(Il)liquid Hedge Lock-Ups. Thought of the Day 107.0

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Hedge funds have historically limited their participation in illiquid investments, preferring to match their investment horizon to the typical one-year lock-up periods that their investors agree to. However, many hedge funds have increasingly invested in illiquid assets in an effort to augment returns. For example, they have invested in private investments in public equity (PIPEs), acquiring large minority holdings in public companies. Their purchases of CDOs and CLOs (collateralized loan obligations) are also somewhat illiquid, since these fixed income securities are difficult to price and there is a limited secondary market during times of crisis. In addition, hedge funds have participated in loans, and invested in physical assets. Sometimes, investments that were intended to be held for less than one year have become long-term, illiquid assets when the assets depreciated and hedge funds decided to continue holding the assets until values recovered, rather than selling at a loss. It is estimated that more than 20% of total assets under management by hedge funds are illiquid, hard-to-price assets. This makes hedge fund asset valuation difficult, and has created a mismatch between hedge fund assets and liabilities, giving rise to significant problems when investors attempt to withdraw their cash at the end of lock-up periods.

Hedge funds generally focus their investment strategies on financial assets that are liquid and able to be readily priced based on reported prices in the market for those assets or by reference to comparable assets that have a discernible price. Since most of these assets can be valued and sold over a short period of time to generate cash, hedge funds permit investors to invest in or withdraw money from the fund at regular intervals and managers receive performance fees based on quarterly mark-to-market valuations. However, in order to match up maturities of assets and liabilities for each investment strategy, most hedge funds have the ability to prevent invested capital from being withdrawn during certain periods of time. They achieve this though “lock-up” and “gate” provisions that are included in investment agreements with their investors.

A lock-up provision provides that during an initial investment period of, typically, one to two years, an investor is not allowed to withdraw any money from the fund. Generally, the lock-up period is a function of the investment strategy that is being pursued. Sometimes, lock-up periods are modified for specific investors through the use of a side letter agreement. However, this can become problematic because of the resulting different effective lock-up periods that apply to different investors who invest at the same time in the same fund. Also, this can trigger “most favored nations” provisions in other investor agreements.

A gate is a restriction that limits the amount of withdrawals during a quarterly or semi- annual redemption period after the lock-up period expires. Typically gates are percentages of a fund’s capital that can be withdrawn on a scheduled redemption date. A gate of 10 to 20% is common. A gate provision allows the hedge fund to increase exposure to illiquid assets without facing a liquidity crisis. In addition, it offers some protection to investors that do not attempt to withdraw funds because if withdrawals are too high, assets might have to be sold by the hedge fund at disadvantageous prices, causing a potential reduction in investment returns for remaining investors. During 2008 and 2009, as many hedge fund investors attempted to withdraw money based on poor returns and concerns about the financial crisis, there was considerable frustration and some litigation directed at hedge fund gate provisions.

Hedge funds sometimes use a “side pocket” account to house comparatively illiquid or hard-to-value assets. Once an asset is designated for inclusion in a side pocket, new investors don’t participate in the returns from this asset. When existing investors withdraw money from the hedge fund, they remain as investors in the side pocket asset until it either is sold or becomes liquid through a monetization event such as an IPO. Management fees are typically charged on side pocket assets based on their cost, rather than a mark-to-market value of the asset. Incentive fees are charged based on realized proceeds when the asset is sold. Usually, there is no requirement to force the sale of side pocket investments by a specific date. Sometimes, investors accuse hedge funds of putting distressed assets that were intended to be sold during a one-year horizon into a side pocket account to avoid dragging down the returns of the overall fund. Investors are concerned about unexpected illiquidity arising from a side pocket and the potential for even greater losses if a distressed asset that has been placed there continues to decline in value. Fund managers sometimes use even more drastic options to limit withdrawals, such as suspending all redemption rights (but only in the most dire circumstances).

Velocity of Money

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The most basic difference between the demand theory of money and exchange theory of money lies in the understanding of quantity equation

M . v = P . Y —– (1)

Here M is money supply, P is price and Y is real output; in addition, v is constant velocity of money. The demand theory understands that (1) reflects the needs of the economic individual for money, not only the meaning of exchange. Under the assumption of liquidity preference, the demand theory introduces nominal interest rate into demand function of money, thus exhibiting more economic pictures than traditional quantity theory does. Let us, however concentrate on the economic movement through linearization of exchange theory emphasizing exchange medium function of money.

Let us assume that the central bank provides a very small supply M of money, which implies that the value PY of products manufactured by the producer will be unable to be realized only through one transaction. The producer has to suspend the transaction until the purchasers possess money at hand again, which will elevate the transaction costs and even result in the bankruptcy of the producer. Then, will the producer do nothing and wait for the bankruptcy?

In reality, producers would rather adjust sales value through raising or lowering the price or amount of product to attempt the realization of a maximal sales value M than reserve the stock of products to subject the sale to the limit of velocity of money. In other words, producer would adjust price or real output to control the velocity of money, since the velocity of money can influence the realization of the product value.

Every time money changes hands, a transaction is completed; thus numerous turnovers of money for an individual during a given period of time constitute a macroeconomic exchange ∑ipiYi if the prices pi can be replaced by an average price P, then we can rewrite the value of exchange as ∑ipiYi = P . Y. In a real economy, the producer will manage to make P . Y close the money supply M as much as possible through adjusting the real output or its price.

For example, when a retailer comes to a strange community to sell her commodities, she always prefers to make a price through trial and error. If she finds that higher price can still promote the sales amount, then she will choose to continue raising the price until the sales amount less changes; on the other hand, if she confirms that lower price can create the more sales amount, then she will decrease the price of the commodity. Her strategy of pricing depends on price elasticity of demand for the commodity. However, the maximal value of the sales amount is determined by how much money the community can supply, thus the pricing of the retailer will make her sales close this maximal sale value, namely money for consumption of the community. This explains why the same commodity can always be sold at a higher price in the rich area.

Equation (1) is not an identical equation but an equilibrium state of exchange process in an economic system. Evidently, the difference M –  P . Y  between the supply of money and present sales value provides a vacancy for elevating sales value, in other words, the supply of money acts as the role of a carrying capacity for sales value. We assume that the vacancy is in direct proportion to velocity of increase of the sales value, and then derive a dynamical quantity equation

M(t) - P(t) . Y(t)  =  k . d[P(t) . Y(t)]/d(t) —– (2)

Here k is a positive constant and expresses a characteristic time with which the vacancy is filled. This is a speculated basic dynamical quantity equation of exchange by money. In reality, the money supply M(t) can usually be given; (2) is actually an evolution equation of sales value P(t)Y(t) , which can uniquely determine an evolving path of the price.

The role of money in (2) can be seen that money is only a medium of commodity exchange, just like the chopsticks for eating and the soap for washing. All needs for money are or will be order to carry out the commodity exchange. The behavior of holding money of the economic individuals implies a potential exchange in the future, whether for speculation or for the preservation of wealth, but it cannot directly determine the present price because every realistic price always comes from the commodity exchange, and no exchange and no price. In other words, what we are concerned with is not the reason of money generation, but form of money generation, namely we are concerned about money generation as a function of time rather than it as a function of income or interest rate. The potential needs for money which you can use various reasons to explain cannot contribute to price as long as the money does not participate in the exchange, thus the money supply not used to exchange will not occur in (2).

On the other hand, the change in money supply would result in a temporary vacancy of sales value, although sales value will also be achieved through exchanging with the new money supply at the next moment, since the price or sales volume may change. For example, a group of residents spend M(t) to buy houses of P(t)Y(t) through the loan at time t, evidently M(t) = P(t)Y(t). At time t+1, another group of residents spend M(t+1) to buy houses of P(t+1)Y(t+1) through the loan, and M(t+1) = P(t+1)Y(t+1). Thus, we can consider M(t+1) – M(t) as increase in money supply, and this increase can cause a temporary vacancy of sales value M(t+1) – P(t)Y(t). It is this vacancy that encourages sellers to try to maximize sales through adjusting the price by trial and error and also real estate developers to increase or decrease their housing production. Ultimately, new prices and production are produced and the exchange is completed at the level of M(t+1) = P(t+1)Y(t+1). In reality, the gap between M(t+1) and M(t) is often much smaller than the vacancy M(t+1) – P(t)Y(t), therefore we can approximately consider M(t+1) as M(t) if the money supply function M(t) is continuous and smooth.

However, it is necessary to emphasize that (2) is not a generation equation of demand function P(Y), which means (2) is a unique equation of determination of price (path), since, from the perspective of monetary exchange theory, the evolution of price depends only on money supply and production and arises from commodity exchange rather than relationship between supply and demand of products in the traditional economics where the meaning of the exchange is not obvious. In addition, velocity of money is not contained in this dynamical quantity equation, but its significance PY/M will be endogenously exhibited by the system.

Acausal Propagation. Thought of the Day 62.1

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Whereas the Proca theory is the unique local linear massive variant of Maxwell’s electromagnetism, the most famous massive gravity with 6∞3 degrees of freedom, the Freund-Maheshwari-Schonberg massive gravity, is just one member (albeit the best in some respects) of a 2-parameter family of massive theories of gravity, all of which satisfy universal coupling. Adding a mass term involves adding a term quadratic in the potential; higher-order (cubic, quartic, etc.) self-interaction terms might also be present. The nonlinearity of the Einstein tensor implies, in contrast to the electromagnetic case, that there is no obviously best choice for defining the gravitational potential. While any such definition requires a background metric ημν in order that the potential vanish when gravity is turned off (typically flat space-time), thus making massive theories bimetric, one can still choose among gμν − ημν , √-ggμν − √-ηημν, gμν − ημν and so on, as well as various nonlinear choices such as gμαηαβgβν − ημν. In some cases the availability of nonlinear field redefinitions might make some expressions that look like mass term + interaction term with one definition of the gravitational potential, appear as a pure quadratic mass term with another definition; nonetheless the Einstein tensor remains nonlinear, no matter what definition of the potential is used. By contrast, the linearity of the Maxwell field strength tensor makes it natural to have a mass term that is also linear in Aμ in the field equations (and hence quadratic in Aμ in the Lagrangian density). While one can explore introducing nonlinear algebraic terms in Aμ describing self-interactions in electromagnetism, such terms induce acausal propagation if not chosen carefully.

Potential Synapses. Thought of the Day 52.0

For a neuron to recognize a pattern of activity it requires a set of co-located synapses (typically fifteen to twenty) that connect to a subset of the cells that are active in the pattern to be recognized. Learning to recognize a new pattern is accomplished by the formation of a set of new synapses collocated on a dendritic segment.

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Figure: Learning by growing new synapses. Learning in an HTM neuron is modeled by the growth of new synapses from a set of potential synapses. A “permanence” value is assigned to each potential synapse and represents the growth of the synapse. Learning occurs by incrementing or decrementing permanence values. The synapse weight is a binary value set to 1 if the permanence is above a threshold.

Figure shows how we model the formation of new synapses in a simulated Hierarchical Temporal Memory (HTM) neuron. For each dendritic segment we maintain a set of “potential” synapses between the dendritic segment and other cells in the network that could potentially form a synapse with the segment. The number of potential synapses is larger than the number of actual synapses. We assign each potential synapse a scalar value called “permanence” which represents stages of growth of the synapse. A permanence value close to zero represents an axon and dendrite with the potential to form a synapse but that have not commenced growing one. A 1.0 permanence value represents an axon and dendrite with a large fully formed synapse.

The permanence value is incremented and decremented using a Hebbian-like rule. If the permanence value exceeds a threshold, such as 0.3, then the weight of the synapse is 1, if the permanence value is at or below the threshold then the weight of the synapse is 0. The threshold represents the establishment of a synapse, albeit one that could easily disappear. A synapse with a permanence value of 1.0 has the same effect as a synapse with a permanence value at threshold but is not as easily forgotten. Using a scalar permanence value enables on-line learning in the presence of noise. A previously unseen input pattern could be noise or it could be the start of a new trend that will repeat in the future. By growing new synapses, the network can start to learn a new pattern when it is first encountered, but only act differently after several presentations of the new pattern. Increasing permanence beyond the threshold means that patterns experienced more than others will take longer to forget.

HTM neurons and HTM networks rely on distributed patterns of cell activity, thus the activation strength of any one neuron or synapse is not very important. Therefore, in HTM simulations we model neuron activations and synapse weights with binary states. Additionally, it is well known that biological synapses are stochastic, so a neocortical theory cannot require precision of synaptic efficacy. Although scalar states and weights might improve performance, they are not required from a theoretical point of view.

Conjuncted: Gauge Theory

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Weyl introduced as a phase factor an exponential in which the phase α is preceded by the imaginary unit i, e.g., e+iqα(x), in the wave function for the wave equations (for instance, the Dirac equation is (iγμμ − m)ψ = 0). It is here that Weyl correctly formulated gauge theory as a symmetry principle from which electromagnetism could be derived. It had been shown that for a quantum theory of charged particles interacting with the electromagnetic field, invariance under a gauge transformation of the potentials required multiplication of the wave function by the now well-know phase factor. Yang cited Weyl’s gauge theory results as reported by Pauli as a source for Yang-Mills gauge theory; although Yang didn’t find out until much later that these were Weyl’s results. Moreover, Pauli did not explicitly mention Weyl’s geometric interpretation. It was only much after Yang and Mills published their article that Yang realized the connection between their work and geometry. Yang says

Excessive Subjective Transversalities. Thought of the Day 33.0

In other words, object and subject, in their mutual difference and reciprocal trajectories, emerge and re-emerge together, from transformation. The everything that has already happened is emergence, registered after its fact in a subject-object relation. Where there was classically and in modernity an external opposition between object and subject, there is now a double distinction internal to the transformation. 1) After-the-fact: subject-object is to emergence as stoppage is to process. 2) In-fact: “objective” and “subjective” are inseparable, as matter of transformation to manner of transformation… (Brian Massumi Deleuze Guattari and Philosophy of Expression)

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Massumi makes the case, after Simondon and Deleuze and Guattari, for a dynamic process of subjectivity in which subject and object are other but their relation is transformative to their terms. That relation is emergence. In Felix Guattari’s last book, Chaosmosis, he outlines the production of subjectivity as transversal. He states that subjectivity is

the ensemble of conditions which render possible the emergence of individual and/or collective instances as self-referential existential Territories, adjacent, or in a delimiting relation, to an alterity that is itself subjective.

This is the subject in excess (Simondon; Deleuze), overpowering the transcendental. The subject as constituted by all the forces that simultaneously impinge upon it; are in relation to it. Similarly, Simondon characterises this subjectivity as the transindividual, which refers to

a relation to others, which is not determined by a constituted subject position, but by pre-individuated potentials only experienced as affect (Adrian Mackenzie-Transductions_ bodies and machines at speed).

Equating this proposition to technologically enabled relations exerts a strong attraction on the experience of felt presence and interaction in distributed networks. Simondon’s principle of individuation, an ontogenetic process similar to Deleuze’s morphogenetic process, is committed to the guiding principle

of the conservation of being through becoming. This conservation is effected by means of the exchanges made between structure and process… (Simondon).

Or think of this as structure and organisation, which is autopoietic process; the virtual organisation of the affective interval. These leanings best situate ideas circulating through collectives and their multiple individuations. These approaches reflect one of Bergson’s lasting contributions to philosophical practice: his anti-dialectical methodology that debunks duality and the synthesised composite for a differentiated multiplicity that is also a unified (yet heterogeneous) continuity of duration. Multiplicities replace the transcendental concept of essences.

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.

 

Prometheus and Hinduism. Note Quote.

Prometheus: Yes, I caused mortals to cease foreseeing their doom.
Chorus: Of what sort was the cure that you found for this affliction?
Prometheus: I caused blind hopes to dwell within their breasts.
Chorus: A great benefit was this you gave to mortals.
Prometheus: In addition, I gave them fire.
Chorus: What! Do creatures of a day now have flame-eyed fire?
Prometheus: Yes, and from it they shall learn many arts.
Aeschylus, Prometheus Bound

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After the coming into being of the world, the stories tell us, everything had found its place. But one creature, capable of lofty thought, was still missing. When Kronos ruled Olympus, the deathless gods decided to fashion a golden race of mortal men. Knowing of the divine seed that slumbered in the Earth, only recently separated from the heavenly aether, Prometheus mixed clay and running water. He shaped this into likenesses of the all-controlling gods, including also qualities taken from all the animals. This is how the first humans came into existence. In the course of ages, after Zeus had banished the ancient gods to Tartarus, humans populated the Earth, but lumbered witless as if in a dream. They did not know how to see, hear, or understand, or how to create things with their hands. Prometheus’s empathy led him to steal for them the forbidden divine fire hidden by Zeus, which allowed him to teach them skills and sciences that used all their potentials.

Angered by the theft, Zeus plotted revenge on both humanity and its benefactor. He had Hephaestus, smith of the gods, create a beautiful virgin, Pandora, who was furnished with disastrous gifts by Athena, Aphrodite, and other gods. When a box she was carrying was opened on Earth, all evils and diseases escaped from it and spread among mankind. One single good thing, Hope, had not escaped when she clapped the lid closed. Meanwhile Prometheus was dragged to earth’s remotest wilderness and bound to a rock over a terrifying abyss with chains that could not be undone. Every day an eagle came and ate from his liver, which would regenerate each night. He endured this torment for centuries until the hero Hercules set him free.

This myth calls to mind stories of divine fire brought to mankind in many other traditions.

The allegory of the fire of Prometheus is another version of the rebellion of the proud Lucifer [“light-bringer”], who was hurled down to the bottomless pit, or simply unto our Earth, to live as man. The Hindu Lucifer, the Mahasura, is also said to have become envious of the Creator’s resplendent light, and, at the head of inferior Asuras (not gods, but spirits), to have rebelled against Brahma; for which Siva hurled him down to Patala. But, as philosophy goes hand in hand with allegorical fiction in Hindu myths, the devil is made to repent, and is afforded the oppor­tunity to progress.

Also in Hinduism are the Manasaputras or “sons of mind,” who brought mankind the fire of thought. In the Nordic Edda the name of the god Loki – a blood brother of Odin – comes from the old word liuhan, “to illuminate.”

What then is the inner significance behind these particular stories? Long ago the early human race had undergone a certain amount of evolution but “thinkers” had not yet been born: nature had succeeded in developing a suitable body but the soul-giving principle, the fire of self-conscious thought, had not yet been awakened. Adam and Eve, to a certain extent, existed in paradise without self-awareness. Like Lucifer, Prometheus is an allegorical representation of the incarnation of our higher self, the awakening of the active, self-reflective capacity for thought. This subject is therefore of the highest significance for human evolution.

It is owing to this rebellion of intellectual life against the morbid inactivity of pure spirit, that we are what we are — self-conscious, thinking men, with the capabilities and attributes of Gods in us, for good as much as for evil. Hence the rebels are our saviours. . . . It is only by the attractive force of the contrasts that the two opposites — Spirit and Matter — can be cemented on Earth, and, smelted in the fire of self-conscious experience and suffering, find themselves wedded in Eternity.

By the gods allying themselves with us for this period of development, it became possible for us to attain knowledge and wisdom. But why was Prometheus harshly punished? Other legends suggest a motive; for instance Genesis reports:

And the Lord God said, “The man has now become like one of us, knowing good and evil. He must not be allowed to reach out his hand and take also from the tree of life and eat, and live forever.” So the Lord God banished him from the Garden of Eden to work the ground from which he had been taken. After he drove the man out, he placed on the east side of the Garden of Eden cherubim and a flaming sword flashing back and forth to guard the way to the tree of life. – 3:22-4

As with Pandora’s box, all evil in this world arose from the joining of the spiritual with the human world. Many commentators see in this a question of guilt, but this misses the crux of the matter: Adam and Eve are driven out of paradise because, with the power of thought, there is no longer any paradise for them. The human being, equipped with the divine capacity for self-reflective thought, can use this newly-won strength to create or destroy, to accomplish wonderful things or great crimes. One day we will ascend again and establish a human race worthy of the gods, but there is still a long way to go in overcoming “I am I” (egoic awareness) to reach “I am” (universal consciousness).

This evolutionary process is also clearly reflected in symbolism. Spirit, represented by a vertical line, is linked with the material world, represented by a horizontal line. Together these give rise to the cross, the son or third logos. If this logos becomes active, as with the awakening capacity for thought through the incarnation of the higher self, then this cross begins to turn. The turning of the cross produces the swastika, a symbol found in many religions. Quite a number of terracotta discs were found under the ruins of ancient Troy that contained this symbol in two forms:  Svastika1 and Svastika2. Again, Pramantha, the Vedic divine carpenter, unites himself with Arani, nature or Maya (illusion). They produce the divine boy Agni, god of fire. In the Bible too, Joseph is a carpenter, a master builder, and Mary is very reminiscent of Maya. Their child is mankind, with the fire of self-aware thought bestowed by the Holy Spirit. The son of the creator nailed to the cross – is he not a symbol of this process that speaks the same clear language as the legend of Prometheus, spirit chained to the cross of matter? The Crucified Titan is the personified symbol of the collective Logos, the ‘Host’, and of the ‘Lords of Wisdom’ or the heavenly man, who incarnated in Humanity.

We are also told that the suffering of Prometheus – the “one who foresees” – will end. He who has sacrificed himself for mankind is redeemed out of pity by the demigod Hercules, a son of Zeus, despite the fact that he may not take off the indestructible chains (karma). Still, the vulture – our base nature – will no longer come to eat the Titan’s liver. Human mental development, accelerated by the incarnation of the higher self, became unbalanced, with physical and moral development unable to keep pace. Once we regain our inner equilibrium, we will recognize our true destiny and nature, release the god chained within us, and as mankind conquer the darkness of ignorance.

Dance of the Shiva, q’i (chee) and Tibetan Sunyata. Manifestation of Mysticism.

अनेजदेकं मनसो जवीयो नैनद्देवाप्नुवन्पूर्वमर्षत् ।
तद्धावतोऽन्यान्नत्येति तिष्ठत् तस्मिन्नापो मातरिश्वा दधाति ॥

anejadekaṃ manaso javīyo nainaddevāpnuvanpūrvamarṣat |
taddhāvato’nyānnatyeti tiṣṭhat tasminnāpo mātariśvā dadhāti ||

The self is one. It is unmoving: yet faster than the mind. Thus moving faster, It is beyond the reach of the senses. Ever steady, It outstrips all that run. By its mere presence, the cosmic energy is enabled to sustain the activities of living beings.

तस्मिन् मनसि ब्रह्मलोकादीन्द्रुतं गच्छति सति प्रथमप्राप्त इवात्मचैतन्याभासो गृह्यते अतः मनसो जवीयः इत्याह ।

tasmin manasi brahmalokādīndrutaṃ gacchati sati prathamaprāpta ivātmacaitanyābhāso gṛhyate ataḥ manaso javīyaḥ ityāha |

When the mind moves fast towards the farthest worlds such as the brahmaloka, it finds the Atman, of the nature of pure awareness, already there; hence the statement that It is faster than the mind.

नित्योऽनित्यानां चेतनश्चेतनानाम्
एको बहूनां यो विदधाति कामान् ।
तमात्मस्थं योऽनुपश्यन्ति धीराः
तेषां शान्तिः शाश्वतं नेतरेषाम् ॥

nityo’nityānāṃ cetanaścetanānām
eko bahūnāṃ yo vidadhāti kāmān |
tamātmasthaṃ yo’nupaśyanti dhīrāḥ
teṣāṃ śāntiḥ śāśvataṃ netareṣām ||

He is the eternal in the midst of non-eternals, the principle of intelligence in all that are intelligent. He is One, yet fulfils the desires of many. Those wise men who perceive Him as existing within their own self, to them eternal peace, and non else.

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Eastern mysticism approaches the manifestation of life in the cosmos and all that compose it from a position diametrically opposed to the view that prevailed until recently among the majority of Western scientists, philosophers, and religionists. Orientals see the universe as a whole, as an organism. For them all things are interconnected, links in a chain of beings permeated by consciousness which threads them together. This consciousness is the one life-force, originator of all the phenomena we know under the heading of nature, and it dwells within its emanations, urging them as a powerful inner drive to grow and evolve into ever more refined expressions of divinity. The One manifests, not only in all its emanations, but also through those emanations as channels: it is within them and yet remains transcendent as well.

The emphasis is on the Real as subject whereas in the West it is seen as object. If consciousness is the noumenal or subjective aspect of life in contrast to the phenomenal or objective — everything seen as separate objects — then only this consciousness can be experienced, and no amount of analysis can reveal the soul of Reality. To illustrate: for the ancient Egyptians, their numerous “gods” were aspects of the primal energy of the Divine Mind (Thoth) which, before the creation of our universe, rested, a potential in a subjective state within the “waters of Space.” It was through these gods that the qualities of divinity manifested.

A question still being debated runs: “How does the One become the many?” meaning: if there is a “God,” how do the universe and the many entities composing it come into being? This question does not arise among those who perceive the One to dwell in the many, and the many to live in the One from whom life and sustenance derive. Despite our Western separation of Creator and creation, and the corresponding distancing of “God” from human beings, Western mystics have held similar views to those of the East, e.g.: Meister Eckhart, the Dominican theologian and preacher, who was accused of blasphemy for daring to say that he had once experienced nearness to the “Godhead.” His friends and followers were living testimony to the charisma (using the word in its original connotation of spiritual magnetism) of those who live the life of love for fellow beings men like Johannes Tauler, Heinrich Suso, the “admirable Ruysbroeck,” who expressed views similar to those of Eastern exponents of the spiritual way or path.

In old China, the universe was described as appearing first as q’i (chee), an emanation of Light, not the physical light that we know, but its divine essence sometimes called Tien, Heaven, in contrast to Earth. The q’i energy polarized as Yang and Yin, positive and negative electromagnetism. From the action and interaction of these two sprang the “10,000 things”: the universe, our world, the myriads of beings and things as we perceive them to be. In other words, the ancient Chinese viewed our universe as one of process, the One energy, q’i, proliferating into the many.

In their paintings Chinese artists depict man as a small but necessary element in gigantic natural scenes. And since we are parts of the cosmos, we are embodiments of all its potentials and our relationship depends upon how we focus ourselves: (1) harmoniously, i.e., in accord with nature; or (2) disharmoniously, interfering with the course of nature. We therefore affect the rest: our environment, all other lives, and bear full responsibility for the outcome of our thoughts and acts, our motivations, our impacts. Their art students were taught to identify with what they were painting, because there is life in every thing, and it is this life with which they must identify, with boulders and rocks no less than with birds flying overhead. Matter, energy, space, are all manifestations of q’i and we, as parts thereof, are intimately connected with all the universe.

In India, the oneness of life was seen through the prism of successive manifestations of Brahman, a neuter or impersonal term in Sanskrit for divinity, the equivalent of what Eckhart called the Godhead. Brahman is the source of the creative power, Brahma, Eckhart’s Creator; and also the origin of the sustaining and supporting energy or Vishnu, and of the destructive/regenerative force or Siva. As these three operate through the cosmos, the “world” as we know it, so do they also through ourselves on a smaller scale according to our capacity. Matter is perceived to be condensed energy, Chit or consciousness itself. To quote from the Mundaka Upanishad:

By the energism of Consciousness Brahman is massed; from that: Matter is born and from Matter Life and Mind and the worlds . . .

In another Hindu scripture, it is stated that when Brahma awakened from his period of rest between manifestations, he desired to contemplate himself as he is. By gazing into the awakening matter particles as into a mirror, he stirred them to exhibit their latent divine qualities. Since this process involves a continuous unfoldment from the center within, an ever-becoming, there can never be an end to the creativity — universal “days” comprising trillions of our human years, followed by a like number of resting “nights.”

We feel within ourselves the same driving urge to grow that runs through the entire, widespread universe, to express more and more of what is locked up in the formless or subjective realm of Be-ness, awaiting the magic moment to come awake in our phase of life.

Tibetan metaphysics embraces all of this in discussing Sunyata, which can be viewed as Emptiness if we use only our outer senses, or as Fullness if we inwardly perceive it to be full of energies of limitless ranges of wave-lengths/frequencies. This latter aspect of Space is the great mother of all, ever fecund, from whose “heart” emerge endless varieties of beings, endless forces, ever-changing variations — like the pulsing energies the new physicists perceive nuclear subparticles to be.

In the Preface to his Tao of physics Fritjof Capra tells how one summer afternoon he had a transforming experience by the seashore as he watched the waves rolling in and felt the rhythm of his own breathing. He saw dancing motes revealed in a beam of sunlight; particles of energy vibrating as molecules and atoms; cascades of energy pouring down upon us from outer space. All of this coming and going, appearing and disappearing, he equated with the Indian concept of the dance of Siva . . . he felt its rhythm, “heard” its sound, and knew himself to be a part of it. Through this highly personal, indeed mystical, experience Capra became aware of his “whole environment as being engaged in a gigantic cosmic dance.”

This is the gist of the old Chinese approach to physics: students were taught gravitation by observing the petals of a flower as they fall gracefully to the ground. As Gary Zukav expresses it in his Dancing Wu Li Masters: An Overview of the New Physics:

The world of particle physics is a world of sparkling energy forever dancing with itself in the form of its particles as they twinkle in and out of existence, collide, transmute, and disappear again.

That is: the dance of Siva is the dance of attraction and repulsion between charged particles of the electromagnetic force. This is a kind of “transcendental” physics, going beyond the “world of opposites” and approaching a mystical view of the larger Reality that is to our perceptions an invisible foundation of what we call “physical reality.” It is so far beyond the capacity or vocabulary of the mechanically rational part of our mind to define, that the profound Hindu scripture Isa Upanishad prefers to suggest the thought by a paradox:

तदेजति तन्नैजति तद्दूरे तद्वन्तिके ।
तदन्तरस्य सर्वस्य तदु सर्वस्यास्य बाह्यतः ॥

tadejati tannaijati taddūre tadvantike |
tadantarasya sarvasya tadu sarvasyāsya bāhyataḥ ||

It moves. It moves not.  It is far, and it is near. It is within all this, And It is verily outside of all this.

Indeed, there is a growing recognition mostly by younger physicists that consciousness is more than another word for awareness, more than a by-product of cellular activity (or of atomic or subatomic vibrations). For instance, Jack Sarfatti, a quantum physicist, says that signals pulsating through space provide instant communication between all parts of the cosmos. “These signals can be likened to pulses of nerve cells of a great cosmic brain that permeates all parts of space (Michael Talbot, Mysticism and the New Physics).” Michael Talbot quotes Sir James Jeans’ remark, “the universe is more like a giant thought than a giant machine,” commenting that the “substance of the great thought is consciousness” which pervades all space. Or as Schrödinger would have it:

Consciouness is never experienced in the plural, only in the singular….Consciouness is a singular of which the plural is unknown; that; there is only one thing and that, what seems to be a plurality is merely a series of different aspects of this one thing, produced by a deception (the Indian Maya).

Other phenomena reported as occurring in the cosmos at great distances from each other, yet simultaneously, appear to be connected in some way so far unexplained, but to which the term consciousness has been applied.

In short, the mystic deals with direct experience; the intuitive scientist is open-minded, and indeed the great discoveries such as Einstein’s were made by amateurs in their field untrammeled by prior definitions and the limitations inherited from past speculations. This freedom enabled them to strike out on new paths that they cleared and paved. The rationalist tries to grapple with the problems of a living universe using only analysis and whatever the computer functions of the mind can put together.

The theosophic perspective upon universal phenomena is based on the concept of the ensoulment of the cosmos. That is: from the smallest subparticle we know anything about to the largest star-system that has been observed, each and all possess at their core vitality, energy, an active something propelling towards growth, evolution of faculties from within.

The only “permanent” in the whole universe is motion: unceasing movement, and the ideal perception is a blend of the mystical with the scientific, the intuitive with the rational.

Priest’s Razor: Metaphysics. Note Quote.

Quantum-Physics-and-Metaphysics

The very idea that some mathematical piece employed to develop an empirical theory may furnish us information about unobservable reality requires some care and philosophical reflection. The greatest difficulty for the scientifically minded metaphysician consists in furnishing the means for a “reading off” of ontology from science. What can come in, and what can be left out? Different strategies may provide for different results, and, as we know, science does not wear its metaphysics on its sleeves. The first worry may be making the metaphysical piece compatible with the evidence furnished by the theory.

The strategy adopted by da Costa and de Ronde may be called top-down: investigating higher science and, by judging from the features of the objects described by the theory, one can look for the appropriate logic to endow it with just those features. In this case (quantum mechanics), there is the theory, apparently attributing contradictory properties to entities, so that a logic that does cope with such feature of objects is called forth. Now, even though we believe that this is in great measure the right methodology to pursue metaphysics within scientific theories, there are some further methodological principles that also play an important role in these kind of investigation, principles that seem to lessen the preferability of the paraconsistent approach over alternatives.

To begin with, let us focus on the paraconsistent property attribution principle. According to this principle, the properties corresponding to the vectors in a superposition are all attributable to the system, they are all real. The first problem with this rendering of properties (whether they are taken to be actual or just potential) is that such a superabundance of properties may not be justified: not every bit of a mathematical formulation of a theory needs to be reified. Some of the parts of the theory are just that: mathematics required to make things work, others may correspond to genuine features of reality. The greatest difficulty is to distinguish them, but we should not assume that every bit of it corresponds to an entity in reality. So, on the absence of any justified reason to assume superpositions as a further entity on the realms of properties for quantum systems, we may keep them as not representing actual properties (even if merely possible or potential ones).

That is, when one takes into account other virtues of a metaphysical theory, such as economy and simplicity, the paraconsistent approach seems to inflate too much the population of our world. In the presence of more economical candidates doing the same job and absence of other grounds on which to choose the competing proposals, the more economical approaches take advantage. Furthermore, considering economy and the existence of theories not postulating contradictions in quantum mechanics, it seems reasonable to employ Priest’s razor – the principle according to which one should not assume contradictions beyond necessity – and stick with the consistent approaches. Once again, a useful methodological principle seems to deem the interpretation of superposition as contradiction as unnecessary.

The paraconsistent approach could take advantage over its competitors, even in the face of its disadvantage in order to accommodate such theoretical virtues, if it could endow quantum mechanics with a better understanding of quantum phenomena, or even if it could add some explanatory power to the theory. In the face of some such kind of gain, we could allow for some ontological extravagances: in most cases explanatory power rules over matters of economy. However, it does not seem that the approach is indeed going to achieve some such result.

Besides that lack of additional explanatory power or enlightenment on the theory, there are some additional difficulties here. There is a complete lack of symmetry with the standard case of property attribution in quantum mechanics. As it is usually understood, by adopting the minimal property attribution principle, it is not contentious that when a system is in one eigenstate of an observable, then we may reasonably infer that the system has the property represented by the associated observable, so that the probability of obtaining the eigenvalue associated is 1. In the case of superpositions, if they represented properties of their own, there is a complete disanalogy with that situation: probabilities play a different role, a system has a contradictory property attributed by a superposition irrespective of probability attribution and the role of probabilities in determining measurement outcomes. In a superposition, according to the proposal we are analyzing, probabilities play no role, the system simply has a given contradictory property by the simple fact of being in a (certain) superposition.

For another disanalogy with the usual case, one does not expect to observe a sys- tem in such a contradictory state: every measurement gives us a system in particular state, never in a superposition. If that is a property in the same foot as any other, why can’t we measure it? Obviously, this does not mean that we put measurement as a sign of the real, but when doubt strikes, it may be a good advice not to assume too much on the unobservable side. As we have observed before, a new problem is created by this interpretation, because besides explaining what is it that makes a measurement give a specific result when the system measured is in a superposition (a problem usually addressed by the collapse postulate, which seems to be out of fashion now), one must also explain why and how the contradictory properties that do not get actualized vanish. That is, besides explaining how one particular property gets actual, one must explain how the properties posed by the system that did not get actual vanish.

Furthermore, even if states like 1/√2 (| ↑x ⟩ + | ↓x ⟩) may provide for an example of a  candidate of a contradictory property, because the system seems to have both spin up and down in a given direction, there are some doubts when the distribution of probabilities is different, in cases such as 2/√7 | ↑x ⟩ + √(3/7) | ↓x ⟩. What are we to think about that? Perhaps there is still a contradiction, but it is a little more inclined to | ↓x⟩ than to | ↑x⟩? That is, it is difficult to see how a contradiction arises in such cases. Or should we just ignore the probabilities and take the states composing the superposition as somehow opposed to form a contradiction anyway? That would put metaphysics way too much ahead of science, by leaving the role of probabilities unexplained in quantum mechanics in order to allow a metaphysical view of properties in.