French-American mathematician who explored a new class of mathematical shapes known as "fractals," died recently at the age of 85 in Cambridge? ?->(Show Answer!)

1. French-American mathematician who explored a new class of mathematical shapes known as "fractals," died recently at the age of 85 in Cambridge?

Answer: Benoit Mandelbrot.

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MCQ-> Read the following passage carefully and answer the questions given at the end.The movement to expel the Austrians from Italy and unite Italy under a republican government had been gaining momentum while Garibaldi was away. There was a growing clamour, not just from Giuseppe Mazzini's republicans, but from moderates as well, for a General capable of leading Italy to independence. Even the King of Piedmont, for whom Garibaldi was still an outlaw under sentence of death, subscribed to an appeal for a sword for the returning hero. Meanwhile, the 'year of revolutions', 1848, had occurred in which Louis Philippe had been toppled from the French throne. In Austria, an uprising triggered off insurrections in Venice and Milan, and the Austrian garrisons were forced out. The King of Piedmont, Charles Albert ordered his troops to occupy these cities. There had also been insurrections in Sicily, causing the King Ferdinand II, to grant major constitutional freedoms in 1849, prompting both the Pope and Charles Albert to grant further concessions.Meanwhile, largely ignorant of these developments, Garibaldi was approaching Italy at a leisurely pace, arriving at Nice on 23 June 1848 to a tumultuous reception. The hero declared himself willing to fight and lay down his life for Charles Albert, who he now regarded as a bastion of Italian nationalism.Mazzini and the republicans were horrified, regarding this as outright betrayal: did it reflect Garibaldi's innate simple-mindedness, his patriotism in the war against Austria, or was it part of a deal with the monarchy? Charles Albert had pardoned Garibaldi, but to outward appearances he was still very wary of the General and the Italian Legion he had amassed of 150 'brigands'. The two men met near Mantua, and the King appeared to dislike him instantly. He suggested that Garibaldi's men should join his army and that Garibaldi should go to Venice and captain a ship as a privateer against the Austrians.Garibaldi, meanwhile, met his former hero Mazzini for the first time, and again the encounter was frosty. Seemingly rebuffed on all sides, Garibaldi considered going to Sicily to fight King Ferdinand II of Naples, but changed his mind when the Milanese offered him the post of General - something they badly needed when Charles Albert's Piedmontese army was defeated at Custoza by the Austrians. With around 1,000 men, Garibaldi marched into the mountains at Varese, commenting bitterly: 'The King of Sardinia may have a crown that he holds on to by dint of misdeeds and cowardice, but my comrades and I do not wish to hold on to our lives by shameful actions'.The King of Piedmont offered an armistice to the Austrians and all the gains in northern Italy were lost again. Garibaldi returned to Nice and then across to Genoa, where he learned that, in September 1848, Ferdinand II had bombed Messina as a prelude to invasion - an atrocity which caused him to be dubbed 'King Bomba'. Reaching Livorno he was diverted yet again and set off across the Italian peninsula with 350 men to come to Venice's assistance, but on the way, in Bologna, he learned that the Pope had taken refuge with King Bomba. Garibaldi promptly altered course southwards towards Rome where he was greeted once again as a hero. Rome proclaimed itself a Republic. Garibaldi's Legion had swollen to nearly 1,300 men, and the Grand Duke of Tuscany fled Florence before the advancing republican force.However, the Austrians marched southwards to place the Grand Duke of Tuscany back on his throne. Prince Louis Napoleon of France despatched an army of 7,000 men under General Charles Oudinot to the port of Civitavecchia to seize the city. Garibaldi was appointed as a General to defend Rome.The republicans had around 9,000 men, and Garibaldi was given control of more than 4,000 to defend the Janiculum Hill, which was crucial to the defence of Rome, as it commanded the city over the Tiber. Some 5,000 well-equipped French troops arrived on 30 April 1849 at Porta Cavallegeri in the old walls of Rome, but tailed to get through, and were attacked from behind by Garibaldi, who led a baton charge and was grazed by a bullet slightly on his side. The French lost 500 dead and wounded, along with some 350 prisoners, to the Italians, 200 dead and wounded. It was a famous victory, wildly celebrated by the Romans into the night, and the French signed a tactical truce.However, other armies were on the march: Bomba's 12,500-strong Neapolitan army was approaching from the south, while the Austrians had attacked Bologna in the north. Garibaldi too, a force out of Rome and engaged in a flanking movement across the Neapolitan army's rear at Castelli Romani; the Neapolitans attacked and were driven off leaving 50 dead. Garibaldi accompanied the Roman General, Piero Roselli, in an attack on the retreating Neapolitan army. Foolishly leading a patrol of his men right out in front of his forces, he tried to stop a group of his cavalry retreating and fell under their horses, with the enemy slashing at him with their sabres. He was rescued by his legionnaires, narrowly having avoided being killed, but Roselli had missed the chance to encircle the Neapolitan army.Garibaldi boldly wanted to carry the fight down into the Kingdom of Naples, but Mazzini, who by now was effectively in charge of Rome, ordered him back to the capital to face the danger of Austrian attack from the north. In fact, it was the French who arrived on the outskirts of Rome first, with an army now reinforced by 30,000. Mazzini realized that Rome could not resist and ordered a symbolic stand within the city itself, rather than surrender, for the purposes of international propaganda and to keep the struggle alive, whatever the cost. On 3 June the French arrived in force and seized the strategic country house, Villa Pamphili.Garibaldi rallied his forces and fought feverishly to retake the villa up narrow and steep city streets, capturing it, then losing it again. By the end of the day, the sides had 1,000 dead between them. Garibaldi once again had been in the thick of the fray, giving orders to his troops and - fighting, it was said, like a lion. Although beaten 'off for the moment, the French imposed a siege in the morning, starving the city of provisions and bombarding its beautiful centre.On 30 June the French attacked again in force, while Garibaldi, at the head of his troops, fought back ferociously. But there was no prospect of holding the French off indefinitely, and Garibaldi, decided to take his men out of the city to continue resistance in the mountains. Mazzini fled to Britain while Garibaldi remained to fight for the cause. He had just 4,000 men, divided into two legions, and faced some 17,000 Austrians and Tuscans in the north, 30,000 Neapolitans and Spanish in the south, and 40,000 French in the west. He was being directly pursued by 8,000 French and was approaching Neapolitan and Spanish divisions of some 18,000 men. He stood no chance whatever. The rugged hill country was ideal, however, for his style of irregular guerrilla warfare, and he manoeuvred skilfully, marching and counter-marching in different directions, confounding his pursuers before finally aiming for Arezzo in the north. But his men were deserting in droves and local people were hostile to his army: he was soon reduced to 1500 men who struggled across the high mountain passes to San Marino where he found temporary. refuge.The Austrians, now approaching, demanded that he go into exile in America. He was determined to fight on and urged the ill and pregnant Anita, his wife, to stay behind in San Marino, but she would not hear of it. The pair set off with 200 loyal soldiers along the mountain tracks to the Adriatic coast, from where Garibaldi intended to embark for Venice which was still valiantly holding out against the Austrians. They embarked aboard 13 fishing boats and managed to sail to within 50 miles of the Venetian lagoon before being spotted by an Austrian flotilla and fired upon.Only two of Garibaldi's boats escaped. He carried Anita through the shallows to a beach and they moved further inland. The ailing Anita was placed in a cart and they reached a farmhouse, where she died. Her husband broke down into inconsolable wailing and she was buried in a shallow grave near the farmhouse, but was transferred to a churchyard a few days later. Garibaldi had no time to lose; he and his faithful companion Leggero escaped across the Po towards Ravenna.At last Garibaldi was persuaded to abandon his insane attempts to reach Venice by sea and to return along less guarded routes on the perilous mountain paths across the Apennines towards the western coast of Italy. He visited his family in Nice for an emotional reunion with his mother and his three children - but lacked the courage to tell them what had happened to their mother.Find the correct statement:
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MCQ-> Mathematicians are assigned a number called Erdos number (named after the famous mathematician, Paul Erdos). Only Paul Erdos himself has an Erdos number of zero. Any mathematician who has written a research paper with Erdos has an Erdos number of 1.For other mathematicians, the calculation of his/her Erdos number is illustrated below:Suppose that a mathematician X has co-authored papers with several other mathematicians. 'From among them, mathematician Y has the smallest Erdos number. Let the Erdos number of Y be y. Then X has an Erdos number of y+1. Hence any mathematician with no co-authorship chain connected to Erdos has an Erdos number of infinity. :In a seven day long mini-conference organized in memory of Paul Erdos, a close group of eight mathematicians, call them A, B, C, D, E, F, G and H, discussed some research problems. At the beginning of the conference, A was the only participant who had an infinite Erdos number. Nobody had an Erdos number less than that of F.On the third day of the conference F co-authored a paper jointly with A and C. This reduced the average Erdos number of the group of eight mathematicians to 3. The Erdos numbers of B, D, E, G and H remained unchanged with the writing of this paper. Further, no other co-authorship among any three members would have reduced the average Erdos number of the group of eight to as low as 3.• At the end of the third day, five members of this group had identical Erdos numbers while the other three had Erdos numbers distinct from each other.• On the fifth day, E co-authored a paper with F which reduced the group's average Erdos number by 0.5. The Erdos numbers of the remaining six were unchanged with the writing of this paper.• No other paper was written during the conference.The person having the largest Erdos number at the end of the conference must have had Erdos number (at that time):
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MCQ-> A difficult readjustment in the scientist's conception of duty is imperatively necessary. As Lord Adrain said in his address to the British Association, unless we are ready to give up some of our old loyalties, we may be forced into a fight which might end the human race. This matter of loyalty is the crux. Hitherto, in the East and in the West alike, most scientists, like most other people, have felt that loyalty to their own state is paramount. They have no longer a right to feel this. Loyalty to the human race must take its place. Everyone in the West will at once admit this as regards Soviet scientists. We are shocked that Kapitza who was Rutherford's favourite pupil, was willing when the Soviet government refused him permission to return to Cambridge, to place his scientific skill at the disposal of those who wished to spread communism by means of H-bombs. We do not so readily apprehend a similar failure of duty on our own side. I do not wish to be thought to suggest treachery, since that is only a transference of loyalty to another national state. I am suggesting a very different thing; that scientists the world over should join in enlightening mankind as to the perils of a great war and in devising methods for its prevention. I urge with all the emphasis at my disposal that this is the duty of scientists in East and West alike. It is a difficult duty, and one likely to entail penalties for those who perform it. But, after all, it is the labours of scientists which have caused the danger and on this account, if on no other, scientists must do everything in their power to save mankind from the madness which they have made possible. Science from the dawn of History, and probably longer, has been intimately associated with war. I imagine that when our ancestors descended from the trees they were victorious over the arboreal conservatives because flints were sharper than coconuts. To come to more recent times, Archimedes was respected for his scientific defense of Syracuse against the Romans; Leonardo obtained employment under the Duke of Milan because of his skill in fortification, though he did mention in a postscript that he could also paint a bit. Galileo similarly derived an income from the Grant Duke of Tuscany because of his skill in calculating the trajectories of projectiles. In the French Revolution, those scientists who were not guillotined devoted themselves to making new explosives. There is therefore no departure from tradition in the present day scientists manufacture of A-bombs and H-bomb. All that is new is the extent of their destructive skill.I do not think that men of science can cease to regard the disinterested pursuit of knowledge as their primary duty. It is true that new knowledge and new skills are sometimes harmful in their effects, but scientists cannot profitably take account of this fact since the effects are impossible to foresee. We cannot blame Columbus because the discovery of the Western Hemisphere spread throughout the Eastern Hemisphere an appallingly devastating plague. Nor can we blame James Watt for the Dust Bowl although if there had been no steam engines and no railways the West would not have been so carelessly or so quickly cultivated To see that knowledge is wisely used in primarily the duty of statesmen, not of science; but it is part of the duty of men of science to see that important knowledge is widely disseminated and is not falsified in the interests of this or that propaganda.Scientific knowledge has its dangers; but so has every great thing. And over and beyond the dangers with which it threatens the present, it opens up, as nothing else can, the vision of a possible happy world, a world without poverty, without war, with little illness. And what is perhaps more than all, when science has mastered the forces which mould human character, it will be able to produce populations in which few suffer from destructive fierceness and in which the great majority regard other people, not as competitors, to be feared, but as helpers in a common task. Science has only recently begun to apply itself to human beings except in their purely physical aspect. Such science as exists in psychology and anthropology has hardly begun to affect political behaviour or private ethics. The minds of men remain attuned to a world that is fast disappearing. The changes in our physical environment require, if they are to bring well being, correlative changes in our beliefs and habits. If we cannot effect these changes, we shall suffer the fate of the dinosaurs, who could not live on dry land.I think it is the duty of science. I do not say of every individual man of science, to study the means by which we can adapt ourselves to the new world. There are certain things that the world quite obviously needs; tentativeness, as opposed to dogmatism in our beliefs: an expectation of co-operation, rather than competition, in social relations, a lessening of envy and collective hatred These are things which education could produce without much difficulty. They are not things adequately sought in the education of the present day.It is progress in the human sciences that we must look to undo the evils which have resulted from a knowledge of the physical world hastily and superficially acquired by populations unconscious of the changes in themselves that the new knowledge has made imperative. The road to a happier world than any known in the past lies open before us if atavistic destructive passion can be kept in leash while the necessary adaptations are made. Fears are inevitable in our time, but hopes are equally rational and far more likely to bear good fruit. We must learn to think rather less of the dangers to be avoided than of the good that will be within our grasp if we believe in it and let it dominate our thoughts. Science, whatever unpleasant consequences it may have by the way, is in its very nature a liberator, a liberator of bondage to physical nature and, in time to come a liberator from the weight of destructive passion. We are on the threshold of utter disaster or unprecedented glorious achievement. No previous age has been fraught with problems so momentous and it is to science that we must look for happy issue.The duty of science, according to the author is :-
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MCQ-> The persistent patterns in the way nations fight reflect their cultural and historical traditions and deeply rooted attitudes that collectively make up their strategic culture. These patterns provide insights that go beyond what can be learnt just by comparing armaments and divisions. In the Vietnam War, the strategic tradition of the United States called for forcing the enemy to fight a massed battle in an open area, where superior American weapons would prevail. The United States was trying to re-fight World War II in the jungles of Southeast Asia, against an enemy with no intention of doing so. Some British military historians describe the Asian way of war as one of indirect attacks, avoiding frontal attacks meant to overpower an opponent. This traces back to Asian history and geography: the great distances and harsh terrain have often made it difficult to execute the sort of open-field clashes allowed by the flat terrain and relatively compact size of Europe. A very different strategic tradition arose in Asia. The bow and arrow were metaphors for an Eastern way of war. By its nature, the arrow is an indirect weapon. Fired from a distance of hundreds of yards, it does not necessitate immediate physical contact with the enemy. Thus, it can be fired from hidden positions. When fired from behind a ridge, the barrage seems to come out of nowhere, taking the enemy by surprise. The tradition of this kind of fighting is captured in the classical strategic writings of the East. The 2,000 years' worth of Chinese writings on war constitutes the most subtle writings on the subject in any language. Not until Clausewitz, did the West produce a strategic theorist to match the sophistication of Sun-tzu, whose Art of War was written 2,300 years earlier. In Sun-tzu and other Chinese writings, the highest achievement of arms is to defeat an adversary without fighting. He wrote: "To win one hundred victories in one hundred battles is not the acme of skill. To subdue the enemy without fighting is the supreme excellence." Actual combat is just one among many means towards the goal of subduing an adversary. War contains too many surprises to be a first resort. It can lead to ruinous losses, as has been seen time and again. It can have the unwanted effect of inspiring heroic efforts in an enemy, as the United States learned in Vietnam, and as the Japanese found out after Pearl Harbor. Aware of the uncertainties of a military campaign, Sun-tzu advocated war only after the most thorough preparations. Even then it should be quick and clean. Ideally, the army is just an instrument to deal the final blow to an enemy already weakened by isolation, poor morale, and disunity. Ever since Sun-tzu, the Chinese have been seen as masters of subtlety who take measured actions to manipulate an adversary without his knowledge. The dividing line between war and peace can be obscure. Low-level violence often is the backdrop to a larger strategic campaign. The unwitting victim, focused on the day-to-day events, never realizes what's happening to him until it's too late. History holds many examples. The Viet Cong lured French and U.S. infantry deep into the jungle, weakening their morale over several years. The mobile army of the United States was designed to fight on the plains of Europe, where it could quickly move unhindered from one spot to the next. The jungle did more than make quick movement impossible; broken down into smaller units and scattered in isolated bases, US forces were deprived of the feeling of support and protection that ordinarily comes from being part of a big army. The isolation of U.S. troops in Vietnam was not just a logistical detail, something that could be overcome by, for instance, bringing in reinforcements by helicopter. In a big army reinforcements are readily available. It was Napoleon who realized the extraordinary effects on morale that come from being part of a larger formation. Just the knowledge of it lowers the soldier's fear and increases his aggressiveness. In the jungle and on isolated bases, this feeling was removed. The thick vegetation slowed down the reinforcements and made it difficult to find stranded units. Soldiers felt they were on their own. More important, by altering the way the war was fought, the Viet Cong stripped the United States of its belief in the inevitability of victory, as it had done to the French before them. Morale was high when these armies first went to Vietnam. Only after many years of debilitating and demoralizing fighting did Hanoi launch its decisive attacks, at Dienbienphu in 1954 and against Saigon in 1975. It should be recalled that in the final push to victory the North Vietnamese abandoned their jungle guerrilla tactics completely, committing their entire army of twenty divisions to pushing the South Vietnamese into collapse. This final battle, with the enemy's army all in one place, was the one that the United States had desperately wanted to fight in 1965. When it did come out into the open in 1975, Washington had already withdrawn its forces and there was no possibility of re-intervention. The Japanese early in World War II used a modern form of the indirect attack, one that relied on stealth and surprise for its effect. At Pearl Harbor, in the Philippines, and in Southeast Asia, stealth and surprise were attained by sailing under radio silence so that the navy's movements could not be tracked. Moving troops aboard ships into Southeast Asia made it appear that the Japanese army was also "invisible." Attacks against Hawaii and Singapore seemed, to the American and British defenders, to come from nowhere. In Indonesia and the Philippines the Japanese attack was even faster than the German blitz against France in the West. The greatest military surprises in American history have all been in Asia. Surely there is something going on here beyond the purely technical difficulties of detecting enemy movements. Pearl Harbor, the Chinese intervention in Korea, and the Tet offensive in Vietnam all came out of a tradition of surprise and stealth. U.S. technical intelligence – the location of enemy units and their movements was greatly improved after each surprise, but with no noticeable improvement in the American ability to foresee or prepare what would happen next. There is a cultural divide here, not just a technical one. Even when it was possible to track an army with intelligence satellites, as when Iraq invaded Kuwait or when Syria and Egypt attacked Israel, surprise was achieved. The United States was stunned by Iraq's attack on Kuwait even though it had satellite pictures of Iraqi troops massing at the border. The exception that proves the point that cultural differences obscure the West's understanding of Asian behavior was the Soviet Union's 1979 invasion of Afghanistan. This was fully anticipated and understood in advance. There was no surprise because the United States understood Moscow's worldview and thinking. It could anticipate Soviet action almost as well as the Soviets themselves, because the Soviet Union was really a Western country. The difference between the Eastern and the Western way of war is striking. The West's great strategic writer, Clausewitz, linked war to politics, as did Sun-tzu. Both were opponents of militarism, of turning war over to the generals. But there all similarity ends. Clausewitz wrote that the way to achieve a larger political purpose is through destruction of the enemy's army. After observing Napoleon conquer Europe by smashing enemy armies to bits, Clausewitz made his famous remark in On War (1932) that combat is the continuation of politics by violent means. Morale and unity are important, but they should be harnessed for the ultimate battle. If the Eastern way of war is embodied by the stealthy archer, the metaphorical Western counterpart is the swordsman charging forward, seeking a decisive showdown, eager to administer the blow that will obliterate the enemy once and for all. In this view, war proceeds along a fixed course and occupies a finite extent of time, like a play in three acts with a beginning, a middle, and an end. The end, the final scene, decides the issue for good. When things don't work out quite this way, the Western military mind feels tremendous frustration. Sun-tzu's great disciples, Mao Zedong and Ho Chi Minh, are respected in Asia for their clever use of indirection and deception to achieve an advantage over stronger adversaries. But in the West their approach is seen as underhanded and devious. To the American strategic mind, the Viet Cong guerrilla did not fight fairly. He should have come out into the open and fought like a man, instead of hiding in the jungle and sneaking around like a cat in the night. According to the author, the main reason for the U.S. losing the Vietnam war was
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MCQ-> In the modern scientific story, light was created not once but twice. The first time was in the Big Bang, when the universe began its existence as a glowing, expanding, fireball, which cooled off into darkness after a few million years. The second time was hundreds of millions of years later, when the cold material condensed into dense suggests under the influence of gravity, and ignited to become the first stars.Sir Martin Rees, Britain’s astronomer royal, named the long interval between these two enlightements the cosmic ‘Dark Age’. The name describes not only the poorly lit conditions, but also the ignorance of astronomers about that period. Nobody knows exactly when the first stars formed, or how they organized themselves into galaxies — or even whether stars were the first luminous objects. They may have been preceded by quasars, which are mysterious, bright spots found at the centres of some galaxies.Now two independent groups of astronomers, one led by Robert Becker of the University of California, Davis, and the other by George Djorgovski of the Caltech, claim to have peered far enough into space with their telescopes (and therefore backwards enough in time) to observe the closing days of the Dark age.The main problem that plagued previous efforts to study the Dark Age was not the lack of suitable telescopes, but rather the lack of suitable things at which to point them. Because these events took place over 13 billion years ago, if astronomers are to have any hope of unravelling them they must study objects that are at least 13 billion light years away. The best prospects are quasars, because they are so bright and compact that they can be seen across vast stretches of space. The energy source that powers a quasar is unknown, although it is suspected to be the intense gravity of a giant black hole. However, at the distances required for the study of Dark Age, even quasars are extremely rare and faint.Recently some members of Dr Becker’s team announced their discovery of the four most distant quasars known. All the new quasars are terribly faint, a challenge that both teams overcame by peering at them through one of the twin Keck telescopes in Hawaii. These are the world’s largest, and can therefore collect the most light. The new work by Dr Becker’s team analysed the light from all four quasars. Three of them appeared to be similar to ordinary, less distant quasars. However, the fourth and most distant, unlike any other quasar ever seen, showed unmistakable signs of being shrouded in a fog because new-born stars and quasars emit mainly ultraviolet light, and hydrogen gas is opaque to ultraviolet. Seeing this fog had been the goal of would-be Dark Age astronomers since 1965, when James Gunn and Bruce Peterson spelled out the technique for using quasars as backlighting beacons to observe the fog’s ultraviolet shadow.The fog prolonged the period of darkness until the heat from the first stars and quasars had the chance to ionise the hydrogen (breaking it into its constituent parts, protons and electrons). Ionised hydrogen is transparent to ultraviolet radiation, so at that moment the fog lifted and the universe became the well-lit place it is today. For this reason, the end of the Dark Age is called the ‘Epoch of Re-ionisation’. Because the ultraviolet shadow is visible only in the most distant of the four quasars, Dr Becker’s team concluded that the fog had dissipated completely by the time the universe was about 900 million years old, and oneseventh of its current size.In the passage, the Dark Age refers to
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