Ranging from ancient times to twentieth-century theories of time and space, looks at how exploring the circle has lead to increased knowledge about the physical universe.
Mathematical Reasoning and the Physical Universe
Author: Ernest Zebrowski
Publisher: Rutgers University Press
In Landscape of the Mind, John F. Hoffecker explores the origin and growth of the human mind, drawing on archaeology, history, and the fossil record. He suggests that, as an indirect result of bipedal locomotion, early humans developed a feedback relationship among their hands, brains, and tools that evolved into the capacity to externalize thoughts in the form of shaped stone objects. When anatomically modern humans evolved a parallel capacity to externalize thoughts as symbolic language, individual brains within social groups became integrated into a "neocortical Internet," or super-brain, giving birth to the mind. Noting that archaeological traces of symbolism coincide with evidence of the ability to generate novel technology, Hoffecker contends that human creativity, as well as higher order consciousness, is a product of the superbrain. He equates the subsequent growth of the mind with human history, which began in Africa more than 50,000 years ago. As anatomically modern humans spread across the globe, adapting to a variety of climates and habitats, they redesigned themselves technologically and created alternative realities through tools, language, and art. Hoffecker connects the rise of civilization to a hierarchical reorganization of the super-brain, triggered by explosive population growth. Subsequent human history reflects to varying degrees the suppression of the mind's creative powers by the rigid hierarchies of nationstates and empires, constraining the further accumulation of knowledge. The modern world emerged after 1200 from the fragments of the Roman Empire, whose collapse had eliminated a central authority that could thwart innovation. Hoffecker concludes with speculation about the possibility of artificial intelligence and the consequences of a mind liberated from its organic antecedents to exist in an independent, nonbiological form.
Human Evolution and the Archaeology of Thought
Author: John F. Hoffecker
Publisher: Columbia University Press
Category: Social Science
The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life.
Author: Ravi Agarwal,Syamal Sen
Refuting the accepted belief that mathematics is exact and infallible, the author examines the development of conflicting concepts of mathematics and their implications for the physical, applied, social, and computer sciences
The Loss of Certainty
Author: Morris Kline
Publisher: Oxford University Press, USA
Category: American literature
Arts & humanities
Author: Institute for Scientific Information (Philadelphia)
Like Douglas Hofstadter’s Gödel, Escher, Bach, and David Berlinski’s A Tour of the Calculus, Euclid in the Rainforest combines the literary with the mathematical to explore logic—the one indispensable tool in man’s quest to understand the world. Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.
Discovering Universal Truth in Logic and Math
Author: Joseph Mazur
Journal of Literature, Science, the Fine Arts, Music and the Drama
This inexpensive paperback uses lively language to put mathematics in an interesting, historical context and points out the many links to art, philosophy, music, computers, navigation, science, and technology. The arithmetic, algebra, and geometry are presented in a way that makes them relevant to daily life as well as larger issues. Topics include: Oh So Mysterious Egyptian Mathematics; Mesopotamia Here We Come; Those Incredible Greeks; Greeks Bearing Gifts; Must All Good Things Come to an End?; Europe Smells the Coffee; Mathematics Marches On; A Few Good Men; A Most Amazing Century of Mathematical Marvels!; The Age of Euler; A Century of Surprises; Ones and Zeros; Some More Math Before You Go.
A Brief History
Author: Marty Lewinter,William Widulski
Publisher: Pearson College Division
Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.
Author: Mario Livio
Publisher: Simon and Schuster
In this delightful book, Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can.
Using Physical Reasoning to Solve Problems
Author: Mark Levi
Publisher: Princeton University Press
Book description to come.
Author: Russell Howell,James Bradley
Publisher: Harper Collins