The Thought of a Thought - Edgar Allan Poe



Edgar Allan Poe (1809-1849) is best known as a literary figure, a writer of short stories and poetry, but a surprising amount of his thought was devoted to natural science, with which he seems to have had a love-hate relationship, as illustrated by his "Sonnet to Science"


Science! true daughter of Old Time thou art!

Who alterest all things with thy peering eyes.

Why preyest thou thus upon the poet's heart...?


In this attitude Poe is somewhat reminiscent of Goethe (1749-1832), who spent so much time and effort on his own private theory of colors and the indivisibility of light, trying to overthrow the teachings of Newton (1642-1727).  Indeed, Goethe himself is said to have valued his "scientific" work more highly than his literary creations (an opinion not shared by anyone else).  Another artist who struggled with the emerging scientific culture was William Blake (1757-1827), who wrote


Mock on, Mock on, Voltaire, Rouseau,

Mock on, Mock on, 'tis all in vain...

The Atoms of Democritus

And Newton's Particles of light

Are sands upon the red sea shore

Where Israel's tents do shine so bright.


The fascination and ambivalence these men felt toward Newton, the personification of Science, is well illustrated by Blake's famous painting "The Ancient of Days", showing a kneeling God-like/Satanic figure spanning the darkness with a compass of light.  Remarkably, Blake's illustration of "Newton" is essentially the same figure, in the same pose, viewed from the side.




This gives some idea of how great, throughout the 19th century, was the prestige of Newton as the discoverer of the only true laws of nature, the indisputable confidant of God, especially among intellectuals, including poets and artists as well as scientists.  It's not surprising that many creative and independent men felt, as Blake put it, that


I must create a system, or be enslaved by another man's.

I will not reason and compare, my business is to create.


We may also remember Laplace's remark that


Newton was the greated genius who ever existed and the luckiest, because we cannot find more than once a system of the world to establish.


What does this leave for his successors? Since Newton associated every action with a re-action, it's only fitting that there was a reaction against the scientific Enlightenment of the 18th century, leading to the Romanticism of the 19th century.  One characteristic of those who rebelled against the Newtonian approach to knowledge and understanding was (and still is) an antipathy for mathematics.  Prior to the scientific revolution, it was possible for scholastic philosophers and thinkers of all kinds to engage with the great questions of natural science in the verbal and teleological tradition, but Galileo and Newton effectively put an end to this.  Among serious thinkers with little or no inclination toward mathematics, imagine how discouraging must be the famous words of Galileo:


Philosophy is written in this grand book - I mean the universe - which stands continuously open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written.  It is written in the language of mathematics... without which it is humanly impossible to understand a single word of it.  Without these one is wandering about in a dark labyrinth.


In response, men like Blake and Goethe reply that mathematics is merely "narrow reasoning and comparing", and does not constitute comprehension.  As Blake wrote, "...May God us keep / from single vision and Newton's sleep!"  This was a sentiment with which Poe sympathized.  Ironically, despite (or perhaps because of) their common standings as scientific dilettantes, Poe disparaged Goethe as insufficiently analytical.  In contrast, Poe often regarded himself as a paragon of rational thought (like his detective Dupin), but he seems to have held a characteristically Romantic view of rationality, seeking to apply an artistic esthetic as the ultimate criterion for "scientific" truth.  For example, he acknowledged the seemingly unassailable validity of Newton's mechanics and his law of universal gravitation, but he felt deeply that a true understanding of these things was lacking in the mathematical Newtonian world view.  In various writings Poe presented (often surreptitiously) his own thoughts on natural science, culminating in one of his final major works, the prose poem called "Eureka" (1848), in which he ostensibly describes what we might call his Theory of Everything. 


It's easy to question whether Poe was really serious about the scientific (or quasi-scientific) ideas that are expressed in Eureka and other works.  A plausible case can be made that he was perpetrating a gigantic intellectual hoax (similar to Sokal's hoax of the 1990's).  In support of this point of view we could, for example, note that Poe had at times referred unflatteringly to Alexander von Humboldt, the world-famous scientists to whom Eureka is dedicated "with profound respect".  Was Poe just pulling our legs?  It's certainly possible, but we shouldn't overlook the fact that Poe seems to have had a love-hate relationship with just about everything and everyone.  For example, his reviews characteristically alternated wildly between praise and scorn, between adoration and contempt.  Poe's style was well-enough known to be an object of parody; one satirical imitation of his reviews had him calling a book "a mass of insufferable trash, without one redeeming quality" and then "one of the most delightful books".  After reading Poe's (authentic) review of her poetry, Elizabeth Barrett was appalled by "the two extremes of laudation and reprehension, folded in on one another... you would have thought it had been written by a friend and a foe, each stark mad with love and hate, and writing the alternate passages".  Perceptively she speculated that it seems as if the reviewer was experiencing some kind of "crisis".  Similarly his aggressive attacks on Longfellow were accompanied by claims that Poe had a very high admiration for him.  The same pattern is to be seen in Poe's personal letters, such as to his foster father John Allen, in which he alternates between "insolence and cravenness" (as his biographer Kenneth Silverman nicely expressed it.)  For this reason, it's difficult to confidently judge what - if anything - Poe meant to be taken seriously, and what was simply a hoax.  Possibly he had ideas which he wished would be taken seriously, but as a defense mechanism he presented them always in a form that could plausibly be sloughed off as a joke.


Examples of Poe's "scientific" ideas can be found in many of his short stories.  In fact, some of those stories seem to be little more than literary pretexts for the presentation of abstract notions that Poe wished to express, but knew would be ridiculed if he presented them as serious scientific ideas.   For example, the story "Mesmeric Revelation" consists of the words of a dying man who has been placed in a trance to ease his suffering, and in this state he is questioned by his attendant.  The mesmerized man discourses on "unparticled matter", a medium thinner and more tenuous than the "luminiferous ether" permeating all of space.  He suggests that thought (as opposed to mind) consists of motions of this unparticled matter.  He also discusses the (then) current theory that the luminiferous ether exerts a drag on comets and accounts for anomalies in their orbital motions.  Interestingly, several years later Poe discussed this very same subject (in the first person) in Eureka, but by that time he had learned that more careful analyses of the comet orbits had eliminated the "anomalies", so there was no longer any justification for the ether.  (Would he have made this correction if he had simply been joking all along?)


Another story into which Poe inserted his scientific ideas is "The Unparalleled Adventure of One Hans Pfaall", which facetiously describes a journey from the Earth to the Moon in a hot air balloon, and observations of the Moon made from the Earth by means of a gigantic telescope.  At the end of this tale, Poe added five pages of "Notes" in which he ostensibly drops the pretense and discusses the obvious fallacies of such stories.  Again he reviews topics that he was later to include in "Eureka", such as the astronomical observations of Lord Ross, and various other points of astronomy, buoyancy, optics, and so on.  He concludes by scolding all previous authors of such "moon trip" stories for being "utterly uninformed in respect to astronomy", and claims that "Hans Pfaall" has at least a semblance of verisimilitude (unlike all other such stories that have appeared), and that it represents a sound application of scientific principles "so far as the whimsical nature of the subject would permit".


In his famous story "Descent into the Maelstrom" Poe includes remarks on Archimedes and fluid dynamics (e.g., the flow of fluids past spheres and cylinders), and it isn't surprising that Archimedes' famous exclamation of discovery would become the title of Poe's later Theory of Everything.  Interestingly, we find references to the mythical Mare Tenebrarum (Sea of Darkness) described by the mysterious Nubian geographer Ptolemy Hephestion repeated not only in "Maelstrom" and "Eureka", but also in "Eleonora", "Mellonta Tauta", and "Berenice".  In his story "The Power of Words" we find a discussion of Laplacian determinism and the ether as the "medium of creation".  The story "Three Sundays in a Week" gives an amusing look at the relativity of time under the influence of motion, and it's easy to imagine Henri Poincare reading Poe, who was almost more popular in France than in America at the end of the 19th century. 


One of the most systematic efforts of Poe to discuss technological and scientific ideas was in the story "1002nd Tale of Scheherazade", which consists of a series of seemingly incredible claims substantiated by footnotes providing the scientific basis.  In these notes Poe has occasion to discuss petrified forests, phosphorescent fungus, the maximum speed of travel achieved by humans up to that time (71 miles per hour in a train), chess-playing automatons, Babage's calculating machine, electrolysis, platinum wires with a diameter of 1/18000 of an inch (used in telescopes), the frequency of violet light (900,000,000 cycles per second) as determined by Newton, voltaic piles, the telegraph, optical experiments, the Daguerreotype, the speed of light (which he gives as 167,000 miles per second, the same value he quotes in Eureka), the parallax observations of the star 61 Cygni (which he also discusses in Eureka), Lord Ross' observations of stars millions of light years away (which he also mentions in Eureka), and so on.


Beginning in 1844 Poe wrote a series of articles which were published under the title of "Marginalia", consisting of a fascinating compilation of notes he had taken on various subjects.  Some are no more than epigrams ("I make no exception, even in Dante's favor: - the only thing well said of Purgatory is that a man may go farther and fare worse"), whereas others are extensive discussions of literary, social, or scientific matters.  These articles contain some remarkable passages that seem to anticipate important scientific ideas of later generations.  For example, consider his appraisal of time, which could easily have suggested the operational definition of time put forward by Henri Poincare (1854-1912) about 50 years later (in France, where Poe was widely read), leading the way to special relativity:


We appreciate time by events alone. For this reason we define time (somewhat improperly) as the succession of events; but the fact itself--that events are our sole means of appreciating time-- [leads to] the erroneous idea that events are time--that the more numerous the events, the longer the time; and the converse. This erroneous idea [we would] absolutely entertain in all cases, but for our practical means of correcting the impression--such as clocks, and the movements of the heavenly bodies--whose revolutions, after all, we only assume to be regular.


This is a remarkable passage, not only for its grasp of the operational meaning of time, but also for the observation that we only assume (or perhaps we should say define) the motions of clocks and the planet's, etc., to be regular.  In effect, Poe has understood that our "uniform measure" of time is really just the largest and most consistent equivalence class of mutually uniform sequences of similar events.  Even today Poe's appreciation of this point would be considered sophisticated.  He goes on to make the analogous observations about space - indeed he seems always to have noted the interchangeability of time and space, going so far in "Eureka" as to assert that "Space and Duration are one".  Naturally we shouldn't credit Poe for the spacetime of Poincare, Einstein and Minkowski, but it is nevertheless an interesting premonition, and, as noted above, Poe was widely read in Europe, especially France, where Poincare quite likely would have encountered some of his writings.


Poe was born in Boston in 1809.  His natural parents, Elizabeth (Arnold) and David Poe, were both actors, but Edgar and his older brother and younger sister were orphaned by the age of two, and were split up and sent to live with separate foster-families.  Edgar was taken in by John and Frances Allan of Richmond, Virginia.  When Edgar was 6 the Allan's moved to England, and Edgar attended a boarding school in London until he was 11, when the family moved back to Virginia.  At the age of 17 Edgar enrolled at the University of Virginia, where he was one of the top students academically, but he took to drinking and gambling, and was forced to leave after just one year.  By this time his foster-mother had died, and John Allan was not interested in having anything more to do with Edgar.  Back in Boston, Edgar tried unsuccessfully to find a job, and then enlisted in the Army under an assumed name (Edgar A. Perry).  While stationed at Fort Independence in Boston Harbor he managed to get a book of his poems published, anonymously.  About this time he apparently suffered a nervous breakdown and was discharged from the Army in 1829, and eventually went to live with his aunt, Maria (Poe) Clemm and her daughter Virginia, who he later married.  During this time he published another book of poetry.


In the summer of 1830 Edgar applied and was accepted at West Point, but he began drinking and gambling again, and was court-martialed early in 1831.  (While at West Point he encouraged the belief that he was a descendant of Benedict Arnold.)  By this time John Allan had completely disowned him (refusing even to answer the letters that Edgar addressed to "Dear Pa"), so Edgar moved back in with his Aunt Clemm.  In 1833 he won a $50 prize for a short story he submitted to a Baltimore magazine, and this led to jobs writing for various periodicals.  The prize story was "MS. Found In A Bottle".  (This motif seems to have had a particular appeal to Poe, because 15 years later he began his final work, "Eureka", with another "manuscript found in a bottle".)  


About this time it's possible that Edgar took up the use of opium in the form of laudanum, following in the footsteps of other artists of that period, such as Samuel Taylor Coleridge (1772-1834), Elizabeth Barrett, and others.  Laudanum was widely available in those days, prescribed for all manner of afflictions.  Coleridge had become addicted to opium after it had been prescribed to help him cope with a serious illness as a young man, and he remained addicted to the drug for the rest of his life, despite his efforts to get free of it.  His great masterpiece, "Kubla Khan", on the subject of poetic inspiration - a subject on which Poe also wrote - was composed as he was emerging from an opium dream.  (Incidentally, an attempt by the rulers of China to shut down the opium trade led to the war of 1839-1842 between Great Britain and China.)  The extent of Poe's use of opium is not know, although we do know that Poe attempted suicide in 1848 by taking an overdose of laudanum. 


Throughout the years from 1833 to 1848 Poe continued to write short stories, literary criticism, and poetry, inter-mixed with nervous breakdowns and alcoholic episodes.  His last book was "Eureka", published in 1848, dedicated "with very profound respect" to Alexander von Humboldt (1769-1859), the world-famous German naturalist.  In late September 1849 Poe had another alcoholic relapse, and his whereabouts during the five days from September 28 to October 3 are unknown.  On the 3rd a doctor was asked to come to a saloon in Baltimore, near  a place where Poe had been found lying unconscious in the sidewalk.  He was taken to Washington College Hospital, where he died on October 7 after days of delirium and tremors.  Reportedly his last words were "Lord help my poor soul".


Eureka itself is a fascinating book.  Poe called it a "prose poem", though he seems to have been conflicted about what it really was, and what he should call it.  Poe certainly gave evidence throughout his career of being able to summon enough critical judgement to construct viable works, even in his worst state of deterioration.  His romantic (not to say kooky) side may have believed that Eureka contained The Answers to all The Big Questions, the ultimate scientific theory of everything, but the sober editor in him surely recognized that what he had written was nothing like a scientific work - certainly not in the Newtonian mathematical sense - and would never be taken seriously by the scientific community.  Accordingly, he prefaced the book with the somewhat awkward disclaimer "What I here propound is true...nevertheless, it is as a Poem only that I wish this work to be judged...".  He later wrote in a desperate letter to his dear Aunt Maria that he no longer had any will to live, because since completing Eureka he felt he could accomplish nothing more.  If this was all part of a hoax, and he regarded Eureka as nothing more than a joke and a demonstration of how gullible people are, then it was a remarkably elaborate and well-played joke.  We'll review Eureka as it stands.  Regardless of how seriously Poe intended it, it contains some very interesting passages and suggestions of ideas that came into mainstream science only decades after Poe's death.


Poe sums up the basic premise of his world view with the words


In the original unity of the first things lies the secondary cause of all things, with the germ of their inevitable annihilation.


This brings to mind the youthful poems of Dylan Thomas (1914-1953), with whom Poe had much in common, including their peculiar poetic symbolism, their lyricism, and their public readings, not to mention their early deaths due to alcoholism:


The force that through the green fuse drives the flower,

drives my green age, that blasts the roots of trees, is my destroyer.


Poe begins Eureka (whose title is obviously from Archimedes' exclamation in his bath tub when he discovered the law of buoyancy) by directing the reader's attention to


...a remarkable letter, which appears to have been found corked in a bottle and floating on the Mare Tenebrarum...  The date of this letter, I confess, surprises me even more particularly than its contents; for it seems to have been written in the year two thousand eight hundred and forty-eight.


In other word, the manuscript in the bottle is dated 2848 AD, exactly 1000 years in Poe's future.  (Poe is generally credited as the originator of modern science fiction, in addition to being the originator of the modern detective story in such works as "Murders in the Rue Morgue".)  In the manuscript, an observer of the distant future comments satirically on the foolish philosophical notions of the past, especially the idea that there are only two roads to truth, namely, the a priori deductive method of Aries Tottle and the a posteriori inductive method of Hog, i.e., the Baconian method.  (We're asked to make allowances for the possibility that the historical names may have been corrupted over the centuries).  Since Aries is the Ram, this dichotomy is presented as a dialectic between the Hog and the Ram.  The point made by the futuristic observer is that both of these methods approach truth by means of a definite path from here to there, either from the general to the specific or from the specific to the general, whereas he contends that all real knowledge is acquired by intuitive leaps which are neither inductive nor deductive.


This is intriguing, because it anticipates the intuitionist approach to mathematics and logic espoused by L. E. J. Brouwer, Poincare, and others of a later generation.  Indeed Poe's futuristic observer goes on to explicitly discuss axiomatics and the basic principles of reasoning, even challenging what Aries Tottle called the Law of the Excluded Middle, i.e., the proposition that exactly one of [A] and [not A] must be true.  This was precisely the point of Brouwer's attack on formalism and logicism at the beginning of the next century.  But Poe (or his futuristic spokesman) goes even further and declares that two contradictory statements can both be true, or at least that we have no basis for an axiom asserting that they cannot.  He approvingly quotes John Stuart Mill (1806-1873) as saying that our ability or inability to conceive of something is in no case to be taken as a criterion of truth.  Alas this profound assertion turns out to be the only insight of Mill's that Poe (or his spokesman) can endorse.  The letter pokes fun at Mill by implying that he was just parroting the ideas of Jeremy Bentham (1748-1832, almost exactly contemporaneous with Goethe), who was Mill's teacher.  Bentham was a proponent of Utilitarianism, and as such was a natural object of Poe's derision.  (He is mentioned more than once in Poe's writings.)  Interestingly, although highly regarded in his own time, the modern verdict on Mill is that "his mind was essentially illogical, and his philosophy was notable mainly for its intricate sophistry".  (See R. P. Anschutz's "Philosophy of J. S. Mill", 1953.)


Regarding Poe's suggestion that contradictory things might both be true, one wonders if Walt Whitman (1819-1892) might have been influenced by those comments when he later wrote that he was content – even proud - to be large enough to entail contradictions. Whitman too was part of the on-going reaction against Newtonian science (see his "When I Heard the Learn'd Astronomer"), as was his almost exact contemporary, Herman Melville (1819-1891), whose imagery for poems like "The Portent", not to mention the prose poem "Moby Dick", owes much to Poe's influence.


The letter from the future concludes with an appreciation of Johannes Kepler, who is said to have essentially just guessed his three laws of planetary motion in leaps of pure imagination.  He is compared with Champollion (1790-1832), the decipherer of ancient Egyptian hieroglyphics, and we are challenged to decide whether such feats are accomplished by inductive or deductive reasoning.  The final words of the letter quote Kepler's famous exclamation when he discovered his third law


I care not whether my work be read now or by posterity.  I can afford to wait a century for readers when God himself has waited six thousand years for an observer.  I triumph.  I have stolen the golden secret of the Egyptians.  I will indulge my sacred fury.


The sense of poetic unity that Poe regarded so highly in literature is evident here in the "Egyptian connection" between Champollion and Kepler's quote.  Poe's literary esthetic is also apparent in the stress he placed on the individuality of the universe, just as he argued that a short story must be grasped as an individual entity.  (It's interesting how accurately the futuristic letter-writer knew the names of Champollion and Kepler, in contrast with his confusion as to the names of Aristotle and Bacon.)


Poe then takes up the subject of infinity, arguing that the word does not actually express an idea, but only an effort at one.  The word "infinity", he says, represents but the thought of a thought.  Ironically he echoes Aristotle here, who likewise maintained that the completed infinity was inconceivable, and that the word "infinity" is to be understood simply as signifying the tendency to endlessness, a process without end.  We also note that Poe denies the axiom of infinity on grounds that he earlier agreed (with Mill) were invalid, namely, the grounds of inconceivability.  He argues that we cannot actually conceive of infinity, and therefore it must not be admitted.  Furthermore, in considering whether the Universe itself may be finite or infinite, and whether conceiving of one of these alternatives is more impossible than conceiving of the other, he says it makes no sense to talk about more or less impossible tasks, because "a task is either possible or not possible, there are no gradations".  Readers would be more likely to accept this uncritically if Poe had not, just a few pages earlier, argued so vehemently that mutually contradictory propositions cannot be ruled out a priori.  Perhaps his most persuasive remark on the problem of infinity is that the Deity has not designed it to be solved.


Poe draws a distinction between what he calls the universe of stars and the universe of space, and he borrows Pascal's description in saying that the universe proper (by which Poe means the universe of space) is a sphere whose center is everywhere and whose circumference is nowhere.  The universe of stars, Poe contends, is necessarily finite, and all matter must once have been compressed into a single individual point.  Then at some epoch God caused this point to radiate a huge (but finite) number of discrete atoms in spherical waves emanating outward from the central point.  He also believes that the matter must be distributed homogeneously, and he spends considerable time trying to reconcile how all matter can emanate from a central point and yet be distributed uniformly.  He seems very pleased to see a way - which he believes to be the unique way - for this to happen.  He reasons that the outermost shell of particles must have been emitted with the greatest "force" (which is why they are outermost), and he guesses that the force must have been proportional to the square of the shell's radius.  He also asserts that the number of particles in each shell is directly proportional to the force with which the shell was emanated.  As a result, the number of particles at any given radius from the center is proportional to the square of the radius.  Since the surface area of a sphere goes as the square of the radius, he argues that this gives uniform density of particles throughout space.  Poe further explains that the irradiation of all matter from the original oneness must inevitably be reversed, and all the atoms of the universe will coalesce back into oneness.  The similarity is obvious between Poe's vision and 20th century ideas about a cosmological "Big Bang" from a single quantum fluctuation, producing a finite but unbounded homogeneous universe. 


In formulating his geometrical theory of the Universe, Poe was evidently was groping for a model such as is provided by the expanding surface of a sphere, but doesn't seem to have availed himself of this model.  As a result he is forced later to address a possible objection to his theory, namely, that the outermost shell has nothing in front of it, and represents an asymmetry.  He could have avoided this by using a closed-surface model, but instead he argues ingeniously (if not entirely persuasively) that the natural principles of action are not applicable to the boundary, because that is by definition the demarcation of the limits of the Universe in which the principles apply.  We might charitably allow that Poe intuited the existence of a model of perfectly homogeneous and symmetrical expansion, without boundary, even though he wasn't able to explicitly conceive of it.


Poe's explanation for the Newtonian inverse square law of gravitation was essentially just to regard the natural tendency for atoms to return to the center as a reaction to the force that propelled them to their present radial distance from the center, which (recall) he has decided must be proportional to the square of the radial distance.  He then argues, with imperfect clarity, that by running the process in reverse, the reaction force tending to impel atoms back toward the center is the inverse of the original outward force, and hence is inversely proportional to the square of the distance.  With some effort we might charitably be able to construe this as an attempt to apply Gauss' law, showing that conservation of "charge" requires the force of gravity to fall off in inverse proportion to the surface area.  However, Poe's verbal argument seems to hang on using the word "inverse" in two distinct senses, one meaning a reversal of direction, and the other meaning the reciprocal of a value.  In addition, he argues unpersuasively that a general tendency toward the original center of mass (so to speak) is sufficient to imply universal mutual gravitation between every pair of atoms.  (He is on much firmer ground when he later argues the converse, i.e., that mutual attraction between every pair of particles in a spherical cloud has the effect of drawing each atom toward the center.)  It's also interesting to notice again that Poe's notion of each particle's tendency to "return to where it belongs" is distinctly Aristotlean.


In a more interesting direction, Poe re-interprets Newton's law of gravitation by placing it on a discrete basis, saying that the force of each atom toward every other atom is inversely proportional to the distance between them.  Thus he eliminates the continuous mass variable, and makes gravity a discrete force between identical unit atoms.  The notion of atomism dates back to Leucippus and Democritus (c. 450 BC), and was discussed (and rejected) by Aristotle (384-322 BC).  It was taken up again by Epicurus (341-270 BC), whose ideas have come down to us in the form of the long poem "De Rerum Natura" (On the Nature of Things) by the Latin Poet Lucretius (c. 50 BC).  Subsequently the authority of Aristotle was sufficient to keep atomism out of the mainstream of philosophical thought for over sixteen centuries.  Atomism was only revived in modern times by Pierre Gassendi (1592-1655) and later by John Dalton (1766-1844).  Poe makes no mention of Dalton, but he does allude at one point to "the true Epicurean atoms", so it seems that his inspiration may have been the earlier sources.  Nevertheless, the atomistic view was not widely accepted in the scientific community until the 20th century (and was vigorously rejected by the likes of Ernst Mach (1838-1916)), so Poe was certainly ahead of his time by basing his world view so unequivocally on atomism.  Also, the atomistic structure enabled Poe to make the modern-sounding claim that the Universe is established on a purely geometrical basis, involving only discrete distances and their relations.  (Oddly enough, Poe never mentions Pythagoras.)  He even asserts that matter is nothing other than conceptual placeholders for the relations, suggesting that the relations themselves are the primary ontological entities. 


Incidentally, when Poe refers to "atoms", it seems he is referring to what we would call sub-atomic elementary particles, such as electrons and protons.  He does, however, decline to claim that even these are indivisible.  He invokes the principle of simplicity to suggest that the particles must be of one kind, of one nature, yet each an individual entity, and undivided, although not indivisible


...only because He who created it [i.e., divided the original oneness], by dint of his Will, can by an infinitely less energetic exercise of the same Will, as a matter of course, divide it.


Poe's insistence on the individuality of the elementary particles seems not entirely consistent with the interchangeability of particles in quantum mechanics, but there is certainly a sense in which our modern elementary particles are both identical and individual, so we can credit Poe with focusing attention on this subtle issue.


Even more interesting is Poe's intuition that the variety of structure and forms which we observe in the configurations of matter requires some force of repulsion, "a separate something... to prevent proximate atoms from lapsing at once... into absolute oneness among themselves".  Indeed the question of what keeps the electron and proton of a hydrogen atom separate, when their mutual attraction (and the radiation of orbital energy) ought to cause them to immediately collapse into each other, was a puzzle that occupied physicists such as Neils Bohr (1885-1962) in the early 20th century.  Even if we "solve" this problem by postulating a minimal quantum "orbit", we still must ask what prevents all the electrons in an atom from occupying the same orbital state, i.e., how can we account for the variety of atomic structure, and for the chemical interactions between atoms?  The modern answers to these questions involve the quantization of energy states of an atom, along with Wolfgang Pauli's (1900-1958) exclusion principle, according to which two fermions cannot occupy the same quantum state.  This principle alone accounts for the intricate valence shell structure of atoms, necessary for all the variety of substances and chemical interactions that we observe in nature.  These are deep waters, and perhaps we can understand Poe when he says


The design of the repulsion - the necessity for its existence - I have endeavored to show, but from all attempt at investigating its nature have religiously abstained; this on account of an intuitive conviction that the principle at issue is strictly spiritual - lies in a recess impervious to our present understanding - lies involved in what now - in our human state - is not to be considered - in a consideration of Spirit in itself.  I feel, in a word, that here the God has interposed, and here only, because here and here only the knot demanded the interposition of the God.


In general Poe seeks to identify all attraction (the tendency to return to unity) as gravity, and all repulsion as what he called electricity, in which he included the phenomena of magnetism and also heat.  But he was surely aware that magnetism is bi-polar, i.e., both attractive and repulsive, and the same is true for electrostatic forces.  Conversely, the tendency of bosons to occupy the same quantum state - making lasers possible - could be regarded as an attractive force.  It seems that, in order to make any sense of Poe's discussion, we must make some allowances for his qualitative classification of forces and effects, at least when trying to place them in correspondence with the elements of modern theories.  For example, he says


The amount of electricity.. of two bodies [i.e., the electrical force between them] is proportional to the difference between the respective sums of atoms of which the bodies are composed.


which makes sense, and can actually be construed as (more or less) true in common situations, provided we allow the word "atoms" to signify electrons, because most manifestations of electrostatic force that we observe are due to an imbalance of electrons.  Of course, to make the sums come out correctly in general we need to account for the relative number of positive charges, as well as the effects of the interacting valence shells.  As Poe says, "Man neither knows, nor employs, a force sufficient to bring two atoms into contact" - at least until the first man-made fusion reactions in the 1950's.  Poe also claimed that ultimately the force of gravity must overwhelm the repulsive forces between atoms, which brings to mind the process of gravitational collapse involved in the modern stellar model of the progression from white dwarfs to neutron stars to "black holes", finally overcoming the exclusion principle.


One of the most intriguing intuitions in Poe's "Eureka" is his identification of electricity and magnetism with light.  He says


To electricity... we may not be wrong in referring the various physical appearances of light, heat, and magnetism.


This is impressive because it wasn't until a generation later that James Clerk Maxwell (1831-1879) unified optics with electromagnetism by suggesting that light is an electromagnetic wave, and it wasn't until 1905 that Albert Einstein (1879-1955) showed how magnetism is really just electricity viewed from a different frame of reference.  (Incidentally, numerologists have made much of the fact that Newton was born the same year Galileo died, making allowances for calendar differences, but it seems to be less commonly remarked that Einstein was born the same year Maxwell died.)


Another interesting parallel between Poe's ideas and modern theories is the dichotomy between gravity (attraction, body, material) on the one hand, and the multitudinous phenomena of electricity, magnetism, heat, light, etc. (repulsion, soul, spiritual), on the other.  This corresponds to the dichotomy in modern physics between gravitation as a phenomena of spacetime itself - i.e., the left hand side of Einstein's field equations - and all the remaining forces and entities of nature, which we collectively group on the "right hand side" of Einstein's field equations.


Next Poe defends his thesis that the material of the universe of atoms is actually a finite spherical cloud of particles rather than an infinite uniform expanse of particles.  His argument is that if the cloud of particles extended infinitely in all directions, there would be infinitely many material particles in all directions surrounding any given particle, so it's resulting direction of forced motion would be indeterminate.  He says there can be no difference in magnitude between two infinite numbers, so the forces of attraction on each particle would be balanced, and nothing would ever move.  This is interesting because it's essentially the same argument that Newton made (in a letter to Bentley) in favor of an infinite static universe.  However, according to Newtonian theory the gravitational potential goes as 1/r, so the potential at any point in a uniformly distributed infinite cloud of particles would be infinite.  This is now recognized as a fatal flaw in simplistic Newtonian cosmologies, and it seems fair to say that, on this point, the non-mathematical romantic (Poe) saw more clearly than Newton himself.  (On the other hand, from a strictly mathematical standpoint, Poe's remark about all infinities being equal might be challenged by Georg Cantor (1845-1918) in light of his notion of cardinalities.)


In the next section Poe gives a flowing description of the nebular hypothesis for the formation of the solar system.  This was originally put forward by Immanuel Kant (1724-1804), combining Newtonian mechanics with Descartes idea of a vortex, and it was further elaborated by Pierre Laplace (1749-1827).  Ironically, Poe's futuristic letter writer heaps derision on Kant earlier in "Eureka" (changing the K in Kant to a C), and yet this is the cosmology that Poe finds most plausible.  Perhaps he attributed it entirely to Laplace, who he seems to have regarded as an imaginative speculator akin to Kepler.  In any case, Poe does not seem to be aware of the relatively slow rotation rate of the Sun, and the difficulty this poses for the nebular hypothesis.


Throughout "Eureka" Poe notes (correctly) several astronomical facts, such as that the Moon's orbital and rotational motion are gravitationally linked (explaining why only one face is ever visible from Earth), that the rotating planets are actually spheroids, bulging at their equators due to their rotation, and that the center of the Sun is not exactly the inertial center of the solar system.  He also says (incorrectly) that the Moon must be slightly self-luminous, because it is faintly visible even when the near face is in shadow.  In addition he offers some remarkably Velikovskian speculations about how the formation of the planet Venus might have affected life on Earth in the distant past, referring specifically to the ultra-tropical vegetation found on the Melville islands.  From this outlandish topic he immediately switches to a subject that is actually of scientific interest today.  He says, matter-of-factly,


...we know that there exist non-luminous suns - that is to say, suns whose existence we determine through the movements of others, but whose luminosity is not sufficient to impress us.


He doesn't elaborate on what tell-tale "movements" he is referring to, but presumably it was the movements of the visible components of binary star systems.  (The relative motions of visible components were first observed by Hershel in 1803.)  The only other motion he could conceivably have meant is the rotation of the galaxies, which even today presents a puzzle to astronomers and physicists, because the amount of visible matter seems insufficient to hold them together given their observed rotation rates.  This is regarded as evidence for a large amount of "dark matter" in galaxies, which goes part of the way toward putting the mass density of the universe near the critical point. 


However, Poe explicitly rejects the suggestion of J. Fourrier (1768-1830) and J. H. Madler that the galaxy is rotating about a supermassive center, because he conceives of our galaxy (and all others) as being roughly spherical, and he prefers the idea of inward convergence rather than rotation.  He also challenges the possibility that any evidence of such rotation, with a period of more than 100 million years, could have been detected over the brief time of historical observations.  It's remarkable that Poe, writing in 1848, was knowledgeable of Madler's work in this area, since it was only in 1848 that Madler though he had found a general motion about a center of gravity in the Pleiades, which Poe specifically mentions.  He must have been writing about these astronomical discoveries as they appeared in current periodicals.  In any case, Poe's skepticism about Madler's alleged discovery turned out to be justified, because subsequent observations showed that Madler had been misled by the effects of parallax due to the Sun's own motions.  On the other hand, it is now accepted that many galaxies, including the Milky Way, are disk/spiral-shaped, and do indeed rotate about their centers, with periods of hundreds of millions of years.  Also, the "reveries" of Fourrier about a supermassive body at the center of the galaxy, which Poe thought hardly even "worth a sneer", have lately been given credence, and it is considered quite possible that a huge gravitationally collapsed conglomeration of stars (possibly a black hole) lies at the center of many galaxies.


One striking aspect of Poe's review of astronomy is his apparent conviction that the objects which had formerly been discerned only as hazy "nebulae" are, in fact, other galaxies, similar to the Milky Way galaxy in which our Sun resides.


The clusters...are merely what we have been in the practice of designating "nebulae" - and of these "nebulae", one is of paramount interest to mankind.  I allude to the Galaxy, or Milky Way... The Galaxy, let me repeat, is but one of the clusters which I have been describing - but one of the mis-called "nebulae" revealed to us... as faint hazy spots in various quarters of the sky.  We have no reason to suppose the Milky Way really more extensive than the least of these "nebulae".


These comments are remarkable, considering they were written in 1848, because one typically finds in modern astronomy books the claim that "At the opening of this [20th] century we did not know that there are galaxies beyond our own."  The Shapley-Curtis Debate of 1920 was a famous dispute among astronomers as to the nature of the hazy nebulae.  We're told that it wasn't until 1924 that Edwin Hubble announced his findings on Cephid variables in Andromeda, proving that the nebulae were, indeed, other "island universes" akin to the Milky Way.  We're also told by modern texts that the rotation of our Galaxy was never even imagined until about 1940, and yet Poe quotes Madler's estimate of 117 million years for the period of rotation (compared with the modern figure of 200 million years).  Since Poe wrote "Eureka" in 1848, this all seems to suggest that modern astronomers have a somewhat imperfect recollection of how and when certain important conceptions were formed.


Another apparent anomaly concerns the speed of light.  According to the history books, the best estimate in 1729 was based on Bradley's aberration sightings, giving a value of 188,500 miles per second.  In 1849, the year of Poe's death (and the year after he wrote "Eureka"), Fizeau used a toothed wheel to measure the speed of light as 194,000 miles per second, and this value was not improved until Foucault's rotating mirror measurements in 1869, which yielded a value of about 184,760 miles per second.  Oddly enough, in 1848, Poe (who was obviously well informed) stated that the speed of light is 167,000 miles per second.  There is no indication of where he got this value, which is more than 10% low.  Is this just a misprint?  Or did a widely available source in Poe's time give this value?


One particularly interesting passage in "Eureka" concerns Poe's thoughts on "the important phenomena of vitality [life], consciousness, and thought".


Looking at the matter, first, in detail, we perceive that not merely the manifestation of vitality, but the importance, consequences, and elevation of character, keep pace, very closely, with the heterogeneity, or complexity, of the animal structure... Now this is in precise accordance with what we know of the succession of animals on the Earth.  As it has proceeded in its condensation, superior and still superior races have appeared.  Is it impossible that the successive geological revolutions... have themselves been produced by... successive variations in the solar influence on the Earth?  Were this idea tenable, we should not be unwarranted in the fancy [of]... yet a new modification of the terrestrial surface, a modification from which may spring a race both materially and spiritually superior to Man.


Needless to say, this was not the first suggestion of the evolutionary development of life on Earth, ascending in complexity to more and more superior species.  Jean Lamarck (1744-1829) published his theory of gradual evolution of life forms throughout geologic history in 1801.  (Lamarck's belief that acquired traits were passed on to offspring was later discredited by studies of genetics.)  Still, it wasn't until 1858, nearly ten years after Poe's death, that Charles Darwin (1809-1882) published his theory of evolution and natural selection - simultaneously with Alfred Wallace (1823-1913).  The fact that Poe and Darwin were the same age (and were both schooled in England) is suggestive of the possibility of common influences in the educational basis and intellectual climate of that time.


Yet another fascinating passage in "Eureka" contains Poe's consideration of what we today call Olber's Paradox.  This was first mentioned by the Swiss astronomer J. de Cheseaux in 1744, but received little notice until it was independently rediscovered and publicized by Heinrich Olbers (1758-1840) in 1826.  The paradox is based on the premise that the universe contains an infinite, static, and uniform distribution of infinitely old stars with constant brightness.  On this basis we should expect every point of the night (and daytime) sky to shine with infinite brightness (just as the gravitational potential should be infinite), or, if we assumed each star was opaque and not in thermal equilibrium, then at least as brightly as the surface of the Sun, because every line of sight would terminate on a star.  Poe describes this paradox (without mentioning either de Cheseaux or Olbers), and uses it to bolster his claim that the Universe of stars must therefore be finite.  He does, however, offers two ingenious considerations by which it might be possible to reconcile an infinite universe of stars with the dark night sky.  First, he points out the possibility that some stars may be so far distant that no light from them could have yet reached us.  He doesn't say what he means by "yet", i.e., he doesn't say when the star is assumed to have begun shining, but presumably his reasoning applies only if the age of the universe (of stars) is finite.  Poe discounts this possibility, saying that we have absolutely no reason to think it is the case, and it requires us to assume a universe of infinite extent but finite age.  Nevertheless, this is essentially the modern resolution of Olber's paradox based on the Big Bang cosmology, which implies that the universe has a finite age.


The second explanation, if it can properly be called that, is even more intriguing.  Poe suggests that, just as the local stars form a cluster, and just as the local galaxies form a cluster of clusters, we could argue that there may be an infinite hierarchy of clusters of clusters.


Have we, or have we not, an analogical right to the inference that this perceptible Universe - that this cluster of clusters - is but one of a series of clusters, the rest of which are invisible through distance - through the diffusion of their light being so excessive, ere it reaches us, as not to produce upon our retinas a light-impression...?


We can illustrate a hierarchy of clusters by means of the simple schematic shown below



Obviously we could take three copies of the above figure and form a still larger triangle, and so on.  Suppose each dot represents a particle of mass, and suppose the distances between the particles in the smallest triangles are all r.  Also, suppose the distances between the centers of these triples at the next level is 4r, and the distances between the centers of those triples is 16r, and so on.  Now, the gravitational potential exerted on one of these particles by its two immediate neighbors is proportional to 2/r.  At the next level, there are 3(2) = 6 particles, and they are each roughly 4r away, so their contribution to the potential of the original particle is 6/(4r).  At the next level there are 9(2) = 18 particles, each of which is roughly 16r away, so the contribution to the potential is 18/(16r).  If we imagine an infinitely extended hierarchy of clusters following this same pattern, the total gravitational potential at a point is given by the infinite geometric summation



Thus the gravitational potential converges to a finite value, and, by the same token, the mean level of illumination of the night sky would be finite, with a value dependent on the number k of components per cluster and the ratio f of distances between clusters from one level to the next.  The sum converges provided the ratio k/f is less than 1, and with a sufficiently small ratio the higher-order terms can be made as small as we like, despite the fact that we are assuming an infinite number of infinitely old particles.  The reason Olber's Paradox does not apply to this case is that we are not assuming the particles are uniformly distributed.  This hierarchy of clusters is similar to what today are commonly called fractal structures, such as Sierpinski's gasket.


Next we find Poe's presentation of Kepler's laws, even including a formal definition of an ellipse:


An ellipse is a curve, returning into itself, one of whose diameters is longer than the other.  In the longer diameter are two points, equidistant from the middle of the line, and so situated otherwise that if, from each of them a straight line be drawn to any one point of the curve, the two lines, taken together, will be equal to the longer diameter itself.


It would be interesting to know if this was Poe's own wording, from memory, or if he borrowed it from an elementary geometry text.  He goes on to praise Kepler (again) for guessing his three laws of planetary motion, which he says were "subsequently demonstrated and accounted for by the patient and mathematical Newton".  Poe seems to be defensive here, commenting that is far too fashionable to sneer at all speculation under the comprehensive sobriquet, "guess-work".  The point to be considered is, who guesses.  In guessing with Plato, we spend our time to better purpose, now and then, than in hearkening to a demonstration by Alemaeon.


Should we surmise that Poe's speculations have been sneered at?  Did he ever submit any of his guess-work to a scientific journal?  If so, it isn't hard to imagine what the response would have been.


"Eureka" continues with Poe's recitation of the distances to the known planets, which he tries to convey by means of counter-factuals comparisons, e.g., if the distance from the Sun to the Earth were one foot, then the distance to Neptune ("Leverrier's planet", discovered only in 1846, just two years prior to Poe's writing "Eureka") would be 40 feet.  He then goes on to say "and the star Alpha Lyrae would be 159", but here Poe is being theatrical for effect, because he then explains that although the ratio of 159 to 40 may seem great, he omitted to say that Alpha Layrae would be 159 miles in this account.  He then discusses the use of parallax from different points on the Earth's orbit to determine the distance to stars, noting Besel's recent parallax observations of 61 Cygni.  Lastly he recounts the observations of Lord Rosse (formerly William Parsons) who in 1845 built a telescope with a mirror 6 feet in diameter, with which he discovered the spiral structure of some nebulae, and estimated the distances to nebulae as far away as 100 million light-years.  Thus, the images we see today are in fact the images of things that occurred 100 million years ago.  It is this discussion of the convertibility between distance and time, with the speed of light as the conversion factor, that prompts Poe to assert that "Space and Duration are one".


From this identification of space and time, Poe goes on to discuss the identity, or rather the reciprocity, between cause and effect in all natural phenomena.  Here he distinguishes between human constructions and the Divine.  As he says human constructions a particular cause has a particular effect; a particular intention brings to pass a particular object; but this is all; we see no reciprocity.  The effect does not react upon the cause; the intention does not change relations with the object.  In Divine constructions the object is either design or object as we choose to regard it - and we may take at any time a cause for an effect, or the converse - so that we can never absolutely decide which is which.


This can be seen narrowly as an expression of the time-reversibility of natural laws, which in itself is interesting, but Poe is getting at something deeper here, seeing beyond the absolute predictability of Laplace's determinism to a conception of the entire universe including its entire history, all grasped at once as a single individual entity, rather than as an artificial sequence of disjoint causes and effects.  He reverts to the literary esthetic to describe this as follows:


The pleasure which we derive from any display of human ingenuity is in the ratio of the approach to this species of reciprocity [between cause and effect].  In the construction of plot, for example, in fictitious literature, we should so arrange the incidents that we shall not be able to determine, of any one of them, whether it depends on any other one or upholds it.  In this sense, of course, perfection of plot is really, or practically, unattainable - but only because it is a finite intelligence that constructs.  The plots of God are perfect.  The universe is a plot of God.


In the remaining pages of "Eureka", Poe struggles with what he seems to have regarded as a crucial question, namely, whether the galaxies are rotating and thereby stable configurations, or not rotating and therefore "in a state of progressive collapse".  He rightly perceives a reluctance on the part of the leading astronomers of his day (John Herschel, Madler, Dr. Nichol) to conclude that the structures of the universe are collapsing in on themselves, returning to unity as Poe would say, "on account of a prejudice; - merely because the supposition is at war with a pre-conceived and utterly baseless notion - that of the endlessness - that of the eternal stability of the Universe."  Indeed, as late as 1917, Einstein succumbed to this same prejudice when he introduced the cosmological constant to his field equations in an effort to force them to yield an eternal static solution.  Only when Hubble observed the dynamic expansion of the Universe did Einstein finally discard that prejudice and recognize the necessity of Poe's premise of a dynamic Universe with a finite past - and quite possibly a finite future ending in complete collapse.


Poe goes on to stress the importance of symmetry principles for guiding our investigations, along with the principle of perfect consistency, in words that could easily have been written by the mature Einstein a century later.  He then discusses the case of Enck's comet, whose orbital variations led many people to believe (for a time) that some tenuous ether permeating space must be influencing it's progress.  However, Lagrange "came to the rescue", showing that a more accurate analysis of the orbit, taking into account all the known perturbing effects, completely explained the motions of the comet.  Poe says "The facts thus demonstrated do away, of course, with all necessity for supposing an ether..."  However, Poe has in mind a different sort of ether, "radically different from the ether of the astronomers, inasmuch as theirs is matter and mind is not".  Poe's ether is


a subtle influence which we know to be ever in attendance upon matter, although becoming manifest only through matter's heterogeneity.  To this influence- without daring to touch it at all in any effort to explain its awful nature - I have referred the various phenomena of electricity, heat, light, magnetism; and more - of vitality, consciousness, and thought - in a word, of spirituality.


There seems to be an echo here of Blake's "fearful symmetry", and a forerunner of the more recent speculative ideas of Roger Penrose on the possible connections between quantum phenomena and consciousness.  Poe continues with a suggestion that, following the universal collapse into unity, there might be succeeding generations of Universes: "a new and perhaps totally different set of conditions may ensue - another creation and irradiation returning into itself", similar to the "mix-master cosmologies" discussed by modern authors.


At the end of "Eureka" Poe returned to his natural poetic mode, and presented this lyrical conclusion which, had he lived, would have made stirring material for one of his public readings:


The phenomena on which our conclusions must at this point depend, are merely spiritual shadows, but not the less thoroughly substantial.  We walk about, amid the destinies of our world existence, encompassed by dim but ever present memories of a destiny more vast - very distant in bygone time, and infinitely awful... conscious, first, of a proper identity, secondly and by faint indeterminate glimpses, of an identity with the Divine Being... Think that the sense of individual identity will be gradually merged in a general consciousness - that Man, ceasing imperceptibly to feel himself Man, will at length attain that awfully triumphant epoch when he shall recognize his existence as that of Jehovah.  In the mean time bear in mind that all is Life - Life within Life - the less within the greater, and all within the Spirit Divine.


The obviously sacrilegious and pantheistic nature of these words were deeply troubling to Poe's friends.  The earlier lecture ("The Universe") on which Eureka was based had apparently concluded in a way that seemed harmonious with Christianity, but Poe added this new ending to Eureka, and lost close friends because of it, most notably Louisa Shew, who broke off their relationship.  She told Poe that he would only be saved by the love of a woman "fond and strong enough to manage his affair in his best interest", and Poe agreed.  He wrote that "unless some true and tender and pure womanly love saves me, I shall hardly last a year longer...".  He died the next year.


It's notable that throughout "Eureka" Poe seems to adopt a strictly relational view of motion.  For example, although he contends that all the particles are attracted back to a central point of origin, he is careful to explain that the attraction is not really to the abstract point of space, but between the particles.  It just so happens that each particle, wherever it resides, sees more of its fellow particles in the direction of the center, so all move in that direction.  As Poe says


Nothing like location was conceived as their origin.  Their source lies in the principle, Unity.  This is their lost parent.  This they seek always - immediately - in all directions - wherever it is even partially to be found; thus appeasing, in some measure, the ineradicable tendency, while on the way to its absolute satisfaction in the end.


Knowing Poe's life history, orphaned at the age of 2, separated from his brother and sister, the metaphor is especially touching, and this passage more than any other in "Eureka" reveals the true nature of the work.  It would be going too far to say the entire book is a conscious allegory, because it seems clear that (at least on some level) Poe took the scientific implications seriously, but it's also clear that his scientific ideas were deeply grounded in his own spiritual and emotional needs and outlook.  Hence the book's preface is addressed, somewhat surprisingly, considering Poe's pride in his own powers of rationality


To those who love me and whom I love - to those who feel rather than to those who think - to the dreamers and those who put faith in dreams as in the only realities - I offer this Book of Truths, not in its character of Truth-Teller, but for the Beauty that abounds in its Truth; constituting it true.  To these I present the composition as an Art Product alone - let us say as a Romance, or, if I be not urging too lofty a claim, as a Poem.


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