Physics I: Chapter 16

Reference: Beginning Physics I

CHAPTER 16: THERMODYNAMICS II: GAS LAWS, THE ATOMIC VIEW, AND STATISTICAL MECHANICS

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KEY WORD LIST

Molecular Mass, Mole, Avogadro’s Number, Boltzmann Constant, Universal Gas Constant, Ideal Gas Law, Average Kinetic Energy, Mean Square Velocity, Internal Energy, Heat Capacity, Molar Heat Capacity, Equipartition of Energy, Statistical Mechanics, Law of Dulong and Petit

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GLOSSARY

For details on the following concepts, please consult CHAPTER 16.

MOLECULAR MASS
A mass of any substance whose numerical value in grams is the same as its atomic or molecular mass is called a gram atomic or molecular mass of that substance.

MOLE
One gram atomic or molecular mass of any substance is called a mole of that substance.

AVOGADRO’S NUMBER (NA)
The number of atoms or molecules in a mole of any substance is this a universal constant called Avogadro’s Number.

BOLTZMANN CONSTANT (k)
This is a universal constant:           

k = 1.38 x 10-23 J/(particle. K)

UNIVERSAL GAS CONSTANT (R)

R = NAk = 8.31 J / (mol . K)

IDEAL GAS LAW
For any confined diluted gas:        

PV = nRT

The result from the laws of statistical mechanics is

AVERAGE KINETIC ENERGY
The average translational kinetic energy per molecule in a sample of ideal gas is

This gives a fundamental meaning to the concept of temperature.

MEAN SQUARE VELOCITY
The mean square velocity (v2)av is the average value of the square of the magnitude of velocity of the gas molecules.

At a given temperature the lighter molecules have greater velocities since the average kinetic energy is the same for all gases at a given temperature.

INTERNAL ENERGY (U)
In our infinitesimal “billiard ball” model of a monoatomic gas, the only energy is translational kinetic energy. Therefore, the internal energy is:

If we add some heat to our system, we must have,

HEAT CAPACITY (C)
Heat capacity is the total amount of heat needed to produce a degree rise in temperature. For a constant volume process,

MOLAR HEAT CAPACITY (cv)
The heat capacity per mole for an ideal gas at constant volume:

The heat capacity per mole for an ideal gas at constant pressure:

EQUIPARTITION OF ENERGY
These results, in which each degree of freedom that involves energy (with certain restrictions) contribute the same value (1/2 kT) to the average energy, are called the law of equipartition of energy.

STATISTICAL MECHANICS
Thermodynamics and statistical mechanics thus allowed for the indirect study of the physics of the realm of atoms and molecules, which lead to the realization that Newtonian mechanics does not apply in this realm. This in turn led to the formulation of the new “quantum” mechanics in the early twentieth century.

LAW OF DULONG AND PETIT
A study of the actual values of the molar heat capacities of crystalline solids at constant volume shows that at high temperatures they all have essentially the same molar heat capacity 3R (six degrees of freedom). But all real crystal solids have molar heat capacities that decrease to zero as the Kelvin temperature decreases to zero. This is because the assumption of Newtonian mechanics do not hold.

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The Unknowable of the Eighth Dynamic

Please see Course on Subject Clearing

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The Scientific Method

We don’t know everything. We find that there are gaps in what we know. To fill those gaps we make a postulate and develop a theory based on it. The theory then predicts phenomenon, which, if verified, validates the theory and the postulate. If it cannot be verified, then one goes back to the drawing board. This is the scientific method. Using this method we build up a network of postulates and considerations consistent with what we observe. 

But how far can we go with this system. Can we know everything?

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Dimensions and Duality

If we know everything, there would be no doubts, perplexities and confusions. There would be total certainty. There would not be any unanswered questions. One would be able to resolve any suffering; and a perfect life would be achievable.

But the universe is not unipolar. It has dimensions; and each dimension is made up of gradients that lead to two opposites. If there is perfection, there must also be imperfection. If there are things known, then there must be things unknown. If there are aspects of this universe that are knowable, then there must also be aspects that are unknowable.  

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Knowable and Unknowable

It is this Unknowable that Hinduism have labeled Brahman, and Judaism has labeled YHVH. It is the Unknowable that generates the knowable. The unknowable forms the background of all that is knowable. 

If you look carefully, you will find that everything you know is based on your considerations. Yes, there are sensations that you pick up; but, then, your considerations interpret them for you. So, you only know your considerations. Beyond those considerations lies the unknowable. Hinduism defines Brahman as THAT which is not the outcome of any consideration. Judaism forbids the original pronunciation of YHVH.

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Auditing the Unknowable

When we are resolving anomalies, we are auditing the Unknowable. The unknowable trickles into our consciousness in the form of intuition and becomes knowable. This process is endless.

Here is what Herbert Spencer wrote on the subject of Unknowable.

Durant 1926: The Unknowable (Herbert Spencer)

Here are the earlier essays from the blog on this subject.

  1. Knowable and Unknowable September 5, 2010
  2. The Paradox of Unknowable May 8, 2011
  3. The Algebra of Unknowable May 18, 2011
  4. Definition of Unknowable June 25, 2011
  5. Research into Unknowable November 3, 2011
  6. What is Unknowable? November 10, 2011
  7. The Factors of Unknowable November 13, 2011
  8. Infinity and Unknowable December 17, 2011
  9. More on Unknowable February 11, 2012
  10. The Unknowables November 5, 2013
  11. Universe and AwarenessSeptember 30, 2014
  12. Unknowable and Postulates November 24, 2022

The above may be looked upon as the auditing of the Eighth Dynamic, which was outlined by Hubbard but not explained. To audit, subject clear the above data.

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HINDUISM: Coming of Age in the Universe

Reference: Hinduism

Note: The original Text is provided below.
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The universe is like the Kalpataru tree. It grants all wishes, but together with consequences. It wises the soul up as it passes through it.

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Summary

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Comments

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Original Text

With God in pivotal position in the Hindu scheme, we can return to human beings to draw together systematically the Hindu concept of their nature and destiny. 

Individual souls, or jivas, enter the world mysteriously; by God’s power we may be sure, but how or for what reason we are unable fully to explain. Like bubbles that form on the bottom of a boiling teakettle, they make their way through the water (universe) until they break free into the limitless atmosphere of illumination (liberation). They begin as the souls of the simplest forms of life, but they do not vanish with the death of their original bodies. In the Hindu view spirit no more depends on the body it inhabits than body depends on the clothes it wears or the house it lives in. When we outgrow a suit or find our house too cramped, we exchange these for roomier ones that offer our bodies freer play. Souls do the same.

Worn-out garments
Are shed by the body:
Worn-out bodies
Are shed by the dweller. (Bhagavad-Gita, II:22)

This process by which an individual jiva passes through a sequence of bodies is known as reincarnation or transmigration of the soul—in Sanskrit samsara, a word that signifies endless passage through cycles of life, death, and rebirth. On the subhuman level the passage is through a series of increasingly complex bodies until at last a human one is attained. Up to this point the soul’s growth is virtually automatic. It is as if the soul were growing as steadily and normally as a plant and receiving at each successive embodiment a body that, being more complex, provides the needed largess for its new capabilities.

With the soul’s graduation into a human body, this automatic, escalator-like mode of ascent comes to an end. Its entry into this exalted habitation is evidence that the soul has reached self-consciousness, and with this estate come freedom, responsibility, and effort.

The mechanism that ties these new acquisitions together is the law of karma. The literal meaning of karma (as we encountered it in karma yoga) is work, but as a doctrine it means, roughly, the moral law of cause and effect. Science has alerted the West to the importance of causal relationships in the physical world. Every physical event, we are inclined to believe, has its cause, and every cause will have its determinate effects. India extends this concept of causation to include moral and spiritual life as well. To some extent the West has as well. “As a man sows, so shall he reap”; or again, “Sow a thought and reap an act, sow an act and reap a habit, sow a habit and reap a character; sow a character and reap a destiny”—these are ways the West has put the point. The difference is that India tightens up and extends its concept of moral law to see it as absolute; it brooks no exceptions. The present condition of each interior life—how happy it is, how confused or serene, how much it sees—is an exact product of what it has wanted and done in the past. Equally, its present thoughts and decisions are determining its future experiences. Each act that is directed upon the world has its equal and opposite reaction on oneself. Each thought and deed delivers an unseen chisel blow that sculpts one’s destiny.

This idea of karma and the completely moral universe it implies carries two important psychological corollaries. First, it commits the Hindu who understands it to complete personal responsibility. Each individual is wholly responsible for his or her present condition and will have exactly the future he or she is now creating. Most people are not willing to admit this. They prefer, as the psychologists say, to project—to locate the source of their difficulties outside themselves. They want excuses, someone to blame so that they may be exonerated. This, say the Hindus, is immature. Everybody gets exactly what is deserved—we have made our beds and must lie in them. Conversely, the idea of a moral universe closes the door on chance or accident. Most people have little idea how much they secretly bank on luck—hard luck to justify past failures, good luck to bring future successes. How many people drift through life simply waiting for the breaks, for that moment when a lucky lottery number brings riches and a dizzying spell of fame. If you approach life this way, says Hinduism, you misjudge your position pathetically. Breaks have nothing to do with protracted levels of happiness, nor do they happen by chance. We live in a world in which there is no chance or accident. Those words are simply covers for ignorance.

Because karma implies a lawful world, it has often been interpreted as fatalism. However often Hindus may have succumbed to this interpretation, it is untrue to the doctrine itself. Karma decrees that every decision must have its determinate consequences, but the decisions themselves are, in the last analysis, freely arrived at. To approach the matter from the other direction, the consequences of one’s past decisions condition one’s present lot, as a card player finds himself dealt a particular hand while remaining free to play that hand in a variety of ways. This means that the career of a soul as it threads its course through innumerable human bodies is guided by its choices, which are controlled by what the soul wants and wills at each stage of the journey.

What its wants are, and the order in which they appear, can be summarized quickly here, for previous sections have considered them at length. When it first enters a human body, a jiva (soul) wants nothing more than to taste widely of the sense delights its new physical equipment makes possible. With repetition, however, even the most ecstatic of these falls prey to habituation and grows monotonous, whereupon the jiva turns to social conquests to escape boredom. These conquests—the various modes of wealth, fame, and power—can hold the individual’s interest for a considerable time. The stakes are high and their attainment richly gratifying. Eventually, however, this entire program of personal ambition is seen for what it is: a game—a fabulous, exciting, history-making game, but a game all the same.

As long as it holds one’s interest, it satisfies. But when novelty wears off, when a winner has acknowledged with the same bow and pretty little speech the accolades that have come so many times before, he or she begins to yearn for something new and more deeply satisfying. Duty, the total dedication of one’s life to one’s community, can fill the need for a while, but the ironies and anomalies of history make this object too a revolving door. Lean on it and it gives, but in time one discovers that it is going round and round. After social dedication the only good that can satisfy is one that is infinite and eternal, whose realization can turn all experience, even the experience of time and apparent defeat, into splendor, as storm clouds drifting through a valley look different viewed from a peak that is bathed in sunshine. The bubble is approaching the water’s surface and is demanding final release.

The soul’s progress through these ascending strata of human wants does not take the form of a straight line with an acute upward angle. It fumbles and zigzags its way toward what it really needs. In the long run, however, the trend of attachments will be upward—everyone finally gets the point. By “upward” here is meant a gradual relaxation of attachment to physical objects and stimuli, accompanied by a progressive release from self-interest. We can almost visualize the action of karma as it delivers the consequences of what the soul reaches out for. It is as if each desire that aims at the ego’s gratification adds a grain of concrete to the wall that surrounds the individual self and insulates it from the infinite sea of being that surrounds it; while, conversely, each compassionate or disinterested act dislodges a grain from the confining dike. Detachment cannot be overtly assessed, however; it has no public index. The fact that someone withdraws to a monastery is no proof of triumph over self and craving, for these may continue to abound in the imaginations of the heart. Conversely, an executive may be heavily involved in worldly responsibilities; but if he or she manages them detachedly—living in the world as a mudfish lives in the mud, without the mud’s sticking to it—the world becomes a ladder to ascend.

Never during its pilgrimage is the human spirit completely adrift and alone. From start to finish its nucleus is the Atman, the God within, exerting pressure to “out” like a jack-in-the-box. Underlying its whirlpool of transient feelings, emotions, and delusions is the self-luminous, abiding point of the transpersonal God. Though it is buried too deep in the soul to be normally noticed, it is the sole ground of human existence and awareness. As the sun lights the world even when cloud-covered, “the Immutable is never seen but is the Witness; It is never heard but is the Hearer; it is never thought, but is the Thinker; is never known, but is the Knower. There is no other witness but This, no other knower but This.” But God is not only the empowering agent in the soul’s every action. In the end it is God’s radiating warmth that melts the soul’s icecap, turning it into a pure capacity for God.

What happens then? Some say the individual soul passes into complete identification with God and loses every trace of its former separateness. Others, wishing to taste sugar, not be sugar, cherish the hope that some slight differentiation between the soul and God will still remain—a thin line upon the ocean that provides nevertheless a remnant of personal identity that some consider indispensable for the beatific vision.

Christopher Isherwood has written a story based on an Indian fable that summarizes the soul’s coming of age in the universe. An old man seated on a lawn with a group of children around him tells them of the magic Kalpataru tree that fulfills all wishes. “If you speak to it and tell it a wish; or if you lie down under it and think, or even dream, a wish, then that wish will be granted.” The old man proceeds to tell them that he once obtained such a tree and planted it in his garden. “In fact,” he tells them, “that is a Kalpataru over there”.

With that the children rush to the tree and begin to shower it with requests. Most of these turn out to be unwise, ending in either indigestion or tears. But the Kalpataru grants them indiscriminately. It has no interest in giving advice.

Years pass, and the Kalpataru is forgotten. The children have now grown into men and women and are trying to fulfill new wishes that they have found. At first they want their wishes to be fulfilled instantly, but later they search for wishes that can be fulfilled only with ever-increasing difficulty.

The point of the story is that the universe is one gigantic Wishing Tree, with branches that reach into every heart. The cosmic process decrees that sometime or other, in this life or another, each of these wishes will be granted—together, of course, with consequences. There was one child from the original group, however, so the story concludes, who did not spend his years skipping from desire to desire, from one gratification to another. For from the first he had understood the real nature of the Wishing Tree. “For him, the Kalpataru was not the pretty magic tree of his uncle’s story—it did not exist to grant the foolish wishes of children—it was unspeakably terrible and grand. It was his father and his mother. Its roots held the world together, and its branches reached beyond the stars. Before the beginning it had been—and would be, always.”

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JUDAISM: The Hallowing of Life

Reference: Judaism

[NOTE: In color are Vinaire’s comments.]

The basic manual for the hallowing of life is this Law, the first five books of the Bible, the Torah.

Up to this point in our effort to enter the Jewish perspective, we have been dealing with ideas as these occurred to the Jews in their struggle to make sense out of life. As an entrance to Judaism this serves a purpose, for ideas have a universality that makes them intelligible even to outsiders. We have reached a point, however, where (if we are to move deeper into the understanding of this faith) we must table further consideration of Jewish ideas and look at Jewish practices.

A deeper understand of Jewish faith comes from Jewish practices rather than from Jewish ideas.

We must consider Jewish ceremonies and observances, for it is generally agreed that Judaism is less an orthodoxy than an orthopraxis; Jews are united more by what they do than by what they think. One evidence of this is that Jews have never promulgated an official creed that must be accepted to belong to this faith. Observance, on the other hand—the circumcision of males, for example—is decisive. This emphasis on practice gives Judaism something of an oriental flavor; for whereas the West, influenced by the Greek partiality for abstract reason, emphasizes theology and creed, the East has approached religion through ritual and narrative. The difference is between the abstract and the concrete. Does Plato or Dostoevsky get closer to reality? Is love better expressed through words or an embrace?

Jews are united more by what they do than by what they think. This emphasis on practice gives Judaism something of an oriental flavor.

Before turning to Jewish ritual as such, it will be well to speak briefly of ritual in general, for despite its place in every religion we have thus far not addressed it directly. From a narrowly rational or utilitarian point of view, ritual is nonsense, a waste any way we look at it. All that money lavished on candles, cathedrals, prayer books, and incense; all the time spent in worship and sacrament; all the energy that goes into rising up and sitting down, kneeling and prostration, circumambulation and singing—to what end? It isn’t cost effective, we say. Moreover, it has about it an arbitrariness that makes it almost incomprehensible from the outside. A popular magazine carries a photograph of a chief-of-state rubbing noses with an Eskimo. To Eskimos rubbing noses is a friendship ritual. To us it’s simply funny.

From a narrowly rational or utilitarian point of view, rituals, in general, are nonsense.

Yet with all its arbitrariness and seeming waste, ritual plays a part in life that nothing else can fill, a part that is by no means confined to religion. For one thing, it eases us through tense situations and times of anxiety. Sometimes the anxiety is mild—during introductions, for example. I am introduced to a stranger. Not knowing how he or she will respond, I don’t know how to proceed. What should I say? What should I do? Ritual covers my uncertainty and awkwardness. It tells me to extend my hand and say “How do you do?” or “I’m pleased to meet you.” And in so doing it brings form out of chaos. It provides the moment I need to get my bearings. The awkwardness is over. I have recovered my balance and am ready to explore freer behavior.

Like postulates, rituals also provide some stability to ease us through tense situations and times of anxiety. 

If we need ritual to help us through situations as inconsequential as a casual introduction, how much more when we find ourselves really at a loss. Death is the glaring example. Stunned by tragic bereavement, we would founder completely if we were thrown on our own and had to think our way through the ordeal. This is why death, with its funerals and memorial services, its wakes and sitting shiva, is the most ritualized rite of passage. Ritual, with its prepared score to orchestrate the occasion, channels our actions and feelings at a time when solitude would be unbearable. And in the process it softens the blow. “Ashes to ashes, dust to dust”—the words don’t say whose ashes, for this is everybody; all of us. Ritual also rouses courage: “The Lord giveth and the Lord taketh away; blessed be the name of the Lord!” Finally, ritual sets death in perspective, connecting this particular death with its universal archetype. The deceased takes his or her place in the company of humankind, one step in the endless march of life into death and death into life again, with the continuum stretching both ways toward eternity.

Death, with its funerals and memorial services, its wakes and sitting shiva, is the most ritualized rite of passage. 

From the triviality of an introduction to the trauma of death, ritual smooths life’s transitions as perhaps nothing else can. But it also serves another function. In times of happiness it can intensify experience and raise joy to celebration. Here the examples are birthdays, weddings, and most simply a family’s evening meal. Here, in this best meal of the day, when perhaps for the first time the family is relaxed and together, a blessing can be something more than the starting line for a food race. It can hallow the occasion. The opposite of dead weight, it consecrates a daily pleasure.

Rituals like birthdays, weddings, and most simply a family’s evening meal, can intensify experience and raise joy to celebration.

Against these background observations concerning the place of ritual in life generally, we turn now to its place in Judaism, where it aims to hallow life—ideally, all life. The nineteenth chapter of Leviticus capsules the point when God says to Moses, “You shall be holy for I, your God, am holy!” What does holiness involve? To many moderns the word is empty; but those who feel the stir of wonder and can sense the ineffable pressing in on their lives from every side will know what Plato was talking about when he wrote, “First a shudder runs through you, and then the old awe creeps over you.” Those who have had such experiences will know the blend of mystery, ecstasy, and the numinous, which received classic description in Rudolph Otto’s The Idea of the Holy.

Rituals in Judaism aim to hallow life—to honor it as holy— to feel the awe of ineffable creeping over you.

To speak of the hallowing of life in Judaism is to refer to its conviction that all life down to its smallest element can, if rightly approached, be seen as a reflection of the infinite source of holiness, which is God. The name for this right approach to life and the world is piety, carefully distinguished from piosity, its counterfeit. In Judaism piety prepares the way for the coming of God’s kingdom on earth: the time when everything will be redeemed and sanctified and the holiness of all God’s creation will be transparently evident.

The hallowing of life in Judaism is to refer to its conviction that all life down to its smallest element can, if rightly approached, be seen as a reflection of the infinite source of holiness, which is God. 

The secret of piety consists in seeing the entire world as belonging to God and reflecting God’s glory. To rise in the morning on seeing the light of a new day, to eat a simple meal, to see a stream running between mossy stones, to watch the day slowly turn into evening—even small things like these can mirror God’s majesty. “To the religious man,” writes Abraham Heschel, “it is as if things stood with their backs to him, their faces turned to God.” To accept the good things of life, most of which come to us quite apart from our own efforts, as if they were matters of course without relating them to God, is quite wrong. In the Talmud to eat or drink without first making a blessing over the meal is compared to robbing God of his property. Through all Judaism runs this double theme: We should enjoy life’s goodness, and at the same time we should augment this joy by sharing it with God, just as any joy we feel is augmented when shared with friends. Jewish law sanctions all the good things of life—eating, marriage, children, nature, while elevating them all to holiness. It teaches that people should eat, that they should prepare their tables in the presence of the Lord. It teaches that people should drink, that they should use wine to consecrate the Sabbath. It teaches that people should be merry, that they should dance around the Torah. 

Through all Judaism runs this double theme: We should enjoy life’s goodness, and at the same time we should augment this joy by sharing it with God, just as any joy we feel is augmented when shared with friends. 

If we ask how this sense of the sanctity of all things is to be preserved against the backwash of the world’s routine, the Jew’s chief answer is: through tradition. Without attention, the human sense of wonder and the holy will stir occasionally, but to become a steady flame it must be tended. One of the best ways to do this is to steep oneself in a history that cries aloud of God’s providential acts and mercy in every generation. Against those who would throw the past away with both hands that they may grasp the present more firmly, Judaism accounts the memory of the past a priceless treasure. The most historically minded of all the religions, it finds holiness and history inseparable. In sinking the roots of their lives deep into the past, the Jews draw nourishment from events in which God’s acts were clearly visible. The Sabbath eve with its candles and cup of sanctification, the Passover feast with its many symbols, the austere solemnity of the Day of Atonement, the ram’s horn sounding the New Year, the scroll of the Torah adorned with breastplate and crown—the Jew finds nothing less than the meaning of life in these things, a meaning that spans the centuries in affirming God’s great goodness to God’s people. Even when Jews recall their tragedies and the price their survival has exacted of them, they are vividly aware of God’s sustaining hand. “To live by the Law,” writes a recent Jewish philosopher, “is to live within time the life of eternity.”

The human sense of wonder and the holy must be tended constantly by steeping oneself in a history that cries aloud of God’s providential acts and mercy in every generation. 

The basic manual for the hallowing of life is this Law, the first five books of the Bible, the Torah. When in the traditional synagogue service the time comes for returning the Torah to the Ark, the people recite a line from the Book of Proverbs: “It is a tree of life to those who grasp it.” There is meaning in this simile, for a tree is symbolic of life itself, of the miracle whereby inert elements of sun and rain and soil are drawn into the mystery of growth. So, too, for the Jews, the Torah. It too is a creative power that can elicit and sustain holiness in the lives of those whose flowering world would otherwise become dry stones. “It is a tree of life to those who grasp it.”

The basic manual for the hallowing of life is this Law, the first five books of the Bible, the Torah.

HINDUISM: “Thou Before Whom All Words Recoil”

Reference: Hinduism

Note: The original Text is provided below.
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God is the ultimate postulate. It is Sat, Chit, Ananda—the oneness of existence, the consciousness of things as they are, and the bliss of total comprehension.

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Summary

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Comments

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Original Text

The first principle of Japanese ikebana flower arrangement is to learn what to leave out. This is also the first principle to be learned in speaking of God, the Hindus insist. People are forever trying to lay hold of Reality with words, only in the end to find mystery rebuking their speech and their syllables swallowed by silence. The problem is not that our minds are not bright enough. The problem lies deeper. Minds, taken in their ordinary, surface sense, are the wrong kind of instrument for the undertaking. The effect, as a result, is like trying to ladle the ocean with a net, or lasso the wind with a rope. The awe-inspiring prayer of Shankara, the Thomas Aquinas of Hinduism, begins with the invocation, “Oh Thou, before whom all words recoil.”

The human mind has evolved to facilitate survival in the natural world. It is adapted to deal with finite objects. God, on the contrary, is infinite and of a completely different order of being from what our minds can grasp. To expect our minds to corner the infinite is like asking a dog to understand Einstein’s equation with its nose. This analogy becomes misleading if, pressed in a different direction, it suggests that we can never know the Abysmal God. The yogas, we have seen, are roads to precisely such realization. But the knowledge to which they lead transcends the knowledge of the rational mind; it rises to the deep yet dazzling darkness of the mystical consciousness. The only literally accurate description of the Unsearchable of which the ordinary mind is capable is neti…neti, not this…not this. If you traverse the length and breadth of the universe saying of everything you can see and conceive, “not this…not this,” what remains will be God.

And yet words and concepts cannot be avoided. Being the only equipment at our mind’s disposal, any conscious progress toward God must be made with their aid. Though concepts can never carry the mind to its destination, they can point in the right direction. 

We may begin simply with a name to hang our thoughts on. The name the Hindus give to the supreme reality is Brahman, which has a dual etymology, deriving as it does from both br, to breathe, and brih, to be great. The chief attributes to be linked with the name are sat, chit, and ananda; God is being, awareness, and bliss. Utter reality, utter consciousness, and utterly beyond all possibility of frustration—this is the basic Hindu view of God. Even these words cannot claim to describe God literally, however, for the meanings they carry for us are radically unlike the senses in which they apply to God. What pure being would be like, being infinite with absolutely nothing excluded, of this we have scarcely an inkling. Similarly with awareness and joy. In Spinoza’s formulation God’s nature resembles our words about as much as the dog star resembles a dog. The most that can be said for these words is that they are pointers; our minds do better to move in their direction than in the opposite. God lies on the further side of being as we understand it, not nothingness; beyond minds as we know them, not mindless clay; beyond ecstasy, not agony. 

This is as far as some minds need go in their vision of God: infinite being, infinite consciousness, infinite bliss—all else is at best commentary, at worst retraction. There are sages who can live in this austere, conceptually thin atmosphere of the spirit and find it invigorating; they can understand with Shankara that “the sun shines even without objects to shine upon.” Most people, however, cannot be gripped by such high-order abstractions. That C. S. Lewis is among their number is proof that their minds are not inferior, only different. Professor Lewis tells us that while he was a child his parents kept admonishing him not to think of God in terms of any form, for these could only limit his infinity. He tried his best to heed their instructions, but the closest he could come to the idea of a formless God was an infinite sea of grey tapioca. 

This anecdote, the Hindus would say, points up perfectly the circumstance of the man or woman whose mind must bite into something concrete and representational if it is to find life-sustaining meaning. Most people find it impossible to conceive, much less be motivated by, anything that is removed very far from direct experience. Hinduism advises such people not to try to think of God as the supreme instance of abstractions like being or consciousness, and instead to think of God as the archetype of the noblest reality they encounter in the natural world. This means thinking of God as the supreme person (Ishvara or Bhagavan), for people are nature’s noblest crown. Our discussion of bhakti yoga, the path to God through love and devotion, has already introduced us to God conceived in this way. This, in Pascal’s Western idiom, is the God of Abraham, Isaac, and Jacob, not the God of the philosophers. It is God as parent, lovingly merciful, omniscient, almighty, our eternal contemporary, the companion who understands.

God so conceived is called Saguna Brahman, or God-with-attributes as distinct from the philosophers’ more abstract Nirguna Brahman, or God-without-attributes. Nirguna Brahman is the ocean without a ripple; Saguna Brahman the same ocean alive with swells and waves. In the language of theology, the distinction is between personal and transpersonal conceptions of God. Hinduism has included superb champions of each view, notably Shankara for the transpersonal and Ramanuja for the personal; but the conclusion that does most justice to Hinduism as a whole and has its own explicit champions like Sri Ramakrishna is that both are equally correct. At first blush this may look like a glaring violation of the law of the excluded middle. God may be either personal or not, we are likely to insist, but not both. But is this so? What the disjunction forgets, India argues, is the distance our rational minds are from God in the first place. Intrinsically, God may not be capable of being two contradictory things—we say may not because logic itself may melt in the full blaze of the divine incandescence. But concepts of God contain so much alloy to begin with that two contradictory ones may be true, each from a different angle, as both wave and particles may be equally accurate heuristic devices for describing the nature of light. On the whole India has been content to encourage the devotee to conceive of Brahman as either personal or transpersonal, depending on which carries the most exalted meaning for the mind in question.

God’s relation to the world likewise varies according to the symbolism that is embraced. Conceived in personal terms, God will stand in relation to the world as an artist to his or her handiwork. God will be Creator (Brahma), Preserver (Vishnu), and Destroyer (Shiva), who in the end resolves all finite forms back into the primordial nature from which they sprang. On the other hand, conceived transpersonally, God stands above the struggle, aloof from the finite in every respect. “As the sun does not tremble, although its image trembles when you shake the cup filled with water in which the sun’s light is reflected; thus the Lord also is not affected by pain, although pain be felt by that part of him which is called the individual soul.” The world will still be God-dependent. It will have emerged in some unfathomable way from the divine plenitude and be sustained by its power. “He shining, the sun, the moon and the stars shine after Him; by His light all is lighted. He is the Ear of the ear, the Mind of the mind, the Speech of the speech, the Life of life, the Eye of the eye.” But God will not have intentionally willed the world, nor be affected by its inherent ambiguity, imperfections, and finitude.

The personalist will see little religious availability in this idea of a God who is so far removed from our predicaments as to be unaware of our very existence. Is it not religion’s death to despoil the human heart of its final treasure, the diamond of God’s love? The answer is that God serves an entirely different function for the transpersonalist, one that is equally religious, but different all the same. If one is struggling against a current it is comforting to have a master swimmer by one’s side. It is equally important that there be a shore, solid and serene, that lies beyond the struggle as the terminus of all one’s splashings. The transpersonalist has become so possessed by the goal as to forget all else, even the encouragement of supporting companions.

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