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BABBAGE'S CALCULATING MACHINE.
“Now, it must be remarked, 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 100,000,002d 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 to all the succeeding laws; 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 yet enable us to predict the periods at which the more distant laws will be introduced.”! *
This illustration must not be taken as suborned to establish more than it strictly proves. It is, doubtless, not only a wise but a necessary provision in our nature, that the constancy of any sequence in the past should inspire us with faith that it will continue in the future. Without such faith, the common economy of life would stand still. Uncertain whether to-morrow's sun would rise as did the sun of to-day, or whether the seasons would continue their regular alternations, our lives would pass amid scruples and hesitations. All calculation would be baffled; all industry would sink under discouragement.
The chances, so incalculably great, in most cases, as
*“ Ninth Bridgewater Treatise," by Charles Babbage, 2d ed., London, 1838, pp. 34 to 39. The passage bas been already quoted by another, in connection with a physiological question.
THAT WHICH HAS BEEN
for all practical purposes to amount to certainty, are in favor of the constancy of natural sequences. The corresponding expectations, common to man with the lower animals, are instinctive.
All this is not only true, but it is palpable to our overy-day consciousness,-a truth whereupon is based the entire superstructure of our daily hopes and actions. The wheel, with its divided surface, ever revolving, does present, to human eyes, uniformity of sequence, age after age; and when the unbroken chain has run on from thousands to millions, we are justified, amply justified, in expecting that the next term will obey the same law that determined its antecedent. All I have sought to do in this argument is to keep alive in our minds the conviction, that there may be a hundred million and second term, at which the vast induction fails; and that, if such does appear, we have no right to conclude that the change, unprecedented as it must seem to us, is not as necessary a consequence of an original adjustment as was the seemingly infinite uniformity that preceded it.
The extreme rarity of what I have called changebearing laws of nature is to be conceded; but not the improbability of their existence. In a world all over which is stamped the impress of progress, and which, for aught we know, may continue to endure through countless ages, laws of such a character, self-adapted to a changeful state of things, may be regarded as of likely occurrence.*
* Modern science is revealing to us glimpses that may brighten into positive proof of this hypothesis. Sir John Herschel, writing to Lyell the geologist, and alluding to what he calls that “mystery of mysteries, the replacement of extinct species by others," says,
“For my own part, I cannot but think it an inadequate conception of the Creator, to assume it as granted that His combinations are exhausted upon any one of the theaters of their former exercise; though in this, as in all
MAY NOT ALWAYS BE.
But it suffices for the present argument to establish the possibility of such laws. If they are possible, then, in regard to any alleged occurrence of modern times, (strange in character, perhaps, but coming to us well attested, we are barred from asserting that, because contrary to past experience, it would be miraculous, and is consequently impossible. We are as strictly barred from this as are the visitors to Mr. Babbage's engine from pronouncing, when the long uniformity of a past sequence is unexpectedly violated, that the inventor has been dealing in the black art and is trenching on the supernatural.*
His other works, we are led by all analogy to suppose that He operates through a series of intermediate causes, and that, in consequence, the origination of fresh species, could it ever come under our cognizance, would be found to be a natural, in contradistinction to a miraculous, process ; although we may perceive no indication of any process, actually in progress, which is likely to issue in such a result.”—Herschel's letter of Feb. 20, 1836, published in Appendix to Babbage's work above cited, p. 226.
* Reading this chapter more than a year after it was written-namely, in March, 1859—to a private circle of friends in London, one of them called my attention, in connection with its argument, to an article then just published in the (London) Athenæum, attributed (correctly, I believe) to Professor De Morgan, of the London University. It proved to be a review of that strange self-commitment of an able man, virtually following Hume's false lead, Faraday's extraordinary lecture on “Mental Training," delivered, before Prince Albert, at the Royal Institution. And it was a satisfaction to me, on referring to the article, to find, from the pen of one of the first mathematicians of Europe, such a paragraph as the following:
“ The natural philosopher, when he imagines a physical impossibility which is not an inconceivability, merely states that his phenomenon is against all that has been hitherto known of the course of nature. Before he can compass an impossibility, he has a huge postulate to ask of his reader or hearer, a postulate which nature never taught: it is that the future is always to agree with the past. How do you know that this sequence of phenomena always will be? Answer, Because it must be. But how do you know that it must be? Answer, Because it always has been. But then, even granting that it always has been, how do you know that what always has been always will be? Answer, I feel my mind compelled to that conclusion. And how do you know that the leanings of your mind are always toward truth? Because I am infallible, the answer ought to
Nay, there are far stronger reasons against such presumption in our case than in that of the supposed spectator before the calculating machine. He has observed the entire series, even to the hundred millionth term. How insignificant the fraction that has passed before our eyes! How imperfect our knowledge of that portion which has passed before the eyes of our ancestors ! How insufficient, then, are the data for a decision that the past uniformity has been unbroken!
And herein, beyond all question, do we find a source of error infinitely more frequent than is the failure to recognize a change-bearing law. I have set forth the existence of such laws as a possibility beyond human denial; yet only as an argument to meet an extreme case,-a case so exceedingly rare that, notwithstanding its certain possibility, it may never present itself to our observation. So far as the scope of our limited experience extends, the argument, how undeniable soever, may have no practical application. It may never be our fortune to stand before the Great Machine at the moment when the hundred million and second term, unexpectedly presenting itself, indicates a departure from all former precedent.
Among the laws which we see at work, it may chance that we shall never observe one which some ancestor has not seen in operation already. Nay, that chance is a probable one. In other words, if a phenomenon actually present itself which we are tempted to regard as a violation of natural law, it is more likely-ten thousand to one that a similar phenomenon has already shown itself more or less frequently in the past, than that it presents itself now for the first time in the history of our race. be: but this answer is never given.”—Atheneum, No. 1637, of March 12, 1859, p. 350.
AN ERROR OF TWO PHASES.
The source of our error, then, when we mistake the extraordinary for the miraculous, is far more frequently in our ignorance of what has been than in our false conceptions of what may be.
The error itself, from either source arising, is a grave one, entailing important practical consequences, which have varied in their prevailing character at different periods of the world. In our day the usual result is incredulity, in advance of examination, as to all phenomena that seem, to our limited experience, incapable of rational explanation. One or two centuries
ago the same error often assumed a different form. When a phenomenon presented itself to the men of that day, the cause of which they did not comprebend, and which seemed to them, for that reason, out of the course of nature, they were wont to take it for granted that it happened either through the agency of the devil, or else by special interposition of the Deity in attestation of some contested truth. Thus, Racine relates what he calls the miraculous cure of Mademoiselle Perrier, the niece of Pascal, and then an inmate of the celebrated Convent of Port Royal; and Pascal himself seeks to prove that this miracle was necessary to religion, and was performed in justification of the nuns of that convent, ardent Jansenists, and for that reason under the ban of the Jesuits. La Place, treating the whole as imposture, adduces it as a lamentable example—"afflicting to see and painful to read”—of that blind credulity which is sometimes the weakness of great men.*
* See Introduction to his “ Théorie analytique des Probabilités," (7th vol. of his works, Paris, 1847,) p. 95.
For the story itself the reader is referred to Racine's "Abrégé de l'Histoire de Port Royal,” Paris, 1693. The alleged miracle occurred in 1656. The young girl, Perrier, bad been afflicted with a lachrymal fistula. To the diseased eye was applied a relic,-said to be a thorn from the crown which the Jewish soldiers in mockery placed on the head of Christ. The