Best Epistemology Philosophy

The authors credit six key principles: simplicity, unexpectedness, concreteness, credibility, emotions and stories. They illustrate these principles with a host of stories, some familiar (Kennedy's stirring call to "land a man on the moon and return him safely to the earth" within a decade) and others very funny (Nora Ephron's anecdote of how her high school journalism teacher used a simple, embarrassing trick to teach her how not to "bury the lead").

In this indispensable guide, we discover that sticky messages of all kinds–from the infamous “kidney theft ring” hoax to a coach’s lessons on sportsmanship to a vision for a new product at Sony– draw their power from the same six traits. It’s a fast-paced tour of success stories (and failures)– the Nobel Prize-winning scientist who drank a glass of bacteria to prove a point about stomach ulcers; the charities who make use of “the Mother Teresa Effect”; the elementary-school teacher whose simulation actually prevented racial prejudice. Unabashedly inspired by Malcolm Gladwell's bestselling The Tipping Point, the brothers Heath—Chip a professor at Stanford's business school, Dan a teacher and textbook publisher—offer an entertaining, practical guide to effective communication. They illustrate these principles with a host of stories, some familiar (Kennedy's stirring call to "land a man on the moon and return him safely to the earth" within a decade) and others very funny (Nora Ephron's anecdote of how her high school journalism teacher used a simple, embarrassing trick to teach her how not to "bury the lead"). Adult/High School—While at first glance this volume might resemble the latest in a series of trendy business advice books, ultimately it is about storytelling, and it is a how-to for crafting a compelling narrative.

As Tom Nichols shows in The Death of Expertise , this rejection of experts has occurred for many reasons, including the openness of the internet, the emergence of a customer satisfaction model in higher education, and the transformation of the news industry into a 24-hour entertainment machine. ”Nichols expands his 2014 article published by The Federalist with a highly researched and impassioned book that's well timed for this post-election period... strongly researched textbook for laymen will have many political and news junkies nodding their heads in agreement." ”This may sound like a rant you have heard before, but Nichols has a sense of humour and chooses his examples well. ”Excellent...makes important points and offers valuable insight, particularly when it comes to the role of the internet and social media in our political environment...essential reading for anyone interested in this pressing subject." Citizens - now so proudly ill-informed that they cannot even make use of expert opinion in fulfilling their civic role - must rediscover a sense of responsibility. ".

In the book that People magazine proclaimed “beguiling” and “fascinating,” Robert Greene and Joost Elffers have distilled three thousand years of the history of power into 48 essential laws by drawing from the philosophies of Machiavelli, Sun Tzu, and Carl Von Clausewitz and also from the lives of figures ranging from Henry Kissinger to P.T. Elffers's layout (he is identified as the co-conceiver and designer in the press release) is stylish, with short epigrams set in red at the margins. Each law, with such allusive titles as "Pose as a Friend, Work as a Spy," "Get Others to Do the Work for You, But Always Take the Credit," "Conceal Your Intentions," is demonstrated in four ways?using it correctly, failing to use it, key aspects of the law and when not to use it. Illustrations are drawn from the courts of modern and ancient Europe, Africa and Asia, and devious strategies culled from well-known personae: Machiavelli, Talleyrand, Bismarck, Catherine the Great, Mao, Kissinger, Haile Selassie, Lola Montes and various con artists of our century.

"Cheap grace," Bonhoeffer wrote, "is the grace we bestow on ourselves...grace without discipleship....Costly grace is the gospel which must be sought again and again, the girl which must be asked for, the door at which a man must know....It is costly because it costs a man his life, and it is grace because it gives a man the only true life." The Cost of Discipleship , first published in German in 1937, was Bonhoeffer's answer to the questions, "What did Jesus mean to say to us?

In the book that People magazine proclaimed “beguiling” and “fascinating,” Robert Greene and Joost Elffers have distilled three thousand years of the history of power into 48 essential laws by drawing from the philosophies of Machiavelli, Sun Tzu, and Carl Von Clausewitz and also from the lives of figures ranging from Henry Kissinger to P.T. THE BESTSELLING BOOK FOR THOSE WHO WANT POWER, WATCH POWER, OR WANT TO ARM THEMSELVES AGAINST POWER .

However, according to Hofstadter, the formal system that underlies all mental activity transcends the system that supports it. Besides being a profound and entertaining meditation on human thought and creativity, this book looks at the surprising points of contact between the music of Bach, the artwork of Escher, and the mathematics of Gödel. Hofstadter's great achievement in Gödel, Escher, Bach was making abstruse mathematical topics (like undecidability, recursion, and 'strange loops') accessible and remarkably entertaining. Escher, Kurt Gödel: biographical information and work, artificial intelligence (AI) history and theories, strange loops and tangled hierarchies, formal and informal systems, number theory, form in mathematics, figure and ground, consistency, completeness, Euclidean and non-Euclidean geometry, recursive structures, theories of meaning, propositional calculus, typographical number theory, Zen and mathematics, levels of description and computers; theory of mind: neurons, minds and thoughts; undecidability; self-reference and self-representation; Turing test for machine intelligence.

Each chapter presents a concise explanation of the argument, followed by a response illustrating the problems and fallacies inherent in it. Whether you're an atheist, a believer or undecided, this book offers a solid foundation for building your own inquiry about the concept of God. Armin Navabi is a former Muslim from Iran and the founder of Atheist Republic, a non-profit organization with over one million fans and followers worldwide that is dedicated to offering a safe community for atheists around the world to share their ideas and meet like-minded individuals.

The Third Edition of the bestselling text Research Design by John W. Creswell enables readers to compare three approaches to research—qualitative, quantitative, and mixed methods—in a single research methods text. Written in a user-friendly manner, Creswell's text does not rely on technical jargon. Presents the preliminary steps of using philosophical assumptions in the beginning of the book Provides an expanded discussion on ethical issues Emphasizes new Web-based technologies for literature searches Offers updated information about mixed methods research procedures Contains a glossary of terms Highlights “research tips” throughout the chapters incorporating the author’s experiences over the last 35 years. He teaches courses on mixed methods research, qualitative inquiry, and general research design. He also co-founded the SAGE journal, the Journal of Mixed Methods Research , and has been a popular speaker on mixed methods and qualitative research in the US and abroad.

One of the most influential philosophers and theologians in history, St. Thomas Aquinas was the father of modern philosophy of religion, and is infamous for his "proofs" for God’s existence. — Fulvio di Blasi, President, Thomas International. "Lucid, cogent, and compelling.

The Daily Stoic offers 366 days of Stoic insights and exercises, featuring all-new translations from the Emperor Marcus Aurelius, the playwright Seneca, or slave-turned-philosopher Epictetus, as well as lesser-known luminaries like Zeno, Cleanthes, and Musonius Rufus. — Maria Popova , editor of Brain Pickings "A richly rewarding spring of practical wisdom to help you focus on what's in your control, eliminate false and limiting beliefs, and take more effective action. — Jack Canfield , co-author of The Success Principles ™. and the Chicken Soup for the Soul ®. series. " The Daily Stoic is a treasure for managing our choices, overcoming self-deception, and learning to act according to the true worth of things while keeping the common good always in view.

The Conspiracy against the Human Race is renowned horror writer Thomas Ligotti's first work of nonfiction. Should the human race voluntarily put an end to its existence? Do we even know what it means to be human?

Its many fans include a former governor and movie star (Arnold Schwarzenegger), a hip hop icon (LL Cool J), an Irish tennis pro (James McGee), an NBC sportscaster (Michele Tafoya), and the coaches and players of winning teams like the New England Patriots, Seattle Seahawks, Chicago Cubs, and University of Texas men’s basketball team. Ryan Holiday shows us how some of the most successful people in history—from John D. Rockefeller to Amelia Earhart to Ulysses S. Grant to Steve Jobs—have applied stoicism to overcome difficult or even impossible situations. Read this book!”. — Steven Pressfield , author of The War of Art and Gates of Fire. This surprising book shows you how to craft a life of wonder by embracing obstacles and challenges.”. — Chris Guillebeau , author of The $100 Startup "A very, very good book with lots of examples about people who had to overcome great obstacles to have success." Ryan’s book is a how-to guide for just that.”. — James Altucher , investor and author of Choose Yourself “Ryan Holiday has written a brilliant and engaging book, well beyond his years. “Even though I was familiar with the basis for this book — the ancient philosophy of stoicism: overcoming obstacles through the practice of wisdom, courage, self-control, and mindfulness — it felt like a revelation when I read it.” —Allison K. Hill , Los Angeles Daily News.

In The Prince he does not explain what he thinks the best ethical or political goals are, except the control of one's own fortune, as opposed to waiting to see what chance brings. And that more virtue meant less reliance on chance was a classically influenced "humanist commonplace" in Machiavelli's time, as Fischer says, even if it was somewhat controversial. He used the words "virtue" and "prudence" to refer to glory-seeking and spirited excellence of character, in strong contrast to the traditional Christian uses of those terms, but more keeping with the original pre-Christian Greek and Roman concepts from which they derived. Machiavelli's descriptions in The Prince encourage leaders to attempt to control their fortune gloriously, to the extreme extent that some situations may call for a fresh "founding" (or re-founding) of the "modes and orders" that define a community, despite the danger and necessary evil and lawlessness of such a project. Machiavelli justifies this position by explaining how if "a prince did not win love he may escape hate" by personifying injustice and immorality; therefore, he will never loosen his grip since "fear is held by the apprehension of punishment" and never diminishes as time goes by. Niccolò di Bernardo dei Machiavelli (3 May 1469 – 21 June 1527) was a Florentine historian, politician, diplomat, philosopher, humanist, and writer.

Cutting through the haze of academia and untangling complicated theories to show how our social, political, and ethical ideas are formed, The Philosophy Book contextualizes the information around time periods, innovative thinkers, method, and philosophical approach. DK's aim is to inform, enrich, and entertain readers of all ages, and everything DK publishes, whether print or digital, embodies the unique DK design approach. DK acts as the parent company for Alpha Books, publisher of the Idiot's Guides series and Prima Games, video gaming publishers, as well as the award-winning travel publisher, Rough Guides.

In this classic book on thinking, the book describes how each of us shapes the events around us, creating our own lives. in abundance. As himself Allen describes, “ It shows how, in his own thought-world, each man holds the key to every condition, good or bad, that enters into his life, and that, by working patiently and intelligently upon his thoughts, he may remake his life, and transform his circumstances. EFFECT OF THOUGHT ON CIRCUMSTANCES 7.

Among the philosophers considered are: Pythagoras, Heraclitus, Parmenides, Empedocles, Anaxagoras, the Atomists, Protagoras, Socrates, Plato, Aristotle, the Cynics, the Sceptics, the Epicureans, the Stoics, Plotinus, Ambrose, Jerome, Augustine, Benedict, Gregory the Great, John the Scot, Aquinas, Duns Scotus, William of Occam, Machiavelli, Erasmus, More, Bacon, Hobbes, Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, Rousseau, Kant, Hegel, Schopenhauer, Nietzsche, the Utilitarians, Marx, Bergson, James, Dewey, and lastly the philosophers with whom Lord Russell himself is most closely associated—Cantor, Frege, and Whitehead, coauthor with Russell of the monumental Principia Mathematica. They invented mathematics and science and philosophy; they first wrote history as opposed to mere annals; they speculated freely about the nature of the world and the ends of life, without being bound in the fetters of any inherited orthodoxy. What occurred was so astonishing that, until very recent times, men were content to gape and talk mystically about the Greek genius. Philosophy begins with Thales, who, fortunately, can be dated by the fact that he predicted an eclipse which, according to the astronomers, occurred in the year 585 B.C. The early development of civilization in Egypt and Mesopotamia was due to the Nile, the Tigris, and the Euphrates, which made agriculture very easy and very productive. The Egyptians were preoccupied with death, and believed that the souls of the dead descend into the underworld, where they are judged by Osiris according to the manner of their life on earth. They left no permanent mark on Egypt, but their presence there must have helped to spread Egyptian civilization in Syria and Palestine. When Greek colonists in Asia Minor found temples to her, they named her Artemis and took over the existing cult. Christianity transformed her into the Virgin Mary, and it was a Council at Ephesus that legitimated the title "Mother of God" as applied to Our Lady. A rich priestly caste elaborated the ritual and the theology, and fitted together into a pantheon the several divinities of the component parts of the empire. Magic, divination, and astrology, though not peculiar to Babylonia, were more developed there than elsewhere, and it was chiefly through Babylon that they acquired their hold on later antiquity. Weapons, until about 1000 B.C., were made of bronze, and nations which did not have the necessary metals on their own territory were obliged to obtain them by trade or piracy. Piracy was a temporary expedient, and where social and political conditions were fairly stable, commerce was found to be more profitable. What survives of Cretan art gives an impression of cheerfulness and almost decadent luxury, very different from the terrifying gloom of Egyptian temples. The centre of the Cretan civilization was the so-called "palace of Minos" at Knossos, of which memories lingered in the traditions of classical Greece. The palaces of Crete were very magnificent, but were destroyed about the end of the fourteenth century B.C., probably by invaders from Greece. The bull-fights were religious celebrations, and Sir Arthur Evans thinks that the performers belonged to the highest nobility. Before the destruction of the Minoan culture, it spread, about 1600 B.C., to the mainland of Greece, where it survived, through gradual stages of degeneration, until about 900 B.C. This mainland civilization is called the Mycenaean; it is known through the tombs of kings, and also through fortresses on hill- tops, which show more fear of war than had existed in Crete. The older art products in the palaces are either actually of Cretan workmanship, or closely akin to those of Crete. The Mycenaean civilization, which had been weakened by the warfare of the Ionians and Achaeans, was practically destroyed by the Dorians, the last Greek invaders. Both during the later part of the Mycenaean age and after its end, some of the invaders settled down and became agriculturists, while some pushed on, first into the islands and Asia Minor, then into Sicily and southern Italy, where they founded cities that lived by maritime commerce. It was in these maritime cities that the Greeks first made qualitatively new contributions to civilization; the supremacy of Athens came later, and was equally associated, when it came, with naval power. In these valleys little separate communities grew up, living by agriculture, and centering round a town, generally close to the sea. In such circumstances it was natural that, as soon as the population of any community grew too great for its internal resources, those who could not live on the land should take to seafaring. In Sparta, a small aristocracy subsisted on the labour of oppressed serfs of a different race; in the poorer agricultural regions, the population consisted mainly of farmers cultivating their own land with the help of their families. The kings were not absolute, like those of Egypt and Babylonia; they were advised by a Council of Elders, and could not transgress custom with impunity. The early tyrants, like the Medici, acquired their power through being the richest members of their respective plutocracies. Often the source of their wealth was the ownership of gold and silver mines, made the more profitable by the new institution of coinage, which came from the kingdom of Lydia, adjacent to Ionia. One of the most important results, to the Greeks, of commerce or piracy -- at first the two are scarcely distinct -- was the acquisition of the art of writing. They learnt the art from the Phoenicians, who, like the other inhabitants of Syria, were exposed to both Egyptian and Babylonian influences, and who held the supremacy in maritime commerce until the rise of the Greek cities of Ionia, Italy, and Sicily. In the fourteenth century, writing to Ikhnaton (the heretic king of Egypt), Syrians still used the Babylonian cuneiform; but Hiram of Tyre (969-936) used the Phoenician alphabet, which probably developed out of the Egyptian script. The Greeks, borrowing from the Phoenicians, altered the alphabet to suit their language, and made the important innovation of adding vowels instead of having only consonants. There can be no doubt that the acquisition of this convenient method of writing greatly hastened the rise of Greek civilization. From his time onward, the Athenian youth learnt Homer by heart, and this was the most important part of their education. The Homeric poems, like the courtly romances of the later Middle Ages, represent the point of view of a civilized aristocracy, which ignores as plebeian various superstitions that are still rampant among the populace. Guided by anthropology, modern writers have come to the conclusion that Homer, so far from being primitive, was an expurgator, a kind of eighteenth-century rationalizer of ancient myths, holding up an upper-class ideal of urbane enlightenment. There were other darker and more savage elements in popular religion, which were kept at bay by the Greek intellect at its best, but lay in wait to pounce in moments of weakness or terror. In the time of decadence, beliefs which Homer had discarded proved to have persisted, half buried, throughout the classical period. Certain rites were performed, which were intended, by sympathetic magic, to further the interests of the tribe, especially in respect of fertility, vegetable, animal, and human. The winter solstice was a time when the sun had to be encouraged not to go on diminishing in strength; spring and harvest also called for appropriate ceremonies. These were often such as to generate a great collective excitement, in which individuals lost their sense of separateness and felt themselves at one with the whole tribe. All over the world, at a certain stage of religious evolution, sacred animals and human beings were ceremonially killed and eaten. Fertility rites without such cruel aspects were common throughout Greece; the Eleusinian mysteries, in particular, were essentially agricultural in their symbolism. Fate exercised a great influence on all Greek thought, and perhaps was one of the sources from which science derived the belief in natural law. They fight, and feast, and play, and make music; they drink deep, and roar with laughter at the lame smith who waits on them. "Tantalos, the Asiatic founder of the dynasty, began its career by a direct offence against the gods; some said, by trying to cheat them into eating human flesh, that of his own son Pelops. He won his famous chariot-race against Oinomaos, king of Pisa, by the connivance of the latter's charioteer, Myrtilos, and then got rid of his confederate, whom he had promised to reward, by flinging him into the sea. The curse descended to his sons, Atreus and Thyestes, in the form of what the Greeks called ate, a strong if not actually irresistible impulse to crime. Atreus in turn secured his brother's banishment, and recalling him under pretext of a reconciliation, feasted him on the flesh of his own children. The curse was now inherited by Atreus' son Agamemnon, who offended Artemis by killing a sacred stag, sacrificed his own daughter Iphigenia to appease the goddess and obtain a safe passage to Troy for his fleet, and was in his turn murdered by his faithless wife Klytaimnestra and her paramour Aigisthos, a surviving son of Thyestes. Homer as a finished achievement was a product of Ionia, i.e. of a part of Hellenic Asia Minor and the adjacent islands. The rest of Greece succeeded in preserving its independence at the battles of Salamis and Plataea, after which Ionia was liberated for a time. Greece was divided into a large number of small independent states, each consisting of a city with some agricultural territory surrounding it. Then there were purely agricultural rural communities, such as the proverbial Arcadia, which townsmen imagined to be idyllic, but which really was full of ancient barbaric horrors. The inhabitants worshipped Pan, and had a multitude of fertility cults, in which, often, a mere square pillar did duty in place of a statue of the god. This was connected, not with the Olympians, but with Dionysus, or Bacchus, whom we think of most naturally as the somewhat disreputable god of wine and drunkenness. The way in which, out of his worship, there arose a profound mysticism, which greatly influenced many of the philosophers, and even had a part in shaping Christian theology, is very remarkable, and must be understood by anyone who wishes to study the development of Greek thought. Respectable matrons and maids, in large companies, would spend whole nights on the bare hills, in dances which stimulated ecstasy, and in an intoxication perhaps partly alcoholic, but mainly mystical. Like all communities that have been civilized quickly, the Greeks, or at least a certain proportion of them, developed a love of the primitive, and a hankering after a more instinctive and passionate way of life than that sanctioned by current morals. To the man or woman who, by compulsion, is more civilized in behaviour than in feeling, rationality is irksome and virtue is felt as a burden and a slavery. This habit began to be important with the rise of agriculture; no animal and no savage would work in the spring in order to have food next winter, except for a few purely instinctive forms of action, such as bees making honey or squirrels burying nuts. True forethought only arises when a man does something towards which no impulse urges him, because his reason tells him that he will profit by it at some future date. Hunting requires no forethought, because it is pleasurable; but tilling the soil is labour, and cannot be done from spontaneous impulse. The institution of private property brings with it the subjection of women, and usually the creation of a slave class. In intoxication, physical or spiritual, he recovers an intensity of feeling which prudence had destroyed; he finds the world full of delight and beauty, and his imagination is suddenly liberated from the prison of every-day preoccupations. In one of them, Bacchus is the son of Zeus and Persephone; while still a boy, he is torn to pieces by Titans, who eat his flesh, all but the heart. Orphic tablets have been found in tombs, giving instructions to the soul of the dead person as to how to find his way in the next world, and what to say in order to prove himself worthy of salvation. He has no respect for the coldly self-righteous well-behaved man, who, in his tragedies, is apt to be driven mad or otherwise brought to grief by the gods in resentment of his blasphemy. At Eleusis, where the Eleusinian mysteries formed the most sacred part of Athenian State religion, a hymn was sung, saying: In the Bacchae of Euripides, the chorus of Maenads displays a combination of poetry and savagery which is the very reverse of serene. The dance of the Maenads on the mountain side was not only fierce; it was an escape from the burdens and cares of civilization into the world of non-human beauty and the freedom of wind and stars. We are bound to a wheel which turns through endless cycles of birth and death; our true life is of the stars, but we are tied to earth. Only by purification and renunciation and an ascetic life can we escape from the wheel and attain at last to the ecstasy of union with God. Their prototype in mythology is not Olympian Zeus, but Prometheus, who brought fire from heaven and was rewarded with eternal torment. "But the Greek nation was too full of youthful vigour for the general acceptance of a belief which denies this world and transfers real life to the Beyond. A full millennium was to pass before these ideas -- in a quite different theological dress, it is true -- achieved victory in the Greek world." It seems probable that educated Athenians; even in the best period, however rationalistic they may have been in their explicitly conscious mental processes, retained from tradition and from childhood a more primitive way of thinking and feeling, which was always liable to prove victorious in times of stress. The most balanced statement known to me is in John Burnet's Early Greek Philosophy, especially Chapter II, "Science and Religion." A conflict between science and religion arose, he says, out of "the religious revival which swept over Hellas in the sixth century B.C.," together with the shifting of the scene from Ionia to the West. In particular, the worship of Dionysus, which came from Thrace, and is barely mentioned in Homer, contained in germ a wholly new way of looking at man's relation to the world. "The new religion -- for in one sense it was new, though in another as old as mankind -- reached its highest point of development with the foundation of the Orphic communities. The poems which contained their theology were ascribed to the Thracian Orpheus, who had himself descended into Hades, and was therefore a safe guide through the perils which beset the disembodied soul in the next world." Burnet goes on to state that there is a striking similarity between Orphic beliefs and those prevalent in India at about the same time, though he holds that there cannot have been any contact. The Orphics, unlike the priests of Olympian cults, founded what we may call "churches," i.e. religious communities to which anybody, without distinction of race or sex, could be admitted by initiation, and from their influence arose the conception of philosophy as a way of life.

Why do tall parents have shorter children? Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God. Manil Suri, The Washington Post : “Brilliantly engaging.... Ellenberg’s talent for finding real-life situations that enshrine mathematical principles would be the envy of any math teacher. I am reminded of the great writer of recreational mathematics, Martin Gardner: Ellenberg shares Gardner’s remarkable ability to write clearly and entertainingly, bringing in deep mathematical ideas without the reader registering their difficulty.”. [Ellenberg]writes that, at its core, math is a special thing and produces a feeling of understanding unattainable elsewhere: ‘You feel you’ve reached into the universe’s guts and put your hand on the wire.’ Math is profound, and profoundly awesome, so we should use it well—or risk being wrong….Witty and expansive, Ellenberg’s math will leave readers informed, intrigued and armed with plenty of impressive conversation starters.”. Relying on remarkably few technical formulas, Ellenberg writes with humor and verve as he repeatedly demonstrates that mathematics simply extends common sense. Steven Pinker, Johnstone Family Professor of Psychology, Harvard University; author of How the Mind Works : “The title of this wonderful book explains what it adds to the honorable genre of popular writing on mathematics. Like Lewis Carroll, George Gamow, and Martin Gardner before him, Jordan Ellenberg shows how mathematics can delight and stimulate the mind. Steven Strogatz, Schurman Professor of Applied Mathematics, Cornell University, and author, The Joy of x : “With math as with anything else, there’s smart, and then there’s street smart. John Allen Paulos, author of Innumeracy and A Mathematician Reads the Newspaper : “Through a powerful mathematical lens Jordan Ellenberg engagingly examines real-world issues ranging from the fetishizing of straight lines in the reporting of obesity to the game theory of missing flights, from the relevance to digestion of regression to the mean to the counter-intuitive Berkson’s paradox, which may explain why handsome men don’t seem to be as nice as not so handsome ones. Ellenberg shows his readers how to magnify common sense using the tools usually only accessible to those who have studied higher mathematics.