It is all about generalizing the concepts of space and dimension.
Matrix algebra involves transformations to appropriate forms by sometimes changing the basis.
EigneValues are a very good example where the Vectors are first converted to the basis of eignevectors. The calculations with the transormation is easier since A*x=LAMBDA*x for all eignevectors. After calculations are done , the transformation is again done to the original basis.
Saturday, January 3, 2009
Modernism
Four Literary "isms" Inside Modernism
1. Whereas Realism attempted to portray external objects and events as the common or middle class man sees them in everyday life, impressionism tries to portray the psychological impressions these objects and events make on characters, emphasizing the role of individual perception and exploring the nature of the conscious and unconscious mind.
2. Whereas Realism tried to focus on these external objects and events, expressionism tried to express the inner vision, the inner emotion, or the inner spiritual reality that seem more important than the external realities of objects and events.
3. Whereas Realism focused on external objects and events as they are (verisimilitude), surrealism tried to liberate the subconscious, to see connections overlooked by the logical mind, to deny the supreme authority of rationality and so portray objects and events as they seem rather than as they are.
4. Whereas Realism tried to show the supreme importance of rationalness and reason, absurdism tried to duplicate in literature the absurd conditions of contemporary life: nameless millions dying in wars, commonplace horrors such as the Holocaust, a world in which "God is dead" cast mankind afloat in a chartless and unknowable world void of a spiritual center, the ultimate absurd circumstances in which contemporary humankind found itself.
Source : http://vc.ws.edu/engl2265/unit4/Modernism/all.htm
1. Whereas Realism attempted to portray external objects and events as the common or middle class man sees them in everyday life, impressionism tries to portray the psychological impressions these objects and events make on characters, emphasizing the role of individual perception and exploring the nature of the conscious and unconscious mind.
2. Whereas Realism tried to focus on these external objects and events, expressionism tried to express the inner vision, the inner emotion, or the inner spiritual reality that seem more important than the external realities of objects and events.
3. Whereas Realism focused on external objects and events as they are (verisimilitude), surrealism tried to liberate the subconscious, to see connections overlooked by the logical mind, to deny the supreme authority of rationality and so portray objects and events as they seem rather than as they are.
4. Whereas Realism tried to show the supreme importance of rationalness and reason, absurdism tried to duplicate in literature the absurd conditions of contemporary life: nameless millions dying in wars, commonplace horrors such as the Holocaust, a world in which "God is dead" cast mankind afloat in a chartless and unknowable world void of a spiritual center, the ultimate absurd circumstances in which contemporary humankind found itself.
Source : http://vc.ws.edu/engl2265/unit4/Modernism/all.htm
Music : Introduction
Music is an art form whose medium is sound organized in time. Common elements of music are pitch (which governs melody and harmony), rhythm (and its associated concepts tempo, meter, and articulation), dynamics, and the sonic qualities of timbre and texture. The word derives from Greek μουσική (mousike), "(art) of the Muses".[1]
The creation, performance, significance, and even the definition of music vary according to culture and social context. Music ranges from strictly organized compositions (and their recreation in performance), through improvisational music to aleatoric forms. Music can be divided into genres and subgenres, although the dividing lines and relationships between music genres are often subtle, sometimes open to individual interpretation, and occasionally controversial. Within "the arts", music may be classified as a performing art, a fine art, and auditory art.
To people in many cultures, music is inextricably intertwined into their way of life. Greek philosophers and ancient Indians defined music as tones ordered horizontally as melodies and vertically as harmonies. Common sayings such as "the harmony of the spheres" and "it is music to my ears" point to the notion that music is often ordered and pleasant to listen to. However, 20th-century composer John Cage thought that any sound can be music, saying, for example, "There is no noise, only sound."[2] According to musicologist Jean-Jacques Nattiez, "the border between music and noise is always culturally defined—which implies that, even within a single society, this border does not always pass through the same place; in short, there is rarely a consensus.… By all accounts there is no single and intercultural universal concept defining what music might be, except that it is 'sound through time'.
The creation, performance, significance, and even the definition of music vary according to culture and social context. Music ranges from strictly organized compositions (and their recreation in performance), through improvisational music to aleatoric forms. Music can be divided into genres and subgenres, although the dividing lines and relationships between music genres are often subtle, sometimes open to individual interpretation, and occasionally controversial. Within "the arts", music may be classified as a performing art, a fine art, and auditory art.
To people in many cultures, music is inextricably intertwined into their way of life. Greek philosophers and ancient Indians defined music as tones ordered horizontally as melodies and vertically as harmonies. Common sayings such as "the harmony of the spheres" and "it is music to my ears" point to the notion that music is often ordered and pleasant to listen to. However, 20th-century composer John Cage thought that any sound can be music, saying, for example, "There is no noise, only sound."[2] According to musicologist Jean-Jacques Nattiez, "the border between music and noise is always culturally defined—which implies that, even within a single society, this border does not always pass through the same place; in short, there is rarely a consensus.… By all accounts there is no single and intercultural universal concept defining what music might be, except that it is 'sound through time'.
Saturday, December 27, 2008
Art : Functions
Non-Motivated :
1. Basic human instinct for harmony, balance, rhythm
2. Experience of the mysterious
3. Expression of the imagination
4. Universal communication. e.g. Rocks placed on top of a mountain.
5. Ritualistic and symbolic functions
Motivated :
1. Communcation .e.g. Maps
2. Art as Entertainment.e.g. Video Games.
3. Art for political change.
4. Art for psychological and healing purposes.
5. Art for social inquiry, subversion and/or anarchy. e.g. Graffiti
6. Art for propaganda, or commercialism
The functions of art described above are not mutually exclusive, as many of them may overlap. For example, art for the purpose of entertainment may also seek to sell a product, i.e. the movie or video game. One of the central challenges of post-modern art (after the 1970s), is that as the world becomes increasingly utilitarian, functional, and market-driven, the presence of the non-motivated arts, or art which is ritualistic or symbolic, becomes increasingly rare.
Source : Wikipedia
1. Basic human instinct for harmony, balance, rhythm
2. Experience of the mysterious
3. Expression of the imagination
4. Universal communication. e.g. Rocks placed on top of a mountain.
5. Ritualistic and symbolic functions
Motivated :
1. Communcation .e.g. Maps
2. Art as Entertainment.e.g. Video Games.
3. Art for political change.
4. Art for psychological and healing purposes.
5. Art for social inquiry, subversion and/or anarchy. e.g. Graffiti
6. Art for propaganda, or commercialism
The functions of art described above are not mutually exclusive, as many of them may overlap. For example, art for the purpose of entertainment may also seek to sell a product, i.e. the movie or video game. One of the central challenges of post-modern art (after the 1970s), is that as the world becomes increasingly utilitarian, functional, and market-driven, the presence of the non-motivated arts, or art which is ritualistic or symbolic, becomes increasingly rare.
Source : Wikipedia
Philosophy : Different Schools
This page is where I copy a brief run down of the main branches of philosophy. At the top of this list I've put the 3 main subdivisions of philosophy, namely epistemology, ethics and metaphysics, into which the majority of philosophical activity falls. Apart from this the list is in alphabetical ordering. In each entry I've also tried to name a few of the most important works in each branch, though obviously there are far more than I could list here, particularly in the main 3 branches. To be honest, pretty much every one of the hundred of so classic works of philosophy could probably be listed under those 3 as classic, so I've just tried to keep it to the most central ones, and my personal favourites.
Epistemology: The philosophy of knowledge. Concerned with such questions as, is knowledge of anything really possible, is our knowledge certain, how do we get our knowledge, what things can we have knowledge about, what exactly is knowledge, etc. Classic works include Descartes' Meditations, Locke's An Essay Concerning Human Understanding, Hume's Treatise on Human Nature, and Kant's Critique of Pure Reason. Almost all the major philosophers have written on this subject, though it is less popular nowadays.
Ethics: This is probably the most self-explanatory of all the branches. Concerned with such things as what is good/evil, is there such a thing as objective morals or are they created by us, or some other being, how we should live our lives, and so on. Classic works include Plato's Republic, Aristotle's Nichomachean Ethics, Kant's Groundwork for the Metaphysics of Morals, Nietzsche's Beyond Good and Evil.
Metaphysics: Meta means above; this is the study of the nature of things above physics. Metaphysics covers the kinds of things most people probably think of if asked what philosophy covers e.g. those 'big questions', such as, is there God, why are we here, what is the ultimate nature of the universe, and so on. Another important area of metaphysics is the nature of substance, that is, what is the universe really made of, a particular favourite of mine. Metaphysics has often come under attack for being too abstract to actually have any worth, particularly famously by A.J. Ayer. Classic works include Aristotle's Metaphysics, Spinoza's Ethics (which unsurprisingly also is a classic work on Ethics), and almost anything written by Leibniz.
Aesthetics: The philosophy of art. Concerned with questions like why do we find certain things beautiful, what makes things great art, so on. Classic works include Aristotle's Rhetoric and Poetics, Schopenhauer and Hegel's lectures, Kant's Critique of Judgement. Plato had a famously dim view of this branch.
Philosophy of Education: Fairly self-explanatory. A minor branch, mainly concerned with what is the correct way to educate a person. Classic works include Plato's Republic, Locke's Thoughts Concerning Education, and Rousseau's Emile.
Philosophy of History: Fairly minor branch (not as minor as education), although highly important to Hegel and those who followed him, most notably Marx. It is the philosophical study of history, particularly concerned with the question whether history (i.e. the universe and/or humankind) is progressing towards a specific end? Hegel argued that it was, as did Marx. Classic works include Vico's New Science, and Hegel and Marx's works.
Philosophy of Language: Ancient branch of philosophy which gained prominence in the last century under Wittgenstein. Basically concerned with how our languages affect our thought. Wittgenstein famously asserted that the limits of our languages mark the limits of our thought. Classic works include Plato's Cratylus, Locke's Essay, and Wittgenstein's Tractatus Logico-Philosophicus.
Philosophy of Law: Also called Jurisprudence. Study of law attempting to discern what the best laws might be, how laws came into being in the first place, attempting to delimit human laws from natural laws, whether we should always obey the law, and so on. Law isn't often directly dealt with by philosophers, but much of political philosophy obviously has a bearing on it.
Logic: The study of the proper methods of thinking and reasoning. Logic languages, like Predicate Logic, promise to produce arguments which, if the premises are true, can only lead to true conclusions. Logic is slightly different than the other branches as it aims to suggest the correct ways of studying philosophy in general. Classic works include Aristotle's Prior and Posterior Analytics, and Russell and Whitehead's Principia Mathematica.
Philosophy of Mathematics: Study of mathematics concerned with issues such as, is mathematics real or created by us, is it necessary to understand the world, do perfect mathematical forms exist in the real world, and so on. Principia Mathematica is almost certainly the most important work in this field.
Philosophy of Mind: Study of the mind, attempting to ascertain exactly what the mind is, how it interacts with our body, do other minds exist, how does it work, and so on. Probably the most popular branch of philosophy right now, it has expanded to include issues of AI. Classic works include Plato's Republic and Wittgenstein's Philosophical Investigations, although every major philosopher has had some opinion at least on what the mind is and how it works.
Philosophy of Politics: Closely related to ethics, this is a study of government and nations, particularly how they came about, what makes good governments, what obligations citizens have towards their government, and so on. Classic works include Plato's Republic, Hobbes' Leviathan, Locke's Two Treatises, and J.S. Mill's On Liberty.
Philosophy of Religion: Theology is concerned with the study of God, recommending the best religious practises, how our religion should shape our life, and so on. Philosophy of religion is concerned with much the same issues, but where Theology uses religious works, like the Bible, as it's authority, philosophy likes to use reason as the ultimate authority.
Philosophy of Science: Study of science concerned with whether scientific knowledge can be said to be certain, how we obtain it, can science really explain everything, does causation really exist, can every event in the universe be described in terms of physics and so on. Also popular in recent times, classic works include Hume's Treatise on Human Nature, Kripke's Naming and Necessity, Kuhn's Structure of Scientific Revolutions.
Further refeerence : http://www.importanceofphilosophy.com/FiveBranchesMain.html
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