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The Imagination of Ada
Lovelace
An Experimental Humanities
Approach
David De Roure @dder
Pip Willcox @pipwillcox
A context
Jacquard	
loom	
London:!
the!
Waltz!
Lovelace!
born!
Darwin:!
Origin of !
Species!
Babbage!
dies!
Helmholtz:!
Sensations!
of Tone!
Dickens!
dies!
Markov!
born!
Lovelace!
dies!
Austen!
dies!
Lovelace!
presented!
Lovelace!
meets!
Babbage!
Wheatstone:	
telegraph	
Coronation:	
Victoria	
Lovelace:!
Translator’s!
Notes!
Images
ByCreator:CharlesHayter(NationalPortraitGallery)[PublicdomainorPublicdomain],via
WikimediaCommons.
ByRichardWestall(died1836)[Publicdomain],viaWikimediaCommons.
Scannedfrom TheCalculatingPassionofAdaByron byJoanBaum.Originallyfromthe
Lovelace-ByronCollection. [Publicdomain],viaWikimediaCommons.
[Publicdomain]viaWikimediaCommons:http://pages.cpsc.ucalgary.ca/~elliotk/portfolio/ada/
AdaLovelace/Earllovelace.gif.
ByH.Lenthall,sucessortoMrKilburn,222RegentStreet,London([1])[Publicdomain],via
WikimediaCommons
Anne Isabella
(Annabella) Milbanke	
1792 – 1860	
George Gordon Byron	
1788 – 1824	
Augusta Ada Byron
1815 – 1852	
m. 1835	
m. 1815	
William King	
1805 – 1893	
Byron King Noel	
1836 – 1862	
Anne Isabella Noel Blunt	
1837 – 1917	
Ralph Gordon King
Noel Milbanke	
1839 – 1906	
Augusta Ada Noel Byron
Images:ByCreator:CharlesHayter(NationalPortraitGallery)[PublicdomainorPublicdomain],
viaWikimediaCommons
ByRichardWestall(died1836)[Publicdomain],viaWikimediaCommons
ByUnknown(JohnMurrayPublishersLondon)(ScannedfromByronandhisWorldbyDerek
Parker.)[Publicdomain],viaWikimediaCommons
ByStippleengravingbyAndrewBirrell,afterSylvesterHarding[Publicdomain],viaWikimedia
Commons.
[Publicdomain]viahttp://www.thisbrighton.co.uk/Images/city-politics/dr-william-king.jpg.
ThomasPhillips[Publicdomain],viaWikimediaCommons.
BySophiaElizabethDeMorgan(MemoirofAugustusDeMorgan)[Publicdomain],via
WikimediaCommons
Anne Isabella
(Annabella) Milbanke	
1792 – 1860	
George Gordon Byron	
1788 – 1824	
Augusta Ada Byron
1815 – 1852	
William Frend	
1757 – 1841	
William King	
1786 – 1865	
Mary Fairfax Somerville	
1780 – 1872	
Augustus de Morgan	
1806 – 1871	
Augusta Ada Noel Byron
The daughter
Images
ByCreator:CharlesHayter(NationalPortraitGallery)[PublicdomainorPublicdomain],via
WikimediaCommons.
ByRichardWestall(died1836)[Publicdomain],viaWikimediaCommons.
Scannedfrom TheCalculatingPassionofAdaByron byJoanBaum.Originallyfromthe
Lovelace-ByronCollection. [Publicdomain],viaWikimediaCommons.
Mad, bad, and
dangerous to know
—Caroline Lamb
Mathematical,
methodical, and moral
—Annabella Byron
Science vs. Creativity?
Lovelace to Augustus De Morgan
Copyright.AllAdaLovelacemanuscriptimagesontheClayMathematicsInstitutewebsiteare
©2015TheLovelaceByronPapers,reproducedby permissionofPollingerLimited.
http://www.claymath.org/publications/ada-lovelaces-
mathematical-papers
Images
AntoineClaudet. Daguerreotype ofAdaLovelace,ownedbyGeoffreyBond.
AlfredEdwardChalon[Publicdomain],viaWikimediaCommons
AntoineClaudet[Publicdomain],viaWikimediaCommons.
A generative friendship, 1833 –1852
ByUnknownstaffartistforTheIllustratedLondonNews[Publicdomain],via
WikimediaCommons
Charles Babbage
•  Mathematician, philosopher, inventor,
mechanical engineer, polemicist
•  Fellow of the Royal Society, 1815
•  Founding member of Astronomical
Society, 1820
•  Lucasian Professor of Mathematics,
University of Cambridge, 1828 – 1839
•  1791-1871
Photograph:DavidDeRourefromanexhibitionatTheScienceMuseum,London,UK.
Difference Engine #1
Assembled by Henry Prevost
Babbage after his father’s death
25,000 parts, 15 tons, 2.4m high, £17,000
Imagecredit:UCLLibrary,https://www.lms.ac.uk/2015/queen-of-the-sciences
Sophia Frend on Lovelace
“While other visitors gazed at the working
of this beautiful instrument with the sort of
expression, and I dare say the sort of
feeling, that some savages are said to
have shown on first seeing a looking-glass
or hearing a gun… Miss Byron, young as
she was, understood its working, and saw
the great beauty of the invention.”
—Sophia Frend (later de Morgan)
Sophia de Morgan, Memoir of Augustus De Morgan (1882).	
https://archive.org/details/memoirofaugustus00demorich
Image:creatorunknown,[Publicdomain],viaWikimediaCommons
Babbage to Michael Faraday
“that Enchantress who has
thrown her magic spell around
the most abstract of Sciences has
grasped it with a force which few
masculine intellects (in our
country at least) could have
exerted.”
ByUser:geni(PhotobyUser:geni)[GFDL(http://www.gnu.org/copyleft/fdl.html)orCCBY-SA
4.0-3.0-2.5-2.0-1.0(http://creativecommons.org/licenses/by-sa/4.0-3.0-2.5-2.0-1.0)],via
WikimediaCommons
Difference Engine #2
Built 1989 – 1991 after Babbage’s
plans and Allan Bromley’s work.
Babbage’s improved plans: 1847 – 1849
Computing by
steam video
MargaretSarahCarpenter[Publicdomain],viaWikimediaCommons
Lovelace on Babbage
“What a mountain I have to climb! It
is enough to frighten anyone who
had not all that most insatiable &
restless energy, which from my
babyhood has been the plague of
your life and my own. However it
has found food I believe at last.”
“He is beyond measure careless and
desultory at times. I shall be willing
to be his whipper-in.”
Talking of Lovelace and Babbage
"There is one subject ancillary to Babbage on which far too much has been
written…It is no exaggeration to say that she was a manic-depressive with the
most amazing delusions about her own talents, and a rather shallow
understanding of both Charles Babbage and the Analytical Engine…I guess
someone has to be the most overrated figure in the history of computing."
—Collier (1990)
https://podcasts.ox.ac.uk/series/ada-lovelace-symposium-
celebrating-200-years-computer-visionary
Ada Lovelace Symposium
10–11 December 2015
Lovelace translates and notates Menebrea
“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.”
Photograph:PipWillcox,fromTaylor’sScientificMemoirsprovidedbyMagdalenCollegeLibrary
DMRN+9
Numbers Into Notes
30 November 2015
http://www.oerc.ox.ac.uk/news/ada-sketches-emily-howard	
Photographsbykindpermissionof
AngelaGuyton/ScienceMuseum
Emily Howard
Lasse Rempe-Gillen
Lily Caunt
Aidan Marsden
German Martinez Merino
Rosie Middleton
Copyright:SydneyPadua,
http://sydneypadua.com/2dgoggles/the-marvellous-
analytical-engine-how-it-works/
Sydney Paduahttp://sydneypadua.com/
Ada Lovelace: Notes and Numbers
“… the Mill has two 50 digit Ingress Axes to which arguments
are transferred, with the first Ingress Axis having an auxiliary
50 digit Primed Axis which receives the most significant 50
digits when a 100 digit number is divided by a number of up
to 50 digits. Results from an arithmetic operation appear on
the Mill's 50 digit Egress Axis, which is also accompanied by a
50 digit Primed axis which, in the case of division, receives the
quotient while the remainder appears on the main Egress
Axis. In addition, the Mill has a Run-up Lever which is
activated when exceptional conditions arise during an
arithmetic operation.”
John	Walker	h,ps://www.fourmilab.ch/babbage/
https://www.fourmilab.ch/babbage/emulator.html	
N0 35 . modulus	
N1 82 . number of numbers	
N2 1 . a	
N3 1 . b	
N4 0 . number counter	
N5 2 . constant 2	
	
(?	
	
/	
L2	
L0	
S2	
P	
L3	
L0	
S3	
P	
	
+	
L2	
L3	
S2	
	
L2	
L3	
S3	
	
L4 . update count	
L5	
S4	
	
-	
L4	
L1	
)
Ada Lovelace: Notes and Numbers all	 F4-A5	 D1-C4	
Fib	35	Theme	(F4-A5)
Fib	35	Puffle	(D1-C4)
Piano
Harp
Piano
Xylophone
Tuba
3
4
4
4
4
4
4
&
Fibonacci mod 35 ('Puffle')
PipWillcox
David De Roure
for Analytical Engine, Piano, Harp, andTuba
? ∑
&
& ∑ ∑
? ∑
&
? ∑ ∑
œ œ œ ‰™
œ
r ≈ œ
œ
Œ Ó Ó
Œ
Ϫ
j ≈ œ
r ‰™ œ
J
‰
Ó Ó œ
œ œ œ
œ
œ
œ
œ
œ
œ
Œ œ
j ‰ œ
œ
≈ ‰ œ œ
≈ œ œ
œ ‰
œ
œ ‰™ œ
R
Œ œ
j ‰ Œ Ó
Ó Ó Œ
œ
œ
œ
œ
Ϫ
œ
œ œ œ
œ œ
Ó
Ó ‰
œ œ œ œ
œ
The Imagination of Ada Lovelace
The Imagination of Ada Lovelace
http://numbersintonotes.net	
Numbers Into Notes
1. Generate a sequence of numbers using an Analytical Engine algorithm.
2. Reduce these numbers to a smaller range of numbers, using clock arithmetic.
3. Play Numbers Into Notes: explore, visualize and play the number sequence interactively.
4. Export this data to music notation, MIDI, a number roll, or a W3C PROV-N graph.
Euler’s sequence: https://oeis.org/A275314	
http://numbersintonotes.net	
Mathematics in Lovelace’s day
Fibonacci—Lagrange noted periodic functions in
Fibonacci numbers in 1774, the “Pisano period’
Pi—Pi was calculated by hand to 100 decimal places in
1706 using Machin's algorithm
Golden Ratio—The number that the ratio of successive
Fibonacci numbers converges to (1.618...)
Prime numbers—Calculated here using the Sieve of
Eratosthenes
Random—Musical dice games were popular in the
1700s and generate random numbers
Factorials—The notation for factorial, e.g. 20!, was
introduced in 1808
Consonance— A mathematical function for calculating
consonance was defined by Leonhard Euler in1739
20!
http://numbersintonotes.net
The Imagination of Ada Lovelace
Computational creativity?
MargaretSarahCarpenter[Publicdomain],viaWikimediaCommons
“The Analytical Engine has no
pretensions 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.”
Boden’s Lovelace questions:
1. Helping human creativity
2. Appearing creative
3. Recognizing creativity
4. Creating
Numbers Into Notes: the première
Photographs:DavidDeRoure
https://soundcloud.com/alain_du_norde/the-gift-
the-algorithm-beyond-autonomy-and-control
•  Programmable circuit boards: Arduinos	
•  Replicating Numbers Into Notes Web app	
•  Controlled by co-creating participants	
•  Selecting and mapping a subset of notes	
•  Learning to suggest augmentations	
Music engines
“The engine is capable, under certain
circumstances, of feeling about to
discover which of two or more possible
contingencies has occurred, and of then
shaping its future course accordingly.”
Photographs:DavidDeRoureandPipWillcox
Lovelace:
The Imagination of Ada Lovelace
Material algorithms
USB	
MIDI	
•  Hardware is a physical object
containing the algorithm
•  Plugs in anywhere that
expects a MIDI keyboard
•  Algorithm can be “gifted”
c = a + b;
if (c >= m) { c -= m; }
a = b;
b = c;
CharlesWheatstone
“A MURDER HAS GUST BEEN COMMITTED AT
SALT HILL AND THE SUSPECTED MURDERER
WAS SEEN TO TAKE A FIRST CLASS TICKET TO
LONDON BY THE TRAIN WHICH LEFT SLOUGH
AT 742 PM HE IS IN THE GARB OF A KWAKER…”
https://en.wikipedia.org/wiki/Cooke_and_Wheatstone_telegraph
(John Tawell, 1845)
Imagecredit:NewYorkPublicLibrary.[Public
An information machine
“not only the mental and the
material, but the theoretical and
the practical in the mathematical
world, are brought into more
intimate and effective connexion
with each other.
…We may say most aptly, that
the Analytical Engine weaves
algebraical patterns just as the
Jacquard-loom weaves flowers
and leaves.”
The Imagination of Ada Lovelace
Gradus[n_] :=
Plus @@ (Flatten[Table[#1, {#2}] & @@@ FactorInteger[n]] - 1) + 1	
a(n) = A001414(n) - A001222(n) + 1	
where	
A001414 = sum of primes dividing n (with repetition)	
A001222 = Number of prime divisors of n counted with multiplicity
The Imagination of Ada Lovelace
The Imagination of Ada Lovelace
www.rncm.ac.uk/prism/
The Imagination of Ada Lovelace
Thinking through making
Galey, A., Ruecker, S. ‘How a prototype
argues.’ Literary and Linguistic Computing
2010, (25)4: 405-24. doi:10.1093/llc/fqq021.
“It makes a difference whether we think in terms of
processes or of products.”
“a prototype is a theory”—Lev Manovich (2007)
“one of the goals of the designer has been deliberately to carry
out an interpretive act in the course of producing an artifact"
Experimental humanities:
methods and practices
1.  Taking inspiration from ideas of the past
2.  Generating and testing hypotheses
3.  Designing digital artefacts
4.  Informing intuitions
5.  Explicating interpretations
6.  Engaging with scholars and citizens
7.  Evaluating and co-creating iterations
The explorer
“Those who have learned
to walk on the thresholds
of unknown worlds…may
then with the fair white
wings of Imagination hope
to sore further into the
unexplored amidst which
we live.”
ByHenryPhillips(1820–1868),sonofThomasPhillips[Publicdomain],viaWikimediaCommons
This research is supported by the FAST project funded
by the UK Engineering and Physical Sciences
Research Council (EP/L019981/1)
Imagecredit:NewYorkPublicLibrary.[Publicdomain]
With particular thanks to:
Pip Willcox

• Alan Chamberlain
• Graham Klyne
• Emily Howard
• Ursula Martin
• Lasse Rempe-Gillen
• David Weigl
•  AHRC Transforming
Musicology
•  Ada Lovelace
Symposium
Thank you

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