古老的傳統認為，畢達哥拉斯發明了和諧。據說有一天，他經過一個鍛造廠，聽到裡面傳來一陣奇妙的聲音，便冒險進去一探究竟。他發現五個人正用五把鐵鎚敲打。令他驚訝的是，他發現五把錘子中有四把的比例奇妙無比，組合在一起後，他得以重建音樂定律。但還有第五把錘子。畢達哥拉斯看到並聽到了它，但他無法測量它，也無法推斷它不和諧的聲音。因此，他放棄了它。
這把錘子究竟是什麼，以至於畢達哥拉斯如此果斷地選擇拒絕它？在《第五把錘子》一書中，丹尼爾·海勒-羅森清晰地闡述了這一傳奇般的姿態如何為理解廣義的和諧提供了一把鑰匙。自古以來，「和諧」就不僅僅是指音樂聲音理論的名稱；它構成了科學理解感性世界的典範。自然，透過和諧，被轉錄於數學的理想元素之中。然而，這種轉錄一次又一次地遭遇到一個根本的極限：自然界中的某些東西無法被記錄在一套理想的單位中。第五把錘子，卻頑固地繼續敲擊。
《第五把錘》共八章，如同同一音階的音調般相互關聯，探討了這敲擊之聲及其迴響，它們在理解自然界的各種嘗試中都曾出現過。在伽利略之前和之後，古代思想和早期現代科學與哲學，以截然不同卻又互補的方式，遭遇了自然界中一個令人不安的維度，並試圖對其進行解釋和解決。
面對不均衡，他們揭示了自身的根本目標和限制。從音樂到形而上學，從美學到天文學，從柏拉圖和波愛修斯到開普勒、萊布尼茨和康德，《第五錘》探索了感知世界的秩序如何持續暗示著一種音符和字母都無法完全轉錄的現實。
The Fifth Hammer: Pythagoras and the Disharmony of the World
Daniel Heller-Roazen
A revolutionary history and theory of harmony from music to metaphysics
Daniel Heller-Roazen is the Arthur W. Marks ’19 Professor of Comparative Literature at Princeton University. His is the author, most recently, of Absentees: On Variously Missing Persons; No One’s Ways: An Essay on Infinite Naming; and Dark Tongues: The Art of Rogues and Riddlers. His books have been translated into many languages. Heller-Roazen is a Fellow of the American Academy of Arts and Science and received the medal of the Collège de France in 2010.
丹尼爾·海勒-羅森是普林斯頓大學2019屆亞瑟·W·馬克斯比較文學教授。他的最新著作包括《缺席者：論各種失蹤者》、《無人之道：論無限命名》和《黑暗的舌頭：流氓和謎語人的藝術》。他的著作已被翻譯成多種語言。海勒-羅森是美國藝術與科學學院院士，並於2010年榮獲法蘭西學院獎章。
Zone Books
An ancient tradition holds that Pythagoras invented harmony. It is said that one day, he wandered by a forge and, hearing a wondrous sound come from within, ventured in to investigate. He found five men hammering with five hammers. To his astonishment, he discovered that four of the five hammers stood in a marvelous set of proportions, which, when combined, allowed him to reconstruct the laws of music. But there was also a fifth hammer. Pythagoras saw and heard it, but he could not measure it; nor could he reason its discordant sound. He therefore discarded it.
What was this hammer, such that Pythagoras chose so decidedly to reject it? In The Fifth Hammer, Daniel Heller-Roazen lucidly shows how that fabled gesture offers a key for understanding ideas of harmony in the broadest sense of the term. Since antiquity, “harmony” has been a name for more than a theory of musical sounds; it has constituted a paradigm for the scientific understanding of the sensible world. Nature, through harmony, has been transcribed in the ideal elements of mathematics. But, time and again, the transcription has run up against one fundamental limit: something in nature resists being written down in a set of ideal units. A fifth hammer, obstinately, continues to sound.
In eight chapters, linked together like the tones of a single scale, The Fifth Hammer explores the sounds and echoes of that percussion, as they have made themselves felt on the most varied of attempts to understand the natural world. In vastly different and yet complementary ways, ancient thought and early modern science and philosophy, before and after Galileo, encountered a troubling dimension of nature, which they sought to interpret and resolve.
Confronting disproportion, they revealed their fundamental aims and limits. From music to metaphysics, from aesthetics to astronomy, and from Plato and Boethius to Kepler, Leibniz and Kant, The Fifth Hammer explores the ways in which orderings of the sensible world have continued to suggest a reality that neither notes nor letters can fully transcribe.
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