“Now, reader,” says Mr. Babbage, “let me ask you how long you will have counted before you are firmly convinced that the engine has been so adjusted, that it will continue, while its motion is maintained, to produce the same series of natural numbers? Some minds are so constituted, that, after passing the first hundred terms, they will be satisfied that they are acquainted with the law. After seeing five hundred terms few will doubt, and after the fifty thousandth term the propensity to believe that the succeeding term will be fifty thousand and one, will be almost irresistible. That term will be fifty thousand and one; and the same regular succession will continue; the five millionth and the fifty millionth term will still appear in their expected order, and one unbroken chain of natural numbers will pass before your eyes, from one up to one hundred million.
“True to the vast induction which has been made, the next succeeding term will be one hundred million and one; but the next number presented by the rim of the wheel, instead of being one hundred million and two, is one hundred million ten thousand and two. The whole series from the commencement being thus,—
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| . | ||
| . . | ||
| . . . | ||
| 99,999,999 | ||
| 100,000,000 | ||
| regularly as far as | 100,000,001 | |
| 100,010,002 | the law changes. | |
| 100,030,003 | ||
| 100,060,004 | ||
| 100,100,005 | ||
| 100,150,006 | ||
| 100,210,007 | ||
| 100,280,008 | ||
| . . . | ||
| . . . | ||
| . . . |
“The law which seemed at first to govern this series failed at the hundred million and second term. This term is larger than we expected by 10,000. The next term is larger than was anticipated by 30,000, and the excess of each term above what we had expected forms the following table:—
| 10,000 |
| 30,000 |
| 60,000 |
| 100,000 |
| 150,000 |
| . . . |
| . . . |
being, in fact, the series of triangular numbers, [208] each multiplied by 10,000.
“If we now continue to observe the numbers presented by the wheel, we shall find, that for a hundred, or even for a thousand terms, they continue to follow the new law relating to the triangular numbers; but after watching them for 2761 terms, we find that this law fails in the case of the 2762d term.
“If we continue to observe, we shall discover another law then coming into action, which also is dependent, but in a different manner, on triangular numbers. This will continue through about 1430 terms, when a new law is again introduced which extends over about 950 terms, and this, too, like all its predecessors, fails, and gives place to other laws, which appear at different intervals.
“Now it must be observed that the law that each number presented by the engine is greater by unity than the preceding number, which law the observer had deduced from an induction of a hundred million instances, was not the true law that regulated its action, and that the occurrence of the number 100,010,002 at the 100,000,002nd term was as necessary a consequence of the original adjustment, and might have been as fully foreknown at the commencement, as was the regular succession of any one of the intermediate numbers to its immediate antecedent. The same remark applies to the next apparent deviation from the new law, which was founded on an induction of 2761 terms, and also to the succeeding law, with this limitation only—that, whilst their consecutive introduction at various definite intervals, is a necessary consequence of the mechanical structure of the engine, our knowledge of analysis does not enable us to predict the periods themselves at which the more distant laws will be introduced.”
It is not difficult to apply the philosophy of this passage to the question under consideration. It must be borne in mind that the gestation of a single organism is the work of but a few days, weeks, or months; but the gestation (so to speak) of a whole creation is a matter probably involving enormous spaces of time. Suppose that an ephemeron, hovering over a pool for its one April day of life, were capable of observing the fry of the frog in the water below. In its aged afternoon, having seen no change upon them for such a long time, it would be little qualified to conceive that the external branchiæ of these creatures were to decay, and be replaced by internal lungs, that feet were to be developed, the tail erased, and the animal then to become a denizen of the land. Precisely such may be our difficulty in conceiving that any of the species which people our earth is capable of advancing by generation to a higher type of being. During the whole time which we call the historical era, the limits of species have been, to ordinary observation, rigidly adhered to. But the historical era is, we know, only a small portion of the entire age of our globe. We do not know what may have happened during the ages which preceded its commencement, as we do not know what may happen in ages yet in the distant future. All, therefore, that we can properly infer from the apparently invariable production of like by like is, that such is the ordinary procedure of nature in the time immediately passing before our eyes. Mr. Babbage’s illustration powerfully suggests that this ordinary procedure may be subordinate to a higher law which only permits it for a time, and in proper season interrupts and changes it. We shall soon see some philosophical evidence for this very conclusion.