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math

Examples

\left(3-x\right) \times \left( \frac{2}{3-x} \right) = \left(3-x\right) \times \left( \frac{3}{2-x} \right)


2 = \left( \frac{\left(3-x\right) \times 3}{2-x} \right)


4-2x = 9-3x \!


-2x+3x = 9-4 \!


\int_a^x \int_a^s f(y)\,dy\,ds = \int_a^x f(y)(x-y)\,dy\,


\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}{3^m\left(m\,3^n+n\,3^m\right)}


u'' + p(x)u' + q(x)u=f(x),\,\,\,x>a


|\bar{z}| = |z|, |(\bar{z})^n| = |z|^n, arg(z^n) = n\,arg(z)\,


\lim_{z\rightarrow z_0} f(z)=f(z_0)\,


\phi_n(\kappa) = \frac{1}{4\pi^2\kappa^2} \int_0^\infty \frac{\sin(\kappa R)}{\kappa R} \frac{\partial}{\partial R}\left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR\,


\int_0^\infty x^\alpha \sin(x)\,dx = 2^\alpha \sqrt{\pi}\, \frac{\Gamma(\frac{\alpha}{2}+1)}{\Gamma(\frac{1}{2}-\frac{\alpha}{2})}\,


\phi_n(\kappa) = 0.033C_n^2\kappa^{-11/3},\,\,\,\frac{1}{L_0}<\!\!<\kappa<\!\!<\frac{1}{l_0}\,


f(x) = {a_0\over 2} + \sum_{n=1}^\infty a_n\cos({2n\pi x \over T}) + b_n\sin({2n\pi x\over T})\,


f(x) = \begin{cases}1 & -1 \le x < 0\\
 \frac{1}{2} & x = 0\\x&0<x\le 1\end{cases}


\Gamma(z) = \int_0^\infty e^{-t} t^{z-1} \,dt\,


J_p(z) = \sum_{k=0}^\infty \frac{(-1)^k\left(\frac{z}{2}\right)^{2k+p}}{k!\Gamma(k+p+1)}\,


{}_pF_q(a_1,...,a_p;c_1,...,c_q;z) = \sum_{n=0}^\infty \frac{(a_1)_n\cdot\cdot\cdot(a_p)_n}{(c_1)_n\cdot\cdot\cdot(c_q)_n}\frac{z^n}{n!}\,


\Gamma(n+1) = n \Gamma(n), n>0\,


\int_0^1 \frac{1}{\sqrt{-lnx}} dx\,


\int_0^\infty e^{-st}t^{x-1}\,dt,\,\,\,s>0\,



table

Stories Ma Nature Shamanism The Papalagi

Greetings



Ice2

Why
Are some icicles long
Some short?
-Onitsura-

We are poets and sages in so far as we
do not ask such questions, or rather ...
in asking them we expect no answer and
do not desire one.
To keep things in this state of wonder
and suspense, to want without desire to
love deeply without attachment, this is
the real part of all our living.
Then the different lengths of the icicles,
the different heights of wooden pilings,
the difference between the sun and the
moon, these things are of perpetual and
never-ending surprise, for ...

"A long thing is ...
the Long Body of Buddha;
A short thing is ...
the Short Body of Buddha."

-R.H.Blyth-
Haiku Vol4 Autumn/Winter


<img alt="Chinese for "utilization"" src="http://www.duckdaotsu.org/2/utilization.gif" style="width: 52px; height: 16px;">

Table Template

These are some useful templates.

Nombre Completo de la Nación
Full name of nation
Official language Official language(s)
Capital Capital
Head of state Head-of-state
Head of government Head-of-government
Area Area
Population Population
Independence Date
Currency Currency
Wiki

To the right is an example of a Wikipedia-style country info box. Below is what it looks like raw. An explanation will be given below. Don't panic!

{| border=1 align=right cellpadding=4 cellspacing=0 width=300 style="margin: 0 0 1em 1em; background: #f9f9f9; border: 1px #aaaaaa solid; border-collapse: collapse; font-size: 95%;"
|+ <big>'''Nombre Completo de la Nación'''</big><br> <big>'''Full name of nation'''</big>
|-
|'''Official language''' || Official language(s)
|-
|'''Capital''' || Capital
|-
|'''Head of state''' || Head-of-state
|-
|'''Head of government''' || Head-of-government
|-
|'''Area''' || Area
|-
|'''Population''' || Population
|-
|'''Independence''' || Date
|-
|'''Currency''' || Currency
|}

This looks quite complex, but really isn't as bad as it looks. The first line (up to font-size: 95%;") must be kept unaltered, in order to preserve uniformity.

The second line gives the header to the table. It is suggested that the last line of the header be the English translation of the name, and the first be the name in the native language(s). If a different script is used, that should be at the very top (for an example, see Japan (Rebellion of 61)). Each heading begins with <big>''' and ends with '''</big>. The <br> tag separates multiple headings.

Each data point is in the following form:
|'''Category''' || Data

And each point is sperated by
|-

Finally, the table must end with |}

To make a cell that covers two columns (as in, for example, the flag, motto, and world maps in Wikipedia's country entires - see http://en.wikipedia.org/wiki/Luxembourg for an example), use a line like this:

|colspan=2 align=center | [[image:wiki.png]]

This will add the image file (in this case, our wiki's logo) to the table

new projects

How Strange and Marvelous!

from "The Tibetan Book of the Great Liberation," by Padmasambhava, trans W. Y. Evans-Wentz, ed Stephen Mitchell, in "The Enlightened Mind," p62-64:

Since there is really no duality, separation is unreal. Until duality is transcended and at-one-ment realized, enlightenment cannot be attained. Both samsara and nirvana, an inseparable unity, are your own mind. It is only because of deluded ideas, which you are free to accept or reject, that you wander in the world of samsara. Practice the Dharma, grasp the essence of these teachings, and free yourself from every attachment. When you seek your mind in its true state, you will find it quite intelligible, although it cannot be seen. In its true state, mind is naked, immaculate, transparent, empty, timeless, uncreated, unimpeded; not realizable as a separate thing, but as the unity of all things, yet not composed of them; undifferentiated, self-radiant, indivisible, and without qualities. Your own mind is not separate from other minds; it shines forth, unobscured, for all living beings. Your own mind is originally as pure and empty as the sky. To know whether or not this is true, look inside your own mind. Without beginning or ending, your original wisdom has been shining forever, like the sun. To know whether or not this is true, look inside your own mind. Your original wisdom is as continuous and unstoppable as the current of a mighty river. To know whether or not this is true, look inside your own mind. When you realize that all phenomena are as unstable as the air, they lose their power to fascinate and bind you. To know whether or not this is true, look inside your own mind. All phenomena are your own ideas, self-conceived in the mind, like reflections in a mirror. To know whether or not this is true, look inside your own mind. Arising spontaneously and free as the clouds in the sky, all phenomena fade away by themselves. To know whether or not this is true, look inside your own mind. Again and again, look inside your own mind. When you look outward into the emptiness of space, you will find no place where the mind is shining. When you look into your own mind in search of the radiance, you will find nothing that shines. This self-originated clear light is eternal and unborn. How strange and marvelous! Since it is unborn, it cannot die. How strange and marvelous! Although it is absolute reality, there is no one to perceive it. How strange and marvelous! Although it wanders in samsara, it is undefiled by evil. How strange and marvelous! Although it sees the Buddha, it is unattached to good. How strange and marvelous! Although it is possessed by all beings, it is not recognized by them. How strange and marvelous! Although the clear light of reality shines inside their own mind, most people look for it outside. How strange and marvelous! Since there is nothing to meditate on, there is no meditation. Since there is nowhere to go astray, there is no going astray. Without meditating, without going astray, look into the true state, where self-awareness, self-knowledge, self-illumination shine resplendently. This is called the enlightened mind. These teachings are immeasurably deep and contain all wisdom. Although they are to be contemplated in a variety of ways, there are no two such things as contemplation and contemplator. When fully contemplated, these teachings merge with the seeker, although when sought, the seeker himself cannot be found. Thereupon the goal of the seeking is attained, and the end of the search. At this point there is nothing more to be sought, and no need to seek anything. Although there are no two such things as knowing and not knowing, there are profound and innumerable forms of meditation; and it is surpassingly excellent in the end to know your own mind. Since there are no two things as meditation and meditator, if, by those who practice or do not practice meditation, the meditator is sought and not found, thereupon the goal of meditation is reached and also the end of meditation itself. Since there are no two such things as meditation and object of meditation, there is no need to fall under the sway of ignorance; for as the result of meditation on the original serenity of the mind, the uncreated wisdom instantaneously shines forth. Although there is an innumerable variety of profound practices, they do not exist for your mind in its true state; for there are no two such things as existence and non-existence. Since there are no two such things as practice and practitioner, if, by those who practice or do not practice, the practitioner of practice is sought and not found, thereupon the goal of practice is reached and also the end of practice itself. The uncreated, self-radiant wisdom of your original mind, actionless, immaculate, transcendent over acceptance and rejection, is itself the perfect practice.


from "The Tibetan Book of the Great Liberation," Padmasambhava, trans Evans-Wentz, p236:

It matters not what name may carelessly be applied to mind; truly mind is one, and apart from mind there is naught else. That Unique One Mind is foundationless and rootless. There is nothing else to be realized.

The Hermit in Lore: the I Ching

The I ching or Book of Changes is an ancient Chinese literary source originating as a divination manual. It presents hexagrams accompanied by explanatory commentaries and text. Although consulted for divination, the work acquired the reputation of being a reservoir of philosophical wisdom, for which it was as widely consulted in subsequent centuries. Because this origin and transformation is pre-Confucian, the I ching provides an excellent resource not interpolated by later tradition. It has special relevance to the study of Chinese eremiticism.

Renunciation of service became a philosophical issue under Confucius, whose ethics took up the perennial issue of service to society and state versus reclusion. The Confucian concept of reclusion, it must be remembered, is still rudimentary, referring to abstention, not a hermit lifestyle. There should be no antiquarianism or historical anachronism in studying the I ching.

The I ching likely was originally consulted by government officials for making decisions. Advice to the ruler of the state is a common application of divination in all cultures, using devices such as taking of augury and astrology. But as a literary source, the I ching embodies specific modes of behavior and responses to crises. Their meanings are general, of course, even vague, but the consultant is expected to apply the established principle of the hexagram to an immediate situation. Some hexagrams advise actions which came to be understood as the origins of eremiticism, advising an "eremitic" solution.

A hexagram consists of a unit of six horizontal lines, with accompanying commentary: Judgment, Image, and Lines, the latter a descriptive meaning of each line in detail. The lines are of two sets (top and bottom) and are solid or broken into two. The sequence of the lines from lowest to highest represents a specific natural phenomenon that, in turn, suggests an interpretation relevant to the consultant.

<img src="../images/tun.gif" align="left" border="0" height="66" hspace="10" vspace="2" width="54">The most obvious hexagram relevant to the construction of a Chinese personality of eremiticism is number 33: tun or the pinyin dun. Here the hexagram represents "retreat." The original sense suggests caution and the avoidance of danger, as in a military situation, but the commentary universalizes the context to human affairs in general. Retreat is not cowardice or flight. Retreat is perspicacious, the wise perception of when to abandon the field  (of battle, social engagement, etc.). The commentary for Judgment is more specific:

Mountain under heaven: the image of retreat.
Thus the superior man keeps the inferior at a distance,
Not angrily but with reserve.

   

The mountain and the firmament part of retreat from one another. The wise man ("superior" as heaven, embodying wisdom) rises above the inferior man ("inferior" as mountain). He keeps distance because the mountain can never reach him, neither in the psychological nor physical sense. The wise man's retreat is not motivated by hatred or anger but dignity. The mountain reaches a standstill, while the heavens ascend ever indefinitely.

The I ching further analyzes each line of the hexagram. The top line retreats, representing a period of danger or precariousness. The commentary advises inaction (the famous wu-wei of later Taoism).

At the tail in retreat.
This is dangerous.
One must not wish to undertake anything.

   

The second line from the top means:

  

He holds him fast with yellow ox hide.
No one can tear him loose.

   

The color yellow signifies "middle." The inferior man is held fast by strong ox hide, hence bound by duty. The inferior man presses the superior and does not allow the latter to go, as in the Judgment statement.

Line three:

   A halted retreat
Is nerve-wracking and dangerous.
To retain people as men and maid servants
Brings good fortune.

During the dangerous retreat, it is advised to take care of clinging servants. Obviously, the advise is addressed to men at court, of some means, who have run into trouble with the court ethos. By naming servants as a distinct group which the consultant should not abandon in hardheartedness as he withdraws from the court, it becomes clear that the inferior men are not the servants but those who gentlemen who serve the emperor and officials. This passage may reflect charity or pragmatism. The clinging inferiors of line two are no longer here.

Line 4:

   

Voluntary retreat brings good fortune to the superior man
And downfall to the inferior man.

   

This line reemphasizes the superior man's disposition as positive and marked by integrity. He is not forced to retreat but chooses a wiser more dignified way. His absence will further plunge the inferior onto downfall, already anticipated by the superior.

Line 5:

   

Friendly retreat.
Perseverance brings good fortune.

This line confirms that the timing of the retreat allows for an amicable resolution between superior and inferior, despite the danger referred to in an earlier commentary. The superior must be firm in conviction, nevertheless, to achieve the desired outcome.


Line 6:

Cheerful retreat
Everything serves to further.

   

Circumstances for retreat are now clear and a mood of cheerfulness can be entertained. Such a clarity establishes success for the path ahead.

The thirty-third hexagram has been detailed because it so irrefutably establishes an ethos of reclusion so early in ancient China. Though the contexts deals with civil service in a literal sense, and cannot be presumed to establish a universal motive for eremiticism, this hexagram does lay out the circumstances necessary for an eremiticism of the future. Chinese eremiticism would thus, in this and the immediate Confucian period that follows, be characterized by a highly-principled social criteria, namely, the individual's capacity to reject social and civic norms in favor of personal integrity and freedom.

Here are other hexagrams indirectly confirming and extending the concepts of the third-third:

  1. The Creative (Ch'ien or qian)
  2. The Receptive (k'un),
  6. Conflict (Sung or song)
18. Work on What has been Spoiled (Ku or gu)
36. Darkening of the light (Ming I or mingyi)
52. Keeping Still, Mountains (Ken or gen)
60. Limitation (Chieh or jie)

Each develops a perspective on the concept of reclusion, all within the context of government service. Exploring the I ching from this historical angle is a refreshing experience. As a conclusion, the commentary on line six of hexagram 18 (Ku) is unambiguous and aptly describes the earliest philosophy of wisdom as reclusion, and the wise man as recluse:

He does not serve kings and princes,
Sets himself higher goals.

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