The Fifth Hammer: Pythagoras and the Disharmony of the World by Daniel Heller-Roazen

The Fifth Hammer: Pythagoras and the Disharmony of the World Reviews

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  A.J. McMahon

  I was really hoping for much more of an interesting and coherent argument than this book contained in the end. The book opens with an introduction to the legend of the fifth hammer: the story goes that Pythagoras, when entering the famous smithy with its musical hammers, found that there were in fact five hammers but only four of them were involved in forming the harmonic intervals that had attracted his attention in the first place, and the fifth had no place in his scheme of things and so was left out. The implication of the existence of the fifth hammer might be that there is a dimension of reality that cannot be formulated in any of our schemes of things, or to put it another way that not only are there more things in heaven and earth than exist in our philosophy, but there are things in heaven and earth which cannot be expressed in any system of representation. Daniel Heller-Roazen at first sounds as if he is going to make something of this starting point but he never really goes anywhere except round and round in circles. It seemed to me that the author bit off more than he could properly chew. Just about worth reading for the occasionally interesting passages.
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  Karen Chung

  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.
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  Alex Delogu

  Having read Echolalia and been blown away by the breadth of scholarship, I was hit by the depth of it in this one. It is a real deep-dive into the trajectory of Pythagorean philosophy up through Oresme, Kant, and Kepler.
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  Alexander

  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 quite 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 consequences.
  
  Indeed, 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.
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  Tony Gualtieri

  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 requires the reader to make connections that the author only implies.
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  Humphrey

  I thought it was a raucous good read.