bluuebunny/crossref_metadata_2025 huggingface dataset:
The Blackwater, Ballitore, Trinity and the Reformer
Authors: Bourke Richard
Published: May 2018

Burke spent the first twenty years of his life in Ireland, dividing his time between Cork, Kildare, and Dublin. These different locations corresponded to distinct cultural environments: his Catholic relations, his Quaker school, and his Church of Ireland upbringing. As a youth he believed that custom could be educated by reason, enabling individuals to transcend their cultural confinement. It was only later, in the 1750s, that he came to contend that our rational faculties could productively be constrained by habit. This chapter discusses the formation of Burke's early prejudices and charts his commitment to the idea that their cruder manifestations could be improved by a process of rational inquiry. By the late 1740s, while editing The Reformer after graduating from Trinity College Dublin, he was campaigning to accelerate that process by contributing to the refinement of national taste.
The Philosophical Enquiry: Science of the Passions, 1757
Authors: Bourke Richard
Published: May 2018

This chapter focuses on Burke's Philosophical Enquiry into the Origin of our Ideas of the Sublime and Beautiful. Philosophical Enquiry takes up the thread of preoccupations that absorbed him throughout his twenties. It begins with an exploration of the classical theory of mixed emotions, focusing on Aristotle's signature categories of pity and terror. It proceeds to elucidate the affective psychology of manners, probing the feeling of exhilaration unleashed by pride and the instinct for subordination based on fear. Challenging the deist assumptions of a number of predecessors, Burke argues for the dependence of moral taste on duty. In the process, he articulates the reliance of ethics on religion, and traces the origins and development of superstition. The work also recapitulates Burke's antipathy to stoicism, along with his response to the leading moralists of the age, above all the writings of Hutcheson, Mandeville, and Berkeley, as well as Dubos, Condillac, Hume, and Smith. Although the Enquiry is not a comprehensive treatise in moral philosophy, it provides access to Burke's theory of human nature as it sets about accounting for uniform features of the mind.
The Advent of Crisis
Authors: Bourke Richard
Published: May 2018

This chapter details Burke's political life from 1785 to 1790. Burke's support for a range of causes won an audience in the Commons from the middle of the decade: principally, opposition to the transportation of convicts in 1785 and moves to abolish the slave trade in 1789. Yet in the same period, Burke felt compelled to defend the authority of prescription. In opposing Pitt's Bill for parliamentary reform in 1785 and his attempt to impose restraints on the conduct of the regent in 1788–9, Burke supported existing arrangements in terms of established convention. Pragmatic conventions and original rights then collided with the French Revolution. By the early autumn of 1789, Burke was adamant that the rage in France against established usage would prove destructive of the principles of society and government.
The Great Primaeval Contract
Authors: Bourke Richard
Published: May 2018

This chapter focuses on Burke's Reflections on the Revolution in France, which occupies a non-standard position within the canon of past political thought. Its production was determined by immediate circumstance rather than philosophical reflection. In terms of the conditions of its composition, the Reflections is roughly comparable to Locke's Two Treatises of Government insofar as both were prompted by compelling practicalities. But even here, Locke was a scholar and tutor turned counsellor and polemicist, whereas Burke was a responsible politician. The Reflections is a defense of the British constitutional setup, including existing relations between church and state. As such it is an attack on figures hostile to the Anglican establishment as well as to the principle of parliamentary monarchy. Its immediate target was the nonconformist preacher Richard Price, who sought with various fellow travelers to undermine ecclesiastical and political arrangements in Britain.
Whig Principles And Jacobin Dogma, 1791–1793
Authors: Bourke Richard
Published: May 2018

This chapter details Burke's political life from 1791 to 1793. After 1790, Burke's career was shaped by the reaction to the Reflections. The work was a sophisticated polemical assault on attempts to reduce the rights and responsibilities of citizenship to a perilous ideal of self-government. However, it was widely construed as an attack on the equality of human beings and the accountability of governments to the people whom they ruled. In fact, it was a critique of the resort to primitive equality as a justification for destroying equitable relations in civil society. At the same time, its aim was to distinguish responsible government from popular tyranny. From Burke's vantage, the doctrine of the rights of man represented a crusade against the values of cohesion and responsibility, and was therefore liable to shatter society and government altogether. However, the force of his argument was drowned out by subsequent political rhetoric.
The Pursuit Of Hastings, 1788–1796
Authors: Bourke Richard
Published: May 2018

This chapter details the final years of Burke's protracted stand against wrongdoing in India, which brought setbacks followed by radical disenchantment. He delivered the Presents and Contracts charges with stamina and gusto, but the prolongation of the trial soon began to count against him. He started to reflect again about the sentiment of humanity: it was fortified by custom among people who shared a culture, yet it required the support of rhetoric if it was to gain traction among strangers. The force of persuasion could not sustain the cause through the dreariness of judicial proceedings. After the acquittal of his adversary in April 1795 Burke was disheartened; with the award of an annuity to Hastings the following year he felt beaten. Campaigning through his final illness against the search for peace with France while striving to save Ireland from the prospect of dreadful strife, Burke would look back on the India business as a draining undertaking.
Discovering the Solar System
Authors: Chambers John , Mitton Jacqueline
Published: May 2018

This chapter illustrates how the solar system turned out to be much larger than previously imagined. In the 2nd century AD, Greek astronomer Claudius Ptolemy, working in the Egyptian city of Alexandria, put the distance of the Sun at a mere 1,210 Earth radii, an estimate that had stood for 1,500 years. These years were a time of great scientific upheaval spurred by new instruments and techniques, and the development of powerful mathematical tools. Not only were astronomers coming to appreciate the true scale of the solar system, their entire picture of the solar system and the universe was being turned on its head. Beliefs about the solar system that had gone almost unchallenged for more than a thousand years were being called into question or overturned completely.
Worlds of Rock and Metal
Authors: Chambers John , Mitton Jacqueline
Published: May 2018

This chapter explains how planetesimals—the basic building blocks of planets—are essentially invisible from here on Earth. To understand how planetesimals evolve into planets, one must examine material left over from planetary growth in the solar system, and make use of computer simulations. When planetesimals first formed, they were probably loosely bound mixtures of dust grains, chondrules, and other debris that happened to exist in the solar nebula at the time. As these planetesimals grew hot, volatile materials such as ices and organic tars would have melted and evaporated, ultimately making their way to the surface where they escaped into space. Some reactions between rock and water took place, but the temperature never rose high enough for rocky materials to melt, leaving behind planetesimals composed entirely of rock and metal.
The Making of the Moon
Authors: Chambers John , Mitton Jacqueline
Published: May 2018

This chapter considers how the very existence of the Moon, the only large satellite in the inner solar system, is a puzzle. The Moon is sufficiently large that one would think of it as a planet if it traveled around the Sun rather than Earth. Much of what the public now knows about the Moon comes from space missions, beginning in the 1960s and early 1970s. Six American Apollo missions each landed two astronauts on the surface. Three of the Soviet Union's unmanned Luna spacecraft touched down on the surface and then returned to Earth. After a long gap, lunar exploration resumed in the 1990s, when NASA's Clementine and Lunar Prospector spacecraft went into orbit. Recently, the pace of exploration has increased again, with the European Space Agency, Japan, China, and India, as well as NASA, all sending missions to the Moon.
Earth, Cradle of Life
Authors: Chambers John , Mitton Jacqueline
Published: May 2018

This chapter studies the composition of early Earth, which consisted of two layers: a dense iron-rich core at the center, surrounded by a thick rocky mantle. Gradually, Earth acquired a third layer, a thin basaltic crust on the floor of the ocean. In a few places, the basaltic rock became thick enough to poke up above the waves to form the first primitive continents. As the basalt cooled, it grew denser and eventually became heavier than the mantle below. This configuration was unstable, and in places, the heavy basaltic crust began to sink, or subduct, back into the mantle, where it eventually mixed with rocks deep in Earth's interior. As the basaltic crust subducted, it pulled neighboring material with it, making room for new crust to form and setting up the conditions necessary for plate tectonics—the process of crustal recycling that continues to operate on Earth today.
Kant: Was ist Aufklärung?
Authors: Ferrone Vincenzo
Published: May 2018

This chapter focuses on Immanuel Kant's analysis/view of the cultural phenomenon called Aufklärung and his argument that the Enlightenment was “a great act of courage, a passionate invitation never to be afraid of emancipation.” In 1784, Kant published a short essay advancing an “Idea for a Universal History from a Cosmopolitan Point of View.” The article discussed the growing importance of the Aufklärung and distinguished between the traditional “work of practicing empirical historians” and the effort to draft instead an “[i]dea of universal history.” The chapter considers Kant's views on the “enlightenment,” whether we now live in an enlightened age, and the clash between faith in God and Enlightenment reason. It also examines Kant's description of the Enlightenment as a precise modality of the exercise of reason, which was animated by a strong “spirit of freedom” and intimately connected with mankind's natural need for knowledge.
Hegel
Authors: Ferrone Vincenzo
Published: May 2018

This chapter examines how Georg Wilhelm Friedrich Hegel addressed the major philosophical issue of the Enlightenment—the dilemma of man— in terms of the “dialectical moment,” linking it to the theme of the self-foundation and sublation of the crisis opened by modernity. At the beginning of the nineteenth century, Hegel laid the foundations of what is known as the philosophers' Enlightenment in the name of a concept of philosophy entirely different from that of Immanuel Kant and other Enlightenment figures: he shifed the focus from the primacy of the subject to that of the spirit. Hegel placed the emphasis on the organic union of man and universe, within which eternal nature operates, rather than on an abstractly determined individual tending towards his own happiness. The chapter also considers Hegel's philosophy of unification and “conciliation.”
Horkheimer and Adorno
Authors: Ferrone Vincenzo
Published: May 2018

This chapter examines the claim by Max Horkheimer and Theodor Adorno, articulated in their work Dialektik der Aufklärung that the Enlightenment underwent a dialectical reversal that paradoxically transformed it into a new form of myth, a totalitarian religion devoted solely to an instrumental rationalism whose final aim was to creatie a dehumanized society dominated by science and technology. Dialektik der Aufklärung began with the adventures of Odysseus (the first Dialektik der Aufklärungrer) and traveled on all the way to Adolf Hitler's totalitarianism and the American mass consumerism in their own day. Horkheimer and Adorno indicted what they saw as the historical failure of the Enlightenment's emancipation project. They took issue with the philosophy of the subject as described in Georg Wilhelm Friedrich Hegel, appropriating both Karl Marx's critique of ideologies and Friedrich Nietzsche's unmasking of subjective reason as a smokescreen for the will to power.
Foucault
Authors: Ferrone Vincenzo
Published: May 2018

This chapter examines how Michel Foucault reformulated the philosophical issue of the Enlightenment by moving from a deliberate rereading of the Hegelian Centaur to an advocacy of the “death of man”—the extinction of a rational platform of knowledge along the lines developed by Immanuel Kant and the Enlightenment at the end of the eighteenth century. It considers Foucault's genealogical historiography, a new and original tool for the analysis of history, and his arguments against the idea of a necessary and defining connection between knowledge and virtue, which had been the core identity of the Enlightenment, the link between power and knowledge, and the rise of disciplinary violence in the history of the Western world. Finally, it explores Foucault's view that “critique is the movement by which the subject gives himself the right to question truth on its exercise of power, and to question power on its discourses of truth.”
For a Defense of Historical Knowledge
Authors: Ferrone Vincenzo
Published: May 2018

This chapter argues that historians must go beyond the premises of the paradigm of the Centaur and uphold the autonomy and prerogatives of historical knowledge with respect to the Enlightenment. It suggests that the correct question to ask a historian is not “What is the Enlightenment?” but rather “What was it?” and that we should ask what is it that we know about the Enlightenment's significance in the history of Europe during the Ancien Régime. On the other hand, the historian questioned should not think of the Enlightenment as a kind of philosophia perennis. The chapter also considers Ernst Cassirer's declaration of faith in Immanuel Kant and Isaac Newton's scientific rationalism and Michel Foucault's attempt to revive the paradigm of the Centaur as “historico-philosophical practice” in the wake of the great German historiography of the Aufklärung.
What Was the Enlightenment?
Authors: Ferrone Vincenzo
Published: May 2018

This chapter examines the unifying element, and the ultimate defining trait of, the Enlightenment style of thought that pervaded the new humanism of the moderns: a radical cultural reform of the European identity that was implicit in the Enlightenment idea of civilization. It also considers the Enlightenment's critique of traditional revealed religions in relation to its humanism of the moderns in the context of Ancien Régime Europe. The chapter first considers the effects of the traditional reading of Immanuel Kant's philosophy and the historical discontinuity between the humanisms of earlier centuries and Enlightenment humanism before discussing Voltaire's view of religion as a necessity and a useful tool in the life of man.
The Golden Ticket
Authors: Fortnow Lance
Published: May 2018

The P versus NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. This book provides a nontechnical introduction to P versus NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. The book traces the history and development of P versus NP, giving examples from a variety of disciplines, including economics, physics, and biology. It explores problems that capture the full difficulty of the P versus NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The book explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.
Proving P ≠ NP
Authors: Fortnow Lance
Published: May 2018

This chapter focuses on a few of the ideas that people have tried to solve the P versus NP problem. These have not panned out to anything close to a solution to the problem. To prove P ≠ NP one needs to show that no algorithm, even those that have not been discovered yet, can solve some NP problem. It is simply very difficult to show that something cannot be done. However, it is not a logically impossible task. The only known serious approach to the P versus NP problem today is due to Ketan Mulmuley from the University of Chicago. He has shown how solving some difficult problems in a mathematical field called algebraic geometry may lead to a proof that P ≠ NP. However, resolving these algebraic geometry problems will require mathematical techniques far beyond what is available today.
From Wars to the Great War: A Hero Is Born
Authors: Hanioğlu M. Şükrü
Published: May 2018

This chapter looks at Mustafa Kemal Atatürk's quest for heroism. As he expressed it in a personal letter to a female friend, he had “grand desires” to render extraordinary services to his homeland. Circumstances, however, were not yet favorable to the realization of that ambition. Up until the Great War, he remained an obscure figure little known outside the circle of young Committee of Union and Progress's (CUP) officers. The German-inspired reorganization of the Ottoman military on the eve of the Great War paved the way for Mustafa Kemal's ascendance. Like many of his colleagues, he agreed with Colmar von der Goltz's opinion that “to make war means to attack.” Mustafa Kemal maintained that only nations inspired by the Japanese attack code of “kōgeki seishin” (aggressive spirit) could carry out successful offensive wars.
Muslim Communism? The Turkish War of Independence
Authors: Hanioğlu M. Şükrü
Published: May 2018

This chapter focuses on the Turkish War of Independence. Fighting between 1919 and 1922 on two principal fronts—against the British-backed Greeks in the West and the unsupported Armenians in the East—the nationalists, led by Mustafa Kemal Atatürk, exploited the protracted conflict to solidify their hold on power. Mustafa Kemal emerged as one of the principal leaders of the popular struggle against partition. Nevertheless, when he returned to Istanbul later that month, he joined public opinion in expressing the hope that “the British would respect the freedom of our nation and the independence of our state” and that “there would not be a more benevolent friend of the Ottomans than the British.” Such hopes notwithstanding, Mustafa Kemal grasped more quickly than most of his colleagues that Allied diplomacy was pursuing objectives wholly at odds with those of the burgeoning Turkish nationalist movement.
Nationalism and Kemalism
Authors: Hanioğlu M. Şükrü
Published: May 2018

This chapter examines Turkish nationalism and Kemalism. The elimination of Islam as an ideological pillar of the main Ottoman successor state created a legitimacy vacuum at the center of the regime. Furthermore, the abolition of the sultanate and the dissolution of the Committee of Union and Progress (CUP) had given rise to a second void necessitating the creation of substitute foci for popular allegiance—both personal and institutional. Mustafa Kemal Atatürk sought to fill this lacuna with a new civic religion buttressed by a number of cults. The new ideology, unsurprisingly, was a modified, scientifically sanctioned version of Turkish nationalism. In the 1930s, Mustafa Kemal's followers and party pulled together various strands of several associated cults to create Kemalism, an all-encompassing state ideology based on his sayings and writings.
Conclusion
Authors: Hanioğlu M. Şükrü
Published: May 2018

This concluding chapter demonstrates that while Mustafa Kemal Atatürk played a momentous role in the transition from the Ottoman order to modern Turkey, his work cannot be considered that of a sagelike dispenser of wisdom who came to the scene with novel ideas and an original program. He was a down-to-earth leader who strove to realize a vision not by depending on any one ideology but by utilizing a range of sources—some with dubious intellectual pedigrees—without paying much attention to contradictions among them. He was the individual who transformed an intellectual utopia envisaged by a marginal group into a political program and then proceeded to implement it vigorously as head of state. Consequently, despite the radical changes that it brought about, the Turkish transformation led by Atatürk was not a rupture with the Late Ottoman past but, in important respects, its continuation.
Mathematics without Apologies
Authors: Harris Michael
Published: May 2018

What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers, this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on the author's personal experiences as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, the book reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, the book touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? The book takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.
How to Explain Number Theory at a Dinner Party
Authors: Harris Michael
Published: May 2018

This chapter begins with the author's account of a dinner party that he attended in the spring of 2008. One of the guests, an actress, had turned to him and asked, “What is it you do in number theory, anyway?” His response to the actress and the conversation that ensued lasted at most ten minutes. However, he has always felt that he could have done better. The chapter then presents what the author feels should have been his answer. The discussion has been broken up into short sessions in order to impede the accumulation of formulas, as the author works his way up to the guiding problem of the Birch–Swinnerton–Dyer conjecture. This chapter contains the first session.
Not Merely Good, True, and Beautiful
Authors: Harris Michael
Published: May 2018

This chapter considers two proposed paradigm shifts that are challenging the professional autonomy to which mathematics has grown attached. The first proposal stems from the economic crisis that began in 2008, which placed universities under enormous stress. Thus, mathematicians, when presenting the case for research support to the powers that be, now find it necessary to point to potential commercial or industrial spinoffs. The second proposed paradigm shift arises from within the profession. It stems from an observation that proofs in some areas of mathematics are growing increasingly elaborate, involving in some cases hundreds of pages of calculations or expertise in too many areas to be fully understood by any one mathematician. Traditional methods exhaust the physical limits of human beings as presently configured and for that reason are deemed inadequate to confer legitimacy on some of the most remarkable theorems of the past few decades.
The Habit of Clinging to an Ultimate Ground1
Authors: Harris Michael
Published: May 2018

This chapter suggests that notions of real interest to mathematicians are not on the printed page but lurk behind the doors of conception. It is believed that they will someday emerge and shed so much light on earlier concepts that the latter will disintegrate into marginalia. By their very nature, they elude precise definition, so that on the conventional account they are scarcely mathematical at all. Coming to grips with them is not to be compared with attempting to solve an intractable problem. Instead, it harbors a more fundamental obscurity. One cannot even formulate a problem, much less attempt to solve it; the items (notions, concepts) in terms of which the problem would be formulated have yet to be invented. How then can we talk to one another, or to ourselves, about the mathematics we were born too soon to understand?
The Veil of Maya
Authors: Harris Michael
Published: May 2018

Scholarship seems to have failed to consider which metaphorical veil, or Schleier, Hilbert was inviting his listeners to lift, among the many on offer to an educated German in the late nineteenth century. Rather than assuming Hilbert sought to awaken the prurient inclinations of coming generations, it is safest to assume that he was thinking of the “veil of Isis” that Schiller introduced into German poetry, that Kant identified with the barrier separating human understanding from the Ding an sich, and that Schlegel enjoined his reader to tear. The piercing of this veil has enjoyed a long career as a metaphor for the pursuit of the scientific knowledge of nature. This chapter considers Mongré's essay “The Veil of Maya” [Der Schleier der Maja].
Greece and the Idolatry of Debt
Authors: Sandbu Martin
Published: May 2018

This chapter evaluates the case of Greece's sovereign debt crisis. Greece only makes up one-fiftieth of the eurozone economy. The problems it has caused the monetary union, however, are out of all proportion to its size. Greece is where the sovereign debt crisis started; and it is the one eurozone economy whose membership of the euro remains unsettled. That is why a detailed examination of Greece's travails is the right place to start a retelling of Europe's crisis. It reveals just how stubbornly the eurozone has stuck to the goal of trading financial transfers for more centralised power — from the first crisis in early 2010 to the renewed stand-off between Greece and the rest of the eurozone after left-wing radicals won power in Athens in January 2015.
Ireland: The Private Is Political
Authors: Sandbu Martin
Published: May 2018

This chapter examines the case of Ireland's sovereign debt crisis. It was six months after Greece had been subjected to the troika's tutelage in return for a vast bridge loan, and the eurozone had set up a rescue fund in case other euro states lost access to market funding. Dublin's deficit was on course to hit an incredible 31 per cent of GDP, most of it due to the cost of bailing out collapsing Irish banks. Rumours were rife that Ireland was about to become the first to apply to the new European Financial Stability Facility (EFSF) for financial aid, which would place Irish economic policy, too, under the troika's whip. But even with Dublin's borrowing costs soaring and International Monetary Fund (IMF) officials spotted in the capital, one frazzled government minister after another denied that a eurozone rescue was imminent.
If Europe Dared to Write Down Debt
Authors: Sandbu Martin
Published: May 2018

This chapter offers an alternative history in which the eurozone did the right thing from the beginning. As a denunciation of past mistakes and an admonition for future policy, it shows that restructurings could have been managed in ways that were as orderly as the bail-outs that actually took place, if not more so, and with much greater fairness. Europe's economic well-being and political health would have been vastly better as a result. Two things would have been very different. First, the custodians of the single currency would not have been faced with temptations to put the euro's integrity in doubt. Second, greater national autonomy would have encouraged better collective solutions — both because the negotiations over what those solutions should be would have been more balanced, and because the greater room for policy manoeuvre by national governments would have produced a wider range of policy proposals.
Positive Feedbacks
Authors: Sornette Didier
Published: May 2018

This chapter examines the main mechanisms leading to positive feedbacks, that is, self-reinforcement, such as imitative behavior and herding between investors. It shows that positive feedbacks contribute to the development of speculative bubbles, preparing the instability for a major crash. After providing an overview of feedbacks and self-organization in economics, the chapter explains how positive feedback on prices can arise due to hedging of derivatives and investment strategies with an “insurance portfolio.” It then describes a general mechanism for positive feedback, known as the “herd” or “crowd” effect, based on imitation processes. It also presents empirical evidence of herding by financial analysts and the relationship between “anti-imitation” and self-organization before concluding with an analysis of cooperative behaviors resulting from imitation, focusing on the Ising model of cooperative behavior and the complex evolutionary adaptive systems of boundedly rational agents.
Heavenly Mathematics
Authors: Van Brummelen Glen
Published: May 2018

This chapter reviews topics in plane trigonometry, first by considering ancient ideas that the Earth is round, focusing on tales of Christopher Columbus trying to convince the Spanish court that the Earth is not a disc but a sphere, making it possible to sail westward from Portugal to India. It then discusses the dimensions of the Earth and computes a table of sines. In particular, it looks at the trigonometric table of Claudius Ptolemy, who included a remarkable collection of models for the motions of the heavenly bodies in his astronomical masterpiece, Mathematical Collection. In early Europe, the most prodigious set of trigonometric tables was the Opus palatinum, composed by Georg Rheticus. The chapter concludes with calculations to find the distance to the Moon using only simple measurements.
Areas, Angles, and Polyhedra
Authors: Van Brummelen Glen
Published: May 2018

This chapter explains how to find the area of an angle or polyhedron. It begins with a discussion of how to determine the area of a spherical triangle or polygon. The formula for the area of a spherical triangle is named after Albert Girard, a French mathematician who developed a theorem on the areas of spherical triangles, found in his Invention nouvelle. The chapter goes on to consider Euler's polyhedral formula, named after the eighteenth-century mathematician Leonhard Euler, and the geometry of a regular polyhedron. Finally, it describes an approach to finding the proportion of the volume of the unit sphere that the various regular polyhedra occupy.
Introduction
Authors: Nahin Paul J.
Published: May 2018

This introductory chapter considers the work of mathematician George Boole (1815–1864), whose book An Investigation of the Laws of Thought (1854) would have a huge impact on humanity. Boole's mathematics, the basis for what is now called Boolean algebra, is the subject of this book. It is also called mathematical logic, and today it is a routine analytical tool of the logic-design engineers who create the electronic circuitry that we now cannot live without, from computers to automobiles to home appliances. Boolean algebra is not traditional or classical Aristotelian logic, a subject generally taught in college by the philosophy department. Boolean algebra, by contrast, is generally in the hands of electrical engineering professors and/or the mathematics faculty.
Logic Switching Circuits
Authors: Nahin Paul J.
Published: May 2018

Today's digital circuitry is built with electronic technology that the telephone engineers of the 1930s and the pioneer computer designers of the 1940s would have thought to be magic. The first real digital technology took the form of electromagnetic relays in telephone switching exchanges. Then came vacuum tube digital circuitry, discrete transistors, integrated transistor circuits, and so on. But the one thing that remains the same is the math, the Boolean algebra that is the central star of this book. This chapter describes the technology that Shannon himself used in his switching analyses. It covers Switches and the logical connectives, a classic switching design problem, electromagnetic relay, the ideal diode and the relay logical AND and OR, and the bi-stable relay latch.
Boole, Shannon, and Probability
Authors: Nahin Paul J.
Published: May 2018

George Boole and Claude Shannon shared a deep interest in the mathematics of probability. Boole's interest was, of course, not related to the theory of computation—he was a century too early for that—while Shannon's mathematical theory of communication and information processing is replete with probabilistic analyses. There is, nevertheless, an important intersection between what the two men did, which is shown in this chapter. The aim is to provide a flavor of how they reasoned and of the sort of probabilistic problem that caught their attention. Once we have finished with Boole's problem, the reader will see that it uses mathematics that will play a crucial role in answering Shannon's concern about “crummy” relays.
Some Combinatorial Logic Examples
Authors: Nahin Paul J.
Published: May 2018

The entire point of Shannon's 1948 “A Mathematical Theory of Communication” was to study the theoretical limits on the transmission of information from point A (the source) to point B (the receiver) through an intervening medium (the channel). The information is imagined first to be encoded in some manner before being sent through the channel. Shannon considers two distinct types of channels: the so-called continuous channel that would carry, for example, a continuous signal like the human voice; and the so-called discrete channel that would carry, again for example, a keyboard's output in the form of a digital stream of bits. This chapter focuses on this second case. In a perfect world the digital stream would arrive at the receiver exactly as it was sent, but in the real world the channel is noisy and so, occasionally, a bit will arrive in error.
Sequential-State Digital Circuits
Authors: Nahin Paul J.
Published: May 2018

This chapter begins by discussing two sequential state problems. The first example drives home the point that the concept of a physical system changing state with time predates Shannon and Boole by centuries. The second example uses a more modern situation that just about everyone of driving age has encountered: the automated parking garage. It then argues that the design of a sequential state digital machine is simply that of determining how to interconnect these individual latches so as to transition from state to state with the goal of accomplishing a desired task. The remainder of the chapter shows how the latch can be modified in several important ways to arrive at the practical logic element called the clocked, edge-triggered flip-flop, and concludes with the design of a specific machine.
Beyond Boole and Shannon
Authors: Nahin Paul J.
Published: May 2018

Boole and Shannon never studied the physics of computation. Obviously Boole simply could not have, as none of the required physics was even known in his day, and Shannon was nearing the end of his career when such considerations were just beginning. And yet, both Boole's algebra and Shannon's information concepts to make many of our calculations. This chapter touches on how fundamental physics—the uncertainty principle from quantum mechanics, and thermodynamics, for example—constrain what is possible, in principle, for the computers of the far future. It argues that while there are indeed finite limitations, present-day technology falls so far short of those limits that there will be good employment for computer technologists for a very long time to come.
Persons in a World of Things
Authors: Mittleman Alan L.
Published: May 2018

This chapter focuses on the reality of persons in a world of things. It begins and ends with some relevant views drawn from the Jewish philosophers Buber (1878–1965), Heschel (1907–72), and Joseph B. Soloveitchik (1903–93). Framed by the Jewish concerns, it turns to a philosophical exploration of human personhood. The chapter begins by consiering Sellars's classic essay on the scientific and manifest images of “man-in-the-world.” Sellars shows how urgent and difficult it is to sustain a recognizable image of ourselves as persons in the face of scientism. With additional help from Nagel and Kant, it argues that persons cannot be conceptually scanted in a world of things. Notwithstanding the explanatory power of science, there is more to life than explanation. Explanation of what we are needs supplementing by a conception of who we are, how we should live, and why we matter. Those are questions to which Jewish sources can speak.
Building Castles in the Sky
Authors: McCray W. Patrick
Published: May 2018

In the mid-1970s, Gerard O'Neill's ideas and designs for human settlements in space began to secure a beachhead in American popular culture. This chapter shows how he extended the engineering-oriented foundation for his visioneering to a wider base of enthusiasts. Through conferences, workshops, and the accretion of new ideas, O'Neill continued to describe a future in which space-based settlements remained plausible, at least in technical terms, and desirable. At the same time, his “humanization of space” idea mutated as journalists, politicians, writers, college students, and counterculture figures embraced or opposed it. This inherently messy process reflected a decade marked by social confusion, political realignment, and economic uncertainty.
Scythian Philosophy
Authors: Beckwith Christopher I.
Published: May 2018

This chapter sets out the book's purpose, which is to show not only that Pyrrho's complete package is similar to Early Buddhism, but also that the same significant parts and interconnections occur in the same way in both systems. The earliest sources on Early Pyrrhonism and Early Buddhism are examined closely, including in some cases determining what “Early” means. They show that the close parallel between Early Pyrrhonism and Early (Pre-Normative) Buddhism is systemic and motivated by the same internal logic. Pyrrho's journey to Central Asia and India with Alexander thus had an outcome for the future of philosophy that has lasted down to the present.
Jade Yoga and Heavenly Dharma
Authors: Beckwith Christopher I.
Published: May 2018

This chapter considers the relationship of Early Buddhism to Chinese thought during the Warring States period (ca. 450 BC–221 BC). Chinese thought was in a nearly constant state of flux, if not turmoil, during the Warring States period, which began shortly after the death of Confucius. Ideas related to the Early Buddhism attested in the fragments of Pyrrho and Megasthenes are clearly present in Warring States writings, especially Early Taoist texts, including the Laotzu, the Chuangtzu, as well as the anonymous Jade Yoga Inscription. Some of the Early Taoist material is approximately contemporaneous with Pyrrho and Megasthenes. It seems that this material's appearance in China is connected to the fact that Central Asia, including Bactria and Gandhāra, was part of the Achaemenid Persian Empire down to Alexander's invasion and conquest of the region in 330–325 BC.
Natural Complexity
Authors: Charbonneau Paul
Published: May 2018

This book provides a short, hands-on introduction to the science of complexity using simple computational models of natural complex systems—with models and exercises drawn from physics, chemistry, geology, and biology. By working through the models and engaging in additional computational explorations suggested at the end of each chapter, readers very quickly develop an understanding of how complex structures and behaviors can emerge in natural phenomena as diverse as avalanches, forest fires, earthquakes, chemical reactions, animal flocks, and epidemic diseases. This book provides the necessary topical background, complete source codes in Python, and detailed explanations for all computational models. Ideal for undergraduates, beginning graduate students, and researchers in the physical and natural sciences, this unique handbook requires no advanced mathematical knowledge or programming skills and is suitable for self-learners with a working knowledge of precalculus and high-school physics. The book enables readers to identify and quantify common underlying structural and dynamical patterns shared by the various systems and phenomena it examines, so that they can form their own answers to the questions of what natural complexity is and how it arises.
Iterated Growth
Authors: Charbonneau Paul
Published: May 2018

This chapter shows how complex shapes and forms encountered in the natural world result from a growth process driven by the repeated action of simple “rules.” To examine this general idea, the chapter focuses on cellular automata, arguably the simplest type of computer programs conceivable yet can sometimes exhibit behaviors that are extremely complex. Cellular automata are also a classic example of simple rules being able to produce complex global “patterns” that cannot be inferred or predicted even if we have complete, a priori knowledge of these rules. The chapter first considers cellular automata in one and two spatial dimensions before discussing a zoo of two-dimensional structures from simple rules. It then describes the role of agents in iterated growth as well as emergent structures and behaviors that can be produced by cellular automata. The chapter includes exercises and further computational explorations, along with suggested materials for further reading.
Aggregation
Authors: Charbonneau Paul
Published: May 2018

This chapter explores how naturally occurring inanimate structures grow by accretion of smaller-sized components, focusing on one specific accretion process: diffusion-limited aggregation (DLA). In DLA, particles move about in random fashion, but stick together when they come into contact. Clumps of particles then form and grow further by colliding with other individual particles, or clumps of particles. Over time, one or more aggregates of individual particles will grow. After providing an overview of how DLA works, the chapter describes its numerical implementation and shows a representative simulation of a two-dimensional DLA aggregate. It then considers two peculiar geometrical properties of aggregates resulting from the DLA process, namely self-similarity and scale invariance, and shows that rule based growth through DLA can lead to the buildup of complex structures, sometimes exhibiting fractal geometry. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.
Percolation
Authors: Charbonneau Paul
Published: May 2018

This chapter explores a lattice-based system where complex structures can arise from pure randomness: percolation, typically described as the passage of liquid through a porous or granular medium. In its more abstract form, percolation is an exemplar of criticality, a concept in statistical physics related to phase transitions. A classic example of criticality is liquid water boiling into water vapor, or freezing into ice. The chapter first provides an overview of percolation in one and two dimensions before discussing the use of a tagging algorithm for identifying and sizing clusters. It then considers fractal clusters on a lattice at the percolation threshold, scale invariance of power-law behavior, and critical behavior of natural systems. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.
Earthquakes
Authors: Charbonneau Paul
Published: May 2018

This chapter examines the natural complexity of earthquakes. Earthquakes release energy that is quantified by their magnitude m, a logarithmic measure of seismic wave amplitudes. The number N of earthquakes having a magnitude larger than m in a given area and time interval is expressed by the Gutenberg–Richter law. This power-law reflects scale invariance in the dynamics of earthquakes, and the chapter begins by reproducing this property using a simple mechanical model, the Burridge–Knopoff stick–slip model of seismic faults. The chapter then discusses the Olami–Feder–Christensen lattice-based implementation of the Burridge–Knopoff earthquake model using the Python code. It also describes a representative simulation on a 128 x 128 lattice, the behavior of the Olami–Feder–Christensen model, and earthquake forecasting. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.
American Misfits and the Making of Middle-Class Respectability
Authors: Wuthnow Robert
Published: May 2018

How did Americans come to think of themselves as respectable members of the middle class? Was it just by earning a decent living? Or did it require something more? And if it did, what can we learn that may still apply? The quest for middle-class respectability in nineteenth-century America is usually described as a process of inculcating positive values such as honesty, hard work, independence, and cultural refinement. But clergy, educators, and community leaders also defined respectability negatively, by maligning individuals and groups—“misfits”—who deviated from accepted norms. This book argues that respectability is constructed by “othering” people who do not fit into easily recognizable, socially approved categories. It demonstrates this through an in-depth examination of a wide variety of individuals and groups that became objects of derision. We meet a disabled Civil War veteran who worked as a huckster on the edges of the frontier, the wife of a lunatic who raised her family while her husband was institutionalized, an immigrant religious community accused of sedition, and a wealthy scion charged with profiteering. Unlike respected Americans who marched confidently toward worldly and heavenly success, such misfits were usually ignored in paeans about the nation. But they played an important part in the cultural work that made America, and their story is essential for understanding the “othering” that remains so much a part of American culture and politics today.
Introduction
Authors: Wuthnow Robert
Published: May 2018

This introductory chapter discusses how Americans in the nineteenth century pursued the American Dream. It argues that moving the American Dream from the stratosphere in which it is often discussed into the mundane realities of everyday life forces it to be considered differently. The topics of relevance cease to be the long-term trajectory through which protagonists rise from rags to riches and become instead questions about the immediate contexts in which people live. It suggests that what we might call middle-class respectability gets us further than continuing to discuss the American Dream as an ideal or philosophy of life. Middle-class respectability was something that people may have aspired to as an ideal, but it was modeled, learned, and exhibited in practice.