A Female Genius: How Ada Lovelace Started the Computer Age (14 page)

Babbage got up from his chair, wished his Prime Minister good morning, and abruptly left the room.

Presumably Ada very quickly heard from Babbage about Peel’s rejection. We can readily imagine Ada being sympathetic, but what happened when Babbage met Peel can only have reinforced Ada’s conviction that Babbage needed some significant help to advance the interests of the Analytical Engine in the circles of influential people Babbage needed on his side. We can see this clearly from the period from June to September 1843, which is the best documented one of Ada’s friendship with Babbage.

After Menabrea’s article was published in the Swiss journal
Bibliothèque Universelle de Genève
in October 1842, Babbage is known to have scribbled a personal note in his own papers on February 7 1843, stating that he had had a meeting with Ada ‘under new circumstances’. While it seems likely that this was relating to Ada’s involvement in the Menabrea translation, we can’t know this for certain. It could also be his dashed hopes after the disastrous meeting with Peel. Ada did not start work on her own, additional, material until May or June, but it seems likely that by February 1843 she had drafted her translation of Menabrea’s article.

Ada’s translation sets out clearly the background of Babbage’s new Engine and explains how even the finest mathematical minds have been unable to translate even simple mathematics into a machine that executes in numbers what mathematicians describe on paper in mathematical symbols.

The rigid exactness of those laws which regulate numerical calculations must frequently have suggested the employment of material instruments, either for executing the whole of such calculations or for abridging them; and thence have arisen several inventions having this object in view.

For instance, the much-admired machine of Pascal is now simply an object of curiosity, which, whilst it displays the powerful intellect of its inventor, is yet of little utility in itself. Its powers extended no further than the execution of the first four operations of arithmetic, and indeed were in reality confined to that of the first two, since multiplication and division were the result of a series of additions and subtractions.

The chief drawback hitherto on most of such machines is, that they require the continual intervention of a human agent to regulate their movements, and thence arises a source of errors; so that, if their use has not become general for large numerical calculations, it is because they have not in fact resolved the double problem which the question presents, that of
correctness
in the results, united with
economy
of time.

The text continues to underline the significance of and credits Babbage with ‘the realisation of a gigantic idea.’ His machine was ‘capable of executing not merely arithmetical calculations, but even all those of analysis.’

What is meant here is the field of mathematics that is called analytical (or Leibnizian) calculus, which the Analytical Society that Babbage had been part of had so successfully introduced at Cambridge University. This type of mathematics works with numbers that are infinite (beyond expression in digits) or numbers whose fraction is infinitely small and can never be expressed in sufficient number of digits. A mere calculating machine, such as the original Difference Engine, would only be able to start with incomplete numbers and its calculations would therefore by definition be next to useless to cover this important area of mathematics.

If Babbage could have got it to work on cogwheels, the Analytical Engine would have been amazing. This new machine would in effect be able to work correctly both with exact numbers as well as ‘imaginary’ numbers, that is to say numbers you can only approximate and never express exactly in reality.

The imagination is at first astounded at the idea of such an undertaking; 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.

Ada did not need to be a genius mathematician to translate Menabrea’s article itself, but she did need to have a good understanding of what Menabrea was talking about, and also – this is not a trivial observation – she obviously needed to love the subject of the Analytical Engine, or she would hardly have wanted to do the translation in the first place.

Altogether, Menabrea’s translation is about 8,000 words in length. It may seem short, but given the number of mathematical formulas and highly technical detail it is a dense and rich brew, so much so that the article contains one small error in the translation that neither Ada nor Babbage picked up. The French original reads at some point ‘
Cependant, lorsque le cos de …
’ It should have read ‘
Cependant, lorsque le cas de …
’ But the printer had swapped the French word ‘cas’ with the word ‘cos’, a mathematical symbol. The result is something that leads to mathematical gibberish in the context of the machine, which some have used to argue against Ada’s brilliance, though not in the same breath against Babbage’s – perhaps because it would be hard to defend the claim in the face of his well-documented achievements in so many areas other than the Analytical Engine, his lifetime project.

Babbage’s reference to Ada in
Passages
was supplemented, and indeed complemented, by a paragraph he wrote to Ada’s son Byron on June 14 1857, nearly five years after Ada’s death, and seven years before
Passages
was published. In the letter Babbage observed to Byron Lovelace:

In the memoir of Mr Menabrea and still more in the excellent Notes appended by your mother you will find the only comprehensive view of the powers of the Analytical Engine which the mathematicians of the world have yet expressed.

Ada appended her own writing about the Analytical Engine as
Notes by the Translator
immediately following her translation of Menabrea’s article. Ada’s own material has come to be known as her
Notes
. There are seven of them, given successive letters from A to G. Altogether the
Notes
are about 20,000 words long, more than twice as long as the translation.

It is important to point out that much of the content of Ada’s
Notes
is highly technical material about how the Analytical Engine is designed to operate and carry out its functions.

However, in addition to technical writings,
Ada’s
Notes
include general observations about the Analytical Engine. It is these that show the real nature of Ada’s achievement in an accessible way.

This passage, close to the beginning of Ada’s
Notes
, shows her her passion for explaining in succinct terms to the world what Babbage’s Analytical Engine is, and what it means:

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to
operations
, as distinguished from
the objects operated upon
and from the
results
of the operations performed upon those objects, is very strikingly defined and separated.

It is well to draw attention to this point, not only because its full appreciation is essential to the attainment of any very just and adequate general comprehension of the powers and mode of action of the Analytical Engine, but also because it is one which is perhaps too little kept in view in the study of mathematical science in general.

It is, however, impossible to confound it with other considerations, either when we trace the manner in which that engine attains its results, or when we prepare the data for its attainment of those results.

It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with
operations
should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine.

The confusion, the difficulties, the contradictions which, in consequence of a want of accurate distinctions in this particular, have up to even a recent period encumbered mathematics in all those branches involving the consideration of negative and impossible quantities, will at once occur to the reader who is at all versed in this science, and would alone suffice to justify dwelling somewhat on the point, in connection with any subject so peculiarly fitted to give forcible illustration of it as the Analytical Engine.

What Ada is emphasising here is the clear distinction between data and processing: a distinction we tend to take for granted today, but which – like so much of her thinking about computers – was in her own day not only revolutionary but truly visionary. In none of Babbage’s writings does he consider that the new Engine might be used for anything other than mathematics. He himself, with slight condescension, acknowledges this by calling Ada his ‘interpretess.’

Ada continues:

It may be desirable to explain, that by the word
operation
, we mean
any process which alters the mutual relation of two or more things
, be this relation of what kind it may. This is the most general definition, and would include all subjects in the universe.

In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the
results
of operations are those peculiar results which correspond to the nature of the subjects of operation.

But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.

Ada is here seeking to do nothing less than invent the science of computing, and separate it from the science of mathematics. What she calls ‘the science of operations’ is indeed in effect computing.

Unlike Babbage, Ada saw the practical uses of the Analytical Engine and foresaw the digitisation of music as CDs or synthesisers and their ability to generate music.

The operating mechanism can even be thrown into action independently of any object to operate upon (although of course no
result
could then be developed).

Again, 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.

Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

This most impressive passage shows how Ada sees mathematics and its relationship to philosophy in general. The Cambridge academic and novelist C.P. Snow in 1959 would lament in a lecture called The Two Cultures that our society divides itself into science or the humanities. But in this passage the daughter of Byron – perhaps to the horror of modern poets – writes that mathematics provides the invisible threads that can express everything in the tangible world. Here she leaps well beyond Babbage’s Analytical Engine and how it expressed mathematics in the real world, to a philosophical topic that is hotly debated by leading scientists today, and advanced practically by the increasing sophistication of software companies such as Google, who are mining an ever-expanding ocean of data that no human could ever generate.

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 connection 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.

This 158-word sentence is very likely one of the longest sentences in the history of science, but it is also one of the most intriguing. Ada succeeds in this one sentence in linking mathematics, science, religion and philosophy.

In the next passage, which follows immediately on from the above, Ada’s grasp of the vital point that the Analytical Engine and the Jacquard loom are, at heart, doing the same kind of thing is a wonderful and enormous conceptual leap that stakes her claim to be a major figure – and unquestionably the leading female figure – in the prehistory of the computer. It shows that she understood exactly what a computer was.

In a terse paragraph she explains (perhaps better than Babbage ever could, who as designer saw many trees but perhaps no longer the forest itself) the essential relationship between the Analytical Engine and the Jacquard loom and how it is different from the earlier invention.

The distinctive characteristic of the Analytical Engine… is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs…