Wednesday, September 12, 2012
The United States committed its greatest democide during the Second World War. This was in the indiscriminate area bombing of German and Japanese cities, including Hiroshima and Nagasaki. Not all American strategic bombing was of this type. Early in the war the American Air Force concentrated on precision bombing of both Germany and Japan. But as the war progressed British pressure and American bomber losses in such bombing persuaded the Americans to join the British in broadly targeting the center of urban areas. Regarding Japan, the apparent lack of success of precision bombing led to the assumption of command over the bombing by General Curtis Lemay, who was disposed to massive area bombing of Japanese cities.
Over 3 million innocent people lost their lives during the vietnam war... about 60,000 of those were american soldiers.
Civilian Victims of USA "Foreign Policy" for 17 years:
1991 - Iraq - 200,000
1992 - Somalia - 7,000
1974-1992 - Angola - 650,000 +
1986-1994 - Colombia - 20,000 +
1995-1998 - Turkey - 27,000 +
1997 - Rwanda - 6,000
1965-1997 - Indonesia - 1,000,000
1990-1997 - Iraq - 1,200,000 +
1998 - Afghanistan - 2,000 +
1986-1998 - Guatemala - 200,000
1999 - Yugoslavia - thousands
1999 - Iraq - hundreds
1991-1999 - Kuwait, Iraq - 1,620
2000-2002 - Palestinian Territories - hundreds
2001 - Afghanistan - 23,000 +
1995-2001 - Peru - unknown
2002 - Angola - unknown
2002 - Iraq - unknown
2003 - Afghanistan - 300 +
2003 - Algeria - hundreds
2003 - Iraq - 17,000 +
1976-2003 - Indonesia - 12,000 +
2003-2004 - Palestinian Territories - 1,400 +
2003-2007 - Iraq - 1,000,000 +
2006 - Palestine, Lebanon - 1,300 + (to August)
2006 - Haiti - 8,000 + (to September)
2007 - Somalia - 2,000 +
2008 - South Ossetia - 2,000 +
We shall examine the contributions of Indian mathematics in this article, but before looking at this contribution in more detail we should say clearly that the “huge debt” is the beautiful number system invented by the Indians on which much of mathematical development has rested. Laplace put this with great clarity:-
The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius.
We shall look briefly at the Indian development of the place-value decimal system of numbers later in this article and in somewhat more detail in the separate article Indian numerals. First, however, we go back to the first evidence of mathematics developing in India.
Histories of Indian mathematics used to begin by describing the geometry contained in the Sulbasutras but research into the history of Indian mathematics has shown that the essentials of this geometry were older being contained in the altar constructions described in the Vedic mythology text the Shatapatha Brahmana and the Taittiriya Samhita. Also it has been shown that the study of mathematical astronomy in India goes back to at least the third millennium BC and mathematics and geometry must have existed to support this study in these ancient times.
The first mathematics which we shall describe in this article developed in the Indus valley. The earliest known urban Indian culture was first identified in 1921 at Harappa in the Punjab and then, one year later, at Mohenjo-daro, near the Indus River in the Sindh. Both these sites are now in Pakistan but this is still covered by our term “Indian mathematics” which, in this article, refers to mathematics developed in the Indian subcontinent. The Indus civilisation (or Harappan civilisation as it is sometimes known) was based in these two cities and also in over a hundred small towns and villages. It was a civilisation which began around 2500 BC and survived until 1700 BC or later. The people were literate and used a written script containing around 500 characters which some have claimed to have deciphered but, being far from clear that this is the case, much research remains to be done before a full appreciation of the mathematical achievements of this ancient civilisation can be fully assessed.
We often think of Egyptians and Babylonians as being the height of civilisation and of mathematical skills around the period of the Indus civilisation, yet V G Childe in New Light on the Most Ancient East (1952) wrote:-
India confronts Egypt and Babylonia by the 3rd millennium with a thoroughly individual and independent civilisation of her own, technically the peer of the rest. And plainly it is deeply rooted in Indian soil. The Indus civilisation represents a very perfect adjustment of human life to a specific environment. And it has endured; it is already specifically Indian and forms the basis of modern Indian culture.
We do know that the Harappans had adopted a uniform system of weights and measures. An analysis of the weights discovered suggests that they belong to two series both being decimal in nature with each decimal number multiplied and divided by two, giving for the main series ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500. Several scales for the measurement of length were also discovered during excavations. One was a decimal scale based on a unit of measurement of 1.32 inches (3.35 centimetres) which has been called the “Indus inch”. Of course ten units is then 13.2 inches which is quite believable as the measure of a “foot”. A similar measure based on the length of a foot is present in other parts of Asia and beyond. Another scale was discovered when a bronze rod was found which was marked in lengths of 0.367 inches. It is certainly surprising the accuracy with which these scales are marked. Now 100 units of this measure is 36.7 inches which is the measure of a stride. Measurements of the ruins of the buildings which have been excavated show that these units of length were accurately used by the Harappans in construction.
It is unclear exactly what caused the decline in the Harappan civilisation. Historians have suggested four possible causes: a change in climatic patterns and a consequent agricultural crisis; a climatic disaster such flooding or severe drought; disease spread by epidemic; or the invasion of Indo-Aryans peoples from the north. The favourite theory used to be the last of the four, but recent opinions favour one of the first three. What is certainly true is that eventually the Indo-Aryans peoples from the north did spread over the region. This brings us to the earliest literary record of Indian culture, the Vedas which were composed in Vedic Sanskrit, between 1500 BC and 800 BC. At first these texts, consisting of hymns, spells, and ritual observations, were transmitted orally. Later the texts became written works for use of those practicing the Vedic religion.
The next mathematics of importance on the Indian subcontinent was associated with these religious texts. It consisted of the Sulbasutras which were appendices to the Vedas giving rules for constructing altars. They contained quite an amount of geometrical knowledge, but the mathematics was being developed, not for its own
sake, but purely for practical religious purposes. The mathematics contained in the these texts is studied in some detail in the separate article on the Sulbasutras.
The main Sulbasutras were composed by Baudhayana (about 800 BC), Manava (about 750 BC), Apastamba (about 600 BC), and Katyayana (about 200 BC). These men were both priests and scholars but they were not mathematicians in the modern sense. Although we have no information on these men other than the texts they wrote,
we have included them in our biographies of mathematicians. There is another scholar, who again was not a mathematician in the usual sense, who lived around this period. That was Panini who achieved remarkable results in his studies of Sanskrit grammar. Now one might reasonably ask what Sanskrit grammar has to do with mathematics. It certainly has something to do with modern theoretical computer science, for a mathematician or computer scientist working with formal language theory will recognise just how modern some of Panini’s ideas are.
The Indian Sulbasutras
All that is known of Vedic mathematics is contained in the Sulbasutras. This in itself gives us a problem, for we do not know if these people undertook mathematical investigations for their own sake, as for example the ancient Greeks did, or whether they only studied mathematics to solve problems necessary for their religious rites. Some historians have argued that mathematics, in particular geometry, must have also existed to support astronomical work being undertaken around the same period.
Colonel Dunlap's Coup
A fictionalized essay that has been circulating within the Pentagon offers a blunt warning on several fronts.
by Thomas E. Ricks
It is the year 2012. The American military has carried out a successful coup d'etat. Jailed and awaiting execution for resistance to the coup, a retired military officer writes to an old comrade, explaining how the coup came about.
So begins a treatise entered last year in the National Defense University's Chairman of the Joint Chiefs of Staff Strategy Essay Competition. Titled "The Origins of the American Military Coup of 2012," and written by an active-duty Air Force officer, the essay went on to be selected as one of two winners of the competition. The author, Lieutenant Colonel Charles Dunlap, was honored by General Colin Powell at the awards ceremony.
Looking back from a vantage point supposedly twenty years in the future, Dunlap writes that after years of being handed the tough jobs the rest of the government seemed incapable of handling, the military simply decided to step in and run the show. Like all science fiction, Dunlap's essay is really about the present. His coup entices the reader to his real subject: the worrisome drift of the U.S. military into civilian affairs.
"Faced with intractable national problems on one hand, and an energetic and capable military on the other," Dunlap's condemned prisoner warns, "it can be all too seductive to start viewing the military as a cost-effective solution. We made a terrible mistake when we allowed the armed forces to be diverted from its original purpose." The prisoner sees a kind of inevitability to the coup. Amid rising crime, failing schools, a stagnant economy, and a gridlocked political system, the can-do U.S. military stood out in a no-solution society. Having remade themselves in the aftermath of Vietnam, the armed forces emerged from the Gulf War as "America's most--and perhaps only--trusted arm of government."
American coup d'etat: Military thinkers discuss the unthinkable
TrineDay Releases The Most Dangerous Book in the World
Investigative researcher-author S.K. Bain has not only gone outside the box, he has exposed a much bigger and stranger box than anyone has posited before, taking the reader inside the minds of the power-mad psychopaths responsible for the "New Pearl Harbor."
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