Robert Peel, twice Prime Minister of the United Kingdom, came acros...
### Jacquard's Loom
During the 18th century, French weavers deve...
Lady Byron received an unusually broad education as the only daught...
It wouldn't be until 1868 that women started to be admitted to the ...
Charles Babbage, designed two classes of engines:
1. Difference En...
*Difference Engine prototype ...
### ENIAC
The Electronic Numerical Integrator and Computer (ENIA...
*A general plan of the Analyt...
### Bernoulli Numbers
The Bernoulli Numbers $B_{n}$ are a sequence...
What shall we do to get rid of Mr. Babbage and
his calculating Machine? Surely if completed it
would be worthless as far as science is con-
cerned?
—British Prime Minister Sir Robert Peel, 1842
1
The Analytical Engine does not occupy common
ground with mere ‘calculating machines.’ … In
enabling mechanism to combine together gen-
eral 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 mathe-
matical science. A new, a vast and powerful lan-
guage is developed for the future use of analysis
…
—A.A. Lovelace, “Notes by A.A.L.,” 1843
2
Charles Babbage’s Difference Engine and
Analytical Engine, conceived in the first half of
the 19th century, are often seen as anticipating
key design features used in modern computing,
even though none of Babbage’s extraordinary
devices was fully built in his lifetime. Augusta
Ada Lovelace, née Byron, who worked against
the restrictions on women of her day to suc-
cessfully train as a mathematician, worked
closely with Babbage to describe the more
advanced of his Engines, the Analytical Engine,
in a collection of “Notes” published in Taylor’s
Scientific Memoirs in 1843. Lovelace’s vision of
the Engines’ potential for the future of compu-
tation may now be seen as having exceeded
Babbage’s own vision for his machines in sev-
eral key ways. She became the first person
known to have crossed the intellectual thresh-
old between conceptualizing computing as
only for calculation on the one hand, and on
the other hand, computing as we know it
today: with wider applications made possible
by symbolic substitution.
In an early background interview at the
Science Museum (London) for the historical
documentary film about collaboration between
Lovelace and Babbage, To Dream Tomorrow,
3
Babbage authority Doron Swade mentioned
that he thought Babbage and Lovelace had
“very different qualities of mind.” Swade’s
observation proved to be of enormous value for
our subsequent research.
An examination of the original Lovelace and
Babbage documents shows that, whereas Bab-
bage concentrated on the number-crunching
possibilities of his new designs, Lovelace went
beyond number-crunching to see possibilities for
wider applications. She wrote:
Supposing, for instance, that the fundamental
relations of pitched sounds in the science of har-
mony and of musical composition were suscep-
tible of such expression and adaptations, the
engine might compose elaborate and scientific
pieces of music of any degree of complexity or
extent.
4
Aware that the punched card mechanism
guiding the decision list of the Analytical Engine
was taken by Babbage from the Jacquard loom
and that Jacquard had created pictures of great
complexity by this means, she noted: “We may
Lovelace & Babbage and the Creation
of the 1843 ‘Notes’
John Fuegi and Jo Francis
Flare/MITH
Augusta Ada Lovelace worked with Charles Babbage to create a
description of Babbage’s unbuilt invention, the Analytical Engine, a
highly advanced mechanical calculator often considered a forerunner
of the electronic calculating computers of the 20th century. Ada
Lovelace’s “Notes,” describing the Analytical Engine, published in
Taylor’s Scientific Memoirs in 1843, contained a ground-breaking
description of the possibilities of programming the machine to go
beyond number-crunching to “computing” in the wider sense in
which we understand the term today. This article expands on
research first presented by the authors in their documentary film, To
Dream Tomorrow.
16 IEEE Annals of the History of Computing Published by the IEEE Computer Society 1058-6180/03/$17.00 © 2003 IEEE
say most aptly, that the Analytical Engine weaves
algebraical patterns just as the Jacquard-loom
weaves flowers and leaves.”
5
Making her own
independence of thought clear within the
“Notes,” she wrote:
Whether the inventor of this engine had any
such views in his mind while working on the
invention, or whether he may subsequently ever
have regarded it under this phase, we do not
know; but it is one that forcibly occurred to our-
selves
6
on becoming acquainted with the means
through which analytical combinations are actu-
ally attained by the mechanism.
4
In order for us to look closely at the original
Lovelace and Babbage documents written at
the time the “Notes” were being created, we
had to go to a number of different archives. We
also had to take care when examining most
published accounts. Most extant books tended
to be either primarily accounts of Lovelace with
Babbage as an important but subsidiary figure,
or accounts of Babbage with Lovelace often
reduced to a largely marginal figure. In con-
trast, it was our intention in making To Dream
Tomorrow to examine and acknowledge what
each one did as an individual, as well as what
the two achieved working together.
Since the “Notes” are the single most compre-
hensive description of the more advanced capa-
bilities of the Analytical Engine and since a
full-scale Analytical Engine was never built, the
“Notes” constitute the main conduit through
which Babbage’s extraordinarily advanced engi-
neering ideas influenced future generations.
Consequently, the “Notes” and Lovelace’s role in
creating them, and the question of the extent to
which she went beyond the ideas of Babbage are
of historical significance.
Lovelace’s letters to Babbage, with a large array
of other vital Babbage materials, are held at the
British Library in London. A large number of
Babbage’s drawings and notes, used by Doron
Swade and the late Allan Bromley to reconstruct
plans for Babbage’s various “Engines” (some of the
plans of which have been published in the IEEE
Annals), are at London’s Science Museum. A num-
ber of Babbage’s letters to Lovelace are in the
Byron/Lovelace collection at Oxford’s Bodleian
Library. Lovelace Estate Records (the documents
showing the financial and other material condi-
tions under which Ada worked after she married
in 1835), are held at the County Historical Archive
in Woking, UK. As these historic materials have
never been published in their entirety, their inter-
relationship has often remained almost entirely
unexamined.
Over the last four years, to gain access to
and to use Augusta Ada Lovelace materials, we
needed to obtain the permission of Ada’s great-
great-grandson, the current Earl of Lytton. Lord
Lytton was pleased at, among other things, the
idea of taking a fresh look at the role in Ada’s
education of his great-great-great-grandmoth-
er, Lady Byron. Ada grew up essentially in a sin-
gle-parent home; Lady Byron left the abusive
household of the famous poet Lord Byron
when Ada was five weeks old. Lady Byron (who
had herself received some training in mathe-
matics) was primarily responsible for Ada’s edu-
cation up to and including the time Ada met
Charles Babbage when she was 17 and he 42,
and she first saw Babbage’s prototype
Difference Engine, a mechanical calculator.
It is important to note what happens both
for Ada and Charles Babbage in the 10 years
that lie between Ada Byron’s first view of the
prototype Difference Engine in 1833 and the
creation of the “Notes” in 1843. In this period,
the ideas of Babbage undergirding the more
advanced calculating device, the Analytical
Engine, emerged. Ada was present as the key
new ideas were discussed between Charles
Babbage and the great science expositor, Mary
Somerville. By 1834, both Somerville and
Babbage were mentors for the then 18-year-old
Ada, and Babbage supplied Ada with a number
of engineering drawings so she could better
understand his newest designs.
Though Ada Byron (like her mother before
her) was barred, as a woman, from attending
university in England at that time, she worked
with a series of tutors in mathematics. After
meeting Babbage, her mathematical studies
began to focus on what she needed to know to
advance her understanding of the principles
behind Babbage’s Difference and Analytical
Engines. Her study advanced even after she
married William, soon-to-be named Earl of
Lovelace, and had three children in a little over
three years; the last born in July 1839. In 1840
she began a series of tutorials with Augustus De
Morgan, professor of mathematics at University
College, London.
Babbage had first received a grant from the
British government in 1823 to begin to build a
Difference Engine. Yet, despite expending large
sums of public funds and a great deal of his
own money, by 1833 he had failed to complete
more than the small prototype Difference
Engine. This prototype is a fully functioning
device that can be seen today at the Science
Museum in London. By 1834, however,
Babbage began talking about having an even
more complex undertaking to displace the ear-
October–December 2003 17
lier one. As Ada, over a span of a decade,
extended her capacities for understanding
Babbage’s Engines, in the same period, Babbage
himself felt frustrated by being unable to con-
vince British authorities of the importance of
his latest design, a proposal for an Analytical
Engine of vastly greater scope than his earlier
Difference Engine. But, by now, the British gov-
ernment was frustrated by almost two decades
of dealings with Babbage. On 11 November
1842 the inventor had a meeting with the
Prime Minister, Sir Robert Peel. Babbage (as we
know from his own notes
7
) spent more time
attacking the government than describing the
new Engine. Peel, for his part, had, prior to the
meeting, solicited support to call Babbage’s
work officially worthless. The meeting was a
disaster. Both men talked past one another. On
January 5, 1843, Babbage was informed that
the government had sent the prototype of the
Difference Engine to the King’s College
Museum.
8
In March, Peel formally withdrew
support for the project, and only a single voice
in Parliament was raised on Babbage’s behalf.
By 1843 it was clear that Babbage, for all his
technical brilliance, had been rejected in
England for further government funding for
completing either the older Difference Engine
or the newer Analytical Engine.
Before the formal rejection by Peel in
1842–1843, Babbage had gone to Turin in the
fall of 1840 hoping to line up foreign support
for his plans. Before going to Turin he had had
printed the 24-in. by 36-in. “Plan, #25,” one
version of the ever-changing Analytical Engine
design. In Turin, a young engineer, Luigi
Menabrea, took notes on Babbage’s talks and
began to prepare an article based on what
Babbage presented. Menabrea’s article,
“Notions sur la machine analytique,” was pub-
lished in the journal Bibliothèque Universelle de
Genève, in October 1842.
When copies of the Menabrea article reached
England in the fall of 1842 and Babbage had had
his disastrous meeting with Peel, the French lan-
guage article was discussed by Ada Lovelace and
the inventor, Charles Wheatstone. Both Lovelace
and Wheatstone were probably better informed
about the Difference and Analytical Engines
than anyone other than Babbage himself and
possibly Somerville, and they had more knowl-
edge than Menabrea, who had met Babbage only
briefly in Turin. Wheatstone, a close friend of
Babbage and Lovelace, was one of the best
informed people in Britain on developing and
marketing new technologies. By 1837, the
Cooke/Wheatstone Telegraph had been patent-
ed, financed, built and marketed with a highly
successful advertising campaign promoting the
device. Wheatstone had also worked on designs
for calculating by machinery as we know from
an 18 May 1839 entry in Babbage’s Notebook:
“Yesterday saw Wheatstone’s model for telegraph
and his drawings for Multiplication Engine.”
According to Anthony Hyman who cites the
Babbage Notebook, “Wheatstone’s apparatus
gave Babbage the idea that he might use electro-
mechanical switching instead of mechanical
techniques for the Calculating Engines.”
9
Considering the date, 1839, the idea is
breathtaking, coming almost a century ahead
of Howard Aiken making his first advanced cal-
culator proposals to IBM.
10
Even though
Babbage had not adopted Wheatstone’s electro-
mechanical switching in 1839, in 1937 Aiken
directly mentioned Babbage’s engine designs as
a precursor and joked, “If Babbage had lived 75
years later I would have been out of a job.”
11
Descriptions of Babbage’s designs were also
turned up by Konrad Zuse in Berlin as part of
his “prior art” patent search in 1937, and simi-
lar references crop up as well in accounts of the
work of John von Neumann. H.J. Gray notes:
“John von Neumann urged that all the
machine units be connected … so that the
machine could be used as a computer of the
Babbage type ... This was done and ENIAC was
operated in this fashion until it retired.”
12
A
further link is a reported conversation of John
von Neumann with S. Frankel cited by Andrew
Hodges.
13
Hodges also notes that Turing was
aware both of Babbage and Lovelace.
14
Thus
some links can be shown between key 20th-
century figures in computer history (Turing,
Aiken, von Neumann), and the work done in
England in the early 1840s, but dismissed by
the British government then as worthless.
In the fall of 1842, aware of what had happened
between Babbage and Peel, Wheatstone and
Lovelace, not yet mentioning the idea to Babbage
as he was ill after his meeting with Peel, thought it
could help the cause of advancing Babbage’s work
in England if Ada would translate the Menabrea
article into English. She was skilled in French, as her
mother had arranged for her to study languages
from childhood on and encouraged her to polish
her skills during a 15-month period they had spent
abroad. Lovelace went ahead with the translation
over the winter of 1842–1843. As she was far more
knowledgeable than Menabrea about Babbage’s
designs, she provided footnotes as she went along,
tactfully correcting a number of Menabrea’s errors.
In early 1843, Lovelace showed Babbage
what she had been working on over the winter.
Babbage’s response shows the high regard in
which he held Lovelace’s intellect and her
18 IEEE Annals of the History of Computing
Lovelace & Babbage and the 1843 ‘Notes’
understanding of his work. Babbage recollect-
ed 20 years later:
Some time after the appearance of [Menabrea’s]
memoir the late Countess of Lovelace informed
me that she had translated the memoir of
Menabrea. I asked why she had not herself writ-
ten 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.
15
The resulting “Notes” are three times the length
of Menabrea’s essay and contain the most
influential insights.
Lovelace (as we can confirm from her letters
held at the British Library), wrote the “Notes”
mainly at Ockham Park, an hour south of
London. Babbage wrote back to her from his
Dorset Street house in London, adjacent to his
custom-built, fireproof workshop. They met
together to discuss problems and to do proof-
reading at Ada’s London house, 12 St. James’s
Square. Records in Lovelace’s, Babbage’s, and
Wheatstone’s handwriting at the British Library
and at the Bodleian Library allow us to follow
in an almost hourly way how the “Notes” came
into being over the summer of 1843. With mul-
tiple mail deliveries each day, and with more
missives delivered by personal messenger, one
gets a sense of the mutual excitement, colle-
giality, but sometimes fierce frustration on both
sides of the exchange. The letters crossed and
recrossed as Lovelace’s working days sometimes
stretched to 18 hours.
One remarkable feature of Lovelace’s
“Notes” is that they describe not the physical
reality of a single existing Analytical Engine
but what historian of technology Sadie Plant
has called “a virtual machine.” “It is virtual on
two levels,” said Plant when interviewed for
To Dream Tomorrow. “She is,” notes Plant,
“writing the program for a virtual machine,
for a future machine in effect.” Most of the
mechanical parts for the Engine did not yet
exist, and the drawings, even when they did
exist and Babbage could put his hands on
them, were incompatible as they reflected dif-
ferent stages of design over a nine-year period.
We know that, even at the last stage, as the
“Notes” were in press, Babbage told Lovelace
on 18 August 1843:
My Dear Lady Lovelace I much fear the drawings
will not be very intelligible. They were never
published and only a few proofs were taken. I
will endeavour to find a complete set and bring
them with me on Monday.”
16
To create a comprehensive description of
the Analytical Engine that did not (and indeed
does not) exist, a machine that was in a con-
stant state of flux in Lovelace’s and Babbage’s
lifetime and for which Babbage had difficulty
turning up a full, internally consistent set of
drawings—was to attempt something of almost
inconceivable difficulty. Swade reports in The
Cogwheel Brain how immensely difficult it was
for him and Allan Bromley, even over a period
of several years, to work through thousands of
pages of Babbage’s “Notes” in order to under-
stand a vast, unbuilt, constantly changing enti-
ty. Groping to arrive at correct formulations
during a single intense summer of work in
1843, Lovelace and Babbage exchanged letters
that are startlingly modern, almost email-like:
abrupt, often informal, dashed off, and sent
with uncorrected errors.
Lovelace in the summer of 1843 was 27
years old and saw herself, as she noted in a let-
ter to a relative, as “a fully professional per-
son.”
17
Her letters to Babbage mix respect with
banter, and sometimes the bluntest frankness
when he loses papers or fails to remain focused
on the task at hand. Tellingly, she often wrote
“My Dear Babbage,” using the form of male-to-
male, colleague-to-colleague address of the
Victorian era. Babbage, who was in 1843 in his
early fifties, addressed her as “My Dear Lady
Lovelace.”
The following letters give us a sense from
Babbage’s perspective of how the work was pro-
ceeding. Babbage, from Dorset St. 30 June
1843, writes to Lovelace at Ockham Park in
such a hurry that not enough postage was put
on the letter, so it is marked on the envelope
“More To Pay.”
My Dear Lady Lovelace
I am delighted with Note D. It is in your usual
clear style and requires only one triffling [sic]
alteration which I will make. This arises from our
not having yet had time to examine the outline
of the mechanical part. …
I enclose a copy of the integration. I am still
working at some most entangled notations of
Division but see my way through them at the
expense of heavy labour, from which I shall not
shrink as long as my head can bear it. I have
been somewhat impeded for the last few days.
Your latest information was the most agreeable.
Ever my dear Lady Lovelace Sincerely yours C.
Babbage.
18
October–December 2003 19
On Sunday, 2 July 1843, Babbage wrote:
I am very reluctant to return the admirable and
philosophic view of the Abral. [sic] Engine con-
tained in Note A. Pray do not alter it and do let me
have it returned on Monday. I send also the rest
of Note D. There is still one triffling (sic) misap-
prehension about the Variable cards—A Variable
card may order any number of Variables to receive
the same number upon theirs at the same instant
of time—But a Variable card never can be direct-
ed to order more than one Variable to be given off
at once because the mill could not receive it and
the mechanism would not permit it. All this was
impossible for you to know by intuition and the
more I read your Notes the more surprised I am at
them and regret not having earlier explored so
rich a vein of the noblest metal.
The account of them stands thus
A Sent to Lady L. F Retained by Lady L
B With CB G Where is it gone??
C Ditto H With CB
D Sent to Lady L
E With CB
I have not seen Mr. Wheatstone and am
ashamed to write until I can positively put the
whole of the Notes into his hands.
I will attend your commands tomorrow And
am ever most truly yours C. Babbage
19
Lovelace wrote back at once to Babbage, her
second letter to him that day. She had decided
that, since Babbage had made a mistake about
how she viewed the variable cards, she would
need to see him the next day in London to get
several points clarified. She playfully and tact-
fully points out that in fact no Note C had ever
existed.
Ockham, Sunday 6 o’clock. I have worked inces-
santly and most successfully all day. You will
admire the Table and Diagram extremely.
They have been made out with extreme care
and all the indices most minutely and scrupu-
lously attended to. Lord L[ovelace] is at this
moment kindly inking it all over for me. I had to
do it in pencil.
You must bring all the Notes with you tomor-
row as I have observations to make on each one
and especially on this final one H.
There never was a note C. I do not know why
I chose H instead of C and thus insulted the lat-
ter worthy letter.
I cannot imagine what you mean about the
Variable-Cards; since I never either supposed in
my own mind that one Variable-card could give
off more than one Variable at a time; nor have (as
far as I can make out) expressed such an idea in
any passage whatsoever …
20
Having met with Babbage in London to
work through the observations each had made,
Lovelace wrote to him, both to clarify the issue
of the variable cards and to convey her decision
to assert her authorship of the “Notes” in a let-
ter dated 4 July 1843:
Ockham, Tuesday Morning … Lord L. suggests
my signing the translation and the Notes, by
which he means simply putting … “translated by
A.A.L;” & adding to each Note the initials A.A.L.
It is not my wish to proclaim who has written it;
at the same time that I rather wish to appear any-
thing that may tend hereafter to individualize and
identify it with other productions of the said A.A.L.
My third topic, tho’ my last is my most anx-
ious and important. I have yesterday evening
and this morning very amply analyzed the ques-
tion of the number of Variable Cards, as men-
tioned in the final Note H (or G?). And I find that
you and 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 inscribe 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.
The fact is that if my own composition about
the Variable Cards in Note D had been strictly fol-
lowed by myself in Note H this error would not
have occurred. The confusion has arisen simply
from the circumstance of applying to the Variable
Cards, facts which relate to the Operation-Cards.
In Note D it is very well and lucidly demonstrat-
ed that every simple operation demands the use
of at least those Variable Cards. It does not signi-
fy whether the operations be in cycles or not. A
million successive additions would each demand
the use of these new Variable Cards under ordi-
nary circumstances. In Note H, the erroneous
lines are founded on the hasty supposition that
the cycle or recurring group of Operation-Cards
(13 . . . . . 23) will be fed by a cycle or recurring
group of Variable-Cards.
I enclose what I believe it ought to be. If already
gone to the printer we must alter that passage in
the proofs unless you could call at the printers
and there paste over the amendment.
21
20 IEEE Annals of the History of Computing
Lovelace & Babbage and the 1843 ‘Notes’
She commented further on the technical
issues in another letter to Babbage, probably also
of 4 July. This letter is dated only “Tuesday
1843,” but the context makes plain that it was
written near the time of the 4 July letter:
My Dear Babbage.
I hope you will approve of what I send. I have
taken much pains with it. I have explained that
there would be, in his instance & in many others,
a recurring group or cycle of Variable as well as of
Operation Cards; and I have (I think very judi-
ciously and easily) touched on the only departures
from perfect identity which could exist during the
repetitions of (13 . . . . . 23); and yet have not com-
mitted myself by saying if the departures would
require to be met by the introduction of one or
more new cards or not; but have simply indicated
that as the associations follow a regular rule, they
would be easily provided for. I think I have done it
admirably and diplomatically (Here comes in the
intrigante and politician!) Ever yours A.L.
22
Lovelace’s Note F describes how the
Analytical Engine could be used to calculate the
values of the Bernoulli numbers. Lovelace,
knowing that Babbage believed the Engine
could have the capacity to handle Bernoulli
numbers, as he had discussed in a letter circa
January 1841 to the German savant Alexander
von Humboldt,
23
took it upon herself to make
sure there was a written description and demon-
stration of how this could be done. She writes
from Ockham Park on Wednesday, 5 July 1843:
I do not go to town until Monday. Keep yourself
open if you can for that day in case there is any-
thing I wish to see you about which is very like-
ly. 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 and sifting to the very
bottom all the ways of deducing the Bernoulli
Numbers. In the manner I am grappling with
this subject; and connecting it with the others, I
shall be some days upon it. …
“Labore ipse voluptas” [Labor Is Its Own
Reward] is in very deed my motto! And (as I hint-
ed just now), it is perhaps well for this world that
my line and inclination is more the spiritual; and
that I have not taken it into my head or lived in
times or circumstances calculated to put into my
head to deal with the sword, poison, and intrigue
in the place of x, y, & z. …
24
In the archive, this letter is followed in folio
354 by a very brief note from Babbage dated
Wednesday, July 1843, presumably of 5 July:
“Return sheet with two corrections. Right
about Card requiring new Variable.”
25
This was typical of a staccato to and fro. Ada,
writing the “Notes,” queried Babbage, as the
inventor of the yet unbuilt Engine, as to
whether or not he anticipated his Engine could
do something and do it as she understood it.
Babbage’s replies suggest that he had learned
something new about his own machine from
Lovelace’s queries and speculations. For
instance, a letter headed “Ockham Thurs. Morn.
1843” reminds us that Lovelace was attempting
a description of what Babbage himself was still
in the process of clarifying. She wrote:
My Dear Babbage. I have read your papers over
with great attention. But I want you to answer me
the following question by return post. The day I
called on you, you wrote off on a scrap of paper
(which I have unluckily lost); that the Difference
Engine would do [Authors’ note: Lovelace draws
a small triangle here] (something or other)
[Authors’ note: The parentheses are hers] but that
the Analytical Engine would do [Authors’ note:
Lovelace again draws a triangle here] (something
else that is absolutely general). Be kind enough to
write this out properly for me; and then I think I
can make some very good Notes. …
26
On 10 July 1843, Lovelace wrote:
My Dear Babbage. … I want to put in something
about Bernouilli’s Numbers in one of my Notes
as an example of how an implicit function may
be worked out by the engine without having
been worked out by human head or hands first.
Give me the necessary data and formulae. Yours
ever AAL
27
The correspondence brings to life the actual
process of editing and proofreading:
July 1843 Ockham Tuesday Morning. My Dear
Babbage. … What I want to know is this: can
you be with me in town at 4 o’ clock. This is in
order that I may read over aloud with you all the
Notes. ...
28
The fact Lovelace wanted to go through the
“Notes” with Babbage, and had previously sent
him her translation of Menabrea to check
makes it clear that proofreading was a joint
undertaking, supplemented in the customary
way by the printers. Given this fact, it seems
odd to dismiss (as one severe critic has done)
29
only Lovelace for failing to catch an error made
by the Swiss printer (an error of “cas” for “cos.”
October–December 2003 21
uncaught by Menabrea), and then using this to
claim Lovelace knew little about mathematics.
By the end of July, Lovelace and Babbage
appeared to be on the final lap. Lovelace, the
mother of three children with the Earl of
Lovelace, jokingly wrote about the “Notes” as
though they were her first child:
Ockham Thursday morning July 27, 1843: My
Dear Babbage. … To say the truth I am rather
amazed at them [the Notes] & I have made Lord
Lovelace laugh much by the dryness with which
I remarked “Well. I am very much satisfied with
this first child of mine. He is an enormously fine
baby and will grow to be a man of the first mag-
nitude and power.”
30
A meticulous worker, Lovelace struggled not
only with the difficulty of the material but also
with the errors of the printers and Babbage
himself. On 28 July 1843, Lovelace wrote to
Babbage from St James’s Square:
The beginning of Note G (by which I mean the
Table & all that precedes it) never has been
returned into my hands; a small part of the
remainder was, but that I speedily gave you back,
& there it is, now printed.—
The missing part must be either at your house
or at the printer’s; & it seems to me very unlikely
that you should have retained it. So altogether I
would wager almost anything that it is at the
office; or that if lost, it has been lost there.
At the same time, I have also fancied you were
a little harum-scarum & inaccurate now & then
about the exact order & arrangement of sheets,
pages, & paragraphs & c. (witness that paragraph
which you so carelessly pasted over!)
I suppose I must set to work to write some-
thing better, if I can, as a substitute. The same pre-
cisely I could not recall. I think I should be able
in a couple of days to do something. However I
should be deucedly inclined to swear at you, I will
allow.
I desire my messenger to wait; as it possible
you may have something to communicate more
agreeable.
I go soon after seven. I believe I shall not be in
Town myself on Monday as I expected. Yours
A.L.
31
“Ockham Sunday Afternoon August 1,
1843,” Lovelace writes:
I am half beside myself with hurry and work. … I
wish you were as accurate and as much to be
relied on as I am myself. You might often save me
much trouble if you were; whereas you in reality
add to my trouble not infrequently and there is at
any rate always the anxiety of doubting if you will
not get me into a scrape even when you don’t.
By the way, I hope you do not take upon your-
self to alter any of my corrections. I must beg you
not. They all have some very sufficient reason.
And you have made a pretty mess and confusion
in one or two places (which I will show you
sometime) where you have ventured on my
M.S.’s to insert or alter a phrase or word and have
utterly muddled the sense …
32
From Lovelace’s letters, it is clear that she
thought the intense working period was yielding
the desired result: a strong, persuasive article,
describing the capabilities and functioning of the
Analytical Engine, to generate interest and sup-
port for its construction. But, by early August the
tone of exchanges is increasingly acerbic as
Lovelace realizes that Babbage is trying to con-
vince the printer to include one of his diatribes
(which he was, however, unwilling to sign).
Babbage wanted, at the last minute, to prevent
the publication of the article unless he could
fulminate at length in the same issue about the
way he had been and was being treated by the
government. But Lovelace overrode him and had
the printer proceed as originally planned. A key
Babbage letter does not appear to have survived
as it is not at the Bodleian in the Lovelace/Byron
Collection. His letter must have been written
around the beginning of August 1843 because
Ada Lovelace’s letter of 5 August 1843 is clearly
in response to something from him about her
overruling him on going ahead with the article.
She made her views clear in a letter to Babbage
from Ockham on Sunday, 6 August 1843:
My Dear Babbage … On the one point of not with-
drawing the translation & Notes from the
Memoir, or consenting to its separate publication,
I was entirely and finally decided; as I think nei-
ther for your advantage nor my own, to do so;
added to my opinion that it would under the cir-
cumstances be dishonorable and unjustifiable …
Be assured that I am your best friend; but that I
never can or will support you in acting on prin-
ciples which I conceive to be not only wrong in
themselves, but suicidal.
33
In his reply of Tuesday, 8 August 1843,
Babbage protested her decision, yet seemed to
acknowledge her authority to make it:
My Dear Lady Lovelace
I leave the Ms and also the proofs of the Notes
I recd. last night and promised to send this
evening.
22 IEEE Annals of the History of Computing
Lovelace & Babbage and the 1843 ‘Notes’
I will write to Printer to say you will send them
up by post direct to them.
This direct communication will save time and
there is very little to spare for this Number ought
to be out in the course of a very few days.
I have nothing to add at present except that
you do me injustice in supposing I wished you to
break any engagement with the Editor. I wished
you to ask him to allow you to withdraw from it.
Had the Editor been in England I believe he
would at my request have inserted my defense or
forborn to have printed the paper—As it stands
I have done all I can at present to defend myself
and having failed in the most important part
shall make the best I can of the rest. Ever truly
yours C. Babbage
34
Babbage’s supposition about the editor’s
wishes did not turn out to be true. The editor
backed Lovelace, not Babbage. Opposition to
Babbage’s diatribe idea was unanimous. Neither
Wheatstone nor Charles Lyell, the eminent
geologist and mutual friend of Lovelace and
Babbage, thought Babbage’s interests would be
served by yet another attack. Despite the advice
of his closest friends, Babbage published his
diatribe separately, in a different magazine, a
few weeks later.
35
Whatever Babbage might decide to do,
Lovelace keenly felt her own responsibility for
this project. On Tuesday, 8 August 1843, she
wrote to her mother:
I have been harassed and puzzled in a most per-
plexing manner by the conduct of Mr. Babbage
… I am sorry to come to the conclusion that he
is one of the most impracticable, selfish, and
intemperate persons one can have to do with …
But I am happy to find that W. [Authors’ note:
“W.” indicated William, her husband.] &
Wheatstone entirely approves my conduct and
means. I declared at once to Babbage that no
power should induce me to lend myself to any of
his quarrels … and that I should myself commu-
nicate in a direct manner with the editors … He
was furious. I imperturbable … I only want you
to understand that all my time and my energy
have been miserably absorbed the last few days;
for what between Babbage and the editors both
pressing hard in different directions, I have been
torn to pieces …
36
Angry or not, Lovelace remained focused on
the central issue that the specific purpose of the
translation and “Notes” was to advance the
actual building of a machine, rather than again
to attack the government. In a candid letter to
Babbage, she offered her talents and resources
to pursue the building of the Analytical Engine,
provided he himself would stick to the techni-
cal aspects of the project. From Ockham Park
on Monday, 14 August 1843, Lovelace wrote to
Babbage:
I have now touched on all the grounds which
can be taken on the supposition of its really being
pernicious to your interests that I have thus allowed
the article to appear ... My moral standard, such
as it is, I must stick to; as long as it is my moral
standard. … I have a right to expect from you the
belief that I do sincerely and honestly take this
view. [I]f your knowledge of me does not furnish
sufficient grounds for doing so, then I can only
say that no natural knowledge of any two
human beings in this life can give fixed and sta-
ble grounds for faith and confidence then Adieu
to all truth and to everything most generous in
this world!
I must now come to a practical question
respecting the future. …
If I am able to lay before you in the course of
a year or two explicit and honourable proposi-
tions for executing your engine (such as are
approved by persons whom you may now name
to be referred to for their approbation) would
there be any chance of you allowing myself and
such parties to conduct the business for you;
your own undivided energies being devoted to the
execution of the work; all these matters being
arranged for you on terms which your own
friends should approve?
You will wonder over this last query. But I
strongly advise you not to reject it as chimerical.
You do not know the grounds I have for believ-
ing that such a contingency may come within
my power and I wish to know before I allow my
mind to employ its energies any further on the
subject, that I shall not be wasting thought and
power for no purpose or result … Yours ever most
sincerely A.A.L.
37
A letter she wrote to her mother the next
day confirms that the printers were recognizing
her as author of the “Notes.” Tuesday, 15
August 1843:
… I was unexpectedly summoned by the print-
ers who needed a further supervision and as it is
actually to be out I understand tomorrow, there
was no time for post communications. No one
can estimate the trouble of interminable labour of
having to revise the printing of mathematical for-
mulae. You will receive a few copies (amongst a
hundred that are printed separately for me). …
If he [Babbage] does consent to what I pro-
pose, I shall probably be enabled to keep him out
October–December 2003 23
of much hot water; and to bring his engine to
consummation (which all I have seen of him and
his habits the last 3 months, makes me scarcely
anticipate it ever will be, unless someone really
exercises a strong co-ercive influence over him).
He is beyond measure careless and desultory at
times. …
38
With the final material delivered to the
printer and with most of the errors corrected,
and after months of 18-hour days spent
describing the possibilities of an extraordinari-
ly complex virtual machine, Lovelace now con-
fessed herself often very tired. Lovelace came
up to London around 18 August to meet
Babbage. He was still furious about not having
had his own way on the idea of appending a
diatribe to the “Notes.” He scribbled a curt
memo in the margin of Lovelace’s letter of 14
August: “Saw AAL this morning and refused all
the conditions.” Instead of using publication of
the Memoir with the “Notes” as a descriptive
model of a strategy for gaining public under-
standing and support to get the Engine
financed and constructed, Babbage would con-
tinue until his death in 1871 to go his own,
often irascible, way.
By 24 August 1843, the volume of Taylor’s
Scientific Memoirs with the translation of
Menabrea’s “Memoir” and the “Notes”
appeared. Lovelace wrote to her mother: “We
are by no means desirous of making it
[Authors’ note: authorship of the “Notes”] a
secret although I do not wish the importance
of the thing to be exaggerated and over-
rated.”
39
Charles Wheatstone wrote on 25
August 1843:
My Dear Lady Lovelace, I called yesterday at the
printer’s and was informed that a separate copy
of your paper had been forwarded by post to
Ockham, and the new number of the Scientific
Memoirs sent to St. James’ Square … Yours very
truly C. Wheatstone.
40
Reaction to the work was swift and positive. The
paper, so Michael Faraday, famous for his
chemical and electrical experiments, declared to
Babbage on 1 September, was so complex it was
well over his own head.
41
Menabrea asked
Babbage to pass along his congratulations “à
cette noble Dame, A.A.L.”
42
With
congratulations pouring in, even Babbage was
pleased, and he swiftly reconciled with Lovelace,
concluding a letter to her of 12 September 1843,
with the extravagant: “Ever my fair Interpretess
Your faithful slave C. Babbage”
43
Babbage expert, Doron Swade (having
examined the extensive exchange of letters and
the resulting “Notes”), when interviewed for To
Dream Tomorrow, commented:
Ada saw something that Babbage in some sense
failed to see. In Babbage’s world his engines were
bound by number. He saw that the machines
could do algebra in the narrow sense that they
could manipulate plus and minus signs. But all
his calculating engines, his Difference Engine
and his Analytical Engine, which is the pro-
grammable general-purpose machine, were all
bound by number: They manipulated number as
a manifestation of quantity, as a measure of
quantity. What Lovelace saw—what Ada Byron
saw—was that number could represent entities
other than quantity. So once you had a machine
for manipulating numbers, if those numbers rep-
resented other things, letters, musical notes, then
the machine could manipulate symbols of which
number was one instance, according to rules. It
is this fundamental transition from a machine
which is a number cruncher to a machine for
manipulating symbols according to rules that is
the fundamental transition from calculation to
computation—to general-purpose computa-
tion—and looking back from the present high
ground of modern computing, if we are looking
and sifting history for that transition, then that
transition was made explicitly by Ada in that
1843 paper.
As Swade is fully aware, “[T]he Analytical
Engine,” as A.A.L. so clearly stressed, “does not
occupy common ground with mere ‘calculating
machines’.” This formulation, based on what
only existed as a virtual machine in 1843, went
beyond any known statement of Babbage, and
beyond distinguished predecessors in mechan-
ical calculation such as Blaise Pascal and
Gottfried Wilhelm Leibniz. A.A.L. anticipated
advanced work in the next century of Alan
Turing, Konrad Zuse, Howard Aiken, Grace
Hopper, and John von Neumann. Looking far
ahead to that time when a general-purpose
machine would no longer be declared worthless
but would in fact be built, Lovelace argued that
such a machine would serve as a springboard
for an ever-increasing number of discoveries,
many of which would remain unimaginable
until such time as the machine was built and
could be run. She wrote in Note A:
[V]ery valuable practical results would be devel-
oped by the extended powers of the Analytical
Engine, some of which would be brought forth
by the daily increasing requirements of science
and by a more intimate practical acquaintance
24 IEEE Annals of the History of Computing
Lovelace & Babbage and the 1843 ‘Notes’
with the powers of the engine, were it in actual
existence.
44
Lovelace was to be proven right, but it
would take over 100 years. Only after the early
ENIAC (“a computer of the Babbage type,” as
H.J. Gray described it) was built to run rapid
calculations for ballistics tables did engineers
and programmers, such as John von Neumann
and Grace Hopper, begin to move beyond what
Lovelace had called “mere calculating
machines” and begin, in Swade’s words, “to
manipulate symbols according to rules.” With
these developments in the mid-20th century,
the paradigm shift Lovelace had made in 1843
would start to become our everyday reality.
References and notes
1. British Library, London, additional manuscript
(hereafter “add’l ms.”) 40,514, folio 223.
2. A.A. Lovelace, “Notes by A.A.L. [August Ada
Lovelace],” Taylor’s Scientific Memoirs, London,
vol. III, 1843, pp. 666-731. These notes were
originally printed in both Charles Babbage and His
Calculating Engines: Selected Writings by Charles
Babbage and Others, P. Morrison and E. Morrison,
eds., Dover Publications, 1961 (which includes
the full text of the Menabrea translation and the
1843 Notes, pp. 225-297), and in Faster Than
Thought, B.V. Bowden, ed., Sir Isaac Pitman &
Sons, Ltd., 1953, pp. 341-408. A.A. Lovelace’s
translation of Menabrea together with her
“Notes” are also on the Web: http://www.
fourmilab.ch/babbage/sketch.html.
3. For information about the film, see
http://www.mith.umd.edu/flare and
http://www.computer.org/annals/an2002/extras
/a405602x.htm.
4. P. Morrison and E. Morrison, eds., Charles
Babbage and His Calculating Engines …, p. 249.
5. Ibid., p. 252.
6. She is, of course using the customary plural of
scholarly writers of the time.
7. British Library, add’l ms. 37,192, folios 189-194.
8. British Library, add’l ms. 37,192, folio 326.
9. A. Hyman, Charles Babbage, Pioneer of the Com-
puter, Princeton Univ. Press, 1982, p. 227.
10. I.B. Cohen, Howard Aiken: Portrait of a Computer
Pioneer, MIT Press, p. 63.
11. Cited by D. Swade, Charles Babbage and His Cal-
culating Engines, Science Museum, 1991, p. 34.
12. Cited from H.J. Gray’s Digital Computer Engineer-
ing, Prentice-Hall, 1963, in the annoted bibliog-
raphy given by B. Randell, ed., The Origins of
Digital Computers: Selected Papers, Springer Ver-
lag, 1973, p. 420.
13. A. Hodges, Alan Turing: The Enigma, Vintage, p.
304.
14. Ibid., p. 297 and pp. 357-358.
15. Cited by D. Swade, The Cogwheel Brain, pp. 160-
161.
16. Byron/Lovelace Collection, Bodleian Library,
Oxford, UK, box 168, folio 47, recto and verso.
17. Cited by B.A. Toole, Ada, the Enchantress of Num-
bers, p. 225. We might note that as we did our
own transcriptions of letters, in a number of cases
our reading and dating differs from Toole’s. Ideal-
ly, all these documents should be put directly on
the Web so that various people can do their own
decipherments of texts that are often extremely
hard to read. In some cases, Toole has very use-
fully included facsimiles of some of the handwrit-
ten documents, an excellent practice.
18. Byron/Lovelace Collection, Bodleian Library, box
168, folio 43, recto and verso.
19. Byron/Lovelace Collection, Bodleian Library, box
168, folio 45, recto and verso, and folio 46, recto.
October–December 2003 25
Bibliography
B.V. Bowden, ed., Faster Than Thought, Sir Isaac Pitman & Sons, Ltd.,
1953. Includes the text of Lovelace’s translation of Menabrea and
the full text of her “Notes.”
M. Campbell-Kelly and W. Aspray, Computer, Basic Books, 1996.
I.B. Cohen, Howard Aiken: Portrait of a Computer Pioneer, MIT Press, 1999.
J. Fuegi and J. Francis, To Dream Tomorrow, 2003, documentary film
with Doron Swade, Sadie Plant, Miranda Seymour, David Herbert,
Michael Lindgren, and direct Lovelace descendant, the Earl of
Lytton; http://www.mith.umd.edu/flare. Also see http://www.
computer.org/annals/an2002/extras/a405602x.htm.
D. Herbert, Lady Byron and Earl Shilton, Hinckley and District Museum,
Leicestershire, 1997.
A. Hodges, Alan Turing: The Enigma, Vintage, 1992.
A. Hyman, Charles Babbage, Pioneer of the Computer, Princeton Univ.
Press, 1982.
M. Lindgren, Glory and Failure: The Difference Engines of Johann Müller,
Charles Babbage, and Georg and Edvard Scheutz, translated from
Swedish by C.G. McKay, Linköping, 1987.
A.A. Lovelace’s Translation of Menabrea together with her “Notes” are
on the Web: http://www.fourmilab.ch/babbage/sketch.html.
P. Morrison and E. Morrison, eds., Charles Babbage and His Calculating
Engines: Selected Writings by Charles Babbage and Others, Dover
Publications, 1961. Includes the full text of the Menabrea
translation and the 1843 Notes.
S. Plant, zeros + ones: Digital Women + the New Technoculture,
Doubleday, 1997.
B. Randell, ed., The Origins of Digital Computers, Springer Verlag, 1973.
Contains a number of vital historical papers and a lengthy, superbly
annotated bibliography.
J. Shurkin, Engines of the Mind, W.W. Norton & Co., 1984.
D. Swade, The Cogwheel Brain, Little, Brown and Co., 2000. The US edi-
tion of the same book: The Difference Engine: Charles Babbage and the
Quest to Build the First Computer, Viking, 2001.
B.A. Toole, Ada, The Enchantress of Numbers, Strawberry Press, 1992. Has
the best collection of Ada Byron Lovelace letters now in print.
20. British Library, add’l ms. 37,192, folio 337.
21. British Library, add’l ms. 37,192, folio 344.
22. British Library, add’l ms. 37,192, folio 348.
23. British Library, add’l ms. 37,191, folio 638.
24. British Library, add’l ms. 37,192, folios 351-352.
25. British Library, add’l ms. 37,192, folio 354.
26. British Library, add’l ms. 37,192, folios 357-358.
27. British Library, add’l ms. 37,192, folio 362.
28. British Library, add’l ms. 37,192, folios 386-725.
29. See D.A. Stein, Ada, A Life and a Legacy, MIT
Press, 1985, p. xi, where much is made of “her
[emphasis added] curiously ignored translation of
a printer’s error.” Stein claimed that if Lovelace
missed a proofreading error, she must have been
unsound in mathematics. Stein then argues we
must see Babbage as the primary author of the
“Notes” (though he, too, missed the printer’s
error) and see Lovelace’s centrality as what Stein
calls a “mythology” (p. ix). However, from the
surviving letters of Babbage, Lovelace,
Wheatstone, Lyell, Faraday, Menabrea, and the
editors of Taylor’s Scientific Memoirs, it is clear that
proofreading was done with Babbage, and that
the original typesetting error was missed by
Menabrea. The original documentation shows
that all contemporaries of Lovelace and Babbage,
having first-hand knowledge of how the “Notes”
came into being, acknowledged Lovelace at the
time as the primary author.
30. British Library, add’l ms. 37,192, folios 393-394.
31. British Library, add’l ms. 37,192, folios 398-399.
32. British Library, add’l ms. 37,192, folios 414-415.
33. Letter is given in full in B.A. Toole, Ada, pp. 219-
222.
34. Byron/Lovelace Collection, Bodleian Library, box
168, folios 41 and 42.
35. D. Swade, Cogwheel, p. 163.
36. Byron/Lovelace Collection, Bodleian Library, box
42, folio 76.
37. British Library, add’l ms. 37,192, folios 425-426.
38. Byron/Lovelace Collection, Bodleian Library, box
42, folios 86-88.
39. Byron/Lovelace Collection, Bodleian Library, box
42, folios 101-102.
40. British Library, add’l ms. 54,089, folio 37.
41. British Library, add’l ms. 37,192, folio 445.
42. British Library, add’l ms. 37,192, folio 46.
43. British Library, add’l ms. 54,089, folio 54.
44. P. Morrison and E. Morrison, eds., Charles
Babbage and His Calculating Engines …, p. 256.
John Fuegi is currently a Mary-
land Institute for Technology in
the Humanities (MITH) Fellow
and the Clara and Robert Vam-
bery Distinguished Professor of
Comparative Studies at the
University of Maryland, Col-
lege Park. He has taught at Har-
vard University, the Freie Universität, Berlin, and has
held American Council of Learned Societies, Guggen-
heim, and Rockefeller Awards. He founded and cur-
rently chairs Flare Productions.
Jo Francis taught for many years
in Thailand and the US before
joining Flare Productions, a not-
for-profit educational filmmak-
ing organization affiliated with
the Maryland Institute for
Technology in the Humanities
(MITH). She is a MITH Fellow
and has received national and international recogni-
tion for her teaching and her work in film.
Readers may contact John Fuegi and Jo Francis at
jf@flarefilms.org.
For further information on this or any other com-
puting topic, please visit our Digital Library at
http://computer.org/publications/dlib.
26 IEEE Annals of the History of Computing
Lovelace & Babbage and the 1843 ‘Notes’
*Difference Engine prototype from the Science Museum in London*
Lady Byron received an unusually broad education as the only daughter of wealthy, liberal, forward-thinking parents. She studied history, poetry, mathematics, literature, French, Italian, Latin, Greek, drawing and dancing.
### Bernoulli Numbers
The Bernoulli Numbers $B_{n}$ are a sequence of signed rational numbers that can be defined by the exponential generating function:
$$\frac{x}{e^x - 1} = \sum_{n=0}^\infty \frac{B_n x^n}{n!}, ~~~|x|<2\pi.$$
These numbers arise in the series expansions of trigonometric functions, and are extremely important in number theory and analysis.
The first few Bernoulli numbers $B_{n}$ are:
$$ B_{0} = 1 $$
$$ B_{1} = -\frac{1}{2} $$
$$ B_{2} = \frac{1}{6} $$
$$ B_{4} = -\frac{1}{30} $$
$$ B_{6} = \frac{1}{42} $$
### ENIAC
The Electronic Numerical Integrator and Computer (ENIAC), was the first electronic general-purpose computer. It was developed during the Second World War at the University of Pennsylvania for a number of purposes, such as ballistics calculations, combined fully electronic functioning, digital operation, and programmability.
It was capable of calculating 2,037 digits of pi in about 70 hours.
It wouldn't be until 1868 that women started to be admitted to the University of London. Ada Lovelace died in 1852 at the age of 36.
Robert Peel, twice Prime Minister of the United Kingdom, came across Babbage's engines on two separate occasions. In both instances he controlled the funding that determined the fate of the engines.
As Home Secretary in 1822 he was lobbied by a supporter of Babbage to fund a full-sized calculating engine. Peel was skeptical. But following a favorable report by the Royal Society the Treasury approved funding and the construction of Difference Engine No. 1 went ahead.
In 1842, when Prime Minister for the second time, Babbage appealed to Peel for a decision on whether government wished to complete the Engine, stalled since 1833, or scrap it. Peel axed the project following advice from George Biddell Airy, Babbage's energetic antagonist. John Herschel's elaborately supportive petition was to no avail. Babbage secured an interview with Peel in the hope of reversing the decision. The meeting was catastrophic. They argued and Babbage stormed out.
*Sir Robert Peel*
Charles Babbage, designed two classes of engines:
1. Difference Engines
2. Analytical Engines
Difference engines are so called because of the mathematical principle on which they are based: the method of finite differences. This method uses only arithmetical addition and removes the need for multiplication and division which are more difficult to implement mechanically. You can think of difference engines are strictly calculators. They cannot be used for general arithmetical calculation.
The Analytical Engine is much more than a calculator and marks the progression from the mechanized arithmetic of calculation to fully-fledged general-purpose computation. There were at least three designs at different stages of the evolution of his ideas.
*A general plan of the Analytical Engine from 1840*
### Jacquard's Loom
During the 18th century, French weavers developed a series of innovations for automating the process of textile weaving. French weaver and merchant Joseph Jacquard (1752–1834), perfected the earlier French inventions into a fully automatic loom that was able to weave complex textile patterns based on a chain of punched cards.
Different textile patterns could be produced by using a different set of punched cards. Jacquard’s punched-card looms used a binary system: A hole in the punched cardboard let a hook through, which lifted a thread, thus producing a different pattern from the hooks that were blocked by the cardboard.
*Model of a Jacquard loom*