Monday, October 31, 2011

The funny thing about the future

Here is the thing about the future.
Every time you look at, it changes.
it changes, because you looked at it,
and that changes everything else.

quoted from "Next", last scene.


We can travel through time,
because time is what we were and what we will be.

We can visit, live and interpret
the past, the future and the present
a million time ...

The past is mutable, because we change,
the future is mutable, because we dream.

Time is the drawing, not the canvas.
and all the drawings are on the same canvas.

Pick yours. And pick it as many times as you want.
You are all the stories, not just the story being told.

Nothing special happened today.
That's enough for me to celebrate.

Friday, September 23, 2011

Human butterfly

I fear death,
cause I can't comprehend life.

My logic fogs my
capacity to feel

and as I get older,
my thoughts are more
a burden than a gain.

My feelings
have always been
my best wealth.

A glimpse of love and pain.
And I am so grateful for it.

Tuesday, June 28, 2011

Love costs all we are and will be

In the flush of love's light
we dare be brave
And suddenly we see
that love costs all we are
and will ever be.
Yet it is only love
which sets us free.

Maya Angelou - Touched by An Angel

The definition and etymology of the sanskrit word "Maya"

from Myths and Symbols of Indian Art and Civilization, by Heinrich Zimmer
New York: Harper & Row, 1962, pp. 24-26.

The Hindu mind associates such ideas as "transitory, ever-changing, elusive, ever-returning," with "unreality," and conversely, imperishable, changeless, steadfast, and eternal," with "the real." As long as the experiences and sensations that stream through the consciousness of an individual remain untouched by any widening, devaluating vision, the perishable creatures that appear and vanish in the unending cycle of life (samsara, the round of rebirth) are regarded by him as utterly real. But the moment their fleeting character is discerned, they come to seem almost unreal – an illusion or mirage, a deception of the senses, the dubious figment of a too restricted, ego-centered consciousness. When understood and experienced in this manner, the world is Maya-maya, "of the stuff of Maya." Maya is "art": that by which an artifact, an appearance, is produced. Maya is precisely the maker’s power or art, "Magic" in Jacob Boehme’s sense: "It is a mother in all three worlds, and makes each thing after the model of that thing’s will. It is not the understanding, but it is a creatrix according to the understanding, and lends itself to good or to evil . . . from eternity a ground and support of all things ... In sum: Magic is the activity in the Will-spirit." (Sex Puncta Mystica, V. -- Ananda K. Coomaraswami)

The noun maya is related etymologically to "measure." It is from the root ma, which means "to measure or lay out instance, the ground plan of a building, or the outlines of a figure); to produce, shape, or create; to display." Maya is the measuring out, or creation, or display of forms; maya is any illusion, trick, artifice, deceit, jugglery, sorcery, or work of witchcraft; an illusory image or apparition, phantasm, deception, of the sight; maya is also any diplomatic trick or political artifice designed to deceive. The maya of the gods is their power to assume diverse shapes by displaying at will various aspects of their subtle essence. But the gods are themselves the productions of a greater maya: the spontaneous self-transformation of an originally undifferentiated, all-generating divine Substance. And this greater maya produces, not the gods alone, but the universe in which they operate. All the universes co-existing in space and succeeding each other in time, the planes of being and the creatures of those planes whether natural or supernatural, are manifestations from an inexhaustible, original and eternal well of being, and are made manifest by a play of maya. In the period of non-manifestation, the interlude of the cosmic night, maya ceases to operate and the display dissolves.

Maya is Existence: both the world of which we are aware, and ourselves who are contained in the growing and dissolving environment, growing and dissolving in our turn. At the same time, Maya is the supreme power that generates and animates the display: the dynamic aspect of the universal Substance. Thus it is at once, effect (the cosmic flux), and cause (the creative power). In the latter regard it is known as Shakti, "Cosmic Energy." The noun shakti is from the root shak, signifying "to be able, to be possible." Shakti is power, ability, capacity, faculty, strength, energy, prowess; regal power; the power of composition, poetic power, genius; the power or signification of a word or term; the power inherent in cause to produce its necessary effect; an iron spear, lance, pike, dart; a sword"; shakti is the female organ; shakti is the active power of a deity and is regarded, mythologically, as his goddess-consort and queen.

Maya-Shakti is personified as the world-protecting, feminine, maternal side of the Ultimate Being, and as such, stands for the spontaneous, loving acceptance of life’s tangible reality. Enduring the suffering, sacrifice, death and bereavements that attend all experience of the transitory, she affirms, she is, she represents and enjoys, the delirium of the manifested forms. She is the creative joy of life: herself the beauty, the marvel, the enticement and seduction of the living world. She instills into us - and she is, herself – surrender to the changing aspects of existence. . . .

Now the character of Maya-Shakti-Devi (devi = "goddess") is multifariously ambiguous. Having mothered the universe and the individual (macro- and microcosm) as correlative manifestations of the divine, Maya then immediately muffles consciousness within the wrappings of her perishable production. The ego is entrapped in a web, a queer cocoon. "All this around me," and "my own existence" – experience without and experience within – are the warp and woof of the subtle fabric. Enthralled by ourselves and the effects of our environment, regarding the bafflements of Maya as utterly real, we endure an endless ordeal of blandishment, desire and death; whereas, from a standpoint just beyond our ken (that represented in the perennial esoteric tradition and known to the illimited, supra-individual consciousness of ascetic, yogic experience) Maya – the world, the life, the ego, to which we cling – is as fugitive and evanescent as cloud and mist.

The aim of Indian thought has always been to learn the secret of the entanglement, and, if possible, to cut through into a reality outside and beneath the emotional and intellectual convolutions that enwrap our conscious being.

Tuesday, May 17, 2011

Integral of rational function


The word catenary is derived from the Latin word catena, which means "chain". The English word catenary is usually attributed to Thomas Jefferson, who wrote in a letter to Thomas Paine on the construction of an arch for a bridge:
I have lately received from Italy a treatise on the equilibrium of arches, by the AbbĂ© Mascheroni. It appears to be a very scientifical work. I have not yet had time to engage in it; but I find that the conclusions of his demonstrations are, that every part of the catenary is in perfect equilibrium.[5]
It is often said that Galileo thought the curve of a hanging chain was parabolic. In his Two New Sciences (1638), Galileo says that a hanging cord is an approximate parabola, and he correctly observes that this approximation improves as the curvature gets smaller and is almost exact when the elevation is less than 45°. That the curve followed by a chain is not a parabola was proven by Joachim Jungius (1587–1657); this result was published posthumously in 1669.

de Moivre's formula

de Moivre's formula 
From http://en.wikipedia.org/wiki/De_Moivre's_formula:

By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos (nx) and sin (nx) in terms of cos x and sin x. Furthermore, one can use a generalization of this formula to find explicit expressions for the nth roots of unity, that is, complex numbers z such that zn = 1.

Legendre's differential equation


They are named after Adrien-Marie Legendre. This ordinary differential equation is frequently encountered in physics and other technical fields. In particular, it occurs when solving Laplace's equation (and related partial differential equations) in spherical coordinates.

The Legendre differential equation may be solved using the standard power series method. The equation has regular singular points at x = ±1 so, in general, a series solution about the origin will only converge for |x| < 1. When n is an integer, the solution Pn(x) that is regular at x = 1 is also regular at x = −1, and the series for this solution terminates (i.e. is a polynomial).