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The Last Poem of James Clerk Maxwell Daniel S The Last Poem of James Clerk Maxwell Daniel S. Silver “My soul’s an amphicheiral by a relative of Tait. The poem was published in knot,” proclaimed the great- The Life of James Clerk Maxwell, an extensive and est mathematical physicist definitive biography written in 1882 by Lewis of the nineteenth century. Campell and William Garnett. It has since been re- Many are familiar with produced many times, often altered and with little James Clerk Maxwell for his or no explanation. The poem appears below in its elegant equations describ- original form including Maxwell’s indentation. ing the electromagnetic field Superscripts in the poem and text refer to end- or for his profound ideas notes. Some words and phrases in the poem reap- about the kinetic theory of pear later in boldface as they are explained. gases and thermodynamics. Fewer know that Maxwell To Hermann Stoffkraft, Ph.D. was a compulsive poet. This A Paradoxical Ode is the story of Maxwell’s last After Shelley poem, written during his James Clerk Maxwell final days in 1878. An enig- I matic piece, expressed with odd references to topology, My soul’s an amphicheiral knot cosmology, and evolution, Paradoxical Ode in fact Upon a liquid vortex wrought reflects Maxwell’s private thoughts about the rela- By Intellect in the Unseen residing, tionship between science and religion, choice and While thou dost like a convict sit chance, death and eternity. With marlinspike1 untwisting it Paradoxical Ode was composed for a close Only to find my knottiness abiding;2 friend, the Scottish physicist Peter Guthrie Tait. Since all the tools for my untying The two had known each other since their school days at Edinburgh Academy. In 1867 Tait had dem- In four-dimensioned space are lying, onstrated the mutual interaction of smoke-rings in Where playful fancy intersperses his laboratory for the benefit of William Thomson Whole avenues of universes; (the recently knighted Lord Kelvin). Thomson Where Klein and Clifford fill the void rashly proposed a “vortex atom theory”, assert- With one unbounded, finite homaloid, 3 ing that knotted vortices in the ether comprise all Whereby the Infinite is hopelessly destroyed. chemical elements. Tait was now laboring hard to classify knots. II The original version of Paradoxical Ode was written on three sheets of plain paper. It is pre- But when thy Science lifts her pinions served in a scrapbook that was recently donated In Speculation’s wild dominions, to the James Clerk Maxwell Foundation, Edinburgh, I treasure every dictum thou emittest; While down the stream4 of Evolution Daniel S. Silver is professor of mathematics at the Uni- We drift, and look for no solution versity of South Alabama, Mobile. His email address is But that of the survival of the fittest.5 [email protected]. Till in that twilight of the gods 1266 NOTICES OF THE AMS VOLUME 55, NUMBER 10 When earth and sun are frozen clods, Intellect in the Unseen is the first of several When, all its energy degraded,6 references to The Unseen Universe or Physical Matter in æther shall have faded, Speculations on a Future State, a book that Tait We, that is, all the work we’ve done, co-authored with (yet another) Scottish physicist, As waves in æther, shall for ever run Balfour Stewart, in 1875. In it they argued that In swift-expanding spheres, through heavens religious miracles and the immortality of the beyond the sun. soul are compatible with modern science. God III is hidden from us because all human thought is “conditioned”, an idea that traces back to Kant. Great Principle of all we see, Nevertheless, the “principle of Continuity”, which Thou endless Continuity! Unseen Universe announced, comforts all with By thee are all our angles gently rounded;7 the gentle reassurance that nature will never do Our misfits are by thee adjusted, anything to confound us permanently: And as I still8 in thee have trusted, So let my methods never be confounded! [W]hat the principle of Continuity de- O never may direct Creation mands is an endless development of Break in upon my contemplation, the conditioned. We claim it as the Still may the causal chain, ascending, heritage of intelligence that there shall Appear unbroken and unending, be an endless vista, reaching from eter- And, where that chain is lost to sight nity to eternity, in each link of which we shall be led only from one form of Let viewless fancies9 guide my darkling10 flight the conditioned to another, never from Through Æon11-haunted worlds, in order infinite. the conditioned to the unconditioned ∂p 12 or absolute, which would be to us no ∂t better than an impenetrable intellec- tual barrier. … Finally our argument Besides wordplay, Maxwell’s nonscientific pas- has led us to regard the production of sions included literature and philosophy. Para- the visible universe as brought about doxical Ode is a pastiche of a passage from the by an intelligent agency residing in the lyrical drama, Prometheus Unbound, by the English unseen. romantic poet Percy Shelley. The first verse of Paradoxical Ode accurately Stewart and Tait wrote Unseen Universe in suggests that Maxwell was familiar with new response to John Tyndall’s mathematical ideas of the day. He understood a Presidential Address to the knot to be a simple closed curve in 3-dimensional British Association for the space, just as we do today. An amphicheiral knot Advancement of Science is one that can be deformed to its mirror image, during the previous year. As while liquid vortex is a reference to Thomson’s controversy raged over the vortex atom theory. teaching of science at the From correspondence between Tait and Max- Catholic University in Ire- well, we know that Maxwell was directly involved land, Tyndall, an Irish physi- in the nascent subject of knot theory, although cist and successful popu- he did not publish any knot theoretical results of larizer of science, had felt his own. the need to speak out. “All Maxwell’s interest in knots, and topology in religious theories, schemes general, had a serious side. It was Maxwell who and systems, which embrace informed Tait about the work of Johann Bene- notions of cosmogony, or dict Listing, a student of Gauss, who coined the which otherwise reach into word “topology” in 1848 and had begun his own the domain of science,” Tyn- study of knots. Maxwell’s Treatise on Magnetism dall contended, “must, in so and Electricity made early and profound use of far as they do this, submit John Tyndall Listing’s homological notions. In it, we find a new to the control of science, interpretation of Gauss’s linking integral for two and relinquish all thought disjoint, simple closed curves as the work done by of controlling it.” Tyndall’s a charged particle moving along a path described call for reason over revelation was seen by some, by one knot against the magnetic field induced including Stewart and Tait, as an attack on religion. by an electrical current running though the other. Unseen Universe was hastily written and was a huge Maxwell was fascinated by the idea that two knots success. The authors published anonymously until can have zero algebraic linking number and yet be the fourth edition appeared. A trefoil knot adorned the spine and title page. inseparable. NOVEMBER 2008 NOTICES OF THE AMS 1267 Just a few years be- Mathematical Soci- fore Paradoxical Ode ety. By the term, was composed, Felix Clifford meant Klein had published a “flat” space of a proof that any knot any number of di- can be undone in four- mensions, that is, dimensioned space. By a space with cur- the time that the poem vature zero. Max- was sent to Tait, the well’s use of the American magician and term is perplex- medium Henry Slade ing.14 However, his had incorporated the intention becomes idea into his act, claim- clearer when we ing to unknot ropes in understand that the fourth dimension. most scientists of Edwin Abbott’s multidi- his day believed mensional exploration, that the universe Flatland, would appear is flat and that a Ludwig Büchner five years later. flat universe is Like many, Maxwell necessarily infi- was interested in specu- nite. Likely, Maxwell understood that while the lations about a fourth first assertion might be true, the second is not. He dimension. In an amus- attended the1873 Bradford meeting of the British ing letter to C. J. Monroe, Association for the Advancement of Science at dated 1871, he doubted which Clifford showed how to construct flat tori Title page of Unseen Universe. that we live in a universe as quotients of Euclidean space. of more than 3 spatial At Northwestern University in 1893, Klein sum- dimensions: “If you have 4 dimensions this be- marized the situation: comes a puzzle—for first, if three of them are in our space, then which three?” It is evident from this point of view In a multidimensional world, many things such many assertions concerning space as whole avenues of universes are possible. Stew- made by previous writers are no lon- art and Tait were not timid about transporting a ger correct (e.g., that infinity of space novel scientific theory to unfamiliar surroundings. is a consequence of zero curvature), so Readers of Unseen Universe learned that their every that we are forced to the opinion that thought and action broadcasts eternal vibrations our geometrical demonstrations have throughout the perfect ether. Inconveniently, no absolute objective truth, but are nothing in our visible world, including fluids, is true only for the present state of our perfect.
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