Passages from the Life of a Philosopher

my subsequent labours, to which I attach great importance. First, I have been led to conceive the most important elements of another Engine upon a new principle (the details of which are reduced accurately to paper), the power of which over the most complicated analytical operations appears nearly unlimited; but no portion of which is yet commenced. I have called this engine, in contradistinction to the other, the Analytical Engine. Secondly, I have invented and brought to maturity a system of signs for the explanation of machinery, which I have called Mechanical Notation, by means of which the drawings, the times of action, and the trains for the transmission of force, are expressed in a language at once simple and concise. Without the aid of this language I could not have invented the Analytical Engine; nor do I believe that any machinery of equal complexity can ever be contrived without the assistance of that or of some other equivalent language. The Difference Engine No. 2, to which I shall presently refer, is entirely described by its aid. Thirdly, in labouring to perfect this Analytical Machine of greater power and wider range of computation, I have discovered the means of simplifying and expediting the mechanical processes of the first or Difference Engine. After what has passed, I cannot expect the Government to undertake the construction of the Analytical Engine, and I do not offer it for that purpose. It is not so matured as to {105} enable any other person, without long previous training and application, even to attempt its execution; and on my own part, to superintend its construction would demand an amount of labour, anxiety, and time which could not, after the treatment I have received, be expected from me. I therefore make no such offer. But that I may fulfil to the utmost of my power the original expectation that I should be able to complete, for the Government, an Engine capable of calculating astronomical and nautical Tables with perfect accuracy, such as that which is described in the Reports of the Royal Society, I am willing to place at the disposal of Government (if they will undertake to execute a new Difference Engine) all those improvements which I have invented and have applied to the Analytical Engine. These comprise a complete series of drawings and explanatory notations, finished in 1849, of the Difference Engine No. 2,—an instrument of greater power as well as of greater simplicity than that formerly commenced, and now in the possession of the Government. I have sacrificed time, health, and fortune, in the desire to complete these Calculating Engines. I have also declined several offers of great personal advantage to myself. But, not­with­stand­ing the sacrifice of these advantages for the purpose of maturing an engine of almost in­tel­lec­tual power, and after expending from my own private fortune a larger sum than the Government of England has spent on that machine, the execution of which it only commenced, I have received neither an acknowledgment of my labours, nor even the offer of those honours or rewards which are allowed to fall within the reach of men who devote themselves to purely scientific investigations. I might, perhaps, advance some claims to consideration, founded on my works and {106} cont­ri­bu­tions in aid of various departments of industrial and physical science,—but it is for others to estimate those services. I now, however, simply ask your Lordship to do me the honour to consider this statement and the offer I make. I prefer no claim to the distinctions or the advantages which it is in the power of the Crown or the Government to bestow. I desire only to discharge whatever imagined obligation may be supposed to rest upon me, in connexion with the original undertaking of the Difference Engine; though I cannot but feel that whilst the public has already derived advantage from my labours, I have myself experienced only loss and neglect. If the work upon which I have bestowed so much time and thought were a mere triumph over mechanical difficulties, or simply curious, or if the execution of such engines were of doubtful practicability or utility, some justification might be found for the course which has been taken; but I venture to assert that no mathematician who has a reputation to lose will ever publicly express an opinion that such a machine would be useless if made, and that no man distinguished as a Civil Engineer will venture to declare the construction of such machinery impracticable. The names appended to the Report of the Committee of the Royal Society fully justify my expressing this opinion, which I apprehend will not be disputed. And at a period when the progress of physical science is obstructed by that exhausting in­tel­lec­tual and manual labour, indispensable for its advancement, which it is the object of the Analytical Engine to relieve, I think the application of machinery in aid of the most complicated and abstruse calculations can no longer be deemed unworthy of the attention of the country. In fact, there is no reason why mental as {107} well as bodily labour should not be economized by the aid of machinery. With these views I have addressed your Lordship, as the head of the Government; and whatever may be my sense of the injustice that has hitherto been done me, I feel, in laying this rep­re­sen­ta­tion before your Lordship, and in making the offer I now make, that I have discharged to the utmost limit every implied obligation I originally contracted with the country. I have the honour to be, &c., &c., &c., CHARLES BABBAGE. Dorset Street, Manchester Square. June 8, 1852. As this question was one of finance and of calculation, the sagacious Premier adroitly turned it over to his Chancellor of the Exchequer—that official being, from his office, supposed to be well versed in both subjects. The opinion pronounced by the novelist and financier was, “That Mr. Babbage’s projects appear to be so indefinitely expensive, the ultimate success so problematical, and the expenditure certainly so large and so utterly incapable of being calculated, that the Government would not be justified in taking upon itself any further liability.”—Extract from the Reply of Earl Derby to the application of the Earl of Rosse, K.P., President of the Royal Society. 〈REFERRED TO THE CHANCELLOR OF THE EXCHEQUER.〉 The answer of Lord Derby to Lord Rosse was in substance— That he had consulted the Chancellor of the Exchequer, who pronounced Mr. Babbage’s project as— {108} 1. “Indefinitely expensive.” 2. “The ultimate success problematical.” 3. “The expenditure utterly incapable of being calculated.” 1. With regard to the “indefinite expense.” Lord Rosse had proposed to refer this question to the President of the Institution of Civil Engineers, who would have given his opinion after a careful examination of the drawings and notations. These had not been seen by the Chancellor of the Exchequer; and, if seen by him, would not have been comprehended. The objection that its success was “problematical” may refer either to its mechanical construction or to its math­e­mat­i­cal principles. Who, possessing one grain of common sense, could look upon the unrivalled workmanship of the then existing portion of the Difference Engine No. 1, and doubt whether a simplified form of the same engine could be executed? As to any doubt of its math­e­mat­i­cal principles, this was excusable in the Chancellor of the Exchequer, who was himself too practically acquainted with the fallibility of his own figures, over which the severe duties of his office had stultified his brilliant imagination. Far other figures are dear to him—those of speech, in which it cannot be denied he is indeed pre-eminent. Any junior clerk in his office might, however, have told him that the power of computing Tables by differences merely required a knowledge of simple addition. As to the impossibility of ascertaining the expenditure, this merges into the first objection; but a poetical brain must be pardoned when it repeats or amplifies. I will recall to the ex-Chancellor of the Exchequer what Lord Rosse really {109} proposed, namely, that the Government should take the opinion of the President of the Institution of Civil Engineers upon the question, whether a contract could be made for constructing the Difference Engine, and if so, for what sum. But the very plan proposed by Lord Rosse and refused by Lord Derby, for the construction of the English Difference Engine, was adopted some few years after by another administration for the Swedish Difference Engine. Messrs. Donkin, the eminent Engineers, made an estimate, and a contract was in consequence executed to construct for Government a fac-simile of the Swedish Difference Engine, which is now in use in the department of the Registrar-General, at Somerset House. There were far greater mechanical difficulties in the production of that machine than in the one the drawings of which I had offered to the Government. From my own experience of the cost of executing such works, I have no doubt, although it was highly creditable to the skill of the able firm who constructed it, but that it must have been commercially unprofitable. Under such circumstances, surely it was harsh on the part of the Government to refuse Messrs. Donkin permission to exhibit it as a specimen of English workmanship at the Exhibition of 1862. 〈HIS OPINION WORTHLESS.〉 But the machine upon which everybody could calculate, had little chance of fair play from the man on whom nobody could calculate. If the Chancellor of the Exchequer had read my letter to Lord Derby, he would have found the opinion of the Committee of the Royal Society expressed in these words:— “They consider the former [the abstract math­e­mat­i­cal principle] as not only sufficiently clear in itself, but as already admitted and acted on by the Council in their former proceedings. {110} “The latter [its public utility] they consider as obvious to every one who considers the immense advantage of accurate numerical tables in all matters of calculation, especially in those which relate to astronomy and navigation.”—Report of the Royal Society, 12th Feb., 1829. Thus it appears:— 1st. That the Chancellor of the Exchequer presumed to set up his own idea of the utility of the Difference Engine in direct opposition to that of the Royal Society. 2nd. That he refused to take the opinion of the highest mechanical authority in the country on its probable cost, and even to be informed whether a contract for its construction at a definite sum might not be attainable: he then boldly pronounced the expense to be “utterly incapable of being calculated.” 〈DIFFERENCE ENGINE No. 2. FEELS FOR THE CHANCELLOR OF THE EXCHEQUER.〉 This much-abused Difference Engine is, however, like its prouder relative the Analytical, a being of sensibility, of impulse, and of power. It can not only calculate the millions the ex-Chancellor of the Exchequer squandered, but it can deal with the smallest quantities; nay, it feels even for zeros.23 It is as conscious as Lord Derby himself is of the presence of a negative quantity, and it is not beyond the ken of either of them to foresee the existence of impossible ones.24 23 It discovers the roots of equations by feeling whether all the figures in a certain column are zeros. 24 It may be necessary to explain to the unmath­e­mat­i­cal reader and to the ex-Chancellor of the Exchequer that impossible quantities in algebra are something like mare’s-nests in ordinary life. Yet should any unexpected course of events ever raise the {111} ex-Chancellor of the Exchequer to his former dignity, I am sure he will be its friend as soon as he is convinced that it can be made useful to him. It may possibly enable him to un-muddle even his own financial accounts, and to ——— But as I have no wish to crucify him, I will leave his name in obscurity. The Herostratus of Science, if he escape oblivion,