Politics of Teleonomies of Blockchain…Thought of the Day 155.0

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All of this starts with the dictum, “There are no men at work”.

The notion of blockchain is a decentralized polity. Blockchain is immutable, for once written on to the block, it is practically un-erasable. And most importantly, it is collateralized, in that, even if there is a lack thereof of physical assets, the digital ownership could be traded as a collateral. So, once you have a blockchain, you create a stack that could be database controlled using a Virtual Machine, think of it as some sort of digital twin. So, what exactly are the benefits of this decentralized digital polity? One crucial is getting rid of intermediaries (unless, one considers escrow accounts as an invisible intermediary!, which seldom fulfills the definitional criteria). So, in short, digital twinning helps further social scalability by getting intermediaries o to an invisible mode. Now, when blockchains are juxtaposed with algorithmically run machines (AI is just one branch of it), one gets the benefits of social scalability with analytics, the ever-increasing ocean of raw data hermeneutically sealed into information for utilitarian purposes. The advantages of decentralized polity and social scalability compiles for a true democratic experience in an open-sourced modeling, where netizens (since we still are mired in the controversy of net neutrality) experience participatory democracy.
How would these combine with exigencies of scarce nature or resources? It is here that such hackathons combine the ingenuity of blockchain with AI in a process generally referred to as “mining”. This launch from the nature as we know is Nature 2.0. To repeat, decentralized polity and social scalability creates a self-sustaining ecosystem in a sense of Anti-Fragility (yes, Taleb’s anti-fragile is a feedback into this) with autonomously created machine learning systems that are largely correctional in nature on one hand and improving learning capacities from the environment on the other. These two hands coordinate giving rise to resource manipulation in lending a synthetic definition of materialities taken straight from physics textbooks and scared-to-apprehend materialities as thermodynamic quotients. And this is where AI steams up in a grand globalized alliance of machines embodying agencies always looking for cognitive enhancements to fulfill teleonomic life derived from the above stated thermodynamic quotient of randomness and disorder into gratifying sensibilities of self-sustenance. Synthetic biologists (of the Craig Venter and CRISPR-like lines) call this genetic programming, whereas singularitarians term it as evolution, a break away from simulated evolution that defined initial days of AI. The synthetic life is capable of decision making, the more it is subjected to the whims and fancies of surrounding environment via the process of machine learning leading to autonomous materialities with cognitive capabilities. These are parthenogenetic machines with unencumbered networking capacities. Such is the advent of self-ownership, and taking it to mean to nature as we have hitherto known is a cathectic fallacy in ethics. Taking to mean it differently in a sense of establishing a symbiotic relationship between biology and machines to yield bio machines with characteristics of biomachinations, replication (reproduction, CC and CV to be thrown open for editing via genetic programming) and self-actualization is what blockchain in composite with AI and Synthetic Biology is Nature 2.0.
Yes, there are downsides to traditional mannerisms of thought, man playing god with nature and so on and so on…these are ethical constraints and thus political in undertones, but with conservative theoretics and thus unable to come to terms with the politics of resource abundance that the machinic promulgates…

Adjacency of the Possible: Teleology of Autocatalysis. Thought of the Day 140.0

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Given a network of catalyzed chemical reactions, a (sub)set R of such reactions is called:

  1. Reflexively autocatalytic (RA) if every reaction in R is catalyzed by at least one molecule involved in any of the reactions in R;
  2. F-generated (F) if every reactant in R can be constructed from a small “food set” F by successive applications of reactions from R;
  3. Reflexively autocatalytic and F-generated (RAF) if it is both RA and F.

The food set F contains molecules that are assumed to be freely available in the environment. Thus, an RAF set formally captures the notion of “catalytic closure”, i.e., a self-sustaining set supported by a steady supply of (simple) molecules from some food set….

Stuart Kauffman begins with the Darwinian idea of the origin of life in a biological ‘primordial soup’ of organic chemicals and investigates the possibility of one chemical substance to catalyze the reaction of two others, forming new reagents in the soup. Such catalyses may, of course, form chains, so that one reagent catalyzes the formation of another catalyzing another, etc., and self-sustaining loops of reaction chains is an evident possibility in the appropriate chemical environment. A statistical analysis would reveal that such catalytic reactions may form interdependent networks when the rate of catalyzed reactions per molecule approaches one, creating a self-organizing chemical cycle which he calls an ‘autocatalytic set’. When the rate of catalyses per reagent is low, only small local reaction chains form, but as the rate approaches one, the reaction chains in the soup suddenly ‘freeze’ so that what was a group of chains or islands in the soup now connects into one large interdependent network, constituting an ‘autocatalytic set’. Such an interdependent reaction network constitutes the core of the body definition unfolding in Kauffman, and its cyclic character forms the basic precondition for self-sustainment. ‘Autonomous agent’ is an autocatalytic set able to reproduce and to undertake at least one thermodynamic work cycle.

This definition implies two things: reproduction possibility, and the appearance of completely new, interdependent goals in work cycles. The latter idea requires the ability of the autocatalytic set to save energy in order to spend it in its own self-organization, in its search for reagents necessary to uphold the network. These goals evidently introduce a – restricted, to be sure – teleology defined simply by the survival of the autocatalytic set itself: actions supporting this have a local teleological character. Thus, the autocatalytic set may, as it evolves, enlarge its cyclic network by recruiting new subcycles supporting and enhancing it in a developing structure of subcycles and sub-sub-cycles. 

Kauffman proposes that the concept of ‘autonomous agent’ implies a whole new cluster of interdependent concepts. Thus, the autonomy of the agent is defined by ‘catalytic closure’ (any reaction in the network demanding catalysis will get it) which is a genuine Gestalt property in the molecular system as a whole – and thus not in any way derivable from the chemistry of single chemical reactions alone.

Kauffman’s definitions on the basis of speculative chemistry thus entail not only the Kantian cyclic structure, but also the primitive perception and action phases of Uexküll’s functional circle. Thus, Kauffman’s definition of the organism in terms of an ‘autonomous agent’ basically builds on an Uexküllian intuition, namely the idea that the most basic property in a body is metabolism: the constrained, organizing processing of high-energy chemical material and the correlated perception and action performed to localize and utilize it – all of this constituting a metabolic cycle coordinating the organism’s in- and outside, defining teleological action. Perception and action phases are so to speak the extension of the cyclical structure of the closed catalytical set to encompass parts of its surroundings, so that the circle of metabolism may only be completed by means of successful perception and action parts.

The evolution of autonomous agents is taken as the empirical basis for the hypothesis of a general thermodynamic regularity based on non-ergodicity: the Big Bang universe (and, consequently, the biosphere) is not at equilibrium and will not reach equilibrium during the life-time of the universe. This gives rise to Kauffman’s idea of the ‘adjacent possible’. At a given point in evolution, one can define the set of chemical substances which do not exist in the universe – but which is at a distance of one chemical reaction only from a substance already existing in the universe. Biological evolution has, evidently, led to an enormous growth of types of organic macromolecules, and new such substances come into being every day. Maybe there is a sort of chemical potential leading from the actually realized substances and into the adjacent possible which is in some sense driving the evolution? In any case, Kauffman claims the hypothesis that the biosphere as such is supercritical in the sense that there is, in general, more than one action catalyzed by each reagent. Cells, in order not to be destroyed by this chemical storm, must be internally subcritical (even if close to the critical boundary). But if the biosphere as such is, in fact, supercritical, then this distinction seemingly a priori necessitates the existence of a boundary of the agent, protecting it against the environment.

Momentum of Accelerated Capital. Note Quote.

high-frequency-trading

Distinct types of high frequency trading firms include independent proprietary firms, which use private funds and specific strategies which remain secretive, and may act as market makers generating automatic buy and sell orders continuously throughout the day. Broker-dealer proprietary desks are part of traditional broker-dealer firms but are not related to their client business, and are operated by the largest investment banks. Thirdly hedge funds focus on complex statistical arbitrage, taking advantage of pricing inefficiencies between asset classes and securities.

Today strategies using algorithmic trading and High Frequency Trading play a central role on financial exchanges, alternative markets, and banks‘ internalized (over-the-counter) dealings:

High frequency traders typically act in a proprietary capacity, making use of a number of strategies and generating a very large number of trades every single day. They leverage technology and algorithms from end-to-end of the investment chain – from market data analysis and the operation of a specific trading strategy to the generation, routing, and execution of orders and trades. What differentiates HFT from algorithmic trading is the high frequency turnover of positions as well as its implicit reliance on ultra-low latency connection and speed of the system.

The use of algorithms in computerised exchange trading has experienced a long evolution with the increasing digitalisation of exchanges:

Over time, algorithms have continuously evolved: while initial first-generation algorithms – fairly simple in their goals and logic – were pure trade execution algos, second-generation algorithms – strategy implementation algos – have become much more sophisticated and are typically used to produce own trading signals which are then executed by trade execution algos. Third-generation algorithms include intelligent logic that learns from market activity and adjusts the trading strategy of the order based on what the algorithm perceives is happening in the market. HFT is not a strategy per se, but rather a technologically more advanced method of implementing particular trading strategies. The objective of HFT strategies is to seek to benefit from market liquidity imbalances or other short-term pricing inefficiencies.

While algorithms are employed by most traders in contemporary markets, the intense focus on speed and the momentary holding periods are the unique practices of the high frequency traders. As the defence of high frequency trading is built around the principles that it increases liquidity, narrows spreads, and improves market efficiency, the high number of trades made by HFT traders results in greater liquidity in the market. Algorithmic trading has resulted in the prices of securities being updated more quickly with more competitive bid-ask prices, and narrowing spreads. Finally HFT enables prices to reflect information more quickly and accurately, ensuring accurate pricing at smaller time intervals. But there are critical differences between high frequency traders and traditional market makers:

  1. HFT do not have an affirmative market making obligation, that is they are not obliged to provide liquidity by constantly displaying two sides quotes, which may translate into a lack of liquidity during volatile conditions.
  2. HFT contribute little market depth due to the marginal size of their quotes, which may result in larger orders having to transact with many small orders, and this may impact on overall transaction costs.
  3. HFT quotes are barely accessible due to the extremely short duration for which the liquidity is available when orders are cancelled within milliseconds.

Besides the shallowness of the HFT contribution to liquidity, are the real fears of how HFT can compound and magnify risk by the rapidity of its actions:

There is evidence that high-frequency algorithmic trading also has some positive benefits for investors by narrowing spreads – the difference between the price at which a buyer is willing to purchase a financial instrument and the price at which a seller is willing to sell it – and by increasing liquidity at each decimal point. However, a major issue for regulators and policymakers is the extent to which high-frequency trading, unfiltered sponsored access, and co-location amplify risks, including systemic risk, by increasing the speed at which trading errors or fraudulent trades can occur.

Although there have always been occasional trading errors and episodic volatility spikes in markets, the speed, automation and interconnectedness of today‘s markets create a different scale of risk. These risks demand that exchanges and market participants employ effective quality management systems and sophisticated risk mitigation controls adapted to these new dynamics in order to protect against potential threats to market stability arising from technology malfunctions or episodic illiquidity. However, there are more deliberate aspects of HFT strategies which may present serious problems for market structure and functioning, and where conduct may be illegal, for example in order anticipation seeks to ascertain the existence of large buyers or sellers in the marketplace and then to trade ahead of those buyers and sellers in anticipation that their large orders will move market prices. A momentum strategy involves initiating a series of orders and trades in an attempt to ignite a rapid price move. HFT strategies can resemble traditional forms of market manipulation that violate the Exchange Act:

  1. Spoofing and layering occurs when traders create a false appearance of market activity by entering multiple non-bona fide orders on one side of the market at increasing or decreasing prices in order to induce others to buy or sell the stock at a price altered by the bogus orders.
  2. Painting the tape involves placing successive small amount of buy orders at increasing prices in order to stimulate increased demand.

  3. Quote Stuffing and price fade are additional HFT dubious practices: quote stuffing is a practice that floods the market with huge numbers of orders and cancellations in rapid succession which may generate buying or selling interest, or compromise the trading position of other market participants. Order or price fade involves the rapid cancellation of orders in response to other trades.

The World Federation of Exchanges insists: ― Exchanges are committed to protecting market stability and promoting orderly markets, and understand that a robust and resilient risk control framework adapted to today‘s high speed markets, is a cornerstone of enhancing investor confidence. However this robust and resilient risk control framework‘ seems lacking, including in the dark pools now established for trading that were initially proposed as safer than the open market.

Black Hole Complementarity: The Case of the Infalling Observer

The four postulates of black hole complementarity are:

Postulate 1: The process of formation and evaporation of a black hole, as viewed by a distant observer, can be described entirely within the context of standard quantum theory. In particular, there exists a unitary S-matrix which describes the evolution from infalling matter to outgoing Hawking-like radiation.

Postulate 2: Outside the stretched horizon of a massive black hole, physics can be described to good approximation by a set of semi-classical field equations.

Postulate 3: To a distant observer, a black hole appears to be a quantum system with discrete energy levels. The dimension of the subspace of states describing a black hole of mass M is the exponential of the Bekenstein entropy S(M).

We take as implicit in postulate 2 that the semi-classical field equations are those of a low energy effective field theory with local Lorentz invariance. These postulates do not refer to the experience of an infalling observer, but states a ‘certainty,’ which for uniformity we label as a further postulate:

Postulate 4: A freely falling observer experiences nothing out of the ordinary when crossing the horizon.

To be more specific, we will assume that postulate 4 means both that any low-energy dynamics this observer can probe near his worldline is well-described by familiar Lorentz-invariant effective field theory and also that the probability for an infalling observer to encounter a quantum with energy E ≫ 1/rs (measured in the infalling frame) is suppressed by an exponentially decreasing adiabatic factor as predicted by quantum field theory in curved spacetime. We will argue that postulates 1, 2, and 4 are not consistent with one another for a sufficiently old black hole.

Consider a black hole that forms from collapse of some pure state and subsequently decays. Dividing the Hawking radiation into an early part and a late part, postulate 1 implies that the state of the Hawking radiation is pure,

|Ψ⟩= ∑ii⟩E ⊗|i⟩L —– (1)

Here we have taken an arbitrary complete basis |i⟩L for the late radiation. We use postulates 1, 2, and 3 to make the division after the Page time when the black hole has emitted half of its initial Bekenstein-Hawking entropy; we will refer to this as an ‘old’ black hole. The number of states in the early subspace will then be much larger than that in the late subspace and, as a result, for typical states |Ψ⟩ the reduced density matrix describing the late-time radiation is close to the identity. We can therefore construct operators acting on the early radiation, whose action on |Ψ⟩ is equal to that of a projection operator onto any given subspace of the late radiation.

To simplify the discussion, we treat gray-body factors by taking the transmission coefficients T to have unit magnitude for a few low partial waves and to vanish for higher partial waves. Since the total radiated energy is finite, this allows us to think of the Hawking radiation as defining a finite-dimensional Hilbert space.

Now, consider an outgoing Hawking mode in the later part of the radiation. We take this mode to be a localized packet with width of order rs corresponding to a superposition of frequencies O(r−1s). Note that postulate 2 allows us to assign a unique observer-independent s lowering operator b to this mode. We can project onto eigenspaces of the number operator bb. In other words, an observer making measurements on the early radiation can know the number of photons that will be present in a given mode of the late radiation.

Following postulate 2, we can now relate this Hawking mode to one at earlier times, as long as we stay outside the stretched horizon. The earlier mode is blue-shifted, and so may have frequency ω* much larger than O(r−1s) though still sub-Planckian.

Next consider an infalling observer and the associated set of infalling modes with lowering operators a. Hawking radiation arises precisely because

b = ∫0 dω B(ω)aω + C(ω)aω —– (2)

so that the full state cannot be both an a-vacuum (a|Ψ⟩ = 0) and a bb eigenstate. Here again we have used our simplified gray-body factors.

The application of postulates 1 and 2 has thus led to the conclusion that the infalling observer will encounter high-energy modes. Note that the infalling observer need not have actually made the measurement on the early radiation: to guarantee the presence of the high energy quanta it is enough that it is possible, just as shining light on a two-slit experiment destroys the fringes even if we do not observe the scattered light. Here we make the implicit assumption that the measurements of the infalling observer can be described in terms of an effective quantum field theory. Instead we could simply suppose that if he chooses to measure bb he finds the expected eigenvalue, while if he measures the noncommuting operator aa instead he finds the expected vanishing value. But this would be an extreme modification of the quantum mechanics of the observer, and does not seem plausible.

Figure below gives a pictorial summary of our argument, using ingoing Eddington-Finkelstein coordinates. The support of the mode b is shaded. At large distance it is a well-defined Hawking photon, in a predicted eigenstate of bb by postulate 1. The observer encounters it when its wavelength is much shorter: the field must be in the ground state aωaω = 0, by postulate 4, and so cannot be in an eigenstate of bb. But by postulate 2, the evolution of the mode outside the horizon is essentially free, so this is a contradiction.

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Figure: Eddington-Finkelstein coordinates, showing the infalling observer encountering the outgoing Hawking mode (shaded) at a time when its size is ω−1* ≪ rs. If the observer’s measurements are given by an eigenstate of aa, postulate 1 is violated; if they are given by an eigenstate of bb, postulate 4 is violated; if the result depends on when the observer falls in, postulate 2 is violated.

To restate our paradox in brief, the purity of the Hawking radiation implies that the late radiation is fully entangled with the early radiation, and the absence of drama for the infalling observer implies that it is fully entangled with the modes behind the horizon. This is tantamount to cloning. For example, it violates strong subadditivity of the entropy,

SAB + SBC ≥ SB + SABC —– (3)

Let A be the early Hawking modes, B be outgoing Hawking mode, and C be its interior partner mode. For an old black hole, the entropy is decreasing and so SAB < SA. The absence of infalling drama means that SBC = 0 and so SABC = SA. Subadditivity then gives SA ≥ SB + SA, which fails substantially since the density matrix for system B by itself is thermal.

Actually, assuming the Page argument, the inequality is violated even more strongly: for an old black hole the entropy decrease is maximal, SAB = SA − SB, so that we get from subadditivity that SA ≥ 2SB + SA.

Note that the measurement of Nb takes place entirely outside the horizon, while the measurement of Na (real excitations above the infalling vacuum) must involve a region that extends over both sides of the horizon. These are noncommuting measurements, but by measuring Nb the observer can infer something about what would have happened if Na had been measured instead. For an analogy, consider a set of identically prepared spins. If each is measured along the x-axis and found to be +1/2, we can infer that a measurement along the z-axis would have had equal probability to return +1/2 and −1/2. The multiple spins are needed to reduce statistical variance; similarly in our case the observer would need to measure several modes Nb to have confidence that he was actually entangled with the early radiation. One might ask if there could be a possible loophole in the argument: A physical observer will have a nonzero mass, and so the mass and entropy of the black hole will increase after he falls in. However, we may choose to consider a particular Hawking wavepacket which is already separated from the streched horizon by a finite amount when it is encountered by the infalling observer. Thus by postulate 2 the further evolution of this mode is semiclassical and not affected by the subsequent merging of the observer with the black hole. In making this argument we are also assuming that the dynamics of the stretched horizon is causal.

Thus far the asymptotically flat discussion applies to a black hole that is older than the Page time; we needed this in order to frame a sharp paradox using the entanglement with the Hawking radiation. However, we are discussing what should be intrinsic properties of the black hole, not dependent on its entanglement with some external system. After the black hole scrambling time, almost every small subsystem of the black hole is in an almost maximally mixed state. So if the degrees of freedom sampled by the infalling observer can be considered typical, then they are ‘old’ in an intrinsic sense. Our conclusions should then hold. If the black hole is a fast scrambler the scrambling time is rs ln(rs/lP), after which we have to expect either drama for the infalling observer or novel physics outside the black hole.

We note that the three postulates that are in conflict – purity of the Hawking radiation, absence of infalling drama, and semiclassical behavior outside the horizon — are widely held even by those who do not explicitly label them as ‘black hole complementarity.’ For example, one might imagine that if some tunneling process were to cause a shell of branes to appear at the horizon, an infalling observer would just go ‘splat,’ and of course Postulate 4 would not hold.

Philosophy of Local Time

Time 01

Let us hypothesize on the notion of local time.

Existence of temporal order: For each concrete basic thing x ∈ Θ, there exist a single ordering relation between their states ≤.

We now give a name to this ordering relation:

Denotation of temporal order: The set of lawful states of x is temporally ordered by the ≤ relation.

The above is a partial order relation: there are pairs of states that are not ordered by ≤; e.g. given an initial condition (x0,v0) for a moving particle, there are states (x1,v1) that are not visited by the particle.

Proper history: A totally order set of states of x is called a proper history of x.

The axiomatics do not guarantee the existence of a single proper history: they allow many of them, as in “The garden of forking paths”. The following axiom forbids such possibility.

Unicity of proper history: Each thing has one and only one proper history.

Arrow of time: The axiomatics describe a kind of “arrow of time”, although it is not related to irreversibility.

A proper history is also an ontological history. The parameter t ∈ M has not to be continuous. The following axiom, a very strong version of Heraclitus’ hypothesis Panta rhei, states that every thing is changing continuously:

Continuity: If the entire set of states of an ontological history is divided in two subsets hp and hf such that every state in hp temporally precedes any state in hf, then there exists one and only one state s0 such that s1 ≤ s0 ≤ s2, where s1 ∈ hp and s2 ∈ hf.

The axiom of continuity is stated in the Dedekind form.

Continuity in quantum mechanics: Although quantum mechanical “changes of state” are usually considered “instantaneous”, theory shows that probabilities change in a continuous way. The finite width of spectral lines also shows a continuous change in time.

Real representation: Given a unit change (s0, s1) there exists a bijection T : h ↔ R such that

h1 = {s(τ)|τ ∈ R} —– (1)
s0 = s(0) —– (2)
s1 = s(1) —– (3)

Local time: The function T is called local time. The unit change (s0, s1) is arbitary. It defines an arbitrary “unit of local time”.

The above theory of local time has an important philosophical consequence: becoming, which is usually conceived as evolution in time, is here more fundamental than time. The latter is constructed as an emergent property of a changing (i.e. a becoming) thing.

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.

Astrobiological Traces Within the Secret Doctrine.

पूर्णस्य पूर्णमादाय पूर्णमेवाशिष्यते

pūrṇasya pūrṇamādāya pūrṇamevāśiṣyate

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

पूर्णमदः पूर्णमादाय पूर्णात् पूर्णमुदच्यते
पूर्णस्य पूर्णमादाय पूर्णमेवाशिष्यते
ॐ शान्तिः शान्तिः शान्तिः ।

pūrṇamadaḥ pūrṇamādāya pūrṇāt pūrṇamudacyate
pūrṇasya pūrṇamādāya pūrṇamevāśiṣyate
oṃ śāntiḥ śāntiḥ śāntiḥ |

‘The invisible (Brahman) is the Full; the visible (the world) too is the Full. From the Full (Brahman), the Full (the visible) universe has come. The Full (Brahman) remains the same, even after the Full (the visible universe) has come out of the Full (Brahman).’

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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The Secret Doctrine of the Ages teaches that the universe came into existence through creative and evolutionary processes; and it demonstrates why both are necessary to explain our origins. It harmonizes the truths of science and religion, while showing that major assumptions of both Darwinism and Fundamentalist Creationism do not bear up to careful examination. By drawing our attention to the questions of why we live and die, of what is mind and substance, the Secret Doctrine helps us realize that wisdom begins with understanding how very little we really know. Yet it also affirms that the most perplexing problems can be solved; that of the progeny of one cosmos.

Evolution means unfolding and progressive development, derived from the Latin evolutio: “unrolling,” specifically of a scroll or volume — suggestively connoting the serial expression of previously hidden ideas. A climb from the bottom of the Grand Canyon reveals an unmistakable evolutionary story: of the appearance of progressively more complex species over a lengthy period of time. But how actually did this happen? The compelling evidence of nature contradicts the week-long special creation postulated by Bible literalists. Darwinian theory is also proving unsatisfactory, as a growing number of scientists are relegating its major claims to the category of “mythology. “Though not assenting to any metaphysical implications, Harvard paleontologist Stephen Jay Gould declared in 1980 that the modern synthetic theory of evolution, “as a general proposition, is effectively dead, despite its persistence as textbook orthodoxy.” Pierre-P. Grassé, former president of the French Academy of Sciences and editor of the 35-volume Traité de Zoologie, was more forceful:

Their success among certain biologists, philosophers, and sociologists notwithstanding, the explanatory doctrines of biological evolution do not stand up to an objective, in-depth criticism. They prove to be either in conflict with reality or else incapable of solving the major problems involved. Through the use and abuse of hidden postulates, of bold, often ill-founded extrapolations, a pseudoscience has been created. It is taking root in the very heart of biology and is leading astray many biochemists and biologists, who sincerely believe that the accuracy of fundamental concepts has been demonstrated, which is not the case.

While most critics readily acknowledge that natural selection and gene changes partially explain variation in species or microevolution, they point out that Darwinism has failed spectacularly to describe the origin of life and the mechanism of macroevolution: the manner in which higher types emerge.

Textbook theory asserts that life on earth began with the formation of DNA and RNA, the first self-replicating molecules, in a prebiotic soup rich in organic compounds, amino acids, and nucleotides. Robert Shapiro, professor of chemistry at New York University, wrote:

many scientists now believe that neither the atmosphere described nor the soup had ever existed. Laboratory efforts had also been made to prepare the magic molecule from a simulation of the soup, and thus far had failed.

Even if the purported soup existed elsewhere in the universe, and DNA were brought to earth by meteorite, comet, or some other means, there remains the enigma of how it was originally synthesized. Astrobiology.

In the first place, several mathematicians have shown the astronomical improbability of chance mutations “evolving” any organized system — neither complex DNA molecules nor higher organisms. The 10-20 billion year time frame presently assigned to our universe is far too short a period, given known mutation rates. Moreover, nothing in empirical experience suggests that unguided trial and error — i.e., random mutation — will produce anything but the most trivial ends. Research biologist Michael Denton writes that to “get a cell by chance would require at least one hundred functional proteins to appear simultaneously in one place” — the probability of which has been calculated at the negative figure 1 followed by 2,000 zeros — a staggeringly remote possibility, to say nothing of the lipids, polysaccharides, and nucleic acids also needed to form a viable, reproducing cell.

The same reasoning applies to the extraordinary number of coordinated, immediately useful mutations required to produce “organs of extreme perfection,” such as the mammalian brain, the human eye, and the sophisticated survival mechanisms (including inter-species symbiotic systems) of the plant and animal kingdoms. There is simply no justification, according to Denton, for assuming that blind physical forces will self-organize “in the finite time available the sorts of complex systems which are so ubiquitous in nature.” In observing the sheer elegance and ingenuity of nature’s purposeful designs, scientists like Denton can hardly resist the logic of analogy. The conclusion may have religious implications, he says, but the inference is clear: nature’s systems are the result of intelligent activity.

Another enigmatic problem is the absence in fossil strata of finely-graded transitional forms between major groups of species, i.e., between reptiles and birds, land mammals and whales, and so forth. Darwin himself recognized this as one of the “gravest” impediments to his theory and tried to defend it by asserting “imperfection of the geologic record.” Yet over a century of intensive search has failed to disclose the hypothetical missing links. Thus far only conjecture, or imagination, has been able to fill in how gills became lungs, scales became feathers, and legs became wings — for the record of nature on this point is still a secret.

Darwin also worried over one of nature’s most formidable barriers to macroevolutionary change: hybrid limits. Artificial breeding shows that extreme variations are usually sterile or weak. Left to themselves these hybrid varieties — if they are able to reproduce at all — revert to ancestral norms or eventually die out. In this sense, natural selection, environmental pressures, and genetic coding tend as much to weed out unusual novelties, as to ensure the survival of the fittest of each typea fact which is confirmed by the fossil record. Unquestionably, species adapt and change within natural limits; refinement occurs, too, as in flowering plants. But no one has yet artificially bred, genetically engineered, or observed in nature a series of chromosomal changes, micro or macro, resulting in a species of a higher genus. There are no “hopeful monsters,” except, perhaps, in a poetic sense. Trees remain trees, birds birds, and the problem of how higher types originate has not been solved by Darwin or his successors.

We do not give up our dogmas easily, scientific or religious. Obviously, ideas should be examined for their intrinsic value, not blindly accepted because somebody tells us “Science has proven” or the “Bible says so,” or again, because the Secret Doctrine teaches it. But with science’s recognized ignorance of first causes and macroevolutionary mechanisms, as well as the failure of scriptural literalism to provide satisfactory explanations, there remain the questions about our origins, purpose, and destiny. The answers to these questions are, in a sense, nature’s secret doctrines. Her evolutionary pattern suggests, however, that they are not hopelessly beyond knowing. Just as from the conception of a human embryo to a fully-developed adult, so from the first burst outward of the primordial cosmic atom, the progressive unfolding of intelligence is a natural and observable process. The whole universe seems bent on discovering itself and its reason for being.

The concept of the universe evolving for purposes of self-discovery and creative expression is found not only in modern European philosophy, such as Hegel’s, but also in ancient myths the world over, some of which sound surprisingly up-to-date. The Hindu Puranas, for example, speak of our universe as Brahma, and of alternating periods of cosmic activity and rest as the Days and Nights of Brahma, each of which spans over four billion years — an oscillating universe reminiscent of modern cosmological theory. In each “creation” Brahma attempts to fashion an ever-more perfected mankind, in the process of which he serially evolves from his own consciousness and root substance all of nature’s kingdoms: atoms, minerals, plants, animals, and so forth. Conversely, the stories allude also to the striving of mankind and, for that matter, of all sentient beings, to become Brahma-like in quality — i.e., to express more and more of the hidden mind pattern of the cosmos.

We often look down on ancient traditions as moldy superstitions. While this judgment may well apply to the rind of literalism and later accretions, concealed within and giving life to every religion are core ideas which bear the hallmark of insight. Biblical Genesis also, when read allegorically as is done in gnostic and kabbalistic schools, yields a picture of evolutionary growth and perfectibility, both testaments clearly implying that we are sibling gods of wondrous potential. But are the secret doctrines spoken of in these older traditions expressions of truth or simply romantic wish-fulfilling fantasy? Can they teach us anything relevant about our heritage and our future? It is to such questions that the modern book entitled The Secret Doctrine addresses itself. Impulsed by divinity and guided by karma (cause and effect), each of us has been periodically manifesting since eternity through all the kingdoms, from sub-mineral through human, earning our way to the next realm and beyond. Although seeded with godlike potential, we are not irrevocably fated to an unsought destiny. Karma is a philosophy of merit, and within our power is the capacity to choose — to evolve and create — our own future. We give life and active existence to our thoughts and, to a very large extent, we become what we think we are, or would like to be. This affects ourselves for good or evil, and it affects all others — profoundly so.

Holism. Note Quote.

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It is a basic tenet of systems theory/holism as well as of theosophy that the whole is greater than the sum of its parts. If, then, our individual minds are subsystems of larger manifestations of mind, how is it that our own minds are self-conscious while the universal mind (on the physical plane) is not? How can a part possess a quality that the whole does not? A logical solution is to regard the material universe as but the outer garment of universal mind. According to theosophy the laws of nature are the wills and energies of higher beings or spiritual intelligences which in their aggregate make up universal mind. It is mind and intelligence which give rise to the order and harmony of the physical universe, and not the patterns of chance, or the decisions of self-organizing matter. Like Capra, the theosophical philosophy rejects the traditional theological idea of a supernatural, extracosmic divine Creator. It would also question Capra’s notion that such an extracosmic God is the self-organizing dynamics of the physical universe. Theosophy, on the other hand, firmly believes in the existence of innumerable superhuman, intracosmic intelligences (or gods), which have already passed through the human stage in past evolutionary cycles, and to which status we shall ourselves one day attain. There are two opposing views of consciousness: the Western scientific view which considers matter as primary and consciousness as a by-product of complex material patterns associated with a certain stage of biological evolution; and the mystical view which sees consciousness as the primary reality and ground of all being. Systems theory accepts the conventional materialist view that consciousness is a manifestation of living systems of a certain complexity, although the biological structures themselves are expressions of “underlying processes that represent the system’s self-organization, and hence its mind. In this sense material structures are no longer considered the primary reality” (Turning Point). This stance reaffirms the dualistic view of mind and matter. Capra clearly believes that matter is primary in the sense that the physical world comes first and life, mind, and consciousness emerge at a later stage. That he chooses to call the self-organizing dynamics of the universe by the name “mind” is beside the point. If consciousness is regarded as the underlying reality, it is impossible to regard it also as a property of matter which emerges at a certain stage of evolution. Systems theory accepts neither the traditional scientific view of evolution as a game of dice, nor the Western religious view of an ordered universe designed by a divine creator. Evolution is presented as basically open and indeterminate, without goal or purpose, yet with a recognizable pattern of development. Chance fluctuations take place, causing a system at a certain moment to become unstable. As it “approaches the critical point, it ‘decides’ itself which way to go, and this decision will determine its evolution”. Capra sees the systems view of the evolutionary process not as a product of blind chance but as an unfolding of order and complexity analogous to a learning process, including both independence from the environment and freedom of choice. However, he fails to explain how supposedly inert matter is able to “decide,” “choose,” and “learn.” This belief that evolution is purposeless and haphazard and yet shows a recognizable pattern is similar to biologist Lyall Watson’s belief that evolution is governed by chance but that chance has “a pattern and a reason of its own”.

While the materialistic and mystical views of mind seem incompatible and irreconcilable, mind/matter dualism may be resolved by seeing spirit and matter as fundamentally one, as different grades of consciousness-life-substance. Science already holds that physical matter and energy are interconvertible, that matter is concentrated energy; and theosophy adds that consciousness is the highest and subtlest form. From this view there is no absolutely dead and unconscious matter in the universe. Everything is a living, evolving, conscious entity, and every entity is composite, consisting of bundles of forces and substances pertaining to different planes, from the astral-physical through the psychomental to divine-spiritual. Obviously the degree of manifested life and consciousness varies widely from one entity to another; but at the heart of every entity is an indwelling spiritual atom or consciousness-center at a particular stage of its evolutionary unfoldment. More complex material forms do not create consciousness, but merely provide a more developed vehicle through which this spiritual monad can express its powers and faculties. Evolution is far from being purposeless and indeterminate: our human monads issued from the divine Source aeons ago as unself-conscious god-sparks and, by taking embodiment and garnering experience in all the kingdoms of nature, we will eventually raise ourselves to the status of self-conscious gods.

Mutational Law of Karma (कर्म)?

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During the preparation for cell division, for example, before the formation of the gametes or reproductive cells, the chromosomes may “cross over” so that material which originated from the male parent interchanges with that from the female parent. To quote from a standard work on evolutionary theory and genetics, Ernst Mayr’s Evolution and the Diversity of Life:

At some time prior to the formation of the gametes, the two homologous chromosomes exchange equivalent pieces with each other by a process called “crossing over.” By and large (there are many exceptions) no laws seem to determine where the chromosomes will break or how large the pieces will be that are exchanged. Which particular combination of pieces of maternal and paternal chromosomes making up the new chromosome will enter a given egg or spermatozoon is largely a matter of chance, at least in most chromosomes and most species. Likewise, it is largely a matter of accident which chromosomes will go into which germ cell, provided only that each cell receives its full set of chromosomes.

It is easy to attribute events to chance, but this only expresses scientific ignorance as to the real cause.

Another phenomenon is mutation: sometimes genetic codes suddenly change. This, too, is usually attributed to accident or chance, but then it is difficult to explain why any progression is made at all once biological systems have evolved to a certain level of complexity and perfection. The chance of a mutation leading to fatal, or at least less fit, properties is far greater than of a mutation making the individual fitter. Besides “crossing over” and mutation at one or several places on the chromosomes, another uncertain factor that Mayr and others mention is the distribution of chromosomes during reduction division (meiosis) to form reproductive cells. This process affects which side in the gamete the originally paternal or maternal genetic material goes to. Moreover, there are other opportunities for the course of events to be influenced from within: only part of the cell’s genetic code is active at certain times and under certain circumstances. Other parts are not active and may never become so during the present life. Thus, there are many secrets not yet unveiled by science, but nevertheless attributed to “chance.”

Chance, however, has no place in the theosophical view. Whatever happens is karmic, that is, it can be attributed to a cause, and this cause comes from within. In theosophy the different combinations of hereditary qualities in individuals are governed by psychomagnetic attractions inherent in the skandhas (‎स्कन्ध) of the reincarnating entity. Skandhas are the individual’s aggregates of properties — such as higher and lower mental consciousness, feelings, attractions, and physical characteristics — carried over from former lives. Thus, the specific magnetism of the soul, formed by its store of properties, determines which combinations of hereditary qualities will manifest in a particular incarnation. “It is . . . unquestionable that in the case of human incarnations the law of Karma, racial or individual, overrides the subordinate tendencies of ‘Heredity,’ its servant” (The Secret Doctrine).

Swastika (स्वस्तिक). Note Quote.

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H. P. Blavatsky says:

Few world-symbols are more pregnant with real occult meaning than the Swastika.  It is symbolized by the figure 6; for, like that figure, it points in its concrete imagery, as the ideograph of the number does, to the Zenith and the Nadir, to North, South, West, and East; one finds the unit everywhere, and that unit reflected in all and every unit.  It is the emblem of the activity of Fohat, of the continual revolution of the ‘wheels’, and of the Four Elements, the ‘Sacred Four’, in their mystical, and not alone in their cosmic meaning; further, its four arms, bent at right angles, are intimately related, as shown elsewhere, to the Pythagorean and Hermetic scales.  One initiated into the mysteries of the meaning of the Swastika, say the Commentaries, ‘can trace on it, with mathematical precision, the evolution of Kosmos and the whole period of Sandhya’.

The swastika is, par excellence, the symbol of cosmic evolution. It is an image represented in many temples in India, Tibet, China and other countries with Hindu and Buddhist influence (and indeed the very symbol of esoteric Buddhism). Moreover, it is present in the traditions of the Nordic peoples and in pre-colonial Americas.

Being a universal symbol, the swastika cross is also present in the symbol of the theosophical movement.

The representations of Buddha with the Swastika cross on his chest, being called the ‘Seal of the Heart’, are well-known. The swastika is also present in many ancient Christian relics. About its universality, HPB states:

[The] ansated Egyptian cross, or tau, the Jaina cross, or Swastika, and the Christian cross have all the same meaning.

Despite these facts, or maybe because of them, Christian missionaries tried to classify the swastika as “diabolical”, thus trying to destroy one of the oldest sacred symbols, which is also at the origin of “their” own Christian cross. Yet to honestly recognize the evolution of the cross as a symbol would be like accepting that Christianity illegitimately adopted religious images belonging to much earlier traditions.

There is a right-handed swastika and a left-handed one, each revolving in opposite directions. The right-handed is called “swastika” while the left-handed is sometimes called “swavastika.” If clockwise movement signifies natural evolution and life, and counter-clockwise indicates regression or death and is an inversion of nature,  the Nazi “swastika” would represent this inversion. The symbol was chosen possibly because it was thought to be of Nordic origin, and it was used as a caricature of the Christian Cross. The swastika can clearly symbolize good or evil, thus echoing its inherent double nature. But many of its uses in past ages indicate both directions in contexts that were purely spiritual in nature and which strongly suggest another interpretation. The right arm points to heaven, the left to earth, and this varies depending upon the perspective. If the symbol faces away from one, the hooks point counter-clockwise. If the symbol faces one, the hooks point clockwise. These two perspectives symbolize the microcosmic and the macrocosmic. Man, the perceiver, embodies one while reaching out toward the other.

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Being a double symbol, the swastika also represents male and female combined in the hermaphrodite. Thus, it is found carved upon the figure of Ardanari in South India, denoting the pre-sexual state of the Third Root Race. In another old Hindu carving, Vishnu is shown as double-sexed, floating on the water which rises in a semicircle and pours through a swastika representing the source of generation. All subsequent evolution takes place spirally from within, like the directional unfolding of the swastika implicit in the “wheel of Dharma,” the sacred law to which the Buddha pointed. The Upanishads teach that in accordance with natural law, it is necessary to turn the wheel from within, to emulate the fohatic force which expands throughout the Cosmos vitalizing every atom and awakening every conscious center.