In an exciting, fast-paced historical narrative ranging across two centuries, Ronan takes readers on an exhilarating tour of this final mathematical quest to understand symmetry.

Like many ambitious New York City teenagers, Craig Gilner sees entry into Manhattan's Executive Pre-Professional High School as the ticket to his future. Determined to succeed at life—which means getting into the right high school to get into the right college to get the right job—Craig studies night and day to ace the entrance exam, and does. That's when things start to get crazy. At his new school, Craig realizes that he isn't brilliant compared to the other kids; he's just average, and maybe not even that. He soon sees his once-perfect future crumbling away.

In this investigation of the psychological relationship between shape and time, Leyton argues compellingly that shape is used by the mind to recover the past and as such it forms a basis for memory. Michael Leyton's arguments about the nature of perception and cognition are fascinating, exciting, and sure to be controversial. In this investigation of the psychological relationship between shape and time, Leyton argues compellingly that shape is used by the mind to recover the past and as such it forms a basis for memory. He elaborates a system of rules by which the conversion to memory takes place and presents a number of detailed case studies--in perception, linguistics, art, and even political subjugation--that support these rules. Leyton observes that the mind assigns to any shape a causal history explaining how the shape was formed. We cannot help but perceive a deformed can as a dented can. Moreover, by reducing the study of shape to the study of symmetry, he shows that symmetry is crucial to our everyday cognitive processing. Symmetry is the means by which shape is converted into memory. Perception is usually regarded as the recovery of the spatial layout of the environment. Leyton, however, shows that perception is fundamentally the extraction of time from shape. In doing so, he is able to reduce the several areas of computational vision purely to symmetry principles. Examining grammar in linguistics, he argues that a sentence is psychologically represented as a piece of causal history, an archeological relic disinterred by the listener so that the sentence reveals the past. Again through a detailed analysis of art he shows that what the viewer takes to be the experience of a painting is in fact the extraction of time from the shapes of the painting. Finally he highlights crucial aspects of the mind's attempt to recover time in examples of political subjugation.

On the day you were born, you were imprinted with a plan and a purpose – elegant patterns that can be read to see who you really are and what your true calling is. And like your own personal map, the design for each phase of your life journey was created on the day of your birth. Based on ancient Chinese principles of balance and health, this book gives you a rich understanding of your hidden symmetry – the intricate inner design that influences who you are and how your life unfolds. This book is not about astrology or numerology; it is grounded in thousands of years of research about how time moves in natural patterns that profoundly affect you. You can use this knowledge to discover the themes running through your life experience, tap into your core strengths, find lasting love, and do your best work in the world. Jean Haner shows you how to ride the waves instead of fight the current of your life, make the best use of what’s coming in future years, and understand why things happened as they did in the past. Jean will guide you to discover who you really came here to be, recognize the true nature of everyone you meet, and break free of old limitations – to create a life of conscious vitality, joy, ease, and love!

A professor of physics and astronomy studies a theory that time is reversible, and explains how physicists have generally been reluctant to accept the reversibility of time because of the implied causal paradoxes. Illustrations.

Katherine Larson is the winner of the 2010 Yale Series of Younger Poets Competition. With "Radial Symmetry," she has created a transcendent body of poems that flourish in the liminal spaces that separate scientific inquiry from empathic knowledge, astute observation from sublime witness. Larson's inventive lyrics lead the reader through vertiginous landscapes - geographical, phenomenological, psychological - while always remaining attendant to the speaker's own fragile, creaturely self. An experienced research scientist and field ecologist, Larson dazzles with these sensuous and sophisticated poems, grappling with the powers of poetic imagination as well as the frightful realization of the human capacity for ecological destruction. The result is a profoundly moving collection: eloquent in its lament and celebration. Metamorphosis [an excerpt]: We dredge the stream with soup strainers and separate dragonfly and damselfly nymphs - their eyes like inky bulbs, jaws snapping at the light as if the world was full of tiny traps, each hairpin mechanism tripped for transformation. Such a ricochet of appetites insisting life, life, life against the watery dark, the tuberous reeds.

Symmetry: An Introduction to Group Theory and its Application is an eight-chapter text that covers the fundamental bases, the development of the theoretical and experimental aspects of the group theory. Chapter 1 deals with the elementary concepts and definitions, while Chapter 2 provides the necessary theory of vector spaces. Chapters 3 and 4 are devoted to an opportunity of actually working with groups and representations until the ideas already introduced are fully assimilated. Chapter 5 looks into the more formal theory of irreducible representations, while Chapter 6 is concerned largely with quadratic forms, illustrated by applications to crystal properties and to molecular vibrations. Chapter 7 surveys the symmetry properties of functions, with special emphasis on the eigenvalue equation in quantum mechanics. Chapter 8 covers more advanced applications, including the detailed analysis of tensor properties and tensor operators. This book is of great value to mathematicians, and math teachers and students.