Эдгар Аллан По
Eureka: A Prose Poem
I reply, not only that I am warranted in such assumption, but that I should be utterly unwarranted in any other. What I assume is, simply, that an effect is the measure of its cause – that every exercise of the Divine Will will be proportional to that which demands the exertion – that the means of Omnipotence, or of Omniscience, will be exactly adapted to its purposes. Neither can a deficiency nor an excess of cause bring to pass any effect. Had the force which irradiated any stratum to its position, been either more or less than was needed for the purpose – that is to say, not directly proportional to the purpose – then to its position that stratum could not have been irradiated. Had the force which, with a view to general equability of distribution, emitted the proper number of atoms for each stratum, been not directly proportional to the number, then the number would not have been the number demanded for the equable distribution.
The second supposable objection is somewhat better entitled to an answer.
It is an admitted principle in Dynamics that every body, on receiving an impulse, or disposition to move, will move onward in a straight line, in the direction imparted by the impelling force, until deflected, or stopped, by some other force. How then, it may be asked, is my first or external stratum of atoms to be understood as discontinuing their movement at the circumference of the imaginary glass sphere, when no second force, of more than an imaginary character, appears, to account for the discontinuance?
I reply that the objection, in this case, actually does arise out of “an unwarranted assumption” – on the part of the objector – the assumption of a principle, in Dynamics, at an epoch when no “principles,” in anything, exist: – I use the word “principle,” of course, in the objector’s understanding of the word.
“In the beginning” we can admit – indeed we can comprehend – but one First Cause– the truly ultimate Principle– the Volition of God. The primary act– that of Irradiation from Unity – must have been independent of all that which the world now calls “principle” – because all that we so designate is but a consequence of the rëaction of that primary act: – I say “primary” act; for the creation of the absolute material particle is more properly to be regarded as a conception than as an “act” in the ordinary meaning of the term. Thus, we must regard the primary act as an act for the establishment of what we now call “principles.” But this primary act itself is to be considered as continuous Volition. The Thought of God is to be understood as originating the Diffusion – as proceeding with it – as regulating it – and, finally, as being withdrawn from it upon its completion. Then commences Rëaction, and through Rëaction, “Principle,” as we employ the word. It will be advisable, however, to limit the application of this word to the two immediate results of the discontinuance of the Divine Volition – that is, to the two agents, Attraction and Repulsion. Every other Natural agent depends, either more or less immediately, upon these two, and therefore would be more conveniently designated as sub-principle.
It may be objected, thirdly, that, in general, the peculiar mode of distribution which I have suggested for the atoms, is “an hypothesis and nothing more.”
Now, I am aware that the word hypothesis is a ponderous sledge-hammer, grasped immediately, if not lifted, by all very diminutive thinkers, upon the first appearance of any proposition wearing, in any particular, the garb of a theory. But “hypothesis” cannot be wielded here to any good purpose, even by those who succeed in lifting it – little men or great.
I maintain, first, that only in the mode described is it conceivable that Matter could have been diffused so as to fulfil at once the conditions of irradiation and of generally equable distribution. I maintain, secondly, that these conditions themselves have been imposed upon me, as necessities, in a train of ratiocination as rigorously logical as that which establishes any demonstration in Euclid; and I maintain, thirdly, that even if the charge of “hypothesis” were as fully sustained as it is, in fact, unsustained and untenable, still the validity and indisputability of my result would not, even in the slightest particular, be disturbed.
To explain: – The Newtonian Gravity – a law of Nature – a law whose existence as such no one out of Bedlam questions – a law whose admission as such enables us to account for nine-tenths of the Universal phænomena – a law which, merely because it does so enable us to account for these phænomena, we are perfectly willing, without reference to any other considerations, to admit, and cannot help admitting, as a law – a law, nevertheless, of which neither the principle nor the modus operandi of the principle, has ever yet been traced by the human analysis – a law, in short, which, neither in its detail nor in its generality, has been found susceptible of explanation at all– is at length seen to be at every point thoroughly explicable, provided only we yield our assent to – what? To an hypothesis? Why if an hypothesis – if the merest hypothesis – if an hypothesis for whose assumption – as in the case of that pure hypothesis the Newtonian law itself – no shadow of à priori reason could be assigned – if an hypothesis, even so absolute as all this implies, would enable us to perceive a principle for the Newtonian law – would enable us to understand as satisfied, conditions so miraculously – so ineffably complex and seemingly irreconcileable as those involved in the relations of which Gravity tells us, – what rational being could so expose his fatuity as to call even this absolute hypothesis an hypothesis any longer – unless, indeed, he were to persist in so calling it, with the understanding that he did so, simply for the sake of consistency in words?
But what is the true state of our present case? What is the fact? Not only that it is not an hypothesis which we are required to adopt, in order to admit the principle at issue explained, but that it is a logical conclusion which we are requested not to adopt if we can avoid it – which we are simply invited to deny if we can: – a conclusion of so accurate a logicality that to dispute it would be the effort – to doubt its validity beyond our power: – a conclusion from which we see no mode of escape, turn as we will; a result which confronts us either at the end of an inductive journey from the phænomena of the very Law discussed, or at the close of a deductive career from the most rigorously simple of all conceivable assumptions —the assumption, in a word, of Simplicity itself.
And if here, for the mere sake of cavilling, it be urged, that although my starting-point is, as I assert, the assumption of absolute Simplicity, yet Simplicity, considered merely in itself, is no axiom; and that only deductions from axioms are indisputable – it is thus that I reply: —
Every other science than Logic is the science of certain concrete relations. Arithmetic, for example, is the science of the relations of number – Geometry, of the relations of form – Mathematics in general, of the relations of quantity in general – of whatever can be increased or diminished. Logic, however, is the science of Relation in the abstract – of absolute Relation – of Relation considered solely in itself. An axiom in any particular science other than Logic is, thus, merely a proposition announcing certain concrete relations which seem to be too obvious for dispute – as when we say, for instance, that the whole is greater than its part: – and, thus again, the principle of the Logical axiom – in other words, of an axiom in the abstract – is, simply, obviousness of relation. Now, it is clear, not only that what is obvious to one mind may not be obvious to another, but that what is obvious to one mind at one epoch, may be anything but obvious, at another epoch, to the same mind. It is clear, moreover, that what, to-day, is obvious even to the majority of mankind, or to the majority of the best intellects of mankind, may to-morrow be, to either majority, more or less obvious, or in no respect obvious at all. It is seen, then, that the axiomatic principle itself is susceptible of variation, and of course that axioms are susceptible of similar change. Being mutable, the “truths” which grow out of them are necessarily mutable too; or, in other words, are never to be positively depended upon as truths at all – since Truth and Immutability are one.
It will now be readily understood that no axiomatic idea – no idea founded in the fluctuating principle, obviousness of relation – can possibly be so secure – so reliable a basis for any structure erected by the Reason, as that idea – (whatever it is, wherever we can find it, or if it be practicable to find it anywhere) – which is irrelative altogether – which not only presents to the understanding no obviousness of relation, either greater or less, to be considered, but subjects the intellect, not in the slightest degree, to the necessity of even looking at any relation at all. If such an idea be not what we too heedlessly term “an axiom,” it is at least preferable, as a Logical basis, to any axiom ever propounded, or to all imaginable axioms combined: – and such, precisely, is the idea with which my deductive process, so thoroughly corroborated by induction, commences. My particle proper is but absolute Irrelation. To sum up what has been here advanced: – As a starting point I have taken it for granted, simply, that the Beginning had nothing behind it or before it – that it was a Beginning in fact – that it was a beginning and nothing different from a beginning – in short that this Beginning was —that which it was. If this be a “mere assumption” then a “mere assumption” let it be.
To conclude this branch of the subject: – I am fully warranted in announcing that the Law which we have been in the habit of calling Gravity exists on account of Matter’s having been irradiated, at its origin, atomically, into a limited4 sphere of Space, from one, individual, unconditional, irrelative, and absolute Particle Proper, by the sole process in which it was possible to satisfy, at the same time, the two conditions, irradiation, and generally-equable distribution throughout the sphere – that is to say, by a force varying in direct proportion with the squares of the distances between the irradiated atoms, respectively, and the Particular centre of Irradiation.
I have already given my reasons for presuming Matter to have been diffused by a determinate rather than by a continuous or infinitely continued force. Supposing a continuous force, we should be unable, in the first place, to comprehend a rëaction at all; and we should be required, in the second place, to entertain the impossible conception of an infinite extension of Matter. Not to dwell upon the impossibility of the conception, the infinite extension of Matter is an idea which, if not positively disproved, is at least not in any respect warranted by telescopic observation of the stars – a point to be explained more fully hereafter; and this empirical reason for believing in the original finity of Matter is unempirically confirmed. For example: – Admitting, for the moment, the possibility of understanding Space filled with the irradiated atoms – that is to say, admitting, as well as we can, for argument’s sake, that the succession of the irradiated atoms had absolutely no end– then it is abundantly clear that, even when the Volition of God had been withdrawn from them, and thus the tendency to return into Unity permitted (abstractly) to be satisfied, this permission would have been nugatory and invalid – practically valueless and of no effect whatever. No Rëaction could have taken place; no movement toward Unity could have been made; no Law of Gravity could have obtained.
To explain: – Grant the abstract tendency of any one atom to any one other as the inevitable result of diffusion from the normal Unity: – or, what is the same thing, admit any given atom as proposing to move in any given direction – it is clear that, since there is an infinity of atoms on all sides of the atom proposing to move, it never can actually move toward the satisfaction of its tendency in the direction given, on account of a precisely equal and counterbalancing tendency in the direction diametrically opposite. In other words, exactly as many tendencies to Unity are behind the hesitating atom as before it; for it is a mere sotticism to say that one infinite line is longer or shorter than another infinite line, or that one infinite number is greater or less than another number that is infinite. Thus the atom in question must remain stationary forever. Under the impossible circumstances which we have been merely endeavoring to conceive for argument’s sake, there could have been no aggregation of Matter – no stars – no worlds – nothing but a perpetually atomic and inconsequential Universe. In fact, view it as we will, the whole idea of unlimited Matter is not only untenable, but impossible and preposterous.
With the understanding of a sphere of atoms, however, we perceive, at once, a satisfiable tendency to union. The general result of the tendency each to each, being a tendency of all to the centre, the general process of condensation, or approximation, commences immediately, by a common and simultaneous movement, on withdrawal of the Divine Volition; the individual approximations, or coalescences —not cöalitions – of atom with atom, being subject to almost infinite variations of time, degree, and condition, on account of the excessive multiplicity of relation, arising from the differences of form assumed as characterizing the atoms at the moment of their quitting the Particle Proper; as well as from the subsequent particular inequidistance, each from each.
What I wish to impress upon the reader is the certainty of there arising, at once, (on withdrawal of the diffusive force, or Divine Volition,) out of the condition of the atoms as described, at innumerable points throughout the Universal sphere, innumerable agglomerations, characterized by innumerable specific differences of form, size, essential nature, and distance each from each. The development of Repulsion (Electricity) must have commenced, of course, with the very earliest particular efforts at Unity, and must have proceeded constantly in the ratio of Coalescence – that is to say, in that of Condensation, or, again, of Heterogeneity.
Thus the two Principles Proper, Attraction and Repulsion– the Material and the Spiritual – accompany each other, in the strictest fellowship, forever. Thus The Body and The Soul walk hand in hand.
If now, in fancy, we select any one of the agglomerations considered as in their primary stages throughout the Universal sphere, and suppose this incipient agglomeration to be taking place at that point where the centre of our Sun exists – or rather where it did exist originally; for the Sun is perpetually shifting his position – we shall find ourselves met, and borne onward for a time at least, by the most magnificent of theories – by the Nebular Cosmogony of Laplace: – although “Cosmogony” is far too comprehensive a term for what he really discusses – which is the constitution of our solar system alone – of one among the myriad of similar systems which make up the Universe Proper – that Universal sphere – that all-inclusive and absolute Kosmos which forms the subject of my present Discourse.
Confining himself to an obviously limited region – that of our solar system with its comparatively immediate vicinity – and merely assuming – that is to say, assuming without any basis whatever, either deductive or inductive —much of what I have been just endeavoring to place upon a more stable basis than assumption; assuming, for example, matter as diffused (without pretending to account for the diffusion) throughout, and somewhat beyond, the space occupied by our system – diffused in a state of heterogeneous nebulosity and obedient to that omniprevalent law of Gravity at whose principle he ventured to make no guess; – assuming all this (which is quite true, although he had no logical right to its assumption) Laplace has shown, dynamically and mathematically, that the results in such case necessarily ensuing, are those and those alone which we find manifested in the actually existing condition of the system itself.
To explain: – Let us conceive that particular agglomeration of which we have just spoken – the one at the point designated by our Sun’s centre – to have so far proceeded that a vast quantity of nebulous matter has here assumed a roughly globular form; its centre being, of course, coincident with what is now, or rather was originally, the centre of our Sun; and its periphery extending out beyond the orbit of Neptune, the most remote of our planets: – in other words, let us suppose the diameter of this rough sphere to be some 6000 millions of miles. For ages, this mass of matter has been undergoing condensation, until at length it has become reduced into the bulk we imagine; having proceeded gradually, of course, from its atomic and imperceptible state, into what we understand of visible, palpable, or otherwise appreciable nebulosity.
Now, the condition of this mass implies a rotation about an imaginary axis – a rotation which, commencing with the absolute incipiency of the aggregation, has been ever since acquiring velocity. The very first two atoms which met, approaching each other from points not diametrically opposite, would, in rushing partially past each other, form a nucleus for the rotary movement described. How this would increase in velocity, is readily seen. The two atoms are joined by others: – an aggregation is formed. The mass continues to rotate while condensing. But any atom at the circumference has, of course, a more rapid motion than one nearer the centre. The outer atom, however, with its superior velocity, approaches the centre; carrying this superior velocity with it as it goes. Thus every atom, proceeding inwardly, and finally attaching itself to the condensed centre, adds something to the original velocity of that centre – that is to say, increases the rotary movement of the mass.
Let us now suppose this mass so far condensed that it occupies precisely the space circumscribed by the orbit of Neptune, and that the velocity with which the surface of the mass moves, in the general rotation, is precisely that velocity with which Neptune now revolves about the Sun. At this epoch, then, we are to understand that the constantly increasing centrifugal force, having gotten the better of the non-increasing centripetal, loosened and separated the exterior and least condensed stratum, or a few of the exterior and least condensed strata, at the equator of the sphere, where the tangential velocity predominated; so that these strata formed about the main body an independent ring encircling the equatorial regions: – just as the exterior portion thrown off, by excessive velocity of rotation, from a grindstone, would form a ring about the grindstone, but for the solidity of the superficial material: were this caoutchouc, or anything similar in consistency, precisely the phænomenon I describe would be presented.
The ring thus whirled from the nebulous mass, revolved, of course, as a separate ring, with just that velocity with which, while the surface of the mass, it rotated. In the meantime, condensation still proceeding, the interval between the discharged ring and the main body continued to increase, until the former was left at a vast distance from the latter.
Now, admitting the ring to have possessed, by some seemingly accidental arrangement of its heterogeneous materials, a constitution nearly uniform, then this ring, as such, would never have ceased revolving about its primary; but, as might have been anticipated, there appears to have been enough irregularity in the disposition of the materials, to make them cluster about centres of superior solidity; and thus the annular form was destroyed.5 No doubt, the band was soon broken up into several portions, and one of these portions, predominating in mass, absorbed the others into itself; the whole settling, spherically, into a planet. That this latter, as a planet, continued the revolutionary movement which characterized it while a ring, is sufficiently clear; and that it took upon itself also, an additional movement in its new condition of sphere, is readily explained. The ring being understood as yet unbroken, we see that its exterior, while the whole revolves about the parent body, moves more rapidly than its interior. When the rupture occurred, then, some portion in each fragment must have been moving with greater velocity than the others. The superior movement prevailing, must have whirled each fragment round – that is to say, have caused it to rotate; and the direction of the rotation must, of course, have been the direction of the revolution whence it arose. All the fragments having become subject to the rotation described, must, in coalescing, have imparted it to the one planet constituted by their coalescence. – This planet was Neptune. Its material continuing to undergo condensation, and the centrifugal force generated in its rotation getting, at length, the better of the centripetal, as before in the case of the parent orb, a ring was whirled also from the equatorial surface of this planet: this ring, having been ununiform in its constitution, was broken up, and its several fragments, being absorbed by the most massive, were collectively spherified into a moon. Subsequently, the operation was repeated, and a second moon was the result. We thus account for the planet Neptune, with the two satellites which accompany him.
In throwing off a ring from its equator, the Sun re-established that equilibrium between its centripetal and centrifugal forces which had been disturbed in the process of condensation; but, as this condensation still proceeded, the equilibrium was again immediately disturbed, through the increase of rotation. By the time the mass had so far shrunk that it occupied a spherical space just that circumscribed by the orbit of Uranus, we are to understand that the centrifugal force had so far obtained the ascendency that new relief was needed: a second equatorial band was, consequently, thrown off, which, proving ununiform, was broken up, as before in the case of Neptune; the fragments settling into the planet Uranus; the velocity of whose actual revolution about the Sun indicates, of course, the rotary speed of that Sun’s equatorial surface at the moment of the separation. Uranus, adopting a rotation from the collective rotations of the fragments composing it, as previously explained, now threw off ring after ring; each of which, becoming broken up, settled into a moon: – three moons, at different epochs, having been formed, in this manner, by the rupture and general spherification of as many distinct ununiform rings.
By the time the Sun had shrunk until it occupied a space just that circumscribed by the orbit of Saturn, the balance, we are to suppose, between its centripetal and centrifugal forces had again become so far disturbed, through increase of rotary velocity, the result of condensation, that a third effort at equilibrium became necessary; and an annular band was therefore whirled off as twice before; which, on rupture through ununiformity, became consolidated into the planet Saturn. This latter threw off, in the first place, seven uniform bands, which, on rupture, were spherified respectively into as many moons; but, subsequently, it appears to have discharged, at three distinct but not very distant epochs, three rings whose equability of constitution was, by apparent accident, so considerable as to present no occasion for their rupture; thus they continue to revolve as rings. I use the phrase “apparent accident;” for of accident in the ordinary sense there was, of course, nothing: – the term is properly applied only to the result of indistinguishable or not immediately traceable law.
Shrinking still farther, until it occupied just the space circumscribed by the orbit of Jupiter, the Sun now found need of farther effort to restore the counterbalance of its two forces, continually disarranged in the still continued increase of rotation. Jupiter, accordingly, was now thrown off; passing from the annular to the planetary condition; and, on attaining this latter, threw off in its turn, at four different epochs, four rings, which finally resolved themselves into so many moons.
Still shrinking, until its sphere occupied just the space defined by the orbit of the Asteroids, the Sun now discarded a ring which appears to have had eight centres of superior solidity, and, on breaking up, to have separated into eight fragments no one of which so far predominated in mass as to absorb the others. All therefore, as distinct although comparatively small planets, proceeded to revolve in orbits whose distances, each from each, may be considered as in some degree the measure of the force which drove them asunder: – all the orbits, nevertheless, being so closely coincident as to admit of our calling them one, in view of the other planetary orbits.
Continuing to shrink, the Sun, on becoming so small as just to fill the orbit of Mars, now discharged this planet – of course by the process repeatedly described. Having no moon, however, Mars could have thrown off no ring. In fact, an epoch had now arrived in the career of the parent body, the centre of the system. The decrease of its nebulosity, which is the increase of its density, and which again is the decrease of its condensation, out of which latter arose the constant disturbance of equilibrium – must, by this period, have attained a point at which the efforts for restoration would have been more and more ineffectual just in proportion as they were less frequently needed. Thus the processes of which we have been speaking would everywhere show signs of exhaustion – in the planets, first, and secondly, in the original mass. We must not fall into the error of supposing the decrease of interval observed among the planets as we approach the Sun, to be in any respect indicative of an increase of frequency in the periods at which they were discarded. Exactly the converse is to be understood. The longest interval of time must have occurred between the discharges of the two interior; the shortest, between those of the two exterior, planets. The decrease of the interval of space is, nevertheless, the measure of the density, and thus inversely of the condensation, of the Sun, throughout the processes detailed.
Having shrunk, however, so far as to fill only the orbit of our Earth, the parent sphere whirled from itself still one other body – the Earth – in a condition so nebulous as to admit of this body’s discarding, in its turn, yet another, which is our Moon; – but here terminated the lunar formations.
Finally, subsiding to the orbits first of Venus and then of Mercury, the Sun discarded these two interior planets; neither of which has given birth to any moon.
Thus from his original bulk – or, to speak more accurately, from the condition in which we first considered him – from a partially spherified nebular mass, certainly much more than 5,600 millions of miles in diameter – the great central orb and origin of our solar-planetary-lunar system, has gradually descended, by condensation, in obedience to the law of Gravity, to a globe only 882,000 miles in diameter; but it by no means follows, either that its condensation is yet complete, or that it may not still possess the capacity of whirling from itself another planet.
I have here given – in outline of course, but still with all the detail necessary for distinctness – a view of the Nebular Theory as its author himself conceived it. From whatever point we regard it, we shall find it beautifully true. It is by far too beautiful, indeed, not to possess Truth as its essentiality – and here I am very profoundly serious in what I say. In the revolution of the satellites of Uranus, there does appear something seemingly inconsistent with the assumptions of Laplace; but that one inconsistency can invalidate a theory constructed from a million of intricate consistencies, is a fancy fit only for the fantastic. In prophecying, confidently, that the apparent anomaly to which I refer, will, sooner or later, be found one of the strongest possible corroborations of the general hypothesis, I pretend to no especial spirit of divination. It is a matter which the only difficulty seems not to foresee.6
The bodies whirled off in the processes described, would exchange, it has been seen, the superficial rotation of the orbs whence they originated, for a revolution of equal velocity about these orbs as distant centres; and the revolution thus engendered must proceed, so long as the centripetal force, or that with which the discarded body gravitates toward its parent, is neither greater nor less than that by which it was discarded; that is, than the centrifugal, or, far more properly, than the tangential, velocity. From the unity, however, of the origin of these two forces, we might have expected to find them as they are found – the one accurately counterbalancing the other. It has been shown, indeed, that the act of whirling-off is, in every case, merely an act for the preservation of the counterbalance.
After referring, however, the centripetal force to the omniprevalent law of Gravity, it has been the fashion with astronomical treatises, to seek beyond the limits of mere Nature – that is to say, of Secondary Cause – a solution of the phænomenon of tangential velocity. This latter they attribute directly to a First Cause – to God. The force which carries a stellar body around its primary they assert to have originated in an impulse given immediately by the finger – this is the childish phraseology employed – by the finger of Deity itself. In this view, the planets, fully formed, are conceived to have been hurled from the Divine hand, to a position in the vicinity of the suns, with an impetus mathematically adapted to the masses, or attractive capacities, of the suns themselves. An idea so grossly unphilosophical, although so supinely adopted, could have arisen only from the difficulty of otherwise accounting for the absolutely accurate adaptation, each to each, of two forces so seemingly independent, one of the other, as are the gravitating and tangential. But it should be remembered that, for a long time, the coincidence between the moon’s rotation and her sidereal revolution – two matters seemingly far more independent than those now considered – was looked upon as positively miraculous; and there was a strong disposition, even among astronomers, to attribute the marvel to the direct and continual agency of God – who, in this case, it was said, had found it necessary to interpose, specially, among his general laws, a set of subsidiary regulations, for the purpose of forever concealing from mortal eyes the glories, or perhaps the horrors, of the other side of the Moon – of that mysterious hemisphere which has always avoided, and must perpetually avoid, the telescopic scrutiny of mankind. The advance of Science, however, soon demonstrated – what to the philosophical instinct needed no demonstration – that the one movement is but a portion – something more, even, than a consequence – of the other.
