Eureka Part 2

Whether we reach the idea of absolute _Unity_ as the source of All Things, from a consideration of Simplicity as the most probable characteristic of the original action of G.o.d;-whether we arrive at it from an inspection of the universality of relation in the gravitating phaenomena;-or whether we attain it as a result of the mutual corroboration afforded by both processes;-still, the idea itself, if entertained at all, is entertained in inseparable connection with another idea-that of the condition of the Universe of stars as we _now_ perceive it-that is to say, a condition of immeasurable _diffusion_ through s.p.a.ce. Now a connection between these two ideas-unity and diffusion-cannot be established unless through the entertainment of a third idea-that of _irradiation_. Absolute Unity being taken as a centre, then the existing Universe of stars is the result of _irradiation_ from that centre.

Now, the laws of irradiation are _known_. They are part and parcel of the _sphere_. They belong to the cla.s.s of _indisputable geometrical properties_. We say of them, "they are true-they are evident." To demand _why_ they are true, would be to demand why the axioms are true upon which their demonstration is based. _Nothing_ is demonstrable, strictly speaking; but _if_ anything _be_, then the properties-the laws in question are demonstrated.

But these laws-what do they declare? Irradiation-how-by what steps does it proceed outwardly from a centre?

From a _luminous_ centre, _Light_ issues by irradiation; and the quant.i.ties of light received upon any given plane, supposed to be s.h.i.+fting its position so as to be now nearer the centre and now farther from it, will be diminished in the same proportion as the squares of the distances of the plane from the luminous body, are increased; and will be increased in the same proportion as these squares are diminished.

The expression of the law may be thus generalized:-the number of light-particles (or, if the phrase be preferred, the number of light-impressions) received upon the s.h.i.+fting plane, will be _inversely_ proportional with the squares of the distances of the plane.

Generalizing yet again, we may say that the diffusion-the scattering-the irradiation, in a word-is _directly_ proportional with the squares of the distances.

[Ill.u.s.tration]

For example: at the distance B, from the luminous centre A, a certain number of particles are so diffused as to occupy the surface B. Then at double the distance-that is to say at C-they will be so much farther diffused as to occupy four such surfaces:-at treble the distance, or at D, they will be so much farther separated as to occupy nine such surfaces:-while, at quadruple the distance, or at E, they will have become so scattered as to spread themselves over sixteen such surfaces-and so on forever.

In saying, generally, that the irradiation proceeds in direct proportion with the squares of the distances, we use the term irradiation to express _the degree of the diffusion_ as we proceed outwardly from the centre. Conversing the idea, and employing the word "concentralization"

to express _the degree of the drawing together_ as we come back toward the centre from an outward position, we may say that concentralization proceeds _inversely_ as the squares of the distances. In other words, we have reached the conclusion that, on the hypothesis that matter was originally irradiated from a centre and is now returning to it, the concentralization, in the return, proceeds _exactly as we know the force of gravitation to proceed_.

Now here, if we could be permitted to a.s.sume that concentralization exactly represented the _force of the tendency to the centre_-that the one was exactly proportional to the other, and that the two proceeded together-we should have shown all that is required. The sole difficulty existing, then, is to establish a direct proportion between "concentralization" and the _force_ of concentralization; and this is done, of course, if we establish such proportion between "irradiation"

and the _force_ of irradiation.

A very slight inspection of the Heavens a.s.sures us that the stars have a certain general uniformity, equability, or equidistance, of distribution through that region of s.p.a.ce in which, collectively, and in a roughly globular form, they are situated:-this species of very general, rather than absolute, equability, being in full keeping with my deduction of inequidistance, within certain limits, among the originally diffused atoms, as a corollary from the evident design of infinite complexity of relation out of irrelation. I started, it will be remembered, with the idea of a generally uniform but particularly _un_uniform distribution of the atoms;-an idea, I repeat, which an inspection of the stars, as they exist, confirms.

But even in the merely general equability of distribution, as regards the atoms, there appears a difficulty which, no doubt, has already suggested itself to those among my readers who have borne in mind that I suppose this equability of distribution effected through _irradiation from a centre_. The very first glance at the idea, irradiation, forces us to the entertainment of the hitherto unseparated and seemingly inseparable idea of agglomeration about a centre, with dispersion as we recede from it-the idea, in a word, of _in_equability of distribution in respect to the matter irradiated.

Now, I have elsewhere[1] observed that it is by just such difficulties as the one now in question-such roughnesses-such peculiarities-such protuberances above the plane of the ordinary-that Reason feels her way, if at all, in her search for the True. By the difficulty-the "peculiarity"-now presented, I leap at once to _the_ secret-a secret which I might never have attained _but_ for the peculiarity and the inferences which, _in its mere character of peculiarity_, it affords me.

[1] "_Murders in the Rue Morgue_"-p. 133.

The process of thought, at this point, may be thus roughly sketched:-I say to myself-"Unity, as I have explained it, is a truth-I feel it.

Diffusion is a truth-I see it. Irradiation, by which alone these two truths are reconciled, is a consequent truth-I perceive it. _Equability_ of diffusion, first deduced _a priori_ and then corroborated by the inspection of phaenomena, is also a truth-I fully admit it. So far all is clear around me:-there are no clouds behind which _the_ secret-the great secret of the gravitating _modus operandi_-can possibly lie hidden;-but this secret lies _hereabouts_, most a.s.suredly; and _were_ there but a cloud in view, I should be driven to suspicion of that cloud." And now, just as I say this, there actually comes a cloud into view. This cloud is the seeming impossibility of reconciling my truth, _irradiation_, with my truth, _equability of diffusion_. I say now:-"Behind this _seeming_ impossibility is to be found what I desire." I do not say "_real_ impossibility;" for invincible faith in my truths a.s.sures me that it is a mere difficulty after all-but I go on to say, with unflinching confidence, that, _when_ this _difficulty_ shall be solved, we shall find, _wrapped up in the process of solution_, the key to the secret at which we aim. Moreover-I _feel_ that we shall discover _but one_ possible solution of the difficulty; this for the reason that, were there two, one would be supererogatory-would be fruitless-would be empty-would contain no key-since no duplicate key can be needed to any secret of Nature.

And now, let us see:-Our usual notions of irradiation-in fact _all_ our distinct notions of it-are caught merely from the process as we see it exemplified in _Light_. Here there is a _continuous_ outpouring of _ray-streams_, and _with a force which we have at least no right to suppose varies at all_. Now, in any such irradiation _as this_-continuous and of unvarying force-the regions nearer the centre must _inevitably_ be always more crowded with the irradiated matter than the regions more remote. But I have a.s.sumed _no_ such irradiation _as this_. I a.s.sumed no _continuous_ irradiation; and for the simple reason that such an a.s.sumption would have involved, first, the necessity of entertaining a conception which I have shown no man _can_ entertain, and which (as I will more fully explain hereafter) all observation of the firmament refutes-the conception of the absolute infinity of the Universe of stars-and would have involved, secondly, the impossibility of understanding a reaction-that is, gravitation-as existing now-since, while an act is continued, no reaction, of course, can take place. My a.s.sumption, then, or rather my inevitable deduction from just premises-was that of a _determinate_ irradiation-one finally _dis_continued.

Let me now describe the sole possible mode in which it is conceivable that matter could have been diffused through s.p.a.ce, so as to fulfil the conditions at once of irradiation and of generally equable distribution.

For convenience of ill.u.s.tration, let us imagine, in the first place, a hollow sphere of gla.s.s, or of anything else, occupying the s.p.a.ce throughout which the universal matter is to be thus equally diffused, by means of irradiation, from the absolute, irrelative, unconditional particle, placed in the centre of the sphere.

Now, a certain exertion of the diffusive power (presumed to be the Divine Volition)-in other words, a certain _force_-whose measure is the quant.i.ty of matter-that is to say, the number of atoms-emitted; emits, by irradiation, this certain number of atoms; forcing them in all directions outwardly from the centre-their proximity to each other diminis.h.i.+ng as they proceed-until, finally, they are distributed, loosely, over the interior surface of the sphere.

When these atoms have attained this position, or while proceeding to attain it, a second and inferior exercise of the same force-or a second and inferior force of the same character-emits, in the same manner-that is to say, by irradiation as before-a second stratum of atoms which proceeds to deposit itself upon the first; the number of atoms, in this case as in the former, being of course the measure of the force which emitted them; in other words the force being precisely adapted to the purpose it effects-the force and the number of atoms sent out by the force, being _directly proportional_.

When this second stratum has reached its destined position-or while approaching it-a third still inferior exertion of the force, or a third inferior force of a similar character-the number of atoms emitted being in _all_ cases the measure of the force-proceeds to deposit a third stratum upon the second:-and so on, until these concentric strata, growing gradually less and less, come down at length to the central point; and the diffusive matter, simultaneously with the diffusive force, is exhausted.

We have now the sphere filled, through means of irradiation, with atoms equably diffused. The two necessary conditions-those of irradiation and of equable diffusion-are satisfied; and by the _sole_ process in which the possibility of their simultaneous satisfaction is conceivable. For this reason, I confidently expect to find, lurking in the present condition of the atoms as distributed throughout the sphere, the secret of which I am in search-the all-important principle of the _modus operandi_ of the Newtonian law. Let us examine, then, the actual condition of the atoms.

They lie in a series of concentric strata. They are equably diffused throughout the sphere. They have been irradiated into these states.

The atoms being _equably_ distributed, the greater the superficial extent of any of these concentric strata, or spheres, the more atoms will lie upon it. In other words, the number of atoms lying upon the surface of any one of the concentric spheres, is directly proportional with the extent of that surface.

_But, in any series of concentric spheres, the surfaces are directly proportional with the squares of the distances from the centre._[2]

[2] Succinctly-The surfaces of spheres are as the squares of their radii.

Therefore the number of atoms in any stratum is directly proportional with the square of that stratum's distance from the centre.

But the number of atoms in any stratum is the measure of the force which emitted that stratum-that is to say, is _directly proportional_ with the force.

Therefore the force which irradiated any stratum is directly proportional with the square of that stratum's distance from the centre:-or, generally,

_The force of the irradiation has been directly proportional with the squares of the distances._

Now, Reaction, as far as we know anything of it, is Action conversed.

The _general_ principle of Gravity being, in the first place, understood as the reaction of an act-as the expression of a desire on the part of Matter, while existing in a state of diffusion, to return into the Unity whence it was diffused; and, in the second place, the mind being called upon to determine the _character_ of the desire-the manner in which it would, naturally, be manifested; in other words, being called upon to conceive a probable law, or _modus operandi_, for the return; could not well help arriving at the conclusion that this law of return would be precisely the converse of the law of departure. That such would be the case, any one, at least, would be abundantly justified in taking for granted, until such time as some person should suggest something like a plausible reason why it should _not_ be the case-until such period as a law of return shall be imagined which the intellect can consider as preferable.

Matter, then, irradiated into s.p.a.ce with a force varying as the squares of the distances, might, _a priori_, be supposed to return towards its centre of irradiation with a force varying _inversely_ as the squares of the distances: and I have already shown[3] that any principle which will explain why the atoms should tend, according to any law, to the general centre, must be admitted as satisfactorily explaining, at the same time, why, according to the same law, they should tend each to each. For, in fact, the tendency to the general centre is not to a centre as such, but because of its being a point in tending towards which each atom tends most directly to its real and essential centre, _Unity_-the absolute and final Union of all.

[3] Page 44.

The consideration here involved presents to my own mind no embarra.s.sment whatever-but this fact does not blind me to the possibility of its being obscure to those who may have been less in the habit of dealing with abstractions:-and, upon the whole, it may be as well to look at the matter from one or two other points of view.

The absolute, irrelative particle primarily created by the Volition of G.o.d, must have been in a condition of positive _normality_, or rightfulness-for wrongfulness implies _relation_. Right is positive; wrong is negative-is merely the negation of right; as cold is the negation of heat-darkness of light. That a thing may be wrong, it is necessary that there be some other thing in _relation_ to which it _is_ wrong-some condition which it fails to satisfy; some law which it violates; some being whom it aggrieves. If there be no such being, law, or condition, in respect to which the thing is wrong-and, still more especially, if no beings, laws, or conditions exist at all-then the thing can_not_ be wrong and consequently must be _right_. Any deviation from normality involves a tendency to return into it. A difference from the normal-from the right-from the just-can be understood as effected only by the overcoming a difficulty; and if the force which overcomes the difficulty be not infinitely continued, the ineradicable tendency to return will at length be permitted to act for its own satisfaction. Upon withdrawal of the force, the tendency acts. This is the principle of reaction as the inevitable consequence of finite action. Employing a phraseology of which the seeming affectation will be pardoned for its expressiveness, we may say that Reaction is the return from the condition of _as it is and ought not to be_ into the condition of _as it was, originally, and therefore ought to be_:-and let me add here that the _absolute_ force of Reaction would no doubt be always found in direct proportion with the reality-the truth-the absoluteness-of the _originality_-if ever it were possible to measure this latter:-and, consequently, the greatest of all conceivable reactions must be that produced by the tendency which we now discuss-the tendency to return into the _absolutely original_-into the _supremely_ primitive. Gravity, then, _must be the strongest of forces_-an idea reached _a priori_ and abundantly confirmed by induction. What use I make of the idea, will be seen in the sequel.

The atoms, now, having been diffused from their normal condition of Unity, seek to return to--what? Not to any particular _point_, certainly; for it is clear that if, upon the diffusion, the whole Universe of matter had been projected, collectively, to a distance from the point of irradiation, the atomic tendency to the general centre of the sphere would not have been disturbed in the least:-the atoms would not have sought the point _in absolute s.p.a.ce_ from which they were originally impelled. It is merely the _condition_, and not the point or locality at which this condition took its rise, that these atoms seek to re-establish;-it is merely _that condition which is their normality_, that they desire. "But they seek a centre," it will be said, "and a centre is a point." True; but they seek this point not in its character of point-(for, were the whole sphere moved from its position, they would seek, equally, the centre; and the centre _then_ would be a _new_ point)-but because it so happens, on account of the form in which they collectively exist-(that of the sphere)-that only _through_ the point in question-the sphere's centre-they can attain their true object, Unity.

In the direction of the centre each atom perceives more atoms than in any other direction. Each atom is impelled towards the centre because along the straight line joining it and the centre and pa.s.sing on to the circ.u.mference beyond, there lie a greater number of atoms than along any other straight line-a greater number of objects that seek it, the individual atom-a greater number of tendencies to Unity-a greater number of satisfactions for its own tendency to Unity-in a word, because in the direction of the centre lies the utmost possibility of satisfaction, generally, for its own individual appet.i.te. To be brief, the _condition_, Unity, is all that is really sought; and if the atoms _seem_ to seek the centre of the sphere, it is only impliedly, through implication-because such centre happens to imply, to include, or to involve, the only essential centre, Unity. But _on account of_ this implication or involution, there is no possibility of practically separating the tendency to Unity in the abstract, from the tendency to the concrete centre. Thus the tendency of the atoms to the general centre _is_, to all practical intents and for all logical purposes, the tendency each to each; and the tendency each to each _is_ the tendency to the centre; and the one tendency may be a.s.sumed _as_ the other; whatever will apply to the one must be thoroughly applicable to the other; and, in conclusion, whatever principle will satisfactorily explain the one, cannot be questioned as an explanation of the other.

In looking carefully around me for rational objection to what I have advanced, I am able to discover _nothing_;-but of that cla.s.s of objections usually urged by the doubters for Doubt's sake, I very readily perceive _three_; and proceed to dispose of them in order.

It may be said, first: "The proof that the force of irradiation (in the case described) is directly proportional to the squares of the distances, depends upon an unwarranted a.s.sumption-that of the number of atoms in each stratum being the measure of the force with which they are emitted."

I reply, not only that I am warranted in such a.s.sumption, but that I should be utterly _un_warranted in any other. What I a.s.sume 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 pa.s.s 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 ent.i.tled 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 circ.u.mference of the imaginary gla.s.s 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 a.s.sumption"-on the part of the objector-the a.s.sumption 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 G.o.d. 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 reaction 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 G.o.d 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 Reaction, and through Reaction, "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 phaenomena-a law which, merely because it does so enable us to account for these phaenomena, 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 a.n.a.lysis-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 a.s.sent to--what? To an hypothesis? Why _if_ an hypothesis-if the merest hypothesis-if an hypothesis for whose a.s.sumption-as in the case of that _pure_ hypothesis the Newtonian law itself-no shadow of _a priori_ reason could be a.s.signed-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 _in_ductive journey from the phaenomena of the very Law discussed, or at the close of a _de_ductive career from the most rigorously simple of all conceivable a.s.sumptions-_the a.s.sumption, in a word, of Simplicity itself_.