Welfare Economics, or Social Psychic Wellbeing. Note Quote.

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The economic system is a social system in which commodities are exchanged. Sets of these commodities can be represented by vectors x within a metric space X contained within the non-negative orthant of an Euclidean space RNx+ of dimensionality N equal to the number of such commodities.

An allocation {xi}i∈N ⊂ X ⊂ RNx+ of commodities in society is a set of vectors xi representing the commodities allocated within the economic system to each individual i ∈ N.

In questions of welfare economics at least in all practical policy matters, the state of society is equated with this allocation, that is, s = {xi}i∈N, and the set of all possible information concerning the economic state of society is S = X. It is typically taken to be the case that the individual’s preference-information is simply their allocation xi, si = xi. The concept of Pareto efficiency is thus narrowed to “neoclassical Pareto efficiency” for the school of economic thought in which originates, and to distinguish it from the weaker criterion.

An allocation {xi}i∈N is said to be neoclassical Pareto efficient iff ∄{xi}i∈N ⊂ X & i ∈ N : x′i ≻ xi & x′j ≽ xj ∀ j ≠ i ∈ N.

A movement between two allocations, {xi}i∈N → {x′i}i∈N is called a neoclassical Pareto improvement iff ∃i∈N : x′i ≻ xi & x′j ≽ xj ∀ j ≠ i ∈ N.

For technical reasons it is almost always in practice assumed for simplicity that individual preference relations are monotonically increasing across the space of commodities.

If individual preferences are monotonically increasing then x′ii xi ⇐⇒ x′i ≥ xi, and x′ ≻ xi ⇐⇒ xi > x′i2.

This is problematic, because a normative economics guided by the principle of implementing a decision if it yields a neoclassical Pareto improvement where individuals have such preference relations above leads to the following situation.

Suppose that individual’s preference-information is their own allocation of commodities, and that their preferences are monotonically increasing. Take one individual j ∈ N and an initial allocation {xi}i∈N.

– A series of movements between allocations {{xi}ti∈N → {x′i}ti∈N}Tt=1 such that xi≠j = x′i≠j ∀ t and x′j > xj ∀ t and therefore that xj − xi → ∞∀i≠j ∈ N, are neoclassical Pareto improvements. Furthermore, if these movements are made possible only by the discovery of new commodities, each individual state in the movement is neoclassical Pareto efficient prior to the next discovery if the first allocation was neoclassical Pareto efficient.

Admittedly perhaps not to the economic theorist, but to most this seems a rather dubious out- come. It means that if we are guided by neoclassical Pareto efficiency it is acceptable, indeed de- sirable, that one individual within society be made increasingly “richer” without end and without increasing the wealth of others. Provided only the wealth of others does not decrease. The same result would hold if instead of an individual, we made a whole group, or indeed the whole of society “better off”, without making anyone else “worse off”.

Even the most devoted disciple of Ayn Rand would find this situation dubious, for there is no requirement that the individual in question be in some sense “deserving” of their riches. But it is perfectly logically consistent with Pareto optimality if individual preferences concern only to their allocation and are monotonically increasing. So what is it that is strange here? What generates this odd condonation? It is the narrowing of that which the polity care about to each individual allocation, alone, independent of others. The fact that neoclassical Pareto improvements are distribution-invariant because the polity is supposed to care only about their own individual allocation xi ∈ {xi}ti∈N alone rather than broader states of society si ⊂ s as they see it.

To avoid such awkward results, the economist may move from the preference-axiomatic concept of Pareto efficiency to embrace utilitarianism. The policy criterion (actually not immediately representative of Bentham’s surprisingly subtle statement) being the maximisation of some combination W(x) = W {ui(xi)}i∈N of individual utilities ui(xi) over allocations. The “social psychic wellbeing” metric known as the Social Welfare Function.

In theory, the maximisation of W(x) would, given the “right” assumptions on the combination method W (·) (sum, multiplication, maximin etc.) and utilities (concavity, montonocity, independence etc.) fail to condone a distribution of commodities x extreme as that discussed above. By dint of its failure to maximise social welfare W(x). But to obtain this egalitarian sensitivity to the distribution of income, three properties of Social Welfare Functions are introduced. Which prove fatal to the a-politicality of the economist’s policy advice, and introduce presuppositions which must lay naked upon the political passions of the economist, so much more indecently for their hazy concealment under the technicalistic canopy of functional mathematics.

Firstly, it is so famous a result as to be called the “third theorem of welfare economics” that any such function W(·) as has certain “uncontroversially” desirable technical properties will impose upon the polity N the preferences of a dictator i ∈ N within it. The preference of one individual i ∈ N will serve to determine the preference indicated between by society between different states by W(x). In practice, the preferences of the economist, who decides upon the form of W(·) and thus imposes their particular political passions (be they egalitarian or otherwise) upon policy, deeming what is “socially optimal” by the different weightings assigned to individual utilities ui(·) within the polity. But the political presuppositions imported by the economist go deeper in fact than this. Utilitari-anism which allows for inter-personal comparisons of utility in the construction of W(x) requires utility functions be “cardinal” – representing “how much” utility one derives from commodities over and above the bare preference between different sets thereof. Utility is an extremely vague concept, because it was constructed to represent a common hedonistic experiential metric where the very existence of such is uncertain in the first place. In practice, the economist decides upon, extrapolates, assigns to i ∈ N a particular utility function which imports yet further assumptions about how any one individual values their commodity allocation, and thus contributes to social psychic wellbeing.

And finally, utilitarianism not only makes political statements about who in the polity is to be assigned a disimproved situation. It makes statements so outlandish and outrageous to the common sensibility as to have provided the impetus for two of the great systems of philosophy of justice in modernity – those of John Rawls and Amartya Sen. Under almost any combination method W(·), the maximization of W(·) demands allocation to those most able to realize utility from their allocation. It would demand, for instance, redistribution of commodities from sick children to the hedonistic libertine, for the latter can obtain greater “utility” there from. A problem so severe in its political implications it provided the basic impetus for Rawls’ and Sen’s systems. A Theory of Justice is, of course, a direct response to the problematic political content of utilitarianism.

So Pareto optimality stands as the best hope for the economist to make a-political statements about policy, refraining from making statements therein concerning the assignation of dis-improvements in the situation of any individual. Yet if applied to preferences over individual allocations alone it condones some extreme situations of dubious political desirability across the spectrum of political theory and philosophy. But how robust a guide is it when we allow the polity to be concerned with states of society in general? Not only their own individual allocation of commodities. As they must be in the process of public reasoning in every political philosophy from Plato to Popper and beyond.

Odyssey. Note Quote.

In tracing an interpretation of the Odyssey it is not necessary to follow the order of the poem as arranged by Homer or by whoever compiled the Homeric legends; it is easier and more rewarding to take the simple narrative in the natural sequence of events. After leaving the battlefield of Troy, Odysseus embarks for his native isle, “Ithaca the Fair,” expecting to arrive there quickly; but at the very outset a tempest drives the fleet off its course, and a great fight impedes his progress. The destruction of all his ships but one, and of many of the sailors, follows quickly. One of the strangest incidents in this introductory part is the encounter with Polyphemus, the Cyclopean giant with a single eye in the middle of his forehead. Before we shrug him off as a creature of early man’s distorted imagination, we should hold in mind the possibility of a symbolic meaning. Creatures of a similar type were mentioned by many archaic peoples far removed from each other; possibly they referred to some past event in human history, now forgotten.

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After their escape from this one-eyed monster and some further perilous adventures, Odysseus and his companions soon reach the island of the enchantress Circe, who represents the fascination of sensual delights. Odysseus is unaffected by the gross enticements which overwhelm his fellows, now turned into swine by the goddess; and his boldness and “confidence in heaven” finally conquer the temptress and compel her to serve him. She restores the men to human form and instructs Odysseus how to find the way to the Underworld.

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The entrance into Hell or the Underworld, the “open tomb,” has more than one meaning in ancient allegories, and is always introduced in some form in myths of initiation; Orpheus, Aeneas and many others had to make the dread “descent.” In the legend of Perseus and Andromeda, the hero aided by the gods flies to the hideous regions of cold and darkness and destroys the deadly Medusa before he can rescue the princess of Ethiopia from the monster. For Odysseus the event is an ordeal of terror. Circe has warned him that before he may go further, he must gain information about the future from Tiresias, a venerable prophet, who lives with the inhabitants of Hades, though he himself is not dead. The approach to the entire experience is surrounded by fearful dangers and to pass safely through the multitudes of vengeful shades calls for the highest physical and moral courage. Like all heroes of epics of the soul, he has to traverse the Valley of the Shadow of Death: to face the shades, the lingering remains of past sins and errors; then to learn what is necessary for his further progress.

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The tone of the poem changes at this point; the lightness and gaiety with which Odysseus has related his adventures is replaced by a deep solemnity, and the scenes of Hades are described with intense vividness and many touches of realism. Are these portrayals actual revelations of postmortem life? Leaving the more impure regions, Odysseus moves on, sees stern Minos, the Judge of the Dead, and even gets a passing view of the heavenly world or the Elysian fields, where the higher and immortal parts of man are held to exist between incarnations on earth. (Plato and Plutarch give valuable insights into the Greek teachings on this mysterious subject which are found to be practically identical with the Egyptian, Indian, and other ancient views of these after-death states.)

At length, having interviewed the sage Tiresias, Odysseus returns to Circe who outlines the perils still lying ahead on his homeward journey. Then come the hazardous Straits between Scylla and Charybdis, and the subtle allurements of the Sirens. Exquisitely fair, they offer him the satisfaction of the pride of knowledge, telling him they know “Whate’er beneath the sun’s bright journey lies,” and singing with all the charm of celestial music:

Blest is the man ordain’d our voice to hear,
The song instructs the soul, and charms the ear.
Approach! thy soul shall into raptures rise!
Approach! and learn new wisdom from the wise.

Having passed successfully through the trials of the Underworld, will he be overcome by pride and rash self-confidence? Knowing well the overwhelming power of this temptation, the hero takes every precaution, has himself tied to the mast and stops the ears of his crew with wax against the Sirens’ songs. They steer safely through the Straits — only to plunge again into difficulty when his men, to satisfy their gluttony, kill and devour Apollo’s sacred oxen. This so arouses the wrath of the god that he sends a great tempest to destroy the last of Odysseus’ crew, and the brave man is left with nothing but his own strength and the favor of Athena, his guide.

In his desperation and loneliness he meets with a temptation that almost proves his undoing. He succumbs for seven years to the blandishments of the lovely nymph Calypso in her enchanted Atlantean island. Calypso even offers him “immortal life, exempt from age or woe.” But with the help of Athena, the personification of divine wisdom, he summons the strength to resist.

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This is one of the passages in the Odyssey that reveals the high understanding of the poet and the profound quality of his teaching. For here is shown the wide gulf between any artificial prolongation of the life of the personality with its selfish cravings and that genuine immortality born of steadfast aspiration and self-control which leads to union with one’s inner god. Such a philosophy nourishes the roots of our being and reminds us of the words of the Nazarene:

If any man will come after me, let him deny himself, and take up his cross, and follow me. For whosoever will save his life shall lose it: and whosoever will lose his life for my sake shall find it. –– Matthew, 16:24-5

Paul, the wise master builder, in common with the great teachers of antiquity, refers to the same principle when he speaks of being changed “in the twinkling of an eye.” This is a cryptic saying suggesting the spontaneous springing into activity of the power of intuition which sees the difference between a nobler life and the delusions of sensual gratification.

When Odysseus makes his decision, the irresistible power of the Olympian deities is exerted in his favor, Calypso abandons her inducements and, like Circe, is transformed from a temptress into a helper. Odysseus builds a new vessel with his own hands and sets out joyfully for home, a voyage still not without its risks. Upon his arrival, he discovers the terrible conditions to which his wife and son have been reduced by the outrageous conduct of her admirers and soon perceives that his greatest battle is yet to come. His wife, Penelope, who stands for the climax of his endeavors, his goal, does not immediately throw herself into his arms. Ragged, worn, and disguised as an old man, he is not easily recognized by her, though his aged nurse and faithful dog know him quickly. Even when Athena restores him to the prime of life, and to greater dignity and beauty than before, he has to prove his identity to Penelope before she will accept him. This hesitation on her part is not, as some have thought, a blemish on the story; it could not be otherwise. It is traditional that anyone wishing recognition by the higher self must make a clear demand; he must unmistakably recognize and call upon his inner god before it can help him.

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Ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you (Matthew., 7:7).

Odysseus’ supreme opportunity comes when he finds his palace invaded and his wife surrounded by a mob of suitors, all trying to persuade her that he is surely dead and that she should choose a second husband from among them. Repugnant as they are, they have no power over Odysseus, but he must destroy them before he can regain his rightful place. They represent lingering traces of lower desires which must be slain forever if he will be master in his own household. At last the battle is won, the evil forces overpowered, and Odysseus, calm, purified, asserts his noble identity to Penelope and is joyously received by her.

From a practical point of view, the scene of this last struggle and the method adopted by Odysseus in challenging the suitors may appear singular, but there is good warrant for these in the mystical symbolism obviously familiar to Homer. The contest takes place at close quarters, in the confined space of the palace hall, yet the hero has to depend upon his mighty bow for success — the bow that none other can wield — instead of the more logical weapons of sword or spear. The bow is the weapon of Apollo, god of light, and the day of Odysseus’ victory is sacred to that deity. In Hindu philosophy also, the bow, or in some cases the arrow, stands for man himself who must be strong enough in texture to stand the strain. In one of the Upanishads, it says:

Having taken the bow, the great weapon, let him place on it the arrow, sharpened by devotion. Then, having drawn it with a thought directed to That which is, hit the mark, O friend — the Indestructible. . . . It is to be hit by a man who is not thoughtless; and then, as the arrow becomes one with the target, he will become one with Brahman. — Mundaka,II ii, 3-4

The Odyssey closes with the hero, now triumphant as the rightful king and leader, going forth and subduing the few remaining rebels after which, the poet says, the “willing nations knew their lawful lord.” His future reign is left to the imagination, but it is secure in peace and wisdom for, having conquered the enemies in his own house, he cannot fail.

The Womb of Cosmogony. Thought of the Day 30.0

Nowhere and by no people was speculation allowed to range beyond those manifested gods. The boundless and infinite UNITY remained with every nation a virgin forbidden soil, untrodden by man’s thought, untouched by fruitless speculation. The only reference made to it was the brief conception of its diastolic and systolic property, of its periodical expansion or dilatation, and contraction. In the Universe with all its incalculable myriads of systems and worlds disappearing and re-appearing in eternity, the anthropomorphised powers, or gods, their Souls, had to disappear from view with their bodies: — “The breath returning to the eternal bosom which exhales and inhales them,” says our Catechism. . . . In every Cosmogony, behind and higher than the creative deity, there is a superior deity, a planner, an Architect, of whom the Creator is but the executive agent. And still higher, over and around, withinand without, there is the UNKNOWABLE and the unknown, the Source and Cause of all these Emanations. – The Secret Doctrine

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Many are the names in the ancient literatures which have been given to the Womb of Being from which all issues, in which all forever is, and into the spiritual and divine reaches of which all ultimately returns, whether infinitesimal entity or macrocosmic spacial unit.

The Tibetans called this ineffable mystery Tong-pa-nnid, the unfathomable Abyss of the spiritual realms. The Buddhists of the Mahayana school describe it as Sunyata or the Emptiness, simply because no human imagination can figurate to itself the incomprehensible Fullness which it is. In the Eddas of ancient Scandinavia the Boundless was called by the suggestive term Ginnungagap – a word meaning yawning or uncircumscribed void. The Hebrew Bible states that the earth was formless and void, and darkness was upon the face of Tehom, the Deep, the Abyss of Waters, and therefore the great Deep of kosmic Space. It has the identical significance of the Womb of Space as envisioned by other peoples. In the Chaldaeo-Jewish Qabbalah the same idea is conveyed by the term ‘Eyn (or Ain) Soph, without bounds. In the Babylonian accounts of Genesis, it is Mummu Tiamatu which stands for the Great Sea or Deep. The archaic Chaldaean cosmology speaks of the Abyss under the name of Ab Soo, the Father or source of knowledge, and in primitive Magianism it was Zervan Akarana — in its original meaning of Boundless Spirit instead of the later connotation of Boundless Time.

In the Chinese cosmogony, Tsi-tsai, the Self-Existent, is the Unknown Darkness, the root of the Wuliang-sheu, Boundless Age. The wu wei of Lao-tse, often mistranslated as passivity and nonaction, imbodies a similar conception. In the sacred scriptures of the Quiches of Guatemala, the Popol Vuh or “Book of the Azure Veil,” reference is made to the “void which was the immensity of the Heavens,” and to the “Great Sea of Space.” The ancient Egyptians spoke of the Endless Deep; the same idea also is imbodied in the Celi-Ced of archaic Druidism, Ced being spoken of as the “Black Virgin” — Chaos — a state of matter prior to manvantaric differentiation.

The Orphic Mysteries taught of the Thrice-Unknown Darkness or Chronos, about which nothing could be predicated except its timeless Duration. With the Gnostic schools, as for instance with Valentinus, it was Bythos, the Deep. In Greece, the school of Democritus and Epicurus postulated To Kenon, the Void; the same idea was later voiced by Leucippus and Diagoras. But the two most common terms in Greek philosophy for the Boundless were Apeiron, as used by Plato, Anaximander and Anaximenes, and Apeiria, as used by Anaxagoras and Aristotle. Both words had the significance of frontierless expansion, that which has no circumscribing bounds.

The earliest conception of Chaos was that almost unthinkable condition of kosmic space or kosmic expanse, which to human minds is infinite and vacant extension of primordial Aether, a stage before the formation of manifested worlds, and out of which everything that later existed was born, including gods and men and all the celestial hosts. We see here a faithful echo of the archaic esoteric philosophy, because among the Greeks Chaos was the kosmic mother of Erebos and Nyx, Darkness and Night — two aspects of the same primordial kosmic stage. Erebos was the spiritual or active side corresponding to Brahman in Hindu philosophy, and Nyx the passive side corresponding to pradhana or mulaprakriti, both meaning root-nature. Then from Erebos and Nyx as dual were born Aether and Hemera, Spirit and Day — Spirit being here again in this succeeding stage the active side, and Day the passive aspect, the substantial or vehicular side. The idea was that just as in the Day of Brahma of Hindu cosmogony things spring into active manifested existence, so in the kosmic Day of the Greeks things spring from elemental substance into manifested light and activity, because of the indwelling urge of the kosmic Spirit.

Harmonies of the Orphic Mystery: Emanation of Music

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As the Buddhist sage Nagarjuna states in his Seventy Verses on Sunyata, “Being does not arise, since it exists . . .” In similar fashion it can be said that mind exists, and if we human beings manifest its qualities, then the essence and characteristics of mind must be a component of our cosmic source. David Bohm’s theory of the “implicate order” within the operations of nature suggests that observed phenomena do not operate only when they become objective to our senses. Rather, they emerge out of a subjective state or condition that contains the potentials in a latent yet really existent state that is just awaiting the necessary conditions to manifest. Thus within the explicate order of things and beings in our familiar world there is the implicate order out of which all of these emerge in their own time.

Clearly, sun and its family of planets function in accordance with natural laws. The precision of the orbital and other electromagnetic processes is awesome, drawing into one operation the functions of the smallest subparticles and the largest families of sun-stars in their galaxies, and beyond even them. These individual entities are bonded together in an evident unity that we may compare with the oceans of our planet: uncountable numbers of water molecules appear to us as a single mass of substance. In seeking the ultimate particle, the building block of the cosmos, some researchers have found themselves confronted with the mystery of what it is that holds units together in an organism — any organism!

As in music where a harmony consists of many tones bearing an inherent relationship, so must there be harmony embracing all the children of cosmos. Longing for the Harmonies: Themes and Variations from Modern Physics is a book by Frank Wilczek, an eminent physicist, and his wife Betsy Devine, an engineering scientist and freelance writer. The theme of their book is set out in their first paragraph:

From Pythagoras measuring harmonies on a lyre string to R. P. Feynman beating out salsa on his bongos, many a scientist has fallen in love with music. This love is not always rewarded with perfect mastery. Albert Einstein, an ardent amateur of the violin, provoked a more competent player to bellow at him, “Einstein, can’t you count?”

Both music and scientific research, Einstein wrote, “are nourished by the same source of longing, and they complement one another in the release they offer.” It seems to us, too, that the mysterious longing behind a scientist’s search for meaning is the same that inspires creativity in music, art, or any other enterprise of the restless human spirit. And the release they offer is to inhabit, if only for a moment, some point of union between the lonely world of subjectivity and the shared universe of external reality.

In a very lucid text, Wilczek and Devine show us that the laws of nature, and the structure of the universe and all its contributing parts, can be presented in such a way that the whole compares with a musical composition comprising themes that are fused together. One of the early chapters begins with the famous lines of the great astronomer Johannes Kepler, who in 1619 referred to the music of the spheres:

The heavenly motions are nothing but a continuous song for several voices (perceived by the intellect, not by the ear); a music which, through discordant tensions, through sincopes [sic] and cadenzas, as it were (as men employ them in imitation of those natural discords) progresses towards certain pre-designed quasi six-voiced clausuras, and thereby sets landmarks in the immeasurable flow of time. — The Harmony of the World (Harmonice mundi)

Discarding the then current superstitions and misinformed speculation, through the cloud of which Kepler had to work for his insights, Wilczek and Devine note that Kepler’s obsession with the idea of the harmony of the world is actually rooted in Pythagoras’s theory that the universe is built upon number, a concept of the Orphic mystery-religions of Greece. The idea is that “the workings of the world are governed by relations of harmony and, in particular, that music is associated with the motion of the planets — the music of the spheres” (Wilczek and Devine). Arthur Koestler, in writing of Kepler and his work, claimed that the astronomer attempted

to bare the ultimate secret of the universe in an all-embracing synthesis of geometry, music, astrology, astronomy and epistemology. The Sleepwalkers

In Longing for the Harmonies the authors refer to the “music of the spheres” as a notion that in time past was “vague, mystical, and elastic.” As the foundations of music are rhythm and harmony, they remind us that Kepler saw the planets moving around the sun “to a single cosmic rhythm.” There is some evidence that he had association with a “neo-Pythagorean” movement and that, owing to the religious-fomented opposition to unorthodox beliefs, he kept his ideas hidden under allegory and metaphor.

Shakespeare, too, phrases the thought of tonal vibrations emitted by the planets and stars as the “music of the spheres,” the notes likened to those of the “heavenly choir” of cherubim. This calls to mind that Plato’s Cratylus terms the planets theoi, from theein meaning “to run, to move.” Motion does suggest animation, or beings imbued with life, and indeed the planets are living entities so much grander than human beings that the Greeks and other peoples called them “gods.” Not the physical bodies were meant, but the essence within them, in the same way that a human being is known by the inner qualities expressed through the personality.

When classical writers spoke of planets and starry entities as “animals” they did not refer to animals such as we know on Earth, but to the fact that the celestial bodies are “animated,” embodying energies received from the sun and cosmos and transmitted with their own inherent qualities added.

Many avenues open up for our reflection upon the nature of the cosmos and ourselves, and our interrelationship, as we consider the structure of natural laws as Wilczek and Devine present them. For example, the study of particles, their interactions, their harmonizing with those laws, is illuminating intrinsically and, additionally, because of their universal application. The processes involved occur here on earth, and evidently also within the solar system and beyond, explaining certain phenomena that had been awaiting clarification.

The study of atoms here on earth and their many particles and subparticles has enabled researchers to deduce how stars are born, how and why they shine, and how they die. Now some researchers are looking at what it is, whether a process or an energy, that unites the immeasurably small with the very large cosmic bodies we now know. If nature is infinite, it must be so in a qualitative sense, not merely a quantitative.

One of the questions occupying the minds of cosmologists is whether the universal energy is running down like the mechanism of an unwinding Swiss watch, or whether there is enough mass to slow the outward thrust caused by the big bang that has been assumed to have started our cosmos going. In other words, is our universe experiencing entropy — dying as its energy is being used up — or will there be a “brake” put upon the expansion that could, conceivably, result in a return to the source of the initial explosion billions of years ago? Cosmologists have been looking for enough “dark mass” to serve as such a brake.

Among the topics treated by Wilczek and Devine in threading their way through many themes and variations in modern physics, is what is known as the mass-generating Higgs field. This is a proposition formulated by Peter Higgs, a Scottish physicist, who suggests there is an electromagnetic field that pervades the cosmos and universally provides the electron particles with mass.

The background Higgs field must have very accurately the same value throughout the universe. After all, we know — from the fact that the light from distant galaxies contains the same spectral lines we find on Earth — that electrons have the same mass throughout the universe. So if electrons are getting their mass from the Higgs field, this field had better have the same strength everywhere. What is the meaning of this all-pervasive field, which exists with no apparent source? Why is it there? (Wilczek and Devine).

What is the meaning? Why is it there? These are among the most important questions that can be asked. Though physicists may provide profound mathematical equations, they will thereby offer only more precise detail as to what is happening. We shall not receive an answer to the “What” and the “Why” without recourse to meta-physics, beyond the realm of brain-devised definitions.

The human mind is limited in its present stage of evolution. It may see the logical necessity of infinity referent to space and time; for if not infinity, what then is on the other side of the “fence” that is our outermost limit? But, being able to perceive the logical necessity of infinity, the finite mind still cannot span the limitless ranges of space, time, and substance.

If we human beings are manifold in our composition, and since we draw our very existence and sustenance from the universe at large, our conjoint nature must be drawn from the sources of life, substance, and energy, in which our and all other cosmic lives are immersed.

As the authors conclude their fascinating work:

“The worlds opened to our view are graced with wonderful symmetry and uniformity. Learning to know them, to appreciate their many harmonies, is like deepening an acquaintance with some great and meaningful piece of music — surely one of the best things life has to offer.”

Geach and Relative Identity

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The Theory of Relative Identity is a logical innovation due to Peter Thomas Geach  (P.T. Geach-Logic Matters) motivated by the same sort of mathematical examples as Frege’s definition by abstraction. Like Frege Geach seeks to give a logical sense to mathematical talk “up to” a given equivalence E through replacing E by identity but unlike Frege he purports, in doing so, to avoid the introduction of new abstract objects (which in his view causes unnecessary ontological inflation). The price for the ontological parsimony is Geach’s repudiation of Frege’s principle of a unique and absolute identity for the objects in the domain over which quantified variables range. According to Geach things can be same in one way while differing in others. For example two printed letters aa are same as a type but different as tokens. In Geach’s view this distinction does not commit us to a-tokens and a-types as entities but presents two different ways of describing the same reality. The unspecified (or “absolute” in Geach’s terminology) notion of identity so important for Frege is in Geach’s view is incoherent.

Geach’s proposal appears to account better for the way the notion of identity is employed in mathematics since it does not invoke “directions” or other mathematically redundant concepts. It captures particularly well the way the notion of identity is understood in Category theory. According to Baez & Dolan

In a category, two objects can be “the same in a way” while still being different.

So in Category theory the notion of identity is relative in exactly Geach’s sense. But from the logical point of view the notion of relative identity remains highly controversial. Let x,y be identical in one way but not in another, or in symbols: Id(x,y) & ¬Id'(x,y). The intended interpretation assumes that x in the left part of the formula and x in the right part have the same referent, where this last same apparently expresses absolute not relative identity. So talk of relative identity arguably smuggles in the usual absolute notion of identity anyway. If so, there seems good reason to take a standard line and reserve the term “identity” for absolute identity.

We see that Plato, Frege and Geach propose three different views of identity in mathematics. Plato notes that the sense of “the same” as applied to mathematical objects and to the ideas is different: properly speaking, sameness (identity) applies only to ideas while in mathematics sameness means equality or some other equivalence relation. Although Plato certainly recognizes essential links between mathematical objects and Ideas (recall the “ideal numbers”) he keeps the two domains apart. Unlike Plato Frege supposes that identity is a purely logical and domain-independent notion, which mathematicians must rely upon in order to talk about the sameness or difference of mathematical objects, or any other kind at all. Geach’s proposal has the opposite aim: to provide a logical justification for the way of thinking about the (relativized) notions of sameness and difference which he takes to be usual in mathematical contexts and then extend it to contexts outside mathematics (As Geach says):

Any equivalence relation … can be used to specify a criterion of relative identity. The procedure is common enough in mathematics: e.g. there is a certain equivalence relation between ordered pairs of integers by virtue of which we may say that x and y though distinct ordered pairs, are one and the same rational number. The absolute identity theorist regards this procedure as unrigorous but on a relative identity view it is fully rigorous.

New Critique: From Hyper-heteronomy to Autonomy. Thought of the Day 13.0

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The new critique is an invention of a new form of autonomy from hyper-heteronomy, a therapeutics of the pharmakon. This critique is dimensional in that, it is pharmacological, a critique that consists in analyzing the specifics of the pharmaka, a critique that invests its energy in finding the toxic possibilities of individuation, through an approach that is both theoretical and absolute and that is without a context, but not totally context-free, since it is an organological approach, an approach which is always within a context, in the Nietzschean genealogical sense of the term, but is at the same time independent of any particular political situation.

A Theosophist Reading of Spinoza and Bohm. For Whom the Bell Tolls.

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To Spinoza mind and matter were parallel attributes of God or Substance, the great essence of the universe sometimes called in theosophical literature Svabhavat, primordial nature, mind-substance. Svabhavat (from the Sanskrit sva, “self” and bhu, “to become”) means self-becoming. Nothing can exist other than as an emanation from this primordial nature’s eternal action. Nothing, said Spinoza, can exist except this Substance and the unfolding of its attributes. This being so, “creation” had no beginning and will have no end; all things come forth from the Boundless and will therefore continue forever — theosophical ideas found also in Neoplatonism and Gnosticism.

With Spinoza we find emphasis on the essential unity and continuity of all existence, while Pythagoras, Plato, and Leibniz distinguish countless monads in it, centers of activity in every conceivable grade of self-expression. Combining the monad theory with Spinoza’s philosophy, a worldview emerges remarkably in accord with ideas from the Upanishads, Vedanta, Buddhism, and many a thinker from ancient Greece. We find corresponding ideas in the writings of theoretical physicist David Bohm, who also believed that the distinction between animate and inanimate nature is arbitrary, of use in some contexts but ultimately incorrect. He came to the conclusion that, far from being empty, space is an immense ocean of energy, and matter no more than a superficial ripple on that ocean. Everything lies concealed in an “implicate order” and comes forth from it. To illustrate this idea Bohm used the following experiment: the outer of two concentric cylinders is filled with a viscous fluid, such as glycerin, into which is placed a drop of insoluble ink. When the outer cylinder is rotated very slowly, the ink drop threads out, growing thinner and thinner, and eventually becomes invisible. The dye molecules become distributed among the molecules of the liquid as a grey shade. Rotating the cylinder in the opposite direction yields a surprising result: slender threads appear, growing thicker and thicker until, suddenly, the globule of ink is seen once more. This suggests that out of the “holomovement” of the ocean of energy comes forth the known universe with all that is in it.

From the “reality of the first order,” or implicate order, issues the explicate order, the world of forms and living things. In this “reality of the second order” these things have a relatively separate existence, as the Gulf Stream and other currents have a relatively separate existence within the Atlantic Ocean. From atoms to galaxies, all the phenomena of nature emerge from the ocean of the implicate order, make their appearance as “relatively autonomous subtotals,” and at the same time are linked with everything else.

Bohm regarded the universe as an undivided whole, a continuously ongoing process whose “ultimate ground of being is entirely unutterable, entirely implicit.” Space is not a nothingness but is in essence this ultimate ground of being. He employed the image of a crystal through which at absolute zero, according to quantum theory, electrons would pass as if it were empty space. The crystal would then be perfectly homogeneous and would seem nonexistent for the electrons, as space seems nonexistent for us. But when the temperature is raised, inhomogeneities appear, scattering the electrons. If one were to focus the electrons with an electron lens to make a picture of the crystal, it “would then appear that the inhomogeneities exist independently and that the main body of the crystal was sheer nothingness”. Like the school of Parmenides and Zeno in ancient Greece, Bohm regarded space as a plenum, utter fullness, the ground or substratum of all that exists. The matter that we sense is, like flaws in the crystal, inhomogeneities in space, which is the unity that includes both matter and consciousness.

Another physicist whose work endorsed the interconnectedness of things was John S. Bell. Two particles moving away from each other at the speed of light were thought to have lost contact forever, since no signal from one could overtake and influence the other. In 1964 Bell proposed his theory that particles like these do influence each other all the same and therefore, somehow, never lose contact. The theory was experimentally confirmed for the first time in 1972. Science seems to be overstepping its own boundaries, penetrating a realm where mystics have been long before. Not surprisingly modern thinkers are taking note of ancient ideas with amazement and admiration.

When H. P. Blavatsky published The Secret Doctrine in 1888, she stated that the ideas it contained were neither her own nor new. She sketched in bold strokes once again the existence of infinite Space, ground of countless universes, populated and ensouled by numberless monads: not as unconnected, separate things, but as differentiations within the whole. She spoke of “The fundamental identity of all Souls with the Universal Over-Soul,” and gave a vertiginous panorama of the evolutionary track, not of bodies, forms, but of centers of consciousness, monads, from their differentiation within the Oversoul to their grand consummatum est, the attainment of fully self-conscious realization of cosmic consciousness at the end of the world period. A work like The Secret Doctrine could not fail to cause a commotion in those days; recent developments have paved the way for us better to appreciate these thoughts and subscribe to the fundamental unity of man and universe.

The human mind is not extraneous to the mind of the universe. In fact, nothing is conceivable apart from the fundamental space-energy-mind to which the ancient Vedic poet would not give a name. Names indicate qualities, and so imply limitations because every quality excludes its opposite. So the Vedic sage spoke simply of tat, That. In the subtle logic of Buddhist thinking, the absolute fullness of space is called sunyata, emptiness: all that exists is as ripples in this boundless ocean which cannot be said to have this or that form, and which in that sense is “empty.” With their plenum or pleroma the Gnostics and other ancient Mediterranean thinkers emphasized its “fullness,” which comprises all worlds, our visible as well as numerous invisible ones. These worlds may be symbolized as rungs on the unending “ladder of being.” Whether the inhabitants of realms higher than ours are called aeons, angelic orders, or dhyani-buddhas makes no difference. The world is the interaction of a variety of monads, but not all monads necessarily express themselves on the physical level. Although in essence all monads are aspects of the ultimate ground of being, in their forms of manifestation they are infinitely varied. In their totality they constitute nature, the Jacob’s ladder of evolving beings, conjointly weaving the fabric of visible and invisible worlds, the multiplicity of “parallel universes” modern thinkers are beginning to surmise.

Metempsychosis of the Ancients’ Veritability

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The impenetrable veil of arcane secrecy was thrown over the sciences taught in the sanctuary. This is the cause of the modern depreciation of the ancient philosophies. Much of Plato’s public teachings and writings had therefore to consist of blinds or half-truths or allegories, and just as Jesus spoke in parables, so the Mysteries were ever reserved for special groups of neophytes – and, needless to say, they did not reach the Church of the days of Constantine, which never held the keys of the Mysteries, and hence can hardly be said to have lost them.

The ancient philosophers seem to be generally held, even by the least prejudiced of modern critics, to have lacked that profundity and thorough knowledge in the exact sciences of which a couple of last centuries and present are so boastful. It is even questioned whether they understood that basic scientific principle: ex nihilo nihil fit. If they suspected the indestructibility of matter at all – say these commentators – it was not in consequence of a firmly established formula, but only through intuitional reasoning and by analogy. The philosophers themselves had to be initiated into perceptive mysteries, before they could grasp the correct idea of the ancients in relation to this most metaphysical subject. Otherwise – outside such initiation – for every thinker there will be a “Thus far shalt thou go and no further,” mapped out by his intellectual capacity, as clearly and unmistakably as there is for the progress of any nation or race in its cycle by the law of karma. Much of current agnostic speculation on the existence of the “First Cause” is little better than veiled materialism — the terminology alone being different. Even so a thinker as Herbert Spencer speaks of the “Unknowable” occasionally in terms that demonstrate the lethal influence of materialistic thought which, like the deadly sirocco, has withered and blighted most of current ontological speculation. For instance, when he terms the “First Cause” — the Unknowable — a “power manifesting through phenomena,” and an “infinite eternal Energy,” (?) it is clear that he has grasped solely the physical aspect of the mystery of Being — the energies of cosmic substance only. The co-eternal aspect of the ONE REALITY — cosmic ideation — (as to its noumenon, it seems nonexistent in his mind) — is absolutely omitted from consideration.

The doctrine of metempsychosis has been abundantly ridiculed by scientists and rejected by theologians, yet if it had been properly understood in its application to the indestructibility of matter and the immortality of spirit, it would have been perceived that it is a sublime conception. Should we not first regard the subject from the standpoint of the ancients before venturing to disparage its teachers? The solution of the great problem of eternity belongs neither to religious superstition nor to gross materialism. The harmony and mathematical equiformity of the double evolution – spiritual and physical – are elucidated only in the universal numerals of Pythagoras, who built his system entirely upon the so-called metrical speech of the Hindu Vedas.

Theosophical Panpsychism

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Where does mind individually, and consciousness ultimately, originate? In the cosmos there is only one life, one consciousness, which masquerades under all the different forms of sentient beings. This one consciousness pierces up and down through all the states and planes of being and serves to uphold the memory, whether complete or incomplete, of each state’s experience. This suggests that our self-conscious mind is really a ray of cosmic mind. There is a mysterious vital life essence and force involved in the interaction of spirit or consciousness with matter. The cosmos has its memory and follows general pathways of formation based on previous existences, much as everything else does. Aided by memory, it somehow selects out of the infinite possibilities a new and improved imbodiment. When the first impulse emerges, we have cosmic ideation vibrating the first matter, manifesting in countless hierarchies of beings in endless gradations. Born of the one cosmic parent, monadic centers emerge as vital seeds of consciousness, as germs of its potential. They are little universes in the one universe.

Theosophy does not separate the world into organic and inorganic, for even the atoms are considered god-sparks. All beings are continuously their own creators and recorders, forming more perishable outer veils while retaining the indestructible thread-self that links all their various principles and monads through vast cycles of experience. We are monads or god-sparks currently evolving throughout the human stage. The deathless monad runs through all our imbodiments, for we have repeated many times the processes of birth and death. In fact, birth and death for most of humanity are more or less automatic, unconscious experiences as far as our everyday awareness is concerned. How do we think? We can start, for example, with desire which provides the impulse that causes the mind through will and imagination to project a stream of thoughts, which are living elemental beings. These thoughts take various forms which may result in different kinds of actions or creative results. This is another arena of responsibility, for in the astral light our thoughts circulate through other minds and affect them, but those that belong to us have our stamp and return to us again and again. So through these streams of thought we create habits of mind, which build our character and eventually our self-made destiny. The human mind is an ideator resonating with its past, selecting thoughts and making choices, anticipating and creating a pattern of unfolding. Perhaps we are reflecting in the small the operations of the divine mind which acts as the cosmic creator and architect. Some thoughts or patterns we create are limiting; others are liberating. The soul grows, and thoughts are reused and transformed by the mind, perhaps giving them a superior expression. Plato was right: with spiritual will and worthiness we can recollect the wisdom of the past and unlock the higher mind. We have the capacity of identifying with all beings, experiencing the oneness we share together in our spiritual consciousness, that continuous stream that is the indestructible thread-self. All that it was, is, or is becoming is our karma. Mind and memory are a permanent part of the reincarnating ego or human soul, and of the universe as well.

In the cosmos there are many physical, psychic, mental, and spiritual fields — self-organizing, whole, living systems. Every such field is holographic in that it contains the characteristics of every other field within itself. Rupert Sheldrake’s concepts of morphic fields and morphic resonance, for instance, are in many ways similar to some phenomena attributed to the astral light. All terrestrial entities can be considered fields belonging to our living earth, Gaia, and forming part of her constitution. The higher akasic fields resonate with every part of nature. Various happenings within the earth’s astral light are said to result in physical effects which include all natural and human phenomena, ranging from epidemics and earthquakes to wars and weather patterns. Gaia, again, is part of the fields which form the solar being and its constitution, and so on throughout the cosmos.

Like the earth, human beings each have auric fields and an astral body. The fifty trillion cells in our body, as well as the tissues and organs they form, each have their own identity and memory. Our mental and emotional fields influence every cell and atom of our being for better or worse. How we think and act affects not only humanity but Gaia as well through the astral light, the action of which is guided by active creative intelligences. For example, the automatic action of divine beings restores harmony, balancing the inner with the outer throughout nature.

Heidegger’s Bridge to Latency. Note Quote.

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We can understand Heidegger’s choice of the term hermeneutics over alternatives as interpretation when we remember that implicit in the Heideggerian project is the effort to regain a grasp of being that has been lost in modern times and indeed since the time of Plato and Aristotle. One seeks the “hidden weight” of ancient words precisely in order to go behind what is self-evident in modern thinking. This special and intense listening Heidegger calls for is necessary in order to break away from the confines of the modern world view. Hermeneutics, it will be remembered, is the discipline concerned with deciphering utterances from other times, places, and languages–without imposing one’s own categories on them (the hermeneutic problem). It is significant that Heidegger attempts to sharpen his reflection by a conversation with a person from a radically alien world–a Japanese. The atmosphere of the conversation is an effort to understand the most difficult and ineffable conceptions–beauty, utterance, language. A Japanese tentativeness and delicacy pervades the dialogue, and one can understand Heidegger’s fascination with a people whose art strives for the letting-be of what is.

But the use of a Japanese dialogical partner is not the only indication of Heidegger’s effort to transcend the westernized, modern world view. Heidegger explicitly states that the careful listener will put in question “the guiding notions which, under the names ‘expression,’ ‘experience,’ and ‘consciousness,’ determine modern thinking. If one thinks of these conceptions as constituting the make-up of one’s “world,” then what Heidegger has in mind is that interpretation as hermeneutics should be “world-shaking,” a fateful message that shakes the foundations of thought. Only an interpretation that goes outside the prevailing conceptualities can move toward what Heidegger has in mind–“a transformation of thinking.” Unfortunately, the word interpretation fails to suggest a mediation from something outside and alien, but hermeneutics, since it customarily has reference to interpreting ancient texts in another language, has precisely this sense of relating to something essentially other yet capable of being understood.

The mediation Heidegger has in mind here is ontologically significant. It would seem to be a kind of bridge to non-being. The transcending of the already-given world is elsewhere in Heidegger even called the “step back”: a “step back” from presentational thought as such. This “step back” is a movement back from embeddedness in a set of fixed definitions of reality, in order to regain access to a certain realm of “latency” which we might also call our deeper sense of the meaning of being. Heidegger roots his thinking in a latency lying below the level of manifest consciousness. It is not nonbeing in the sense of a mere emptiness but rather a source of being for which the word “latency” seems rather apt. The mediation, in this case, is not between two well-lighted but incommensurate realms of being but between the well-lighted daylight of consciousness and something more like the mysterious night of what lies below and above consciousness. Heidegger clarified in his well-known letter to Richardson that this realm, as ontological nonbeing, is not the transcendental in the sense of Kant’s conditions for the possibility for phenomena but a kind of creative foundation and source for our being-in-the-world.