A Female Genius: How Ada Lovelace Started the Computer Age (15 page)

The bounds of
arithmetic
were however outstepped the moment the idea of applying the cards had occurred; and the Analytical Engine does not occupy common ground with mere ‘calculating machines.’

It holds a position wholly its own; and the considerations it suggests are most interesting in their nature. In enabling mechanism to combine together
general
symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the
most abstract
branch of mathematical science.

In perhaps one of the most visionary sentences written during the entire nineteenth century, she lays out what these cards shall be capable of doing by way of programming the machine. Like the pins of Adam Smith, it is hard to imagine how a simple piece of brocade ever went further in history.

A new, a vast, and a powerful language is developed for the future use of analysis, in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind than the means hitherto in our possession have rendered possible. Thus not only the mental and the material, but the theoretical and the practical in the mathematical world, are brought into more intimate and effective connection with each other.

We are not aware of its being on record that anything partaking in the nature of what is so well designated the
Analytical
Engine has been hitherto proposed, or even thought of, as a practical possibility, any more than the idea of a thinking or of a reasoning machine.

She also addresses succinctly the question that had exercised Prime Minister Robert Peel, who may have wondered what all the fuss was about as both Engines generated numbers (or what Ada calls ‘numerical notation’).

Many persons who are not conversant with mathematical studies, imagine that because the business of the engine is to give its results in
numerical notation
, the
nature of its processes
must consequently be
arithmetical
and
numerical
, rather than
algebraical
and
analytical
.

This is an error. The engine can arrange and combine its numerical quantities exactly as if they were
letters
or any other
general
symbols; and in fact it might bring out its results in algebraical
notation
, were provisions made accordingly.

Babbage’s new Engine could do three things: process mathematical formula written in symbols, crunch numbers and calculate algebraical results in literal notation.

It might develop three sets of results simultaneously, viz.
symbolic
results (as already alluded to in Notes A and B),
numerical
results (its chief and primary object); and
algebraical
results in
literal
notation.

This latter however has not been deemed a necessary or desirable addition to its powers, partly because the necessary arrangements for effecting it would increase the complexity and extent of the mechanism to a degree that would not be commensurate with the advantages, where the main object of the invention is to translate into
numerical
language general formulæ of analysis already known to us, or whose laws of formation are known to us.

Nonetheless, the production
algebraical
results in
literal
notation were only excluded from the new Engine for practical reasons. The machine was able to process all three types.

But 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.

While she states what machines like the Engine may be capable of doing in the future subject to the advance of technology, she is quite clear on what the limitations of the current design are. It cannot assist directly with solving theoretical problems in mathematics. The new engine will only be able to manipulate formulas that are known to be true.

It is desirable to guard against the possibility of exaggerated ideas that might arise as to the powers of the Analytical Engine. In considering any new subject, there is frequently a tendency, first, to
overrate
what we find to be already interesting or remarkable; and, secondly, by a sort of natural reaction, to
undervalue
the true state of the case, when we do discover that our notions have surpassed those that were really tenable.

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. This it is calculated to effect primarily and chiefly of course, through its executive faculties…

Nonetheless, she speculates that using the machine in practice will generate numerical data with regularities – such as the Benouille numbers or the number pi perhaps – that will create new theoretical questions.

[B]ut it is likely to exert an
indirect
and reciprocal influence on science itself in another manner.

For, in so distributing and combining the truths and the formulæ of analysis, that they may become most easily and rapidly amenable to the mechanical combinations of the engine, the relations and the nature of many subjects in that science are necessarily thrown into new lights, and more profoundly investigated.

This is a decidedly indirect, and a somewhat
speculative
, consequence of such an invention. It is however pretty evident, on general principles, that in devising for mathematical truths a new form in which to record and throw themselves out for actual use, views are likely to be induced, which should again react on the more theoretical phase of the subject.

There are in all extensions of human power, or additions to human knowledge, various
collateral
influences, besides the main and primary object attained.

It is this last sentence that separates the intelligence of Ada and Babbage most clearly by type. Babbage had (curiously) little interest in the practical impact of his second engine. His restless energy circled mathematics and the practical technical questions that had escaped the great mathematicians Leibniz and Pascal. The question where things might end up, however, was exactly what drove Ada to support Babbage. There were other interesting and brilliant men in London society, but it was the phenomenal potential that could make Babbage’s engine soar beyond any other intellectual endeavour that attracted her to him.

That did not mean that she was easily seduced by grand scientific claims the way her mother clung to new fads like a moth to a flame. It is important that the technical side of Ada’s
Notes
is often very complex. The fact that this chapter quotes from her non-technical passages ought not to obscure the fact of the main thrust of the essay. The
Notes
and the translation relate almost entirely to the functioning of the machine, not its potential. It was precisely the fact that, in her own assessment, the machine could indeed do exactly what Babbage said it could that made her so interested in it and willing to devote herself to Babbage. Rare perhaps for someone who was largely self-taught rather than schooled, she was clear-sighted about the fact that good science is not about making claims but about formulating assertions that can be disproven. Building the machine would test the truth of what she had written.

To return to the executive faculties of this engine: the question must arise in every mind, are they
really
even able to
follow
analysis in its whole extent? No reply, entirely satisfactory to all minds, can be given to this query, excepting the actual existence of the engine, and actual experience of its practical results.

It took Ada to see what the Analytical Engine truly represented in the forward evolution of human technology. It took Ada to realise that the Jacquard loom provided the first example in the history of human technology of the process of digitisation of daily life and not just mathematics, a process that the Analytical Engine was furthering. Ada realised that the Analytical Engine could be applied to
any
process involving the manipulation of information. She saw and wrote that it heralded the birth of a new science, the science of digitising information, one that went well beyond Babbage’s vision, or the imagination of those around her.

It was a science that tantalisingly might easily have been born in the middle of the nineteenth century Britain rather than a hundred years later.

In the final stanza of the third canto of
Childe Harold’s Pilgrimage
, Byron describes Ada as

The child of love, though born in bitterness,

And nurtured in convulsion.

Ada’s character may have suffered from those convulsions in the same way that Babbage’s was affected by a life bathed in praise, but her mind had not. Where science was concerned it was as sharp as Ockham’s razor.

15

Ada and Babbage met on several occasions during the spring and summer of 1843, a time they seem to have thought of each other as kindred spirits. It is known that Ada got Babbage to check over the proofs of the
Notes
.

Babbage says in his autobiography that he offered to do part of the work on the
Notes
‘to save Lady Lovelace the trouble’.

This part of Ada’s
Notes
is ‘Note G’ dealing with the Bernoulli numbers (in his autobiography, Babbage misspells the name as ‘Bernouilli’). Bernoulli numbers themselves are a sequence of rational numbers that are extremely important in various areas of number theory.

Note G is especially relevant to us today. It describes step by step, in detail, the ‘operations’ through which the punched cards would proceed to weave an even longer sequence of Bernoulli numbers on the Analytical Engine. Note G is highly complex, juggling mathematics and technology. Most importantly of all, it is in effect a program containing instructions for a computer. Even though the Analytical Engine has not so far been built, and the effectiveness of the program cannot be tested until one is, Note G is considered by some to be the first computer program ever written.

The question therefore arises: who can claim the credit of being the first computer programmer? In his memoir Babbage writes that he had ‘offered to do [G] to save Lady Lovelace the trouble.’ But he concedes that she corrected ‘a grave mistake which I had made in the process’.

As it happens Ada’s correspondence relating to Note G was saved from destruction (by her mother Lady Byron, perhaps). There are two letters on successive days that are particularly interesting. Ada wrote to Babbage on Tuesday July 4 and Wednesday July 5 1843. She had been ill, and it is obvious that her hard work on Babbage’s behalf was making her feel better. She writes respectfully to her friend:

Tuesday Morning, Ockham

My Dear Babbage

I now write to you expressly on
three
points; which I have very fully & leisurely considered during the last 18 hours; & think of sufficient importance to induce me to send a servant up so that you may have this letter by half after six this evening. The servant will leave Town tomorrow morning early, but will call for anything you may have for me, at
eight
o’clock in the morning before he goes.

Firstly: the few lines I enclosed you last night about the connexion of (8) with the famous Integral, I by no means intend you to insert, unless you
fully
approve the doing so.

It is perhaps very dubious whether there is any sufficient
pertinence
in noticing
at all
that (8) is an
Integral
…

Secondly: Lord L – suggests my
signing
the translation & the Notes; by which he means, simply putting at the end of the former: ‘
translated by A.A.L;’
& adding to each note the initials A.A.L.

As if working on a medieval cathedral, Ada appears not to have even thought of putting her name to her
Notes
and the translation and it was only upon the prompting of Lord Lovelace – for the time being a mathematics widower – that she thought of putting this forward.

However, on the actual topic of the article she had no reserve and was nothing but forthright, describing Note G as a ‘mess’, not the attribute of a successful computer programme running by necessity from logical step. In the description ‘mess’ one recognises the fertile, gnomic, quixotic and dilettante mind of Babbage himself when attempting to convey his views to third parties such as Robert Peel, Mary Somerville or even his friend Lyell.

My third topic, tho’ my last, is our most anxious & important:-

I have yesterday evening & this morning very amply analysed the question of the
number
of Variable-Cards, as mentioned in the final Note H (or G?). And I find that you & I between us have made a
mess
of it; (for which I can perfectly account, in a very natural manner). I enclose what I wish to insert
instead
of that which is now there. I think the present
wrong
passage is only about eight or ten lines, & is I believe on the
second
of the three great sheets which are to
follow
the Diagram…

I can scarcely describe to you how
very
ill & harassed I felt yesterday. Pray excuse any abruptness or other unpleasantness of manner, if there were any.

I am breathing
well
again today, & am much better in all respects; owing to Dr L’s remedies. He certainly does seem to understand the case, I mean the
treatment
of it, which is the main thing.

As for the
theory
of it, he says truly that
time
&
Providence
alone can develop that. It is so
anomalous
an affair altogether. A
Singular Function
, in very deed!

Think of my having to
walk
(or rather
run
) to the Station, in
half an hour
last evening; while I suppose
you
were feasting & flirting in luxury & ease at your dinner. It must be a very pleasant merry sort of thing to have a
Fairy
in one’s service, mind & limbs! – I envy you! –
I
, poor little Fairy, can only get dull heavy
mortals
, to wait on
me
! –

Ever Yours

A.L.

The next day she corrects the order of cards further in no uncertain terms.

Wednesday, 5 July, Ockham Park

My Dear Babbage

I am much obliged by the contents of your letter, in all respects. Should you find it expedient to substitute the amended passage about the Variable-Cards, there is also
one
other
short
sentence which must be altered similarly. This sentence precedes the passage I sent yesterday by perhaps half a page or more. It is where I explain that for every B after B
5
, operations (13 … .23) have to be repeated; & I believe it runs as follows:

‘Not only are the
Operation
Cards precisely the same for the repetition, but the Variable Cards as well with the exception of one new one to introduce B5 instead of Bs for operation 21 to act upon.’

I should wish to substitute what I enclose.

Babbage’s response to her is not known, and probably lost forever.

But in the same letter she mentions an allusion by him to the ‘imaginary roots’ of their friendship in his response. Oblique as to what exactly the joke is, his words make her puzzle for their meaning and she settles on the word ‘Fairy’ to whom she had compared herself as his helper. It was a word with which she liked to describe herself to others around this time of her marriage. Flirtatiously she only half jokes to him that what she will do in the next ten years will be eternal rather than die with her.

‘Why does my friend prefer
imaginary
roots for our friendship?’ – Just because she happens to have some of that very imagination which
you
would deny her to possess; & therefore she enjoys a little
play
&
scope
for it now & then. Besides this, I deny the
Fairyism
to be entirely
imaginary
; (& it is to the
fairy
similes that I suppose you allude).

That
brain
of mine is something more than merely
mortal
; as time will show; (if only my
breathing
& some other et-ceteras do not make too rapid a progress
towards
instead of
from
mortality).-

Before ten years are over, the Devil’s in it if I have not sucked out some of the life-blood from the mysteries of this universe, in a way that no purely mortal lips or brains could do.

No one knows what almost
awful
energy & power lie yet undevelopped in that
wiry
little system of mine. I say
awful
, because you may imagine that it
might
be under certain circumstances.

Then it is business as usual and she instructs Babbage when she would like him to be available if she has any questions about the Bernoulli numbers she is ‘doggedly attacking and sifting to the very bottom’.

I do not go to Town until Monday. Keep yourself open if you can for that day; in case there should be anything I wish to see you about, which is very likely. But the
evening
I think is most likely to be my time for you, as I rather expect to be engaged incessantly until after 6 o’clock.

I shall sleep in Town that night.-

I am doggedly attacking & sifting to the very bottom, all the ways of deducing the Bernoulli Numbers. In the manner I am grappling with this subject, & connecting it with others, I shall be some days upon it.

I shall then take in succession the
other
subjects that have been suggested to me during my late labours, & treat them similarly.-

‘
Labor ipse voluptas
’ is in
very
deed my motto! – And, (as I hinted just now), it is perhaps well for the world that my line & ambition is over the
spiritual
; & that I have not taken it into my head, or lived in times & circumstances calculated to put it into my head, to deal with the sword, poison, & intrigue, in the place of x, y, & z.

By the way I shall set to work upon
Ohm
tomorrow, & continue it daily until I finish it.

Your
Fairy
for ever

A.A.L.

Ada’s insights into Babbage’s work were not just confined to her understanding of what the Analytical Engine really was. She also understood Babbage and, for all her affection and admiration for him, she knew that if his dreams were to come true, he needed help. And that was why, on August 15 1843, she wrote one of the most poignant letters in the history of the computer. It is also one of the longest. Covering sixteen pages of her close handwriting, it runs to more than 2,000 words.

If there is a moment in Ada’s story when we reach a crossroads where the future of the computer was at stake, this letter provides that moment. Ada’s letter to Babbage constituted an offer to handle, henceforth, what would be regarded today as the management, political and public relations aspects of Babbage’s work on the Analytical Engine. Ada admired Babbage but she was certain that the ornery and undiplomatic aspects of his personality greatly handicapped him when it came to advancing the cause of his Engines.

Ada was perceptive enough to understand something that Babbage never saw: that advancing his project required not only technical wizardry but also needed a velvet yet driven skill at dealing with influential and skeptical people.

He and Ada sometimes had rifts with each other, and this letter shows Ada trying to mend one.

My Dear Babbage

You would have heard from me several days ago, but for the
hot
work that has been going on between me & the printers. This is now happily concluded. I have endeavoured to work up everything to the utmost perfection,
as far as it goes;
& I am now well satisfied on the whole, since I think that
within the sphere of views
I set out with, & in accordance with which the whole contents & arrangement of the Notes are shaped, they are very complete, & even admirable. I could
now
do the thing
far better
; but this would be from setting out upon a wholly different
basis
.

I say you would have heard from me before. Your note (enclosed on Monday with my papers & c), is such as demands a very full reply from me, the writer being so old & so esteemed a friend,
& one whose genius I not only so highly appreciate myself, but wish to see fairly appreciated by others.

Were it not for this desire (which both Lord L – & myself have more warmly at heart than you are as yet at all aware of), coupled with our long-established regard & intercourse, I should say that
the less notice taken by me of that note – the better
; & it was only worthy to be thrown aside with a smile of contempt. The
tone
of it, it is impossible to misunderstand; & as I am myself always a very
‘explicit function of x’
, I shall not pretend to do so; & shall leave to
you
(if you please it) to continue the
‘implicit’
style which is exceedingly marked in the said note.

As I know you will not be
explicit
enough to state the
real
state of your feelings respecting me at this time, I shall do so for you. You feel, my dear Babbage, that
I
have (tho’ in a negative manner)
added
to the list of injuries & of disappointments & mis-comprehensions that you have already experienced in a life by no means smooth or fortunate. You
know
this is your feeling; & that you are deeply hurt about it; & you endeavour to derive a poor & sorry consolation from such sentiments as ‘Well, she didn’t
know
or
intend
the injury & mischief if she has done’ &c.…

I must now come to a practical question respecting the future.
Your
affairs have been, & are, deeply occupying both myself & Lord Lovelace. Our thoughts as well as our conversation have been earnest upon them. And the result is that I have plans for you, which I do not think fit at present to communicate to you; but which I shall either develop, or else throw my energies, my time & pen into the service of some other department of truth & science, according to the reply I receive from you to what I am now going to state. I do beseech you therefore deeply & seriously to ponder over the question how far you can subscribe to my conditions or not. I give to
you
the
first
choice & offer of my services & my intellect. Do not lightly reject them. I say this entirely for
your own
sake, believe me.