“Yes, Kepler was essentially a theorist; but this title, now of so much sanctity, was, in those ancient days, a designation of supreme contempt. It is only now that men begin to appreciate that divine old man—to sympathize with the prophetical and poetical rhapsody of his ever–memorable words. For my part,” continues the unknown correspondent, “I glow with a sacred fire when I even think of them, and feel that I shall never grow weary of their repetition:—in concluding this letter, let me have the real pleasure of transcribing them once again:—‘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.’”
Here end my quotations from this very unaccountable and, perhaps, somewhat impertinent epistle; and perhaps it would be folly to comment, in any respect, upon the chimerical, not to say revolutionary, fancies of the writer—whoever he is—fancies so radically at war with the well–considered and well–settled opinions of this age. Let us proceed, then, to our legitimate thesis, The Universe.
This thesis admits a choice between two modes of discussion:—We may ascend or descend. Beginning at our own point of view—at the Earth on which we stand—we may pass to the other planets of our system—thence to the Sun—thence to our system considered collectively—and thence, through other systems, indefinitely outwards; or, commencing on high at some point as definite as we can make it or conceive it, we may come down to the habitation of Man. Usually—that is to say, in ordinary essays on Astronomy—the first of these two modes is, with certain reservation, adopted:—this for the obvious reason that astronomical facts, merely, and principles, being the object, that object is best fulfilled in stepping from the known because proximate, gradually onward to the point where all certitude becomes lost in the remote. For my present purpose, however,—that of enabling the mind to take in, as if from afar and at one glance, a distinct conception of the individual Universe—it is clear that a descent to small from great—to the outskirts from the centre (if we could establish a centre)—to the end from the beginning (if we could fancy a beginning) would be the preferable course, but for the difficulty, if not impossibility, of presenting, in this course, to the unastronomical, a picture at all comprehensible in regard to such considerations as are involved in quantity—that is to say, in number, magnitude and distance.
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.