ESHS/HSS Annual Meeting

A new perspective on Hamilton’s theory of quaternions

• In Event: Through Archival and Material Sources: New Perspectives in the History of Physics (19th–20th Centuries)

English Abstract

William Rowan Hamilton (1805-1865), Royal Astronomer of Ireland from 1827 to 1865, was one of the greatest mathematicians of his age. Despite the strong and lasting impact that his results had on subsequent developments in physics and mathematics, the highly original philosophical conceptions underlying his work remained largely unknown to the scientific community of the XX century.
Therefore, in this communication, I will offer a new perspective on Hamilton’s work based on his original writings, including materials drawn from unpublished notebooks and correspondence archived at the Trinity College of Dublin. I will discuss how Hamilton’s philosophical views, deeply inspired by Greek thought and reinforced by the reading of Kant, influenced his mathematical researches, with a special focus on the theory of quaternions, to which Hamilton devoted almost exclusively the last twenty years of his career. In particular, I will argue that, in spite of the subsequent emphasis on the algebraical properties of quaternions, Hamilton conceived them chiefly as geometrical objects incorporating the characteristic symmetries of Euclidean space and realizing the old Pythagorean idea of the intertwinement between numbers and figures. One of the few who appreciated this aspect was Peter G. Tait (1831-1901), professor of Natural Philosophy in Edinburgh, who in 1858 started a correspondence with Hamilton about quaternions and became his only true pupil on quaternion methods.
To illustrate all this, I will discuss the so-called Law of the Circular Hodograph, a new geometric characterization of Newton’s law of gravity which Hamilton discovered by quaternion methods. In this way, I will show how a reassessment of Hamilton’s original views can still be of great interest today, from both historical and philosophical perspectives.

Author

• Alessandro Amabile, University of Naples Federico II