From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authored by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional, and analytical relationships between mathematics and music are unfolded and explored (...) with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques. (shrink)

Why does time appear to run in only one direction? We remember the past- but why not the future? We can influence the future- but could we, even theoretically, influence the past? Generations of philosophers and theologians, physicists and mathematicians have puzzles and speculated about these and the many other questions that surround the concept of time. Recent scientific work is said to explain the directionality of time. But time still contains many mysteries- black holes and big bangs, asymmetries and (...) relativities, arrows and loops - that will doubtless continue to occupy us for centuries to come. In this impressive collection of original articles ten internationally known scholars explore and explains the nature of time, apace and now space-time. Founded on the latest developments in thermodynamics, quantum theory and cosmology, their ideas will fascinate anyone interested in Einstein's theory of relativity. (shrink)