But from the perspective of mathematics, groupings of ten are arbitrary, and can have serious shortcomings. Twelve would be better for divisibility, and eight is smaller and well suited to repeated halving. Grouping by two, as in binary code, has turned out to have its own remarkable advantages.Paul Lockhart reveals arithmetic not as the rote manipulation of numbers--a practical if mundane branch of knowledge best suited for balancing a checkbook or filling out tax forms--but as a set of ideas that exhibit the fascinating and sometimes surprising behaviors usually reserved for higher branches of mathematics. The essence of arithmetic is the skillful arrangement of numerical information for ease of communication and comparison, an elegant intellectual craft that arises from our desire to count, add to, take away from, divide up, and multiply quantities of important things. Over centuries, humans devised a variety of strategies for representing and using numerical information, from beads and tally marks to adding machines and computers. Lockhart explores the philosophical and aesthetic nature of counting and of different number systems, both Western and non-Western, weighing the pluses and minuses of each.A passionate, entertaining survey of foundational ideas and methods, Arithmetic invites readers to experience the profound and simple beauty of its subject through the eyes of a modern research mathematician.

    Moreover, the achievements of the early people of Africa are as amazing and inspiring as the achievements of any other people.This history is much older than the Trans-Atlantic Slave Trade.The author introduces his readers to the early civilizations of Africa that existed long before the coming of the Europeans. Among these were the Songhai Empire, the Benin Empire, the Kanem-Borno Empire, the Monomotapa Empire, the Swahili Confederation, the Medieval Nubian kingdoms and the Axumite Empire.The author also introduces the ancient civilizations of Africa particularly those of the Nile Valley such as Nubia and Ancient Egypt.The book is illustrated with 18 images and maps. Finally, the book recommends other books for more in depth study.

    With exceptional clarity, Franz n gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of "Logical Dilemmas: The Life and Work of Kurt G del

    Not only the result of a carving of Korean territories following the Pacific conflicts of the Second World War, it was also a battle of ideologies as General MacArthur’s American military forces occupied the southern half and Stalin’s Soviet forced supported the northern half.Initiated by infantry movements and air raids, the region gradually became mired in a static trench war by July 1951, and would continue to cost both sides in both morale and human lives. The Korean War: History in an Hour is the concise story to one of the most bitter and enduring conflicts of the post-war era.

    These lectures are based on their seminar course at Columbia University on Western intellectual history augmented by additional lectures by selected "guest" lecturers. Gives a guided tour through 3,000 years of Western thought.In 7 containers (26 cm.).Lectures by Darren M. Staloff, Louis Markos, Jeremy Adams, Phillip Cary, Dennis G. Dalton, Alan Charles Kors, Jeremy Shearmur, Kathleen M. Higgins, Robert Hilary Kane, Robert C. Solomon, Douglas Kellner, and Mark W. Risjord.42 audiocassettes (approximately 2520 min.) : analog, Dolby processed + 7 course guidebooks (22 cm).Contents:pt. 1. Classical origins --pt. 2. Christian age --pt. 3. From the Renaissance to the Age of Reason --pt. 4. Enlightenment and its critics --pt. 5. Age of ideology --pt. 6. Modernism and the age of analysis --pt. 7. Age of modernity.

    As exciting as any action/adventure novel, this is actually the story of incredible individuals and engrossing tales behind the most profound, enduring mathematical theorems.Archimedes famously ran naked through the streets shouting, “Eureka, eureka!” after finding a method for measuring the volume of an irregular-shaped object. René Descartes was not only a great French mathematician, philosopher, physicist, and natural scientist; he was also an expert swordsman who traveled with European armies from town to town, dressed in green taffeta and accompanied by a valet. Georg Cantor grappled with mental illness as he explored the highly counterintuitive, bizarre properties of infinite sets and numbers. Emmy Noether struggled to find employment as she laid the mathematical groundwork for modern theoretical physics. And Alexander Grothendieck taught himself mathematics while interned in Nazi concentration camps, only to disappear into the Pyrenees at the zenith of his career.These are just a few stories recounted in this absorbing narrative. In probing the lives of the preeminent mathematicians in history, a Strange Wilderness will leave you entertained and enlightened, with a newfound appreciation of the tenacity, complexity, and brilliance of the mathematical genius.

    It's not likely to be advice you'll hear from anyone else. It is only about an hour to read, but the concepts will ring in your ears for years. [From the Book's Introduction] Many people have been incredibly generous to me throughout the first decade of my career. To return that good karma, I try to pay it forward… to be open and available for people who ask me for insight or advice or just have questions about where to go next. I find myself having many conversations about career decisions. Recently, many of these conversations have repeating many of the same pieces of advice. Over the years I’ve gotten enough positive feedback that publishing these thoughts seems worthwhile. After our conversations I’m often told that this advice was unique, counterintuitive, and valuable. That is a high compliment. And if more people would think the same, then I should put these thought somewhere more scalable and accessible. So, I’ve written them down here.

    So-called illiberal democracy and authoritarian populism are in the political ascendant; the shelves of our bookshops groan with the work of attention-grabbing thinkers insisting that permissiveness, multiculturalism and 'identity politics' have failed us and that we must now fall back on some notion of tradition. We have had our fun, and now it's time to get serious, to shore our fragments against the ruin of postmodernist meaninglessness. It's not only the usual, conservative suspects who have got on board with this argument. Authentocrats critiques the manner in which post-liberal ideas have been mobilised underhandedly by centrist politicians who, at least notionally, are hostile to the likes of Donald Trump and UKIP. It examines the forms this populism of the centre has taken in the United Kingdom and situates the moderate withdrawal from liberalism within a story which begins in the early 1990s. Blairism promised socially liberal politics as the pay-off for relinquishing commitments to public ownership and redistributive policies: many current centrists insist New Labour's error was not its capitulation to the market, but its unwillingness to heed the allegedly natural conservatism of England's provincial working classes. In this book, we see how this spurious concern for 'real people' is part of a broader turn within British culture by which the mainstream withdraws from the openness of the Nineties under the bad-faith supposition that there's nowhere to go but backwards. The self-anointing political realism which declares that the left can save itself only by becoming less liberal is matched culturally by an interest in time-worn traditional identities: the brute masculinity of Daniel Craig's James Bond, the allegedly 'progressive' patriotism of nature writing, a televisual obsession with the World Wars. Authentocrats charges liberals themselves with fuelling the post-liberal turn, and asks where the space might be found for an alternative.

    The guru of Sixties radicals, Alinsky urged his followers to be flexible and opportunistic and say anything to get power, which they can then use to radically change existing social and economic institutions. In this insightful new booklet, Horowitz discusses Alinsky’s work in the 60s—and his advice to radicals to seize any weapon to advance their cause. This became the philosophy of Alinskyite organizations such as ACORN and influenced the future President who came up through the Chicago network created by Alinsky’s network. After analyzing Saul Alinsky’s work and pointing out that the godfather of “social organizing” created “ not salvation but chaos,” Horowitz then he asks the crucial question: “And presidential disciples of Alinsky, what will they create?”

    This concept is at the root of the computational worldview, which basically says that very complex systems — the world we live in — have their beginnings in simple mathematical equations. We've lately come to understand that such an algorithm is only the start of a never-ending story — the real action occurs in the unfolding consequences of the rules. The chip-in-a-box computers so popular in our time have acted as a kind of microscope, letting us see into the secret machinery of the world. In Lifebox, Rucker uses whimsical drawings, fables, and humor to demonstrate that everything is a computation — that thoughts, computations, and physical processes are all the same. Rucker discusses the linguistic and computational advances that make this kind of "digital philosophy" possible, and explains how, like every great new principle, the computational world view contains the seeds of a next step.

    Originally titled The Intelligent Woman's Guide to Conservatism, this little book was essentially a popular version of The Conservative Mind.   Now, a century after its author’s birth, this neglected gem has been recovered. It remains what Kirk intended it to be: an accessible introduction to conservative ideas, especially for the young. With a new title and an introduction by the eminent intellectual historian Wilfred M. McClay, Russell Kirk’s Concise Guide to Conservatism arrives with uncanny timing. The movement that Kirk defined in 1953 is today so contested and fragmented that no one seems able to say with confidence what conservatism means.  This book, as fresh and prophetic as the day it was published sixty years ago, is a reminder that no one can match Russell Kirk in engaging people’s minds and imaginations—an indispensable task in reviving our civilization.

    With his trademark clarity and humor, Holt probes the mysteries of quantum mechanics, the quest for the foundations of mathematics, and the nature of logic and truth. Along the way, he offers intimate biographical sketches of celebrated and neglected thinkers, from the physicist Emmy Noether to the computing pioneer Alan Turing and the discoverer of fractals, Benoit Mandelbrot. Holt offers a painless and playful introduction to many of our most beautiful but least understood ideas, from Einsteinian relativity to string theory, and also invites us to consider why the greatest logician of the twentieth century believed the U.S. Constitution contained a terrible contradiction--and whether the universe truly has a future.

    Graphs are not included, but both the graphs and the concepts behind them are explained; only basic math is included, and you can even skim over the math and still come away with an understanding of the concepts; statistics is not included at all.BASIC ECONOMICS FOR STUDENTS AND NON-STUDENTS ALIKE is an easy way to learn concepts relating to economics and the economy. It is a product of thousands of hours spent online, teaching basic concepts in economics to hundreds of students worldwide over the course of the past several years. From back and forth communications, I have discovered the explanations for the concepts that students find easiest to understand, as well as the areas that most often get misunderstood and under-emphasized.I have worked with students located throughout the United States and from many different countries, on six different continents; students from many different school systems with different points of emphasis; students with different levels of knowledge, different backgrounds, and different levels of interest in the subject. I have received numerous comments and testimonials regarding the teaching methods that I incorporate in BASIC ECONOMICS FOR STUDENTS AND NON-STUDENTS ALIKE.The subject matter included in BASIC ECONOMICS FOR STUDENTS AND NON-STUDENTS ALIKE comes from a compilation of many different textbooks at the introductory and intermediate levels. My goal was to include every subject in economics that normally will be found in an introductory level textbook of economics, microeconomics, or macroeconomics. Since different school systems, different classroom instructors, and different textbooks cover a slightly different combination of topics, BASIC ECONOMICS FOR STUDENTS AND NON-STUDENTS ALIKE is a little more comprehensive than most single introductory textbooks of economics. Some of the topics will be found in introductory classes in some schools, but in intermediate-level classes in other schools.

    They will also develop a deeper understanding of the many interconnections that exist among the different areas of psychology. Goodwin's book not only provides accounts of the lives and contributions of psychology's pioneers set into historical context; it also contains original writings by these psychologists, interwoven with informative comments from the author. The text is written in a conversational and engaging style with discrete attention to recent scholarship in the history of psychology, especially that of the past 150 years.

    L. Mencken is still one of the most enlightening. Mencken wrote this book while still in his 20s, but his penchant for thoroughness was evident even at that young age—in preparation for writing this book, he read Nietzsche's works in their entirety, mostly in the original German. A brief biographical sketch is followed by clear and thorough explanations of Nietzsche's basic concepts and attitudes. Analyzed are Nietzsche's much-misunderstood concept of the superman, his concept of eternal recurrence, his rejection of Christianity, and his basic rationalism and materialism. Included are two essays on Nietzsche that appeared in Mencken's magazine The Smart Set subsequent to the publishing of the original edition of this book. Nearly a century after its original publication, this remains one of the clearest, most concise, and entertaining introductions to Nietzsche to date.