Mathematics and Art: A Cultural History

This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell's comprehensive exploration.

Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians' search for the foundations of their science, such as David Hilbert's conception of mathematics as an arrangement of meaning-free signs, as well as artists' search for the essence of their craft, such as Aleksandr Rodchenko's monochrome paintings. She shows that self-reflection is inherent to the practice of both modern mathematics and art, and that this introspection points to a deep resonance between the two fields: Kurt Gödel posed questions about the nature of mathematics in the language of mathematics and Jasper Johns asked "What is art?" in the vocabulary of art. Throughout, Gamwell describes the personalities and cultural environments of a multitude of mathematicians and artists, from Gottlob Frege and Benoît Mandelbrot to Max Bill and Xu Bing.

Mathematics and Art demonstrates how mathematical ideas are embodied in the visual arts and will enlighten all who are interested in the complex intellectual pursuits, personalities, and cultural settings that connect these vast disciplines.

Music Book Complete

Harmonious Triads: Physicists, Musicians, and Instrument Makers in Nineteenth-Century Germany (Transformations: Studies in the History of Science and Technology)

Historically, music was long classified as both art and science. Aspects of music--from the mathematics of tuning to the music of the celestial spheres--were primarily studied as science until the seventeenth century. In the nineteenth century, although scientists were less interested in the music of the spheres than the natural philosophers of earlier centuries, they remained committed to understanding the world of performing musicians and their instruments. In Harmonious Triads, Myles Jackson analyzes the relationship of physicists, musicians, and instrument makers in nineteenth-century Germany. Musical instruments provided physicists with experimental systems, and physicists' research led directly to improvements in musical-instrument manufacture and assisted musicians in their performances. Music also provided scientists with a cultural resource, which forged acquaintances and future collaborations.Jackson discusses experiments in acoustical vibrations that led to the invention of musical instruments and describes work with adiabatic phenomena that resulted in the improvement of the reed pipe, used by organ builders. He examines the collaborations of physicists and mechanicians aimed at standardizing beat and pitch and considers debates stirred by the standardization of aesthetic qualities. He describes the importance for scientists of choral societies as a vehicle for social life and cultural unity. Finally, he discusses a subject that occupied both physicists and musicians of the era: Could physicists, using the universal principles of mechanics, explain musical skill? Was the virtuosity of a Paganini or a Liszt somehow quantifiable? Jackson's historical consideration of questions at the intersection of music and physics shows us how each discipline helped shape the other.

The Jazz of Physics: The Secret Link Between Music and the Structure of the Universe

More than fifty years ago, John Coltrane drew the twelve musical notes in a circle and connected them by straight lines, forming a five-pointed star. Inspired by Einstein, Coltrane had put physics and geometry at the core of his music. Physicist and jazz musician Stephon Alexander returns the favor, using jazz to answer physics’ most vexing questions about the past and future of the universe.

Following the great minds that first drew the links between music and physics—a list including Pythagoras, Kepler, Newton, Einstein, and Rakim—The Jazz of Physics revisits the ancient realm where music, physics, and the cosmos were one. This cosmological journey accompanies Alexander’s own tale of struggling to reconcile his passion for music and physics, from taking music lessons as a boy in the Bronx to studying theoretical physics at Imperial College, London’s inner sanctum of string theory. Playing the saxophone and improvising with equations, Alexander uncovered the connection between the fundamental waves that make up sound and the fundamental waves that make up everything else. As he reveals, the ancient poetic idea of the “music of the spheres,” taken seriously, clarifies confounding issues in physics.

Whether you are more familiar with Brian Greene or Brian Eno, John Coltrane or John Wheeler, the Five Percent Nation or why the universe is less than five percent visible, there is a new discovery on every page. Covering the entire history of the universe from its birth to its fate, its structure on the smallest and largest scales, The Jazz of Physics will fascinate and inspire anyone interested in the mysteries of our universe, music, and life itself.

A Million Years of Music: The Emergence of Human Modernity

What is the origin of music? In the last few decades this centuries-old puzzle has been reinvigorated by new archaeological evidence and developments in the fields of cognitive science, linguistics, and evolutionary theory. In this path-breaking book, renowned musicologist Gary Tomlinson draws from these areas to construct a new narrative for the emergence of human music. Starting at a period of human prehistory long before Homo sapiens or music existed, Tomlinson describes the incremental attainments that, by changing the communication and society of prehumen species, laid the foundation for musical behaviors in more recent times. He traces in Neandertals and early sapiens the accumulation and development of these capacities, and he details their coalescence into modern musical behavior across the last hundred millennia.

But A Million Years of Music is not about music alone. Tomlinson builds a model of human evolution that revises our understanding of the interaction of biology and culture across evolutionary time-scales, challenging and enriching current models of our deep history. As he tells his story, he draws in other emerging human traits: language, symbolism, a metaphysical imagination and the ritual it gives rise to, complex social structure, and the use of advanced technologies. Tomlinson's model of evolution allows him to account for much of what makes us a unique species in the world today and provides a new way of understanding the appearance of humanity in its modern form.

Music and the Making of Modern Science (MIT Press)

In the natural science of ancient Greece, music formed the meeting place between numbers and perception; for the next two millennia, Pesic tells us in Music and the Making of Modern Science, "liberal education" connected music with arithmetic, geometry, and astronomy within a fourfold study, the quadrivium. Peter Pesic argues provocatively that music has had a formative effect on the development of modern science -- that music has been not just a charming accompaniment to thought but a conceptual force in its own right.

Pesic explores a series of episodes in which music influenced science, moments in which prior developments in music arguably affected subsequent aspects of natural science. He describes encounters between harmony and fifteenth-century cosmological controversies, between musical initiatives and irrational numbers, between vibrating bodies and the emergent electromagnetism. He offers lively accounts of how Newton applied the musical scale to define the colors in the spectrum; how Euler and others applied musical ideas to develop the wave theory of light; and how a harmonium prepared Max Planck to find a quantum theory that reengaged the mathematics of vibration. Taken together, these cases document the peculiar power of music -- its autonomous force as a stream of experience, capable of stimulating insights different from those mediated by the verbal and the visual. An innovative e-book edition available for iOS devices will allow sound examples to be played by a touch and shows the score in a moving line.

Ultimate Mind Control

Drawn from sources deep in China and India, the long-lost secrets of mastering the mental arts of Ame-tsuchi-jitsu are now revealed by martial-arts master Dr. Haha Lung. Those with the courage to explore these forbidden techniques will be rewarded with the skills to master any foe or situation, from the conference room to the battlefield and beyond. Inside these explosive pages, you'll learn:

Black Science : Ancient and Modern Techniques of Ninja Mind Manipulation

The fighting skills of the shadow warrior - the ninja - made them feared throughout Japan. But the wise man had greater fear for their bloodless methods of domination, which the ninja mind masters preferred to crude physical violence. Ninja broke through their enemies' mental defenses using direct attack or stealth, comparing such operations to invading an enemy fortress. In this guided tour through the mysterious realm of the ninja, martial arts experts Dr. Haha Lung and Christopher B. Prowant reveal the secrets that will allow you to tell when someone is lying to you, implant false memories, tailor your attack by using the specific keys to each individual's mind, use verbal patterns and body language to earn your foe's utter trust, interrogate using unbeatable psychological methods and much more.You will also learn the terrifying truth behind modern mind-control, propaganda and brainwashing techniques used by cults (and our own government), as well as take a look ahead to the future of mass mind control. The wars of tomorrow may well be won or lost in the battlefield of the mind. This book could mean the difference between winning your freedom and losing everything.