Nomological Unification and Phenomenology of Gravitation. Thought of the Day 110.0

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String theory, which promises to give an all-encompassing, nomologically unified description of all interactions did not even lead to any unambiguous solutions to the multitude of explanative desiderata of the standard model of quantum field theory: the determination of its specific gauge invariances, broken symmetries and particle generations as well as its 20 or more free parameters, the chirality of matter particles, etc. String theory does at least give an explanation for the existence and for the number of particle generations. The latter is determined by the topology of the compactified additional spatial dimensions of string theory; their topology determines the structure of the possible oscillation spectra. The number of particle generations is identical to half the absolute value of the Euler number of the compact Calabi-Yau topology. But, because it is completely unclear which topology should be assumed for the compact space, there are no definitive results. This ambiguity is part of the vacuum selection problem; there are probably more than 10100 alternative scenarios in the so-called string landscape. Moreover all concrete models, deliberately chosen and analyzed, lead to generation numbers much too big. There are phenomenological indications that the number of particle generations can not exceed three. String theory admits generation numbers between three and 480.

Attempts at a concrete solution of the relevant external problems (and explanative desiderata) either did not take place, or they did not show any results, or they led to escalating ambiguities and finally got drowned completely in the string landscape scenario: the recently developed insight that string theory obviously does not lead to a unique description of nature, but describes an immense number of nomologically, physically and phenomenologically different worlds with different symmetries, parameter values, and values of the cosmological constant.

String theory seems to be by far too much preoccupied with its internal conceptual and mathematical problems to be able to find concrete solutions to the relevant external physical problems. It is almost completely dominated by internal consistency constraints. It is not the fact that we are living in a ten-dimensional world which forces string theory to a ten-dimensional description. It is that perturbative string theories are only anomaly-free in ten dimensions; and they contain gravitons only in a ten-dimensional formulation. The resulting question, how the four-dimensional spacetime of phenomenology comes off from ten-dimensional perturbative string theories (or its eleven-dimensional non-perturbative extension: the mysterious, not yet existing M theory), led to the compactification idea and to the braneworld scenarios, and from there to further internal problems.

It is not the fact that empirical indications for supersymmetry were found, that forces consistent string theories to include supersymmetry. Without supersymmetry, string theory has no fermions and no chirality, but there are tachyons which make the vacuum instable; and supersymmetry has certain conceptual advantages: it leads very probably to the finiteness of the perturbation series, thereby avoiding the problem of non-renormalizability which haunted all former attempts at a quantization of gravity; and there is a close relation between supersymmetry and Poincaré invariance which seems reasonable for quantum gravity. But it is clear that not all conceptual advantages are necessarily part of nature, as the example of the elegant, but unsuccessful Grand Unified Theories demonstrates.

Apart from its ten (or eleven) dimensions and the inclusion of supersymmetry, both have more or less the character of only conceptually, but not empirically motivated ad-hoc assumptions. String theory consists of a rather careful adaptation of the mathematical and model-theoretical apparatus of perturbative quantum field theory to the quantized, one-dimensionally extended, oscillating string (and, finally, of a minimal extension of its methods into the non-perturbative regime for which the declarations of intent exceed by far the conceptual successes). Without any empirical data transcending the context of our established theories, there remains for string theory only the minimal conceptual integration of basic parts of the phenomenology already reproduced by these established theories. And a significant component of this phenomenology, namely the phenomenology of gravitation, was already used up in the selection of string theory as an interesting approach to quantum gravity. Only, because string theory, containing gravitons as string states, reproduces in a certain way the phenomenology of gravitation, it is taken seriously.

La Mettrie’s Man-Machine

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Philosophers’ theories regarding the human soul? Basically there are just two of them: the first and older of the two is materialism; the second is spiritualism.

The metaphysicians who implied that matter might well have the power to think didn’t disgrace themselves as thinkers. Why not? Because they had the advantage (for in this case it is one) of expressing themselves badly. To ask whether unaided matter can think is like asking whether unaided matter can indicate the time. It’s clear already that we aren’t going to hit the rock on which Locke had the bad luck to come to grief in his speculations about whether there could be thinking matter.

The Leibnizians with their ‘monads’ have constructed an unintelligible hypothesis. Rather than materialising the soul, they spiritualised matter. How can we define a being like the so-called ‘monad’ whose nature is absolutely unknown to us?

Descartes and all the Cartesians – among whom Malebranche’s followers have long been included – went wrong in the same way, namely by dogmatising about something of which they knew nothing. They admitted two distinct substances in man, as if they had seen and counted them!

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Poincaré and Geometry of Curvature. Thought of the Day 60.0

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It is not clear that Poincaré regarded Riemannian, variably curved, “geometry” as a bona fide geometry. On the one hand, his insistence on generality and the iterability of mathematical operations leads him to dismiss geometries of variable curvature as merely “analytic”. Distinctive of mathematics, he argues, is generality and the fact that induction applies to its processes. For geometry to be genuinely mathematical, its constructions must be everywhere iterable, so everywhere possible. If geometry is in some sense about rigid motion, then a manifold of variable curvature, especially where the degree of curvature depends on something contingent like the distribution of matter, would not allow a thoroughly mathematical, idealized treatment. Yet Poincaré also writes favorably about Riemannian geometries, defending them as mathematically coherent. Furthermore, he admits that geometries of constant curvature rest on a hypothesis – that of rigid body motion – that “is not a self evident truth”. In short, he seems ambivalent. Whether his conception of geometry includes or rules out variable curvature is unclear. We can surmise that he recognized Riemannian geometry as mathematical, and interesting, but as very different and more abstract than geometries of constant curvature, which are based on the further limitations discussed above (those motivated by a world satisfying certain empirical preconditions). These limitations enable key idealizations, which in turn allow constructions and synthetic proofs that we recognize as “geometric”.

Is General Theory of Relativity a Gauge Theory? Trajectories of Diffeomorphism.

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Historically the problem of observables in classical and quantum gravity is closely related to the so-called Einstein hole problem, i.e. to some of the consequences of general covariance in general relativity (GTR).

The central question is the physical meaning of the points of the event manifold underlying GTR. In contrast to pure mathematics this is a non-trivial point in physics. While in pure differential geometry one simply decrees the existence of, for example, a (pseudo-) Riemannian manifold with a differentiable structure (i.e., an appropriate cover with coordinate patches) plus a (pseudo-) Riemannian metric, g, the relation to physics is not simply one-one. In popular textbooks about GTR, it is frequently stated that all diffeomorphic (space-time) manifolds, M are physically indistinguishable. Put differently:

S − T = Riem/Diff —– (1)

This becomes particularly virulent in the Einstein hole problem. i.e., assuming that we have a region of space-time, free of matter, we can apply a local diffeomorphism which only acts within this hole, letting the exterior invariant. We get thus in general two different metric tensors

g(x) , g′(x) := Φ ◦ g(x) —– (2)

in the hole while certain inital conditions lying outside of the hole are unchanged, thus yielding two different solutions of the Einstein field equations.

Many physicists consider this to be a violation of determinism (which it is not!) and hence argue that the class of observable quantities have to be drastically reduced in (quantum) gravity theory. They follow the line of reasoning developed by Dirac in the context of gauge theory, thus implying that GTR is essentially also a gauge theory. This then winds up to the conclusion:

Dirac observables in quantum gravity are quantities which are diffeomorphism invariant with the diffeomorphism group, Diff acting from M to M, i.e.

Φ : M → M —– (3)

One should note that with respect to physical observations there is no violation of determinism. An observer can never really observe two different metric fields on one and the same space-time manifold. This can only happen on the mathematical paper. He will use a fixed measurement protocol, using rods and clocks in e.g. a local inertial frame where special relativity locally applies and then extend the results to general coordinate frames.

We get a certain orbit under Diff if we start from a particular manifold M with a metric tensor g and take the orbit

{M, Φ ◦g} —– (4)

In general we have additional fields and matter distributions on M which are transformd accordingly.

Note that not even scalars are invariant in general in the above sense, i.e., not even the Ricci scalar is observable in the Dirac sense:

R(x) ≠ Φ ◦ R(x) —– (5)

in the generic case. Thus, this would imply that the class of admissible observables can be pretty small (even empty!). Furthermore, it follows that points of M are not a priori distinguishable. On the other hand, many consider the Ricci scalar at a point to be an observable quantity.

This winds up to the question whether GTR is a true gauge theory or perhaps only apparently so at a first glance, while on a more fundamental level it is something different. In the words of Kuchar (What is observable..),

Quantities non-invariant under the full diffeomorphism group are observable in gravity.

The reason for these apparently diverging opinions stems from the role reference systems are assumed to play in GTR with some arguing that the gauge property of general coordinate invariance is only of a formal nature.

In the hole argument it is for example argued that it is important to add some particle trajectories which cross each other, thus generating concrete events on M. As these point events transform accordingly under a diffeomorphism, the distance between the corresponding coordinates x, y equals the distance between the transformed points Φ(x), Φ(y), thus being a Dirac observable. On the other hand, the coordinates x or y are not observable.

One should note that this observation is somewhat tautological in the realm of Riemannian geometry as the metric is an absolute quantity, put differently (and somewhat sloppily), ds2 is invariant under passive and by the same token active coordinate transformation (diffeomorphisms) because, while conceptually different, the transformation properties under the latter operations are defined as in the passive case. In the case of GTR this absolute quantity enters via the equivalence principle i.e., distances are measured for example in a local inertial frame (LIF) where special relativity holds and are then generalized to arbitrary coordinate systems.

Iain Hamilton Grant’s Schelling in Opposition to Fichte. Note Quote.

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The stated villain of Philosophies of Nature is not Hegelianism but rather ‘neo-Fichteanism’. It is Grant’s ‘Philosophies of Nature After Schelling‘, which takes up the issue of graduating Schelling to escape the accoutrements of Kantian and Fichtean narrow transcendentalism. Grant frees Schelling from the grips of narrow minded inertness and mechanicality in nature that Kant and Fichte had presented nature with. This idea is the Deleuzean influence on Grant. Manuel De Landa makes a vociferous case in this regard. According to De Landa, the inertness of matter was rubbished by Deleuze in the way that Deleuze sought for a morphogenesis of form thereby launching a new kind of materialism. This is the anti-essentialist position of Deleuze. Essentialism says that matter and energy are inert, they do not have any morphogenetic capabilities. They cannot give rise to new forms on their own. Disciplines like complexity theory, non-linear dynamics do give matter its autonomy over inertness, its capabilities in terms of charge. But its account of the relationship between Fichte and Schelling actually obscures the rich meaning of speculation in Hegel and after. Grant quite accurately recalls that Schelling confronted Fichte’s identification of the ‘not I’ with passive nature – the consequence of identifying all free activity with the ‘I’ alone. For Grant, that which Jacobi termed ‘speculative egotism’ becomes the nightmare of modern philosophy and of technological modernity at large. The ecological concern is never quite made explicit in Philosophies of Nature. Yet Grant’s introduction to Schelling’s On the World Soul helps to contextualise the meaning of his ‘geology of morals’.

What we miss from Grant’s critique of Fichte is the manner by which the corrective, positive characterisation of nature proceeds from Schelling’s confirmation of Fichte’s rendering of the fact of consciousness (Tatsache) into the act of consciousness (Tathandlung). Schelling, as a consequence, becomes singularly critical of contemplative speculation, since activity now implies working on nature and thereby changing it – along with it, we might say – rather than either simply observing it or even experimenting upon it.

In fact, Grant reads Schelling only in opposition to Fichte, with drastic consequences for his speculative realism: the post-Fichtean element of Schelling’s naturephilosophy allows for the new sense of speculation he will share with Hegel – even though they will indeed turn this against Kant and Fichte. Without this account, we are left with the older, contemplative understanding of metaphysical speculation, which leads to a certain methodologism in Grant’s study. Hence, ‘the principle method of naturephilosophy consists in “unconditioning” the phenomena’. Relatedly, Meillassoux defines the ‘speculative’ as ‘every type of thinking’ – not acting, – ‘that claims to be able to access some form of absolute’.

In direct contrast to this approach, the collective ‘system programme’ of Hegel, Schelling and Hölderlin was not a programme for thinking alone. Their revolutionised sense of speculation, from contemplation of the stars to reform of the worldly, is overlooked by today’s speculative realism – a philosophy that, ‘refuses to interrogate reality through human (linguistic, cultural or political) mediations of it’. We recall that Kant similarly could not extend his Critique to speculative reason precisely on account of his contemplative determination of pure reason (in terms of the hierarchical gap between reason and the understanding). Grant’s ‘geology of morals’ does not oppose ‘Kanto-Fichtean philosophy’, as he has it, but rather remains structurally within the sphere of Kant’s pre-political metaphysics.

The Sibyl’s Prophecy/Nordic Creation. Note Quote.

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The Prophecy of the Tenth Sibyl, a medieval best-seller, surviving in over 100 manuscripts from the 11th to the 16th century, predicts, among other things, the reign of evil despots, the return of the Antichrist and the sun turning to blood.

The Tenth or Tiburtine Sibyl was a pagan prophetess perhaps of Etruscan origin. To quote Lactantus in his general account of the ten sibyls in the introduction, ‘The Tiburtine Sibyl, by name Albunea, is worshiped at Tibur as a goddess, near the banks of the Anio in which stream her image is said to have been found, holding a book in her hand’.

The work interprets the Sibyl’s dream in which she foresees the downfall and apocalyptic end of the world; 9 suns appear in the sky, each one more ugly and bloodstained than the last, representing the 9 generations of mankind and ending with Judgment Day. The original Greek version dates from the end of the 4th century and the earliest surviving manuscript in Latin is dated 1047. The Tiburtine Sibyl is often depicted with Emperor Augustus, who asks her if he should be worshipped as a god.

The foremost lay of the Elder Edda is called Voluspa (The Sibyl’s Prophecy). The volva, or sibyl, represents the indelible imprint of the past, wherein lie the seeds of the future. Odin, the Allfather, consults this record to learn of the beginning, life, and end of the world. In her response, she addresses Odin as a plurality of “holy beings,” indicating the omnipresence of the divine principle in all forms of life. This also hints at the growth of awareness gained by all living, learning entities during their evolutionary pilgrimage through spheres of existence.

Hear me, all ye holy beings, greater as lesser sons of Heimdal! You wish me to tell of Allfather’s works, tales of the origin, the oldest I know. Giants I remember, born in the foretime, they who long ago nurtured me. Nine worlds I remember, nine trees of life, before this world tree grew from the ground.

Paraphrased, this could be rendered as:

Learn, all ye living entities, imbued with the divine essence of Odin, ye more and less evolved sons of the solar divinity (Heimdal) who stands as guardian between the manifest worlds of the solar system and the realm of divine consciousness. You wish to learn of what has gone before. I am the record of long ages past (giants), that imprinted their experience on me. I remember nine periods of manifestation that preceded the present system of worlds.

Time being inextricably a phenomenon of manifestation, the giant ages refer to the matter-side of creation. Giants represent ages of such vast duration that, although their extent in space and time is limited, it is of a scope that can only be illustrated as gigantic. Smaller cycles within the greater are referred to in the Norse myths as daughters of their father-giant. Heimdal is the solar deity in the sign of Aries – of beginnings for our system – whose “sons” inhabit, in fact compose, his domain.

Before a new manifestation of a world, whether a cosmos or a lesser system, all its matter is frozen in a state of immobility, referred to in the Edda as a frost giant. The gods – consciousnesses – are withdrawn into their supernal, unimaginable abstraction of Nonbeing, called in Sanskrit “paranirvana.” Without a divine activating principle, space itself – the great container – is a purely theoretical abstraction where, for lack of any organizing energic impulse of consciousness, matter cannot exist.

This was the origin of ages when Ymer built. No soil was there, no sea, no cool waves. Earth was not, nor heaven above; Gaping Void alone, no growth. Until the sons of Bur raised the tables; they who created beautiful Midgard. The sun shone southerly on the stones of the court; then grew green herbs in fertile soil.

To paraphrase again:

Before time began, the frost giant (Ymer) prevailed. No elements existed for there were ‘no waves,’ no motion, hence no organized form nor any temporal events, until the creative divine forces emanated from Space (Bur — a principle, not a locality) and organized latent protosubstance into the celestial bodies (tables at which the gods feast on the mead of life-experience). Among these tables is Middle Court (Midgard), our own beautiful planet. The life-giving sun sheds its radiant energies to activate into life all the kingdoms of nature which compose it.

The Gaping Void (Ginnungagap) holds “no cool waves” throughout illimitable depths during the age of the frost giant. Substance has yet to be created. Utter wavelessness negates it, for all matter is the effect of organized, undulating motion. As the cosmic hour strikes for a new manifestation, the ice of Home of Nebulosity (Niflhem) is melted by the heat from Home of Fire (Muspellshem), resulting in vapor in the void. This is Ymer, protosubstance as yet unformed, the nebulae from which will evolve the matter components of a new universe, as the vital heat of the gods melts and vivifies the formless immobile “ice.”

When the great age of Ymer has run its course, the cow Audhumla, symbol of fertility, “licking the salt from the ice blocks,” uncovers the head of Buri, first divine principle. From this infinite, primal source emanates Bur, whose “sons” are the creative trinity: Divine Allfather, Will, and Sanctity (Odin, Vile, and Vi). This triune power “kills” the frost giant by transforming it into First Sound (Orgalmer), or keynote, whose overtones vibrate through the planes of sleeping space and organize latent protosubstance into the multifarious forms which will be used by all “holy beings” as vehicles for gaining experience in worlds of matter.

Beautiful Midgard, our physical globe earth, is but one of the “tables” raised by the creative trinity, whereat the gods shall feast. The name Middle Court is suggestive, for the ancient traditions place our globe in a central position in the series of spheres that comprise the terrestrial being’s totality. All living entities, man included, comprise besides the visible body a number of principles and characteristics not cognized by the gross physical senses. In the Lay of Grimner (Grimnismal), wherein Odin in the guise of a tormented prisoner on earth instructs a human disciple, he enumerates twelve spheres or worlds, all but one of which are unseen by our organs of sight. As to the formation of Midgard, he relates:

Of Ymer’s flesh was the earth formed, the billows of his blood, the mountains of his bones, bushes of his hair, and of his brainpan heaven. With his eyebrows beneficent powers enclosed Midgard for man; but of his brain were surely all dark skies created.

The trinity of immanent powers organize Ymer into the forms wherein they dwell, shaping the chaos or frost giant into living globes on many planes of being. The “eyebrows” that gird the earth and protect it suggest the Van Allen belts that shield the planet from inimical radiation. The brain of Ymer – material thinking – is surely all too evident in the thought atmosphere wherein man participates.

The formation of the physical globe is described as the creation of “dwarfs” – elemental forces which shape the body of the earth-being and which include the mineral. vegetable, and animal kingdoms.

The mighty drew to their judgment seats, all holy gods to hold counsel: who should create a host of dwarfs from the blood of Brimer and the limbs of the dead. Modsogne there was, mightiest of all the dwarfs, Durin the next; there were created many humanoid dwarfs from the earth, as Durin said.

Brimer is the slain Ymer, a kenning for the waters of space. Modsogne is the Force-sucker, Durin the Sleeper, and later comes Dvalin the Entranced. They are “dwarf”-consciousnesses, beings that are miðr than human – the Icelandic miðr meaning both “smaller” and “less.” By selecting the former meaning, popular concepts have come to regard them as undersized mannikins, rather than as less evolved natural species that have not yet reached the human condition of intelligence and self-consciousness.

During the life period or manifestation of a universe, the governing giant or age is named Sound of Thor (Trudgalmer), the vital force which sustains activity throughout the cycle of existence. At the end of this age the worlds become Sound of Fruition (Bargalmer). This giant is “placed on a boat-keel and saved,” or “ground on the mill.” Either version suggests the karmic end product as the seed of future manifestation, which remains dormant throughout the ensuing frost giant of universal dissolution, when cosmic matter is ground into a formless condition of wavelessness, dissolved in the waters of space.

There is an inescapable duality of gods-giants in all phases of manifestation: gods seek experience in worlds of substance and feast on the mead at stellar and planetary tables; giants, formed into vehicles inspired with the divine impetus, rise through cycles of this association on the ladder of conscious awareness. All states being relative and bipolar, there is in endless evolution an inescapable link between the subjective and objective progress of beings. Odin as the “Opener” is paired with Orgalmer, the keynote on which a cosmos is constructed; Odin as the “Closer” is equally linked with Bargalmer, the fruitage of a life cycle. During the manifesting universe, Odin-Allfather corresponds to Trudgalmer, the sustainer of life.

A creative trinity plays an analogical part in the appearance of humanity. Odin remains the all-permeant divine essence, while on this level his brother-creators are named Honer and Lodur, divine counterparts of water or liquidity, and fire or vital heat and motion. They “find by the shore, of little power” the Ash and the Elm and infuse into these earth-beings their respective characteristics, making a human image or reflection of themselves. These protohumans, miniatures of the world tree, the cosmic Ash, Yggdrasil, in addition to their earth-born qualities of growth force and substance, receive the divine attributes of the gods. By Odin man is endowed with spirit, from Honer comes his mind, while Lodur gives him will and godlike form. The essentially human qualities are thus potentially divine. Man is capable of blending with the earth, whose substances form his body, yet is able to encompass in his consciousness the vision native to his divine source. He is in fact a minor world tree, part of the universal tree of life, Yggdrasil.

Ygg in conjunction with other words has been variously translated as Eternal, Awesome or Terrible, and Old. Sometimes Odin is named Yggjung, meaning the Ever-Young, or Old-Young. Like the biblical “Ancient of Days” it is a concept that mind can grasp only in the wake of intuition. Yggdrasil is the “steed” or the “gallows” of Ygg, whereon Odin is mounted or crucified during any period of manifested life. The world tree is rooted in Nonbeing and ramifies through the planes of space, its branches adorned with globes wherein the gods imbody. The sibyl spoke of ours as the tenth in a series of such world trees, and Odin confirms this in The Song of the High One (Den Hoges Sang):

I know that I hung in the windtorn tree nine whole nights, spear-pierced, given to Odin, my self to my Self above me in the tree, whose root none knows whence it sprang. None brought me bread, none served me drink; I searched the depths, spied runes of wisdom, raised them with song, and fell once more from the tree. Nine powerful songs I learned from the wise son of Boltorn, Bestla’s father; a draught I drank of precious mead ladled from Odrorer. I began to grow, to grow wise, to grow greater and enjoy; for me words from words led to new words, for me deeds from deeds led to new deeds.

Numerous ancient tales relate the divine sacrifice and crucifixion of the Silent Watcher whose realm or protectorate is a world in manifestation. Each tree of life, of whatever scope, constitutes the cross whereon the compassionate deity inherent in that hierarchy remains transfixed for the duration of the cycle of life in matter. The pattern of repeated imbodiments for the purpose of gaining the precious mead is clear, as also the karmic law of cause and effect as words and deeds bring their results in new words and deeds.

Yggdrasil is said to have three roots. One extends into the land of the frost giants, whence flow twelve rivers of lives or twelve classes of beings; another springs from and is watered by the well of Origin (Urd), where the three Norns, or fates, spin the threads of destiny for all lives. “One is named Origin, the second Becoming. These two fashion the third, named Debt.” They represent the inescapable law of cause and effect. Though they have usually been roughly translated as Past, Present, and Future, the dynamic concept in the Edda is more complete and philosophically exact. The third root of the world tree reaches to the well of the “wise giant Mimer,” owner of the well of wisdom. Mimer represents material existence and supplies the wisdom gained from experience of life. Odin forfeited one eye for the privilege of partaking of these waters of life, hence he is represented in manifestation as one-eyed and named Half-Blind. Mimer, the matter-counterpart, at the same time receives partial access to divine vision.

The lays make it very clear that the purpose of existence is for the consciousness-aspect of all beings to gain wisdom through life, while inspiring the substantial side of itself to growth in inward awareness and spirituality. At the human level, self-consciousness and will are aroused, making it possible for man to progress willingly and purposefully toward his divine potential, aided by the gods who have passed that way before him, rather than to drift by slow degrees and many detours along the road of inevitable evolution. Odin’s instructions to a disciple, Loddfafner, the dwarf-nature in man, conclude with:

Now is sung the High One’s song in the High One’s hall. Useful to sons of men, useless to sons of giants. Hail Him who sang! Hail him who kens! Rejoice they who understand! Happy they who heed!

Thermodynamics of Creation. Note Quote.

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Just like the early-time cosmic acceleration associated with inflation, a negative pressure can be seen as a possible driving mechanism for the late-time accelerated expansion of the Universe as well. One of the earliest alternatives that could provide a mechanism producing such accelerating phase of the Universe is through a negative pressure produced by viscous or particle production effects. The viscous pressure contributions can be seen as small nonequilibrium contributions for the energy-momentum tensor for nonideal fluids.

Let us posit the thermodynamics of matter creation for a single fluid. To describe the thermodynamic states of a relativistic simple fluid we use the following macroscopic variables: the energy-momentum tensor Tαβ ; the particle flux vector Nα; and the entropy flux vector sα. The energy-momentum tensor satisfies the conservation law, Tαβ = 0, and here we consider situations in which it has the perfect-fluid form

Tαβ = (ρ+P)uαuβ − P gαβ

In the above equation ρ is the energy density, P is the isotropic dynamical pressure, gαβ is the metric tensor and uα is the fluid four-velocity (with normalization uαuα = 1).

The dynamical pressure P is decomposed as

P = p + Π

where p is the equilibrium (thermostatic) pressure and Π is a term present in scalar dissipative processes. Usually, it is associated with the so-called bulk pressure. In the cosmological context, besides this meaning, Π can also be relevant when particle number is not conserved. In this case, Π ≡ pc is called the “creation pressure”. The bulk pressure,  can be seen as a correction to the thermostatic pressure when near to equilibrium, thus, it should be always smaller than the thermostatic pressure, |Π| < p. This restriction, however, does not apply for the creation pressure. So, when we have matter creation, the total pressure P may become negative and, in principle, drive an accelerated expansion.

The particle flux vector is assumed to have the following form

Nα = nuα

where n is the particle number density. Nα satisfies the balance equation Nα = nΓ, where Γ is the particle production rate. If Γ > 0, we have particle creation, particle destruction occurs when Γ < 0 and if Γ = 0 particle number is conserved.

The entropy flux vector is given by

sα = nσuα

where σ is the specific (per particle) entropy. Note that the entropy must satisfy the second law of thermodynamics sα ≥ 0. Here we consider adiabatic matter creation, that is, we analyze situations in which σ is constant. With this condition, by using the Gibbs relation, it follows that the creation pressure is related to Γ by

pc = − (ρ+p)/3H Γ

where H = a ̇/a is the Hubble parameter, a is the scale factor of the Friedmann-Robertson-Walker (FRW) metric and the overdot means differentiation with respect to the cosmic time. If σ is constant, the second law of thermodynamics implies that Γ ≥ 0 and, as a consequence, particle destruction (Γ < 0) is thermodynamically forbidden. Since Γ ≥ 0, it follows that, in an expanding universe (H > 0), the creation pressure pc cannot be positive.

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.

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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.

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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.

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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.

 

Topological Drifts in Deleuze. Note Quote.

Brion Gysin: How do you get in… get into these paintings?

William Burroughs: Usually I get in by a port of entry, as I call it. It is often a face through whose eyes the picture opens into a landscape and I go literally right through that eye into that landscape. Sometimes it is rather like an archway… a number of little details or a special spot of colours makes the port of entry and then the entire picture will suddenly become a three-dimensional frieze in plaster or jade or some other precious material.

The word fornix means “an archway” or “vault” (in Rome, prostitutes could be solicited there). More directly, fornicatio means “done in the archway”; thus a euphemism for prostitution.

Diagrammatic praxis proposes a contractual (push, pull) approach in which the movement between abstract machine, biogram (embodied, inflected diagram), formal diagram (drawing of, drawing off) and artaffect (realized thing) is topologically immanent. It imagines the practice of writing, of this writing, interleaved with the mapping processes with which it folds and unfolds – forming, deforming and reforming both processes. The relations of non-relations that power the diagram, the thought intensities that resonate between fragments, between content ad expression, the seeable and the sayable, the discursive and the non-discursive, mark entry points; portals of entry through which all points of the diagram pass – push, pull, fold, unfold – without the designation of arrival and departure, without the input/output connotations of a black boxed confection. Ports, as focal points of passage, attract lines of resistance or lines of flight through which the diagram may become both an effectuating concrete assemblage (thing) and remain outside the stratified zone of the audiovisual. It’s as if the port itself is a bifurcating point, a figural inflected archway. The port, as a bifurcation point of resistance (contra black box), modulates and changes the unstable, turbulent interplay between pure Matter and pure Function of the abstract machine. These ports are marked out, localized, situated, by the continuous movement of power-relations:

These power-relations … simultaneously local, unstable and diffuse, do not emanate from a central point or unique locus of sovereignty, but at each moment move from one point to another in a field of forces, marking inflections, resistances, twists and turns when one changes direction or retraces one’s steps… (Gilles Deleuze, Sean Hand-Foucault)

An inflection point, marked out by the diagram, is not a symmetrical form but the difference between concavity and convexity, a pure temporality, a “true atom of form, the true object of geography.” (Bernard Cache)

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Figure: Left: A bifurcating event presented figurally as an archway, a port of entry through order and chaos. Right: Event/entry with inflexion points, points of suspension, of pure temporality, that gives a form “of an absolute exteriority that is not even the exteriority of any given interiority, but which arise from that most interior place that can be perceived or even conceived […] that of which the perceiving itself is radically temporal or transitory”. The passing through of passage.

Cache’s absolute exteriority is equivalent to Deleuze’s description of the Outside “more distant than any exterior […] ‘twisted’, folded and doubled by an Inside that is deeper than any interior, and alone creates the possibility of the derived relation between the interior and the exterior”. This folded and doubled interior is diagrammed by Deleuze in the folds chapter of Foucault.

Thinking does not depend on a beautiful interiority that reunites the visible ad articulable elements, but is carried under the intrusion of an outside that eats into the interval and forces or dismembers the internal […] when there are only environments and whatever lies betwen them, when words and things are opened up by the environment without ever coinciding, there is a liberation of forces which come from the outside and exist only in a mixed up state of agitation, modification and mutation. In truth they are dice throws, for thinking involves throwing the dice. If the outside, farther away than any external world, is also closer than any internal world, is this not a sign that thought affects itself, by revealing the outside to be its own unthought element?

“It cannot discover the unthought […] without immediately bringing the unthought nearer to itself – or even, perhaps, without pushing it farther away, and in any case without causing man’s own being to undergo a change by the very fact, since it is deployed in the distance between them” (Gilles Deleuze, Sean Hand-Foucault)

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Figure: Left: a simulation of Deleuze’s central marking in his diagram of the Foucaultian diagram. This is the line of the Outside as Fold. Right: To best express the relations of diagrammatic praxis between content and expression (theory and practice) the Fold figure needs to be drawn as a double Fold (“twice twice” as Massumi might say) – a folded möbius strip. Here the superinflections between inside/outside and content/expression provide transversal vectors.

A topology or topological becoming-shapeshift retains its connectivity, its interconnectedness to preserve its autonomy as a singularity. All the points of all its matter reshape as difference in itself. A topology does not resemble itself. The möbius strip and the infamous torus-to-coffe cup are examples of 2d and 3d topologies. technically a topological surface is totalized, it can not comprise fragments cut or glued to produce a whole. Its change is continuous. It is not cut-copy-pasted. But the cut and its interval are requisite to an emergent new.

For Deleuze, the essence of meaning, the essence of essence, is best expressed in two infinitives; ‘to cut ” and “to die” […] Definite tenses keeping company in time. In the slash between their future and their past: “to cut” as always timeless and alone (Massumi).

Add the individuating “to shift” to the infinitives that reside in the timeless zone of indetermination of future-past. Given the paradigm of the topological-becoming, how might we address writing in the age of copy-paste and hypertext? The seamless and the stitched? As potential is it diagram? A linguistic multiplicity whose virtual immanence is the metalanguage potentiality between the phonemes that gives rise to all language?

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An overview diagram of diagrammatic praxis based on Deleuze’s diagram of the Foucaultian model shown below. The main modification is to the representation of the Fold. In the top figure, the Fold or zone of subjectification becomes a double-folded möbius strip.

Four folds of subjectification:

1. material part of ourselves which is to be surrounded and folded

2. the fold of the relation between forces always according to a particular rule that the relation between forces is bent back in order to become a relation to oneself (rule ; natural, divine, rational, aesthetic, etc)

3. fold of knowledge constitutes the relation of truth to our being and our being to truth which will serve as the formal condition for any kind of knowledge

4. the fold of the outside itself is the ultimate fold: an ‘interiority of expectation’ from which the subject, in different ways, hopes for immortality, eternity, salvation, freedom or death or detachment.

Diagrammatic Political Via The Exaptive Processes

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The principle of individuation is the operation that in the matter of taking form, by means of topological conditions […] carries out an energy exchange between the matter and the form until the unity leads to a state – the energy conditions express the whole system. Internal resonance is a state of the equilibrium. One could say that the principle of individuation is the common allagmatic system which requires this realization of the energy conditions the topological conditions […] it can produce the effects in all the points of the system in an enclosure […]

This operation rests on the singularity or starting from a singularity of average magnitude, topologically definite.

If we throw in a pinch of Gilbert Simondon’s concept of transduction there’s a basis recipe, or toolkit, for exploring the relational intensities between the three informal (theoretical) dimensions of knowledge, power and subjectification pursued by Foucault with respect to formal practice. Supplanting Foucault’s process of subjectification with Simondon’s more eloquent process of individuation marks an entry for imagining the continuous, always partial, phase-shifting resolutions of the individual. This is not identity as fixed and positionable, it’s a preindividual dynamic that affects an always becoming- individual. It’s the pre-formative as performative. Transduction is a process of individuation. It leads to individuated beings, such as things, gadgets, organisms, machines, self and society, which could be the object of knowledge. It is an ontogenetic operation which provisionally resolves incompatibilities between different orders or different zones of a domain.

What is at stake in the bigger picture, in a diagrammatic politics, is double-sided. Just as there is matter in expression and expression in matter, there is event-value in an  exchange-value paradigm, which in fact amplifies the force of its power relations. The economic engine of our time feeds on event potential becoming-commodity. It grows and flourishes on the mass production of affective intensities. Reciprocally, there are degrees of exchange-value in eventness. It’s the recursive loopiness of our current Creative Industries diagram in which the social networking praxis of Web 2.0 is emblematic and has much to learn.