Learning English as a second language

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 Mandelbrot Set    

   Polish-born French mathematician Benoit Mandelbrot coined the term “fractal” to describe complex geometric shapes that, when magnified, continue to resemble the shape’s larger structure. This property, in which the pattern of the whole repeats itself on smaller and smaller scales, is called self similarity. The fractal shown here, called the Mandelbrot set, is the graphical representation of a mathematical function.

Chaos theory

   Despite advances made in systems analysis, many systems remain beyond the reach of current mathematics. Chaos theory, a relatively new area of mathematics, concerns the analysis of unpredictable systems that are extremely sensitive to initial conditions. One important example of a chaotic system is climate. Global climate modeling is an area of mathematical research that seeks to develop models for predicting the weather, given accurate data from weather satellites orbiting Earth. The problem in developing such models arises not from lack of data but from the difficulty of modeling such a complex system (Earth’s atmosphere) with a small number of equations. In such models even a thousand equations may be considered small. The solution of these equations is very sensitive to changes in the initial conditions. The term initial conditions refers to all the measurements at the starting time. A tiny inaccuracy in a single measurement of a chaotic system—such as a temperature variation of a fraction of a degree—can produce large errors in solutions to the model’s equations and predictions.

Applications include the study of turbulent flow in fluids, irregularities in biological systems, population dynamics, chemical reactions, plasma physics, meteorology, the motions of groups and clusters of stars, transportation dynamics, and many other fields.

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Lorenz attractor (strange attractor)

(After Edward Lorenz, its discoverer) A region in the phase space of the solution to certain systems of (non-linear) differential equations. Under certain conditions, the motion of a particle described by such as system will neither converge to a steady state nor diverge to infinity, but will stay in a bounded but chaotically defined region. By chaotic, we mean that the particle's location, while definitely in the attractor, might as well be randomly placed there. That is, the particle appears to move randomly, and yet obeys a deeper order, since is never leaves the attractor.
Lorenz modelled the location of a particle moving subject to atmospheric forces and obtained a certain system of ordinary differential equations. When he solved the system numerically, he found that his particle moved wildly and apparently randomly. After a while, though, he found that while the momentary behaviour of the particle was chaotic, the general pattern of an attractor appeared. In his case, the pattern was the butterfly shaped attractor now known as the Lorenz attractor.
(1996-01-13)

Meteorologist Edward Lorenz tried to model climate in a series of equations during the 1960s. In doing so, he produced a chaotic system of three related differential equations, now known as a Lorenz attractor, or strange attractor. Through his models he discovered the sensitivity of chaotic systems to initial conditions, which he phrased in the question “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”

The Lorenz attractor is an example of a fractal, a pattern produced by applying a function repeatedly, much like pushing a button on a calculator over and over. The sequence {x, f(x), f(f(x)), f(f(f(x))), ...}, when graphed in two dimensions, gives rise to beautiful, complex geometric images such as the Mandelbrot set pictured in this article. These fractal images are named after Benoit Mandelbrot, a Polish-born French mathematician who developed fractal geometry and coined the word fractal. The interesting relationship among fractals, chaos, and unstable phenomena such as turbulence is the subject of a field called nonlinear dynamics.

People using language only to convey information are usually indifferent to the sounds of the words and may feel frustrated by their connotations and multiple denotations. They would rather confine each word to a single, exact meaning. They use, one might say, a fraction of the word and throw away the rest. Poets, on the other hand, use as much of the word as possible. They are interested in connotation and use it to enrich and convey meaning. And they may rely on more than one denotation. Perhaps the purest form of practical language is scientific language. Scientists need a precise language to convey information precisely. The existence of multiple denotations and various overtones of meaning may interfere with this purpose. As a result of this, scientists have even devised special "language" such as the following:

                                                                SO₂ + H₂O = H₂SO₃

In such a statement the symbols are entirely unambiguous; they have been stripped of all connotations and of all denotations but one. The word sulfurous, if it occurred in poetry, might have all kinds of connotations: fire, smoke, brimstone, hell, damnation. But H₂SO₃ means one thing and one thing only: sulfurous acid.

The ambiguity and multiplicity of meanings possessed by words might be an obstacle to the scientist, but they are advantage for the poet who seeks richness of meaning. One resource for that is a multidimensional language using a multidimensional vocabulary, in which the dimensions of connotation and sound are added to the dimension of denotation.

The poet, we may say, plays on many-stringed instrument and sounds more than one note at a time.

The first task in reading poetry, therefore, as in reading any kind of literature, is to develop a sense of language, a feeling for words. One needs to become acquainted with their shape, their color, and their flavor. Two of the ways of doing this are extensive use of the dictionary and extensive reading.  

Dirge (نوحه)

Word History: The history of the word dirge illustrates how a word with neutral connotations, such as direct, can become emotionally charged because of a specialized use. The Latin word dīrige is a form of the verb dīrigere, “to direct, guide,” that is used in uttering commands. In the Office of the Dead dīrige is the first word in the opening of the antiphon for the first nocturn of Matins: “Dirige, Domine, Deus meus, in conspectu tuo viam meam,” “Direct, O Lord, my God, my way in thy sight.” The part of the Office of the Dead that begins with this antiphon was named Dīrige in Ecclesiastical Latin. This word with this meaning was borrowed into English as dirige, first recorded in a work possibly written before 1200. Dirige was then extended to refer to the chanting or reading of the Office of the Dead as part of a funeral or memorial service. In Middle English the word was shortened to dirge, although it was pronounced as two syllables. After the Middle Ages the word took on its more general senses of “a funeral hymn or lament” and “a mournful poem or musical composition,” and developed its one-syllable pronunciation.

Meditation

Private religious devotion or mental exercise, in which techniques of concentration and contemplation are used to reach a heightened level of spiritual awareness.

The practice has existed in all religions since ancient times. In Hinduism it has been systematized in the school of Yoga. One aspect of Yoga, dhyana (Sanskrit: "concentrated meditation"), gave rise to a school of its own among the Buddhists, becoming the basis of Zen. In many religions, meditation involves verbal or mental repetition of a single syllable, word, or text (e.g., a mantra). Visual images (e.g., a mandala) or mechanical devices such as prayer wheels or rosaries can be useful in focusing concentration. In the 20th century, movements such as Transcendental Meditation emerged to teach meditation techniques outside a religious context.

Transcendental Meditation (TM)

Spiritual development technique developed and promoted by Maharishi Mahesh Yogi, a former Hindu ascetic.

A movement that became popular in the West in the 1960s, it is based on specific meditation techniques and is not strictly connected with any religious tradition, though the perspective behind it has roots in Vedanta. Practice entails the mental repetition of a mantra in order to still the activity of thought and experience a deeper level of consciousness. Through this process, the practitioner finds deep relaxation, which can lead to inner joy, vitality, and creativity.

Relaxation Through Meditation

My preference would be to call meditation relaxation – conscious relaxation, chosen relaxation. These are words that are more universally understood, more comfortable. Constantly working toward the goal of discovering my own ability to reach a state of serenity, I have learned to meditate.

Meditating is actually easier than you might imagine. Most of us have dabbled in meditation by participating in conscious relaxation. Maybe during an exercise class or to manage pain at the dentist or anxiety before a test. We start by paying attention to our breathing. The practical effort to focus completely on our breathing takes our minds away from the "mind clutter" that constantly tries to invade our mind and eliminate feelings that will lead to a time of calm. With repeated effort the goal of clearing your mind – to think of nothing, does occur and the process of meditation takes on its own energy. The result is, and I guarantee this, peace, serenity, calmness, eventually opening yourself to new insights.

Meditating for Life

Too much stress, stress reduction, chill out, let it go, detach – familiar phrases to all of us. Our world is fast, fun and exciting. It is also challenging, trying, demanding and frightening. These two sides of our lives produce stress, emotional reactions, anxiety, worry and anticipation. Our bodies and minds can tolerate only so much of any of these. After a while, each of us reaches a saturation point and the results become uncomfortable at best; for some it may be unbearable, even unendurable.

No magic pill is available to eliminate these feelings. The reality is, as the wise old man said, the answer is inside all of us. To manage these universal concerns we must go inside ourselves. Among the steps we can take is the learning and practicing of meditation.

What to Expect

With time and faith in the commitment to practice frequently, (daily meditating is ideal), during your meditation time you may "leave the moment." A feeling of separation exists where the mind is clear, clean and blank. You will still hear sounds around you, but they will not interfere with your meditation.

Sometimes you may weep -- you may not even be aware of what is making you weep. It is your own emotions having a voice of their own. Sometimes you may feel a smile across your face -- that is contentment showing itself. Sometimes you may fall asleep and awaken truly refreshed.

There is no right or wrong behavior during your meditation. It is your time for you. Everyone deserves this kind of personal attention. This is a self-care activity; loving oneself! Teach it to your children instead of a time-out in their room or corner. Teach it to your friends, family, anyone who will listen. We can share this gift and get back as we give. We are all better because of each person who meditates. The peace and joy felt by those who meditate enters the world for all of us as positive energy. From it the world is a better place. Imagine if we all practiced meditation!

 منبع: http://www.learningmeditation.com/

Link: Shakespeare's Biography

Be

( am, is, are ; past: was, were ; past participle: been)

(.pl. & vi): مصدر فعل بودن ، امر فعل بودن ، وجود داشتن ، زيستن ، شدن ، ماندن ، باش

برای مشاهده کاربرد های فعل to be روی ادامه مطلب کلیک کنید.