A Paradoxical Ode

Hermann Stoffkraft
First page of James Maxwell's last poem, "A Paradoxical Ode", sent to Peter Tait, but addressed to the fictional materialist hero Dr. Hermann Stoffkraft of Tait and Balfour Stewart’s 1878 novel Paradoxical Philosopher. [1]
In famous publications, “A Paradoxical Ode / After Shelley” was an 1878 encrypted poem, consisting of three stanzas, addressed to a fiction character Hermann Stoffkraft, but sent to Peter Tait, written by Scottish physicist James Maxwell, the only time he ever expressed his private thoughts about the relationship of science and religion, choice and chance, death and eternity. In loose terms, the poem is Maxwell's final thoughts on (a) whether or not there is a god and he has a soul, (b) whether, conversely to first possibility, all that exists is atoms and voids or matter and force, or (c) whether there is some scientific connection between (a) and (b) or not.

The poem was a reaction to the views expressed in the 1878 novel Paradoxical Philosopher, by Balfour Stewart and Tait, in which the hardened scientific German materialist Stoffkraft (a character modeled Hermann Helmholtz and Ludwig Buchner; his last name meaning "matter-force" in German) is converted to the religious-sided views of the several Christian scientists in the novel, primarily to adopt the so-called "principle of continuity" of afterlife, as presented in the 1875 The Unseen Universe, by Tait and Stewart; which itself had been a reaction to the religion vs science debate that had erupted at the 1874 British Association for the Advancement of Science (BAAS) meeting, stemming from the abrupt comment of Irish physicist John Tyndall that:

“All religious theories, schemes and systems, which embrace notions of cosmogony, or which otherwise reach into the domain of science, must, in so far as they do this, submit to the control of science, and relinquish all thought of controlling it.”

The poem is Maxwell’s rare inner thoughts on this tenuous matter and his last and dying poem, written in his final year as he was in the final stages of stomach cancer, as he went into his 48th year, the same age his mother died previously from the same disease.

The mention of "After Shelley" is a pastiche of English romantic poet Percy Shelley's 1820 Prometheus Unbound, a play concerned with the torments of Prometheus and his suffering at the hands of Zeus. [3]

See also: Maxwell on the soul
In followup to his review, in 1878 Maxwell penned a satirical three-part poem entitled “A Paradoxical Ode”, addressed to Hermann Stoffkraft (the so-called materialistic hero of Paradoxical Philosophy), which he sent to Tait poking fun at their work, themed on the alluded to premise that his soul was an amphicheiral knot, a knot that can be deformed into its mirror image, in a scientific sense, which curiously was Maxwell’s last poem, as he knew he was dying as he wrote it. The original version is reproduced below: [1]

My soul’s an amphicheiral knot (1)
Upon a liquid vortex wrought (14)
By Intellect in the Unseen residing (17)
While thou dost like a convict sit
With marlinspike untwisting it (2)
Only to find my knottiness abiding,
Since all the tools for my untying
In four-dimensioned space are lying (3),
Where playful fancy intersperces,
Whole avenues of universes;
Where Klein and Clifford fill the void
With one unbounded, finite homaloid (4),
Whereby the Infinite (5) is hopelessly destroyed.
amphicheiral knot
The "amphicheiral knot" (a trefoil knot), i.e. a knot that can be deformed into its mirror image, as found on the cover of Balfour Stewart and Peter Tait’s 1875 The Unseen Universe, wherein they argue for the immortality of the soul using thermodynamics. [3]

But when thy Science lifts her pinions
In Speculation’s wild dominions,
I treasure every dictum thou emittest;
While down the stream of Evolution
We drift (6), and look for no solution
But that of survival of the fittest (7),
Till in that twilight of the gods
When earth and sun are frozen clods (13),
When, all its matter degraded (8),
Matter in aether shall have faded,
We, that is, all the work we’ve done (9),
As waves in aether, shall for ever run (16)
In swift expanding spheres, through heavens beyond the sun.

Great Principle of all we see,
Thou endless Continuity! (15)
By thee are all our angles gently rounded,
Our misfits are by thee adjusted,
And as I still (10) in thee have trusted,
So let my methods never be confounded!
O never may direct Creation
Breach in upon my contemplation,
Still may the causal chain ascending,
Appear unbroken and unending,
And where the chain is best to sight
Let viewless fancies guide my darkling (11) flight
Through aeon-haunted worlds, in order infinite (12).

The following are speculative notes to the various riddled lines of the poem:

(1a) An amphicheiral knot is one that can be deformed into its mirror image. In Shelley’s poem, Asia refers to herself as an “enchanted boat” drifting without course or star, driven only “by the instinct of sweet music.”
(1b) In 1867 Tait had demonstrated the mutual interaction of smoke-rings in his laboratory for the benefit of William Thomson. Thomson rashly proposed a “vortex atom theory” (atomic theory), asserting that knotted vortices in the ether comprise all chemical elements. Tait was now laboring hard to classify knots; supposedly to build an knot element periodic table, of some sort.
(2) Convicts might be given the task of recovering hemp from rope by using a marlinspike.
(3) Maxwell was doubted that we live in a world of more than 3 spatial dimensions. In a letter to C.J. Monroe, dated 1871, he asked: “If you have four dimensions this becomes a puzzle, - for first, if three of them are in our space, then which three?”

The Last Poem of James Clerk Maxwell (2008)
2008 article "The Last Poem of James Clerk Maxwell" by American mathematician Daniel Silver, which helped to unearth some of the background to Maxwell's final thoughts. [4]
(4) Three-dimensional space in which the axioms and postulates of Euclid hold.
(5) The Infinite was often identified with God.
(6) In Shelley’s poem, Asia also drifted down a stream.
(7) “Survival of the fittest” was a term invented by philosopher Herbert Spencer.
(8) Dr Stoffkraft asserts that all energy degrades. With the end of humanity, collective consciousness will disappear; degradation of energy is William Thomson's version of the second law.
(9) Perhaps a very personal note.
(10) always.
(11) In the dark.
(12) Likely intended as a bad rhyme.
(13) heat death (Rudolf Clausius' theory of universal end).
(14) Liquid vortex is William Thomson's theory, said to be set in motion by "some supernatural power", as Maxwell comments ("Paradoxical Philosophy", Nature, 19 Dec 1878).
(15) the "principle of continuity", discussed by Maxwell ("Paradoxical Philosophy", Nature, 19 Dec 1878) refers to the conservation of energy used to explain the supposed continuity of the mind or soul in the movement of the universe, in thermodynamic terms, as attempted by Tait and Balfour.
(16) The waves in aether theory refers to Christiaan Huygens' 1678 undulatory theory of light and to Thomas Young's 1803 double-slit experiment, the latter of which, whose theory on color Maxwell cited in his electromagnetic theory of light.
(17) The "unseen intellect" is Tait and Stewart's version of God.

In sum, as noted by the ending lines of the poem, Maxwell considers the thoughts of the paradoxical philosopher to be mere "viewless fancies", but nevertheless all that one has to guide the person at their parting moments. Again, as mentioned, at the time of writing this, his last poem, as well as his Nature review of Stewart and Tait’s energetic immortality theory of the soul, it was known that Maxwell already knew he was dying. This fact is summarized well by American statistical mathematician Daniel Silver, in his well-researched 2007 article “My Soul’s an Amphicheircal Knot: the Last Poem of James Clerk Maxwell”, he comments :

“Questions about the soul’s immortality were no longer merely academic for Maxwell. He was dying, and very likely knew it by now. For months he had been suffering from stomach pains, but he had consulted no doctors. We know from Campbell that when he wrote his review, he was having difficulty swallowing. He would learn soon that he had the same cancer that took his mother at the very same age that he was now. He would die within a year.”

Taped to the bottom of the page of Tait’s scrapbook is an addendum, sent by Maxwell some days afterwards.

Last three lines of Ode to Stoffkraft should be as follows.
While Residents in the Unseen–
Aeons or Emanations – intervene,
And from my shrinking soul the Unconditioned screen.

The mention of soul, or rather his "shrinking soul", or the "ba" as originally formulated in Ra theology, and carried over into Christianity, and thus into Maxwell's poem, is referred to by Maxwell in his "Review: Paradoxical Philosophy", wherein he asks which part of the double mind is responsible for doing right and wrong and in the same vein discusses binding problem, as to whether or not atoms have consciousness. The "unseen", as mentioned, is Tait and Stewart's version of god, and the "unconditioned screen", according to Daniel Silver, is Immanuel Kant and William Hamilton's theory that god is hidden from human thought because humans are "conditioned", and Hamilton was one of Maxwell's instructors at the University of Edinburgh. In any event, we see that Maxwell was a soul theorist in the end.

1. (a) Maxwell, James. (1878). “A Paradoxical Ode / After Shelley”, in: Life of Maxwell, pgs. 649-51; in: Knott, Life of Tait, pgs. 242-43.
(b) Knott, Cargill G. (1911). Life and Scientific Work of Peter Guthrie Tait (Maxwell's review + "A Paradoxical Ode", pg. 241-43). Cambridge University Press.
2. (a) Silver, Daniel S. (2007). “My Soul’s an Amphicheircal Knot: the Last Poem of James Clerk Maxwell”, SouthAlabama.edu.
(b) Brown, Adam. (2006). “Maxwell’s Paradoxical Ode”, research paper, University of South Alabama, Fall Term.
(c) Original copy of "Paradoxical Ode" contained in Tait's scrapbook donated to the James Maxwell Foundation in Edinburgh.
3. Prometheus Unbound (Shelley) – Wikipedia.
4. Silver, Daniel S. (2008). “The Last Poem of James Clerk Maxwell”, Notices of the AMS, 55(10): 1266-70.

Further reading
● Stewart, Balfour and Tait, Peter G. (1875). The Unseen Universe: or Physical Speculations on a Future State. Macmillan.
● Stewart, Belfour and Tait, Peter G. (1878). Paradoxical Philosophy: a Sequel to the Unseen Universe. Macmillan.
● Maxwell, James. (1878). “Review: Paradoxical Philosophy”, in: Scientific Papers, II, pg. 451; in Nature, 19 (19 Dec 1878): 141-43; in: Scientific Papers, 2, 756-62.
● Myers, Greg. (1985). “Nineteenth-Century Popularizations of Thermodynamics and the Rhetoric of Social Prophecy. Victorian Studies, 29: 35-66; esp. 49-63.

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