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Ethics/Nonkilling/Leadership/Abdul Ghaffar Khan

This Course is based mainly on Professor Syed Sikander Mehdi's (University of Karachi) paper Building Nonkilling Muslim Societies: Relevance of Abdul Ghaffar Khan prepared for the First Global Nonkilling Leadership Forum, Mu Ryang Sa Buddhist Temple, Honolulu, Hawai‛i, November 1-4, 2007. The Course is part of the Program on Nonkilling Leadership Development at the School of Nonkilling Studies.

Human killings in Muslim societies abound. Since the end of the Second World War and especially since the end of the Cold War, humans in these societies are being rou-tinely slaughtered and maimed by their own government forces, by the forces of the warlords and by foreign troops. Perhaps it would not be wrong to say that more Mus-lims have been killed in wars, conflicts and violence in the post-Cold War era than the combined total of the non-Muslims killed during the same period. Furthermore, differ-ent kinds of killing are taking place. On the one hand, there is the murder of men, women and children through the direct use of violence in Afghanistan, Iraq, Pakistan and several other Muslim societies, and on the other hand, there is the slow murder of the people because of unavailability of basic human facilities and denial of fundamental human rights. And killing of minds—a sort of genocide of human intellect and human spirit—has been going on in these societies and the world takes very little notice of it.

Worse still, the wholesale slaughter of humans and genocide of the mind and spirit in contemporary Muslim societies are being justified on one pretext or the other. While the powerful media and public opinion leaders including the clash theorists and policy-makers in the developed world are busy crafting arguments in support of demonizing, tribalizing and Red Indianizing the Muslims living in these societies, the Muslim socie-ties themselves are being driven to the ghettoes of exclusion and medieval caves by their tyrannical rulers and power elites and by the puritan Muslim protagonists bran-dishing swords in hands, while romanticizing bigotry and villainizing other faiths and cultures. Both justify human killing. Under these circumstances, is it possible to build up nonkilling, humanistic, progressive, democratic and enlightened Muslim societies? Can such a scheme of things fit into the nonkilling world of Glenn Paige? Can the re-publics of fear, humiliation and shame (what these Muslims states are in at the mo-ment) be transformed into republics of hope, pride, and peace? Answer to these and other related queries ask for visiting Paige’s nonkilling world.

Paige’s nonkilling world, one may point out here, is not a dream world; it is a world which can be real. It is a realizable world, but one has to have a new way of looking at things in order enter this world, to rediscover the culture of peace which was very much there in the different worlds in different eras, to go back to the campaigners of nonviolence, peace and nonkilling and listen to them and plunge into peace action. Likewise, nonkilling, humane, democratic and enlightened Muslim societies are possi-ble, but for this, the politics of the blame game has to be given up. Concerted and fo-cused efforts have to be made for qualitative political and social change. The peace he-roes of Islam and the Muslim societies must be rediscovered and their relevance for building nonkilling Muslim societies must be examined, assessed and appreciated.

It is in this context that this short essay touches upon certain unique features of Ghaffar Khan’s nonviolent struggle during British colonial rule in India and after parti-tion in Pakistan. It highlights the importance and relevance of his role and message for contemporary Muslim societies in particular.

Born in 1890 in Hashtnagar, now known as Asghatnager or “eight towns” in the vil-lage of Utmanzi, Ghaffar Khan is perhaps the greatest Pathan of all times. Undoubtedly he is the most prominent apostle of nonviolence after Gandhi in modern India and one of the outstanding nonviolent leaders of the twentieth century. However, awareness about his life, nonviolent struggle and sufferings is still rather limited and his remarkable contri-bution to peace is still widely unrecognized. It is only in recent years following the pro-tracted war and violence in Afghanistan after entry of Soviet troops in Kabul in December 1979—with unending upheavals and acts of terrorism, especially in the Pakhtun belt cut-ting across Afghan-Pakistan borders—that the post 9/11 panicky world is turning to him for salvation. Being alarmed because of the upsurge of Muslim anger and militancy around the world, the concerned power centers, leading international research institutes focusing on Islam, Muslim societies and terrorism and on peace and nonviolence in these societies in particular look at Ghaffar Khan as the saviour of the future.

Ghaffar Khan, son of Behram Khan, belonged to a very powerful and resourceful family of Utmanzai. He learnt the early lessons of history and politics from his father and learnt more from the narratives of the heroics of his forefathers. The very fact that his grandfather, Saifullah Khan, always sided with his oppressed brethren whenever the British had any clash with the tribes or tried to subjugate them had a profound impact upon him. What also made him proud and prepared him to endure all kinds of suffer-ings and not to compromise on principles was the shining example of his father’s grandfather, Obaidullah Khan, who was hanged by the Durranis, the rulers, for his enlightenment and patriotism.

Popularly known as Bach Khan, Ghaffar Khan entered the challenging world of nonviolent action at an early age and launched a fearless movement against the British colonizers. He traveled the length and breadth of the Indian sub-continent, addressed small groups and big crowds, took part in rallies and demonstrations, mobilized the masses on numerous occasions, and refused to be either purchased or intimidated by the colonial lords. He was frequently arrested, sent to jail or confined in his own house. After India’s partition in 1947, he was harassed, victimized, humiliated and arrested by successive Pakistani governments. The total number of years he spent in the British In-dian jails and Pakistani jails and in confinement at home is thirty long years, but he re-mained defiant and uncomprising on principles. Little wonder that he ruled over the minds and hearts of the Pathans and other freedom- and democracy-loving people in In-dia, Pakistan, Afghanistan and beyond. Even after his death, he continues to rule. Certain important features of his nonviolent struggle are:

* Ghaffar Khan had a religious family background. He was a practicing Muslim, but he never hated other religions or the people of other faith. He used to read the Bible, Gita and Qur’an and even during the period when the area was in the grip of communal violence, he helped, assisted and guided the people of differ-ent religions and frequently went to the riot-torn areas to help the affected people. * He was never intimidated by the religious zealots. He condemned religious bigotry and always said that Islam is a religion of peace and humanism and the best way to serve Allah was to serve his people. * He was very critical of the bad traditions of the Pathan society and often rep-rimanded the Pathans for glorifying wars, fights and revenge. * He not only emphasized the importance of education for both men and women and for boys and girls, but also actively campaigned for opening schools in the villages and cities. * He was a champion of women’s rights and encouraged women to actively participate in political, social and economic activities. * He was a fearless freedom fighter and struggled all his life against all sorts of slaveries. He mobilized the great Khudai Khidmatgar (Servants of God) force and trained them to wage their struggle nonviolently. * He was also an active campaigner for democracy and people’s rights. He de-manded equal opportunity for all and for equitable power and resources-sharing in the independent, sovereign state of Pakistan. * He was a people’s man. The people had full trust in him. They knew that he would not betray their cause and Bach Khan never betrayed their expectation. * He was a champion of Hindu-Muslim unity. As a matter of fact, he was a promoter of the idea of universal love and harmony and peace.

Khan Abdul Ghaffar Khan was very critical of the power elites in Pakistan and condemned state terrorism, increasing religious bigotry and sectarian violence. He chal-lenged the tyrannical rule of the successive governments and condemned the govern-ment for its involvement in the Afghan crisis. He was opposed to military rule in Paki-stan or elsewhere and always said that the people were supreme and sovereign. He strongly favoured peaceful relations between India and Pakistan, between Pakistan and Afghanistan and between the former Soviet Union and Pakistan. He always strongly supported the movements for peace in Pakistan, in its neighborhood, in the Muslim so-cieties and in the world at large.

Ghaffar Khan is highly relevant to this age of terrorism, rising religious militancy, proliferating insecurities and widespread dehumanization. His entire political life spread over eighty years or so is a remarkable record of peace action, fearless and humanistic approach to the critical issues of his time, tremendous consistency in political thinking and action, and willingness to sacrifice and suffer for the cause of the common good. The killing fields of the Muslim societies can clearly be converted into peace zones and productive zones, and the failed and failing Muslim states and the terrorizing states may become more just, more peaceful, and more humane if they follow the footprints of Khan Abdul Ghaffar Khan and listen to the Gautama Buddha of the twentieth century. He was laid to rest in Jalalabad in Afghjanistan in the year 1988, but the Khan who is also known as the Frontier Gandhi must be very restless in his grave—watching with great sadness the killing of humans in Pakistan, Afghanistan, Iraq, and beyond.


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Ethics/Nonkilling/Leadership/Mahatma Gandhi

 * This Course is based mainly on Professor N. Radhakrishnan's (Indian Council of Gandhian Studies) paper Nonkilling Leadership Lessons from Gandhi prepared for the First Global Nonkilling Leadership Forum, Mu Ryang Sa Buddhist Temple, Honolulu, Hawai‛i, November 1-4, 2007. The Course is part of the Program on Nonkilling Leadership Development at the School of Nonkilling Studies.

Lesson 1. Power of Satyagraha
The series of training programs in non-violence that this writer has been organizing in various parts of India and the 100 Special Satyagraha lectures and discussions which I have been privileged to lead in India and abroad in order to understand the Contempo-rary Relevance of Satyagraha and the need for developing and organizing sustained training in nonviolence, offered me very valuable leadership lessons from Gandhi.

 * While the training programs in nonviolence were living experiences the spe-cial lectures and discussions were intellectual encounters with a cross section of people. The emphasis at both these exercises (the training in nonviolence and special Satyagraha lectures) was to help the participants discover how Gandhi demonstrated from his life the power of Satyagraha.
 * We learnt from Gandhi that Satyagraha is action and before one resorts to Satyagraha, one has to become a “Satyagrahi.” In Gandhian Satyagraha, it is never the numbers that count; it is always the quality and dedication, more so when the forces of violence are uppermost.
 * It is often forgotten that it is never the intention of a Satyagrahi to embarrass the wrong-doer. The appeal is never to his fear, it is always to his heart.
 * The Satyagrahi’s object is to convert, not to coerce the wrong-doer. He should avoid artificiality in all his doings. He acts naturally and from inward conviction.

The qualifications Gandhi prescribed for every Satyagrahi are very important in all circumstances, particularly the following five points:

 * He must have a living faith in God, for he is his only Rock.
 * He must believe in truth and nonviolence as his creed and therefore have faith in the inherent goodness of human nature, which he expects to evoke by his truth and love expressed through his suffering.
 * He must be leading a chaste life and be ready and willing for the sake of his cause to give up his life and his possessions.
 * He must carry out with a willing heart all the rules of discipline as may be laid down from time to time.
 * He should carry out the jail rules unless they are specially devised to hurt his self-respect.

Thus Satyagraha to Gandhi was a “surgery of the soul” and not a political expedi-ency. Training in nonviolence should also lead to this creative awakening.

Lesson 2. Complementary nature of duties and rights of citizens
It is Gandhi’s concern for the poor and his own apprehension that any alienation between the masses and the rulers would generate unhealthy tendencies that would retard social jus-tice that one sees in this well-thought-out advice of Gandhi. It also shows that Gandhi’s humanism was not skin-deep and he was convinced that any system that fails to take care of the basic necessities of the people will be a sin to society in particular and humanity in general. A system that fails to feed the starving millions will symbolize only falsehood. To a hungry man God appears only in the form of bread, he reminded his countrymen.

In the schemes of things Gandhi visualized, all are supposed to be partners and mutually supportive and dependent. The trusteeship idea, an extension of Sarvodaya mooted by Gandhi, has not been properly understood and implemented. It envisages the willingness on the part of those who have extra wealth to take care of the less privi-leged on the basis of the awareness that wealth like the other natural resources does not belong to any particular individual. All have equal right over all that nature possesses. Those who have excess of what others don’t have should feel that they have to play the role of the custodians of society.

For Gandhi, rights and duties are complementary and a citizen who is not conscious of his duties has no right to think of his rights. Similarly, Gandhi believed, “There can be no Ram Raj in the present state of iniquitous inequalities in which only a few roll in riches, while the masses do not get even enough to eat.” Does this Gandhian passion for social justice remain a far cry? No one knows. The ruler, in the modern context the state, like Lord Ram, Gandhi’s ideal King is Custodian of not only the physical domain of the peo-ple but also an inspirer of his people to higher realms of spiritual attainments.

Lesson 3. The relevance of the seven social sins Gandhi identified
It may be useful here to remember in this context the advice Gandhi gave to the new rulers of India, which is now known as Gandhi’s Talisman. Gandhi advised:

The visionary and practical nature of most of the Gandhian formulations for social change are revealed in the manner in which Gandhi reproduced in his journal seven sins which a reader had sent him as a note. They are: Politics without Principles, Wealth without Work, Pleasure without Conscience, Knowledge without Character, Commerce without Moral-ity, Science without Humanity and Worship without Sacrifice.

Even a school child will laugh derisively today if anyone mentions any of these qualities. Such is the alarming level to which our public and moral lives have degener-ated. And the Gandhian vision of Ram Rajya by which he meant a classless and just so-ciety has acquired political and religious overtones also and has been reduced to the level of a political debate mostly of academic interest.

Lesson 4. From National Campaign towards a Violence-Free Society (Himsamukth Samaj)
Gandhian Leadership lessons were best revealed in the massive and ambitious national campaigns launched four years ago under the combined auspices of several Gandhian organizations, Voluntary organizations and Universities in India. The Himsamukth Samaj (Violence-Free Society) initiative sought to encourage discussions:
 * To bring about a thorough social change for the establishment of a nonvio-lent social order as Gandhi dreamt.

 * Expose the evil intentions of the anti-social elements that prosper very often on violence, death and destruction.

 * Co-ordinate the activities of youth who are involved in various social works for the establishment of an ideal social order.

 * To be vigilant against narrow communal/political/ regional interests.

 * To organize awareness-creation campaigns against anti-social elements.

 * Every time, everywhere, there have been appropriate and motivated agencies, individuals and social groups working against violence and promoting good-will among people.

 * On the basis of the information gathered and insights received from various quarters, it is intended to prepare comprehensive work reports to which the attention of the authorities is to be drawn.

 * To ensure the co-operation of various organizations and Government ma-chinery to ensure a tension-free society which will be possible only if social justice is ensured, and discrimination of all sorts and exploitation ended.

 * To make effective propaganda to recognize violence and tensions dangerous to progress and well-being of the society.

 * To ensure a violence-free society, ensure co-operation of young men and women who will be prepared to join any initiative, provided they are properly motivated.

Former President of India Shri R. Venkitaraman is the Chief Patron of this campaign while Dr. N. Radhakrishnan is the National Convener and Chief Campaigner of this on-going campaign. The campaign has led:

 * 1) To the successful enlisting of over 168,000 families committed to nonvio-lence as part of a multi-tier people’s campaign against violence, intolerance, and injustice. The focus of this phase was to recognize the importance of families and encourage them to embrace nonviolence as the guiding principle in their life. This was emphasized on the basis of the disturbing manner in which the family as an institution is disintegrating and dialogue as a sustaining force is becoming scarce.
 * 2) To the special programs of National Conferences, Regional and State level discussions and special 100 Satyagraha Centenary Lectures, held in India and abroad as part of the Satyagraha Centenary Programs
 * 3) To the efforts that were made to involve Universities and higher learning to develop peace education programs and involve student communities in con-flict management initiatives.
 * 4) To work out the details of 100 Community Peace Centres (CPC) as a joint initiative of Indira Gandhi National Open University and the Indian Council of Gandhian Studies and launch them on October 2, 2007 with a view to: linking communities with educational institutions; inculcating values in children and youth; bringing academics and activists together; developing conflict-free zones, and contributing to sustainable development.

Though some of these initiatives brought together a large number of Gandhian Ac-tivists, Educators, Human Rights Activists, Scientists, Technocrats, National Leaders, and Political Activists, the Organizers feel that they have to go a long way in order to make it a truly National Movement which will address the basic problem of violence and encourage people to explore the Gandhian option for development. The enormity of the manifestations and power of violence in our society is such that only a Gandhi, Vinoba Bhave or J.P. Narayan could galvanize and sensitize people in large numbers to effectively counter the forces that are responsible for much of the violence the nation witnesses in its daily life.

Terror and violence are spreading like a cancer threatening the very existence of the nation. The State despite all the measures it has been taking seems to be under heavy pres-sure. The sheer size of the nation and the deep penetration made by the forces of violence and terror send shock waves all around. Innocent citizens are blown up and the heartless perpetrators of violence are rejoicing. While all this is happening, the citizens who are caught up in the cross-fires remain fear-struck and helpless expressing just indignation.

In such a situation, can the citizens remain unconcerned, leaving protection of civil-ians and their properties to law-enforcing authorities of the State? Should not the citi-zens also join the efforts of law-enforcing and protection of lives of innocent citizens? The public also has a big role to play in an emergency. We are in such an emergency that terror and violence have assumed such shape that national, massive and well-orchestrated initiatives need to be undertaken in the wake of the emerging and frighten-ing situation in the country and elsewhere.

Violence—leading to killing of all kinds, destruction of properties, harming nature’s balance and leading to a variety of unhealthy trends—needs to be checked. Gandhian Satyagraha and lessons learnt from it are very valuable antidotes.

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Ethics/Nonkilling/Leadership/Leo Tolstoy

 * This Course is based mainly on Professor Koozma J. Tarasoff's (Center for Doukhobor Studies) paper Tolstoy and the Doukhobors prepared for the First Global Nonkilling Leadership Forum, Mu Ryang Sa Buddhist Temple, Honolulu, Hawai‛i, November 1-4, 2007. The Course is part of the Program on Nonkilling Leadership Development at the School of Nonkilling Studies.

Aloha! Tolstoy’s literature is like a huge ocean of creativity and inspiration.

In the evolution of ideas in getting rid of the institution of militarism and war with the creation of a society based on the new paradigm of love and nonkilling,the lessons of Tolstoy and the Doukhobors merit special attention.

As hardworking pioneers living in a communal setting, the Doukhobors first settled in the Crimean region of southern Russia in 1700s. Later they were exiled to the Caucasus between the Caspian and Black Seas. In 1899 one-third or 7,500 were exiled to Canada where some 40,000 reside today. A similar number reside in scattered areas of Russia.

The Doukhobors’ two acts of defiance against militarism in 1895 have been a profound inspiration for them up to the present time. First, on Easter of that year, the young soldier Matvey Lebedev and ten other Doukhobors threw down their guns while training in the Elizavetpol reserve battalion in the Caucasus region of southern Russia, stating that war and Christianity are incompatible. The result was that the dissidents were sent to a disciplinary battalion and exile along with 60 other Doukhobor young men in active service who followed their example (Tarasoff, 2002: 262-263).

Second, on midnight of June 28-29, 1895 (Old Style; new style is 11-12 July), 7,000 Doukhobors in three districts of the Caucasus set ablaze piles of their rifles, pistols and swords (mostly government issues) in the first mass protest in history against war and militarism. The Tsarist government perceived this as treason and its response was swift with severe floggings, killings and exile. This event that literally shook the world (Tarasoff, 2006: 244) attracted the attention of Lev N. Tolstoy, the most popular Russian writer and philosopher of the day. Doukhobors normally lived in peaceful communities. They worked hard, did not kill and were real Christians in action. Tolstoy saw his moral ideas implanted in the lives of these nonkilling pioneers.

Lesson 1. Learning, inspiring, cooperating and acting with conviction
The Arms Burning event was unique. Geographically isolated, it was of a scale, visual impact and ideology that could not be ignored by the government, the church, the media, as well as the most prominent writer of the day Lev Tolstoy. The Doukhobors were prepared for persecutions and death, even though their leader Peter V. Verigin (who was in exile, was influenced by Tolstoy ideas and was in correspondence with him) hoped to receive support from Tolstoy (Sanborn, 1995).

Lev Nicholaevich Tolstoy, his Son Sergei, his friends and the Quakers came together for this great cause of nonkilling and helped the Doukhobors from becoming extinct. Tolstoy penned an “Appeal for Help,” completed his book Resurrection and helped 7,500 Russian dissidents (the most persecuted, about one-third of the whole) to immigrate to Western Canada in 1899.

As a Great Russian writer and philosopher Lev Tolstoy (1828-1910) was indeed a literary artist who was dedicated to nonviolence/nonkilling. His many writings reflected his philosophy. Gradually he evolved from a rich spoiled child to a moral figure, as shown in the evolution of his literary works. At the end of 1856, Tolstoy retired from five years of military service and soon made a six-month tour of Europe. While in Paris, he was so shocked by the guillotine execution of a prisoner that he later was stimulated to lobby for the end of capital punishment. His major epoch work War and Peace (1864-1869) showed the wider picture of war between Russia and Napoleon, and the absurdity of it all.

Lesson 2. Exposing the truth about war and killing is a way to discover alternatives
Tolstoy was one of the first to seriously question the very nature of war, especially the act of killing. In his writings Prisoners of Caucasus and in War and Peace he looked at the psychological causes of war. Why war? What is it about? Why is it driven by some tyrannical power of the divine right of kings, the Gods, or the Empire? Why is it that states conscript men and resources to maintain power (Samson, 1987)?

In answer, Tolstoy exposed the falsehood, hypocrisy and absurdity of war. Soldiers, he said, glory in the mystique of power to the point that they are persuaded to go against their conscience and moral upbringing of “Thou shalt not kill.” They believe in cannon-fodder because they have been hypnotized from childhood in school books, church services, sermons, speeches, books, newspapers, poems and monuments, writes Tolstoy (1893: 508).

Today we can truly say that war is a blight on our civilization and a slavery of our times. It reverberates through the centuries including the hope in recent times of the United Nations to get rid of the scourge of war. The military and their generals, together with the politicians who dictate that men must kill for the state as a patriotic duty as well as the religious leaders who support the cause are all part of the institutions that keep people in slavery. They perpetuate the act of state-sponsored murder and hinder the path towards a nonkilling society. The way to stop the wholesale slaughter of people, wrote Tolstoy, is to refuse supporting war as we have done with the trading of human slaves.

Lesson 3. The importance of values, education, and work for the health of humanity
The search for truth and the meaning of life gave Lev Tolstoy width and depth in becoming a world literary figure as well as a moral leader. In his Socratic quest, he was not afraid to question personal behaviour and societal injustice.

In Anna Karenina (1873-1876) he unveiled the Russian society with its aristocrats, peasants, the military and the church. Then in his book The Kingdom of God is Within You (1893) he laid down his philosophical/religious principles of life. The Kingdom of God which is within you can only be reached by effort, he said, through responsible action and through the search for truth.

Serfs were the majority of the Russian people until 1861 and had no rights. The rich aristocracy had the power and rights. Here Tolstoy reassessed his past, and at his Yasnaya Polyana home he started to understand the injustice of life of his own peasants. He saw the beauty of the common man and was the first to liberate them. Tolstoy opened a school for peasants on his family estate before helping to found 20 more schools in neighbouring villages. He believed in freedom of information and allowed his students to study whatever they desired. As editor of an educational journal, Tolstoy wrote that upper classes had as much to learn from peasants as peasants had to learn from upper classes. The aristocrat-turned-teacher taught them the Golden Rule and believed that truth alone is capable of relieving our global community from the “incalculable ills produced by war” (Tolstoy, 1951: 591). Today, more than 100 schools in Russia work according to Tolstoy’s ideas. These ideas offer a new content based on nonviolent communication between human beings. The students study new disciplines and read many of Tolstoy’s works. When entering these classrooms, Vitaly Remizov, the head of the Tolstoy Museum in Moscow, says one feels “the living breath of Yasnaya Polyana’s dweller, Lev Tolstoy, his invisible presence in everything which is done for the sake of Good and Love. I discover new sides to the author of War and Peace and Anna Karenina — as a teacher whose name is next to the wise of this world. When you reread his lesser known books (because they were banned in tsarist Russia and then in Soviet times)… you realize that there is indeed freedom and truth in this world which can make your life full of meaning” (Remizov, 1998: 52).

No doubt the acceptance of a nonkilling society is a long term process beginning with childhood upbringing as well as family, community, political and social supports. Children’s stories of nonkilling will encourage them to turn to these examples as models of behaviour. Exposing children to Good Works and cooperative games where people work together to solve problems is a step in the right direction. Once this idea of nonviolence/nonkilling is accepted as the norm, then leaders in society could be persuaded to develop new laws reflecting this spirit. Examples include: abolishing capital punishment, recognizing Conscientious Objectors in society, allowing people of conscience to divert their war taxes for a special fund, establishing Departments of Peace in our legislatures, and prohibiting genocide.

Lesson 4. Letters build networks and wisdom for cultivating world citizenship
Tolstoy received over 50,000 letters from all over the world in some 15 languages of which he knew five fluently, but was helped by friends with others. His example of transcending political boundaries around the world is a source of inspiration for all. As he discovered gems of wisdom in his letters, he recorded these in his Diary and later published them in A Calendar of Wisdom. Although he was Russian born, he felt that he was a citizen of the world.

The extent of Tolstoy’s impact on world literature is enormous. In 1893 a French critic Theodor de Wyzewa wrote:

At home, no less a writer than Chekhov confessed in 1884:

Among leading writers and public figures in other countries his moral influence can be traced in the life and works of Mohandas Gandhi in India, Arvid Jarnefelt and Minna Canth in Finland, Romain Rolland and Paul Margueritte in France, Edouard Rod in Switzerland, William Dean Howells and the jurist Ernest Howard Crosby in the U.S.A., Jaime de Magalhaes Lima in Portugal, Tokutomi Roka and Mushakoji Saneatsu in Japan, Albert Skarvan in Slovakia, and Eugen Schmitt in Hungary (Edgerton, 1990: 2).

We can see Tolstoy’s influence everywhere: in world literature, cinema, theatre, education, and university studies. Today almost a century since his death, hundreds of volumes have been published, translated and dedicated to him around the world. In 2010, a major exhibition in Russia is being planned for Tolstoy’s Centennial.

Lesson 5. The Law of Love is central to understanding the peaceful life
Tolstoy reminded us that love is a powerful motivator of life. It is the opposite of what he termed as the Law of Aggression or the Law of Violence. Love provides meaning to life and is central to our morality. As the highest law that guides human life, love can be fulfilled through effort and personal responsibility.

Tolstoy’s The Kingdom of God is Within You is a classic expression about creating a nonkilling world society. It is as fresh and relevant today as it was when Tolstoy wrote it in 1893. One of those people Tolstoy corresponded with was the son of William Lloyd Garrison, the famous champion of the emancipation of Blacks and who coined the phrase “Our country is the world, our countrymen are all mankind.”

In 1838, Garrison took part in a discussion in a Society for the Establishment of Peace among men — on the means of preventing war. He came to the conclusion that the establishment of universal peace can only be founded on the open acknowledgement of the doctrine of nonviolence, as understood by Quakers with whom he had friendly relations. Garrison drew up and laid before the Society a Declaration of Sentiments which the Conference adopted in Boston in 1838. The Declaration stated that war is not only wrong itself, but all preparations for war are wrong (Maude, 1951: 7). The Declaration was so radical that it frightened people and distanced them from it. For that reason, the document is almost unknown today. Yet Tolstoy remembered this Declaration and included it in his book. For Tolstoy, as for the Doukhobors, love is central to human relations and the creation of a society based on human goodness, equality, and justice for all. The doctrine of love is revealed in each of us directly and immediately without intermediaries in spirit and in truth, says Tolstoy. Based on personal action, the law of love is not strictly a precept, but the expression of the very essence of Christ’s teaching from his Sermon on the Mount. Its ideal is nonviolence and love of our enemies. According to Tolstoy, “the recognition of the sanctity of the life of every person is the first and only basis of all morality” (Tolstoy, 1893: 373). The life of man is sacred!

Lesson 6. We can indeed introduce Tolstoy as a nonkilling literary leader
Tolstoy was one of the Big Masters of the Century who raised the Big Issues of society. His works were translated into many languages. Many Russians have endeared him with the title of “Dedushka Tolstoy” [Grandfather Tolstoy]. This is a title that no other Russian writer has received. Several dozen Tolstoy colonies were established in Russia and abroad. A colony in Bulgaria survived for nearly half a century with its own newspapers, journals, publishing houses, book stores, an agricultural colony and a vegetarian organization (Edgerton, 1990: 20).

Tolstoy is relevant today because humanity still faces the same problems of war, torture, disparity between the rich and the poor, inequality, illiteracy, and environmental degradation. The presence of these ills is a scar on us as Homo Sapiens. Tolstoy’s views persist because they were well founded and based on practical experience.

Gandhi regarded Tolstoy as his mentor and used peace and Christian value ideas in his search for justice in India during the rule of Great Britain. Also Martin Luther King Jr. used Tolstoy’s ideas when he peacefully wrestled for the rights of African Americans.

If Tolstoy the wise were alive today, he would be very proud of the Leadership Forum in Honolulu. As a creative teacher whose stature is next to such thinkers as Socrates, Confucius and Pascal, he would recognize that his seeds sown earlier are now taking root across the seas.

All of us here are talking about creating a nonkilling society in the future. Tolstoy had this vision in the late 1800s when he saw the Doukhobor actions and called them as “people of the 25th century.” Maybe he was right. However, we cannot wait for the looming catastrophe. In the 1800s, 14 million people were killed in wars. In the 1900s, 150 million died of institutionalized murder and many more were crippled.

We know the way, as did Tolstoy when he put his theories into action. He put himself in the situation of strife in the face of government and church both of which succumbed to the outmoded addiction of war and violence. He survived and that is why he is remembered today as an important beacon of light on the road to a nonkilling world. He proved that where there is a will, there is a way. Also he reminded us that one wedge (a good creative idea or an invention) drives out another one.

Like a small stone thrown in the water creates ripples, the circle of these ripples widens with the contribution of others. Tolstoy gathered a circle of friends for support. Through his team work, the Doukhobors survived and today carry the seeds of nonkilling by working together with other peace groups, meeting with Gorbachev in the late 1980s, helping children of Chernobyl, lobbying politicians and writing letters to the editor, and using the World Wide Web to foster an idea whose time has come.

The ideas of Tolstoy, Gandhi, King, Doukhobors, Quakers, Mennonites and members of the wider peace community are important because they have shown another way of creating a just and peaceful society without resorting to the outmoded habit of war and violence. Their experience and lessons can make a difference. The sooner each of us understands this, the better we will all become, the more good we will bring to Mother Earth.


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Ethics/Nonkilling/Leadership/Guillermo Gaviria

 * This Course is based mainly on Professor Glenn D. Paige's introductory text on Guillermo Gaviria for the University of Peace (06/23/2003) and Luis Javier Botero's (Government of Antioquia Advisor on Nonviolence) paper Lessons from the Nonviolent Political Leadership of Governor Guillermo Gaviria prepared for the First Global Nonkilling Leadership Forum, Mu Ryang Sa Buddhist Temple, Honolulu, Hawai‛i, November 1-4, 2007. The Course is part of the Program on Nonkilling Leadership Development at the School of Nonkilling Studies.

Introduction
The killing of Antioquia state Governor Guillermo Gaviria Correa on May 5, 2003, among ten hostages massacred by FARC guerrillas in reaction to a military rescue attempt, deprived Colombia and the world of a nonviolent political leader whose legacy is no less significant than those of Gandhi and Martin Luther King, Jr.

He was born in Medellín in 1962, eldest son of a family prominent in politics, publishing and business. A mining management specialist by training at the Colorado School of Mines, after a decade of innovative public service including as Antioquian Secretary of Mines and General Director of the Colombian Roads Institute he campaigned for "A New Antioquia" in 2000 and was overwhelmingly elected Governor by 600,000 of six million people in Colombia's most populous state.

Gaviria's brief but dynamic governorship was profoundly rooted in the principles and practices of nonviolence derived from his Christian faith and serious study of the legacies of Gandhi and King. He explained, "Nonviolence was born with Jesus Christ; it was followed in the past century by Gandhi and Martin Luther King, and in this century it will be the light to guide the people of Antioquia."

He understood Colombia's violence to be the result of "imbalanced" political and socioeconomic conditions and saw participatory nonviolence as a way to bring about needed structural change. "Nonviolence is more than simply no aggression and is more than putting an end to terrorist attacks, kidnappings, threats, and blackmail. Nonviolence aims to break silence and rise up out of passiveness to build a balanced society of justice and social well-being." He wanted all Antioquians to be educated in nonviolence and trained in skills of putting it into practice.

Unlike Gandhi and King, Gaviria as Governor was able to combine the powers of government with those of popular political leadership. He engaged more than 5,000 leaders in a process to clarify Antioquia's priority problems and to suggest solutions for them. This produced a Strategic Plan of Action and a Congruent Peace Plan. Personally leading marches and caravans, together with First Lady Dr. Yolanda Pinto de Gaviria, he awakened citizen participation for implementing action.

The most dramatic of these was the thousand person March of Reconciliation and Solidarity to Caicedo, a mountain coffee growing town 85 miles from the capital Medellín, undertaken over five days from April 17 to 21, 2002. The March was intended to express solidarity with the FARC-threatened people of Caicedo who had declared themselves a nonviolent community and to seek reconciliation with the guerrillas. The Governor had ordered the police and army not to protect the March and not to rescue him or retaliate if he were kidnapped or killed. He had disagreed with Colombian President Andrés Pastrana's February 23 decision to terminate peace talks with the FARC.

On April 21, just short of Caicedo, the March was stopped by the FARC. The Governor embraced his wife, both knowing he might be kidnapped or killed, and went forward with three companions to talk with the guerrillas. Six hours later two returned with the news that the Governor and his Peace Commissioner, former defense minister Gilberto Echeverri Mejia, had been kidnapped. During his year in captivity, the Governor expressed in messages to his wife even greater commitment to nonviolence and said that when free he intended to resume the March to Caicedo.

Gaviria's tragic death on May 5, together with his Peace Commissioner and eight captive soldiers, resulted from the clash of two lethal ideologies. Righteous state violence and righteous revolutionary violence. If either side had understood his nonviolent message all ten would be alive.

Guillermo Gaviria's unique legacy is that a democratically elected political leader can courageously work for nonviolent social justice from the "top down." It is no less important than the courageous legacies of Gandhi and King seeking freedom and justice from the "bottom up." The convergence of these legacies offers the best hope for the survival and well-being of humanity. Transcending death, Gaviria's legacy continues to challenge Colombia and the world in the slogan of the March to Caicedo. " Sí…Hay un camino: la Noviolencia." Yes. . . There is a way: Nonviolence.

What to do?
Let Guillermo Gaviria himself, in his own words, answer this question. To do that, let us go through his most important written legacy: the Letter to the Antioquian People, written just before the beginning of the March to Caicedo; Letter to the FARC-EP, April 20, 2002 (during the march); Letter to his Father, January 2, 2003 (while in captivity); and his diary, written during the captivity and then published as Diario de un gobernador secuestrado: Gui-llermo Gaviria Correa (Revista Número Ediciones, 2005, 339 pages) [English translation to be published by Cascadia Publishing House as Diary of a Kidnapped Colombian Governor.]

Note by Luis Botero
Governor Gaviria was kidnapped by the FARC on April 21, 2002 at the end of the 1,000-persons March to Caicedo seeking dialogue with FARC leaders. He was killed by FARC captors with nine others during an abortive military rescue attempt on May 5, 2003. As Advisor on Nonviolence (Asesor en Noviolencia) to the Governor, my judgment on lessons learned from the March and its tragic aftermath can be summed up briefly as follows.

 * 1) We did not have enough training.
 * 2) We did not make a detailed plan in advance.
 * 3) We did not have a “B plan” in case our leaders were kidnapped.
 * 4) We abandoned nonviolence as the strategy to follow to obtain their release.

The Role of Nonviolence Advisor to the Governor of Antioquia
The goal is to create a nonviolent culture in Antioquia. Through gubernatorial leader-ship we work to: Promote and diffuse the philosophy of nonviolence all over the state. This has been done through two-day workshops, lectures, radio programs, TV programs, forums, magazines, newspapers, peace-days and peace-weeks in universities, schools and towns. According to the General Manager of Teleantioquia, the most important state-owned channel in the country, nonviolence is accepted and recognized as one of the two most important programs in the state in the last 10 years. She thinks that a new way to solve problems has been introduced to the Antioquian people.

Support training of nonviolent leaders
Training of nonviolence leaders is supported. Over 10,000 leaders have attended a two-day workshop; 100 leaders have been trained as trainer-of-trainers (TOT) by LaFayette and Associates; 35 leaders from different towns all over the state have been trained as “leaders for nonviolence and peaceful living”; a group of inmates (20 to 30 people) has been trained in eight different jails all over the state. These inmates have been leaders and teachers of the “Crime Does Not Pay” program which has reached more than 5,000 teenagers and 500 teachers throughout the state. School principals report reduc-tion of fights in the schools and better behavior of students in classrooms. Only two killings in the last five years have been reported in all of those jails. The program has been expanded nationwide by the National Institute of Prisons and Jails.

Both programs, “Crime Does Not Pay” and “Training for Nonviolence and Peaceful Living” have been included in the “Bank of Good Practices to Overcome Conflict” created by the United Nations Development Plan (UNDP) to share good practices with everyone concerned. Many inmates trained in prison are now free and have begun an association called the “Dreams of Freedom Corporation.” They commit themselves not to break the law again. They study, and provide social support and education through contracts with public entities to teach youth that crime does not pay. They also act as an employment agency. The organization has 238 ex-inmates. Only one has broken the law and has been sent back to jail. This is a very low recidivism rate for any group of law breakers anywhere.

Domestic violence is a high priority since it has been proven to kill twice as many people as the internal war. Research shows that domestic violence is the basic reason to join armed groups in 80% of the cases. The “Working Table for the Prevention and Holistic Attention to Domestic Violence” was created in 2005. Several private and pub-lic entities work together permanently on three main issues confronting the Table:

 * 1) Construction of an effective system to detect, respond to and follow up on all reported events of domestic violence. The main problem so far is that there is not a unified way to classify domestic violence. Not even UNICEF has one. Because of that, institutions cannot share information.
 * 2) Strengthening and articulation of all institutions that are working on domestic violence.
 * 3) Promoting and teaching positive, nurturing and nonviolent relations in families.

Teaching advisors to future nonkilling leaders
Since “Example is not the best way to teach but the only one,” any advisor must focus on being a truly nonviolent person. Then the leader has to be taught to behave in a nonviolent way whenever he/she speaks or acts. “Make in yourself the change you want to see in the world.” This only can be accomplished if the leader is truly commit-ted, like former Governor Guillermo Gaviria.

Teaching nonkilling leaders how to use advisors
The way to do this is based on the foregoing. The leader, if truly committed, should understand that he/she has to be as nonviolent as possible. Leaders should have deep nonviolence training and keep permanent contact with their nonviolent advisors, asking them to preview all public speeches, requesting feedback and opinion on most issues. Coherence is essential.


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Ethics/Nonkilling/Leadership

 * This Course is based mainly on Professor James MacGregor Burns's (Williams College) paper Transforming Leadership prepared for the First Global Nonkilling Leadership Forum, Mu Ryang Sa Buddhist Temple, Honolulu, Hawai‛i, November 1-4, 2007. The Course is part of the Program on Nonkilling Leadership Development at the School of Nonkilling Studies.

I salute the eminent men and women taking part in this creative meeting and wish only that I could attend. I look forward to reports of the discussions and to hearing Glenn Paige’s re-flections. Glenn has asked me to comment in advance of the meetings on the role of leader-ship both in thinking about titanic problems such as nonkilling and others such as poverty and inequality. I should explain that I began academic life as a political scientist, and am still one, but I soon branched out into studies of psychology, history, and especially philosophy. From there I went on to do in the mid-20th century some of the early work on leadership, which I defined broadly as to encapsulate studies in all the above disciplines and others.

Early on in my research and thinking about leadership I began to make a distinction between transformational (or transforming, which I prefer) leadership and transac-tional. By the latter term, transactional, I mean the kind of leadership that is exercised through bargaining, negotiating, give-and-take. This leadership is exercised in all socie-ties, I believe, to different degrees and in different ways, and is crucially important in settling differences, but often disintegrates into selfish and even criminal behavior.

I became much more interested in transforming leadership because of its role in the great decisions that societies and nations must make—and may form part of your dis-cussions of nonkilling and its highest hopes. Transforming leadership rises above trans-actional in order to study and promote change in nations’ and peoples’ handling of cru-cial issues of war and peace, social and individual justice, health, environment and to me the most crucial problem, encapsulating all the foregoing—poverty, poverty in all nations but especially in deprived or neglected areas around the world. I associate trans-forming leadership with leaders as different as Gandhi in India and Roosevelt in Amer-ica, although your distinguished participants will know of many other examples. Trans-forming leaders have the capacity to rise above the day-to-day give-and-take and meet the broadest challenges facing their societies. To do this requires both vision and the capacity to change institutions and constitutions and laws.

To discuss transforming leadership, however, makes it imperative to do two things. First, to analyze perhaps the most neglected aspect of leadership-followership. How often do we read about the great leaders who succeeded or failed, without any mention of the fol-lowers who supported or opposed them? Obviously you cannot have leaders without fol-lowers, leadership without followership. Ultimately the test of leadership, indeed, is its abil-ity to mobilize followers and convert them into new leaders who ultimately replace the old.

The second crucial aspect of transforming leadership consists of the principles and ideals—the values—by which it is measured. Here again the distinction between trans-formational and transactional leadership is important. The latter kind of leadership—negotiators, brokers and the like—must operate by what I call ethical standards—honesty, responsibility, reciprocity. Much of our day-to-day political and financial bro-kerage depends on people living up to their promises, and the like.

Even more important, in my view, are the values undergirding transformational lead-ership—values related to freedom, equality, security and the like. These are sometimes called “Western” values but I think of them as global—your able participants would have a better knowledge of this than I. But what I do know is that there was a so-called West-ern Enlightenment, which was a huge and complex and often messy movement, but which fundamentally tested Western societies and government by certain ideals. I do not need to pontificate about this—these ideas and ideals were superbly enunciated and em-bodied in America’s greatest document—the Declaration of Independence, specifically in the resounding words —life, liberty and the pursuit of happiness. Life meaning security of persons and nations, liberty meaning all that we associate with the broad term freedom (as in Franklin Roosevelt’s Four Freedoms), and the pursuit of happiness a kind of vague but evocative Jeffersonian concept. But the crucial aspect of the Declaration is not these high-sounding words alone but the fact that they presented a rational conflict over time in American (and I would add in British, Continental and other worldly societies). Over time Americans and others have argued about security—national or personal, restrictive or life affirming? About liberty—protection against government or realizing broader freedom through government, as in FDR’s Second Bill of Rights? Happiness—open to endless de-bate, but in my view the greatest underpinning of happiness is social and economic equality.

I hope that these feeble words might make a bit of a contribution to what I expect to be creative and constructive discussions in your beautiful land.

title: Ethics/Nonkilling/Leadership


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User:HenkvD

My name is Henk, a Dutch wikimedian (w:nl:Gebruiker:HenkvD).

de:Benutzer:HenkvD fr:Utilisateur:HenkvD

title: User:HenkvD


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The Highschool Help Forum - Science Stream/Physics Help Forum

Link to any subpages this page might have

- - COMMENT ON DELETION OF THIS PAGE I advanced the proposed deletion date of this page by one year due to small doubts about its deletion. By WV policy on "proposed deletions" (prod), this can be "speedy" deleted if you are certain that it should be deleted. Guy vandegrift (discuss • contribs) 10:14, 16 December 2023 (UTC) - -

Left and right boxes

 * Welcome!
 * The Welcome text, has to be informative and you have to convince people this is what THEY need.

Note

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 * Text that will tell the readers what exactly can be done here.


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User talk:Bookwormrwt

 Hello Bookwormrwt, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --AFriedman 21:23, 30 January 2009 (UTC)

 Hi , I am Percy. Nice to meet you. I love the beach, swimming, fishing, and I am currently doing some research at Wikiversity on oceanography. I am also learning to play piano. What do you like? Can I be your mascot?

title: User talk:Bookwormrwt


text: Swedish Language/Medical Terminology

title: Swedish Language/Medical Terminology


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Ethics/Nonkilling/Spiritual/Islam

 * This Course is based mainly on Professor Chaiwat Satha-Anand's (Thammasat University) paper Ants, Birds, Infants, and Humans: Notes on Islam and Nonkilling Politics prepared for the First Global Nonkilling Leadership Forum, Mu Ryang Sa Buddhist Temple, Honolulu, Hawai‛i, November 1-4, 2007. The Course is part of the Program on Nonkilling Spiritual Traditions at the School of Nonkilling Studies.

Violence in Southern Thailand has hitherto claimed more than 3,000 lives of Buddhists and Muslims, ordinary people and government officials since early 2004. General Cha-valit Yongchaiyuth, a former Deputy Prime Minister of Thailand, who was in charge of security affairs during the previous Thaksin government that governed Thailand in the early part of this decade, remarked on this violence that: “Our Muslim brothers (sisters) always greet one another with ‘peace be with you’, but at the same time killings have occurred among themselves which is evidence of deviant (Islamic) teachings.”  In 2003, the PEW Research Center in Washington, DC reported its attitude survey of Muslim respondents in Turkey, Pakistan, Morocco, and Jordan about suicide bombings. It was found that 74 and 86 per cent of respondents in Morocco and Jordan supported the use of suicide bombings by Palestinians against Israelis. But does this mean that most Muslims would support killings? What do Muslims think about killings?

Though these are difficult questions in the absence of a Muslim worldwide survey, if one chooses to believe in survey results despite all kinds of shortcomings, perhaps an answer could be found indirectly by raising the question of the Muslims’ attitude to-wards the place of war in dealing with conflict. In conducting such a survey with more than 6,300 Muslim respondents in 7 countries: Egypt, Iran, Turkey, Pakistan, Indonesia, Malaysia and Kazakhstan, Riaz Hassan found that while figures for those in support of war have been high in the three Middle Eastern countries and Pakistan (from 58-66 %), they are much lower in three other countries: Malaysia 37%, Indonesia 33% and Ka-zakhstan 11%. Could it mean that in these Muslim countries, at least some 60% dis-agree with the use of killing as a way to deal with conflicts in the world? Based on Has-san’s empirical study of more than a decade using massive cross-cultural, cross-national surveys and interviews, I would argue that Muslim attitudes towards killing as a vehicle for solving international conflicts vary significantly in Muslim countries, and that only a small fraction of Muslims actively support killing and killing organizations.

Why such is indeed the case is of profound importance for any attempt to under-stand the Muslims and their proclivity towards nonkilling politics. If religious belief is to be analyzed as conviction politics and not merely as expediency, then there is a need to understand why most Muslims do not support killings by looking at conventional Is-lamic teachings on the value of lives, animals and human, and the ways in which killing is delimited or prohibited through those teachings. For the purpose of this brief paper, I would call attention to how conventional Islamic texts, the Qur’an and the Hadith (Prophetic Traditions) deal with lives of ants, birds, infants, and all human beings.

Ants

Birds

Infants

Humans

Beyond the obvious theme of linking the humans with the animals in the world where all creatures are created by God, I would argue that there are four other issues raised by these teachings which are conducive to the value of nonkilling, and therefore make it pos-sible to understand why killing in general is viewed negatively by most Muslims.

First, the story of the ants while giving permission to kill, especially when the hu-man was attacked first, importantly prohibited the notion of overkill. This is of utmost importance in an age when advanced weapon technology has obliterated the idea of proportionality in the use of violence. Overkill can be made to feel comfortable due to the technologized ability to shield the perpetrators, or societies that support them, from its devastating effects on the victims.

Second, the story of the birds explicitly prohibits the Muslims from killing the young ones. If the notion of young ones is seen from a temporal perspective, then it is clear that they should not be killed because the future(s) should not be killed, but needs to be protected.

Third, the injunction against female infanticide in the first Qur’anic verse cited here, is a clear indication of an Islamic critique of cultural violence which had legiti-mized such practice in Arab cultures for so long. Killing infants in the name of culture is not acceptable, not only in terms of protecting the future(s) stated above, but also because the infants are God’s gifts to the humanity and the world. At their weakest ex-istence, they are the strongest link between parents and children, and more importantly mirroring God’s miracle of creation seen through a child’s birth. In this profound sense, such a culture cannot be tolerated by Muslims since it was the legacy of the age of ignorance and therefore an anathema to the belief in God’s Mercy, perhaps the most important Islamic belief.

Fourth, though the famous Qur’anic verse prohibiting killing because taking even one’s life is equal to killing the whole humanity does have an exceptional clause and therefore is not categorical, it is extremely important to understand that by equating one life to the whole of humanity, this teaching denies killing its most common ground of justification in terms of numbers, understood as collateral damage or “peace dividend” as promoted by General “El Gaucho” Cisneros, a former Peruvian minister and a coup maker who once said that “if it were necessary to kill twenty civilians in order to eliminate two or three ter-rorists, then that action was justified.” This Qur’anic verse has made it impossible to justify the means of killing with ends through numbers, whether in terms of destroying the few for the good of the many or taking the lives of the many for the sake of a greater good.

But then in what ways have these four issues discussed above contributed to nonk-illing politics?

In her study of the politics of jihad by the “Islamists” Roxanne Euben underlines the importance of those who see death and killing as a legitimate and necessary part of the remaking of politics. They believe that violence is a legitimate expression of political action and an end in itself when guided and justified by a divinely authorized plan. She points out that this is in sharp contrast to Hannah Arendt’s idea expounded in her On Violence, that the phenomenon of killing must transpire outside the public realm be-cause such violence is antithetical to the preconditions for political actions. She then suggests that while many political theorists may be skeptical of Arendt’s understanding of politics, quite a few share her conclusion regarding killing, namely “politics is said to end where violence begins because killing for politics entails, in essence, killing politics itself.”

Following the Islamic teachings on the ants, birds, infants, and human life discussed above, the emerging politics underscores the significance of protecting the future(s), dele-gitimizing cultural violence, strengthening the human-Divine relationship, prohibiting kill-ings by refusing to accept the morbid justification of turning human life into a number game, while the existence of killing, if any, is delimited with the notion of proportionality. In this sense, nonkilling politics, legitimized by Islamic teachings, could be seen as the al-ternative remaking of politics for Muslims in the fast changing public sphere.

Notes

1. Matichon (June 3, 2004), p. 1, 15 (In Thai).

2. Cited in Riaz Hassan, Inside Muslim Minds (Carlton, Melbourne: Melbourne University Press, 2008), pp. 122-3.

3. Ibid., p. 124 and Table 3.2 on p. 125.

4. Ibid., pp. 126-7. In Hassan’s words: “only a very small fraction of Muslims actively support jihadi organizations and their activities” (p. 126).

5. See a discussion along this line in Chaiwat Satha-Anand, “The Jahiliyya Factor: Fighting Muslims’ Cultural Resistance to Nonviolence,” in Ralph Summy and Senthil Ram (eds.) Nonviolence: An Al-ternative for Defeating Global Terror(ism) (New York: Nova Science Publishers, 2008).

6. Cited in “Interview with Salomon Lerner,” International Review of the Red Cross, Vol. 88 No.862 (June 2006), pp. 229-230. Roxanne L. Euben, “Killing (for) Politics: Jihad, Martyrdom and Political Action,” Political Theory, Vol.30 No. 1 (February 2002), pp. 4-35.

7. Ibid., p. 26. (my italics).

title: Ethics/Nonkilling/Spiritual/Islam


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Artificial Consciousness/Neural Correlates/Neural Maps

 Neural Maps

One of the problems that scientists have had to solve was the lack of map-ability of the Nervous System, especially in the brain where connections seem opportunistic, and are so dense as to allow literally tens of thousands of connections to a single neuron. Although the selectionists came up with mechanisms that allowed neurons to self-organize into neural groups, there seemed to be a gap between neural groups, and the order that had allowed the neurosurgeons to do mapping of gross cerebral function. The current state of the art in mapping at this gross level is the Brodmann Area Map (It should be noted that while this map has been well published it has been condemned by some researchers due to the fact that the data on which it was based was never published.)

The solution to the gap between Neural Groups and Gross Level maps, came in two stages,first Teuro Kohonen invented a type of neural network called a Self-Organizing Map (SOM) and then Dr. Edelman showed how reentry could create an environment in which such maps could form naturally.

(Note to self, may have this backwards should check sources.)

Although Kohonen's maps are 2 dimensional and are usually used for visualization of higher dimensional data, The main characteristic of these maps is their ability to reduce the dimensionality of complex data. The choice of the dimensionality of the output, is really dependent on the nature of the data being evaluated, and the human penchant for thinking in 4 dimensions (3 spatial dimensions plus time) may simply be because there has been classically no need for more dimensionality in our Neural Maps, and so we have not developed it.

In his book The Remembered Present: A biological Theory of Consciousness Dr. Edelman suggests that these naturally forming SOM's are allowed to some extent to overlap and thus compete for attention. Although there is as yet no adequate explanation why these maps tend to congregate in certain areas of the brain, it is thought that there might be a relationship between the placement of the reentry connections in the brain and where the maps form.

In his book Self Organizing Maps Dr. Kohonen indicates how using such a map, makes possible the learning of the representation of movement in the brain, and how it can be used to drive a robot arm. Experiments using such techniques have proven useful, and some researchers have shown how they can use such technology to teach a monkey to think a robotic arm into position in order to give themselves a treat. Brodmann Areas Map

Brodmann Areas: These areas are probably specialized Maps within the Cerebral cortex

Brodman Areas (* Not all shown on maps)

 * Brodmann Area 1, 2, 3 Primary Somatosensory Cortex
 * Brodmann Area 4 Primary Motor Cortex
 * Brodmann Area 5 Somatosensory Association Center
 * Brodmann Area 6 Premotor Cortex, Supplementary Motor Area
 * Brodmann Area 7 Somatosensory Association Center
 * Brodmann Area 8 Frontal Eye Fields
 * Brodmann Area 9 Dorsolateral Prefrontal Cortex
 * Brodmann Area 10 Anterior Prefrontal Cortex
 * Brodmann Area 11/12 Orbitofrontal area
 * Brodmann Area 13/14* Insular Cortex
 * Brodmann Area 15* Anterior Temporal Lobe
 * Brodmann Area 16*
 * Brodmann Area 17 Primary Visual Cortex(V1)
 * Brodmann Area 18 Secondary Visual Cortex(V2)
 * Brodmann Area 19 Associative Visual Cortex(V3)
 * Brodmann Area 20 Inferior Temporal Gyrus
 * Brodmann Area 21 Middle Temporal Gyrus
 * Brodmann Area 22 Superior Temporal Gyrus
 * Brodmann Area 23 Ventral Posterior Cingulate Gyrus
 * Brodmann Area 24 Ventral Anterior Cingulate Gyrus
 * Brodmann Area 25 Subgenual Cortex
 * Brodmann Area 26 Ectospenial Cortex
 * Brodmann Area 27 Piriform Cortex
 * Brodmann Area 28 Posterior Entorhinal Cortex
 * Brodmann Area 29 Retrosplenial Cingular Cortex
 * Brodmann Area 30 Cingular Cortex
 * Brodmann Area 31 Dorsal Posterior Cingulate Cortex
 * Brodmann Area 32 Dorsal Anterior Cingulate Cortex
 * Brodmann Area 33 Anterior Cingulage Cortex
 * Brodmann Area 34 Anterior Entorhinal Cortex
 * Brodmann Area 35 Preihinal Cortex
 * Brodmann Area 36 ParaHippocampal Cortex
 * Brodmann Area 37 Fusiform Gyrus
 * Brodmann Area 38 Temporopolar Area
 * Brodmann Area 39 Angular Gyrus
 * Brodmann Area 40 Supramarginal gyrus
 * Brodmann Area 41/42 Primary & Associative Auditory Centers
 * Brodmann Area 43 SubCentral Area
 * Brodmann Area 44 ParaOperculus
 * Brodmann Area 45 Pars Triangularum
 * Brodmann Area 46 Dorsolateral Prefrontal Cortex
 * Brodmann Area 47 Inferior Profrontal Gyrus
 * Brodmann Area 48 Retrosubcular Area
 * Brodmann Area 49 -
 * Brodmann Area 50 -
 * Brodmann Area 51 -
 * Brodmann Area 52 Para-Insular area

While the mapping is organized by cell mapping studies using different types of stains, the different types of neurons likely form Neural Groups that have at least similar functions. However we can't determine from the cytoarchitecture exactly which neurons are involved in which maps. As Dr. Edelman states, Neural Groups are interchangeable, within these larger areas. Part of the confusion as to what each of these areas does, comes from the fact that only certain of these areas are involved in primary sensory stimulation, other areas have to be recruited before they begin to process the stimuli. Part of the problem with this is that we might not stimulate the recruitment requirements in lab conditions, and so we may not know what some of the areas actually do.

One Caveat that must be added to this mapping concept, is that Dr. Edelman uses it outside the Cerebral Cortex, other organs may not operate by the same rules as the cerebral cortex, so I tend to question the broad application of things like re-entry, in other organs.


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User:Egm6322.s09.mafia/HW2

 See my comments below. Egm6322.s09 12:26, 7 February 2009 (UTC)

=Second Order PDEs, from Particular to General=

One case
--EGM6322.S09.TIAN 17:46, 24 April 2009 (UTC)

$$\kappa$$ $$= \underline{\kappa} (x,y,u,u_x,u_y)$$ $$\Rightarrow$$

Definition of quasilinear: For a PDE of order n (i.e. highest derivative terms are of order n),coeffients of nth order derivative are functions $$= (x,y,u,u_x,u_y,\frac{\partial^m u}{\partial {x^p y^q}})$$

Here, we assume there are two independent variables, mth order derivative, and $$p+q=m,m<n$$

Another Case
--EGM6322.S09.TIAN 17:45, 24 April 2009 (UTC)

PDEs linear with respect to 2nd derivative, but still non-linear in general:

$$div($$ $$\kappa$$   $$\cdot grad u)+$$ $$f(x,y,u,u_x,u_y)=0$$

Here, $$\kappa =$$ $$\kappa $$ $$(x,y) $$ $$f(x,y,u,u_x,u_y)=0$$ is nonlinear with respect to argues in general, e.g.

$$div($$ $$\kappa$$   $$\cdot grad u)+$$ $$ax^2+by+\sqrt{u}+(u_x)^4+2(u_y)^2=0$$

Homework:Show The Linearity Of The Equation

--EGM6322.S09.TIAN 17:46, 24 April 2009 (UTC)

Show it linear to 2nd derivative, but non-linear in general.

To make it clear,

$$D_1(\cdot):=$$ $$div[$$  $$\kappa$$ $$(x,y)$$   $$\cdot grad (\cdot)]$$

We can do this:

$$D_2(\cdot):=$$ $$D_1(\cdot)+$$ $$(\cdot)^{1/2}+$$ $$[(\cdot)_x]^4+$$ $$[2(\cdot)_y]^2$$

$$D_3(\cdot):=$$ $$D_2(\cdot)+$$ $$ax^2+by$$

The definition of linearity: $$\mathfrak{L} \left( \alpha u + \beta v \right) = \alpha \mathfrak{L} \left( u \right) + \beta \mathfrak{L} \left( v  \right)$$, where $$\forall$$ $$u,v: \Omega \rightarrow \mathbb{R} $$ and $$\forall$$ $$\alpha, \beta \in \mathbb{R}$$

Using this definition of linearity, the above expression for $$D(u)$$ is given as: $$D_1(\cdot) \left( \alpha u + \beta v\right) = div \left[ \mathbf{\kappa} \cdot grad \left( \alpha u + \beta v \right) \right]$$

$$grad(\cdot)$$ is linear $$grad(u) = \frac {\partial u}{\partial x_i} e_i$$ and $$\frac {\partial u}{\partial x_i} (\cdot)$$ is linear $$\therefore$$ $$grad \left( \alpha u + \beta v \right)$$ = $$\alpha \frac {\partial u}{\partial x_i}$$+ $$\beta \frac {\partial v}{\partial x_i}$$= $$  \alpha   grad(u) + \beta  grad(v)$$

Matrix (tensor) multiplication is a linear operator $$\bar{A} \cdot \left( \alpha \bar{x} + \beta \bar{y} \right) = \alpha \bar{A} \bar{x} + \beta \bar{A} \bar{y}$$

$$\therefore$$ $$\mathbf{\kappa} \cdot grad(u) = \alpha \mathbf{\kappa} \cdot grad(u) + \beta \mathbf{\kappa} \cdot grad(v)$$

$$div(\cdot)$$ is linear because it is another differential operator let $$\bar{a}, \bar{b}: \Omega$$ $$\mathbb{R}^3$$ and $$\alpha, \beta \in \mathbb{R}$$

$$\therefore$$ $$div \left( \alpha \bar{a} + \beta \bar{b} \right) = \frac {\partial }{\partial x_i} \left( \alpha a_i + \beta b_i \right) = \alpha \frac {\partial a_i}{\partial x_i} + \beta \frac {\partial b_i}{\partial x_i}$$

Taking all this into consideration, the definition of linearity has been proven.

$$D_1 \left( \alpha u + \beta v \right) = \alpha div \left[ \mathbf{k} \cdot grad(u) \right] + \beta div \left[ \mathbf{k} \cdot grad(v) \right]$$ ,which means, the 2nd derivative part is linear.

Then,

$$D_2(\alpha u + \beta v) =$$ $$D_1(\alpha u + \beta v)+$$ $$(\alpha u + \beta v)^{1/2}+$$ $$[(\alpha u + \beta v)_x]^4+$$ $$2[(\alpha u + \beta v)_y]^2$$

$$\alpha D_2( u ) =$$ $$\alpha D_1( u )+$$ $$\alpha( u )^{1/2}+$$ $$[\alpha( u )_x]^4+$$ $$2[\alpha( u )_y]^2$$

$$\beta D_2( v ) =$$ $$\beta D_1( v )+$$ $$\beta( v )^{1/2}+$$ $$[\beta( v )_x]^4+$$ $$[2\beta( v )_y]^2$$

Obviously,

$$D_2(\alpha u + \beta v) \neq$$ $$\alpha D_2( u ) +$$ $$\beta D_2( v ) $$

$$\therefore$$, $$D_2(\cdot)=$$ $$D_1(\cdot)+$$ $$(\cdot)^{1/2}+$$ $$[(\cdot)_x]^4+$$ $$[2(\cdot)_y]^2$$ is non-linear.

Similarly, we can prove that:

$$D_3(\cdot)=$$ $$D_2(\cdot)+$$ $$ax^2+by$$ is non-linear.

$$\therefore$$, the equation is linear to 2nd order derivative but non-linear in general.

The Expression of Second Order PDEs
--Egm6322.s09.lapetina 01:54, 17 April 2009 (UTC) The expression of second order PDEs shown here is original to Professor Loc Vu-Quoc. It cannot be found in any mainstream texts. In this section we will show how to express Second Order Linear PDEs in a matrix format.

Any PDE can be expressed as:

$$ \left \lfloor \partial_x \; \partial_y \right \rfloor \begin{bmatrix} a & b\\ b & c \end{bmatrix}

\begin{Bmatrix} \partial_x u \\ \partial_y u \end{Bmatrix} +

\left \lfloor d \; e \right \rfloor

\begin{Bmatrix} \partial_x u \\ \partial_y u \end{Bmatrix}

+ fu + g = 0

$$

where the coefficients $$ \left \{ a, b,...,g \right \} $$ are functions of $$ \left \{ x,y \right \} $$ in general (this includes constants).

The first term is $$\alpha$$, a scaler produced from multiplying a row matrix, square matrix, and column matrix.

$$\alpha= \left \lfloor \partial_x \; \partial_y \right \rfloor \begin{bmatrix} a & b\\ b & c \end{bmatrix}

\begin{Bmatrix} \partial_x u \\ \partial_y u \end{Bmatrix}

=

\left \lfloor \partial_x \; \partial_y \right \rfloor

\begin{Bmatrix} au_x+bu_y \\ bu_x+cu_y \end{Bmatrix}

=(au_x)_x+(bu_y)_x+(bu_x)_y+(cu_y)_y

$$.

Using the product rule, this becomes:

$$ \alpha=a {u}_{xx}+a_x u_x +b {u}_{yx}+ b_x u_y+ b {u}_{xy}+ b_y u_x + c {u}_{yy}+ c_y u_y $$

Note: This was required for a homework assignment in Meeting 8.

The nature of $$a$$, $$b$$ and $$c$$ greatly dictates the means by which the second order PDEs can be expressed.

Constant Coefficients
If $$a$$, $$b$$, and $$c$$ are constants, their derivatives with respect to $$x$$ and $$y$$ become zero, and $$\alpha$$ reduces to:

$$\alpha=a {u}_{xx}+2 b {u}_{xy}+c {u}_{yy}$$.

This means that the matrix equation can be expressed as:

$$ a {u}_{xx}+2 b {u}_{xy}+c {u}_{yy}+d u_x+e u_y+f u+g=0 $$.

Two Independent Variables
If $$a$$, $$b$$ or $$c$$ is not a constant, the function becomes

$$\left [ a {u}_{xx}+a_x u_x \right ] + \left [ 2b {u}_{xy} +b_y u_x+ b_x u_y \right ] + \left [c {u}_{yy} + c_y u_y \right ] +d u_x + e u_y + fu+ g=0$$

The first order derivatives can be grouped, and the resulting equation is:

$$ a {u}_{xx}+2 b {u}_{xy}+c {u}_{yy}+\bar d\ u_x+\bar e\ u_y+f u+g=0 $$

where

$$\bar d\ := d+a_x+b_y$$

$$\bar e\ := e+b_x+c_y$$

Note: This was required for homework in meeting 8, and shown in Meeting 9.

Thus, even with $$a$$, $$b$$ or $$c$$ as non-constants, the matrix form of this equation remains:

$$ \left \lfloor \partial_x \; \partial_y \right \rfloor \begin{bmatrix} a & b\\ b & c \end{bmatrix}

\begin{Bmatrix} \partial_x u \\ \partial_y u \end{Bmatrix} +

\left \lfloor d \; e \right \rfloor

\begin{Bmatrix} \partial_x u \\ \partial_y u \end{Bmatrix}

+ fu + g = 0

$$

But the resulting linear equation uses $$ \bar d\ $$ and $$ \bar e\ $$. Thus we gain a more general form of the matrix form of the equation, with minimal adjustment of the linear equation.

Note: Showing this was required for homework in Meeting 9.

Homework Problem Involving Linearity

--Egm6322.s09.lapetina 01:56, 17 April 2009 (UTC)

In this problem it will be proven that the following equation is second order and linear with respect to all orders:

$$ (au_x)_x+(bu_y)_x+(bu_x)_y+(cu_y)_y + d u_x +e u_y +fu+g=0$$,

also expressed as:

$$ \left \lfloor \partial_x \; \partial_y \right \rfloor \begin{bmatrix} a & b\\ b & c \end{bmatrix}

\begin{Bmatrix} \partial_x u \\ \partial_y u \end{Bmatrix} +

\left \lfloor d \; e \right \rfloor

\begin{Bmatrix} \partial_x u \\ \partial_y u \end{Bmatrix}

+ fu + g = 0

$$

where coefficients $$ \left \{ a, b, ... g \right \} $$ are continuous, differentiable functions of independent variables $$x$$ and $$y$$ only, and $$u$$ is a continuous, differentiable function of $$x$$ and $$y$$.

Expanded, it is:

$$ a {u}_{xx}+2 b {u}_{xy}+c {u}_{yy}+\bar d\ u_x+\bar e\ u_y+f u+g=0 $$

where

$$\bar d\ := d+a_x+b_y$$

$$\bar e\ := e+b_x+c_y$$.

From inspection, it is clear that the highest derivative is second, by definition making this a second order PDE.

The second order components of the equation are:

$$a {u}_{xx}$$, $$2 b {u}_{xy}$$ and $$c {u}_{yy}$$, with coefficients $$a$$, $$b$$, and $$c$$, defined as functions of $$x$$ and $$y$$ only. As a result, this equation is linear with respect to the second order.

The first order components of the equation are:

$$(d+a_x+b_y) u_x $$ and $$(e+b_x+c_y) u_y$$.

These coefficients can also be represented as:

$$d + div [a,b]$$ and

$$e+ div[b, c]$$.

The divergence operator is linear, and since $$d$$ and $$e$$ are by definition continuous, differentiable functions of $$x$$ and $$y$$ only, the coefficients

$$\bar d\ := d+div [a,b]$$

and

$$\bar e\ := e+ div[b, c]$$

are linear, and the PDE is linear with respect to the first order.

Finally, $$f$$ and $$g$$ are both functions of $$x$$ and $$y$$ only, making the PDE linear with respect to the zero order.

 You need to define $$\displaystyle {\rm div} [a,b] := a_x + b_y$$, but it is probably best NOT to use this notation, unless you define the vector with $$\displaystyle a$$ and $$\displaystyle b$$ being its components; it is getting more complicated than necessary. Egm6322.s09 12:26, 7 February 2009 (UTC)

Proof of the Mixed Derivative Theorum

--Egm6322.s09.lapetina 01:56, 17 April 2009 (UTC)

This proof is closely paraphrased from Thomas' Calculus.

Assume $$f(x,y)$$ and $$f_x$$, $$f_y$$, $${f}_{xy}$$, and $${f}_{yx}$$ are defined throughout an open region containing point $$\left ( a, b \right )$$ and are all continuous at $$\left ( a, b \right )$$.

Proving the equality of $${f}_{xy} \left ( a, b \right )$$ and $${f}_{yx} \left ( a, b \right )$$ requires four applications of the mean value theorum.

Point $$\left ( a, b \right )$$ lies within a rectangle $$R$$, and let $$ h, k \in \mathbb{R} $$ be numbers such that point $$\left ( a+h, b+k \right )$$ also lies within $$R$$

A value $$\delta$$ exists such that

$$\delta= F(a+h)-F(a)$$, where

$$F(x)=f(x, b+k)-f(x, b)$$

The first application of the mean value theorem is to $$F$$, and as a result:

$$\delta= h F'(c_1)$$, where $$c_1$$ is between $$a$$ and $$a+h$$.

We can take the derivative of $$F$$ with respect to $$x$$, and we are left with

$$F'(x)={f}_{x}(x, b+k)-{f}_{x}(x, b)$$

and

$$\delta= h \left [{f}_{x}(c_1, b+k)-{f}_{x}(c_1, b) \right ]$$

If we apply the mean value theorem to the function $$g(y)=f_x (c_1, y)$$, we have

$$g(b+k)-g(b)=kg'(d_1)$$,

or

$$f_x (c_1, b+k) -f_x (c_1, b)= k{f}_{xy} (c_1, d_1)$$

for some $$d_1$$ between $$b$$ and $$b+k$$, equivalent to one factor of $$\delta$$.

This leaves us with $$\delta = hk {f}_{xy}(c_1,d_1)$$ for some point in a second rectangle, $$R'$$, which has vertices $$(a,b), (a+h, b), (a, b+k), (a+h,b+k)$$, all of which lie within rectangle $$R$$.

Looking back at the original definition of $$\delta, F$$ and $$f$$, we see that

$$\delta = f(a+h, b+k)-f(a+h, b)-f(a, b+k)+f(a,b)$$, which can be expressed as:

$$\delta = \left [f(a+h, b+k)-f(a, b+k) \right ]- \left [f(a+h, b)+f(a,b) \right ]$$

which can be reduced to:

$$\delta= \phi (b+k)- \phi (b)$$

where $$\phi (y) =f(a+h, y)-f(a,y)$$.

Applying the Mean Value Theorem a third time to:

$$\delta = \left [f(a+h, b+k)-f(a, b+k) \right ]- \left [f(a+h, b)+f(a,b) \right ]$$

now results in:

$$\delta = k \phi'(d_2)$$ for some $$d_2$$ between $$b$$ and $$b+k$$.

Differentiating $$\phi$$ by $$y$$ results in:

$$phi'(y)=f_y(a+h, y) -f_y (a,y)$$, which allows $$\delta$$ to be expressed as:

$$\delta= k \left [{f}_{y}(a+h, d_2)-{f}_{y}(a, d_2) \right ]$$.

If we apply the Mean Value Theorem a fourth time, we arrive at:

$$\delta =kh {f}_{yx} (c_2, d_2)$$ for some $$c_2$$ between $$a$$ and $$a+h$$. This means that:

$$\delta={f}_{xy}(c_1, d_1)={f}_{yx}(c_2, d_2)$$ where $$(c_1, d_1)$$ and $$(c_2, d_2)$$ both lie within $$R'$$. If we allow $$h$$ and $$k$$ to approach zero, then the rectangle $$R'$$ converges to a point, and $$c_1=c_2$$ and $$d_1=d_2$$, and $${f}_{xy}(a,b)={f}_{yx}(a,b)$$

Proof that the Divergence Operator is Linear

--Egm6322.s09.lapetina 01:56, 17 April 2009 (UTC)

Prove that the divergence operator is a linear operator.

This relies upon the fact that the derivative, when applied to a continuous function, is itself linear. To prove this we will examine the definition of the derivative:

$$\lim h\rightarrow 0 \left [ \frac{f(x+h)-f(x)} {h}\ \right ]$$

The derivative is both homogeneous and additive, as shown by the Constant Multiple Rule .: $$ \frac{d}{dx} \ (cu)= \lim h\rightarrow 0 \left [ \frac{cu(x+h)-cu(x)} {h}\ \right ]$$

$$\frac{d}{dx} (cu)= c  \lim h\rightarrow 0 \left [ \frac{u(x+h)-u(x)} {h}\ \right ]$$

$$\frac {d}{dx} (cu)=c \frac{du}{dx}$$

and the Derivative Sum Rule:

$$\frac{d}{dx} \ \left [u(x) +v(x) \right ]= \lim h\rightarrow 0 \left [ \frac{\left [u(x+h)+v(x+h) \right ]-\left [u(x)+v(x) \right ]} {h}\ \right ]$$

$$\frac{d}{dx} \ \left [u(x) +v(x) \right ]= \lim h\rightarrow 0 \left [\frac{u(x+h)-u(x)}{h} \ +\frac {v(x+h)-v(x)} {h}\ \right ]$$

$$\frac{d}{dx} \ \left [u(x) +v(x) \right ]= \lim h\rightarrow 0 \frac{u(x+h)-u(x)}{h} \ + \lim h\rightarrow 0\frac {v(x+h)-v(x)} {h} = \frac {du}{dx} +\frac{dv} {dx} $$

Thus the derivative in a single variable is both homogeneous and additive, and therefore linear.

This can be extended to partial derivatives and the divergence operator in the following fashion:

Assume two real vector fields $$\overrightarrow{u}$$ and $$\overrightarrow{v}$$, and $$\alpha, \beta \in \mathbb{R}^n $$.

If the divergence operator satisfies the following equation:

$$\frac{\partial \left ( \alpha u + \beta v \right ) }{\partial x_i}= \alpha \frac{\partial u }{\partial x_i} + \beta \frac {\partial v}{\partial x_i}$$

then it is linear.

Also, if the divergence operator is both homogeneous and additive, it is linear.

By definition,

$$ \frac {\partial \left ( \right)}{\partial x_k} = \sum_{k=1}^n \frac {\partial \left ( \right)}{\partial x_k}$$

For $$\alpha$$, and $$\overrightarrow{u}$$, it is clear that:

$$ \frac {\partial \left ( \alpha \overrightarrow{u} \right)}{\partial x_k} = \frac {\partial \left ( \alpha \overrightarrow{u} \right)}{\partial x_1} + \frac {\partial \left ( \alpha \overrightarrow{u} \right)}{\partial x_2}+ \dots + \frac {\partial \left ( \alpha \overrightarrow{u} \right)}{\partial x_n}$$

Using the product rule, this becomes:

$$ \frac {\partial \left ( \alpha \overrightarrow{u} \right)}{\partial x_k} = \alpha \frac {\partial \left (  \overrightarrow{u} \right)}{\partial x_1} + \alpha \frac {\partial \left ( \overrightarrow{u} \right)}{\partial x_2}+ \dots + \alpha \frac {\partial \left ( \overrightarrow{u} \right)}{\partial x_n} = \alpha \sum_{k=1}^n \frac {\partial \left ( \overrightarrow{u} \right)}{\partial x_k}$$

Therefore, the divergence operator is homogeneous.

To prove that the divergence operator is additive, we will use both $$\overrightarrow{u}$$ and $$\overrightarrow{v}$$. Their vector sum can be expressed as: $$\overrightarrow{u}+ \overrightarrow{v} =\overrightarrow{w}$$

$$ \frac {\partial \left ( \overrightarrow{u} +\overrightarrow{v} \right)}{\partial x_k} = \frac {\partial \left ( \overrightarrow{u} + \overrightarrow{v} \right)}{\partial x_1} + \frac {\partial \left ( \overrightarrow{u} + \overrightarrow{v} \right)}{\partial x_2}+ \dots + \frac {\partial \left ( \overrightarrow{u} + \overrightarrow{v} \right)}{\partial x_n}$$

Because $$\overrightarrow{u}$$ and $$\overrightarrow{v}$$ are both real vector fields, the partial differential can be distributed, and the above statement is equivalent to:

$$ \frac {\partial \left ( \overrightarrow{u} +\overrightarrow{v} \right)}{\partial x_k} = \frac {\partial \left ( \overrightarrow{u}  \right)}{\partial x_1} +  \frac {\partial \left (  \overrightarrow{v} \right)}{\partial x_1} + \frac {\partial \left ( \overrightarrow{u}  \right)}{\partial x_2}+ \frac {\partial \left ( \overrightarrow{v} \right)}{\partial x_2} + \dots + \frac {\partial \left ( \overrightarrow{u} \right)}{\partial x_n} + \frac {\partial \left ( \overrightarrow{v} \right)}{\partial x_n}$$

Which can be expressed as:

$$ \frac {\partial \left ( \overrightarrow{u} +\overrightarrow{v} \right)}{\partial x_k} = \sum_{k=1}^n \frac {\partial \left ( \overrightarrow{u} \right)}{\partial x_k} + \sum_{k=1}^n \frac {\partial \left ( \overrightarrow{v} \right)}{\partial x_k}$$

indicating that the divergence operator is additive.

Because it is both additive and homogeneous, it is a linear operator.

Clarification of topics from R1 (Repeat R1)
--Egm6322.s09.xyz 18:20, 24 April 2009 (UTC)

It has been observed by Dr. Vu-Quoc that some of the basic concepts concerning the topic of linearity and linear operators covered in R1 were not fully understood by students. These concepts were presented a second time by Dr. Vu-Quoc in hopes that he will be more effective in communicating these ideas to students. Linearity (and the linear operator) is important in the study of PDEs. It forms the basis of study for Linear Transformation of Coordinates and future topics. A detailed review of these concepts is given here:

$$\blacktriangleright$$ Students were asked to expand the following expression, $$ D(u):= div \left [ \mathbf{k} \cdot grad(u) \right ] $$    (Coordinate form)
 * $$= \frac{\partial }{\partial x_i} \left [ \mathbf{k_{ij}} \cdot \frac{\partial u}{\partial x_j} \right ]$$ where $$i,j \in {1,2}$$    (Component form)

Most students expanded this equation using Leibniz Rule (aka "Product rule"). To do this would have been incomplete. Dr. Vu-Quoc wanted an expansion of  the two indices (i,j) in the folowing manner:
 * $$= \sum_{i}\sum_{j} \left [ \mathbf{k_{ij}} \cdot \frac{\partial u}{\partial x_j} \right ]$$
 * $$= \frac{\partial }{\partial x_1} \left ( k_{11} \frac{\partial u}{\partial x_1} \right ) + \frac{\partial }{\partial x_1} \left ( k_{12} \frac{\partial u}{\partial x_2} \right ) + \frac{\partial }{\partial x_2} \left ( k_{21} \frac{\partial u}{\partial x_1} \right ) + \frac{\partial }{\partial x_2} \left ( k_{22} \frac{\partial u}{\partial x_2} \right )$$

note: the above expression is the correct solution to the homework given in R1.

Leibniz Rule --Egm6322.s09.xyz 18:20, 24 April 2009 (UTC)

Leibniz Rule, also known as "the Product Rule", is given as, : $$ \left ( f \cdot g \right )^' = f^' \cdot g + f \cdot g^' $$ The product rule is a special form of the chain rule : $$\frac{d}{dx} \left ( ab \right ) = \frac{\partial }{\partial a} \left ( ab \right ) \frac{da}{dx} + \frac{\partial }{\partial b} \left ( ab \right ) \frac{db}{dx} = b \frac{da}{dx} + a \frac{db}{dx}$$ A more generalized form of Leibniz Rule for higher order derivatives is shown with the following expression: $$\left( fg \right)^{(k)} = \sum_{r=0}^k \dbinom{k}{r}f^{(k-r)}g^{(r)}$$

where "$$f,g$$ are real (or complex) functions defined on an open interval of $$\mathbb{R}$$. Also, $$f$$ and $$g$$ are $$k$$ times differentiable" [source:]

$$\blacktriangleright$$ Students were asked to prove that the operator, $$D \left( u \right)$$, is linear. Recall the definition of linearity: $$\mathfrak{L} \left( \alpha u + \beta v \right) = \alpha \mathfrak{L} \left( u \right) + \beta \mathfrak{L} \left( v  \right)$$, where $$\forall$$ $$u,v: \Omega \rightarrow \mathbb{R} $$ and $$\forall$$ $$\alpha, \beta \in \mathbb{R}$$

Using this definition of linearity, the above expression for $$D(u)$$ is given as: $$D \left( \alpha u + \beta v\right) = div \left[ \mathbf{k} \cdot grad \left( \alpha u + \beta v \right) \right]$$

 * note: $$grad(\cdot)$$ is linear
 * $$grad(u) = \frac {\partial u}{\partial x_i} e_i$$ and $$\frac {\partial u}{\partial x_i} (\cdot)$$ is linear
 * $$\therefore$$ $$grad \left( \alpha u + \beta v \right) = \alpha grad(u) + \beta grad(v)$$

 * note: Matrix (tensor) multiplication is a linear operator
 * Recall that $$\bar{A} \cdot \left( \alpha \bar{x} + \beta \bar{y} \right) = \alpha \bar{A} \bar{x} + \beta \bar{A} \bar{y}$$
 * $$\therefore$$ $$\mathbf{k} \cdot grad(u) + \beta \mathbf{k} \cdot grad(v)$$

 * note: $$div(\cdot)$$ is linear because it is another differential operator
 * let $$\bar{a}, \bar{b}: \Omega$$ $$\mathbb{R}^3$$ and $$\alpha, \beta \in \mathbb{R}$$
 * $$\therefore$$ $$div \left( \alpha \bar{a} + \beta \bar{b} \right) = \frac {\partial }{\partial x_i} \left( \alpha a_i + \beta b_i \right) = \alpha \frac {\partial a_i}{\partial x_i} + \beta \frac {\partial b_i}{\partial x_i}$$

Taking all this into consideration, the definition of linearity has been proven.

$$D \left( \alpha u + \beta v \right) = \alpha div \left[ \mathbf{k} \cdot grad(u) \right] + \beta div \left[ \mathbf{k} \cdot grad(v) \right]$$  (verified)$$\surd$$

Definition of a linear operator
--Egm6322.s09.xyz 18:21, 24 April 2009 (UTC)

A linear operator,$$\mathfrak{L} ( \cdot)$$, satifies the following two criteria:

1. Additive
 * $$\mathfrak{L} \left( u + v \right) = \mathfrak{L}(u) + \mathfrak{L}(v)$$ where $$\forall$$$$u,v: \Omega \rightarrow \mathbb{R}$$

 * note:$$\mathfrak{L}\left(1 \cdot u + 1 \cdot v \right) = 1 \cdot \mathfrak{L}(u) + 1 \cdot \mathfrak{L}(v)$$

2. Homogeneous
 * $$\mathfrak{L}(\alpha u) = \alpha \mathfrak{L}(u)$$

 * note: $$ \mathfrak{L}(0) = 0 $$. This means that the image of zero under the $$ \mathfrak{L}(\cdot) $$ is zero if $$\mathfrak{L}(\cdot) $$is linear

Example of linear map for $$\mathbb{R}^n$$ (n-dim case)
--Egm6322.s09.xyz 18:20, 24 April 2009 (UTC)

Given: $$\bar{A}: \mathbb{R}^n \rightarrow \mathbb{R}^n$$ where $$\mathbb{R}^n \ni x $$, $$\mathbb{R}^n \ni y $$, and $$\bar{x} \mapsto \bar{y} = \bar{A} \bar{x}$$. A pictorial representation of this linear map can be found in the image below.

An element of domain and range is a vector and a column matrix, $$\bar{x}$$. The image of $$\bar{x}$$ in range is $$\bar{y}$$. The mapping of $$\bar{x}$$ to $$\bar{y}$$ is $$\bar{A}$$.

note: $$\mathfrak{D}$$omain = $$\mathbb{R}^n$$ and $$\mathfrak{R}$$ange = $$\mathbb{R}^n$$ (this is a more general form). The $$\bar{A}$$ matrix is of the order n x m, i.e. - $$\bar{A} \in \mathbb{R}^{n x m}$$. This can be verified in the following manner: $$\bar{y} = \bar{A} \bar{x}$$ where $$\bar{y}$$ is (n x 1), $$\bar{A}$$ is (n x m), $$\bar{x}$$ is (m x 1) (verified)$$\surd$$

Example of not-linear mapping
--Egm6322.s09.xyz 18:27, 24 April 2009 (UTC)

 NOTE: Avoid the word "non-linear", which is more general; use "not-linear" instead to indicate affine mappings, which are not linear, i.e., not homogeneous. Egm6322.s09 21:48, 8 February 2009 (UTC)

Changed the title to "not-linear" --Egm6322.s09.xyz 18:26, 24 April 2009 (UTC)

Now consider the following mapping: $$\bar{y} = \bar{A}\bar{x} + \bar{b}$$ note: this mapping is not linear because a zero vector for x-matrix does not result in a zero for the y-matrix and therefore is not valid. This is an affine mapping.

$$M: \bar{R}^m \rightarrow \bar{R}^n$$ where $$\bar{R}^m \ni x $$, and $$\bar{x} \mapsto \bar{y} = \bar{A} \bar{x} + \bar{b}$$

Clearly, $$M \left ( \bar{0} \right) = \bar{b}$$. Therefore, $$M \left ( \cdot \right)$$ is not a linear map, it is an affine map.

Notes on Mathematical Syntax
--Egm6322.s09.xyz 18:22, 24 April 2009 (UTC)

The following table is a reference summary of descriptions for special mathematical symbols that are used frequently in this course:

Example: Rotation followed by translation
--Egm6322.s09.xyz 18:22, 24 April 2009 (UTC)

$$

\begin{Bmatrix} y_1\\ y_2 \end{Bmatrix}

=

\begin{bmatrix} R_{11} & R_{12} \\ R_{21} & R_{22} \end{bmatrix}

\begin{Bmatrix} x_1\\ x_2 \end{Bmatrix}

+

\begin{Bmatrix} b_1\\ b_2 \end{Bmatrix}

$$

Jean le Rond d'Alembert (1717 - 1783) --Egm6322.s09.xyz 18:22, 24 April 2009 (UTC)

d'Alembert was a French scholar in the areas of mathematics, fluid mechanics, and physics. He collaborated on one of the first encyclopedias, the Encyclopédie. He died due to a bladder illness, and was buried in an unmarked grave.

Source:

=Transformation of Coordinates=

--Egm6322.s09.lapetina 01:57, 17 April 2009 (UTC)

Functions of coordinate transformation in two dimensions can be expressed as:

$$

\begin{Bmatrix} x\\ y \end{Bmatrix}

= \mathbf{V}

\begin{Bmatrix} \bar {x} \\ \bar {y} \end{Bmatrix}

$$

where $$\mathbf{V}$$ is a two by two matrix.

One example of a linear transformation of coordinates is the rotation of the coordinate axes by an angle $$\theta$$.

The matrix for this is :

$$ \begin{bmatrix} cos \theta & -sin \theta \\ sin \theta & cos \theta \end{bmatrix}

$$

Concepts
--EGM6322.S09.TIAN 17:44, 24 April 2009 (UTC)

In $$div(\cdot)$$ an example of   for $$\mathbb{R}^m$$  $$\to$$ $$\mathbb{R}^n$$  $$(M:\mathbb{R}^m \to \mathbb{R}^n)$$.

$$\mathbb{R}^m, \mathbb{R}^n$$ are space vectors (tensors, matrix). Divide maps vector field (vector-valued function) into a scalar function. In other words, domain and range of $$div(\cdot)$$ are function of spaces.

$$x= \phi (\bar{x},\bar{y})$$

$$y= \psi (\bar{x},\bar{y})$$

Linear coordinate transformation Eq(5) P.9-1

$$u(x,y)=$$ $$u($$ $$x= \phi (\bar{x},\bar{y})$$, $$y= \psi (\bar{x},\bar{y}))$$

$$=u(\bar{x},\bar{y})$$,  which is an abuse of notation by using "u".

$$=\bar{u}(\bar{x},\bar{y})$$,  which is a more rigorous notation.

One Example
--EGM6322.S09.TIAN 17:44, 24 April 2009 (UTC)

Let $$u(x)=ax+b$$

Condition, $$x=\phi (\bar x)$$ $$=sin \bar x$$

$$u(x)=$$ $$u(\phi (\bar x))$$ $$=asin \bar {x} + b$$

=$$u(\bar x)$$ $$\gets$$  abuse of notation

=$$\bar {u} (\bar x)$$  $$\gets$$  more rigorous

Another One
--EGM6322.S09.TIAN 17:43, 24 April 2009 (UTC)

$$u_x(x,y)=$$ $$\frac{\partial u}{\partial x}(x,y)$$ $$=u_x(\phi(\bar{x},\bar{y}),\psi(\bar{x},\bar{y}))$$ $$= \frac{\partial }{\partial x}$$ $$\bar{u}(\bar{x},\bar{y})$$ $$=\frac{\partial \bar u}{\partial \bar x}$$ $$\frac{\partial \bar x}{\partial x}$$ $$+$$ $$\frac{\partial \bar u}{\partial \bar y}$$ $$\frac{\partial \bar y}{\partial y}$$ $$= \bar{u}_\bar {x}$$ $$\frac{\partial \bar x}{\partial x}$$ + $$\bar{u}_\bar {y}$$ $$\frac{\partial \bar y}{\partial x}$$

Define:

$$\bar x$$ = $$\bar {x} (x,y)$$ = $$\bar {\phi} (x,y)$$

$$\bar y$$ = $$\bar {y} (x,y)$$ = $$\bar {\psi} (x,y)$$

$$u_y(x,y)=$$ $$\frac{\partial }{\partial y}\bar u(\bar {x},\bar {y})$$ = $$= \bar{u}_\bar {x}$$ $$\frac{\partial \bar x}{\partial y}$$ + $$\bar{u}_\bar {y}$$ $$\frac{\partial \bar y}{\partial y}$$

Matrix Form
--EGM6322.S09.TIAN 17:42, 24 April 2009 (UTC)

$$\partial_x u=$$ $$\big\lfloor$$ $$\frac{\partial \bar x}{\partial x}$$ $$\frac{\partial \bar y}{\partial x}$$ $$\big\rceil$$ $$\begin{Bmatrix} \partial_ {\bar x} \\ \partial_ {\bar y} \end{Bmatrix} $$ $$(\bar u)$$

Homework:Likewise For $$\partial_y $$ --EGM6322.S09.TIAN 17:41, 24 April 2009 (UTC)

Likewise for $$\partial_y $$

$$\partial_y u=$$ $$\big\lfloor$$ $$\frac{\partial \bar x}{\partial y}$$ $$\frac{\partial \bar y}{\partial y}$$ $$\big\rceil$$ $$\begin{Bmatrix} \partial_ {\bar x} \\ \partial_ {\bar y} \end{Bmatrix} $$ $$(\bar u)$$

Then,

$$\begin{Bmatrix} \partial_ x \\ \partial_ y \end{Bmatrix} $$ = $$\begin{bmatrix} \frac{\partial \bar x}{\partial x} & \frac{\partial \bar y}{\partial x} \\ \frac{\partial \bar x}{\partial y} & \frac{\partial \bar y}{\partial y} \end{bmatrix} $$ $$\begin{Bmatrix} \partial_ {\bar x} \\ \partial_ {\bar y} \end{Bmatrix} $$

$$\begin{bmatrix} \frac{\partial \bar x}{\partial x} & \frac{\partial \bar y}{\partial x} \\ \frac{\partial \bar x}{\partial y} & \frac{\partial \bar y}{\partial y} \end{bmatrix} $$ is known as the Jacobian matrix(sometimes it is defined as transposition of Jacobian matrix).

Easier and more general,

$$(x_1,\cdots,x_n)$$ $$\to$$ $$(\bar{x_1},\cdots,\bar{x_n})$$

Initial notation:$$\bar{x_i}$$ = $$\bar{x_i}$$ $$(x_1,\cdots,x_n)$$

$$J_{n \times n}$$ = $$\begin{bmatrix} \frac{\partial \bar x_i}{\partial x_j} \end{bmatrix}_{n \times n} $$

Here, "$$i$$"is the row index while "$$j$$"is the column index.

Carl Gustav Jacob Jacobi(1804-1851) --EGM6322.S09.TIAN 17:42, 24 April 2009 (UTC)

Jacobian Matrix was named after Carl Gustav Jacob Jacobi, a 19th century mathematician from Prussia. Born in 1804, Jacobi studied at Berlin University and later went on to teach at Königsberg University. He is known for Jacobi's elliptic functions,Jacobian,Jacobi symbol, and Jacobi identity. He died in Berlin in 1851. source:

= References =

= Signatures =

--EGM6322.S09.TIAN 14:49, 6 February 2009 (UTC)Miao Tian --Egm6322.s09.xyz 14:52, 6 February 2009 (UTC) --Egm6322.s09.lapetina 14:53, 6 February 2009 (UTC)

title: User:Egm6322.s09.mafia/HW2


text:
Artificial Consciousness/Neural Correlates/Brain Organ Models

 Brain Organ Models

Dr. Edelman's book Nerual Darwinism: The Theory of Neural Group Selection while it arguably might only properly apply to the cerebral cortex, created an opportunity for larger nerual models to be built, based on the Neural Groups found in different organs of the brain. From these larger neural networks, Dr. Edelman and his contemporarise were able to develop the concept of Brain Based Devices which modeled the operation of organs of the brain, in a simplistic fashion limited mostly by the size of the simulation's host computer cluster.

The following Organs have been modeled in Brain Based Devices. How useful that modeling might be is based partially on the state of knowledge about the operation of the organ at the time of the model being built. As such we need to expect that as our knowledge increases the sophistication of the BBD models might also increase skewing our assumptions about how the organs work.

 * Cerebral Cortex Model
 * Cerebellum Model
 * Thalamus Model
 * Hippocampus Model
 * Basal Ganglia Model

(Note to self, Check with NSI about current list of BBDs)