Srinivasa Ramanujan

The arithmetic class was in progress. The teacher was solving questions on division. On the backboard were drawn three bananas.

“We have three bananas,” the teacher said, “and we have three boys. Can you tell me how many each will get?”

A smart boy in the front row replied, “Each will get one.”

“Right,” the teacher said. “Now, similarly, if 1,000 bananas are distributed among 1,000 boys, each will get one, isn’t that so?”

While the teacher was explaining, a boy sitting in one corner raised his hand and stood up. The teacher stopped and waiting for the boy to speak.

“Sir,” the boy asked, “if no bananas is distributed among no one, will everyone still get one banana?” There was roar of laughter in the class. What a silly question to ask!

“Quite,” the teacher said loudly and thumped the desk. “There is nothing to laugh at. I will just explain what he means to say. For the division of bananas, we divided three by three, saying that each boy will get one banana. Similarly, we divided 1,000 by 1,000 to get one. What he is asking is that if zero banana is divided among zero, will each one get one? The answer is ‘no’. Mathematically, each will get an infinite number of bananas!”

Everyone laughed again. The boys understood the trick arithmetic had played upon them. What they could not understand was why the teacher later complimented the boy who had asked that absurd question.

The boy had asked a question that had taken mathematicians several centuries to answer. Some mathematicians claimed that zero divided by zero was zero. Others claimed it to be unity. It was the Indian mathematician Bhaskara who proved that it is infinity. The boy who asked the intriguing question was Srinivasa Ramanujan. Throughout his life, whether in his native Kumbakonam or Cambridge, he was always ahead of his mathematics teachers.

Ramanujan was born at Erode in Tamil Nadu on December 22, 1887. His father was a petty clerk in a cloth shop. From early childhood it was evident that he was a prodigy. Senior students used to go to his dingy house to get their difficulties in mathematics solved. At the age of 13 Ramanujan was able to get Loney’s Trigonometry from a college library. Not only did he master this rather difficult book but also began his own research. He came forth with many mathematical theorems and formulae not given in the book, though they had been discovered much earlier by great mathematicians.

The most significant turn came two years later when one of his senior friends showed him Synopsis of Elementary Results in Pure and Applied Mathematics by George Shoobridge Carr. For a boy of 15 the title itself must be frightening, but Ramanujan was delighted. He took the book home and began to work on the problems given in it. This book triggered the mathematical genius in him.

Mathematical ideas began to come in such a flood to his mind that he was not able to write all of them down. He used to do problems on loose sheets of paper or on a slate and to jot the results down in notebooks. Before he went abroad he had filled three notebooks, which later became famous as Ramanujan’s Frayed Notebooks. Even today mathematicians are studying them to prove or disprove the results given in them.

Although Ramanujan secured a first class in mathematics in the matriculation examination and was awarded the Subramanyan Scholarship, he failed twice in his first year arts examination in college, as he neglected other subjects such as history, English and physiology. This disappointed his father. When he found the boy always scribbling numbers and not doing much else, he thought Ramanujan had gone mad. “To set him right”, he forced his son to marry. The girl chosen was eight-year-old Janaki.

Ramanujan began to look for a job. He had to find money not only for bread but for paper as well to do his calculations. He needed about 2,000 sheets of paper every month. Ramanujan started using even scraps of paper he found lying in the streets. Sometimes he used a red pen to write over what was written in blue ink on the piece of paper he had picked up.

Unkempt and uncouth, he would visit offices, showing everyone his frayed notebooks and telling them that he knew mathematics and could do a clerical job. But no one could understand what was written in the notebooks and his applications for jobs were turned down.

Luckily for him, he at last found someone who was impressed by his notebooks. He was the Director of the Madras Port Trust, Francis Spring, and he gave Ramanujan a clerical job on a monthly salary of Rs. 25. Later some teachers and educationists interested in mathematics initiated a move to provide Ramanujan with a research fellowship. On May 1, 1913, the University of Madras granted him a fellowship of Rs. 75 a month, though he had no qualifying degree.

A few months earlier, Ramanujan had sent a letter to the great mathematician G.H. Hardy, of Cambridge University, in which he set out 120 theorems and formulae. Among them was what is known as the Reimann series, a topic in the definite integral of calculus. But Ramanujan was ignorant of the work of the German mathematician, George F. Reimann, who had earlier arrived at the series, a rare achievement. Also included was Ramanujan’s conjecture about the kind of questions called “modular”. Pierre Deligne subsequently proved this conjecture to be correct. He also gave a key formula in the hypergeometric series, which came to be named after him.

It did not take long for Hardy and his colleague, J.E. Littlewood, to realize that they had discovered a rare mathematical genius. They made arrangements for Ramanujan’s passage and stay at Cambridge University. On March 17, 1914, he sailed for Britain.

Ramanujan found himself a stranger at Cambridge. The cold was hard to bear and, being a Brahmin and a vegetarian, he had to cook his own food. However, he continued his research in mathematics with determination. In the company of Hardy and littlewood he could forget much of the hardship he had to endure.

In Ramanujan Hardy found an unsystematic mathematician, similar to one who knows the Pythagoras theorem but does not know that a congruent triangle means. Several discrepancies in his research could be attributed to his lack of formal education. Ramanujan played with numbers, as a child would with a toy. It was sheer genius that led him to mathematical “truths”. The task of proving them, so important in science, he left to lesser mortals.

Ramanujan was elected Fellow of the Royal Society on February 28, 1918. He was the second Indian to receive this distinguished fellowship. In October that year he became the first Indian to be elected Fellow of Trinity College, Cambridge. His achievements at Cambridge include the Hardy-Ramanujan-Littlewood circle method in number theory, Roger-Ramanujan’s identities in partition of integers, a long list of the highest composite numbers, besides work on the number theory and the algebra of inequalities. In algebra his work on continued fractions is considered to be equal in importance to that of great mathematicians like Leonard Eular and Jacobi.

While Ramanujan continued his research work, tuberculosis, then an incurable disease, was devouring him. Ramanujan was sent back to India and when he disembarked, his friends found him pale, exhausted and emaciated. To forget the agonizing pain, he continued to play with numbers even on his deathbed. On April 26, 1920, he died at Chetpet in Madras.

Besides being a mathematician, Ramanujan was an astrologer of repute and a good speaker. He used to give lectures on subjects like “God, Zero and Infinity”.

Bhaskara

Leelavati looked entranced at the water-clock her father had brought home. Its movements were fascinating. She had a slight feeling of guilt, for her father had told her never to enter that room. But because it was forbidden territory, its exploration gave her a sense of adventure. And she continued looking at the clock.

Then came disaster, though she was never to know about it. A tiny pearl slipped out of her nose-ring and fell into the clock. She was so alarmed that she fled. And in the excitement of the arrangements being made for her wedding the next day she forget all about the clock and the pearl. Which was not surprising for she was only six years old.

Leelavati was married, but a week later her husband fell off a cliff and died. This was what her father, Bhaskara, a great mathematician and astrologer, had feared. Astrological calculations had shown Bhaskara that, if the marriage of his daughter was not performed at a particular hour on that particular day, she would become a widow. And he had bought the water-clock to ensure that he would know the right time. He did not know that the pearl in it had made the clock inexact. And, going by that clock, he had made an error. Bhaskara thought that it was his astrological calculations that had gone wrong and blamed himself for the tragedy.

In those days, widowed girls were not allowed to marry again. Bhaskara, therefore, began to try to arouse her interest in mathematics, so that she would forget her grief. It is not known how good a mathematician she turned out to be, but he made her immortal in the history of mathematics in India by titling after his daughter a chapter of the book Siddhantasiromani that he wrote when he was only 30 years old. At one time there was even a popular saying: “Whosoever is well-versed with Leelavati can tell the exact number of leaves on a tree.”

The part of the book titled Leelavati dealt essentially with arithmetic. The other three parts were on different aspects of mathematics: Bijaganita dealt with algebra, Coladhyaya with spheres and Grahaganita with planetary mathematics. Basically the book was a text-book, a collection of the works of some eminent scholars like Brahmagupta, Mahavira and Sridhara, after they had been simplified to help students. The book contained problems presented in such a way as to stimulate the student’s interest. It was so popular and authoritative that four to five centuries later it was translated twice into Persian.

Bhaskara was an original thinker, too. He was the first mathematician to declare confidently that any term and infinity is infinity.

In algebra, Bhaskara considered Brahmagupta his guru and mostly extended Brahmagupta’s work. But his introduction of Chakrawal, or the cyclic method, to solve algebraic equation is a remarkable contribution. It was only after six centuries that European mathematicians like Galois, Euler and Lagrange rediscovered this method and called it “inverse cyclic”. Determination of the area and volume of a sphere in a rough integral calculus manner was also mentioned for the first time in his book. It contained some important formulas and theorems in trigonometry and permutation and combination.

Bhaskara can also be called the founder of differential calculus. He had conceived it several centuries before Isaac Newton and Gottfried Leibniz, who are considered in the West to be the founders of this subject. He had even given an example of what is now called “differential coefficient” and the basic idea of what is now known as “Rolle’s theorem”. Although Bhaskara attained such excellence in calculus, no one in the land took any notice of it.

As an astronomer Bhaskara is renowned for his concept of Tatkalikagati, which means instantaneous motion. This enables astronomers to determine the motion of the planets accurately.

Bhaskara was born in 1114 at Bijjada Bida (Bijapur, Karnataka) in the Sahyadri Hills. He learnt mathematics from his saintly father. Later, the works of Brahmagupta inspired him so much that he devoted himself entirely to mathematics. At the age of 69 he wrote his second book, Karanakutuhala, a manual of astronomical calculations. Though it is not as well known as his other book, it is still referred to in making calendars.

Brahmagupta

The mathematician who first framed the rules of operation for zero was Brahmagupta. He was also to give a solution to indeterminate equations of the type ax² + 1 = y² and the founder of a branch of higher mathematics called “Numerical analysis”. No wonder Bhaskara, the great mathematician, conferred on him the title of Ganakachakrachudamani, the gem of the circle of mathematicians.

Brahmagupta was born at Bhillamala (Bhinmal), in Gujarat, in 598 A.D. He became court astronomer to King Vyaghramukha of the Chapa dynasty. Of his two treatises, Brahmasphutasiddhanta and Karanakhandakhadyaka, the first is the more famous. It was a corrected version of the old astronomical text, Brahmasiddhanta. It was translated into Arabic, but erroneously titled Sind Hind. For several centuries the treatise remained a standard work of reference in India and the Arab countries.

Brahmasphutasiddhanta also contains chapters on arithmetic and algebra. Brahmagupta’s major contribution is the rules of operation for zero. He declared that addition or subtraction of zero to or from any quantity, negative or positive, does not affect it. He also added that the product of any quantity by zero is zero and division of any quantity by zero is infinity. He, however, wrongly claimed that division of zero by zero was zero.

He also framed rules to solve a simple equation of the type ax + b = 0 and a quadratic equation of the type ax² + bx + c = 0, as well as methods to sum up a geometric series. Besides, he noted the difference between algebra and arithmetic and so was the first mathematician to treat them as two separate branches of mathematics.

Brahmagupta’s Karanakhandakhadyaka is a hand-book on astronomical calculations. In this he effectively used algebra for the first time in calculations. But Brahmagupta always was careful not to anger the priests. His wives were orthodox, in keeping with the beliefs held during those times, and he criticized Aryabhata, who said the earth was not stationary. But he believed that the earth was round.

About gravity he said: “Bodies fall towards the Earth”.

Patanjali

Although the Upanishads and the Atharvaveda mention yoga, it was only in the second century B.C. that its fundamentals and techniques were adequately presented. The man who did this was Patanjali in his Yogasutras (Yoga aphorisms).

According to Patanjali, there are channels called nadi and centres called chakra in the human body. If these are tapped, the hidden energy in the body called Kundalini can be released, enabling the body to acquire “supernatural” powers. Patanjali gives eight stages. Yama (universal moral commandments), Niyama (self-purification through discipline), Asana (posture), Pranayama (breath-control), Pratyahara (withdrawal of mind from external objects), Dharana (concentration), Dhyana (meditation), and Samadhi (state of superconsciousness). It is the last stage which is the more difficult and which enables one to attain “Godhead”.

Patanjali gives a beautiful analogy to explain how God is attained through yoga. Our mind, he says, is like the surface of a pond. Just as we cannot see the jewel lying at the bottom of the pond because of the breeze disturbing its surface, we do not see the divine in us because our mind is in constant agitation. If the surface of the pond is undisturbed, one can see the jewel at the bottom. So also, if the mind is kept calm, with the doors to the external world closed, one can see God within.

Only in the last few decades have scientists begun to recognize the powers of yoga. It has now been established by experiments that through the practice of yoga several ailments, mental and physical, can be cured. Tests conducted on yogis show that they do acquire extraordinary powers. For instance, they can live without oxygen or food for a long a time. Research is now in progress in laboratories all over the world to probe further the merits of yoga. What Patanjali advocated several centuries is now receiving the attention it deserves.

Aryabhata

Nearly five hundred years after the birth of Christ a ritual was held near Khagola, the famous astronomical observatory at the University of Nalanda near Kusumapura (Patna), to mark the “birth” of a treatise that was to lay the foundation of a new school of thought in astronomy.

When the bell at the university tolled at 12 noon on March 21,499 A.D., a chorus of vedic chants filled the air. And priests, after prayers before a havan, led a 23-year-old astronomer to a platform. Silence prevailed as the astronomer sprinkled holy water on the parchment and pen lying on a desk placed on the platform. Chanting holy verses, he gazed at the sun overhead and prostrated himself in obeisance before sitting at the desk. Taking the pen, he wrote the first letter of the treatise while the priests chanted slokas and the large crowd of learned men showered flowers on him.

The young astronomer was Aryabhata and the treatise was Aryabhatiya. Born in 476 in Kerala, Aryabhata had come to complete his studies at the University of Nalanda, which was then a great centre of learning. When his treatise was recognized as a masterpiece, the then Gupta ruler Buddhagupta, made him head of the university.

Aryabhata was the first to deduce that the earth is round and that it rotates on its own axis, creating day and night. He declared that the moon is dark and shines only because of sunlight. Solar and lunar eclipses, he believed, occurred not because Rahu gobbled the sun and the moon, as Hindu mythology claimed, but because of the shadows cast by the earth and the moon.

He, however, believed in the geocentric concept of the universe that the earth is the center of the universe. To explain the “erratic” movements of some planets, he like the Greek king Ptolemy, made use of “epicycle”. But his method was superior to Ptolemy’s.

In mathematics Aryabhata’s contributions are equally valuable. He gave the value of ? (pi) as 3.1416, claiming, for the first time, that it was an approximation. And he was the first mathematician to give what later came to be called the tables of Sines. His method to find a solution to indeterminate equations of the type ax – by = c is also recognized the world over. He also devised a novel method to express large numbers such as 100,000,000,000 in words. He developed this method to write unwieldy numbers in poetic form. The consise but somewhat difficult-to-grasp Aryabhatiya also dealt with other aspects of mathematics and astronomical calculations, namely, geometry, mensuration, square root, cube root, progression and celestial sphere.

In his old age Aryabhata also wrote another treatise, Aryabhatasiddhanta. It was a text-book for day-to-day astronomical calculations as well as a guide to determine auspicious times for various rituals. Even today Aryabhata’s astronomical data are used in preparing panchangs (Hindu calendars).

Kanada

What is the relationship between man, the universe and their creator? This question has always intrigued philosophers and thinkers. Between 600 B.C. and 200 A.D. there were several attempts by Indian philosophers to find an answer to the question.

One of these was Kanada, who, in about 600 B.C. at Prabhasa propounded the Vaisesikasutra (Peculiarity Aphorisms). Today, we realize that these sutras are a blend of science, philosophy and religion. Their essence is the atomic theory of matter. If Kanada’s sutras are analysed, one would find that his atomic theory was far more advanced than those forwarded later by the Greek philosophers, Leucippus and Democritus. In fact, he gave the name paramanu (atom) to an indivisible entity of matter.

According to Kanada, everything is made up of paramanu. When matter is divided, then further divided, till no further division is possible, the remaining indivisible entity is called paramanu. This entity does not exist in a free state, nor can it be sensed through any human organ. It is eternal and indestructible.

Kanada added-and it is here that he took a lead over other philosophers-that there are a variety of paramanu as different as the different classes of substances then believed to exist, namely, earth, water, air and fire. Each paramanu has a peculiar property which is the same as the class of substance it belongs to. It is only because of this peculiarity of paramanu that the theory was called Vaisesikasutras.

Kanada also claimed that an inherent urge made one paramanu combine with another. If two paramanu belonging to one class of substance combined, a dwinuka (binary molecule) was produced, which had properties similar to those of the two original paramanu. Paramanu belonging to different classes of substance could also combine in large numbers.

The idea of chemical change was also put forward by Kanada. He claimed heat was responsible for any change. The properties of paramanu also changed when heated. He gave the examples of the blackening of a new earthen pot and the ripening of a mango to illustrate the action of heat. All things seen in the universe were, therefore, formed, Kanada said, because of the peculiarity of paramanu, their variety, the variety of ways in which they combined and the action of heat.

Susruta

It was midnight when Susruta was awakened by a frantic knocking at the door.

“Who’s out there?” asked the aged doctor, taking a lighted torch from its socket in the wall and approaching the door.

“I’m a traveler, by revered Susruta,” was the anguished reply. “A tragedy has befallen me. I need your help…”

Susruta opened the door. What he saw was a man kneeling before him, tears flowing from his eyes and blood from his disfigured nose.

“Get up, my son, and come in,” said Susruta. “Everything will be all right. But be quiet, now.”

He led the stranger to a neat and clean room, with surgical instruments on its walls. Unfolding a mattress he asked him to sit on it after taking off his robe and washing his face with water and the juice of a medicinal plant. Susruta then offered the traveler a mug of wine and began preparing for the operation.

With a large leaf of creeper brought from the garden, he measured the size of the stranger’s nose. Taking a knife and forceps from the wall, he held them over a flam and cut a strip of flesh from the stranger’s cheek. The man moaned, but the wine had numbed his senses.

After banding the cut in the cheek, Susruta cautiously inserted two pipes into the stranger’s nostrils and transplanted the flesh to the disfigured nose. Moulding the flesh into shape he dusted the nose with powdered liquorice, red sandalwood and extract of Indian barberry. He then enveloped the nose in cotton, sprinkled some refined oil of sesame on it and finally put a bandage. Before the traveler left, he was given instructions on what to do and what not to and a list of medicines and herbs he was to take regularly. He was also asked to come back after a few weeks to be examined.

In this manner did Susruta mend a nose some 26 centuries ago. And what he did is not greatly different from what a plastic surgeon would do today. In fact, Susruta is today recognized as the father of plastic surgery all over the world. His treatise, Susrutasamhita, has considerable medical knowledge of relevance even today. It indicates that India was far ahead of the rest of the world in medical knowledge. In the eighth century A.D. Susrutasamhita was translated into Arabic as Kitab-Shaw Shoon-a-Hindi and Kitab-i-Susrud.

Born in the sixth century B.C., Susruta was a descendant of the Vedic sage Visvamitra. He learnt surgery and medicine at the feet of Divodasa Dhanvantari in his hermitage at Varanasi. Later, he became an authority in not only surgery but other branches of medicine.

He was the first physician to advocate what is today known as the “caesarean” operation. He was also expert in removing urinary stones, locating and treating fractures and doing eye operations for cataract. Several centuries before Joseph Lister, he put forth the concept of asepsis. His suggestion to give wine to patients about to be operated upon makes him also the father of anaesthesia.

In his treatise, Susruta lists 101 types of instruments. His Samdamsa yantras are the first forms of the modern surgeon’s spring forceps and dissection and dressing forceps. In fact, his system of naming surgical tools after the animals or birds they resemble in shape, for example crocodile forceps, hawkbill forceps, is adopted even today.

Susruta was also an excellent teacher. He told his pupils that one could become a good physician only if one knew both theory and practice. He advised his pupils to use carcases and models for practice before surgery.

iaddition to classifying worms that infect the human body, leeches for bloodletting, medicinal herbs, alkalis and metals, Susruta gave a vague classification of animals.

Pablo Picasso

Pablo Picasso To say that Pablo Picasso dominated Western art in the 20th century is, by now, the merest commonplace. Before his 50th birthday, the little Spaniard from Malaga had become the very prototype of the modern artist as public figure. No painter before him had had a mass audience in his own lifetime. The total public for Titian in the 16th century or Velazquez in the 17th was probably no more than a few thousand people – though that included most of the crowned heads, nobility and intelligentsia of Europe. Picasso’s audience – meaning people who had heard of him and seen his work, at least in reproduction – was in the tens, possibly hundreds, of millions.

He and his work were the subjects of unending analysis, gossip, dislike, adoration and rumor. He was a superstitious, sarcastic man, sometimes rotten to his children, often beastly to his women. He had contempt for women artists. His famous remark about women being “goddesses or doormats” has rendered him odious to feminists, but women tended to walk into both roles open-eyed and eagerly, for his charm was legendary. Whole cultural industries derived from his much mythologized virility. He was the Minotaur in a canvas-and-paper labyrinth of his own construction.

He was also politically lucky. Though to Nazis his work was the epitome of “degenerate art,” his fame protected him during the German occupation of Paris, where he lived; and after the war, when artists and writers were thought disgraced by the slightest affiliation with Nazism or fascism, Picasso gave enthusiastic endorsement to Joseph Stalin, a mass murderer on a scale far beyond Hitler’s, and scarcely received a word of criticism for it, even in cold war America.

No painter or sculptor, not even Michelangelo, had been as famous as this in his own lifetime. And it is quite possible that none ever will be again, now that the mandate to set forth social meaning, to articulate myth and generate widely memorable images has been so largely transferred from painting and sculpture to other media: photography, movies, television. Though Marcel Duchamp, that cunning old fox of conceptual irony, has certainly had more influence on nominally vanguard art over the past 30 years than Picasso, the Spaniard was the last great beneficiary of the belief that the language of painting and sculpture really mattered to people other than their devotees. And he was the first artist to enjoy the obsessive attention of mass media. He stood at the intersection of these two worlds. If that had not been so, his restless changes of style, his constant pushing of the envelope, would not have created such controversy – and thus such celebrity.

In today’s art world, a place without living culture heroes, you can’t even imagine such a protean monster arising. His output was vast. This is not a virtue in itself – only a few paintings by Vermeer survive, and fewer still by the brothers Van Eyck, but they are as firmly lodged in history as Picasso ever was or will be. Still, Picasso’s oeuvre filled the world, and he left permanent marks on every discipline he entered. His work expanded fractally, one image breeding new clusters of others, right up to his death.

Moreover, he was the artist with whom virtually every other artist had to reckon, and there was scarcely a 20th century movement that he didn’t inspire, contribute to or – in the case of Cubism, which, in one of art history’s great collaborations, he co-invented with Georges Braque – beget. The exception, since Picasso never painted an abstract picture in his life, was abstract art; but even there his handprints lay everywhere – one obvious example being his effect on the early work of American Abstract Expressionist painters, Arshile Gorky, Jackson Pollock and Willem de Kooning, among others.

Much of the story of modern sculpture is bound up with welding and assembling images from sheet metal, rather than modeling in clay, casting in bronze or carving in wood; and this tradition of the open constructed form rather than solid mass arose from one small guitar that Picasso snipped and joined out of tin in 1912. If collage – the gluing of previously unrelated things and images on a flat surface – became a basic mode of modern art, that too was due to Picasso’s Cubist collaboration with Braque. He was never a member of the Surrealist group, but in the 1920s and ‘30s he produced some of the scariest distortions of the human body and the most violently irrational, erotic images of Eros and Thanatos ever committed to canvas. He was not a realist painter/reporter, still less anyone’s official muralist, and yet Guernica remains the most powerful political image in modern art, rivaled only by some of the Mexican work of Diego Rivera.

Picasso was regarded as a boy genius, but if he had died before 1906, his 25th year, his mark on 20th century art would have been slight. The so-called Blue and Rose periods, with their wistful etiolated figures of beggars and circus folk, are not, despite their great popularity, much more than pendants to late 19th century Symbolism. It was the experience of modernity that created his modernism, and that happened in Paris. There, mass production and reproduction had come to the forefront of ordinary life: newspapers, printed labels, the overlay of posters on walls – the dizzily intense public life of signs, simultaneous, high-speed and layered. This was the cityscape of Cubism.

Picasso was not a philosopher or a mathematician (there is no “geometry” in Cubism), but the work he and Braque did between 1911 and 1918 was intuitively bound to the perceptions of thinkers like Einstein and Alfred North Whitehead: that reality is not figure and void, it is all relationships, a twinkling field of interdependent events. Long before any Pop artists were born, Picasso latched on to the magnetism of mass culture and how high art could refresh itself through common vernaculars. Cubism was hard to read, willfully ambiguous, and yet demotic too. It remains the most influential art dialect of the early 20th century. As if to distance himself from his imitators, Picasso then went to the opposite extreme of embracing the classical past, with his paintings of huge dropsical women dreaming Mediterranean dreams in homage to Corot and Ingres.

His “classical” mode, which he would revert to for decades to come, can also be seen as a gesture of independence. After his collaboration with Braque ended with his comment that “Braque is my wife” – words that were as disparaging to women as to Braque – Picasso remained a loner for the rest of his career. But a loner with a court and maitresses en titre. He didn’t even form a friendship with Matisse until both artists were old. His close relationships tended to be with poets and writers.

Though the public saw him as the archetypal modernist, he was disconnected from much modern art. Some of the greatest modern painters – Kandinsky, for instance, or Mondrian – saw their work as an instrument of evolution and human development. But Picasso had no more of a Utopian streak than did his Spanish idol, Goya. The idea that art evolved, or had any kind of historical mission, struck him as ridiculous. “All I have ever made,” he once said, “was made for the present and in the hope that it will always remain in the present. When I have found something to express, I have done it without thinking of the past or the future.” Interestingly, he also stood against the Expressionist belief that the work of art gains value by disclosing the truth, the inner being, of its author. “How can anyone enter into my dreams, my instincts, my desires, my thoughts … and above all grasp from them what I have been about – perhaps against my own will?” he exclaimed.

To make art was to achieve a tyrannous freedom from self-explanation. The artist’s work was mediumistic (“Painting is stronger than me, it makes me do what it wants”), solipsistic even. To Picasso, the idea that painting did itself through him meant that it wasn’t subject to cultural etiquette. None of the other fathers of Modernism felt it so strongly – not Matisse, not Mondrian, certainly not Braque.

In his work, everything is staked on sensation and desire. His aim was not to argue coherence but to go for the strongest level of feeling. He conveyed it with tremendous plastic force, making you feel the weight of forms and the tension of their relationships mainly by drawing and tonal structure. He was never a great colorist, like Matisse or Pierre Bonnard. But through metaphor, he crammed layers of meaning together to produce flashes of revelation. In the process, he reversed one of the currents of modern art. Modernism had rejected storytelling: what mattered was formal relationships. But Picasso brought it back in a disguised form, as a psychic narrative, told through metaphors, puns and equivalences.

The most powerful element in the story – at least after Cubism – was sex. The female nude was his obsessive subject. Everything in his pictorial universe, especially after 1920, seemed related to the naked bodies of women. Picasso imposed on them a load of feeling, ranging from dreamy eroticism (as in some of his paintings of his mistress Marie-Therese Walter in the ‘30s) to a sardonic but frenzied hostility, that no Western artist had made them carry before. He did this through metamorphosis, recomposing the body as the shape of his fantasies of possession and of his sexual terrors. Now the hidden and comparatively decorous puns of Cubism (the sound holes of a mandolin, for instance, becoming the mask of Pierrot) came out of their closet. “To displace,” as Picasso described the process, “to put eyes between the legs, or sex organs on the face. To contradict. Nature does many things the way I do, but she hides them! My painting is a series of cock-and-bull stories.”

There seems little doubt that the greatest of Picasso’s work came in the 30 years between Les Demoiselles d’Avignon (1907) and Guernica (1937). But of course he didn’t decline into triviality. Consistently through the war years and the ‘50s, and even now and then in the ‘60s and ‘70s, he would produce paintings and prints of considerable power. Sometimes they would be folded into series of variations on the old masters and 19th century painters he needed to measure himself against, such as Velazquez and Goya, or Poussin, Delacroix, Manet and Courbet. In his last years particularly, his production took on a manic and obsessive quality, as though the creative act (however repetitious) could forestall death. Which it could not. His death left the public with a nostalgia for genius that no talent today, in the field of painting, can satisfy.

Tenzing Norgay

The highest place on earth – Everest – has a distinct taste of tameness. Never really known as a tricky, technical climb, the real challenge of climbing Everest lay in solving the problems of its extreme altitude, sudden outbreaks of bad weather and inaccessibility. But these problems have been mitigated with high-tech equipment and clothing, satellite weather bulletins and a base camp that provides warm food, shelter and bottled oxygen. Today, climbing Everest seems like a trip to Disneyland with groups swarming like ants on a piece of cake every May.

Yet, every once in a while the mountain asserts itself, like in 1996 when eight people died on its slopes on one day to make it one of the worst disasters in Everest’s history. It was a grim warning: Everest can still win.

It’s incidents like these that put Tenzing Norgay’s and Edmund Hillary’s achievement in 1953 in the right perspective. Back then Everest was unreachable, tantalising, deadly. A mountain that had defeated 15 other expeditions. Some of the strongest climbers had perished while trying to climb it. The North Pole had been reached in 1909, the South Pole in 1911. But Everest – often called The Third Pole – had defied all man’s efforts until an impish Sherpa from Darjeeling and a gawky beekeeper from New Zealand came along. Their feat electrified the world, made them legends in every language – partly because they were men of heroic mould and represented the spirit of the times.

For Tenzing, born in Thami village of the Everest region – an 11th child of 13 children – it spelt a kind of wondrous stardom. For India, stumbling out of a postcolonial haze, Tenzing was like a virile new south Asian icon. Nehru personally befriended him and set him up as director of field training in the country’s first mountaineering institute in Darjeeling with the message: “Now you will make a thousand Tenzings”.

But there were pitfalls to this popularity. First, a kind of East-West rift was created by South Asian journalists who after speaking to Tenzing wrote up fictitious accounts of how the Sherpas virtually carried the sahibs up the peak. Then, both India and Nepal claimed Tenzing to be theirs. But the man from Thami was learning fast – he told the world: I was born in the womb of Nepal and raised in the lap of India.”

Tenzing was probably happiest away from the crowds and politics. The two things he held close to his heart were his community, the Sherpas and the love of climbing. For the Sherpas, of course, he was a champion, someone who had broken the shackles of an unprivileged life. But his bestknown legacy to Indian mountaineering is the Himalayan Mountaineering Institute (HMI), which he nurtured almost up to his death in 1986 – churning out superb mountaineers.

It was here that he was at his pragmatic best – using the skills he’d learned over a lifetime and passing them down to younger generations. And they were simple skills-those of courage, determination, resourcefulness and the ability to put up with hardship. Skills that had held him in good stead – and made him a figure as large as the mountains he loved.

William Lilly

William Lilly (April 30, 1602-1681), was a very well-known English astrologer and occultist during his time. Lilly was particularly adept at interpreting the astrological charts drawn up and used in horary astrology, as this was his specialty. He caused much controversy in 1666 for alledgedly predicting the Great Fire of London some 14 years before it happened.

Because of this many people thought that he in fact may have started it, but there is no evidence to support these claims. He was born in 1602 at Diseworth in Leicestershire, where his family were long-established yeomen. He received a basic classical education at the school of Ashby-de-la-Zouch, but makes a point of saying that his master never taught logic. At the age of seventeen, his father having fallen into poverty, he went to London and was employed in attendance on an elderly couple. His master, at his death in 1627, left him an annuity of $20; and, Lilly having soon afterwards married the widow, she, dying in 1633, left him property to the value of about $1000.

He now began to dabble in astrology, reading all the books on the subject he could fall in with, and occasionally trying his hand at unravelling mysteries by means of his art. The years 1642 and 1643 were devoted to a careful revision of all his previous reading, and in particular, having lighted on Valentine Naibod ’s Commentary on Alcabitius , he “seriously studied him and found him to be the profoundest author he ever met with.” About the same time he tells us that he ?did carefully take notice of every grandaction betwixt king and parliament, and did first then incline to believe that as all sublunary affairs depend on superior causes, so there, was: a possibility of discovering them by the configurations of the superior bodies.” And, having thereupon “made some essays,” he “found encouragement to proceed further, and ultimately framed to himself that method which he ever afterwards followed.”

Lilly’s most comprehensive book was published in 1647 and was entitled Christian Astrology. It was so large that it came in three separate volumes, and it remains popular even today and has never gone totally out-of-print. It is considered one of the classic texts for the study of traditional astrology from the Middle Ages.

He then began to issue his prophetical almanacs and other works, which met with serious attention from some of the most prominent members of the Long Parliament. If we may believe his statements, Lilly was on intimate terms with Bulstrode Whitlock , William Lenthall the speaker, Sir Philip Stapleton , Elias Ashmole and others. Even John Selden seems to have acknowledged him, and probably the chief difference between him and the mass of the community at the time was that, while others believed in the general truth of astrology, he ventured to specify the future events to which he referred.

Even from his own account, however, it is evident that he did not trust implicitly to the indications given by the aspects of the heavens, but kept his eyes and ears open for any information which might make his predictions safe. It appears that he had correspondents both at home and in foreign parts to keep him conversant with the probable current of affairs. Not a few of his exploits indicate rather the quality of a clever police detective than of a profound astrologer.

After the Restoration he very quickly fell into disrepute. His sympathy with the parliament, which his predictions had generally shown, was not calculated to bring him into royal favour. He came under the lash of Butler, who, making allowance for some satiric exaggeration, has given in the character of Sidrophel a probably not very incorrect picture of the man; and, having by this time amassed a tolerable fortune, he bought a small estate at Hersham in Surrey, to which he retired, and where he diverted the exercise of his peculiar talents to the practice of medicine. He died in 1681.

Lilly’s life of himself, published after his death, is still worth looking into as a remarkable record of credulity. So lately as 1852 a prominent London publisher put forth a new edition of Lilly’s Christian Astrology, “with numerous emendations adapted to the improved state of the science.” This entry was originally from the 1911 Encyclopedia Britannica.

Enrico fermi

Enrico Fermi (September 29, 1901 – November 28, 1954) was an Italian physicist most noted for his work on beta decay, the development of the first nuclear reactor, and for the development of quantum theory. Fermi won the 1938 Nobel Prize in Physics for his work on nuclear fission.

Early years and education

Enrico Fermi was born in Rome, Italy in 1901. When his brother Giulio died during a minor surgery in 1915, 14-year-old Enrico threw himself into the study of physics as a way of coping with his grief. According to his later recollection, he would walk each day in front of the hospital where Giulio had died, until he could look back at the event with detachment.

A friend of the family, Adolfo Amidei, guided the young Fermi’s study of algebra, trigonometry, analytic geometry, calculus and theoretical mechanics. Amidei also suggested Fermi attend not a university in Rome but to apply to the prestigious “Scuola Normale Superiore” of Pisa, a special university-college for selected gifted students in 1918. Fermi did especially well, and the examiner at the Scuola Normale thought the 17-year-old Fermi’s competition essay worthy of a doctoral exam. He graduated with a doctorate in 1922, and the next year left for the University of Göttingen, then the center of the quantum physics world. Fermi became unhappy, though, with what he saw as an excessively formal theoretical style under the influence of Max Born, and so after six months left for the University of Leiden, Netherlands, to work with Paul Ehrenfest. While there, he also met Albert Einstein.

Physics in Rome

Fermi took a professorship in Rome (the first for theoretical physics in Italy, created for him by professor Orso Maria Corbino, director of the Institute of Physics). Corbino worked a lot to help Fermi in selecting his team, which soon was joined by notable minds like Edoardo Amaldi, Bruno Pontecorvo, Franco Rasetti and Emilio Segrè. For the theoretical studies only, Ettore Majorana also took part in what was soon nicknamed “the boys of Via Panisperna” (after the name of the road in which the Institute had its labs – now in the main campus in Roma I).

The group went on with its now famous experiments, but in 1933 Rasetti left Italy for Canada and the United States, Pontecorvo went to France, Segrè left to teach in Palermo.

During their time in Rome, Fermi and his group made important contributions to many practical and theoretical aspects of physics. Some of these include Fermi-Dirac statistics, the theory of beta decay, and the discovery of slow neutrons, which was to prove pivotal for the working of nuclear reactors.

Mussolini and the Manhattan Project

Fermi remained in Rome until 1938.

In 1938, Fermi won the Nobel Prize in Physics for his “demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons”.

After Fermi received the prize in Stockholm, he, his wife Laura, and their children emigrated to New York. By this time, the Fascist government in Italy had instituted anti-Semitic laws, and Fermi’s wife, Laura Capon, was Jewish. Soon after his arrival in New York, Fermi began working at Columbia University.

At Columbia, Fermi verified the initial nuclear fission experiment of Hahn and Fritz Strassman (with the help of Booth and Dunning). Fermi then began studies that led to the construction of the first nuclear pile.

Fermi recalled the beginning of the project in a speech given in 1954 when he retired as President of the American Physical Society:
“I remember very vividly the first month, January, 1939, that I started working at the Pupin Laboratories because things began happening very fast. In that period, Niels Bohr was on a lecture engagement at the Princeton University and I remember one afternoon Willis Lamb came back very excited and said that Bohr had leaked out great news.

The great news that had leaked out was the discovery of fission and at least the outline of its interpretation. Then, somewhat later that same month, there was a meeting in Washington where the possible importance of the newly discovered phenomenon of fission was first discussed in semi-jocular earnest as a possible source of nuclear power.”

After the famous letter signed by Albert Einstein (transcribed by Leó Szilárd) to President Franklin D. Roosevelt in 1939, the Navy awarded Columbia University the first Atomic Energy funding of US$ 6,000. The money was used in studies which led to the first nuclear reactor—a massive “pile” of graphite bricks and uranium fuel which went critical on December 2, 1942, at the University of Chicago. This experiment was a landmark in the quest for energy, and it was typical of Fermi’s brilliance. Every step had been carefully planned, every calculation meticulously done by him. When man first achieved the first self sustained nuclear chain reaction, a coded phone call was made to one of the leaders of the Manhattan Project, James Conant: ‘The Italian navigator has landed in the new world… The natives were very friendly’.

The chain-reacting pile was important not only for its help in assessing the properties of fission—needed for understanding the internal workings of an atomic bomb—but because it would serve as a pilot plant for the massive reactors which would be created in Hanford, Washington, which would then be used to “breed” the plutonium needed for the bombs used at the Trinity test and Nagasaki. Eventually Fermi and Szilard’s reactor work was folded into the Manhattan Project.

He became a naturalized citizen of the United States of America in 1944.

Post-war work

In Fermi’s 1954 address to the APS he also said, “Well, this brings us to Pearl Harbor. That is the time when I left Columbia University, and after a few months of commuting between Chicago and New York, eventually moved to Chicago to keep up the work there, and from then on, with a few notable exceptions, the work at Columbia was concentrated on the isotope separation phase of the atomic energy project, initiated by Booth, Dunning and Urey about 1940”.

Fermi was widely regarded as the only physicist of the twentieth century who excelled both theoretically and experimentally (see link below in ‘References’). The well-known historian of physics, C. P. Snow, says about him, “If Fermi had been born a few years earlier, one could well imagine him discovering Rutherford’s atomic nucleus, and then developing Bohr’s theory of the hydrogen atom. If this sounds like hyperbole, anything about Fermi is likely to sound like hyperbole”. Fermi’s ability and success stemmed as much from his appraisal of the art of the possible, as from his innate skill and intelligence. He disliked complicated theories, and while he had great mathematical ability, he would never use it when the job could be done much more simply. He was famous for getting quick and accurate answers to problems which would stump other people.

An instance of this was seen during the first atomic bomb test in New Mexico on July 16, 1945. As the blast wave reached him, Fermi dropped bits of paper. By measuring the distance they were blown, he could compare to a previously computed table and thus estimate the bomb energy yield. He estimated 10 kilotons of TNT, the measured result was 18.6. (Rhodes, page 674). Later on, this method of getting approximate and quick answers through back of the envelope calculations became informally known as the ‘Fermi method’.

Fermi’s most disarming trait was his great modesty, and his ability to do any kind of work, whether creative or routine. It was this quality that made him popular and liked among people of all strata, from other Nobel Laureates to technicians.

Henry DeWolf Smyth, who was Chairman of the Princeton Physics department, had once invited Fermi over to do some experiments with the Princeton cyclotron. Walking into the lab one day, Smyth saw the distinguished scientist helping a graduate student move a table, under another student’s directions! Another time, a Du Pont executive made a visit to see him at Columbia. Not finding him either in his lab or his office, the executive was surprised to find the Nobel Laureate in the machine shop, cutting sheets of tin with a big pair of shears.

When he submitted his famous paper on beta decay to the prestigious journal Nature, the journal’s editor turned it down because “it contained speculations which were too remote from reality”. Thus, Fermi saw the theory published in Italian and in German before it was published in English.

He never forgot this experience of being ahead of his time, and used to tell his protégés: “Never be first; try to be second”.

On November 28, 1954, Fermi died of stomach cancer in Chicago and was interred there in Oak Woods Cemetery. He was 53. As Eugene Wigner wrote: “Ten days before Fermi had passed away he told me, ‘I hope it won’t take long.’ He had reconciled himself perfectly to his fate”.

Jonas Salk

Jonas Salk (October 28, 1914 – June 23, 1995) is the discoverer/inventor of the eponymous Salk vaccine (see polio vaccine). Salk was born in New York City. He spent his career as a professor at the University of Pittsburgh. Later in his career, Salk devoted much of his energy to developing an AIDS vaccine.

His vaccine was one of the first successful attempts at immunization against a virus, specifically the Poliomyelitis virus. The vaccine provides the recipient with immunity against Polio, and was seminal in the near eradication of a once widely-feared disease. Salk used a "killed" virus technique which required the patient to be injected with the vaccine. The patient would develop immunity to the live disease due to the body’s earlier reaction to the killed virus. By contrast, Albert Sabin developed a "live" vaccine which was released in 1961, and which could be taken orally.

Unlike some scientists who sought wealth or fame accompanying their innovations, Salk stated "’Who owns my polio vaccine? The people! Could you patent the sun?". The Salk Institute in La Jolla, California was named in Jonas Salk’s honor.

Galileo Galilei

Galileo Galilei (Pisa, February 15, 1564 – Arcetri, January 8, 1642), was a Tuscan astronomer, philosopher, and physicist who is closely associated with the scientific revolution. His achievements include improving the telescope, a variety of astronomical observations, the first law of motion, and supporting Copernicanism effectively. He has been referred to as the “father of modern astronomy,” as the “father of modern physics,” and as “father of science.” His experimental work is widely considered complementary to the writings of Francis Bacon in establishing the modern scientific method. Galileo’s career coincided with that of Johannes Kepler. The work of Galileo is considered to be a significant break from that of Aristotle. In addition, his conflict with the Roman Catholic Church is taken as a major early example of the conflict of authority and freedom of thought, particularly with science, in Western society.

Early career

Galileo was born in Pisa, Italy, as the son of Vincenzo Galilei, a mathematician and musician.

He attended the University of Pisa, but was forced to “drop out” for financial reasons. However, he was offered a position on its faculty in 1589 and taught mathematics. Soon after, he moved to the University of Padua, and served on its faculty teaching geometry, mechanics, and astronomy until 1610. During this time he explored science and made many landmark discoveries.

Experimental science

In the pantheon of the scientific revolution, Galileo takes a high position because of his pioneering use of quantitative experiments with results analyzed mathematically. There was no tradition of such methods in European thought at that time; the great experimentalist who immediately preceded Galileo, William Gilbert, did not use a quantitative approach. However, Galileo’s father, Vincenzo Galilei, had performed experiments in which he discovered what may be the oldest known non-linear relation in physics, between the tension and the pitch of a stretched string. Galileo also contributed to the rejection of blind allegiance to authority (like the Church) or other thinkers (such as Aristotle) in matters of science and to the separation of science from philosophy or religion. These are the primary justifications for his description as “father of science.”

In the 20th century some authorities challenged the reality of Galileo’s experiments, in particular the distinguished French historian of science Alexandre Koyre. The experiments reported in Two New Sciences to determine the law of acceleration of falling bodies, for instance, required accurate measurements of time, which appeared to be impossible with the technology of the 1600s. According to Koyre, the law was arrived at deductively, and the experiments were merely illustrative thought experiments.

Later research, however, has validated the experiments. The experiments on falling bodies (actually rolling balls) were replicated using the methods described by Galileo (Settle, 1961), and the precision of the results was consistent with Galileo’s report. Later research into Galileo’s unpublished working papers from as early as 1604 clearly showed the reality of the experiments and even indicated the particular results that led to the time-squared law (Drake, 1973).

Astronomy

Although the popular idea of Galileo inventing the telescope is inaccurate, he was one of the first people to use the telescope to observe the sky. Based on sketchy descriptions of telescopes invented in the Netherlands in 1608, Galileo made one with about 8x magnification, and then made improved models up to about 20x. On August 25, 1609, he demonstrated his first telescope to Venetian lawmakers. His work on the device also made for a profitable sideline with merchants who found it useful for their shipping businesses. He published his initial telescopic astronomical observations in March 1610 in a short treatise entitled Sidereus Nuncius (Sidereal Messenger).

On January 7, 1610 Galileo discovered three of Jupiter’s four largest satellites (moons): Io, Europa, and Callisto. Ganymede he discovered four nights later. He determined that these moons were orbiting the planet since they would occasionally disappear; something he attributed to their movement behind Jupiter. He made additional observations of them in 1620. Later astronomers overruled Galileo’s naming of these objects, changing his Medicean stars to Galilean satellites. The demonstration that a planet had smaller planets orbiting it was problematic for the orderly, comprehensive picture of the geocentric model of the universe, in which everything circled around the Earth.

Galileo noted that Venus exhibited a full set of phases like the Moon. The heliocentric model of the solar system developed by Copernicus predicted that all phases would be visible since the orbit of Venus around the Sun would cause its illuminated hemisphere to face the Earth when it was on the opposite side of the Sun and to face away from the Earth when it was on the Earth-side of the Sun.

rast, the geocentric model of Ptolemy predicted that only crescent and new phases would be seen, since Venus was thought to remain between the Sun and Earth during its orbit around the Earth. Galileo’s observation of the phases of Venus proved that Venus orbited the Sun and lent support to (but did not prove) the heliocentric model.

Galileo was one of the first Europeans to observe sunspots, although there is evidence that Chinese astronomers had done so before. The very existence of sunspots showed another difficulty with the perfection of the heavens as assumed in the older philosophy. And the annual variations in their motions, first noticed by Francesco Sizzi, presented great difficulties for either the geocentric system or that of Tycho Brahe. A dispute over priority in the discovery of sunspots led to a long and bitter feud with Christoph Scheiner; in fact, there can be little doubt that both of them were beaten by David Fabricius and his son Johannes.

He was the first to report lunar mountains and craters, whose existence he deduced from the patterns of light and shadow on the Moon’s surface. He even estimated the mountains’ heights from these observations. This led him to the conclusion that the Moon was “rough and uneven, and just like the surface of the Earth itself”, and not a perfect sphere as Aristotle had claimed.

Galileo observed the Milky Way, previously believed to be nebulous, and found it to be a multitude of stars, packed so densely that they appeared to be clouds from Earth. He also located many other stars too distant to be visible with the naked eye.

Galileo observed the planet Neptune in 1611, but took no particular notice of it; it appears in his notebooks as one of many unremarkable dim stars.

Physics

Galileo’s theoretical and experimental work on the motions of bodies, along with the largely independent work of Kepler and Rene Descartes, was a precursor of the Classical mechanics developed by Sir Isaac Newton. He was a pioneer, at least in the European tradition, in performing rigorous experiments and insisting on a mathematical description of the laws of nature.

One of the most famous stories about Galileo is that he dropped balls of different masses from the Leaning Tower of Pisa to demonstrate that their velocity of descent was independent of their mass (excluding the limited effect of air resistance). This was contrary to what Aristotle had taught: that heavy objects fall faster than lighter ones, in direct proportion to weight. Though the story of the tower first appeared in a biography by Galileo’s pupil Vincenzo Viviani, it is not now generally accepted as true. However, Galileo did perform experiments involving rolling balls down inclined planes, which proved the same thing: falling or rolling objects (rolling is a slower version of falling) are accelerated independently of their mass.

He determined the correct mathematical law for acceleration: the total distance covered, starting from rest, is proportional to the square of the time (This law is regarded as a predecessor to the many later scientific laws expressed in mathematical form.). He also concluded that objects retain their velocity unless a force —often friction— acts upon them, refuting the accepted Aristotelian hypothesis that objects “naturally” slow down and stop unless a force acts upon them. This principle was incorporated into Newton’s laws of motion (1st law).

Galileo also noted that a pendulum’s swings always take the same amount of time, independently of the amplitude. While Galileo believed this equality of period to be exact, it is only an approximation appropriate to small amplitudes. It is good enough to regulate a clock, however, as Galileo may have been the first to realize. (See Technology below)

In the early 1600s, Galileo and an assistant tried to measure the speed of light.

Good on different hilltops, each holding a shuttered lantern. Galileo would open his shutter, and, as soon as his assistant saw the flash, he would open his shutter. At a distance of less than a mile, Galileo could detect no delay in the round-trip time greater than when he and the assistant were only a few yards apart. While he could reach no conclusion on whether light propagated instantaneously, he recognized that the distance between the hilltops was perhaps too small for a good measurement.

Galileo is lesser known for, yet still credited with being one of the first to understand sound frequency. After scraping a chisel at different speeds, he linked the pitch of sound to the spacing of the chisel’s skips (frequency).

In his 1632 Dialogue Galileo presented a physical theory to account for tides, based on the motion of the Earth. If correct, this would have been a strong argument for the reality of the Earth’s motion. (The original title for the book, in fact, described it as a dialogue on the tides; the reference to tides was removed by order of the Inquisition.) His theory gave the first insight into the importance of the shapes of ocean basins in the size and timing of tides; he correctly accounted, for instance, for the negligible tides halfway along the Adriatic Sea compared to those at the ends. As a general account of the cause of tides, however, his theory was a failure.

Mathematics

While Galileo’s application of mathematics to experimental physics was innovative, his mathematical methods were the standard ones of the day. The analyses and proofs relied heavily on the Eudoxian theory of proportion, as set forth in the fifth book of Euclid’s Elements. This theory had become available only a century before, thanks to accurate translations by Tartaglia and others; but by the end of Galileo’s life it was being superseded by the algebraic methods of Descartes, which a modern finds incomparably easier to follow.

Galileo produced one piece of original and even prophetic work in mathematics: Galileo’s paradox, which shows that there are as many perfect squares as there are whole numbers, even though most numbers are not perfect squares. Such seeming contradictions were brought under control 250 years later in the work of Georg Cantor.

Technology

Galileo made a few contributions to what we now call technology as distinct from pure physics, and suggested others. This is not the same distinction as made by Aristotle, who would have considered all Galileo’s physics as techne or useful knowledge, as opposed to episteme, or philosophical investigation into the causes of things.

In 1595-1598, Galileo devised and improved a “Geometric and Military Compass” suitable for use by gunners and surveyors. This expanded on earlier instruments designed by Niccolo Tartaglia and Guidobaldo del Monte. For gunners, it offered, in addition to a new and safer way of elevating cannons accurately, a way of quickly computing the charge of gunpowder for cannonballs of different sizes and materials. As a geometric instrument, it enabled the construction of any regular polygon, computation of the area of any polygon or circular sector, and a variety of other calculations.

About 1606-1607 (or possibly earlier), Galileo made a thermometer, using the expansion and contraction of air in a bulb to move water in an attached tube.

In 1609, Galileo was among the first to use a refracting telescope as an instrument to observe stars, planets or moons.

In 1610, he used a telescope as a compound microscope, and he made improved microscopes in 1623 and after.

This appears to be the first clearly documented use of the compound microscope.

In 1612, having determined the orbital periods of Jupiter’s satellites, Galileo proposed that with sufficiently accurate knowledge of their orbits one could use their positions as a universal clock, and this would make possible the determination of longitude. He worked on this problem from time to time during the remainder of his life; but the practical problems were severe. The method was first successfully applied by Giovanni Domenico Cassini in 1681 and was later used extensively for land surveys; for navigation, the first practical method was the chronometer of John Harrison.

In his last year, when totally blind, he designed an escapement mechanism for a pendulum clock. The first fully operational pendulum clock was made by Christiaan Huygens in the 1650s.

He created sketches of various inventions, such as a candle and mirror combination to reflect light throughout a building, an automatic tomato picker, a pocket comb that doubled as an eating utensil, and what appears to be a ballpoint pen.

Church controversy

Galileo was a practicing Catholic, yet his writings on Copernican heliocentrism disturbed some in the Catholic Church who believed in a geocentric model of the solar system. They argued that heliocentrism was in direct contradiction of the Bible, at least as interpreted by the church fathers, and the highly revered ancient writings of Aristotle and Plato (especially among the Dominican order, facilitators of the Inquisition).

The geocentric model was generally accepted at the time for several reasons. By the time of the controversy, the Catholic Church had largely abandoned the Ptolemaic model for the Tychonian model in which the Earth was at the center of the Universe, the Sun revolved around the Earth and the other planets revolved around the Sun. This model is geometrically equivalent to the Copernican model and had the extra advantage that it predicted no parallax of the stars, an effect that was impossible to detect with the instruments of the time. In the view of Tycho and many others, this model explained the observable data of the time better than the geocentric model did. (That inference is valid, however, only on the assumption that no very small effect had been missed: that the instruments of the time were absolutely perfect, or that the Universe could not be much larger than was generally believed at the time. As to the latter, belief in the large, possibly infinite, size of the Universe was part of the heretical beliefs for which Giordano Bruno had been burned at the stake in 1600.)

An understanding of the controversies, if it is even possible, requires attention not only to the politics of religious organizations but to those of academic philosophy. Before Galileo had trouble with the Jesuits and before the Dominican friar Caccini denounced him from the pulpit, his employer heard him accused of contradicting Scripture by a professor of philosophy, Cosimo Boscaglia, who was neither a theologian nor a priest. The first to defend Galileo was a Benedictine abbot, Benedetto Castelli, who was also a professor of mathematics and a former student of Galileo’s. It was this exchange that led Galileo to write the Letter to Grand Duchess Christina. (Castelli remained Galileo’s friend, visiting him at Arcetri near the end of Galileo’s life, after months of effort to get permission from the Inquisition to do so.)

However, real power lay with the Church, and Galileo’s arguments were most fiercely fought on the religious level. The late nineteenth and early twentieth century historian Andrew Dickson White wrote from an anti-clerical perspective:
The war became more and more bitter. The Dominican Father Caccini preached a sermon from the text, “Ye men of Galilee, why stand ye gazing up into heaven?” and this wretched pun upon the great astronomer’s name ushered in sharper weapons; for, before Caccini ended, he insisted that “geometry is of the devil,” and that “mathematicians should be banished as the authors of all heresies.” The Church authorities gave Caccini promotion.
Father Lorini proved that Galileo’s doctrine was not only heretical but “atheistic,” and besought the Inquisition to intervene.

hop of Fiesole screamed in rage against the Copernican system, publicly insulted Galileo, and denounced him to the Grand-Duke. The Archbishop of Pisa secretly sought to entrap Galileo and deliver him to the Inquisition at Rome. The Archbishop of Florence solemnly condemned the new doctrines as unscriptural; and Paul V, while petting Galileo, and inviting him as the greatest astronomer of the world to visit Rome, was secretly moving the Archbishop of Pisa to pick up evidence against the astronomer.

But by far the most terrible champion who now appeared was Cardinal Robert Bellarmine, one of the greatest theologians the world has known. He was earnest, sincere, and learned, but insisted on making science conform to Scripture. The weapons which men of Bellarmin’s stamp used were purely theological. They held up before the world the dreadful consequences which must result to Christian theology were the heavenly bodies proved to revolve about the Sun and not about the Earth.

Their most tremendous dogmatic engine was the statement that “his pretended discovery vitiates the whole Christian plan of salvation.” Father Lecazre declared “it casts suspicion on the doctrine of the incarnation.” Others declared, “It upsets the whole basis of theology. If the Earth is a planet, and only one among several planets, it can not be that any such great things have been done specially for it as the Christian doctrine teaches. If there are other planets, since God makes nothing in vain, they must be inhabited; but how can their inhabitants be descended from Adam? How can they trace back their origin to Noah’s ark? How can they have been redeemed by the Saviour?” Nor was this argument confined to the theologians of the Roman Church; Melanchthon, Protestant as he was, had already used it in his attacks on Copernicus and his school. (White, 1898; online text)

In 1616, the Inquisition warned Galileo not to hold or defend the hypothesis asserted in Copernicus’s On the Revolutions, though it has been debated whether he was admonished not to “teach in any way” the heliocentric theory. When Galileo was tried in 1633, the Inquisition was proceeding on the premise that he had been ordered not to teach it at all, based on a paper in the records from 1616; but Galileo produced a letter from Cardinal Bellarmine that showed only the “hold or defend” order.

Mozart

Wolfgang Amadeus Mozart (January 26, 1756 – December 5, 1791) is considered one of the greatest composers of European classical music (or more specifically, Viennese Classical music). He composed an astonishingly large amount of chamber, symphonic, religious, and operatic works as well as works for various solo instruments- most notably the keyboard. Although highly unappreciated during his lifetime, Mozart was admired by later composers and his works are frequently played today.

Life Family and early childhood years

Mozart was born in Salzburg, which is now in modern-day Austria but at the time was the capital of a small independent Archbishopric within the Holy Roman Empire, to his father Leopold and his mother Anna Maria Pertl Mozart. He was baptized on the day after his birth at St. Rupert’s Cathedral as Johannes Chrysostomus Wolfgangus Theophilus Mozart but his name changed many times over the years.

The years of travel

Mozart’s musical ability started to become apparent when he was a toddler. He was the son of Leopold Mozart, one of Europe’s leading musical pedagogues, whose influential textbook Versuch einer grundlichen Violinschule (“Essay on the fundamentals of violin playing”) was published in 1756, the same year as Mozart’s birth. Mozart received intensive musical training from his father, including instruction in both the piano and violin. Musically, he developed very rapidly and began to compose his own works at the age of five.

Leopold soon realized that he could earn a substantial income by showcasing his son as a Wunderkind in the courts of Europe. Mozart gained fame as a prodigy capable of playing blindfolded or with his hands behind his back, and for his ability to improvise wonderfully and at length on difficult passages he had never seen before. His older sister, Maria Anna, nicknamed “Nannerl”, was a talented pianist and often accompanied her brother on Leopold’s tours. Mozart wrote a number of piano pieces, in particular duets and duos, to play with her. On one occasion when Mozart became ill, Leopold expressed more concern over the loss of income than over his son’s well-being. Constant travel and cold weather may have contributed to his subsequent illness later in life.

During his formative years, Mozart completed several journeys throughout Europe, beginning with an exhibition in 1762 at the Court of the Elector of Bavaria in Munich, then in the same year at the Imperial Court in Vienna. A long concert tour soon followed (three and a half years), which took him with his father to the courts of Munich, Mannheim, Paris, London, The Hague, again to Paris, and back home via Zurich, Donaueschingen, and Munich.

ent to Vienna again in late 1767 and remained there until December 1768. After one year spent in Salzburg, three trips to Italy followed: from December 1769 to March 1771, from August to December 1771, and from October 1772 to March 1773. During the first of these trips, Mozart met G.B. Martini in Bologna, and was accepted as a member of the famous Accademia Filarmonica. A highlight of the Italian journey, which is now an almost legendary tale, occurred when he heard Gregorio Allegri’s Miserere once in performance, then wrote it out in its entirety from memory, only returning a second time to correct minor errors.

In September of 1777, accompanied only by his mother, Mozart began a tour of Europe that included Munich, Mannheim, and Paris, where his mother died. During his trips, Mozart met a great number of musicians and acquainted himself with the works of other great composers. He came to know the work of J.S. Bach and G.F. Handel; and he met Joseph Haydn, who declared to Leopold, “Before God and as an honest man I tell you that your son is the greatest composer known to me either in person or by name. He has taste and, what is more, the most profound knowledge of composition.”. Even non-musicians caught Mozart’s attention: he was so taken by the sound created by Benjamin Franklin’s glass harmonica that he composed several pieces of music for it.

Mozart in Vienna

In 1781 Mozart visited Vienna in the company of his employer, the harsh Prince-Archbishop Colloredo, and fell out with him. According to Mozart’s own testimony, he was dismissed literally “with a kick in the seat of the pants.” Despite this, Mozart chose to settle and develop his career in Vienna after its aristocracy began to take an interest in him.

On August 4, 1782, he married Constanze Weber (also spelled “Costanze”) against his father’s wishes. He and Constanze had six children, of whom only two survived infancy. Neither of these two, Karl Thomas (1784-1858) or Franz Xaver Wolfgang (later a minor composer himself; 1791-1844), married or had children.

1782 was an auspicious year for Mozart’s career; his opera The Abduction from the Seraglio was a great success, and he began a series of concerts at which he premiered his own piano concertos as conductor and soloist.

As an adult, Mozart, influenced by the ideas of the eighteenth century European Enlightenment, became a Freemason and worked fervently and successfully to convert his father before the latter’s death in 1787. His last opera, The Magic Flute, includes Masonic themes and allegory. He was in the same Masonic Lodge as Joseph Haydn.

Mozart’s life was fraught with financial difficulty and illness. Often, he received no payment for his work, and what sums he did receive were quickly consumed by his extravagant lifestyle.

Mozart spent the year 1786 in Vienna in an apartment which may be visited today at Domgasse 5 behind St. Stephen’s Cathedral; it was here that Mozart composed Le nozze di Figaro. He then followed this up in 1787 with one of his greatest works, Don Giovanni.

Illness and death

Mozart’s final illness and death are difficult scholarly topics, obscured by Romantic legends and replete with conflicting theories. Scholars disagree about the course of decline in Mozart’s health – particularly at what point Mozart became aware of his impending death, and whether this awareness influenced his final works. The Romantic view holds that Mozart declined gradually, and that his outlook and compositions paralleled this decline. In opposition to this, some contemporary scholarship points out correspondence from Mozart’s final year indicating that he was in good cheer, as well as evidence that Mozart’s death was sudden and a shock to his family and friends.

The actual cause of Mozart’s death is also a matter of conjecture. His death record listed “hitziges Frieselfieber” (“severe miliary fever”), a description that does not suffice to identify the cause as it would be diagnosed in modern medicine. In fact, dozens of theories have been proposed, which include trichinosis, mercury poisoning, and rheumatic fever. The contemporary practice of bleeding medical patients is also cited as a contributing cause.

Mozart died around 1 a.m. on December 5, 1791 while he was working on his final composition, the Requiem (unfinished when he died).

According to popular legend, Mozart was penniless and forgotten when he died, and was buried in a pauper’s grave. In fact, though he was no longer as fashionable in Vienna as he had once been, he continued to have a well-paid job at court and receive substantial commissions from more distant parts of Europe, Prague in particular. Many of his begging letters survive, but they are evidence not so much of poverty as of his habit of spending more than he earned. He was not buried in a “mass grave”, but in a regular communal grave according to the 1783 laws.

In 1809, Constanze married Danish diplomat Georg Nikolaus von Nissen (1761-1826). Being a fanatic of Mozart, he edited vulgar passages out of many of the composer’s letters and wrote a Mozart biography.

Works, musical style, and innovations

Mozart was a prolific composer and wrote in many genres. Among his best works are his operas, piano concertos, symphonies, string quartets, and string quintets. Mozart also wrote a great deal of music for solo piano, chamber music, and religious music including masses. He also composed many dances, divertimenti, and other forms of light entertainment.

Influence

Many important composers since Mozart’s time have worshipped or at least been in awe of Mozart. Rossini averred, “He is the only musician who had as much knowledge as genius, and as much genius as knowledge.” Beethoven told his pupil Ries that he (Beethoven) would never be able to think of a melody as great as a certain one in the first movement of Mozart’s Piano Concerto No. 24. Beethoven also paid homage to Mozart by writing sets of variations on several of his themes: for example, the two sets of variations for cello and piano on themes from Mozart’s Magic Flute, and cadenzas to several of Mozart’s piano concertos, most notably the Piano Concerto No. 20 K. 466. After the only meeting between the two composers, Mozart noted that Beethoven would “give the world something to talk about.” As well, Tchaikovsky wrote his Mozartiana in praise of him; and Mahler died with the word “Mozart” on his lips.

The Kochel catalog

In the decades following Mozart’s death there were several attempts to catalog his compositions, but it was not until 1862 that Ludwig von Kochel succeeded in this enterprise. Many of his famous works are referred to now by only their Kochel catalog number; for example, the Piano Concerto in A major is often referred to simply as “K. 488” or “KV 488”. The catalogue has undergone six revisions since.

Myths

Mozart is unusual among composers for being the subject of many legends and myths. An example is the story that Mozart composed his Requiem with the belief it was for himself. Some of these myths may be based in fact, but sorting out fabrications from real events is a vexing and continuous task for Mozart scholars. Dramatists and screenwriters, free from responsibilities of scholarship, have found excellent material among these legends.

An especially popular case is the supposed rivalry between Mozart and Antonio Salieri, and, in some versions, the tale that it was poison received from the latter that provoked Mozart’s death; this is the subject of Aleksandr Pushkin’s play Mozart and Salieri, Nicolai Rimsky-Korsakov’s opera Mozart et Salieri, and Peter Shaffer’s play Amadeus. The last of these has been made into a feature-length film of the same name. Shaffer’s play attracted criticism for portraying Mozart as vulgar and loutish, a characterization felt by many to be unfairly exaggerated.

Shakuntala Devi

Shakuntala Devi (Born 1939 in Bangalore, India) is an Indian mathematician often referred to as a “human calculator”. She demonstrated the multiplication of two 13-digit numbers 7,686,369,774,870×2,465,099,745,779 picked at random by the Computer Department of Imperial College, London, on June 18, 1980 in 28 seconds. Her correct answer was 18,947,668,177,995,426,462,773,730.

In 1977, she extracted the 23rd root of a 201-digit number mentally. At the age of six, Shakuntala demonstrated her talents at the University of Mysore, before a huge gathering of professors and students of higher studies in mathematics. With lightning rapidity and precision, she declared right answers mentally working out calculations for the most complicated problems. At the age of eight, she thrilled the learned audience of Annamalai University.

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William Lilly

William Lilly (April 30, 1602-1681), was a very well-known English astrologer and occultist during his time. Lilly was particularly adept at interpreting the astrological charts drawn up and used in horary astrology, as this was his specialty. He caused much controversy in 1666 for alledgedly predicting the Great Fire of London some 14 years before it happened.

Because of this many people thought that he in fact may have started it, but there is no evidence to support these claims. He was born in 1602 at Diseworth in Leicestershire, where his family were long-established yeomen. He received a basic classical education at the school of Ashby-de-la-Zouch, but makes a point of saying that his master never taught logic. At the age of seventeen, his father having fallen into poverty, he went to London and was employed in attendance on an elderly couple. His master, at his death in 1627, left him an annuity of $20; and, Lilly having soon afterwards married the widow, she, dying in 1633, left him property to the value of about $1000.

He now began to dabble in astrology, reading all the books on the subject he could fall in with, and occasionally trying his hand at unravelling mysteries by means of his art. The years 1642 and 1643 were devoted to a careful revision of all his previous reading, and in particular, having lighted on Valentine Naibod ’s Commentary on Alcabitius , he “seriously studied him and found him to be the profoundest author he ever met with.” About the same time he tells us that he ?did carefully take notice of every grandaction betwixt king and parliament, and did first then incline to believe that as all sublunary affairs depend on superior causes, so there, was: a possibility of discovering them by the configurations of the superior bodies.” And, having thereupon “made some essays,” he “found encouragement to proceed further, and ultimately framed to himself that method which he ever afterwards followed.”

Lilly’s most comprehensive book was published in 1647 and was entitled Christian Astrology. It was so large that it came in three separate volumes, and it remains popular even today and has never gone totally out-of-print. It is considered one of the classic texts for the study of traditional astrology from the Middle Ages.

He then began to issue his prophetical almanacs and other works, which met with serious attention from some of the most prominent members of the Long Parliament. If we may believe his statements, Lilly was on intimate terms with Bulstrode Whitlock , William Lenthall the speaker, Sir Philip Stapleton , Elias Ashmole and others. Even John Selden seems to have acknowledged him, and probably the chief difference between him and the mass of the community at the time was that, while others believed in the general truth of astrology, he ventured to specify the future events to which he referred.

Even from his own account, however, it is evident that he did not trust implicitly to the indications given by the aspects of the heavens, but kept his eyes and ears open for any information which might make his predictions safe. It appears that he had correspondents both at home and in foreign parts to keep him conversant with the probable current of affairs. Not a few of his exploits indicate rather the quality of a clever police detective than of a profound astrologer.

After the Restoration he very quickly fell into disrepute. His sympathy with the parliament, which his predictions had generally shown, was not calculated to bring him into royal favour. He came under the lash of Butler, who, making allowance for some satiric exaggeration, has given in the character of Sidrophel a probably not very incorrect picture of the man; and, having by this time amassed a tolerable fortune, he bought a small estate at Hersham in Surrey, to which he retired, and where he diverted the exercise of his peculiar talents to the practice of medicine. He died in 1681.

Lilly’s life of himself, published after his death, is still worth looking into as a remarkable record of credulity. So lately as 1852 a prominent London publisher put forth a new edition of Lilly’s Christian Astrology, “with numerous emendations adapted to the improved state of the science.”

This entry was originally from the 1911 Encyclopedia Britannica.