Category Archives: Science

NMT (No-Me Teaching) new series 67

NMT (No-Me Teaching) new series 67:

Some   Ramana Maharshi quotes:

Your own Realization is the best help possible help to others. But there really are no others to be helped. A Realized being sees only the Self, just like a goldsmith estimating the gold in various items of jewelry sees only gold. When you identify yourself with the Body then only the forms & shapes are there. But when you transcend your Body the others disappear along with your Body-consciousness. Do plants, trees, etc. exist at all apart from the Self ? Find it out. You think that you see them. Thought is projected out from the Self. Find out from where it rises. Thoughts will cease to rise & the Self alone will remain.

 It is like a Cinema-show. There is the light on the screen & the shadows flitting across it impress the audience as the enactment of some piece. If in the same play an audience also is shown on the screen as part of the performance. the seer & the seen will then both be on the screen. Apply it to yourself. You are the screen. The Self has created the Ego. The Ego has its accretions of thoughts which are displayed as the World, the trees & the plants of which you are asking. In Reality, all these are nothing but the Self. If you see the Self, the same will be found to be all, everywhere & always. Nothing but the Self exists.

Fine-Tuned Universe 47:

[In the unreal reflection called the “Universe”, a product of an unreal Mind, even there, Infinite Intelligence is evident and inspiring.]

 

So far the issue has been whether Fine-Tuning, in the relatively precise sense that that term has acquired in Cosmology, is likely to find fresh application in Biology.

The answer has been, on the whole, negative.  But suppose one were to address the issue more broadly.  Fine-Tuning is an instance of Design, real or apparent; but Design is itself a much broader category. The indications of design in the living World described in loving detail by 17th-century exponents of Natural Theology, such as Robert Boyle & John Ray, did not point to Fine-Tuning as the clue to the involvement of Intelligence.  Fine-Tuning is a highly specific sort of clue, as we have seen, leading to a specific set of alternative responses. Searching for evidence of design in the living world today, on the other hand, might perhaps have a higher likelihood of success, judging by the record, than trying to find analogs of Fine-Tuning there.

Might one infer, then, to something like design from claims of evolutionary inevitability or convergence? One could, of course, if one were to postulate a directive agency of some sort at work within the evolutionary process, itself impelling the process onward to higher and higher levels of complexity. Bergson’s “´elan vital” & Teilhard de Chardin’s “radial energy” would be of this sort. But it has to be said that suggestions of this kind have, on the whole, met with a frosty reception from evolutionary biologists. Such views challenge the overall adequacy of the neo-Darwinian explanatory framework, not a popular stand; critics respond that this framework is perfectly capable of handling whatever directions evolution can be shown to have taken.

It was the introduction of this framework that undermined the case for Design in the first place Design, that is, that would be associated with specific complex features of the living World. Its modern proponents often present the neo-Darwinian framework as having potentially universal applicability: wherever in the Universe a certain set of conditions, centered on descent with modification, is to be found, Evolution is bound to occur.

The only contingencies that arise in this scenario have to do with the satisfying of the required conditions & the presence in advance of reproducing organisms.  How well a Darwinian type of schema applies to the Origin of the first cells is still a matter of debate.

Holding that the contingencies are easily satisfied so that life must be commonplace throughout the vast Spaces & Times of the Universe, he “Pregnancy” thesis, as suggested to some that such a profusion would indicate the agency of Design in some form. Yet one wonders why frequency of occurrence, as against rarity, should of itself be significant in this context. If anything, extreme rarity would appear to be a more likely lead, if it could be established. But this is to barely scratch the surface of the burgeoning Life Sciences.

The prospects for finding indications in those Sciences for Fine-Tuning proper may not be bright.  But perhaps the notion of Design might still prove capacious enough to extend into current discussions of such themes as optimality & Fitness.

It would need to do so at the Cosmic level. At the local level of Terrestrial Biology, the Many-World alternative would be all too obvious so that even the appearance of design would hardly be countenanced. It may be worth recalling at this point, for the historical morals that might be drawn, an earlier appeal to Cosmic Fitness that elicited many of the same questions.

“Fitness of the Environment”

Henderson’s celebrated book, “The Fitness of the Environment is often cited as a harbinger of the fine-tuning theme in discussions of the place of Life in the Universe.  Having worked through the complexities of that theme, we are now in a better position to judge how close his contributions came to the contemporary notion of Fine-Tuning, and in what ways & for what reasons they fell short of it.

Henderson is not talking about the fitness of life for the environment in which it finds itself. He makes it clear that this can be explained along Darwinian lines: natural selection has shaped life to survive and, when possible, thrive in the particular environment it inhabits and to compensate for changes in that environment.

But this was not what Henderson meant by “fitness of the environment.” It was not where he believed a complement to the Darwinian account needed to be given.

What had struck him was the multiple “fitnesses” of the physical environment for the biochemistry of life in general. And by “environment,” he meant to include both the “external” and “internal,” with emphasis on the latter, following the practice initiated by Claude Bernard, who had had much to say about the milieu, as he termed it. Henderson was intrigued by the crucial roles that Water & Carbon dioxide & at a deeper level their 3 elemental constituents, Hydrogen, Oxygen, & most especially Carbon, played in all living processes. Those processes required complexity, as well as the capacity for self-regulation and metabolism. The properties of the 3 elements and the two compounds made from them seemed to him so ideally suited to these requirements, a conclusion worked out by him in impressive empirical detail that some sort of explanation of this was called for.

Henderson’s concern was not with particular environments, such as that of Earth, but with the cosmic environment (as he saw it) that is revealed by astronomy. He went to some lengths to argue the optimality of the advantages offered by the 2 key compounds and, thus, of their 3 component elements as well. He discussed the possibility that water and carbon might be of frequent occurrence on other planets, arguing for the superiority of water over any other known solvent in the biotic context, as well as for carbon over silicon. He did not go as far as to propose them as necessary conditions for life, a more difficult case to make. Nevertheless, some resonances with the account of Fine-Tuning sketched above were already apparent.

His main theme was the remarkable Fitness of the Chemical Environment for Life, and his problem was how to account for this. He ruled out chance: the coincidences between the properties of the favored elements and the needs of life are too remarkable for this to be a plausible response. Likewise, he dismissed design as an alternative explanation. The notion of design was outside the realm of science; besides, to an agnostic like himself, it held no attraction.

What is particularly striking is that he also excluded the Many-Universe alternative, the response favored by many recent cosmologists. He realized that talking about the superior merits in the Biotic context of the three favored elements might  suggest comparison with other possible chemistries that had a different repertoire of elements.

But this would introduce “other possible worlds in which matter may have different properties and energy different forms.”  And he will have nothing to do with such purely speculative “hypothetical worlds,” restricting himself quite explicitly to the chemistry of the cosmos that we know.

This was sufficient, in his estimate, to make his point about the remarkable biotic optimality of the three elements and their compounds.  Nowhere in his discussion did Henderson suggest the specifically Anthropic factor of a Selection Effect caused by our necessarily finding ourselves in the only one of a large Ensemble of universes in which we could find ourselves. It clearly would not have occurred to him, any more than to anyone else of his time, to take seriously the possibility of an ensemble of other actually existing universes governed by different physical laws as a means of solving his problem.

He had already made his negative attitude clear in regard to hypothetical alternative chemistries. But more to the point, as far as the comparison with Fine-Tuning is concerned, his argument was not specifically Anthropic in the first place.  He talked about the conditions for life in general, about what makes life flourish.  Human Life was not central to the point he was making, as it is in the Fine-Tuning argument.

Some more selected verses from the Ramana Maharshi disciple Master Nome:

Regarding the great aphorism (proclamation, mahavakya): “Thou art That”, wise Sages declare that the primary meaning of That is the Absolute Brahman. Likewise, the primary meaning of Thou is the Knower, or “I”.

The essential meaning of That is the True Self. Likewise, the essential meaning of Thou is only pure Being, pure Consciousness.  The meaning of both That & Thou is thus the same, & this identity is what art expresses.  “Art” is an expression of complete Identity.

That complete Identity is realized by relinquishing other ideas regarding That, & most importantly, by Self-Inquiry into Thou.  The deeper the Self-Inquiry into Thou, the more That is known as it is, for Thou art That.

No repetition of the idea: “I am That“, “I am the Self”, or “I am Brahman” is intended. For such implies the difference between the instructed & the instruction; between the meditator, the meditation, & the meditated upon; between the one desiring Liberation & the Liberation itself.  Repetition further implies difference between the self who would know & the Self to be known; between the realizer & that realized.

The Non-Dual Teaching of Identity with the Absolute Self, Brahman, is to be practiced by Self-Inquiry, full of clear discrimination, that frees one of the false notion of Do-er-ship, of being a sensing entity, of being an experiencer, of being a thinker, & such.  Thus one discerns that the one Self is not the Body, Mind, or Ego, or anything connected with these. Then one knows one’s own true Self to be truly Brahman.

The Knowledge of the Self becomes possible only when the Ego vanishes.  What remains is Self-evident, the Self-knowable, the eternally existing, the forever liberated that has never been bound.  The Freedom & Happiness of this Realization have no cause or reason.  This Freedom & Happiness are self-existing, as Being itself is.  Only un-Happiness & Bondage seem to have reasons. By inquiry, these apparent reasons are found to be merely Ignorance.

When the Knowledge that one is the Self, Brahman, is not veiled by certain false notions, the Self-Knowledge becomes firm. Those are the false notions that Reality is something other than the formless, motionless, immutable Self, & that Happiness is other than the blissful Self.  Then, the mis-identification of the Self with the Body or any other form becomes impossible.

The direct path of Knowledge is that in which one discriminates as described here, renounces the actions of the Body & the Mind. The direct path of Knowledge frees one from the ideas of being a Performer, Experiencer, Thinker, etc., abides free of outer sensing & inner conceiving activities, & thus know the Self to be That.

The practice of the Teaching of Thou art That is the Self-Inquiry: “Who am I ?”  Self-Knowledge is firm when the Knowledge of the Self, which is the Absolute, is not contradicted by the false notions that one lacks Bliss & has desires.  Self-Knowledge is firm when the Self-Knowledge is not contradicted by the false notions that one is not Consciousness & a Do-er. Self-Knowledge is firm when the Self-Knowledge is not contradicted by the false notions that one is not Being, but instead a bound entity.

Calculus for Yogis, part 10:

To partially explain how the previously mentioned “complex” Exponential is related to Sine & Cosine, we can do that by peeking at what are called “imaginary” numbers.  Quadratic [x2] & more complicated functions yield solutions with apparent radicals [square roots] with negative arguments, an impossibility for Real Numbers.

To give an expression to such “imaginary” numbers [apparent radicals with negative arguments]. Unity is replaced by the square root of  1, designated as i . So  5 has  5x  the magnitude.  When added to a Real Number, any Imaginary Number constitutes part of a Complex Number.  When plotted on an Argand Diagram, with an Imaginary axis taking the place of  a Y axis, we can see the Imaginary Number system, not as fanciful, but as “orthogonal” or at a Right Angle to the Real Number system, another “dimension” of sorts.

In any case, the “complex” Exponential,  eix  =  cos x   +  i sin x .  Besides connecting the Exponential to the Sine & Cosine functions, a connection already seen in the similarity of their Infinite Series expressions, complex numbers allows us a few straightforward Analogies.  In saying that the Imaginary Axis is in some ways at “right angles” to the Real Number Axis is seen again in Electronics phasor diagrams in which an Imaginary Axis is set at Right angles to the Horizontal X-axis.  That Imaginary Axis represents a Capacitance Inductance axis at right angles to a Real Axis which is parallel to Voltage & Current in a Resistor [for a Series RLC relationship].

In other words, Inductance & Capacitance are in some ways opposed to each other.  And their combined difference when combined with Resistance is plotted as a Vector between the Axes on a Phasor Diagram.  This Vector than is a Complex Number composed of an Imaginary Number, for difference between Inductance & Capacitance, & a Real Number for Resistance, or more correctly, the Resistive Impedance.

So then composite Complex Numbers, with the term Imaginary, is not in that sense just a factor of Imagination.  And the ordinary numbers, called Real Numbers, are not so much more Real.  It’s more like the Imaginary Number system is another number system “orthogonal” to or, as it were, at some kind of Right angles to do ordinary number system.

So instead of an Inductance Capacitance difference, we really meant a difference in the Impedance that this Capacitive, & the Impedance that is Inductive.  Electronics aside, this provides us with an analogy for an Indian principle of 3 guna’s or “qualities” of the Mind.

These 3 characteristics of Mind & Nature, Inert Tamas, Restless Rajas, & Elevating Sattva are seen in ancient Indian Sankhya Philosophy.

The moral is that to model opposing the Inert Capacitive guna Tamas with the Restless Inductive guna Rajas, we might use a final difference between the 2 “impedances”.  This joint Impedance then, when combined with the Resistive Impedance which represents a more Real guna Sattva as a description for a mode of Mind.  That mode of Mind can be optimized for Meditation.

Now Resistance happens to be the reciprocal of the term we most likely compare to the elevating guna Sattva, namely the Conductance. So we let Conductance [or its Reactance] be compared to Sattva.  We seek to put the Mind in a more of a pure Conductance mode prior to transcending all 3 guna’s.  To do this, we can either attempt to attenuate both Rajas & Tamas to 0, or as a second-best have their posing strengths cancel each other out, just as Inductive Impedance can cancel out Capacitive Impedance.

Applicable diagrams for a simple RLC series circuit & some of the relevant equations are seen above.  In plain English (& Sanskrit), we would like to eliminate the Rajas mode & the Thomas mode, Restlessness & Inertia.  Or else we can 1st have them cancel each other out, & then emphasize the Sattva elevating mode.  Then we transcend all 3 guna’s.

The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through:  

www.jpstiga.com/

http://jstiga.wixsite.com/nonduality/

or with Caps-sensitive:

http://sdrv.ms.YPOgkX/

Duplicates (but with graphics) have been available on:

http://www.blogger.com     as  “Being-as-Consciousness, Non-Duality – new & final version” with link:

http://being-as-consciousness.blogspot.com/

[But from now on, they will be different & still usually daily.]

There is no Creation, no Destruction, no Bondage, no longing to be freed from Bondage, no striving for Liberation, nor anyone who has attained Liberation. Know that this to be Ultimate Truth.”   the “no creation” school of Gaudapada, Shankara, Ramana, Nome Ajata Vada

for very succinct summary of the teaching & practice, see:  www.ajatavada.com/

NMT (No-Me Teaching) new series 66

NMT (No-Me Teaching) new series 66:

Some   Ramana Maharshi quotes:

Even the thought “l do not realize” is a hindrance. In fact, the Self alone is.

 Our real nature is mukti. But we are imagining we are bound & are making various, strenuous attempts to become free, while we are all the while free. This will be understood only when we reach that stage.

We will be surprised that we were frantically trying to attain something which we have always been &   are.

 A man goes to sleep in this hall. He dreams he has gone on a world tour, is roaming over hill &  dale, forest & country, desert & sea, across various continents & alter many years of weary & strenuous travel, returns to this country, reaches & walks in. Just at that moment he wakes up & finds he has not moved an inch but was sleeping where he lay down. He has not returned after great effort to this hall, but is & always has been in the hall. It is exactly like that. If he is asked. “Why being free, do we imagine that we are bound ?”  “Why being in the hall did you imagine you were on a World adventure, crossing hill & dale, desert & sea ?”  It is all Mind or Maya [Illusion].  

 See if the unreal has come to be. There is no such thing as the unreal, from another standpoint.

 The Self alone exists. When you try to trace the Ego, which is the basis of the perception of the World & everything else, you find the Ego does not exist at all & neither does all this creation that you see.

 The ajnani sees only the Mind which is a mere reflection. If the light of pure Consciousness because his Mind is extroverted & has never sought its source.

 Just as a small pot of water Reflects the enormous Sun within the narrow limits of the pot, even so the vasanas or latent tendencies of the Mind of the individual, acting as The reflecting medium, catch the all-pervading, infinite light of Consciousness. The form of this Reflection is the phenomenon called the Mind. Seeing only this Reflection, the ajnani is deluded into the belief that he is a finite being, the jiva, the individual self.

Fine-Tuned Universe 46:

[In the unreal reflection called the “Universe”, a product of an unreal Mind, even there, Infinite Intelligence is evident and inspiring.]

This 2nd element in every fine-tuning discussion draws on Biology only in the most general and speculative way. This is not the sort of Biology that one finds in a textbook, but the kind science-fiction writers without number have used in imagining living forms that escape almost any restriction that analogies with the Terrestrial Life we know would be likely to impose. So the search for conditions necessary for any form of life throughout the universe has to proceed very warily indeed. Still, the conditions that have so far played a part in the Fine-Tuning discussions (the need for elements more complex than Hydrogen & Helium to form the material basis of living process, the need for several generations of Stars to generate the heavier elements, etc.) seem reasonably secure.

But the problem is that we do not have a Cosmic Biology in the sense in which we do have a Cosmic Physics & Chemistry. The Life forms of Earth, & consequently the Biology built on them, have been shaped by the innumerable particularities of the Terrestrial environment over Billions of years.  Countless independent causal lines have crossed and recrossed to form the unique biota of the Earth of today & yesterday.  The limited Teleonomic order imposed by Natural Selection on individual Evolutionary lineages is nowhere near enough to yield anything that could plausibly count as a Cosmic Biology. The evidence of convergence in the Evolutionary record, so persuasively presented in recent work, does carry some weight in suggesting Universals of various kind.  But this still falls far short of providing an abstract framework within which all living processes would have to fit.

The prospect of terrestrial Biology’s suggesting a direct Fine-Tuning relationship on its own account might therefore be regarded as problematic.  It would seem that some feature of the complex Living Processes described in our Biology would have to demand Fine-Tuning on the part of some underlying physical parameter.

The immediate problem here is that Living Processes, as these are understood in Terrestrial Biology, do not necessarily have Cosmic scope.  Other worlds could well be found in our Universe where Biological processes of a substantially different sort flourish, calling into question the significance of an Earth-related “Fine-Tuning.”

The 2nd problem, of course, would be to establish a link to a physical parameter requiring Fine-Tuning for the Biological Process to go forward.

Still, it is worth carrying the matter a stage further. Take the issue of inevitability in Evolutionary Biology, for instance.  A good case can be made for holding that Evolution tends to converge over the course of time on certain favored forms.  Some would go even further, starting with the Origin of Life in a suitable Environment & moving easily to the eventual appearance of a Technologically competent civilization capable of communicating with us.

Others, however, would emphatically reject any suggestion of overall directionality in the Evolutionary Process, pointing to the many sources of contingency along the way – notably the occurrence of a major catastrophe on a global scale.

In a different, although related, context, the Origin of Life is taken by some to be of common, even inevitable, occurrence across the Cosmos, whereas others would see complex Life, at least, as a rare event, dependent on a host of contingent factors.

Does this issue bear on considerations of Fine-Tuning ?  Strictly speaking, this hardly seems to be the case.  Fine-Tuning connotes a certain precariousness, a condition barely met.  Features such as inevitability or convergence in the story of Evolution convey just the opposite. Evolutionary sequences are sometimes said to converge on forms possessing specific functions with no hint of the Environmental constraints required for this to happen.

Claims of Inevitability or Convergence could be either broadly empirical, based on scrutiny of the historical record of Terrestrial Evolution, or broadly theoretical, based on how Darwinian evolution is supposed to work in general terms.  But in neither case does anything like Fine-Tuning appear to be involved quite the reverse, it might seem. Nor is the broader claim any better: that the cosmos is pregnant with Life & the Origin of Life faces no particular barrier in the widest variety of cosmic circumstances.

One might argue that a Universe of this bio-philic sort is antecedently unlikely & that some specific sort of Fine-Tuning at the physical level is responsible for our Universe’s being bio-philic rather than more sparing in offering Life support.  This would seem to reduce to the Fine-Tuning argument in Physics that we have already seen, although this could depend on what connotation, exactly, one attaches to “bio-philic”.

Adapted from some  verses from a great Sage:

TIME & SENSES:

Past description, Present description, & Future description, which are known by thought-forms, can only be illusory.  This leaves timeless Consciousness as the ever present underlying condition.  We can consider the manner in which one seems to know of the World of sense objects in Thought.  The sense of touch, for instance, provides a variety of intermittent signals, describing textures & shapes, but all in a vague hardly localizable collection.

When one Perception is in Consciousness, no other can be there in Consciousness.  Nor can any other Perception in fact exist elsewhere because there is nowhere else.  If storage of other Perceptions could occur in some other place, realm, or domain, outside of Consciousness, how would it be known ?  If not present in Consciousness at a give moment, then where can that Perception be stored or hidden ?  And so with only one partial sensory Perception present & existing at any one time, the Sensation of the World is always an incomplete, vague, & sketchy impression at best.  We can compare this Mind-colored and filled-in illusion to the sketchy shadows of a dimly lit Rope, being mistaken for an entire Snake.  Once the light of clarity is cast upon the “Snake”, it is seen & known to have been a Rope all along.  Once the sketchy structure of the Sense-World is recognized for what it is, pure Consciousness remains apparent as the sole Reality.

Each Sense takes no account of any other Sense.  We must take Sights & Sounds & artificially link them with Sensations of Touch in order to construct a World at all.  Just like intermittent Sounds, so likewise do flickering momentary Visual pictures get blended with each other, & then with Sound track to create the “movie” of the World.

The old Hollywood movie “Brainstorm” reiterated the often played Science Fiction theme of total Sound-Sight-Feel-Taste-Smell-Think-Feel recording & playback on advanced multi-sensory & multi-cerebral recording media.  Whether it be electronic media, or hallucinatory drugs, psychotic distortion, hypnosis, dream, or physical illusions like mirage & rainbow, the question remains, how do we know for sure that the World we seem to experience right now is any more Real than any of these ?   Why could we not be like some sci-fi, Science Fiction character, an intergalactic espionage agent captured & plugged into a Vat or some other fabricated Life experience ?

While not a serious question, the point still merits fanciful contemplation.  Looking through the gaps that separate the Senses & the Time intervals between momentary Perceptions themselves, we see into a formless continuum upon which the ghost-like multi-sense-media image of the World is cast.  In looking back from that formless continuum, we are actually looking back from pure Consciousness.  The Perennial Philosophy of Vedanta declares the Sense images to be insubstantial shadows in that one Reality of Consciousness.

And then again, every Perception, be it well combined together with other perceptions or not, is itself only a particular type of thought-form.  And if Thoughts cannot contact one another, how are they to be combined ?  For all these thought-forms, Consciousness is the combiner, the holder, the viewer, the substratum.  At the very least, even if the World were taken as valid, then the option still remains to identify with Consciousness rather than with these objects.  In terms of the Quantum Mechanical Measurement problem, the question could be taken up from the viewpoint of being Consciousness rather than from the ordinary viewpoint of being a Body-object in a World of other objects.  The Senses present disjointed data interpreted as a World.

Calculus for Yogis, part 9:

The Laplace transform, like the Fourier transform (& there are many other transforms) display that pattern seen in integration by parts where the integral of a product of functions allows us to transform our description from one Variable to another Variable.

In Quantum Mechanical Hilbert Space, the Fourier transforms between Distance space & Momentum space.  In crystallography, it does so between Reciprocal space that determines Diffraction & Distance space, describing position of atoms in the crystal.

Both the Laplace & Fourier transforms, especially the Laplace transform, have some of there usefulness in the ability to exchange more intricate processes for addition processes.  We saw this in a similar way in use of Logarithms to substitute addition for multiplication.  In the case of Fourier transform, especially the Sine & Cosine are key elements.

With that in mind, we further our exploration of Sine & Cosine by considering a Unit Radius Circle & the Intersection of that Radius with the Circumference. If that Point of Intersection was the Point of reference, then its Horizontal position is the  x  Coordinate.  This would be the Cosine of the Angle between the Radius Line & the Horizontal X axis.  The Point’s Vertical position, the  y  Coordinate would be the Sine.

If we allowed that Point to revolve at a uniform speed CCW around the Circle, we could to shine a light from left to right & cast a shadow of that Point, bobbing up & down, in simple Harmonic motion, like a spring.  Part of that range could also be cast by the shadow of a Pendulum.

If we were to cast a shadow from a light below onto screen above, we would see the point moving to & fro in simple Harmonic motion, again representing the rise and fall of the Cosine [image rotated 90o].  If we were to allow those Points to have a pen attached in some way & have a uniform-speed of chart paper rolling underneath that pen. we would trace out a wavelike curve.  These in fact would be the graphs of the Cosine & Sine functions.

These Waves describe many physical phenomena, including Alternating Current. And so, we find that the Fourier transform is very useful in Electronics simply it exactly because of its component Cosine & Sine functions.  Again in Complex Space, the Exponential Function serves the role of combining these 2.

The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through:  

www.jpstiga.com/

http://jstiga.wixsite.com/nonduality/

or with Caps-sensitive:

http://sdrv.ms.YPOgkX/

Duplicates (but with graphics) have been available on:

http://www.blogger.com     as  “Being-as-Consciousness, Non-Duality – new & final version” with link:

http://being-as-consciousness.blogspot.com/

[But from now on, they will be different & still usually daily.]

There is no Creation, no Destruction, no Bondage, no longing to be freed from Bondage, no striving for Liberation, nor anyone who has attained Liberation. Know that this to be Ultimate Truth.”   the “no creation” school of Gaudapada, Shankara, Ramana, Nome Ajata Vada

for very succinct summary of the teaching & practice, see:  www.ajatavada.com/

NMT (No-Me Teaching) new series 65

NMT (No-Me Teaching) new series 65:

Some   Ramana Maharshi quotes:

In Non-duality, Meditation may be regarded as by the Self, for there is no other Knower, & upon the Self, since there is no Object of the Meditation. In Meditation upon Self-Knowledge one cannot stand apart from the Self to contemplate upon Self-Knowledge. 

Knowing the Self is being the Self, & Being means Existence, one’s own Existence.

No one denies one’s Existence any more than one denies one’s eyes, although one cannot see them.

The trouble lies with your desire to objectify the Self, in the same way as you objectify your eyes when you place a mirror before them.

You have been so accustomed to objectivity that you have lost the knowledge of yourself, simply because the Self cannot be objectified.

Who is to know the Self ?   Can the insentient Body know it ?

All the time you speak & think of your “I”, yet when questioned you deny knowledge of it.

You are the Self, yet you ask how to know the Self.

 The many objective differences are not real but are mere superimpositions on Self, which is of nature of True Knowledge.

If the idea “l am the Body” is accepted, selves are multiple.

The state in which this “I am the Body” idea vanishes is the Self since in that state there are no other objects.

Since the Body itself does not exist in the natural outlook of the real Self, but only in the extroverted outlook of the Mind which is deluded by the power of Illusion, to call Self, the Space of Consciousness, dehi [the possessor of the Body, lit: cremation fuel] is wrong.

The World does not exist without the Body, the Body never exists without the Mind, the Mind never exists without Consciousness, & Consciousness never exists without Reality.

For the wise one who has known Self by diving within himself, there is nothing other than Self to be known.

Since the Ego which identifies the Body as “I” has perished, the wise one is the formless Existence-Consciousness.

The jnani knows he is the Self & that nothing, neither his Body nor anything else, exists but the Self.

What difference could presence or absence of a Body make ?

Fine-Tuned Universe 45:

[In the unreal reflection called the “Universe”, a product of an unreal Mind, even there, Infinite Intelligence is evident and inspiring.]

Haldane asked: Must we assume that the Universe is composed at the outset of Matter – eternal, unchangeable, & independent ?  Henderson had said: Biology deals, not merely with the “efficient” causes of ordinary Physics & Chemistry, but also with what Aristotle called “final” causes.”

It is in the Biological facts that “Teleology is revealed as immanent in Nature as of its essence & no mere accident appearing in the Physical Environment & not only in organisms.

Haldane believed: Biological concepts must be extended to the Inorganic world.  While knowledge of how this would work is not now present, it requires only a further extension of knowledge. Haldane’s hope for the future was that: Physics & Chemistry would be penetrated by conceptions akin to those of Biology.  If this occurs, “Teleological reasoning will take a natural place in the Physical Sciences”

This is not where Henderson was going; & in a later criticism Haldane stressed how his & Henderson’s divergent views & also the extent to which Henderson’s commitment to the understanding that living things are Physico-Chemical systems further separated them.

Henderson later reported that he stepped back even farther from Teleological guides. He also stated that he

became significantly more skeptical of Metaphysics – to the extent that he regretted some of his earlier writings, seeing the discussion of “Teleology, Vitalism, & so forth, more or less irrelevant & immature.

He noted that he had been less skeptical than he should have been & claimed that much of what he wrote in attempting to explain “Fitness” in Metaphysical & Teleological terms was meaningless.  But he did not reject “Fitness” as a concept & continued to see it as a valuable, & perhaps even the most interesting, part of his Scientific work.

Henderson restated the claims he originally for the critical role of Carbon, Hydrogen, & Oxygen, which “make up a unique ensemble of properties . . . which are of the highest importance in the Evolutionary process,” making Diversity possible.

These elements, he emphasized, provide the “fittest ensemble of characteristics for durable mechanism.”  He still claimed: “For these facts I have no explanation to offer. All that I can say is that they exist, that they are antecedent to Organic adaptations, that they resemble them, & that they can hardly be due to chance.”.

“Fitness” did not challenge & provoke his contemporaries to take up the concept & use it as a guide to further scientific work. His later work on Physiological systems much more clearly evoked the laboratory labors of his contemporaries. Its detailed analysis of what he referred to as “an immensely complex system in equilibrium” served as a vigorous stimulant to further experiment & explanation.

“Fitness” remains to this day a symbol of attempts to provide broader explanation of the complexity of the Worlds of the living & the non-living. Henderson’s pre-World War I book was written at a time when the atom was gaining its redefinition at the hands of Rutherford, Rydberg, Mosley, & Bohr. This was before important new forms of chemical bonding had been established, & Biochemistry was still in its infancy.

One of  Henderson’s conjectures was that: “A possible abode of Life not unlike the earth apparently

must be a frequent occurrence in Space” & that perhaps even “‘thousands” of such planets exist. He further noted the current expectation of there being “many thousand million millions” of such possible abodes for Life.”

It is in this sense that Henderson’s “Fitness” takes on an expansive meaning. It has fueled renewed

interest in the Origin of Life & the obvious extension: the synthesis of Life in the laboratory.

Some more selected verses from the Ramana Maharshi disciple Master Nome:

The supposedly knowing Mind & the Universe known are both imagined.  Existence-Knowledge, which is Being-Consciousness, that alone is real.  The Reality exists without anything else.  That Self is alone the Knower & the Known, but any forms given to Knower & Known are only imagined.   Difference, which manifests only in the Mind within the Waking & Dream States, such difference is unreal.  Non-Dual Consciousness alone exists.

The ancient Sages gave their instruction in Silence & with Teaching that reveals how “That you are, (tat tvam asi).”  Inquiry into this instruction removes all ideas, of what is not the Self, from the Self.  This is like the proverbial negation the Analogy’s snake from the rope. Negation of the not-Self is never negation of a reality, but rather a negation of false assumptions or superimposition.  If real things would have to be negated, Liberation would be transitory, or not occur at all.  For how would it be possible for anything truly existent to go out of existence, or for something to actually change its nature.

Self-Inquiry & negation eliminate only Ignorance & Illusion.  All that is objective, & also the Ego, are negated by Self-Inquiry & negation summed up as neti, netinot this, not this”.  Such reveal Being, which is Consciousness, the one Self.

The Ego is ignorantly assumed to be the Self &, thus the Knower.  The conception of the Mind determine whether one is endowed with wrong knowledge, doubtful knowledge, or true knowledge.  With mis-identification, there is wrong knowledge. Then, what is regarded as knowledge is actually Ignorance.  Thereby arises self-caused Delusion regarding Happiness, Identity, & Reality.

With spiritual practice, wrong knowledge gives way to yet-doubtful knowledge. This means there is some actual knowledge regarding Happiness, Identity, & Reality. But this knowledge is not yet steady for it is either a conviction, without direct experience, or a conviction fused with some experience. But still, it is not steady because there remains the need to destroy remaining tendencies to mis-identify.

True Knowledge, however, is that state in which Knowledge is invariable. Also, here knowing & Being are one & the same. At all times, the same Consciousness is the only Knower, even when it appears as an Ego, a dissolving Ego, or as purely Ego-less.  This is just like a clear crystal appearing as if endowed with different colors or as transparent, according to the proximity of various colors, or the absence of them. In Truth, all such states & their content are known by the Self, have their apparent existence by the Self, which is free from them & depends on no thought whatsoever to know itself.  Even so, all such states & their content do not exist apart from the Self, though the Self itself can never be other than the Knowledge, Being itself.

Calculus for Yogis, part 8

First off, we attend to one of the various topics used in introducing Derivatives, topics that we have omitted, or in this case put off so far, for the sake of simplicity.

In previous examples we had talked about   y  being a function of   x   so that  y  is graphed on the Vertical scale &  x   is graphed on a Horizontal scale.  We also said that another Independent Variable like Time,  t   could be the horizontal scale.

Well graphs aside for the moment, both  y  &  x   can be functions of   t , while   y   remains a function of   x .  In that case,  with   x   being of the function of     &   y  begins as a function of   x ,  then what is called  y   as a function of    t   is a “composition” of the functions  y   &  x   in terms of   x‘s   variable   t .

(y  x)(t) = y(x(t))

Please know that the Rule for taking the Derivative of that Composition is called the Chain Rule.  In terms of just the differentials  d y,  d x,  d , it looks like they could be canceled & the expression below could be proven by simple canceling of terms.  That is a useful way of remembering how it works, but it doesn’t quite work that simply. That aside the Chain Rule is:

y/ d t  =   (d y/ d x)  x  ( d x/ d t)        the Chain Rule

The foregoing, that is: taking the Derivative of the function of a function, called the Derivative of a composition of functions, for purposes was a necessary prelude to an easy introduction to the next basic pattern that we had put off.  And that would be the general pattern or formula for taking the Derivative of one function times another, the Product of 2 functions.  Both are functions of the same Variable.  For instance, we can take Time as our Independent Variable & we have x & y to both be Dependent Variables, functions of Time,  t .

Then if we take the Time Derivative of the product  xy  it turns out as :

d(xy)/dt  =   y dx/dt   +   x dy/dt ,   which bears some resemblance to the Chain Rule, which it should when we consider (xy) to be a fuction of  x  &  y namely “multiplication” of the two.

d(xy)/dt  =  [d(xy)/dx]  x  [dx/dt]  + [d(xy)/dy]  x  [dy/dt]

=   y (dx/dt)  +  x (dy/dt)

thus the same Product Rule as above.  In other words, the Product Rule shows one function times the Derivative of the other, plus that other function times the Derivative of the 1st function, as it were, taking turns having the Derivative taken while simply multiplying by the other function.  We can also affirm the simpler expression in terms of just “differentials”

d(xy)  =   x dy   +   y dx

When we take the trimmed–down inverse of the Derivative or just the “differentials”, that inverse sometimes called the Anti–Derivative, the trimmed–down Indefinite Integral, of each of those last 3 terms:

∫ d(xy)  =  xy    =  ∫  x dy   +   ∫  y dx    , or rearranged to:

∫  x dy    =    xy       ∫  y dx

Corresponding to the Integral expression is on in terms of sums & differences:

n                                                                          n

Σ  fk     gk   =   [fn+1  gn+1     fm gm]  –   Σ gk+1    fk

= m                                                                    k = m

Again to put the Integral expression in other words, if taking the Integral of 1 Variable, such as  x  in terms of  y, is difficult, then we can instead take the Integral of that other Variable, such as  y  in terms of  x.  Taking the  xy  part as one kind of  “fix”  among various corrective factors, we here see for the 1st time, a relating of:

∫  x dy     to:    ∫  y dx

The Integral pattern of is more clearly a “change of Variable” from:   x  to   .

 x y   =   ∫ dy    +   ∫y dx

d/dt[ x y]   =    dy/dt    +   y dx/dt

d/[ x y]   =    dy    +   y dx

F (z)   =   ∫ (x)  e–2πxz dx   , taken from  –  ∞  to  

f (x)   =   ∫ (x)  e2πxz dz   , taken from  –  ∞  to  

Corresponding to Integral expression is the Fourier Series in terms of Sums:

.                                          N

sin (x)  =   1/2 Ao  +  Σ    [ An cos 2 n/P    +   An sin 2 n/P  ]

.                                        k = m

The Laplace transform, like the Fourier transform transforms a expression in ordinary Variables to one in a Frequency or “imaginaryFrequencytype Variable.

F (s)   =   ∫ (t)  e–st dx   , taken from  –  ∞  to  

f (t)   =   1/ 2πi  ∫ (x)  est ds   , taken from   γ – ∞   to   γ + 

To the Integral expression there is no corresponding is the “Laplace Series” in terms of Sums.

The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through:  

www.jpstiga.com/

http://jstiga.wixsite.com/nonduality/

or with Caps-sensitive:

http://sdrv.ms.YPOgkX/

Duplicates (but with graphics) have been available on:

http://www.blogger.com     as  “Being-as-Consciousness, Non-Duality – new & final version” with link:

http://being-as-consciousness.blogspot.com/

[But from now on, they will be different & still usually daily.]

There is no Creation, no Destruction, no Bondage, no longing to be freed from Bondage, no striving for Liberation, nor anyone who has attained Liberation. Know that this to be Ultimate Truth.”   the “no creation” school of Gaudapada, Shankara, Ramana, Nome Ajata Vada

for very succinct summary of the teaching & practice, see:  www.ajatavada.com/

NMT (No-Me Teaching) new series 64

NMT (No-Me Teaching) new series 64:

Some   Ramana Maharshi quotes:

All that you need do is to find out the origin of the “I-thought” & abide there.  Your efforts can extend only thus far. Then the Beyond will take care of itself.

The Ego-Self appears & disappears & is transitory, whereas the real Self is permanent.

You wrongly seem to identify the real Self with the Ego-Self.  See if that mistake has come about. The Ego-Self does not exist at all.

To whom is the trouble ?  The trouble also is imagined. Trouble & pleasure are only for the Ego.

Take care of yourself.  Let the World take care of itself.  See your Self.  If you are the Body there is the gross World also.  If you are spirit all is Spirit alone.

Do it yourself 1st  then see if the question of others arises afterwards. 

There is no goal to be reached, nothing to be attained.  You are the Self.  You exist always.  No more can be predicated of the Self than that it exists.

Seeing God or the Self is only being the Self or yourself.

Seeing is being. You, being the Self, want to know how to attain the Self. 

It is something like a man being somewhere & asking how many ways there are to reach the place & which is the best way for him. All that is required of you is to give up the thought that you are this Body & to give up all thoughts of the external things or the not-Self.     

People say they aren’t able to know the all pervading Self.

Even the smallest child says, “l exist. I do. This is mine.”

Everyone understands that the thing “I” is always existent.  Only when the “l” is there, is there feeling you are the Body.

Knowing one that is always “visible” is one’s own Self, is it necessary to search with a light ?

To say that we do not know the atma swarupa [the real nature of the Self] which is not different but which is in one‘s own Self is like saying, “l do not know myself.”

The nature of bondage is merely the rising, ruinous thought “I am different from the Reality.”  Since one surely cannot remain separate from the Reality, reject that thought whenever it rises.

 You speak of memory & oblivion of the fullness of the Self.  Oblivion & memory are only thought-forms. They will alternate so long as there are thoughts. But Reality lies beyond these. Memory or oblivion must be dependent on something. That something must be foreign to the Self as well, otherwise there would not be oblivion. That upon which memory & oblivion depend is the idea of the individual self.

 When one looks for it, this individual “I” is not found because it is not real.  Hence this “I” is synonymous with Illusion or Ignorance [maya_, , or ajnana].

To know that there never was Ignorance is the goal of all the spiritual teachings. Ignorance must be of one who is aware. Awareness is jnana.  Jnana is eternal & natural, ajnana is unnatural & unreal.

 In Deep Sleep man is devoid of possessions, including his own Body.

Instead of being unhappy he is quite happy. Everyone desires to sleep soundly.

The conclusion is that Happiness is inherent in man & is not due to external causes.

One must realize the Self in order to open the store of unalloyed Happiness.

 lf a man thinks that his Happiness is due to external causes & his possessions, it is reasonable to conclude that his Happiness must increase with the increase of possessions & diminish in proportion to their diminution. Therefore if he is devoid of possessions, his Happiness should be nil.  What is the real experience of man ?  Does it conform to this  view ?

Fine-Tuned Universe 43:

[In the unreal reflection called the “Universe”, a product of an unreal Mind, even there, Infinite Intelligence is evident and inspiring.]

There is still much that we do not understand about nature. Ultimately the path is based on principles of Chemistry & Physics & Geology – that could plausibly have led from disorganized mixtures of inanimate chemicals to the astonishingly ordered, self-replicating networks of  reactions that provide the basis for life. The fact that we cannot yet understand how an inconceivably large number of tries at an extraordinarily improbable event might lead to “Life” is more a reflection of our limited ability to understand than evidence of a requirement for some new principle. But, having said all of that, we do not know whether Physical Science ultimately explains the origin of Life or whether the explanation will require principles entirely new. Science makes every effort to develop the explanation.

Science may ultimately be successful in rationalizing the origin of Life in terms of physical principles, it should be cautious & claim credit only for the puzzles it has already solved, not those whose solutions still lie in the future.  The central conundrum about the origin of Life – that, as an accidental event, it seems so very improbable is not one that Science has yet resolved. Claiming credit prematurely claiming, in effect, that current Science holds all the answers may stunt the growth of the new ideas that a resolution may require.

We do not understand how Life originated. Order from disorder !  How could it have happened ?   Difficult problems may take time – lots of time – to solve.

The Fitness of the Cosmos, “bio-centric” & “fitted” for Life, “fitness” & “fine-tuning”, raises the question: why can & does Life exist in our Universe ?

Zero-point Energy & the Casimir Effect

Vacuum Zero-point Energy  is vast, seemingly large. Naively, it is infinite, limited only by absence of Planck length short wavelengths.  One phenomenon that is considered as evidence for the Vacuum Zero-point Energy is the Casimir Effect, the quantized Electro-Magnetic Field between a pair of grounded, neutral metal plates. The Vacuum Energy contains contributions from all wavelengths, except those excluded by the spacing between the plates. As the plates draw together, more wavelengths are excluded & the vacuum energy decreases.  The decrease in energy means there must be a Force doing work on the plates as they move. This Force has been measured and found to be in good agreement with the theory.  A spectral “Lamb shift” has also been thought to be partially due to a Zero-point Energy effect.

Some more selected verses from the Ramana Maharshi disciple Master Nome:

If one is immersed in Samsara, the repetitive Cycle of Illusion, Birth, & Deaths, filled with Suffering, the way to liberate oneself is by Self-Knowledge. Liberation, which is the goal of spiritual practice, is one’s own if, inquiring to know the Self, he discards all notions of  “me” & “mine” attains complete certitude as to the Space-like nature of Reality, & “abides” devoid of physical & mental forms, & the assumption of an Ego-entity.

If the Self would change states, such as states of Ignorance & Knowledge, of Bondage & Liberation, that Self would be destructible, & Liberation itself would be artificial or unreal. Liberation is not a change of state from one state into another state.  It is not reasonable to imagine a separation & later union in relation to the Self, for then both would be transitory. Transience cannot be attributed to the Real, just as the unreal cannot be attributed to the Real, or the dual to the Non-Dual.  Since there truly can be neither later union nor prior separation, Liberation cannot consist of an Individual entering into Brahman or Brahman coming to the Individual.  The True Nature of the Self is never destroyed, is changeless, is uncaused, & cannot be obtained or lost.  Any new appearance, or coming into being of any state would be the Effect of a precedent Cause. Such would be changeful, transitory, & not self-existent. Such cannot be permanent Liberation.  Self-Knowledge alone is Liberation.  Knowing the Self to be oneself is the greatest attainment.  To wrongly assume the non-Self to be the Self is Ignorance.

The removal of the superimposed mis-conceptions of what the Self alone is constitutes the path to Liberation.  No other view is reasonable, since such always involves some Dualism, some belief in an existent individual experiencer & a self-existent objective thing. There is also then the conception that Reality becomes other than what it is, & that the unreal actually comes to be.  Liberation cannot be a change of condition, because such involves mutability & thus destructibility, parts or divisions, & a change in its nature.

Any belief that superimposition occurs on some substrate of non-existence, or that belief that Illusion can actually create itself, or that there is no Absolute Self, all such beliefs should be abandoned. This is because of the existence of Being itself is irrefutable. Furthermore, it is not reasonable that something could come out of “nothing”. Superimposition (in Illusion) occurs on some real thing, & this for “someone” who knows the Ignorance.  What is it Ignorance of ?  And who knows is the Ignorance for ?  If one so inquires, one find that Being alone exists, Consciousness alone exists.

Calculus for Yogis, part 7

Now in a certain version of   e  in what’s called “complex space”  describes a Circle even though we don’t see that in ordinary  x   &   y   coordinates, where we see a gradually rising  &  then rapidly rising curve.  The special “complex space” version is graphed as a Circle, often with Radius 1.  If we look, for instance, at a Radius heading to the upper right direction, & at the point where it intersects the Circumference, we can drop a Vertical line & create a Right Triangle that includes as a Base, the  x  axis.

The angle that the Radius line made with that x-axis Base can be called Angle  A .  To some extent  Angle  A   is characterized by the ratio of that Vertical line length to the length of X axis Base.  This “Opposite” side over “Adjacent” side ratio, called the Tangent of  A  is one of the ways to calculate the Slope, in fact the Derivative of the slanting line of the Radius.  This tangent of a, abbreviated as  “tan A”  & can in turn be considered the ratio of 2 other functions of  A.

The vertical line for this unit Radius Circle equals has a length equal to  Sine  A, abbreviated as  “sin A”.  The portion of the x-axis making up the Base has a length equal to  “Cosine A”.  [If the radius were more or less than 1, that proportion would be multiplying these functions, sin A & cos A, but have no effect on tan A.]

So whereas  tan A  is definable as “Opposite over Adjacent”,  sin A  can be defined as “Opposite side over the Radius”, the hypotenuse.  That  =  1   in this case.  The  cos A  can be just found as the  “Adjacent side length over the radius”, again just equal to that length because the Radius  =  1.

More meaningful than defining Sine & Cosine in terms of right triangles is to consider them as the Coordinates of that point of intersection of the Radius & the unit Circle formed by a complex space version of   e x .

In that sense some of this complicated version of   e  is composed of the  Sine of  x  & Cosine x.  We see this showing up in the (Power Series) Polynomial Infinite Series for sin  x  &  cos x .

Recall that:

e x   =  Σ   x n / n !       =    1   +  x    +   x 2 / 2 !    +   x 3 / 3 !     +    ….

n  = 0

& now we compare that to:

sin x  = Σ (1)n  x 2n+1 / (2n+1) /=   x  –   x 3 / 3 !  +   x 5 / 5 !  x 7 / 7 !  .

n  = 0

cos x  =  Σ  (1)n  x 2n / 2n !  =  1   –   x 2 / 2 !   +   x 4 / 4 !   –   x 6 / 6 !  ….

n  = 0

Again, the alternating Minus signs arise out of the “complex space” relationship.

Thus we reduce more complicated Exponential & Trigonometric functions to more ordinary Polynomial terms & compare the Polynomial series for  e x  with the Polynomial series for  sin x  &  cos x  because we know how to take the Derivative of those terms.

We previously took the Derivative of that expression for  e x ,  term by term, to show that the Derivative the of each of terms numerically goes back to, is equal to our initial  e  .

Doing the same for  sin x  &  cos x,  we find that the Derivative each of terms goes back to terms of the other Series,  sin x  to  cos x,  &  vice versa. except that the Minus signs are reversed in the 2nd case.  That is, the exercise shows that: the Derivative of   sin x  is =   cos x,  &  the Derivative of  cos x  is  =   –   sin x .

We saw that we can look at the inverse of the Derivative, in a matter speaking, which is called the Integral, with the so-called “indefinite” Integral. We truly have that inverse to within a added constant, leaving that added constant out, or making it be a 0,  Then we can treat the Indefinite Integral as if it was the inverse of the Derivative.

So looking at a couple of Polynomials like  7 x2  +  4 x  + 3,  we saw that the Derivative is 14 x  +  4 , & for Integral we go the other way to:  7/3 x3  +  4/2 x  + 3x  +  a constant.

Up until now we delayed introducing any version of the symbol for the integral because it’s unduly strange looking, scary, and off putting to the uninitiated.  But will simplify it by saying that the symbol is based on a big “S”.  In fact since it’s a Roman alphabet “S”, in a way. it’s less exotic than the Greek capital “S”, Sigma that we saw for a generic term representation of an Infinite Series.  In any case, that statement just above can be rewritten symbolically as:

d/d x [7 x2  +  4 x  + 3]   =   14 x  +  4                                        (Derivative)    &

∫ [7 x2  +  4 x  + 3] d   =   7/3 x3  +  4/2 x  + 3x  +  a constant     (Integral)

The Analogy we drew was that the Derivative is the projected Perspective toward Happiness, viewing toward the estimated Future, based on the immediate past average; & the Integral is an accumulated memory or record by which we define Reality & Identity , instead of the Happiness.  Looking at these rather complex looking structures created on paper, we van so peak at the Mind, much as elsewhere we compare the Mind to Mathematical Coordinate Spaces.  Math mirrors Mind.

Now there are special reasons for seemingly idle curiosity about sin x   &   cos x .  For one thing, these 2 functions are the building blocks of the many “wave” phenomena that we see in the Sciences.  Back in the area of Mathematics, but Mathematics very applicable to Science, the sin x  &  cos x  are also building blocks for the Fourier transforms.  Fourier transforms & Laplace transforms, Quantum Mechanical Correlation, & similar topics will also be introduced by taking a closer look at the Integral in general.

Derivatives & Integrals can often be determined by systematic rules, like the Power Rule such as is the case for Polynomials.  But in other cases when we take the Integral, solving is more of an art form,  Detective intuition, trial & error, & so forth yield some basic processes, one being Integration by Parts.  We pause in our discussion to look at Integration by parts because it will serve as a foundation for the idea of a Transform.

What we will see is actually closer in form to Conjugate Variables in Quantum Mechanics, which are the basis for the Heisenberg Uncertainty Principle. Quantum Mechanics also uses the Fourier transform to move from ordinary Distance Space to a Transform of that, called Momentum Space. And so with these motivations we will look at Integration by Parts.

The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through:  

www.jpstiga.com/

http://jstiga.wixsite.com/nonduality/

or with Caps-sensitive:

http://sdrv.ms.YPOgkX/

Duplicates (but with graphics) have been available on:

http://www.blogger.com     as  “Being-as-Consciousness, Non-Duality – new & final version” with link:

http://being-as-consciousness.blogspot.com/

[But from now on, they will be different & still usually daily.]

There is no Creation, no Destruction, no Bondage, no longing to be freed from Bondage, no striving for Liberation, nor anyone who has attained Liberation. Know that this to be Ultimate Truth.”   the “no creation” school of Gaudapada, Shankara, Ramana, Nome Ajata Vada

for very succinct summary of the teaching & practice, see:  www.ajatavada.com/

NMT (No-Me Teaching) new series 63

NMT (No-Me Teaching) new series 63:

Some   Ramana Maharshi quotes:

Of 3 classes of spiritual aspirants, the most advanced realize the Self as soon as they are told about its Real Nature.

Those in the 2nd class need to reflect on it for some time before Self-awareness becomes firmly established.

Those in the 3rd category usually need many years of intensive spiritual practice to achieve the goal of Self-realization.

As a metaphor, Combustion describes the 3 levels: Gunpowder ignites with a single spark, Charcoal needs application of heat for a short time, & wet Coal needs to dry out & heat up over a long period of time before it will begin to burn.

For the benefit of those in the top 2 categories it is taught that the Self alone exists & that it can be directly & consciously experienced merely by ceasing to pay attention to the wrong ideas we have about ourselves, These wrong ideas are collectively called the “not-Self‘ since they are an imaginary accretion of wrong notions & misperceptions which effectively veil the true experience of the real Self.

The principal misperception is the idea that the Self is limited to the Body & the Mind. As soon as one ceases to imagine that one is an individual person, inhabiting a particular Body, the of wrong ideas collapse & are replaced by a conscious & permanent awareness of the real Self.

There is no question of effort or practice All that is required is an understanding that the Self is not a goal to be attained, it is merely the awareness that prevails when all the limiting ideas about the not-Self have been discarded.

Perfect Bliss is Brahman.

Perfect Peace is of the Self.

That alone exists & is Consciousness.

Happiness is only the Nature of Self.

Self is not other than perfect Happiness.

Happiness alone exists.

Knowing that & abiding in the state of Self, enjoy Bliss eternally.

Obstacles which hinder Realization the Self are habits of Mind [vasanas].

Overcome the mental habits [vasanas] by realizing the Self.

It is the Ego which raises such difficulties, creating obstacles & then suffering from perplexity of apparent paradoxes.

Find out who makes the Inquiries & Self will be found.

Prior to excerpting the Ramana Maharshi disciple, Master Nome in the text below we continue the series: Fine-Tuned Universe , the premise that a small change in several of the dimensionless fundamental physical constants would make the Universe incapable of Life.

Fine-Tuned Universe 43:

[In the unreal reflection called the “Universe”, a product of an unreal Mind, even there, Infinite Intelligence is evident and inspiring.]

Henderson‘s Biological “Fitness”:.

“Fitness” and “Order” have taken on other meanings more expansive than Henderson intended.  Henderson to limit what he saw as some of the metaphysical turns given. In some ways, these views were unavoidable given Henderson’s own often imprecise ideas and his choice to use a term like “Teleology” & attempt to give it his own meaning.

From early on in the years after “Fitness”, Henderson kept making clear his lack of sympathy with ideas of Vitalism; & although he resisted announcing himself a committed Mechanist [~ Scientist, Physicalist, Atheist, Materialist], he clearly indicated his receptiveness to its explanatory outlook. In his paper “Mechanism, from the standpoint of physical science” he once again revisited the debate begun as early as 1915 & rejected the Vitalism proposed by Haldane.  Haldane’s conviction that it is impossible to conceive organization in physical & chemical terms, this seems by no means impossible to most physiologists. .

When Henderson turned to the organismic views of Alfred North Whitehead he was cautious.  Yet in his review of Whitehead’s “Science and the Modern World”, while clearly appreciative of the development of the concept of organization, the “. . . doctrine Whitehead calls the theory of organic mechanism,” Henderson is not fully enthusiastic.  He notes a “lack of unity in the exposition,” with the author “still engaged in working out his theories.” Although he can “dimly . . . perceive” the possibility of overcoming the difficulties “. . . that have produced the conflicts between Mechanism & Vitalism, & between Freedom & Determinism . . . hope has been so long deferred…it is natural to be a skeptic”.

other perspectives on Biological “Fitness”

Terminology in this context is still somewhat fluid. The term “Multi-Verse” is also often used where a single originating event brings about an Ensemble of Domains that do share a causal relation with one another at the moment of Origin, although not later. We restrict the term “Multi-Verse” to the Infinite Domain with its infinite series of Inflation events.

But this is likely to be the exception. At any rate, in the case of Carbon, recent calculations seem to indicate that the Fine-Tuning first apparent in the Chemistry of the various nuclei involved carries over to the level of basic Physics: were the Strong Force to be greater by as little as 5 %, or the Electro-Magnetic Force to be greater by perhaps 4 %, the production of Carbon & Oxygen in the infant Universe could have shut down.

Chemistry plays a double role here, 1st in revealing the Fine-Tuning required in order that Carbon should form, & 2nd in implying the plausibly necessary role that Carbon plays in the economy of Life generally. These are 2 separate arguments.

But the decisive element in establishing the Fine-Tuning itself still lies at the level of fundamental Physics: must the relevant Physical Constants be constrained within a tight percentage range so that the Chemistry of the Universe should be open to the development of Life ?  Do any other plausible instances of Fine-Tuning exist in the basic Chemistry of the raw materials required for living processes ? .

Fine-Tuning in Biology

What are the prospects for discovering instances of Fine-Tuning in realms other than Physics & Chemistry – in Biology, say ?  It is helpful to draw some inferences 1st from the structure of the Fine-Tuning argument in its native home, Cosmology.

Biological considerations play an indispensable role in all discussions of Cosmic Fine-Tuning. But in this role they are not part of the Fine-Tuning claim itself.  Typically, proponents of Fine-Tuning allege that an unexpected degree of constraint on some Physical parameter or basic constant is necessary if some other Physical condition is to be realizable in the Universe.  Then, in a separate argument, this latter condition is held to be necessary for the Universe’s being open to the development of complex Life.

Some more selected verses from the Ramana Maharshi disciple Master Nome:

If one is immersed in Samsara, the repetitive Cycle of Illusion, Birth, & Deaths, filled with Suffering, the way to liberate oneself is by Self-Knowledge. Liberation, which is the goal of spiritual practice, is one’s own if, inquiring to know the Self, he discards all notions of  “me” & “mine” attains complete certitude as to the Space-like nature of Reality, & “abides” devoid of physical & mental forms, & the assumption of an Ego-entity.

If the Self would change states, such as states of Ignorance & Knowledge, of Bondage & Liberation, that Self would be destructible, & Liberation itself would be artificial or unreal. Liberation is not a change of state from one state into another state.  It is not reasonable to imagine a separation & later union in relation to the Self, for then both would be transitory. Transience cannot be attributed to the Real, just as the unreal cannot be attributed to the Real, or the dual to the Non-Dual.  Since there truly can be neither later union nor prior separation, Liberation cannot consist of an Individual entering into Brahman or Brahman coming to the Individual.  The True Nature of the Self is never destroyed, is changeless, is uncaused, & cannot be obtained or lost.  Any new appearance, or coming into being of any state would be the Effect of a precedent Cause. Such would be changeful, transitory, & not self-existent. Such cannot be permanent Liberation.  Self-Knowledge alone is Liberation.  Knowing the Self to be oneself is the greatest attainment.  To wrongly assume the non-Self to be the Self is Ignorance.

The removal of the superimposed mis-conceptions of what the Self alone is constitutes the path to Liberation.  No other view is reasonable, since such always involves some Dualism, some belief in an existent individual experiencer & a self-existent objective thing. There is also then the conception that Reality becomes other than what it is, & that the unreal actually comes to be.  Liberation cannot be a change of condition, because such involves mutability & thus destructibility, parts or divisions, & a change in its nature.

Any belief that superimposition occurs on some substrate of non-existence, or that belief that Illusion can actually create itself, or that there is no Absolute Self, all such beliefs should be abandoned. This is because of the existence of Being itself is irrefutable. Furthermore, it is not reasonable that something could come out of “nothing”. Superimposition (in Illusion) occurs on some real thing, & this for “someone” who knows the Ignorance.  What is it Ignorance of ?  And who knows is the Ignorance for ?  If one so inquires, one find that Being alone exists, Consciousness alone exists.

Calculus for Yogis, part 6

Now just as we call the Integral the inverse of Derivative, will then Derivative is the inverse of Integral.  This reciprocal kind of relationship also applies to functions themselves.  So the inverse of Multiplication is Division as we saw in going from Polymer Derivative to Integral; & the inverse of Addition is Subtraction.

Well the inverse of something more complicated like the Exponential function acquired the name Logarithm.  This was part of its role in making calculation feasible before they were calculating machines.  The qualities of Exponents are such that Multiplication of Terms raised to a Power involves Addition of the Exponents.  And so the Logarithm creates a relationship between Multiplication & Addition. So devices like a slide rule could use Addition distances to effect Multiplication & tables of Logarithms allowed Addition to serve the purpose of Multiplication,

Logarithms, the inverse of the Exponential function happens to be called the Natural Logarithm designated “ln x” whereas “Log x”  with no special base mentioned is assumed to be aligned with the Decimal number system, meaning the inverse of 10x , that is the Log to the base 10, can often just be called “Log” as the default.

But with computers using Even numbers of what are called “buses” or wires to build on the duality of 0 or 1, of a voltage On /  voltage Off, the Binary number system introduced the usefulness of raising 2 to various powers, or taking the Logarithm to the base 2.

Other Powers of 2 are also useful in computer science, specifically 2 to the 4th which is 16.  This “Hexadecimal” alternative to the Decimal number system uses 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F instead of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.

In any case, the Logarithm serves another good purpose, besides being the Inverse of Exponential.  It gets us around the difficulty of dividing by 0 when we take the Integral of 1/ x .  There it looks like raising the  –1 power to 1 higher would take us to Zero power, thereby “losing” the Variable since x 0  =  1.  Mysteriously, that Integral turns out to be “ln x“;  &  d x/ x  =  d ln x.  On occasion we will glance at “Mysterious” coincidences presented to us by Mathematics.  The relationship between   ln x   &  1/x   is only a minor example, only slightly mysterious.  Uncountable others show up in the annals of Mathematics a few small examples here follows:

    92  =  81                   8 + 1  =  9

  452  =  2025           20 + 25  =  45

  552  =  3025           30 + 25  =  55

  992  =  9807           98 + 01  =  99

2972  =  88209        88 + 209  =  297

7032  =  494209    494 + 209  =  703

9992  =  998001    998 + 001  =  999

1/ 27  =  .0370370370 …      &    1/ 37  =  .0270270270

There are no tricks explaining these coincidences, even multiple coincidences in one expression, like there are tricks in some elementary grade school math puzzles.  These truly amazing coincidences, when by accident noticed by mathematicians & scientists, are sometimes referred to in ways like “God winking at you.”

The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through:  

www.jpstiga.com/

http://jstiga.wixsite.com/nonduality/

or with Caps-sensitive:

http://sdrv.ms.YPOgkX/

Duplicates (but with graphics) have been available on:

http://www.blogger.com     as  “Being-as-Consciousness, Non-Duality – new & final version” with link:

http://being-as-consciousness.blogspot.com/

[But from now on, they will be different & still usually daily.]

There is no Creation, no Destruction, no Bondage, no longing to be freed from Bondage, no striving for Liberation, nor anyone who has attained Liberation. Know that this to be Ultimate Truth.”   the “no creation” school of Gaudapada, Shankara, Ramana, Nome Ajata Vada

for very succinct summary of the teaching & practice, see:  www.ajatavada.com/

NMT (No-Me Teaching) new series 62

 

The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through:  

www.jpstiga.com/

http://jstiga.wixsite.com/nonduality/

or with Caps-sensitive:

http://sdrv.ms.YPOgkX/

Duplicates have been available on:

jstiga.wordpress.com/

[But from now on, they will be different & still usually daily.]

There is no Creation, no Destruction, no Bondage, no longing to be freed from Bondage, no striving for Liberation, nor anyone who has attained Liberation. Know that this to be Ultimate Truth.”   the “no creation” school of Gaudapada, Shankara, Ramana, Nome Ajata Vada

for very succinct summary of the teaching & practice, see:  www.ajatavada.com/

NMT (No-Me Teaching) new series 61

NMT (No-Me Teaching) new series 61:

Some   Ramana Maharshi quotes:

All that you need do is to find out the origin of the “I-thought” & abide there. Your efforts can extend only thus far. Then the Beyond will take care of itself.

The Ego-Self appears & disappears & is transitory, whereas the real Self is permanent.

You wrongly seem to identify the real Self with the Ego-Self.  See if that mistake has come about. The Ego-Self does not exist at all.

To whom is the trouble ?  The trouble also is imagined. Trouble & pleasure are only for the Ego.

Take care of yourself.  Let the World take care of itself.  See your Self.  If you are the Body there is the gross World also.  If you are spirit all is Spirit alone.

Do it yourself 1st  then see if the question of others arises afterwards. 

There is no goal to be reached, nothing to be attained.  You are the Self.  You exist always.  No more can be predicated of the Self than that it exists.

Seeing God or the Self is only being the Self or yourself.

Seeing is being. You, being the Self, want to know how to attain the Self. 

It is something like a man being somewhere & asking how many ways there are to reach the place & which is the best way for him. All that is required of you is to give up the thought that you are this Body & to give up all thoughts of the external things or the not-Self.     

People say they aren’t able to know the all pervading Self.

Even the smallest child says, “l exist. I do. This is mine.”

Everyone understands that the thing “I” is always existent.  Only when the “l” is there, is there feeling you are the Body.

Knowing one that is always “visible” is one’s own Self, is it necessary to search with a light ?

To say that we do not know the atma swarupa [the real nature of the Self] which is not different but which is in one‘s own Self is like saying, “l do not know myself.”

Prior to excerpting the Ramana Maharshi disciple, Master Nome in the text below we continue the series: Fine-Tuned Universe , the premise that a small change in several of the dimensionless fundamental physical constants would make the Universe incapable of Life.

[In the unreal reflection called the “Universe”, a product of an unreal Mind, even there, Infinite Intelligence is evident and inspiring.]

To Jupiter, and beyond the Infinite.               “2001” movie

To Infinity, and Beyond !        Buzz Lightyear, Pixar character & toy “of the decade”

Fine-Tuned Universe 41:

[In the unreal reflection called the “Universe”, a product of an unreal Mind, even there, Infinite Intelligence is evident and inspiring.]

Reasoning “forward” is much more problematic. Although we can imagine many possible mangers for the Birth of Life deep “smokers” [~ volcanoes] in the abyssal depths, tidal pools, hot springs, & many others and although each could plausibly produce primitive precursors to many of the reactions that now constitute cellular metabolism, we have no idea how these simple reactions might have blundered together to make the first proto-cell. Monkeys sitting at typewriters pecking out Shakespeare seems child’s play by comparison. For example, we still do not know:

What were the first catalysts ?  Were they protein-analogs or RNA-analogs or minerals or some other species of which there is now no trace ?

How did the first networks form, & why did they persist ?  One can imagine countless catalytic reactions that might have occurred, but how some of these reactions became self-sustaining networks is entirely obscure.

How could the process that stores the information that specifies the catalysts the RNA or precursor of the primitive cells have evolved ?  The connection between RNA (or its younger, more evolved cousin, DNA) and the proteins that are catalysts, the enzymes, is not at all obvious; how the 2 co-evolved is even less clear.

How did the energetic cycles that power every cell emerge ?  Why is there Potassium ion on the inside of the cell & Sodium ion on the outside? What was the origin of Chemiosmosis the extraordinary complexity of the ATPases the complicated aggregates of proteins that generate ATP using the free energy that derives from differences in the concentration of ions across membranes how could they have evolved ? We simply do not know.

Nothing in the cell violates the Fundamental Laws of Physical Science. The 2nd law of Thermodynamics, the law that describes everything that occurs in the range of sizes relevant to Life, can sleep untroubled.

The flux of Energy now (although not necessarily originally) produced in nuclear reactions in our Sun, transferred to the surface of Earth as sunlight, absorbed by plants in Photosynthesis, captured as Glucose & other compounds, used in the cell to generate the intermediates that make metabolism possible, & ultimately dissipated to Space by radiation as Heat can evidently support Life.  But how Life originated is simply not apparent.  It seems so improbable !  The complexity of the simplest cell eludes our understanding how could it be that any cell, even one simpler than the simplest that we know, emerged from the tangle of accidental reactions occurring in the molecular sludge that covered the prebiotic Earth ?

We do not understand. It is not impossible, but it seems very, very improbable.

This Improbability is the crux of the matter. The scientific method can be paralyzed by problems that require understanding the very improbable occurrences that result from very, very large numbers of throws of the dice.  Sometimes we can understand the statistics of the problem; sometimes we cannot.  How likely is it that a comet will hit the Earth ?  We now have good geological records.  How likely is it that a Star will explode into a Nova ?  There are many, many observable Stars, & we now understand the statistics of Nova formation quite well.

But how likely is it that a newly formed Planet, with surface conditions that support liquid Water, will give rise to Life ?  We have no clue, & no convincing way of estimating.  From what we do now know, the answer falls somewhere between “impossibly unlikely” & “absolutely inevitable.”  We cannot calculate the odds of the spontaneous emergence of cellular Life on a plausible prebiotic Earth in any satisfying and convincing way.

Calculus for Yogis, part 4

There are many ways to approach  e  but one easy way is to look at how simple increase occurs, how, as afore mentioned above, the Derivative, the rate of growth   d y / d x  for  ex  happens to numerically equal the value of   y  =  ex   itself.  This describes that common situation of “the more you got, the more you get.”  Wealth grows faster & faster the larger the amount or principal grows as  et   also.

A savings account, compounded continuously, grows that  et   way which Einstein called “the most amazing thing in the Universe”, which was kind of a joke because he was privy to many amazing things about the Universe.  Some say that we “cannot get our heads around” the Exponential function because a Brain–Mind neuro-circuit “functions” in Exponential functions & like an eyeball, cannot see itself, but only a reflection or photo of an eyeball.

Weatherby way out on the high steep artwork early on in the flat part and reset the scale we get the same appearance so it’s always rising the same way but it always looks like from your present point that the pass was very flat and slow in the future getting incredibly steep this is the rise in CO2 in the atmosphere the rising temperature of the planet in average temperature of the planet in climate change the rising population the rising various pollutants and so on as mentioned increasing bank accounts rise that way and decreasing bank accounts descend according to E to the X into the minor sex which is also the dissent of radioactivity over time in a sample of radioactive material or if that is a pure element or pure isotope

So if we know that  d y / d x  happens to be numerically equal  y  when   y  ex  we must wonder about this curious number   e   which, as it happens can be determined in various mysterious ways, such as the following:

e =   lim  (1 +  1/ x)x

x => ∞

Both a “limit”, like the preceding, & infinite series to be soon mentioned, “converge”, rather than “blow up”, for x  smaller than 1.  When we evaluate e  itself by setting x  = 1  in   ex ,  we get:  e ~   2.72,   e =  2.718281828 …  and then no other repetition occurs right away.  But that early repetition of  18281828  allows us to actually remember to great accuracy because it’s got that 18281828  pattern.

The succeeding numbers vary and are not generally repeating in such a Transcendental number where the number the different numerals goes on forever.  And yet we can say the number in itself has a distinct value, as in saying that   is the value of parenthesis one plus one over  x , all to the  x   in the Limit that  x  goes to Infinity.  Now that’s all more abstract than “the more you got, the more you get.”  & that the rate of increase  numerically equals the value of the function itself.

Then optional notation to augment the Infinite series Polynomial approach that here follows will be veritably “opaque” to the uninitiated but it deserves mention because of its elegance.  The “factorial” for 5, for instance, is  5! = 5×4×3×2×1  =  120.  That same kind of  “count dawn”  works generally, with the quirky Zero case here being:

0!  =  1!  =  1

Much as for the Zeroth Power, the initiated might appreciate that for m  =  n :

=  m ! (m – n) !   =    n ! (n – n) !      n ! (0) !  =   n ! /  1    =   n !

This behavior or definition for  0 !  is necessary for calculating Probability with factorials.

The “factorial” is about the most rapidly growing function of an Integer, & it simplifies even the first few terms of an Infinite series, & more so a generic term.

That’s the easy part, because the other useful optional notation to augment the Infinite series Polynomial approach for use with the generic term is a “Summation” indicated by “Sigma”, the Greek capital letter “S”, namely Σ :

4

Σ n   =   4  + 1  =  10.    [like it or not, take it or not – optional]

n=0

Both a “limit” above & the Infinite series to be soon mentioned, “converge”, rather than “blow up”, for x  smaller than 1.  In the case of infinite series, an approximate value results after a limited number if terms.

For example & for practice, one Series of simple terms suggests modification of the shortcut approach to estimating “uncertainties” in Arithmetic.

1/(1 x)   =    1  +    +    x 2   +  x 3   +   x 4   ….    for small  x]

The same pattern holds for decimals. but is perhaps most easily seen for fractions of .99  & 1.01.  The approximate rule for “uncertainties” states that we keep the same number of “significant figures” as in  1.0/.99  ~  1.0   whereas  1.0/.99  ~  1.01  is more meaningful, even though a ratio of  2  figures  goes to an approximation with 3 figures.  But this treatment follows:

1/ .99   =   1/(1 .01)    ~   1  +  .01  +  .0001    ~    1  +  .01     =   1.01

Likewise, for a fraction of 1.01:

Correspondingly, the “same number of significant figures” yields as in  1.00/1.01  ~  .990   whereas  1.0/1.01  ~  .99  is more meaningful, even though a ratio of  3  figures  goes to an approximation with 2 figures.  But again, this treatment follows:

1/(1 + x)   =    1   –    +    x 2    –  x 3   +   x 4   ….    for small  x

1/1.01  =  1/(1 + .01)    ~    1   –  .01  +  .0001    ~    1   –  .01     =   .99

Aside from the series treatment, the consistency in both cases follows a  1%  “uncertainty”  &   %uncertainty is the truer rule.

In a similar vein, we can familiarize ourselves with Polynomial series with 2 similar approximations:

1/(1 x)2   =     1  +   2  +  3 x 2   + 4 x 3   +  5 x 4   ….    for small  x

&

1/(.99)2    =  1/(1 .01)2     ~    1  +  .02    =   1.02

1/(.99)3    =  1/(1 x)3   =     1  +  3  +  6 x 2   + 10 x 3   +  15 x 4   for small  x

&

1/(1 .01)3      ~    1  +  .03    =   1

To indicate these 2 Polynomial series in the above-mentioned  “Summation”  “Sigma” notation:

1/(1 x)  =       Σ  x n / n   =   1  +    +    x 2   +  x 3   +   x 4   ….    for small  x

n  = 0

1/(1 + x)  =  –  Σ  x n / n   =  –    –  x 2 / –  x 3 / 3  –  x 4 / 4    ….   small  x

n  = 0

1/(1 x)2   =  Σ  n x n –1    1  +   2  +  3 x 2  + 4 x 3  + 5 x 4     …. small  x                             n  = 1

1/(1 x)3  =  1/2   Σ  (n–1) n x n –2   =   1  +  3 +  6 x 2  + 10 x 3  + 15 x 4 

n  = 1

=   0  +  1/2  x  1  x  2  x  x0   +   1/2  x  2  x  3  x  x1   +   1/2  x  3  x  4  x  x 2   +   1/2  x  4  x  5  x   x 3   +   1/2  x  5  x  6  x   x 4

Some more selected verses from the Ramana Maharshi disciple Master Nome:

The basic premise of Non-Duality is that the Absolute exists & that the Absolute is identical with oneself.  Therefore, Self-Knowledge is equated with the Realization of the Absolute.  The basic premise of spiritual practice is that one knows that the Absolute exists & that realizing the Absolute is of utmost importance. This realization is Self-Realization. What is need for this Self-Knowledge, or Realization, is the relinquishment of the assumptions or concepts, that yield the Illusion of Bondage & Suffering.  Knowledge of one’s Being, as it is, yields enduring Freedom & Peace.  The true Self transcends the limitations of any kind of Individuality, Time, Birth, & Death. The Self is impersonal & is not confined to any Body or Individual.

One’s approach to one’s spirituality, meditation, & this Non-Dual Knowledge is of paramount importance, for the approach very much determines the experience. How one views anything determines how it appears to him.  Clarification of one’s understanding of oneself causes one to arrive at Self-Knowledge. To know this as being so, is itself the dawning of that Self-Knowledge.  Deep meditation dissolves the Ego, Ignorance, & Bondage of one who ardently meditates. Self-Inquiry within oneself to know oneself reveals the true Self to be limitless Consciousness, Absolute Being, & unconditioned Bliss.

This one’s very Existence.  One should continue meditating on the Teaching of Self-Knowledge by the practice of Self-Inquiry until one conclusively realizes the Self & abides without the least trace of Ignorance or Bondage. Listening (sravana), reflection (manana), & deep meditation (nididhyasana) are said to constitute ways of practicing Self-Knowledge.  Self-Inquiry: “Who am I ?”, knowing oneself free of mis-identification, & steady Abidance as the Self always, these are the inner experiences of listening (sravana), reflection (manana), & deep meditation (nididhyasana).

The above themes & 1600 pages more are freely available as perused or downloaded PDF’s, the sole occupants of a Public Microsoft Skydrive “Public Folder” accessible through:  

www.jpstiga.com/

http://jstiga.wixsite.com/nonduality/

or with Caps-sensitive:

http://sdrv.ms.YPOgkX/

Duplicates have been available on:

jstiga.wordpress.com/

[But from now on, they will be different & still usually daily.]

There is no Creation, no Destruction, no Bondage, no longing to be freed from Bondage, no striving for Liberation, nor anyone who has attained Liberation. Know that this to be Ultimate Truth.”   the “no creation” school of Gaudapada, Shankara, Ramana, Nome Ajata Vada

for very succinct summary of the teaching & practice, see:  www.ajatavada.com/