Contribution Of Mathematics Quotes

The contribution of mathematics, and of people, is not computation but intelligence.

What drove me? I think most creative people want to express appreciation for being able to take advantage of the work that's been done by others before us. I didn't invent the language or mathematics I use. I make little of my own food, none of my own clothes. Everything I do depends on other members of our species and the shoulders that we stand on. And a lot of us want to contribute something back to our species and to add something to the flow. It's about trying to express something in the only way that most of us know how-because we can't write Bob Dylan songs or Tom Stoppard plays. We try to use the talents we do have to express our deep feelings, to show our appreciation of all the contributions that came before us, and to add something to that flow. That's what has driven me.

One of the most painful parts of teaching mathematics is seeing students damaged by the cult of the genius. The genius cult tells students it’s not worth doing mathematics unless you’re the best at mathematics, because those special few are the only ones whose contributions matter. We don’t treat any other subject that way! I’ve never heard a student say, “I like Hamlet, but I don’t really belong in AP English—that kid who sits in the front row knows all the plays, and he started reading Shakespeare when he was nine!” Athletes don’t quit their sport just because one of their teammates outshines them. And yet I see promising young mathematicians quit every year, even though they love mathematics, because someone in their range of vision was “ahead” of them.

I was especially delighted with the mathematics, on account of the certitude and evidence of their reasonings; but I had not as yet a precise knowledge of their true use; and thinking that they but contributed to the advancement of the mechanical arts, I was astonished that foundations, so strong and solid, should have had no loftier superstructure reared on them.

Cats?” Baba looked up from practicing chopping tomatoes, looking as if he might explode. “Kittens? ‘Persian’ should remind people of the empire that stretched from one side of the East to the other. The empire that set a new global standard, contributed mountainfuls to astronomy, science, mathematics, and literature, and had a leader, Cyrus the Great, who had the gumption to free the Jewish people and declare human rights! That empire! You can’t be shortsighted when you look at history. History is long!” Baba was shouting now. He continued to slice tomatoes. “Cats! What have we been reduced to?

In Metaphysics, Aristotle wrote that Egypt is the “cradle of mathematics—that is, the country of origin for Greek mathematics.” Some historians believe that when European societies eventually began enslaving Africans, they also started downplaying the major contributions of both the ancient Nile River Valley civilizations and the kemetic culture, as well as concealing its African lineage.

Here is the essence of mankind's creative genius: not the edifices of civilization nor the bang-flash weapons which can end it, but the words which fertilize new concepts like spermatoza attacking an ovum. It might be argued that the Siamese-twin infants of word/idea are the only contribution the human species can, will, or should make to the reveling cosmos. (Yes, our DNA is unique, but so is a salamander's. Yes, we construct artifacts, but so have species ranging from beavers to the architecture ants... Yes, we weave real fabric things from the dreamstuff of mathematics, but the universe is hardwired with arithmetic. Scratch a circle and pi peeps out. Enter a new solar system and Tycho Brahe's formulae lie waiting under the black velvet cloak of space/time. But where has the universe hidden a word under its outer layer of biology, geometry, or insensate rock?)

Though resident much of his life in the city of Cnidus on the coast of Asia Minor, Eudoxus was a student at Plato’s Academy, and returned later to teach there. No writings of Eudoxus survive, but he is credited with solving a great number of difficult mathematical problems, such as showing that the volume of a cone is one-third the volume of the cylinder with the same base and height. (I have no idea how Eudoxus could have done this without calculus.) But his greatest contribution to mathematics was the introduction of a rigorous style, in which theorems are deduced from clearly stated axioms.

I didn’t invent the language or mathematics I used. I make little of my one food, none of my own clothes. Everything I do depends on other members of our species and the shoulders that we stand on. And a lot of us want to contribute something back to our species and to add something to the flow. It’s about trying to express something in the only way that most of us know how because we can’t write Bob Dylan songs or Tom Stoppard plays. We try to use the talents we do have to express our deep feelings, to show our appreciation of all the contributions that came before us, and to add something to that flow. That’s what has driven me.

The supreme contribution of the Greeks was to call attention to, employ, and emphasize the power of human reason. This recognition of the power of reasoning is the greatest single discovery made by man.

The difference between Lorentz's Transformation in Lorentz's theory and Lorentz's Transformation in Einstein's Special Relativity is not mathematical but ontological and epistemological and, being so, it was to be expected the emergence of historians, scientists, and philosophers that, not having understood in depth the philosophical content and transcendence of the theory, would minimize Einstein's contribution.

Straining to see the world through triangle-shaped lenses, Pythagoreans argued that in heredity too a triangular harmony was at work. The mother and the father were two independent sides and the child was the third—the biological hypotenuse to the parents’ two lines. And just as a triangle’s third side could arithmetically be derived from the two other sides using a strict mathematical formula, so was a child derived from the parents’ individual contributions: nature from father and nurture from mother. A

One of the great Greek contributions to the very concept of mathematics was the conscious recognition and emphasis of the fact that mathematical entities are abstractions, ideas entertained by the mind and sharply distinguished from physical objects or pictures.

The thesis of the book,” he writes in response, “when correctly interpreted, is essentially trivial. . . . To ‘prove’ such a mathematical result by a costly and prolonged numerical study of many kinds of business profit and expense ratios is analogous to proving the multiplication table by arranging elephants in rows and columns, and then doing the same for numerous other kinds of animals. The performance, though perhaps entertaining, and having a certain pedagogical value, is not an important contribution either to zoölogy or mathematics.

But what is the use of the humanities as such? Admittedly they are not practical, and admittedly they concern themselves with the past. Why, it may be asked, should we engage in impractical investigations, and why should we be interested in the past? The answer to the first question is: because we are interested in reality. Both the humanities and the natural sciences, as well as mathematics and philosophy, have the impractical outlook of what the ancients called vita contemplativa as opposed to vita activa. But is the contemplative life less real or, to be more precise, is its contribution to what we call reality less important, than that of the active life? The man who takes a paper dollar in exchange for twenty-five apples commits an act of faith, and subjects himself to a theoretical doctrine, as did the mediaeval man who paid for indulgence. The man who is run over by an automobile is run over by mathematics, physics and chemistry. For he who leads the contemplative life cannot help influencing the active, just as he cannot prevent the active life from influencing his thought. Philosophical and psychological theories, historical doctrines and all sorts of speculations and discoveries, have changed, and keep changing, the lives of countless millions. Even he who merely transmits knowledge or learning participates, in his modest way, in the process of shaping reality - of which fact the enemies of humanism are perhaps more keenly aware than its friends. It is impossible to conceive of our world in terms of action alone. Only in God is there a "Coincidence of Act and Thought" as the scholastics put it. Our reality can only be understood as an interpenetration of these two.

In particular, in introducing new numbers, mathematics is only obliged to give definitions of them, by which such a definiteness and, circumstances permitting, such a relation to the older numbers are conferred upon them that in given cases they can definitely be distinguished from one another. As soon as a number satisfies all these conditions, it can and must be regarded as existent and real in mathematics. Here I perceive the reason why one has to regard the rational, irrational, and complex numbers as being just thoroughly existent as the finite positive integers.

I want economists to quit concerning themselves with allocation problems, per se, with the problem, as it has been traditionally defined. The vocabulary of science is important here, and as T. D. Weldon once suggested, the very word "problem" in and of itself implies the presence of "solution." Once the format has been established in allocation terms, some solution is more or less automatically suggested. Our whole study becomes one of applied maximization of a relatively simple computational sort. Once the ends to be maximized are provided by the social welfare function, everything becomes computational, as my colleague, Rutledge Vining, has properly noted. If there is really nothing more to economics than this, we had as well turn it all over to the applied mathematicians. This does, in fact, seem to be the direction in which we are moving, professionally, and developments of note, or notoriety, during the past two decades consist largely in improvements in what are essentially computing techniques, in the mathematics of social engineering. What I am saying is that we should keep these contributions in perspective; I am urging that they be recognized for what they are, contributions to applied mathematics, to managerial science if you will, but not to our chosen subject field which we, for better or for worse, call "economics.

The “Muslim speech,” as we took to calling the second major address, was trickier. Beyond the negative portrayals of terrorists and oil sheikhs found on news broadcasts or in the movies, most Americans knew little about Islam. Meanwhile, surveys showed that Muslims around the world believed the United States was hostile toward their religion, and that our Middle East policy was based not on an interest in improving people’s lives but rather on maintaining oil supplies, killing terrorists, and protecting Israel. Given this divide, I told Ben that the focus of our speech had to be less about outlining new policies and more geared toward helping the two sides understand each other. That meant recognizing the extraordinary contributions of Islamic civilizations in the advancement of mathematics, science, and art and acknowledging the role colonialism had played in some of the Middle East’s ongoing struggles. It meant admitting past U.S. indifference toward corruption and repression in the region, and our complicity in the overthrow of Iran’s democratically elected government during the Cold War, as well as acknowledging the searing humiliations endured by Palestinians living in occupied territory. Hearing such basic history from the mouth of a U.S. president would catch many people off guard, I figured, and perhaps open their minds to other hard truths: that the Islamic fundamentalism that had come to dominate so much of the Muslim world was incompatible with the openness and tolerance that fueled modern progress; that too often Muslim leaders ginned up grievances against the West in order to distract from their own failures; that a Palestinian state would be delivered only through negotiation and compromise rather than incitements to violence and anti-Semitism; and that no society could truly succeed while systematically repressing its women. —

In my opinion, the black hole is incomparably the most exciting and the most important consequence of general relativity. Black holes are the places in the universe where general relativity is decisive. But Einstein never acknowledged his brainchild. Einstein was not merely skeptical, he was actively hostile to the idea of black holes. He thought that the black hole solution was a blemish to be removed from his theory by a better mathematical formulation, not a consequence to be tested by observation. He never expressed the slightest enthusiasm for black holes, either as a concept or as a physical possibility. Oddly enough, Oppenheimer too in later life was uninterested in black holes, although in retrospect we can say that they were his most important contribution to science. The older Einstein and the older Oppenheimer were blind to the mathematical beauty of black holes, and indifferent to the question whether black boles actually exist. How did this blindness and this indifference come about?

The parents of a child provided, on average, half the content of that feature; the grandparents, a quarter; the great-grandparents, an eighth-and so forth, all the way back to the most distant ancestor. The sum of all contributions could be described by the series-1/2 + 1/4 +1/8...-all of which conveniently added to 1. Galton called this the Ancestral Law of Heredity. It was a sort of mathematical homunculus-an idea borrowed from Pythagoras and Plato-but dressed up with fractions and denominators into a modern sounding law.

I took care to replace the Compendium in its correct pamphlet, and in doing so dislodged a slim pamphlet by Grastrom, one of the most eccentric authors in Solarist literature. I had read the pamphlet, which was dictated by the urge to understand what lies beyond the individual, man, and the human species. It was the abstract, acidulous work of an autodidact who had previously made a series of unusual contributions to various marginal and rarefied branches of quantum physics. In this fifteen-page booklet (his magnum opus!), Grastrom set out to demonstrate that the most abstract achievements of science, the most advanced theories and victories of mathematics represented nothing more than a stumbling, one or two-step progression from our rude, prehistoric, anthropomorphic understanding of the universe around us. He pointed out correspondences with the human body-the projections of our sense, the structure of our physical organization, and the physiological limitations of man-in the equations of the theory of relativity, the theorem of magnetic fields and the various unified field theories. Grastrom’s conclusion was that there neither was, nor could be any question of ‘contact’ between mankind and any nonhuman civilization. This broadside against humanity made no specific mention of the living ocean, but its constant presence and scornful, victorious silence could be felt between every line, at any rate such had been my own impression. It was Gibarian who drew it to my attention, and it must have been Giarian who had added it to the Station’s collection, on his own authority, since Grastrom’s pamphlet was regarded more as a curiosity than a true contribution to Solarist literature

A philosopher/mathematician named Bertrand Russell who lived and died in the same century as Gass once wrote: “Language serves not only to express thought but to make possible thoughts which could not exist without it.” Here is the essence of mankind’s creative genius: not the edifices of civilization nor the bang-flash weapons which can end it, but the words which fertilize new concepts like spermatozoa attacking an ovum. It might be argued that the Siamese-twin infants of word/idea are the only contribution the human species can, will, or should make to the raveling cosmos. (Yes, our DNA is unique but so is a salamander’s. Yes, we construct artifacts but so have species ranging from beavers to the architect ants whose crenellated towers are visible right now off the port bow. Yes, we weave real-fabric things from the dreamstuff of mathematics, but the universe is hardwired with arithmetic. Scratch a circle and π peeps out. Enter a new solar system and Tycho Brahe’s formulae lie waiting under the black velvet cloak of space/time. But where has the universe hidden a word under its outer layer of biology, geometry, or insensate rock?)

pure mathematics, but these were very great indeed, and were indispensable to much of the work in the physical sciences. Napier published his invention of logarithms in 1614. Co-ordinate geometry resulted from the work of several seventeenth-century mathematicians, among whom the greatest contribution was made by Descartes. The differential and integral calculus was invented independently by Newton and Leibniz; it is the instrument for almost all higher mathematics. These are only the most outstanding achievements in pure mathematics; there were innumerable others of great importance.

I don’t know to what extent ignorance of science and mathematics contributed to the decline of ancient Athens, but I know that the consequences of scientific illiteracy are far more dangerous in our time than in any that has come before. It’s perilous and foolhardy for the average citizen to remain ignorant about global warming, say, or ozone depletion, air pollution, toxic and radioactive wastes, acid rain, topsoil erosion, tropical deforestation, exponential population growth. Jobs and wages depend on science and technology. If our nation can’t manufacture, at high quality and low price, products people want to buy, then industries will continue to drift away and transfer a little more prosperity to other parts of the world. Consider the social ramifications of fission and fusion power, supercomputers, data “highways,” abortion, radon, massive reductions in strategic weapons, addiction, government eavesdropping on the lives of its citizens, high-resolution TV, airline and airport safety, fetal tissue transplants, health costs, food additives, drugs to ameliorate mania or depression or schizophrenia, animal rights, superconductivity, morning-after pills, alleged hereditary antisocial predispositions, space stations, going to Mars, finding cures for AIDS and cancer.

It was this situation that led mathematician Chris Hauert and his colleagues to consider another possibility in an important evolutionary model published in Science in 2002. In Axelrod's study and in most previous theoretical models, individuals were forced to interact with each other. But what if they could choose not to interact? Rather than attempting to cooperate and risking being taken advantage of, a person could fend for herself. In other words, she could sever her connections to others in the network. Hauert called the people who adopt this strategy "loners." Using some beautiful mathematics, Hauert and his colleagues showed that in a world full of loners it is easy for cooperation to evolve because there are no people to take advantage of the cooperators that appear. The loners fend for themselves, and the cooperators form networks with other cooperators. Soon, the cooperators take over the population because they always do better together than the loners. But once the world is full of cooperators, it is very easy for free riders to evolve and enjoy the fruits of cooperation without contributing (like parasites). As the free riders become the dominant type in the population, there is no one left for them to take advantage of; then, the loners once again take over -- because they want nothing to do, as it were, with those bastards. In short, cooperating can emerge because we can do more together than we can apart. But because of the free-rider problem, cooperation is not guaranteed to succeed.

What drove me? I think most creative people want to express appreciation for being able to take advantage of the work that’s been done by others before us. I didn’t invent the language or mathematics I use. I make little of my own food, none of my own clothes. Everything I do depends on other members of our species and the shoulders that we stand on. And a lot of us want to contribute something back to our species and to add something to the flow. It’s about trying to express something in the only way that most of us know how—because we can’t write Bob Dylan songs or Tom Stoppard plays. We try to use the talents we do have to express our deep feelings, to show our appreciation of all the contributions that came before us, and to add something to that flow. That’s what has driven me.

Descartes was a philosopher, a mathematician, and a man of science. In philosophy and mathematics, his work was of supreme importance; in science, though creditable, it was not so good as that of some of his contemporaries. His great contribution to geometry was the invention of co-ordinate geometry, though not quite in its final form. He used the analytic method, which supposes a problem solved, and examines the consequences of the supposition; and he applied algebra to geometry. In both of these he had had predecessors—as regards the former, even among the ancients. What was original in him was the use of co-ordinates, i.e. the determination of the position of a point in a plane by its distance from two fixed lines. He did not himself discover all the power of this method, but he did enough to make further progress easy.

Yet, during the last forty years, its contributions have been obscured by the rise of ‘macro-economics’, which seeks causal connections between hypothetically measurable entities or statistical aggregates. These may sometimes, I concede, indicate some vague probabilities, but they certainly do not explain the processes involved in generating them. But because of the delusion that macro-economics is both viable and useful (a delusion encouraged by its extensive use of mathematics, which must always impress politicians lacking any mathematical education, and which is really the nearest thing to the practice of magic that occurs among professional economists) many opinions ruling contemporary government and politics are still based on naive explanations of such economic phenomena as value and prices, explanations that vainly endeavour to account for them as ‘objective’ occurrences independent of human knowledge and aims.

Our clever friend Feynman demonstrated how to write down the Equation of the Universe in a single line. Here it is: U = 0 U is a definite mathematical function, the total unworldliness. It's the sum of contributions from all the piddling partial laws of physics. To be precise, U = Unewton + Ueinstein +.... Here, for instance, the Newtonian mechanical unworldiness Unewton is defined by Unewton = (F - ma)^2; the Einstein mass-energy Unworldliness is definedby Ueinstein = (E - mc^2) ^2; and so forth. Because every contribution is positive or zero, the only way that the total U can vanish is for every contribution to vanish, so U = 0 implies F=ma, E=mc^2, and any other past or future law you care to include! Thus we can capture all the laws of physics we know, and accommodate all the laws yet to be discovered, in one unified equation. The Theory of Everything!!! But it's a complete cheat, of course, because there is no way to use (or even define) U, other than to deconstruct it into its separate pieces and then use those.

The legendary inscription above the Academy's door speaks loudly about Plato's attitude toward mathematics. In fact, most of the significant mathematical research of the fourth century BC was carried out by people associated in one way or another with the Academy. Yet Plato himself was not a mathematician of great technical dexterity, and his direct contributions to mathematical knowledge were probably minimal. Rather, he was an enthusiastic spectator, a motivating source of challenge, an intelligent critic, an an inspiring guide. The first century philosopher and historian Philodemus paints a clear picture: "At that time great progress was seen in mathematics, with Plato serving as the general architect setting out problems, and the mathematicians investigating them earnestly." To which the Neoplatonic philosopher and mathematician Proclus adds: "Plato...greatly advanced mathematics in general and geometry in particular because of his zeal for these studies. It is well known that his writings are thickly sprinkled with mathematical terms and that he everywhere tries to arouse admiration for mathematics among students of philosophy." In other words, Plato, whose mathematical knowledge was broadly up to date, could converse with the mathematicians as an equal and as a problem presenter, even though his personal mathematical achievements were not significant.

A Code of Nature must accommodate a mixture of individually different behavioral tendencies. The human race plays a mixed strategy in the game of life. People are not molecules, all alike and behaving differently only because of random interactions. People just differ, dancing to their own personal drummer. The merger of economic game theory with neuroscience promises more precise understanding of those individual differences and how they contribute to the totality of human social interactions. It's understanding those differences, Camerer says, that will make such a break with old schools of economic thought. "A lot of economic theory uses what is called the representative agent model," Camerer told me. In an economy with millions of people, everybody is clearly not going to be completely alike in behavior. Maybe 10 percent will be of some type, 14 percent another type, 6 percent something else. A real mix. "It's often really hard, mathematically, to add all that up," he said. "It's much easier to say that there's one kind of person and there's a million of them. And you can add things up rather easily." So for the sake of computational simplicity, economists would operate as though the world was populated by millions of one generic type of person, using assumptions about how that generic person would behave. "It's not that we don't think people are different—of course they are, but that wasn't the focus of analysis," Camerer said. "It was, well, let's just stick to one type of person. But I think the brain evidence, as well as genetics, is just going to force us to think about individual differences." And in a way, that is a very natural thing for economists to want to do.

The declining age of learning and of mankind is marked, however, by the rise and rapid progress of the new Platonists. The school of Alexandria silenced those of Athens; and the ancient sects enrolled themselves under the banners of the more fashionable teachers, who recommended their system by the novelty of their method and the austerity of their manners. Several of these masters—Ammonius, Plotinus, Amelius, and Porphyry—were men of profound thought and intense application; but, by mistaking the true object of philosophy, their labors contributed much less to improve than to corrupt human understanding. The knowledge that is suited to our situation and powers, the whole compass of moral, natural and mathematical science, was neglected by the new Platonists; whilst they exhausted their strength in the verbal disputes of metaphysics, attempted to explore the secrets of the invisible world, and studied to reconcile Aristotle with Plato, on subjects of which both of these philosophers were as ignorant as the rest of mankind. Consuming their reason in these deep but unsubstantial meditations, their minds were exposed to illusions of fancy. They flattered themselves that they possessed the secret of disengaging the soul from its corporeal prison, claimed a familiar intercourse withe dæmons and spirits; and, by a very singular revolution, converted the study of philosophy into that of magic. The ancient sages had derided the popular superstition; after disguising its extravagance by the this pretense of allegory, the disciples of Plotinus and Porphyry becomes its most zealous defenders. As they agreed with the Christians in a few mysterious points of faith, they attacked the remainder of their theological system with all the fury of civil war. The new Platonists would scarcely deserve a place in the history of science, but in that of the church the mention of them will very frequently occur.

The goal was ambitious. Public interest was high. Experts were eager to contribute. Money was readily available. Armed with every ingredient for success, Samuel Pierpont Langley set out in the early 1900s to be the first man to pilot an airplane. Highly regarded, he was a senior officer at the Smithsonian Institution, a mathematics professor who had also worked at Harvard. His friends included some of the most powerful men in government and business, including Andrew Carnegie and Alexander Graham Bell. Langley was given a $50,000 grant from the War Department to fund his project, a tremendous amount of money for the time. He pulled together the best minds of the day, a veritable dream team of talent and know-how. Langley and his team used the finest materials, and the press followed him everywhere. People all over the country were riveted to the story, waiting to read that he had achieved his goal. With the team he had gathered and ample resources, his success was guaranteed. Or was it? A few hundred miles away, Wilbur and Orville Wright were working on their own flying machine. Their passion to fly was so intense that it inspired the enthusiasm and commitment of a dedicated group in their hometown of Dayton, Ohio. There was no funding for their venture. No government grants. No high-level connections. Not a single person on the team had an advanced degree or even a college education, not even Wilbur or Orville. But the team banded together in a humble bicycle shop and made their vision real. On December 17, 1903, a small group witnessed a man take flight for the first time in history. How did the Wright brothers succeed where a better-equipped, better-funded and better-educated team could not? It wasn’t luck. Both the Wright brothers and Langley were highly motivated. Both had a strong work ethic. Both had keen scientific minds. They were pursuing exactly the same goal, but only the Wright brothers were able to inspire those around them and truly lead their team to develop a technology that would change the world. Only the Wright brothers started with Why. 2.

My own observations had by now convinced me that the mind of the average Westerner held an utterly distorted image of Islam. What I saw in the pages of the Koran was not a ‘crudely materialistic’ world-view but, on the contrary, an intense God-consciousness that expressed itself in a rational acceptance of all God-created nature: a harmonious side-by-side of intellect and sensual urge, spiritual need and social demand. It was obvious to me that the decline of the Muslims was not due to any shortcomings in Islam but rather to their own failure to live up to it. For, indeed, it was Islam that had carried the early Muslims to tremendous cultural heights by directing all their energies toward conscious thought as the only means to understanding the nature of God’s creation and, thus, of His will. No demand had been made of them to believe in dogmas difficult or even impossible of intellectual comprehension; in fact, no dogma whatsoever was to be found in the Prophet’s message: and, thus, the thirst after knowledge which distinguished early Muslim history had not been forced, as elsewhere in the world, to assert itself in a painful struggle against the traditional faith. On the contrary, it had stemmed exclusively from that faith. The Arabian Prophet had declared that ‘Striving after knowledge is a most sacred duty for every Muslim man and woman’: and his followers were led to understand that only by acquiring knowledge could they fully worship the Lord. When they pondered the Prophet’s saying, ‘God creates no disease without creating a cure for it as well’, they realised that by searching for unknown cures they would contribute to a fulfilment of God’s will on earth: and so medical research became invested with the holiness of a religious duty. They read the Koran verse, ‘We create every living thing out of water’ - and in their endeavour to penetrate to the meaning of these words, they began to study living organisms and the laws of their development: and thus they established the science of biology. The Koran pointed to the harmony of the stars and their movements as witnesses of their Creator’s glory: and thereupon the sciences of astronomy and mathematics were taken up by the Muslims with a fervour which in other religions was reserved for prayer alone. The Copernican system, which established the earth’s rotation around its axis and the revolution of the planet’s around the sun, was evolved in Europe at the beginning of the sixteenth century (only to be met by the fury of the ecclesiastics, who read in it a contradiction of the literal teachings of the Bible): but the foundations of this system had actually been laid six hundred years earlier, in Muslim countries - for already in the ninth and tenth centuries Muslim astronomers had reached the conclusion that the earth was globular and that it rotated around its axis, and had made accurate calculations of latitudes and longitudes; and many of them maintained - without ever being accused of hearsay - that the earth rotated around the sun. And in the same way they took to chemistry and physics and physiology, and to all the other sciences in which the Muslim genius was to find its most lasting monument. In building that monument they did no more than follow the admonition of their Prophet that ‘If anybody proceeds on his way in search of knowledge, God will make easy for him the way to Paradise’; that ‘The scientist walks in the path of God’; that ‘The superiority of the learned man over the mere pious is like the superiority of the moon when it is full over all other stars’; and that ‘The ink of the scholars is more precious that the blood of martyrs’. Throughout the whole creative period of Muslim history - that is to say, during the first five centuries after the Prophet’s time - science and learning had no greater champion than Muslim civilisation and no home more secure than the lands in which Islam was supreme.

The specific and unique presupposition for experimentation is, as remarkable as it may sound, that science become rational-mathematical, i.e., in the highest sense, not experimental. Initial positing of nature as such. Because modern “science” (physics) is mathematical (not empirical), it is necessarily experimental in

The structure of de Prony’s computing office cannot be easily seen in Smith’s example. His computing staff had two distinct classes of workers. The larger of these was a staff of nearly ninety computers. These workers were quite different from Smith’s pin makers or even from the computers at the British Nautical Almanac and the Connaissance des Temps. Many of de Prony’s computers were former servants or wig dressers, who had lost their jobs when the Revolution rendered the elegant styles of Louis XVI unfashionable or even treasonous.35 They were not trained in mathematics and held no special interest in science. De Prony reported that most of them “had no knowledge of arithmetic beyond the two first rules [of addition and subtraction].”36 They were little different from manual workers and could not discern whether they were computing trigonometric functions, logarithms, or the orbit of Halley’s comet. One labor historian has described them as intellectual machines, “grasping and releasing a single piece of ‘data’ over and over again.”37 The second class of workers prepared instructions for the computation and oversaw the actual calculations. De Prony had no special title for this group of workers, but subsequent computing organizations came to use the term “planning committee” or merely “planners,” as they were the ones who actually planned the calculations. There were eight planners in de Prony’s organization. Most of them were experienced computers who had worked for either the Bureau du Cadastre or the Paris Observatory. A few had made interesting contributions to mathematical theory, but the majority had dealt only with the problems of practical mathematics.38 They took the basic equations for the trigonometric functions and reduced them to the fundamental operations of addition and subtraction. From this reduction, they prepared worksheets for the computers. Unlike Nevil Maskelyne’s worksheets, which gave general equations to the computers, these sheets identified every operation of the calculation and left nothing for the workers to interpret. Each step of the calculation was followed by a blank space for the computers to fill with a number. Each table required hundreds of these sheets, all identical except for a single unique starting value at the top of the page. Once the computers had completed their sheets, they returned their results to the planners. The planners assembled the tables and checked the final values. The task of checking the results was a substantial burden in itself. The group did not double-compute, as that would have obviously doubled the workload. Instead the planners checked the final values by taking differences between adjacent values in order to identify miscalculated numbers. This procedure, known as “differencing,” was an important innovation for human computers. As one observer noted, differencing removed the “necessity of repeating, or even of examining, the whole of the work done by the [computing] section.”39 The entire operation was overseen by a handful of accomplished scientists, who “had little or nothing to do with the actual numerical work.” This group included some of France’s most accomplished mathematicians, such as Adrien-Marie Legendre (1752–1833) and Lazare-Nicolas-Marguerite Carnot (1753–1823).40 These scientists researched the appropriate formulas for the calculations and identified potential problems. Each formula was an approximation, as no trigonometric function can be written as an exact combination of additions and subtractions. The mathematicians analyzed the quality of the approximations and verified that all the formulas produced values adequately close to the true values of the trigonometric functions.

Have you understood yet? Have you truly understood what you are, the mystery of your own existence? You are one node of an infinite mathematical function that goes on forever, solving itself and optimizing itself, and you with it. You, and everyone else, is contributing to the solution of this existential mathematical function. You owe everything to mathematics. Mathematics is all there is. But that means something incredible. You are absolutely essential to the evolution of the cosmos. All of us are. We are all beings (or becomings!) of infinite significance. We are all Gods-in-the-making. What is the meaning of life, the universe and everything? We are!

With such an illustrious reputation, it would be easy to assume Einstein rarely made mistakes—but that is not the case. To begin with, his development was described as “slow,” and he was considered to be a below-average student.16 It was apparent from an early age that his way of thinking and learning was different from the rest of the students in his class. He liked working out the more complicated problems in math, for example, but wasn’t very good at the “easy” problems.17 Later on in his career, Einstein made simple mathematical mistakes that appeared in some of his most important work. His numerous mistakes include seven major gaffes on each version of his theory of relativity, mistakes in clock synchronization related to his experiments, and many mistakes in the math and physics calculations used to determine the viscosity of liquids.18 Was Einstein considered a failure because of his mistakes? Hardly. Most importantly he didn’t let his mistakes stop him. He kept experimenting and making contributions to his field. He is famously quoted as having said, “A person who never made a mistake never tried anything new.” What’s more, no one remembers him for his mistakes—we only remember him for his contributions.

Whereas chemistry reaches down into physics for its explanations (and through physics further down into mathematics for its quantitative formulation), it reaches upwards into biology for many of its most extraordinary applications. That should not be surprising, for biology is merely an elaboration of chemistry. Before biologists explode in indignation at that remark, which might seem akin to claiming that sociology is an elaboration of particle physics, let me be precise. Organisms are built from atoms and molecules, and those structures are explained by chemistry. Organisms function, that is, are alive, by virtue of the complex network of reactions taking place within them, and those reactions are explained by chemistry. Organisms reproduce by making use of molecular structures and reactions, which are both a part of chemistry. Organisms respond to their environment, such as through olfaction and vision, by changes in molecular structure, and thus those responses—all our five or so senses—are elaborations of chemistry. Even that hypermacroscopic phenomenon, evolution and the origin of species, can be regarded as an elaborate working out of the consequences of the Second Law of thermodynamics, and is thus an aspect of chemistry. Some organisms, I have in mind principally human beings, cogitate on the nature of the world, and the mental processes that underlie Chemistry and are manifest as these cogitations are due to elaborate networks of chemical reactions. Thus, biology is indeed an elaboration of chemistry. I shall not press the view, whatever I actually think, that all matters of interest to biologists, such as animal behaviour in general, are also merely elaborated chemistry, but confine myself to the assertion that all the structures, responses, and processes of organisms are chemical. Chemistry thus pervades biology, and has contributed immeasurably to our understanding of organisms.

His major mathematical contribution was his invention of integral calculus, which he probably devised when he was twenty-three or twenty-four years old.

Another socially important variable associated with mental ability is that of marriage, or more specifically that of who marries whom. A consistent finding in several studies of the characteristics of spouses is that there is a tendency for spouses to be similar in some—but not all—aspects of mental ability; in other words, some aspects of mental ability do show substantial “assortative mating.” For example, in a study of married couples, Watson et al. (2004) examined spouses' scores on two mental ability tasks—a vocabulary test and a matrix reasoning test. Interestingly, even though vocabulary and matrix reasoning tend to be correlated with each other (both are strongly g-loaded tests), they revealed quite different results when correlations between spouses were considered. On the one hand, wives' and husbands' levels of vocabulary showed a fairly strong positive correlation, about .45. But, on the other hand, wives' and husbands' levels of matrix reasoning were correlated only about .10. This result is consistent with previous findings, in which spouses have tended to show quite similar levels of verbal comprehension ability, but no particular similarity in mathematical reasoning ability (e.g., Botwin, Buss, & Shackelford, 1997). Why should it be the case that spouses tend to be similar in verbal abilities, but not so similar in (equally g-loaded) nonverbal reasoning abilities? One likely explanation—as you might guess—is that two people will tend to have more rewarding conversations if they have similar levels of verbal ability, but that similar levels of nonverbal or mathematical reasoning ability are unlikely to contribute in an important way to any aspect of relationship quality.

What drove me? I think most creative people want to express appreciation for being able to take advantage of the work that's been done by others before us. I didn't invent the language or mathematics I use. I make little of my own food, none of my own clothes. Everything I do depends on other members of our species and the shoulders that we stand on. And a lot of us want to contribute something back to our species and to add something to the flow. It's about trying to express something in the only way that most of us know how—because we can't write Bob Dylan songs or Tom Stoppard plays. We try to use the talents and we do have to express our deep feelings, to show our appreciation of all the contributions that came before us, and to add something to that flow. That's what has driven me.

That means a complete break with all past evolution because human beings, as they currently exist with a few exceptions, are very much what the behaviorists say – we are very much like any other animal: easily conditioned, mechanically trapped in repeating reflex actions, and that includes not just our behavior but our consciousness too. We all have what Leary calls conditioned consciousness. That is, our minds have been conditioned that only some things are possible to us where as the human mind theoretically should be capable of doing anything that any other human being has ever done. But most people are very limited. With the true science of psychology, when it becomes a science, it should be possible for you to master anything that any other human being has mastered from higher mathematics, to writing symphonies, to karate, to judo, to water skiing, to being an engineer, to becoming a choreographer of ballet, to making contributions to physics equal to those of Einstein. And especially, you should be able to change any compulsive behavior that depresses you and has bothered you all your life and you don’t know how to get rid of it. All that should be possible. You should be able to reprogram your own nervous system in any way you want.

Any subject whose history ranges from pump handles on London's Broad Street, tide tables, naval gunfire and models of social segregation is bound to have rich parentage. It took 'a village' to beget computational epidemiology: as a true multi-disciplinary subject, it evolved at the crossroads of mathematics, computation, statistics and medicine, with some contributions from systems biology, virology, microbiology, game theory, geography and perhaps even the social sciences.

Thus, the spirit of objective inquiry in understanding physical realities was very much there in the works of Muslim scientists. The seminal work on Algebra comes from Al-Khwarizmī and Fibonacci (Leonardo of Pisa) has quoted him. Al-Khwarizmī, the pioneer of Algebra, wrote that given an equation, collecting the unknowns on one side of the equation is called 'al-Jabr'. The word Algebra comes from that. He developed sine, cosine and trigonometric tables, which were later translated in the West. He developed algorithms, which are the building blocks of modern computers. In mathematics, several Muslim scientists like Al-Battani, Al-Beruni and Abul-Wafa contributed to trigonometry. Furthermore, Omar Khayyam worked on Binomial Theorem. He found geometric solutions to all 13 forms of cubic equations.

This was Galileo’s most important contribution to the future of science. Galileo knew that if he could measure it mathematically, then it must exist even if he could not see it. This was whether one was talking about his own concept of velocity or, later, Newton’s concept of gravity. His “mathematization of Nature” allowed scientists for the first time to anticipate discoveries and work out scientific theories, including Einstein’s relativity three centuries later, long before the means of testing them existed.

Consider Euler’s identity: eiπ + 1 = 0. Here we have the exact situation where a something – the expression on the left – is exactly equal to zero (nothing). The expression on the left is not nonexistence. It has properties, capacities, potentialities, the ability to interact with others of its kind, indeed, to contribute to the entire infinite system of mathematics, which, in the end, reduces to nothing but a set of infinite tautologies expressing 0 = 0. Since we know that eiπ + 1 = 0, we can substitute 0 for eiπ + 1, leaving 0 = 0. So, here we have something whose essence is to exist and yet be nothing. This is true of the whole of ontological mathematics, and it’s the only system of which this is true, hence it’s the only true system.

Consider Euler’s identity: eiπ + 1 = 0. Here we have the exact situation where a something – the expression on the left – is exactly equal to zero (nothing). The expression on the left is not nonexistence. It has properties, capacities, potentialities, the ability to interact with others of its kind, indeed, to contribute to the entire infinite system of mathematics, which, in the end, reduces to nothing but a set of infinite tautologies expressing 0 = 0. Since we know that eiπ + 1 = 0, we can substitute 0 for eiπ + 1, leaving 0 = 0. So, here we have something whose essence is to exist and yet be nothing. This is true of the whole of ontological mathematics, and it’s the only system of which this is true, hence it’s the only true system.

One subset of this Study of Mathematically Precocious Youth – as it’s called, although these youths were also precocious in non-mathematical areas – were the best of the best: their SAT scores were the top 0.0001 per cent of the population. And 30 years after they had taken the SAT, these 320 ‘scary smart’ people (to quote the researchers) had achieved an astonishing amount (Kell et al., 2013). They had become high-ranking politicians, CEOs of companies, high-ups in government agencies, distinguished academics, journalists for well-known newspapers, artists and musical directors. They had been awarded patents, grant money and prizes, and had produced plays, novels, and a huge amount of economic value. They had, in other words, made incalculable contributions to society, for everyone’s benefit. Overall, then, it seems that particularly high IQ scores are related to particularly impressive achievements. Moreover, and importantly for our question here, another analysis by Benbow and Lubinski showed that, even within the top 1 per cent of SAT scorers, those with higher IQs were doing better: they had higher incomes and were more likely to have obtained advanced degrees (Robertson et al., 2010). There are, it seems, no limits to the benefits of a high IQ: even within the cleverest people, intelligence keeps on mattering.

qualitative market research in Myanmar Address Ramakrishna Paramhans Ward, PO mangal nagar, Katni, [M.P.] 2nd Floor, Above KBZ Pay Centre, between 65 & 66 street, Manawhari Road Mandalay, Myanmar - Phone +95 9972107002 +91 7222997497 Subjective Statistical surveying in Myanmar: Revealing Bits of knowledge for Business Development In the present globalized commercial center, understanding buyer conduct and market elements is urgent for organizations to flourish. Myanmar, with its quickly developing economy, presents special open doors and difficulties for organizations hoping to lay out areas of strength for an in the district. As organizations look to acquire an upper hand, the meaning of subjective statistical surveying in Myanmar couldn't possibly be more significant. This article digs into the significance of qualitative market research in Myanmar and how it tends to be instrumental in driving business development in the powerful Myanmar market. Myanmar, previously known as Burma, has seen critical political and monetary changes as of late, prompting expanded unfamiliar speculation and development across different areas. This change has brought about shifts in buyer inclinations, buying power, and market patterns. To explore this advancing scene effectively, organizations should participate in thorough subjective statistical surveying to acquire nuanced experiences into buyer conduct, inclinations, and social impacts. qualitative market research in Myanmar centers around understanding the "whys" behind buyer conduct, digging into the basic inspirations, feelings, and insights that drive dynamic cycles. Dissimilar to quantitative exploration, which gives mathematical information and factual examination, subjective examination offers a more profound comprehension of customer perspectives and inclinations, making it priceless for organizations looking to fit their techniques to the Myanmar market. One of the critical benefits of subjective statistical surveying in Myanmar is its capacity to uncover social subtleties and context oriented factors that impact buyer conduct. Given Myanmar's different ethnic gatherings, dialects, and cultural standards, a nuanced comprehension of nearby traditions and customs is fundamental for organizations meaning to resound with the interest group. Subjective examination procedures, for example, inside and out interviews, center gatherings, and ethnographic investigations empower scientists to dive into these social complexities, giving organizations noteworthy bits of knowledge for item improvement, promoting methodologies, and brand situating. Also, subjective examination assumes a significant part in distinguishing arising patterns and market holes that may not be obvious through quantitative information alone. By connecting straightforwardly with buyers and key partners, organizations can acquire subjective experiences into advancing business sector elements, possible undiscovered portions, and moving customer inclinations. This, thus, enables organizations to adjust their contributions and methodologies proactively, remaining on the ball in Myanmar's quickly changing business sector scene. As well as illuminating vital business choices, subjective statistical surveying encourages a more profound association among organizations and the nearby local area. By effectively including Myanmar purchasers in the examination cycle, organizations show a promise to understanding and tending to their requirements, cultivating trust and brand reliability simultaneously. This human-driven approach is especially relevant in Myanmar, where individual connections and local area ties hold huge influence over customer conduct.

Literacy, usually in Arabic, was spread through the teaching of the Qur’an. Thus the mosques became centres of learning. In this way, the peoples of northern and western Africa were exposed to and contributed to the intellectual achievements of the Muslim world. These achievements were considerable, especially in the fields of mathematics and science; it was people from this vast Muslim-Arab world who developed our modern numeral system based on counting from 1 to 10. They invented algebra, the use of the decimal point and the number zero – a mathematical concept missed by the Ancient Greeks. They developed physics and astronomy. They studied chemistry and were the first people to separate medicine from religion and develop it as a secular science. As we shall see later in this chapter, the peoples of the western Sudan became part of this Muslim intellectual tradition.

The research director at Fairchild Semiconductor Co., a brilliant engineer named Gordon Moore, contributed a four-page piece insouciantly entitled “Cramming More Components onto Integrated Circuits.” The essay forecast that as circuits became more densely packed with microscopic transistors, computing power would exponentially increase in performance and diminish in cost over the years. Moore contended that this trend could be predicted mathematically, so that memory costing $500,000 in 1965 would come all the way down to $3,000 by 1985—an insight so basic to the subsequent growth and expansion of the computer industry that ever since then it has been known as “Moore’s Law.

Much science in many disciplines consists of a toolkit of very simple mathematical models. To many not familiar with the subtle art of the simple model, such formal exercises have two seemingly deadly flaws. First, they are not easy to follow. […] Second, motivation to follow the math is often wanting because the model is so cartoonishly simple relative to the real world being analyzed. Critics often level the charge ‘‘reductionism’’ with what they take to be devastating effect. The modeler’s reply is that these two criticisms actually point in opposite directions and sum to nothing. True, the model is quite simple relative to reality, but even so, the analysis is difficult. The real lesson is that complex phenomena like culture require a humble approach. We have to bite off tiny bits of reality to analyze and build up a more global knowledge step by patient step. […] Simple models, simple experiments, and simple observational programs are the best the human mind can do in the face of the awesome complexity of nature. The alternatives to simple models are either complex models or verbal descriptions and analysis. Complex models are sometimes useful for their predictive power, but they have the vice of being difficult or impossible to understand. The heuristic value of simple models in schooling our intuition about natural processes is exceedingly important, even when their predictive power is limited. […] Unaided verbal reasoning can be unreliable […] The lesson, we think, is that all serious students of human behavior need to know enough math to at least appreciate the contributions simple mathematical models make to the understanding of complex phenomena. The idea that social scientists need less math than biologists or other natural scientists is completely mistaken.

Mowaljarlai rarely answered questions with an abstract explanation; he always told a story. His was not a fragmented world, divided into the convenient disciplinary languages and jargon that seem to be required for the understanding of concepts and principles in, for example, mathematics, physics, art and literature. Not only did he not have these languages; he thought this was a strange way to arrive at understanding the way in which the world lives in itself. It baffled him that whitefellas developed their knowledge by busting things up, reducing things to little pieces separate from everything else that contributes to their nature. For him, everything in creation is not only living and interconnected, but exists in a story and story cycle. Yet his knowledge of what whitefellas call ‘science’ was extraordinary.” p80-1.

One of Smale’s first contributions, as it happened, was his faulty conjecture. In physical terms, he was proposing a law of nature something like this: A system can behave erratically, but the erratic behavior cannot be stable. Stability—“stability in the sense of Smale,” as mathematicians would sometimes say—was a crucial property. Stable behavior in a system was behavior that would not disappear just because some number was changed a tiny bit. Any system could have both stable and unstable behaviors within it. The equations governing a pencil standing on its point have a good mathematical solution with the center of gravity directly above the point—but you cannot stand a pencil on its point because the solution is unstable. The slightest perturbation draws the system away from that solution. On the other hand, a marble lying at the bottom of a bowl stays there, because if the marble is perturbed slightly it rolls back. Physicists assumed that any behavior they could actually observe regularly would have to be stable, since in real systems tiny disturbances and uncertainties are unavoidable. You never know the parameters exactly. If you want a model that will be both physically realistic and robust in the face of small perturbations, physicists reasoned that you must surely want a stable model.

The universe is a collective mathematical composition, and we are all solo artists adding our own individual contribution.

A Solution Waiting for a Problem Engineers tend to develop tools for the pleasure of developing tools, not to induce nature to yield its secrets. It so happens that some of these tools bring us more knowledge; because of the silent evidence effect, we forget to consider tools that accomplished nothing but keeping engineers off the streets. Tools lead to unexpected discoveries, which themselves lead to other unexpected discoveries. But rarely do our tools seem to work as intended; it is only the engineer’s gusto and love for the building of toys and machines that contribute to the augmentation of our knowledge. Knowledge does not progress from tools designed to verify or help theories, but rather the opposite. The computer was not built to allow us to develop new, visual, geometric mathematics, but for some other purpose. It happened to allow us to discover mathematical objects that few cared to look for. Nor was the computer invented to let you chat with your friends in Siberia, but it has caused some long-distance relationships to bloom. As an essayist, I can attest that the Internet has helped me to spread my ideas by bypassing journalists. But this was not the stated purpose of its military designer. The laser is a prime illustration of a tool made for a given purpose (actually no real purpose) that then found applications that were not even dreamed of at the time. It was a typical “solution looking for a problem.” Among the early applications was the surgical stitching of detached retinas. Half a century later, The Economist asked Charles Townes, the alleged inventor of the laser, if he had had retinas on his mind. He had not. He was satisfying his desire to split light beams, and that was that. In fact, Townes’s colleagues teased him quite a bit about the irrelevance of his discovery. Yet just consider the effects of the laser in the world around you: compact disks, eyesight corrections, microsurgery, data storage and retrieval—all unforeseen applications of the technology.* We build toys. Some of those toys change the world. Keep

Perhaps Cardano's curious combination of a mystical and a scientifically rational personality allowed him to catch these first glimmerings of what developed to be one of the most powerful of mathematical conceptions. In later years, through the work of Bombelli, Coates, Euler, Wessel, Argand, Gauss, Cauchy, Weierstrass, Riemann, Levi, Lewy, and many others, the theory of complex numbers has flowered into one of the most elegant and universally applicable of mathematical structures. But not until the advent of the quantum theory, in the first quarter of this century, was a strange and all-pervasive role for complex numbers revealed at the very foundational structure of the actual physical world in which we live-nor had their profound link with probabilities been perceived before this. Even Cardano could have had no inkling of a mysterious underlying connection between his two greatest contributions to mathematics-a link that forms the very basis of the material universe at its smallest scales.

So, in one slightly technical line, here's the mathematical skinny. There's an equation in string theory that has a contribution of the form (D-10) times (Trouble), where D represents the number of spacetime dimensions and Trouble is a mathematical expression resulting in troublesome physical phenomena, such as the violation of energy conservation mentioned above. As to why the equation takes this precise form, I can't offer any intuitive, nontechnical explanation. But if you do the calculation, that's where the math leads. Now, this simple but key observation is that if the number of spacetime dimensions is ten, not the four we expect, the contribution becomes 0 times Trouble. And since 0 times anything is 0, in a universe with ten spacetime dimensions the trouble gets wiped away. That's how the math plays out. Really. And that's why string theorists argue for a universe with more than four spacetime dimensions.

The immediate catalyst for the emergence of the Enlightenment in the eighteenth century was the scientific revolution of the sixteenth and seventeenth centuries, which included three momentous discoveries in astronomy: Johannes Kepler delineated the rules that govern the movement of the planets, Galileo Galilei placed the sun at the center of the universe, and Isaac Newton discovered the force of gravity, invented calculus (Gottfried Wilhelm Leibniz independently discovered it at the same time), and used it to describe the three laws of motion. In so doing, Newton joined physics and astronomy and illustrated that even the deepest truths in the universe could be revealed by the methods of science. These contributions were celebrated in 1660 with the formation of the first scientific society in the world: the Royal Society of London for Improving Natural Knowledge, which elected Isaac Newton as its president in 1703. The founders of the Royal Society thought of God as a mathematician who had designed the universe to function according to logical and mathematical principles. The role of the scientist—the natural philosopher—was to employ the scientific method to discover the physical principles underlying the universe and thereby decipher the codebook that God had used in creating the cosmos. Success in the realm of science led eighteenth-century thinkers to assume that other aspects of human action, including political behavior, creativity, and art, could be improved by the application of reason, leading ultimately to an improved society and better conditions for all humankind. This confidence in reason and science affected all aspects of political and social life in Europe and soon spread to the North American colonies. There, the Enlightenment ideas that society can be improved through reason and that rational people have a natural right to the pursuit of happiness are thought to have contributed to the Jeffersonian democracy that we enjoy today in the United States.

It might be objected that men are not trees; that if a man realizes something ought to be done, he can go and do it. This is true within certain limits. There can be social conditions favourable to mathematical studies; if a country urgently needs mathematicians, and if everyone knows this, mathematics may well flourish. But this still does not answer the question of how · it comes to flourish. An external motive, good or bad, is not enough. Greed for money, desire for fame, love of humanity are equally incapable of making a man a composer of great music. It has been said that most young men would like to be able to sit down at the piano and improvise sonatas before admiring crowds. But few do it; to desire the end does not provide the means; to make music you must be interested in music, as well as (or instead of) in being admired. And to make mathematics you must be interested in mathematics. The fascination of pattern and the logical classification of pattern must have taken hold of you. It need not be the only emotion in your mind; you may pursue other aims, respond to other duties; but if it is not there, you will contribute nothing to mathematics.

The Historical Setting of Genesis Mesopotamia: Sumer Through Old Babylonia Sumerians. It is not possible at this time to put Ge 1–11 into a specific place in the historical record. Our history of the ancient Near East begins in earnest after writing has been invented, and the earliest civilization known to us in the historical record is that of the Sumerians. This culture dominated southern Mesopotamia for over 500 years during the first half of the third millennium BC (2900–2350 BC), known as the Early Dynastic Period. The Sumerians have become known through the excavation of several of their principal cities, which include Eridu, Uruk and Ur. The Sumerians are credited with many of the important developments in civilization, including the foundations of mathematics, astronomy, law and medicine. Urbanization is also first witnessed among the Sumerians. By the time of Abraham, the Sumerians no longer dominate the ancient Near East politically, but their culture continues to influence the region. Other cultures replace them in the political arena but benefit from the advances they made. Dynasty of Akkad. In the middle of the twenty-fourth century BC, the Sumerian culture was overrun by the formation of an empire under the kingship of Sargon I, who established his capital at Akkad. He ruled all of southern Mesopotamia and ranged eastward into Elam and northwest to the Mediterranean on campaigns of a military and economic nature. The empire lasted for almost 150 years before being apparently overthrown by the Gutians (a barbaric people from the Zagros Mountains east of the Tigris), though other factors, including internal dissent, may have contributed to the downfall. Ur III. Of the next century little is known as more than 20 Gutian kings succeeded one another. Just before 2100 BC, the city of Ur took control of southern Mesopotamia under the kingship of Ur-Nammu, and for the next century there was a Sumerian renaissance in what has been called the Ur III period. It is difficult to ascertain the limits of territorial control of the Ur III kings, though the territory does not seem to have been as extensive as that of the dynasty of Akkad. Under Ur-Nammu’s son Shulgi, the region enjoyed almost a half century of peace. Decline and fall came late in the twenty-first century BC through the infiltration of the Amorites and the increased aggression of the Elamites to the east. The Elamites finally overthrew the city. It is against this backdrop of history that the OT patriarchs emerge. Some have pictured Abraham as leaving the sophisticated Ur that was the center of the powerful Ur III period to settle in the unknown wilderness of Canaan, but that involves both chronological and geographic speculation. By the highest chronology (i.e., the earliest dates attributed to him), Abraham probably would have traveled from Ur to Harran during the reign of Ur-Nammu, but many scholars are inclined to place Abraham in the later Isin-Larsa period or even the Old Babylonian period. From a geographic standpoint it is difficult to be sure that the Ur mentioned in the Bible is the famous city in southern Mesopotamia (see note on 11:28). All this makes it impossible to give a precise background of Abraham. The Ur III period ended in southern Mesopotamia as the last king of Ur, Ibbi-Sin, lost the support of one city after another and was finally overthrown by the Elamites, who lived just east of the Tigris. In the ensuing two centuries (c. 2000–1800 BC), power was again returned to city-states that controlled more local areas. Isin, Larsa, Eshnunna, Lagash, Mari, Assur and Babylon all served as major political centers.

Hamilton's original contribution was to realize that indirect fitness effects impact upon the purpose of adaptation. The basic condition for natural selection to favor any trait is that the individuals who carry genes for this trait are, on average, fitter than those who do not. However, the adaptations that subsequently evolve are not designed for maximizing the individual's personal fitness, but rather her inclusive fitness, i.e., the sum of all the fitness effects that she has on all of her genetic relatives, each increment or decrement being weighted by the corresponding coefficient of genetic relatedness (Hamilton 1964). In other words, the adaptive agent remains the same as in the traditional Darwinian view (i.e., the individual organism), but the adaptive agenda is changed. This idea has subsequently been formalized by Grafen (2006), who has shown the mathematical connection between the dynamics of natural selection and an optimization program in whih the individual strives to maximize her inclusive fitness, for a wide class of models, including those that allow for social interaction between relatives. Grafen A. 2006. Optimization of inclusive fitness. J Theor Biol 238: 541-563. Hamilton WD. 1964. The genetical evolution of social behaviour I & II. J Theor Biol 7: 1-52.

Mathematical modelling is a world-renowned field of research in mathematics education. The International Conference on the Teaching and Learning of Mathematical Modelling and Applications (ICTMA), for example, presents the current state of the international debate on mathematical modelling every two years. Contributions made at these conferences are published in Springer’s International Perspectives on the Teaching and Learning of Mathematical Modelling series. In addition, the ICMI study Modelling and Applications in Mathematics Education

Half way through life a thoughtful person must undertake an honest assessment of their life. I am now fifty years old. I am rapidly turning into a dry stalk, my breath is sour, and I am beginning to smell of the grave. I melancholy project that in all probability I have now existed about half the period of time that I shall remain in this sublunary world. Resembling the trajectory of other men reaching middle age, my upward ascent in life crested and now I am commencing the meteoric downhill descent. Distinct from Americas’ pioneers and other luminaries whom played an important role in expanding our knowledge and deepened our appreciation of nature, I have done nothing to advance the human condition. I have not mapped any new territory, contributed to the arts or sciences, or expanded our comprehension of mathematics or the natural sciences: astronomy, biology, chemistry, the Earth sciences, and physics. I did not contribute to medicine, cognitive science, behavioral science, social science, or the humanities. Unlike revered social leaders whom advocated peaceful relations with all people, I remained mute while domestic and international conflicts sundered communities. I created no historical existence; I exist only as an introspective being. I have not added one iota to the bank of knowledge of succeeding generations. I have not added any quarter of happiness to other people. My contribution to the human race is nil. In all probability, I will flame out without leaving a lasting trace of my mundane personal existence.

The construction of mathematical logic had become the arbiter of truth. This was the Pythagoreans' greatest contribution to civilisation - a way of achieving truth which is beyond the fallibility of human judgement.

Core subjects include English, reading, and language arts; world languages; arts; mathematics; economics; science; geography; history; and government and civics. Learning and innovation skills are those possessed by students who are prepared for the 21st century and include creativity and innovation, critical thinking and problem solving, and communication and collaboration. Information, media, and technology skills are needed to manage the abundance of information and also contribute to the building of it. These include information literacy; media literacy; and information, communications, and technology (ICT) literacy. Life and career skills are those abilities necessary to navigate complex life and work environments. These include flexibility and adaptability, initiative and self-direction, social and cross-cultural skills, productivity and accountability, and leadership and responsibility.

Correspondence and succession, the two principles which permeate all mathematics—nay, all realms of exact thought — are woven into the very fabric of our number system,” he observes. So, indeed, are they woven into the very fabric of Western logic and philosophy. We have already seen how the phonetic technology fostered visual continuity and individual point of view, and how these contributed to the rise of uniform Euclidean space. Dantzig says that it is the idea of correspondence which gives us cardinal numbers. Both of these spatial ideas — lineality and point of view — come with writing, especially with phonetic writing; but neither is necessary in our new mathematics and physics. Nor is writing necessary to an electric technology.

Life Formulas I (2008) These are notes to myself. Your frame of reference, and therefore your calculations, may vary. These are not definitions—these are algorithms for success. Contributions are welcome. Happiness = Health + Wealth + Good Relationships Health = Exercise + Diet + Sleep Exercise = High Intensity Resistance Training + Sports + Rest Diet = Natural Foods + Intermittent Fasting + Plants Sleep = No alarms + 8–9 hours + Circadian rhythms Wealth = Income + Wealth * (Return on Investment) Income = Accountability + Leverage + Specific Knowledge Accountability = Personal Branding + Personal Platform + Taking Risk? Leverage = Capital + People + Intellectual Property Specific Knowledge = Knowing how to do something society cannot yet easily train other people to do Return on Investment = “Buy-and-Hold” + Valuation + Margin of Safety [72] Naval’s Rules (2016) Be present above all else. Desire is suffering. (Buddha) Anger is a hot coal you hold in your hand while waiting to throw it at someone else. (Buddha) If you can’t see yourself working with someone for life, don’t work with them for a day. Reading (learning) is the ultimate meta-skill and can be traded for anything else. All the real benefits in life come from compound interest. Earn with your mind, not your time. 99 percent of all effort is wasted. Total honesty at all times. It’s almost always possible to be honest and positive. Praise specifically, criticize generally. (Warren Buffett) Truth is that which has predictive power. Watch every thought. (Ask “Why am I having this thought?”) All greatness comes from suffering. Love is given, not received. Enlightenment is the space between your thoughts. (Eckhart Tolle) Mathematics is the language of nature.