Eureka & The Unparalleled Adventure of One Hans Pfaall

Now, distinctness –intelligibility, at all points, is a primary feature in my general design. On important topics it is better to be a good deal prolix than even a very little obscure. But abstruseness is a quality appertaining to no subject per se. All are alike, in facility of comprehension, to him who approaches them by properly graduated steps. It is merely because a stepping-stone, here and there, is heedlessly left unsupplied in our road to the Differential Calculus, that this latter is not altogether as simple a thing as a sonnet by Mr. Solomon Seesaw.

By way of admitting, then, no chance for misapprehension, I think it advisable to proceed as if even the more obvious facts of Astronomy were unknown to the reader. In combining the two modes of discussion to which I have referred, I propose to avail myself of the advantages peculiar to each –and very especially of the iteration in detail which will be unavoidable as a consequence of the plan. Commencing with a descent, I shall reserve for the return upwards those indispensable considerations of quantity to which allusion has already been made.

Let us begin, then, at once, with that merest of words, "Infinity." This, like "God," "spirit," and some other expressions of which the equivalents exist in all languages, is by no means the expression of an idea –but of an effort at one. It stands for the possible attempt at an impossible conception. Man needed a term by which to point out the direction of this effort –the cloud behind which lay, forever invisible, the object of this attempt. A word, in fine, was demanded, by means of which one human being might put himself in relation at once with another human being and with a certain tendency of the human intellect. Out of this demand arose the word, "Infinity;" which is thus the representative but of the thought of a thought.

As regards that infinity now considered –the infinity of space –we often hear it said that "its idea is admitted by the mind –is acquiesced in –is entertained –on account of the greater difficulty which attends the conception of a limit." But this is merely one of those phrases by which even profound thinkers, time out of mind, have occasionally taken pleasure in deceiving themselves. The quibble lies concealed in the word "difficulty." "The mind," we are told, "entertains the idea of limitless, through the greater difficulty which it finds in entertaining that of limited, space." Now, were the proposition but fairly put, its absurdity would become transparent at once. Clearly, there is no mere difficulty in the case. The assertion intended, if presented according to its intention and without sophistry, would run thus: –"The mind admits the idea of limitless, through the greater impossibility of entertaining that of limited, space."

It must be immediately seen that this is not a question of two statements between whose respective credibilities –or of two arguments between whose respective validities –the reason is called upon to decide: –it is a matter of two conceptions, directly conflicting, and each avowedly impossible, one of which the intellect is supposed to be capable of entertaining, on account of the greater impossibility of entertaining the other. The choice is not made between two difficulties; –it is merely fancied to be made between two impossibilities. Now of the former, there are degrees, –but of the latter, none: –just as our impertinent letter-writer has already suggested. A task may be more or less difficult; but it is either possible or not possible: –there are no gradations. It might be more difficult to overthrow the Andes than an ant-hill; but it can be no more impossible to annihilate the matter of the one than the matter of the other. A man may jump ten feet with less difficulty than he can jump twenty, but the impossibility of his leaping to the moon is not a whit less than that of his leaping to the dog-star.

Since all this is undeniable: since the choice of the mind is to be made between impossibilities of conception: since one impossibility cannot be greater than another: and since, thus, one cannot be preferred to another: the philosophers who not only maintain, on the grounds mentioned, man's idea of infinity but, on account of such supposititious idea, infinity itself –are plainly engaged in demonstrating one impossible thing to be possible by showing how it is that some one other thing –is impossible too. This, it will be said, is nonsense; and perhaps it is: –indeed I think it very capital nonsense –but forego all claim to it as nonsense of mine.

The readiest mode, however, of displaying the fallacy of the philosophical argument on this question, is by simply adverting to a fact respecting it which has been hitherto quite overlooked –the fact that the argument alluded to both proves and disproves its own proposition. "The mind is impelled," say the theologians and others, "to admit a First Cause, by the superior difficulty it experiences in conceiving cause beyond cause without end." The quibble, as before, lies in the word "difficulty" –but here what is it employed to sustain? A First Cause. And what is a First Cause? An ultimate termination of causes. And what is an ultimate termination of causes? Finity –the Finite. Thus the one quibble, in two processes, by God knows how many philosophers, is made to support now Finity and now Infinity –could it not be brought to support something besides? As for the quibblers –they, at least, are insupportable. But –to dismiss them: – what they prove in the one case is the identical nothing which they demonstrate in the other.

Of course, no one will suppose that I here contend for the absolute impossibility of that which we attempt to convey in the word "Infinity." My purpose is but to show the folly of endeavoring to prove Infinity itself, or even our conception of it, by any such blundering ratiocination as that which is ordinarily employed.

Nevertheless, as an individual, I may be permitted to say that I cannot conceive Infinity, and am convinced that no human being can. A mind not thoroughly self-conscious –not accustomed to the introspective analysis of its own operations –will, it is true, often deceive itself by supposing that it has entertained the conception of which we speak. In the effort to entertain it, we proceed step beyond step –we fancy point still beyond point; and so long as we Continue the effort, it may be said, in fact, that we are tending to the formation of the idea designed; while the strength of the impression that we actually form or have formed it, is in the ratio of the period during which we keep up the mental endeavor. But it is in the act of discontinuing the endeavor –of fulfilling (as we think) the idea –of putting the finishing stroke (as we suppose) to the conception –that we overthrow at once the whole fabric of our fancy by resting upon some one ultimate and therefore definite point. This fact, however, we fail to perceive, on account of the absolute coincidence, in time, between the settling down upon the ultimate point and the act of cessation in thinking. –In attempting, on the other hand, to frame the idea of a limited space, we merely converse the processes which involve the impossibility.

We believe in a God. We may or may not believe in finite or in infinite space; but our belief, in such cases, is more properly designated as faith, and is a matter quite distinct from that belief proper –from that intellectual belief –which presupposes the mental conception.

The fact is, that, upon the enunciation of any one of that class of terms to which "Infinity" belongs –the class representing thoughts of thought –he who has a right to say that he thinks at all, feels himself called upon, not to entertain a conception, but simply to direct his mental vision toward some given point, in the intellectual firmament, where lies a nebula never to be resolved. To solve it, indeed, he makes no effort; for with a rapid instinct he comprehends, not only the impossibility, but, as regards all human purposes, the inessentiality, of its solution. He perceives that the Deity has not designed it to be solved. He sees, at once, that it lies out of the brain of man, and even how, if not exactly why, it lies out of it. There are people, I am aware, who, busying themselves in attempts at the unattainable, acquire very easily, by dint of the jargon they emit, among those thinkers-that-they-think with whom darkness and depth are synonymous, a kind of cuttle-fish reputation for profundity; but the finest quality of Thought is its self-cognizance; and, with some little equivocation, it may be said that no fog of the mind can well be greater than that which, extending to the very boundaries of the mental domain, shuts out even these boundaries themselves from comprehension.

It will now be understood that, in using the phrase, "Infinity of Space," I make no call upon the reader to entertain the impossible conception of an absolute infinity. I refer simply to the "utmost conceivable expanse" of space –a shadowy and fluctuating domain, now shrinking, now swelling, in accordance with the vacillating energies of the imagination.

Hitherto, the Universe of stars has always been considered as coincident with the Universe proper, as I have defined it in the commencement of this Discourse. It has been always either directly or indirectly assumed –at least since the dawn of intelligible Astronomy –that, were it possible for us to attain any given point in space, we should still find, on all sides of us, an interminable succession of stars. This was the untenable idea of Pascal when making perhaps the most successful attempt ever made, at periphrasing the conception for which we struggle in the word "Universe." "It is a sphere," he says, "of which the centre is everywhere, the circumference, nowhere." But although this intended definition is, in fact, no definition of the Universe of stars, we may accept it, with some mental reservation, as a definition (rigorous enough for all practical purposes) of the Universe proper – that is to say, of the Universe of space. This latter, then, let us regard as "a sphere of which the centre is everywhere, the circumference nowhere." In fact, while we find it impossible to fancy an end to space, we have no difficulty in picturing to ourselves any one of an infinity of beginnings.

As our starting point, then, let us adopt the Godhead. Of this Godhead, in itself, he alone is not imbecile –he alone is not impious who propounds –nothing. "Nous ne connaissons rien," says the Baron de Bielfeld –"Nous ne connaissons rien de la nature ou de l'essence de Dieu: –pour savoir ce qu'il est, il faut etre Dieu meme." – "We know absolutely nothing of the nature or essence of God: – in order to comprehend what he is, we should have to be God ourselves."

"We should have to be God ourselves!" –With a phrase so startling as this yet ringing in my ears, I nevertheless venture to demand if this our present ignorance of the Deity is an ignorance to which the soul is everlastingly condemned.

By Him, however –now, at least, the Incomprehensible –by Him – assuming him as Spirit –that is to say, as not Matter –a distinction which, for all intelligible purposes, will stand well instead of a definition –by Him, then, existing as Spirit, let us content ourselves, to-night, with supposing to have been created, or made out of Nothing, by dint of his Volition –at some point of Space which we will take as a centre –at some period into which we do not pretend to inquire, but at all events immensely remote –by Him, then again, let us suppose to have been created –what? This is a vitally momentous epoch in our considerations. What is it that we are justified –that alone we are justified in supposing to have been, primarily and solely, created?

We have attained a point where only Intuition can aid us: –but now let me recur to the idea which I have already suggested as that alone which we can properly entertain of intuition. It is but the conviction arising from those inductions or deductions of which the processes are so shadowy as to escape our consciousness, elude our reason, or defy our capacity of expression. With this understanding, I now assert –that an intuition altogether irresistible, although inexpressible, forces me to the conclusion that what God originally created –that that Matter which, by dint of his Volition, he first made from his Spirit, or from Nihility, Could have been nothing but Matter in its utmost conceivable state of – what? –of Simplicity?

This will be found the sole absolute assumption of my Discourse. I use the word "assumption" in its ordinary sense; yet I maintain that even this my primary proposition, is very, very far indeed, from being really a mere assumption. Nothing was ever more certainly – no human conclusion was ever, in fact, more regularly –more rigorously de duced: –but, alas! the processes lie out of the human analysis –at all events are beyond the utterance of the human tongue.

Let us now endeavor to conceive what Matter must be, when, or if, in its absolute extreme of Simplicity. Here the Reason flies at once to Imparticularity –to a particle –to one particle –a particle of one kind – of one character –of one nature –of one size –of one form – a particle, therefore, "without form and void" –a particle positively a particle at all points –a particle absolutely unique, individual, undivided, and not indivisible only because He who created it, by dint of his Will, can by an infinitely less energetic exercise of the same Will, as a matter of course, divide it.

Oneness, then, is all that I predicate of the originally created Matter; but I propose to show that this Oneness is a principle abundantly sufficient to account for the constitution, the existing phaenomena and the plainly inevitable annihilation of at least the material Universe.

The willing into being the primordial particle, has completed the act, or more properly the Conception, of Creation. We now proceed to the ultimate purpose for which we are to suppose the Particle created – that is to say, the ultimate purpose so far as our considerations yet enable us to see it –the constitution of the Universe from it, the Particle.

This constitution has been effected by forcing the originally and therefore normally One into the abnormal condition of Many. An action of this character implies reaction. A diffusion from Unity, under the conditions, involves a tendency to return into Unity –a tendency ineradicable until satisfied. But on these points I will speak more fully hereafter.

The assumption of absolute Unity in the primordial Particle includes that of infinite divisibility. Let us conceive the Particle, then, to be only not totally exhausted by diffusion into Space. From the one Particle, as a centre, let us suppose to be irradiated spherically –in all directions –to immeasurable but still to definite distances in the previously vacant space –a certain inexpressibly great yet limited number of unimaginably yet not infinitely minute atoms.

Now, of these atoms, thus diffused, or upon diffusion, what conditions are we permitted –not to assume, but to infer, from consideration as well of their source as of the character of the design apparent in their diffusion? Unity being their source, and difference from Unity the character of the design manifested in their diffusion, we are warranted in supposing this character to be at least generally preserved throughout the design, and to form a portion of the design itself: –that is to say, we shall be warranted in conceiving continual differences at all points from the uniquity and simplicity of the origin. But, for these reasons, shall we be justified in imagining the atoms heterogeneous, dissimilar, unequal, and inequidistant? More explicitly –are we to consider no two atoms as, at their diffusion, of the same nature, or of the same form, or of the same size? –and, after fulfilment of their diffusion into Space, is absolute inequidistance, each from each, to be understood of all of them? In such arrangement, under such conditions, we most easily and immediately comprehend the subsequent most feasible carrying out to completion of any such design as that which I have suggested –the design of variety out of unity –diversity out of sameness – heterogeneity out of homogeneity –complexity out of simplicity –in a word, the utmost possible multiplicity of relation out of the emphatically irrelative One. Undoubtedly, therefore, we should be warranted in assuming all that has been mentioned, but for the reflection, first, that supererogation is not presumable of any Divine Act; and, secondly, that the object supposed in view, appears as feasible when some of the conditions in question are dispensed with, in the beginning, as when all are understood immediately to exist. I mean to say that some are involved in the rest, or so instantaneous a consequence of them as to make the distinction inappreciable. Difference of size, for example, will at once be brought about through the tendency of one atom to a second, in preference to a third, on account of particular inequidistance; which is to be comprehended as particular inequidistances between centres of quantity, in neighboring atoms of different form –a matter not at all interfering with the generally-equable distribution of the atoms. Difference of kind, too, is easily conceived to be merely a result of differences in size and form, taken more or less conjointly: –in fact, since the Unity of the Particle Proper implies absolute homogeneity, we cannot imagine the atoms, at their diffusion, differing in kind, without imagining, at the same time, a special exercise of the Divine Will, at the emission of each atom, for the purpose of effecting, in each, a change of its essential nature: –so fantastic an idea is the less to be indulged, as the object proposed is seen to be thoroughly attainable without such minute and elaborate interposition. We perceive, therefore, upon the whole, that it would be supererogatory, and consequently unphilosophical, to predicate of the atoms, in view of their purposes, any thing more than difference of form at their dispersion, with particular inequidistance after it –all other differences arising at once out of these, in the very first processes of mass-constitution: –We thus establish the Universe on a purely geometrical basis. Of course, it is by no means necessary to assume absolute difference, even of form, among the atoms irradiated –any more than absolute particular inequidistance of each from each. We are required to conceive merely that no neighboring atoms are of similar form –no atoms which can ever approximate, until their inevitable reunition at the end.

Although the immediate and perpetual tendency of the disunited atoms to return into their normal Unity, is implied, as I have said, in their abnormal diffusion; still it is clear that this tendency will be without consequence –a tendency and no more –until the diffusive energy, in ceasing to be exerted, shall leave it, the tendency, free to seek its satisfaction. The Divine Act, however, being considered as determinate, and discontinued on fulfilment of the diffusion, we understand, at once, a reaction –in other words, a satisfiable tendency of the disunited atoms to return into One.

But the diffusive energy being withdrawn, and the reaction having commenced in furtherance of the ultimate design –that of the utmost possible Relation –this design is now in danger of being frustrated, in detail, by reason of that very tendency to return which is to effect its accomplishment in general. Multiplicity is the object; but there is nothing to prevent proximate atoms, from lapsing at once, through the now satisfiable tendency –before the fulfilment of any ends proposed in multiplicity –into absolute oneness among themselves: – there is nothing to impede the aggregation of various unique masses, at various points of space: – in other words, nothing to interfere with the accumulation of various masses, each absolutely One.

For the effectual and thorough completion of the general design, we thus see the necessity for a repulsion of limited capacity –a separate something which, on withdrawal of the diffusive Volition, shall at the same time allow the approach, and forbid the junction, of the atoms; suffering them infinitely to approximate, while denying them positive contact; in a word, having the power –up to a certain epoch –of preventing their Coalition, but no ability to interfere with their Coalescence in any respect or degree. The repulsion, already considered as so peculiarly limited in other regards, must be understood, let me repeat, as having power to prevent absolute coalition, only up to a certain epoch. Unless we are to conceive that the appetite for Unity among the atoms is doomed to be satisfied never; –unless we are to conceive that what had a beginning is to have no end –a conception which cannot really be entertained, however much we may talk or dream of entertaining it – we are forced to conclude that the repulsive influence imagined, will, finally –under pressure of the Uni-tendency collectively applied, but, never and in no degree until, on fulfilment of the Divine purposes, such collective application shall be naturally made –yield to a force which, at that ultimate epoch, shall be the superior force precisely to the extent required, and thus permit the universal subsidence into the inevitable, because original and therefore normal, One. –The conditions here to be reconciled are difficult indeed: –we cannot even comprehend the possibility of their conciliation; –nevertheless, the apparent impossibility is brilliantly suggestive.

That the repulsive something actually exists, we see. Man neither employs, nor knows, a force sufficient to bring two atoms into contact. This is but the well-established proposition of the impenetrability of matter. All Experiment proves –all Philosophy admits it. 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 a consideration of 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 fact, while the tendency of the diffused atoms to return into Unity, will be recognized, at once, as the principle of the Newtonian Gravity, what I have spoken of as a repulsive influence prescribing limits to the (immediate) satisfaction of the tendency, will be understood as that which we have been in the practice of designating now as heat, now as magnetism, now as electricity; displaying our ignorance of its awful character in the vacillation of the phraseology with which we endeavor to circumscribe it.

Calling it, merely for the moment, electricity, we know that all experimental analysis of electricity has given, as an ultimate result, the principle, or seeming principle, heterogeneity. Only where things differ is electricity apparent; and it is presumable that they never differ where it is not developed at least, if not apparent. Now, this result is in the fullest keeping with that which I have reached unempirically. The design of the repulsive influence I have maintained to be that of preventing immediate Unity among the diffused atoms; and these atoms are represented as different each from each. Difference is their character –their essentiality –just as no-difference was the essentiality of their course. When we say, then, that an attempt to bring any two of these atoms together would induce an effort, on the part of the repulsive influence, to prevent the contact we may as well use the strictly convertible sentence that an attempt to bring together any two differences will result in a development of electricity. All existing bodies, of course, are composed of these atoms in proximate contact, and are therefore to be considered as mere assemblages of more or fewer differences; and the resistance made by the repulsive spirit, on bringing together any two such assemblages, would be in the ratio of the two sums of the differences in each: –an expression which, when reduced, is equivalent to this: –The amount of electricity developed on the approximation of two bodies, is proportional to the difference between the respective sums of the atoms of which the bodies are composed. That no two bodies are absolutely alike, is a simple corollary from all that has been here said. Electricity, therefore, existing always, is developed whenever any bodies, but manifested only when bodies of appreciable difference, are brought into approximation.