A Few Quotes from Sketch of the Analytical Engine Invented by Charles Babbage

by Martin F. Johansen, 2013

Here are a few selected quotes from Sketch of the Analytical Engine Invented by Charles Babbage published in 1843. This 30,000 word article is jam-packed with fundamental notions of computer science. The first part of the article was based on a presentation Babbage held in Turin, Italy in 1840 on the Analytical Engine. Based on these presentations, Luigi Menabrea wrote up the first part of the article in French and published it in 1842. In the beginning of the article he writes:

"The illustrious inventor having been kind enough to communicate to me some of his views on this subject during a visit he made at Turin [...]"

The following quote from Babbage's autobiography explains the circumstances of the translation of Menabrea's article by Ada Lovelace and the addition of her notes:

"[...] the late Countess of Lovelace informed me that she had translated the memoir of Menabrea. I asked why she had not herself written an original paper on a subject with which she was so intimately acquainted? To this Lady Lovelace replied that the thought had not occurred to her. I then suggested that she should add some notes to Menabrea's memoir; an idea which was immediately adopted.

We discussed together the various illustrations that might be introduced: I suggested several, but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.

The notes of the Countess of Lovelace extend to about three times the length of the original memoir. Their author has entered fully into almost all the very difficult and abstract questions connected with the subject."

Here follow some selection notes from this work. I have placed some remarks in square brackets.

Human Tasks versus Computer Tasks

"Those labours which belong to the various branches of the mathematical sciences, although on first consideration they seem to be the exclusive province of intellect, may, nevertheless, be divided into two distinct sections; one of which may be called the mechanical, because it is subjected to precise and invariable laws, that are capable of being expressed by means of the operations of matter; while the other, demanding the intervention of reasoning, belongs more specially to the domain of the understanding. This admitted, we may propose to execute, by means of machinery, the mechanical branch of these labours, reserving for pure intellect that which depends on the reasoning faculties."
"The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths. Its province is to assist us in making available what we are already acquainted with."
"[...] the machine is not a thinking being, but simply an automaton which acts according to the laws imposed upon it."


"It is desirable to guard against the possibility of exaggerated ideas that might arise as to the powers of the Analytical Engine."
"[...] what discouragement does the perspective of a long and arid computation cast into the mind of a man of genius, who demands time exclusively for meditation, and who beholds it snatched from him by the material routine of operations!"
"[...] it is by the laborious route of analysis that he [the genious] must reach truth; but he cannot pursue this unless guided by numbers; for without numbers it is not given us to raise the veil which envelopes the mysteries of nature."
"[...] the idea of constructing an apparatus capable of aiding human weakness in such researches, is a conception which, being realized, would mark a glorious epoch in the history of the sciences."
"The confidence which the genius of Mr. Babbage must inspire, affords legitimate ground for hope that this enterprise will be crowned with success [...]"
"[...] more do we hope, that for the honour of our country's reputation in the future pages of history, these causes will not lead to the completion of the undertaking by some other nation or government."

Fundamentals of Computer Science

"[...] the mill is that portion of the machine which works, and the columns of Variables constitute that where the results are represented and arranged."
"[...] the mechanism must include an infinite number of dials, which would in fact render the thing impossible."
"[...] the cards are able to reproduce all the operations which intellect performs in order to attain a determinate result, if these operations are themselves capable of being precisely defined."
"The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations."
"[...] it would be a mistake to suppose that because its results are given in the notation of a more restricted science, its processes are therefore restricted to those of that science. The object of the engine is in fact to give the utmost practical efficiency to the resources of numerical interpretations of the higher science of analysis, while it uses the processes and combinations of this latter."
"[...] it might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine."
"[...] the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves."
"There are some cases which entail cycles of cycles of cycles, to an indefinite extent. Such cases are usually very complicated, and they are of extreme interest when considered with reference to the engine."

Productive Advantages

"[...] it [the Analytical Engine] will afford the following advantages:—First, rigid accuracy. [...] Secondly, economy of time [...] Thirdly, economy of intelligence [..]"
"[...] the engine, from its capability of performing by itself all these purely material operations, spares intellectual labour, which may be more profitably employed."
"Provided we know the series of operations to be gone through, that is sufficient [...] herein may reside a latent value of such an engine almost incalculable in its possible ultimate results."

Scientific Importance

"The imagination is at first astounded at the idea of such an undertaking [inventing the computer]; but the more calm reflection we bestow on it, the less impossible does success appear, and it is felt that it may depend on the discovery of some principle so general, that, if applied to machinery, the latter may be capable of mechanically translating the operations which may be indicated to it by algebraical notation."

Mathematical Philosophy

"Those who view mathematical science, not merely as a vast body of abstract and immutable truths, whose intrinsic beauty, symmetry and logical completeness, when regarded in their connexion together as a whole, entitle them to a prominent place in the interest of all profound and logical minds, but as possessing a yet deeper interest for the human race, when it is remembered that this science constitutes the language through which alone we can adequately express the great facts of the natural world, and those unceasing changes of mutual relationship which, visibly or invisibly, consciously or unconsciously to our immediate physical perceptions, are interminably going on in the agencies of the creation we live amidst: those who thus think on mathematical truth as the instrument through which the weak mind of man can most effectually read his Creator's works, will regard with especial interest all that can tend to facilitate the translation of its principles into explicit practical forms."

Copyright © 2013, Martin F. Johansen