Chicago Parliament of Religions in 1893, Vivekananda said:

All science is bound to come to this conclusion in the long run, Manifestation and not creation, is the word of science today, and the Hindu is only glad that what he has been cherishing in his bosom for ages is going to be taught in more forcible language, and with further light from the latest conclusions of science.

The Samkhyan school uses two terms to represent Nature or Pradhana: Prakrti denoting Nature in its unmodified state, and Vikrti denoting nature in its modified state. The Vedanta similarly speaks of Brahman as the inactive state, and Maya or Shakti as the active state of one and the same primordial non-dual reality. But the Brahman of the Vedanta is the unity of both the spiritual and the non-spiritual, the non-physical and the physical aspects of the universe.

So as the first answer to the question, ‘What is the world?’ we get this child’s answer in his growing knowledge of the discrete entities and events of the outer world and their inter-connections. The second answer is the product of scientific thought, which gives us the knowledge of the one behind the many. All the entities and events of the world are but the modifications or evolutions of one primordial basis reality, be it nature, space- time or cosmic dust.

Although modern scientific thought does not yet have a place for any spiritual reality or principle, scientists like Chardin and Julian Huxley are trying to find a proper place for the experience of the spiritual in the scientific picture of the universe. When this is achieved, the scientific picture, which is close to Vedanta already, will become closer still, and the synthesis of the knowledge of the ‘without’ and the ‘within’ of things will give us the total view of the universe. This is wisdom according to Vedanta, whereas all partial views are just pieces of knowledge or information only.

The Upanishads deal with this ‘within’ of things. Theirs in fact, is the most outstanding contribution on this subject in the human cultural legacy. They term this aspect of reality of things pratyak chaitanya or pratyak atman or pratyak tattva; and they contain the fascinating account of the stages by which the human mind rose from crude beginnings to clear, wholly spiritual heights in the realization of this reality.

How does the world look when we view it from the outside? We seek an answer from the physical sciences. How does it look when we view from the inside? We seek an answer from the non-physical sciences, including the science of religion. And philosophy, as understood in the Upanishadic tradition, is the synthesis of these two answers: Brahmavidyā is Sarvavidyāpratishthā, as the Mundaka Upanishad puts it.

क्षेत्रक्षेत्रज्ञयोर्ज्ञानं यत्तज्ज्ञानम् मतं मम

kṣetrakṣetrajñayorjñānaṃ yattajjñānam mataṃ mama

“The unified knowledge of the ‘without’ and the ‘within’ of things is true knowledge according to Me, as Krishna says in the Gita” (Bhagavad-Gita chapter 13, 2nd Shloka).

From this total viewpoint there is neither inside nor outside; they are relative concepts depending upon some sort of a reference point, e.g.the body; as such, they move within the framework of relativity. Reality knows neither ‘inside’ nor ‘outside’; it is ever full. But these relative concepts are helpful in our approach to the understanding of the total reality.

Thus we find that our knowledge of the manifold of experience the idam, also involves something else, namely, the unity behind the manifold. This unity behind the manifold, which is not perceptible to the senses, is indicated by the term adah meaning ‘that’, indicating something far away, unlike the ‘this’ of the sense experience. ‘This’ is the correlative of ‘that’; ‘this’ is the changeable aspect of reality; ‘that’ is its unchangeable aspect. If ‘this’ refers to something given in sense experience, ‘that’ refers to something transcendental, beyond the experience of the senses. To say ‘this’ therefore also implies at the same time something that is beyond ‘this’. This is an effect as such, it is visible and palpable; and behind it lies the cause, the invisible and the impalpable. Adah, ‘that’, represents the invisible behind the visible, the transcendental behind the empirical, a something that is beyond time and space. In religion this something is called ‘God’. In philosophy it is called tat or adah, That, Brahman, the ultimate Reality, the cause, the ground, and the goal of the universe.

So this verse first tells us that beyond and behind the manifested universe is the reality of Brahman, which is the fullness of pure Being; it then tells us about this world of becoming which, being nothing but Brahman, is also the ‘Full’. From the view of total Reality, it is all ‘fullness’ everywhere, in space-time as well as beyond space-time. Then the verse adds:

पूर्णस्य पूर्णमादाय पूर्णमेवाशिष्यते

pūrṇasya pūrṇamādāya pūrṇamevāśiṣyate

‘From the Fullness of Brahman has come the fullness of the universe, leaving alone Fullness as the remainder.’

What, then, is the point of view or level from which the sentiments of this verse proceed? It is that of the total Reality, the Absolute and the Infinite, in which as we have read earlier, the ‘within’ and the ‘without’ of things merge. The Upanishads call it as ocean of Sachchidānanda, the unity of absolute existence, absolute awareness, and absolute bliss. Itself beyond all distinctions of time and space, it yet manifests itself through all such distinctions. To the purified vision of the Upanishadic sages, this whole universe appeared as the fullness of Being, which was, which is, which shall ever be. In the Bhagavad-Gita (VII. 26) Krshna says:

वेदाहं समतीतानि वर्तमानानि चार्जुन ।
भविष्याणि च भूतानि मां तु वेद न कश्चन ॥

vedāhaṃ samatītāni vartamānāni cārjuna |
bhaviṣyāṇi ca bhūtāni māṃ tu veda na kaścana ||

‘I, O Arjuna, know the beings that are of the past, that are of the present, and that are to come in future; but Me no one knows.’

That fullness of the true Me, says Krshna, is beyond all these limited categories, such as space and time, cause and effect, and substance and attribute.

Why Deleuzean Philosophy Begins at Hegel and Becomes a Correctional Footnote Thereafter ? Note Quote.

That philosophy must be an ontology of sense is a bold claim on Deleuze’s part, and although he takes it from a Hegelian philosophy, the direction in which he develops it across the rest of his work is resolutely, if not infamously, opposed to Hegel. Whereas Hegel will construct a logic of sense which is fundamentally a logic of the concept, Deleuze will deny that sense is reducible to signification and its universal or general concepts. Deleuze will later provide his own logic of the concept, but for him, although the concept will posit itself, this will not be as the immanent thought of the sense or the content of the matter itself, but will rather function to extract or capture a pure event, or the sense at the surface of things. Similarly, although Deleuze will agree that “sense is becoming”, this will not be a becoming in an atemporal logical time, opposed to a historical time that would play it out, but a pure becoming without present, always divided between past and future, without arrow or telos, and actualised in the present while never strictly ‘happening’. The most distinctive difference, however, will be Deleuze’s invocation of a nonsense that cannot be simply incorporated within sense, that will not be sublated and subsumed in the folds of the dialectic, a nonsense that is itself productive of sense. Moving beyond Hegel, Deleuze will deny the reducibility of sense not only to the universal meanings of signification, but also to the functions of reference or denotation. Moreover, he will deny its reducibility to the dimension of manifestation, or the meanings of the subject of enunciation – the ‘I’ who speaks. Sense can neither be found in universal concepts, nor reference to the individual, nor in the intentions of the subject, but is rather that which grounds all three.

Philosophizing Twistors via Fibration

The basic issue, is a question of so called time arrow. This issue is an important subject of examination in mathematical physics as well as ontology of spacetime and philosophical anthropology. It reveals crucial contradiction between the knowledge about time, provided by mathematical models of spacetime in physics and psychology of time and its ontology. The essence of the contradiction lies in the invariance of the majority of fundamental equations in physics with regard to the reversal of the direction of the time arrow (i. e. the change of a variable t to -t in equations). Neither metric continuum, constituted by the spaces of concurrency in the spacetime of the classical mechanics before the formulation of the Particular Theory of Relativity, the spacetime not having metric but only affine structure, nor Minkowski’s spacetime nor the GTR spacetime (pseudo-Riemannian), both of which have metric structure, distinguish the categories of past, present and future as the ones that are meaningful in physics. Every event may be located with the use of four coordinates with regard to any curvilinear coordinate system. That is what clashes remarkably with the human perception of time and space. Penrose realizes and understands the necessity to formulate such theory of spacetime that would remove this discrepancy. He remarked that although we feel the passage of time, we do not perceive the “passage” of any of the space dimensions. Theories of spacetime in mathematical physics, while considering continua and metric manifolds, cannot explain the difference between time dimension and space dimensions, they are also unable to explain by means of geometry the unidirection of the passage of time, which can be comprehended only by means of thermodynamics. The theory of spaces of twistors is aimed at better and crucial for the ontology of nature understanding of the problem of the uniqueness of time dimension and the question of time arrow. There are some hypotheses that the question of time arrow would be easier to solve thanks to the examination of so called spacetime singularities and the formulation of the asymmetric in time quantum theory of gravitation — or the theory of spacetime in microscale.

The unique role of twistors in TGD

Although Lorentzian geometry is the mathematical framework of classical general relativity and can be seen as a good model of the world we live in, the theoretical-physics community has developed instead many models based on a complex space-time picture.

(1) When one tries to make sense of quantum field theory in flat space-time, one finds it very convenient to study the Wick-rotated version of Green functions, since this leads to well defined mathematical calculations and elliptic boundary-value problems. At the end, quantities of physical interest are evaluated by analytic continuation back to real time in Minkowski space-time.

(2) The singularity at r = 0 of the Lorentzian Schwarzschild solution disappears on the real Riemannian section of the corresponding complexified space-time, since r = 0 no longer belongs to this manifold. Hence there are real Riemannian four-manifolds which are singularity-free, and it remains to be seen whether they are the most fundamental in modern theoretical physics.

(3) Gravitational instantons shed some light on possible boundary conditions relevant for path-integral quantum gravity and quantum cosmology.  Unprimed and primed spin-spaces are not (anti-)isomorphic if Lorentzian space-time is replaced by a complex or real Riemannian manifold. Thus, for example, the Maxwell field strength is represented by two independent symmetric spinor fields, and the Weyl curvature is also represented by two independent symmetric spinor fields and since such spinor fields are no longer related by complex conjugation (i.e. the (anti-)isomorphism between the two spin-spaces), one of them may vanish without the other one having to vanish as well. This property gives rise to the so-called self-dual or anti-self-dual gauge fields, as well as to self-dual or anti-self-dual space-times.

(5) The geometric study of this special class of space-time models has made substantial progress by using twistor-theory techniques. The underlying idea is that conformally invariant concepts such as null lines and null surfaces are the basic building blocks of the world we live in, whereas space-time points should only appear as a derived concept. By using complex-manifold theory, twistor theory provides an appropriate mathematical description of this key idea.

A possible mathematical motivation for twistors can be described as follows.  In two real dimensions, many interesting problems are best tackled by using complex-variable methods. In four real dimensions, however, the introduction of two complex coordinates is not, by itself, sufficient, since no preferred choice exists. In other words, if we define the complex variables

z1 ≡ x1 + ix2 —– (1)

z2 ≡ x3 + ix4 —– (2)

we rely too much on this particular coordinate system, and a permutation of the four real coordinates x1, x2, x3, x4 would lead to new complex variables not well related to the first choice. One is thus led to introduce three complex variables u, z1u, z2u : the first variable u tells us which complex structure to use, and the next two are the

complex coordinates themselves. In geometric language, we start with the complex projective three-space P3(C) with complex homogeneous coordinates (x, y, u, v), and we remove the complex projective line given by u = v = 0. Any line in P3(C) − P1(C) is thus given by a pair of equations

x = au + bv —– (3)

y = cu + dv —– (4)

In particular, we are interested in those lines for which c = −b, d = a. The determinant ∆ of (3) and (4) is thus given by

∆ = aa +bb + |a|2 + |b|2 —– (5)

which implies that the line given above never intersects the line x = y = 0, with the obvious exception of the case when they coincide. Moreover, no two lines intersect, and they fill out the whole of P3(C) − P1(C). This leads to the fibration P3(C) − P1(C) → R4 by assigning to each point of P3(C) − P1(C) the four coordinates Re(a), Im(a), Re(b), Im(b). Restriction of this fibration to a plane of the form

αu + βv = 0 —— (6)

yields an isomorphism C2 ≅ R4, which depends on the ratio (α,β) ∈ P1(C). This is why the picture embodies the idea of introducing complex coordinates.


Such a fibration depends on the conformal structure of R4. Hence, it can be extended to the one-point compactification S4 of R4, so that we get a fibration P3(C) → S4 where the line u = v = 0, previously excluded, sits over the point at ∞ of S4 = R∪ ∞ . This fibration is naturally obtained if we use the quaternions H to identify C4 with H2 and the four-sphere S4 with P1(H), the quaternion projective line. We should now recall that the quaternions H are obtained from the vector space R of real numbers by adjoining three symbols i, j, k such that

i2 = j2 = k2 =−1 —– (7)

ij = −ji = k,  jk = −kj =i,  ki = −ik = j —– (8)

Thus, a general quaternion ∈ H is defined by

x ≡ x1 + x2i + x3j + x4k —– (9)

where x1, x2, x3, x4 ∈ R4, whereas the conjugate quaternion x is given by

x ≡ x1 – x2i – x3j – x4k —– (10)

Note that conjugation obeys the identities

(xy) = y x —– (11)

xx = xx = ∑μ=14 x2μ ≡ |x|2 —– (12)

If a quaternion does not vanish, it has a unique inverse given by

x-1 ≡ x/|x|2 —– (13)

Interestingly, if we identify i with √−1, we may view the complex numbers C as contained in H taking x3 = x4 = 0. Moreover, every quaternion x as in (9) has a unique decomposition

x = z1 + z2j —– (14)

where z1 ≡ x1 + x2i, z2 ≡ x3 + x4i, by virtue of (8). This property enables one to identify H with C2, and finally H2 with C4, as we said following (6)

The map σ : P3(C) → P3(C) defined by

σ(x, y, u, v) = (−y, x, −v, u) —– (15)

preserves the fibration because c = −b, d = a, and induces the antipodal map on each fibre.