The Calculus Wars


Book Description

Now regarded as the bane of many college students' existence, calculus was one of the most important mathematical innovations of the seventeenth century. But a dispute over its discovery sewed the seeds of discontent between two of the greatest scientific giants of all time -- Sir Isaac Newton and Gottfried Wilhelm Leibniz. Today Newton and Leibniz are generally considered the twin independent inventors of calculus, and they are both credited with giving mathematics its greatest push forward since the time of the Greeks. Had they known each other under different circumstances, they might have been friends. But in their own lifetimes, the joint glory of calculus was not enough for either and each declared war against the other, openly and in secret. This long and bitter dispute has been swept under the carpet by historians -- perhaps because it reveals Newton and Leibniz in their worst light -- but The Calculus Wars tells the full story in narrative form for the first time. This vibrant and gripping scientific potboiler ultimately exposes how these twin mathematical giants were brilliant, proud, at times mad and, in the end, completely human.




The Calculus of Violence


Book Description

Winner of the Jefferson Davis Award Winner of the Johns Family Book Award Winner of the Army Historical Foundation Distinguished Writing Award “A work of deep intellectual seriousness, sweeping and yet also delicately measured, this book promises to resolve longstanding debates about the nature of the Civil War.” —Gregory P. Downs, author of After Appomattox Shiloh, Chancellorsville, Gettysburg—tens of thousands of soldiers died on these iconic Civil War battlefields, and throughout the South civilians suffered terrible cruelty. At least three-quarters of a million lives were lost during the American Civil War. Given its seemingly indiscriminate mass destruction, this conflict is often thought of as the first “total war.” But Aaron Sheehan-Dean argues for another interpretation. The Calculus of Violence demonstrates that this notoriously bloody war could have been much worse. Military forces on both sides sought to contain casualties inflicted on soldiers and civilians. In Congress, in church pews, and in letters home, Americans debated the conditions under which lethal violence was legitimate, and their arguments differentiated carefully among victims—women and men, black and white, enslaved and free. Sometimes, as Sheehan-Dean shows, these well-meaning restraints led to more carnage by implicitly justifying the killing of people who were not protected by the laws of war. As the Civil War raged on, the Union’s confrontations with guerrillas and the Confederacy’s confrontations with black soldiers forced a new reckoning with traditional categories of lawful combatants and raised legal disputes that still hang over military operations around the world today. In examining the agonizing debates about the meaning of a just war in the Civil War era, Sheehan-Dean discards conventional abstractions—total, soft, limited—as too tidy to contain what actually happened on the ground.




Mathematics and War


Book Description

Mathematics has for centuries been stimulated, financed and credited by military purposes. Some mathematical thoughts and mathematical technology have also been vital in war. During World War II mathematical work by the Anti-Hitler coalition was part of an aspiration to serve humanity and not help destroy it. At present, it is not an easy task to view the bellicose potentials of mathematics in a proper perspective. The book presents historical evidence and recent changes in the interaction between mathematics and the military. It discusses the new mathematically enhanced development of military technology which seems to have changed the very character of modern warfare.




Philosophers at War


Book Description

A blow-by-blow account of the celebrated controversy over the invention of the calculus.




How Not to Be Wrong


Book Description

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.




Infinite Powers


Book Description

This is the captivating story of mathematics' greatest ever idea: calculus. Without it, there would be no computers, no microwave ovens, no GPS, and no space travel. But before it gave modern man almost infinite powers, calculus was behind centuries of controversy, competition, and even death. Taking us on a thrilling journey through three millennia, professor Steven Strogatz charts the development of this seminal achievement from the days of Aristotle to today's million-dollar reward that awaits whoever cracks Reimann's hypothesis. Filled with idiosyncratic characters from Pythagoras to Euler, Infinite Powers is a compelling human drama that reveals the legacy of calculus on nearly every aspect of modern civilization, including science, politics, ethics, philosophy, and much besides.




The Calculus of Conventional War


Book Description

Conventional forces absorb the preponderance of America's defense spending. Further, most experts believe the most likely path to nuclear war is through a failure of conventional defense. It is therefore critical that conventional military balances be assessed rigorously—by techniques that go beyond the familiar static comparison of opposing military inventories and explicitly represent warfare's dynamic factors. For decades, a single set of tools has dominated the dynamic analysis of conventional balances: the Lanchester equations, named for their inventor, Frederick William Lanchester. In this study, Joshua M. Epstein makes two separate contributions. He argues that Lanchester's equations fail to capture the basic dynamics of warfare and that they offer a fundamentally implausible picture of combat. He also presents new, alternative equations of his own. These, he contends, do capture warfare's essential dynamics, which Lanchester theory is incapable of representing. Epstein's methods are of immediate practical relevance in assessing the requirements of defense in the specific contingencies for which the United States and its allies must plan and in setting defense priorities accordingly.




Italian Mathematics Between the Two World Wars


Book Description

This book describes Italian mathematics in the period between the two World Wars. It analyzes the development by focusing on both the interior and the external influences. Italian mathematics in that period was shaped by a colorful array of strong personalities who concentrated their efforts on a select number of fields and won international recognition and respect in an incredibly short time. Consequently, Italy was considered a third mathematical power after France and Germany.




Pakistan's War on Terrorism


Book Description

This book examines Pakistan's strategies in the war against Islamist armed groups that began late 2001, following the 9/11 attacks. The significance of the war inside Pakistan can hardly be understated. Starting in the tribal territories adjacent to Afghanistan, Pakistan’s war has come to engulf the majority of the country through a brutal campaign of suicide bombings. Thousands of Pakistani lives have been lost and the geostrategic balance of the region has been thrown into deep uncertainty. Pakistan's War on Terrorism is an account of a decade-long war following the 9/11 attacks, that is yet to be chronicled in systematic fashion as a campaign of military manoeuvre and terrorist reprisal. It is also an analytic account of Pakistan’s strategic calculus during this time, both in military and political terms, and how these factors have been filtered by Pakistan’s unique strategic culture. This text will be of great interest to students of Asian Politics, Terrorism and Political Violence, and Security Studies in general.




Explaining Contemporary Asian Military Modernization


Book Description

This book proposes a novel theoretical framework of "interactive arming" in order to explain armament dynamics in contemporary Asia. Frequently, the modernisation of contemporary naval forces in Asia is described as an "arms race," with the underlying assumption being that weapons acquisitions and increases in defence expenditure are competitive and bilateral and due to conflicting purposes or mutual fears. This book argues that the concept of an arms race is an unsuitable one for explaining contemporary military modernisation in 21st-century Asia. Instead, it proposes a novel and innovative concept of "interactive arming" and argues that what drives conflict is political rivalry, not weapons acquisitions. Instead of perceiving arming as abnormal behaviour, the book views arming as a natural strategic behaviour of states and military modernisation as a basic requirement for a state’s ability to survive. This book will be of much interest to students of Asian security, strategic studies and international relations in general.