The Fifth Hammer Pythagoras and the Disharmony of the

The Fifth Hammer Pythagoras and the Disharmony of the World This one will give your brain a real workout I think it’s well worth reading if you have any interest at all in harmony and acoustics and how they relate to theoretical mathematics and astronomy One star taken off because I thought chapter 7 was too much rather tedious and not terribly rewarding Kantian philosophy and I couldn’t see a direct connection in it to the thesis of the book But it’s still an excellent work I thought it was a raucous good read Walking past a forge one day a fable tells of Pythagoras enrapt by the sound of five hammers striking in unison consonant in their harmony Here it seemed was a living allegory of the cosmos itself a well ordered expanse of unitary motion and proportion Yet of the five hammers the fifth never did uite fit its discordant chime shattering the spell that so pleased the Greek philosopher Such is the tale that begins Daniel Heller Roazen's intimate little history tracing the insistence of disharmony across the many attempts to expel it from the world from the ineliminable 'remainders' of the musical octave to the limitlessness of a universe unbound The Fifth Hammer is the tale of a little theme with weighty conseuencesIndeed part of the surprise and the delight of H R's book are the unexpected paths followed in pursuit of its subject moving effortlessly among ancient mathematics Kantian moral philosophy and scholastic musical theory weaving an intellectual web as diverse as it is learned Unwedded then to the conventions of genre The Fifth Hammer is at its best when leaning on the bleeding edge of not just history but philosophy too Can one think of number the same way again for instance after learning that the irrationals for a while were not even considered numbers at all? And how much better can one appreciate the genius of Leibniz once his metaphysics of the best of all possible worlds is cast in the light of a theory of musical harmony as recounted here? If anything the book’s problem to the degree that is has one is its seemingly arbitrary selection of chronicles which while all linked by the theme of the disharmonious nonetheless do seem like wanderings among a much wider and not fully explored expanse In some ways the book is a victim of its own success having lit the flame of intellectual curiosity in such an effective manner one can only be let down after the book’s relatively small hundred and fifty page heft Still given the range and depth of cultural and historical notes that The Fifth Hammer does in fact strike there's very little to complain about Recommended for anyone looking for a compelling take on an offbeat path of Western intellectual history Like all of Daniel Heller Roazen's books this traces an obscure theme through pre modern cultural history finding implications wildly divergent from the initial thesis In this case it is the discovery by Pythagoras that musical harmony has its basis in simple integer ratios The beauty of this system is incomplete and attempts to make it so run into problems of the irrational and disharmonious Heller Roazen traces this theme through Boethius and medieval musicologists up to the aesthetics of Kant and the cosmology of Kepler showing how time and again the sounding of the fifth hammer undermines the perfect harmony of their systems The book ends somewhat abruptly without a conclusion and that last few chapters feel like separate essays rather than integrated parts of a whole I'm not sure if this is a benefit or a liability but certainly reuires the reader to make connections that the author only implies An ancient tradition holds that Pythagoras discovered the secrets of harmony within a forge when he came across five men hammering with five hammers producing a wondrous sound Four of the five hammers stood in a marvelous set of proportions harmonizing; but there was also a fifth hammer Pythagoras saw and heard it but he could not measure it; nor could he understand its discordant sound Pythagoras therefore discarded it What was this hammer such that Pythagoras chose so decidedly to reject it Since antiuity harmony has been a name for than a theory of musical sounds; it has offered a paradigm for the scientific understanding of the natural world Nature through harmony has been transcribed in the ideal signs of mathematics But time and again the transcription has run up against one fundamental limit something in nature resists being written down transcribed in a stable set of ideal elements A fifth hammer obstinately continues to sound In eight chapters linked together as are the tones of a single scale The Fifth Hammer explores the sounds and echoes of that troubling percussion as they make themselves felt on the most varied of attempts to understand and represent the natural world From music to metaphysics aesthetics to astronomy and from Plato and Boethius to Kepler Leibniz and Kant this book explores the ways in which the ordering of the sensible world has continued to suggest a reality that no notes or letters can fully transcribe

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