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Digital Architecture
Beyond
Computers

Digital Architecture
Beyond Computers
Fragments of a Cultural
History of Computational
Design
Roberto Bottazzi

BLOOMSBURY VISUAL ARTS
Bloomsbury Publishing Plc
50 Bedford Square, London, WC1B 3DP
, UK
BLOOMSBURY, BLOOMSBURY VISUAL ARTS and the Diana logo are
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First published in Great Britain 2018
Copyright © Roberto Bottazzi, 2018
Roberto Bottazzi has asserted his right under the Copyright, Designs
and Patents Act, 1988, to be identified as Author of this work.
Cover design by Daniel Benneworth-Gray
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Names: Bottazzi, Roberto, author.
Title: Digital architecture beyond computers: fragments of a cultural
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Subjects: LCSH: Architectural design–Data processing. |
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Contents
Preface vi
Acknowledgments xi
Illustrations xiii
Introduction: Designing with computers 1
1 Database 13
2 Morphing 39
3 Networks 59
4 Parametrics 83
5 Pixel 109
6 Random 125
7 Scanning 149
8 Voxels and Maxels 177
Afterword 207
Bibliography 213
Index 228

Preface
Despite digital architecture having carved out an important position within
the contemporary discourse, it is perhaps paradoxical that there is still little
awareness of the history, fundamental concepts, and techniques behind the
use of computers in architectural design. Too often publications concentrate on
technical aspects or on future technologies failing to provide a critical account
of how computers and architecture developed to converge in the field of digital
design. Even more overlooked is the actual medium designers utilize daily to
generate their projects. Software is too often considered as just a series of
tools; this superficial interpretation misses out on the deeper concepts and
ideas nested in it. What aesthetic, spatial, and philosophical concepts have
been converging into the tools that digital architects employ daily? What’s their
history? What kinds of techniques and designs have they given rise to?
The answer to these questions will not be found in technical manuals but
in the history of architecture and sometime adjacent disciplines, such as art,
science, and philosophy. Digital tools conflate complex ideas and trajectories
which can span across several domains and have evolved over many centuries.
Digital Architecture Beyond Computers sets out to unpack them and trace their
origin and permeation into architecture. In introducing the possibilities afforded
by the emergent CAD software, W. J. Mitchell (1944–2010) noticed that “the
application of computer-aided design in architecture lagged considerably behind
applications in engineering. Hostility to the idea amongst architects and ignorance
of the potentials of computer technology, perhaps contributed to this (1977,
p. 40).” Some twenty years later, it was Greg Lynn’s (1999, p. 19) turn to highlight
that “because of the stigma and fear of releasing control of design process
to software, few architects have attempted to use computers as a schematic,
organizing, and generative medium for design.” The present situation seems to
both contradict and confirm these remarks. If, on the one hand, CAD software
has become the media of choice for spatial designers, therefore removing any
stigma; on the other, most architects have simply replaced traditional media with
new ones, without any substantial effect on their design process or outputs. The
conceptual and practical experimentation with computational tools remains a
marginal activity in regard to the building industry as a whole. One reason is the

Prefacevii
still polarized nature of the debate on digital technologies between detractors
and devotees. Both being equally ineffective, albeit in different ways, these
factions suffer from the common tendency of approaching the role of digital tools
in design too narrowly and, consequently, conjure up “premature metaphysics”
of computation (Varenne 2013, p. 97). The former group stubbornly resists
acknowledging that digital tools can be used generatively and therefore struggle
to grasp the wider, often not even spatial, issues at stake when designing with
computers. The latter group, on the other hand, attributes to computers such
degree of novelty and internal coherence to self-validate any outcome.
Transformations in the medium of expression of any creative discipline has
always had rippling effects on its discourse be it theoretical or practical. For
instance, the slow introduction of perspective in the fifteenth and sixteenth
centuries elicited the formation of new schools, professions, and reorganization
of the building site. Strictly starting from the analysis of the actual design process,
the discussion of the case studies eventually branches out to include—whenever
relevant—its cascading impact on related fields, such as division of labor, the
emergence and propagation of new forms of knowledge or learning, the need
for new or different figures, and their impact on public knowledge at large. In
fact, the relation between tools for representation and design has always been a
fluid one in which the means of expression available at any given time determine
the bounds of architectural imagination. As for language, we cannot articulate
feelings or ideas for which we have no words; so architects have not been able to
build or even imagine forms beyond what is allowed by the tools they employed.
The introduction of CAD in the design process has deeply altered the confines
of what is possible, but has not altered this basic principle. In Alexandro Zaera-
Polo’s words “nothing gets built that isn’t transposed onto AutoDesk AutoCAD.”
The ambition of this study is to move beyond this sterile position to critically
survey the relation between digital means of representation and architectural
and urban ideas and forms—whether built or not. The central focus of this
research is therefore software, not only understood as an active component of
the design, an unavoidable media managing the interaction between designers
and designs, but also impacting on the very cognitive structure of design. As
such software is always imbued of cultural values—as Lev Manovich (2013)
noted—demanding a materialistic, which critically examines its very structure,
impact. Whereas critical theory privileges the cultural and social impact of
software overlooking its intrinsic qualities and the ideas that actually shaped it,
technical manuals offer little scrutiny of the very tools they introduce. This does
not necessarily mean that the cultural and social dimensions of digital design will
be categorically omitted in the study; rather they will not act as primary engines

viiiPreface
for innovation and development in this field. Despite the results achieved by
the application of critical theory to many fields, including architecture, when it
comes to digital architecture this approach seems structurally unable to grasp
the intrinsic qualities, constraints, and issues related to generating spatial ideas
with digital devices.
Structure and organization of the book
In introducing his thoughts, Blaise Pascal warned the reader that they should
not have accused him of not having said anything original: what was new in his
work was the disposition of the material. Likewise, here the reader will recognize
names that have been largely discussed in many scholarly works, occasionally
they will encounter genuinely new discussions or topics. Regardless, it is the
very frame within which these conversations take place to constitute the ultimate
novelty of this work: the range of precedents discussed here is brought together
for the first time under the agenda of computational and digital design. The
formula digital architecture conflates two fields—architecture and computation—
whose origins, scopes, and developments are very different from each other and
have only recently merged. Modern computers—which only appeared in their
modern incarnation during the Second World War—are significantly younger
than architecture and built without a precise aim to fulfill—Alan Turing often
talked of them as universal machines. By accepting this basic principle, the book
expands the history of “digital” architecture beyond the history of computers to
highlight how the current generation of digital architects is experimenting with or
evolving ideas and techniques that can be traced as far back as the baroque or
the Renaissance. The characterization of these episodes is independent of the
physical existence of computers at the time, thus implicitly constructing a more
cultural history of digital architecture rather than a purely technical one.
Eight chapters, each dissects specific techniques or concepts currently in
use in digital architecture and design. As the encounter between architects and
computers is opportunistic rather than predetermined, linear and chronological
accounts are utilized as little as possible. Instead, the book proposes a sort
of archaeology of digital-design processes and methods in which multiple
narratives articulated through eight fragments—each corroborated by
numerous case studies—through which the discontinuous and fluid trajectory of
techniques and ideas can be more carefully articulated. The discussion of each
theme contextualizes the use of tools in design: whether it has a generative,
representational, operations, or methodological impact. Some tools have limited
range of use (e.g., contour), whereas others have impacted several aspects

Prefaceix
of design. The discussion of these latter types of tools, such as databases,
voxel, and randomness, will be limited to their impact on spatial design and
organization.
The eight categories identified, one in each chapter are found in the most
popular CAD applications designers employ (morphing, pixel, parametrics,
etc.), yet they are not specific to any proprietary piece of software. They form an
original and accurate vantage point from which to examine what is at stake when
designing with computers. The perimeter of the investigation is software; that
is, the interface between the digital—be it computers or other digital devices,
such as scanners—and design—its culture, techniques, and communication
methods. This is understood in its present configuration, acknowledging that
ideas forging them have changed from period to period. The book contains
inevitable gaps. This is not only because such “vertical” history privileges the
evolution of concepts over an even chronological distribution, but also we
abandoned the idea of an encompassing history of the relation between design
and computation and only discussed those examples that had a paradigmatic
effect on design procedures.
The chapters are arrayed in alphabetical order and it will be left to the reader
to conflate, hybridize, evolve, and critically dissect the notions, concepts,
episodes, and practice listed in the various chapters. This method will not
only mirror the very trajectory through which the practices analyzed came into
being in the first place; but will also be a more earnest structure to capture the
discontinuous relation between design and computation. As for inventions in
other fields, advancements in digital and pre-digital tools often resulted from
the more or less smooth fusion of previously separate notions or devices. Out
of this process of conflation new affordances emerged; a process which also
explains why same episodes, names, or contraptions are recalled in more than
one chapter, albeit within a different context.
The book opens with a short overview of the concepts forming the architecture
of the modern computer. Besides the key chronological developments, the
discussion will also focus on the flexibility and “plasticity” of computation.
Computation in fact finds its root in formal logic, a field straddling between
sciences and humanities. Its basic architecture underpinning all software
architects and designers daily use stems out of a very concise and defined series
of the shared procedures. Although for users Photoshop and Grasshopper may
look like very different, if not antithetical, pieces of software, their procedures
are not. The chapter on databases—a central component of any piece of
software—focuses on the long history of techniques utilized to spatialize data
and their, at times, direct impact on architecture. The chapter on networks can

xPreface
be seen as the extension of the previous one. Whereas databases look at the
spatialization of data at the architectural scale, networks are here understood as
territorial mechanisms coupling space and information. The growth in scale and
complexity of networks is one of the implicit outcomes of this chapter; whereas
the long narrative woven by these first two chapters clearly reveals how much
the success of embedding information depends on the theoretical framework
steering its implementation. Throughout the various cases discussed what
emerges is not only an outstanding series of techniques to spatialize data; but
also, contrary to common perceptions, how data has always needed a material
support to exist, which has often been provided by architecture. “Morphing”
discusses a series of techniques to control curves and surfaces which have had
a direct impact on the formal repertoire of architects. Part of this conversation
overflows into the fourth chapter on the timely theme of parametrics. This is
certainly the most popular theme discussed in the book but, possibly for the same
reason, the one riddled with all sorts of complexities and misunderstandings.
Starting from the great examples of the Roman baroque, the chapter will sketch
out a more material, design-driven understanding of parametric modeling. Some
of the chapters are not dedicated strictly to computational tools but embrace
the composition of the modern computer, which includes digital devices that
have little or no computational power. The chapters on pixels and scanners both
fit this description, as they chart how technologies of representation ended up
impacting design and providing generative concepts. Randomness—the sixth
chapter—is unavoidably the most abstract and complex of the whole book.
Besides the technical complexity in generating genuine random numbers
with computers, it is the computational and philosophical issues which are
foregrounded here. Finally, the last chapter discusses notion of voxel tracing
both its development and impact on contemporary digital design. The chapter
on scanning returns to examine how representational technologies have evolved
from mathematical perspective to the laser scanner. Despite being central to
many digital procedures, this concept has only recently been explicitly exploited
by designers, whereas its historical and theoretical implications have been so far
completely overlooked.

Acknowledgments
This book brings together several strands of research that have been carried out
over the past fifteen years or so. Many institutions, colleagues, professionals, and
students have influenced my views for which I am very thankful. I am particularly
thankful to Frédéric Migayrou not only for providing the afterword to the book,
but also for giving me the opportunity to develop my research and for sharing his
time and immense knowledge with me. At The Bartlett, UCL—where I currently
teach—I would also like to thank Marjan Colletti, Marcos Cruz, Mario Carpo,
Andrew Porter, Mark Smouth, Bob Sheil, Dr. Tony Freeth, and Camilla Wright. At
the University of Westminster—where I also work—I am particularly grateful to
Lindsay Bremner for broadening the theoretical territory within which to discuss
the role of computation in design, Harry Charrington, Richard Difford, Pete Silver,
and Will McLean. During the ten years spent at the Royal College of Art, Nigel
Coates was not only first to believe in my research, but also communicated
me a great passion for writing and publications in general. I am also grateful to
Susannah Hagan—whose Digitalia injected a design-driven angle to the work—
Clive Sall. Amongst the many outstanding projects I followed there, Christopher
Green’s had an impact on my conception of digital design. Parallel strands of
research were developed whilst at the Politecnico of Milan where I would like to
thank Antonella Contin, Raffaele Pe, Pierfranco Galliani, and Alessandro Rocca.
The section on experimental work developed in Italy in the 1960’s and 1970’s
is largely based on the generosity of Leornardo Mosso and Laura Castagno
who gave me the opportunity to analyse their work, Guido Incerti, and Concetta
Collura. The research on the use of digital scanners on architecture was also
developed through conversations with ScanLab and Andrew Saunders. Over the
years some key encounters have changed my views of architecture which have
eventually opened up new avenues for research which have converged in this
book. These are: Oliver Lang, and Raoul Bunschoten.
A special thank you to my teaching partner, Kostas Grigoriadis for his
insights, commitment, and help. I am also grateful to Bloomsbury Academic
for the opportunity they provided me with; particularly, James Thompson—my
editor—who supported this project and nurtured it with is comments, Frances
Arnold, Claire Constable, Monica Sukumar, and Sophie Tann.

xiiAcknowledgments
Finally, I would like to thank my parents for their continuous support. My
deepest gratitude goes to my wife Stefania and my children Aldo, and Emilia who
have not only endured the hectic lifestyle which accompanied the preparation
of the book, but have also supported and encouraged me in every which way
possible. Stefania followed the entire process of this book providing invaluable
knowledge and critical insights at all levels: from the intellectual rationale framing
the work to the detailed feedback on the actual manuscript. Without their
unconditioned love and help all this book would not have existed. It is to them
that this book is dedicated to.

Illustrations
0.1 Antikythera Mechanism. Diagram by Dr. Tony Freet, UCL.
Courtesy of the author 7
0.2 The Computer Tree, ‘US Army Diagram’, (image in the public
domain, copyright expired) 11
1.1 Reconstruction of Camillo’s Theatre by Frances Yates. In F.
Yates, The Art of Memory (1966). © The Warburg Institute 25
1.2 Image of Plate 79 from the Mnemosyne series. © The Warburg
Institute32
1.3 Diagram comparing the cloud system developed by Amazon
with traditional storing methods. Illustration by the author 35
2.1 OMA. Plan of the competition entry for Parc La Villette (1982).
All the elements of the project are shown simultaneously taking
advantage of layering tools in CAD. © OMA 44
2.2 P
. Portoghesi (with V. Giorgini), Andreis House. Scandriglia,
Italy (1963-66). Diagram of the arrangement of walls of the
house in relations to the five fields. © P
. Portoghesi 51
2.3 Computer Technique Group. Running Cola is Africa (1967).
Museum no. E.92-2008. © Victoria Albert Museum 54
3.1 Diagram of the outline of the French departments as they were
redrawn by the 1789 Constitutional Committee. Illustration by
the author 66
3.2 Model of Fuller’s geodesign world map on display at the
Ontario Science Museum. This type of map was the same
used for the Geodomes. © Getty Images 70
3.3 Exit 2008-2015. Scenario “Population Shifts: Cities”. View of
the exhibition Native Land, Stop Eject, 2008-2009 Collection
Fondation Cartier pour l’art contemporain, Paris. © Diller
Scofidio + Renfro, Mark Hansen, Laura Kurgan, and Ben
Rubin, in collaboration with Robert Gerard Pietrusko and
Stewart Smith 80

xiv Illustrations
4.1 Work produced in Re-interpreting the Baroque: RPI Rome
Studio coordinated by Andrew Saunders with Cinzia Abbate.
Scripting Consultant: Jess Maertter. Students: Andrew Diehl,
Erica Voss, Andy Zheng and Morgan Wahl. Courtesy of Andrew
Saunders94
4.2 L. Moretti and IRMOU. Design for a stadium presented as
part of the exhibition ‘Architettura Parametrica’ at the XIII Milan
Triennale (1960). © Archivio Centrale dello Stato 102
4.3 marcosandmarjan. Algae-Cellunoi (2013). Exhibited at the
2013 ArchiLAB Naturalizing Architecture. © marcosandmarjan 106
5.1 Ben Laposky. Oscillon 40 (1952). Victoria and Albert Museum
Collection, no. E.958-2008. © Victoria and Albert Museum 110
5.2 Head-Mounted device developed by Ivan Sutherland at
University of Utah (1968) 115
5.3 West entrance of Lincoln Cathedral, XIth century. © Getty Images 117
7.1 Illustration of Vignola’s ‘analogue’ perspective machine. In
Jacopo Barozzi da Vignola, Le Due Regole della Prospettiva,
edited by E. Danti (1583). (image in the public domain,
copyright expired). Courtesy of the Internet Archive 157
7.2 Sketch of Baldassare Lanci’s Distanziometro. In Jacopo
Barozzi da Vignola, Le Due Regole della Prospettiva, edited by
E. Danti.1583. (image in the public domain, copyright expired).
Courtesy of the Internet Archive 158
7.3 “Automatic” perspective machine inspired by Durer’s sportello.
In Jacopo Barozzi da Vignola, Le Due Regole della Prospettiva,
edited by E. Danti (1583). (image in the public domain,
copyright expired). Courtesy of the Internet Archive 163
7.4 J. Lencker. Machine to extract orthogonal projection drawings
directly fro three-dimensional objects. Published in his
Perspectiva in (1571). (image in the public domain, copyright
expired). Courtesy of the Internet Archive 164
7.5 Terrestrial LIDAR and Ground Penetrating Radar, The
Roundabout at The German Pavilion, Staro Sajmiste, Belgrade.
© ScanLAB Projects and Forensic Architecture 175

Illustrations xv
8.1 Albert Farwell Bemis, The Evolving House, Vol.3 (1936).
Successive diagrams showing how the design of a house can
be imagined to take place “within a total matrix of cubes” to
be delineate by the designer through a process of removal of
“unnecessary” cubes 183
8.2 Leonardo Mosso and Laura Castagno-Mosso. Model of the La
Cittá Programmata (Programmed City) (1968-9). © Leonardo
Mosso and Laura Castagno-Mosso 187
8.3 Diagram describing Richardson’s conceptual model to
“voxelise” of the skyes over Europe to complete his numerical
weather prediction. Illustration by the author 191
8.4 Frederic Kiesler, Endless House. Study for lighting part of the
(1951). © The Museum of Modern Art, New York/Scala, Florence 202
8.5 K. Grigoriadis: Multi-Material architecture. Detail of a window
mullion (2017). © K. Grogoriadis 204

Introduction: Designing
with computers
A machine is not a neutral element, it has got its history, logic,
an organising view of phenomena
Giuseppe Longo (2009)
Before venturing into the more detailed conversations on the role of digital tools
in the design of architecture and urban plans, it is worth laying out a series of
the key definitions and historical steps which have marked the evolution and
culture of computation. Whereas each chapter will discuss specific elements of
computer-aided design (CAD) software, here the focus is on the more general
elements of computation as more abstract and philosophical notions. Built on
formal logic, computers are unavoidably abstracting and encoding their inputs;
whatever media or operation is eventually transformed into strings of discrete 0s
and 1s. What is covered in this short chapter is in no way exhaustive (the essential
bibliography at the end of the chapter provides a starting point for more specific
studies) but clarifies some of the fundamental issues of computation which shall
accompany the reader throughout all chapters.
First, computers are logical machines. We do not refer to a supposed artificial
intelligence computers might have, but rather, literally, to the special branch
of mathematics that some attribute to Plato’s Sofist (approx. 360 BC), which
concerns itself with the applications of principles of formal logic to mathematical
problems. Whereas formal logic studies the “structure” of thinking, its coupling
to mathematics allows to broadly express statements pertaining to natural
languages through algebraic notations, therefore coupling two apparently
distant disciplines: that of algebra and—what we now call—semiotics. It is
this century-long endeavor to create an “algebra of ideas” that has eventually
conflated into the modern computer, compressing a wealth of philosophical and
practical ideas spanning over many centuries. The common formal logic from
which digital computation stems also accounts for the “plasticity” of software:
beyond the various interfaces users interact with, the fundamental operations

2
Digital Architecture Beyond Computers
performed by any software eventually involve manipulation of binary code
consisting of two digits: 0 and 1. This also explains why an increasing number
of software can perform similar tasks: Photoshop and visual scripting language
Grasshopper, for instance, allow to manipulate similar media objects, such as
geometries and movies.
What’s a computer, anyway? It is easier to see how the etymology of the
word derived from the act of computing, of crunching calculations; however,
whenever we buy a computer we actually purchase a series of devices only
some of which actually compute. Computers in fact also include input devices—
keyboard, mouse, etc.—and output ones—monitor, printer, etc.—allowing us
to interact with the actual computing unit. Computation is therefore an action
which is not exclusive to computers; likewise, the word “digital” does not solely
pertain to the domains of computer, as it derives from digits, discreet numerical
quantities (such as those of the fingers of our hands).
Perhaps unsurprisingly given these initial definitions, modern computation is
a rather old project whose foundation can be identified with the groundbreaking
work of Gottfried Leibniz in the seventeenth century. In Herman Goldstine’s words
(1980, p. 9), Leibniz’s contribution can be summarized in four points whose
power still resonate with the work of digital designers today: “His initiation of the
field of formal logic; his construction of a digital machine; his understanding of
the inhuman quality of calculation and the desirability as well as the capability
of automating this task; and, lastly, his very pregnant idea that the machine
could be used for testing hypothesis.” It is this very last point to both reveal
the importance of Leibniz’s thinking and set a richer context for digital design:
this field is still somehow stigmatized for its “impersonal,” rigid rules stifling the
design process, whereas anybody fairly fluent in digital design would know that
the opposite is also true. Computers’ ability to take care of the “inhuman quality
of calculations” frees up conceptual space for the elaboration of alternative
scenarios. As for testing hypotheses, it implies an experimental, open, iterative
relation between designer and computer aiming at fostering innovation.
Before surveying some of the steps toward the construction of modern
computers, it is important to clarify some of the key concepts we will repeatedly
utilize throughout the book.
Analogical and digital computing
Prior to the invention of modern computers in the first part of the twentieth
century, the most advance calculating machines utilized analogous or
continuous computation. Analogue forms of computation were based on

Introduction
3
continuous phenomena. All empirical phenomena are analogical; they always
occur within a continuum. For instance, time flows uninterrupted regardless of
the type of mechanism we are using to measure it. Analogue computers execute
calculations adopting continuous physical elements whose physical properties
are measured—for example, the length of rods is recorded or different current
voltage. As Goldstine (1980, p. 40) reminds us, analogue computing goes
hand in hand with nineteenth-century mathematics: the developments in the
field of mathematics required new types of machines—precisely, analogue
machines—in order to compute the set of equations describing a certain
physical phenomenon. “The designer of an analogue device decides what
operations he wishes to perform and then seeks a physical apparatus whose
laws of operation are analogous to those he wishes to carry out.” The slide ruler
is an example of analogue computing in which logarithms are calculated by
sliding two markers along a graded piece of wood, effectively measuring their
position along a graded edge. The two markers physically represent established
mathematical properties of logarithms stating that the logarithm of a product of
two numbers is the sum of the logarithms of the two numbers. Through these
examples it is possible to discern how computational machines are always an
embodiment of theory, and they are not natural but designed artifacts, informed
by theoretical preoccupations as well as physical limitations.
Modern computers, on the other hand, are digital machines; they operate with
digits combined according to algebraic and logical rules. They do not operate
with continuous quantities—like their analogue counterparts—but rather discrete
ones which capture through numbers what would otherwise be a continuous
experience. The invention of the Western alphabet could very well mark the
introduction of the first discrete system: whereas when we speak the modulation
of sounds is continuous, the alphabet dissects it into a number of defined
symbols—letters. The abacus, Leibniz’s calculating machine, and Charles
Babbage’s (1791–1871) Analytical Engine (proposed in 1837) are examples
of discrete computing machines in which basic calculations such as additions
and subtraction are executed and the results carried over to complete other
operations. In the case of Leibniz’s wheel numerical quantities are engrained on
metal cogs which click to position to return the final desired results. Quantities are
finite and discreet, no longer continuous. Modern computers always discretize;
they reduce continuity to the binary logic of 0s and 1s creating a problematic
conceptual and, at times, practical gap between the natural and the artificial.
These problems are at the center of studies on how computers operate as
ontological and representational machines; though these conversations affect
all areas of computations, this book will particularly concentrate on its impact on

4
design, especially in the use of computer simulations and parametric modelers
to design architecture.
The elegance of binary code
As we mentioned, all data input in or output by computers are formatted in
binary code. The elegance of this system brings together several disciplines and
knowledge which have matured over many centuries. We know that the invention
of binary code greatly precedes its introduction in Leibniz’s work. The German
philosopher’s was, however, motivated by a different desire; that of conceiving
the shortest, in a way the most economic numerical system able to describe and
return the largest number of combinations. Leibniz in fact saw binary numbers
as the starting point of a much bigger endeavor: that of expressing philosophical
thoughts and even natural language statements through algebraic expressions.
Leibniz did make several attempts to both define such a system and test its
applications—for instance, to resolve legal disputes—without much success:
this would fundamentally remain a dream—to borrow Martin Davis’ expression—
that would be quickly forgotten after his death.
Uninterested in Leibniz’s philosophical ambitions, French textile worker
Basile Bouchon developed a system of perforated cards in 1725 to control the
weaving patterns of mechanical looms, which was shortly after improved by
Jean-Baptiste Falcon. Once the cards were fed through the machine, the loom
would automatically alternate the combination of threads to obtain a desired
pattern. Binary logic would find an ideal partner in the material logic of perforated
cards as the unambiguous logic of either holed or plain cells mirrored that of 0s
and 1s. Despite the invention and rapid diffusion of microprocessors, mainframe
computers still used punch cards as material support for software instructions.
Whether aware of Leibniz’s work or not, binary numbers were also the decisive
ingredient in British mathematician George Boole’s (1815–64) work whose
logic basically marked the modern foundation of this discipline and indelibly
shaped how computers work. Boole’s (1852, p. 11) own words well capture the
importance of his work: “The design of the following treatise is to investigate
the fundamental laws of those operations of the mind by which reasoning is
performed: to give expression to them in the symbolical language of Calculus,
and upon this foundation to establish the science of Logic and instruct its
method; . . . and finally to collect from the various elements of truth brought
to view in the course of the inquiries some probable intimations concerning
the nature and constitution of the human mind.” Boole’s invention consisted of

Introduction
5
employing algebraic notation to express logical statements; such connection
was just a brilliant example of scientific thinking but also provided a clear
and coherent bridge between algebra and natural languages. Using the four
arithmetical operations, Boole could translate statements in natural language.
For instance, the * symbol describe a “both” condition: the group of all red cars
could be expressed as, for instance, x = y * z or x = yz; in which y describes
the group of “red objects,” whereas z denotes that of “cars.” The + symbol
described and/or conditions, from which it was possible to quickly infer how the
symbol could also be utilized. The famous exception to the algebraic notation—
which had already been anticipated by Leibniz—was the expression x2
= xx = x,
as adding a group to itself would not produce anything different or new. Boole
(1852, pp. 47–48) introduced binary numeration as “the symbol 0 represents
Nothing,” whereas the symbol 1 represents “‘the Universe’ since this is the only
class in which are found all the individuals that exist in any class. Hence the
respective interpretations of the symbol 0 and 1 in the system of Logic and
Nothing and Universe” (italics in the original).
From the point of view of computation, Boole’s logic basically allowed to
program a computing machine: it supplied a syntax to correctly turn instructions—
linguistics—into machine commands—numbers. It is therefore not a coincidence
that further work in this area—particularly by Gottlob Frege (1848–1925)—also
marked the beginning of modern studies on semiotics. However, the full realization
of this potential would only occur in 1910–13 when Bertrand Russell (1872–
1970) and Alfred North Whitehead (1861–1947) would publish their Principia
Mathematica taking up Boole’s logic (another failed dream, in some respect).
The nineteenth century was also characterized by progresses made in the
development of electricity. Electric circuits would eventually be employed to
control machines and become the “engine” of the modern computer. Switches
in electrical circuits also only have two positions: they are either open or close.
Peirce first intuited that binary code could have been the ideal language to
control the position of the switches. Its application to computation would,
however, only occur in the 1930s when Claude Shannon’s essential work on
information—also discussed in the chapter on randomness—would relate
formal logic (by now, programming), electrical circuitry, and information
transmission under the unifying language of binary numbers. After Shannon’s
work it was possible to compute with a modern computer: that is, to determine
a set of logical steps, translate them into a programming language engendered
with both semantic and syntactic characteristics, which could instruct the
electric apparatus of the computer.

6
This short foray into the evolution of basic programming language for
computers shows how computers came to exploit disparate notions which
eventually converged; since the Jacquard’s loom, computation has been
consisting of a hardware (computing mechanism) and a software (set of
instructions), which will be briefly discussed here.
Data and information
Information is one of the key words of the twentieth century. Its relevance has
increased exponentially not only through the proliferation of new media, but also
through the parallel interest expressed by more established disciplines, such
as philosophy and ethics. The invention of the modern computer surely played
a significant part in growing its popularity: in fact, the computer essentially
performs nothing but manipulations of stored information. The wealth of
knowledge on the subject has not always been beneficial, as several definitions
of the same words emerged responding to the very contexts in which they were
analyzed. Information and data have been defined in semantic, statistical terms
often presenting contrasting definitions.
Rather than attempting to reconcile these differences, we concentrate on the
very material nature of the modern computer and on its intrinsic qualities and
limitations. Computational information is purely a quantitative phenomenon,
unrelated to qualitative, sematic concerns: it can claim no meaning, and
even less truthfulness. To understand the nature and properties of digital
data and information, we have to cast a larger net of categories over the
subject. Contrary to the superficial notion that data is abstract, immaterial
entity, computers first and foremost are material constructs: data stored in
computers exist as the combinations of physical properties. Most often these
are alternate voltages switching between two currents corresponding to binary
numeration. Binary digits—better known as bits—are the building blocks of
digital data. There are sequences of 0s and 1s, without any precise meaning:
they could be characters in a text, songs, 3d models, etc. Groups of bits form
patterns used as codes. Structured and coded strings of bits are finally defined
as data, whereas information is generally defined as data in context. In this
“epistemological chain” of digital data, information marks the threshold in which
the material properties are stored in the hardware can designed. This specific
act is performed through algorithms which allow information to be “interpreted,
manipulated, and filled with meaning” (Ross 1968, p. 11; quoted in Cardodo
Llach 2012, p. 42). Strictly speaking, digital media only deal with information as
this is the deepest editable layer of content in the computer; for this reason we

Introduction
7
have a specific field of studies dedicated to information—i.e., informatics—but
not to data.
Brief history of computers
The modern computers emerged out of the millennia-long development of
artificial apparatuses to assist human calculation. Its origin is found in the
development of calculating machines first manually operated and then based
on activating mechanical parts. Among the most ancient computing devices
we can count the Antikythera mechanism—perhaps the first ever—an analogue
computing orrery discovered on the homonymous shipwreck in Greece. Made
of about thirty interconnected bronze cogs, this device could have been made
between 150 and 100 BC and used for astronomical calculations. The abacus, a
calculating machine based on discrete quantities, emerged much later, around
1200 in China. The emergence of mechanical calculating machines is generally
understood to coincide with Blaise Pascal’s (1623–62) device built in 1642—at
the age of twenty—for his father. The machine, based on a series of rotating
wheels, could solve additions and subtractions. Not long after, in 1673 Leibniz
completed his version of a similar type of machine—often referred to as “Leibniz
wheel” because of its operating principle—which extended its functions to all
four basic mathematical operations.
Falcon’s perforated cards were further developed by Joseph Marie Jacquard
(1752–1834), who connected them to a weaving loom neatly separating the set
of instructions to compute—marking the birth of the notion of software—the
Figure 0.1 Antikythera Mechanism. Diagram by Dr. Tony Freet, UCL. Courtesy of the author.

8
device physically computing it—from hardware. This division still in use was
central not only to the application of computing technologies to everyday tasks
but also to the emergence of information as a separate field in computational
studies. It is interesting to point out the impressive penetration that this machine
had, once again demonstrating that computation is not a recent phenomenon:
in 1812 there were 11,000 Jacquard looms in use in France.1
The principles of the Jacquard loom were also at the basis of Charles
Babbage’s Difference Engine (1843). Operated by punch cards, Babbage’s
machine could store results of temporary calculations in the machine’s memory
and compute polynomials up to the sixth degree. However, the Difference Engine
soon evolved into the Analytical Engine which Babbage worked on for the rest of
his life without ever terminating the construction of what can be considered the
first computer. Its architecture was in principle like that of the Harvard Mark I built
by IBM at the end of the Second World War. The working logic of this machine
consisted of coupling two distinct parts, both fed by perforated cards: the store,
which computed the logical steps to be operated upon the variables, whereas
the mill stored all the quantities on which to perform the operations contained
in the store. This not only meant that the same operations could be applied to
different variables, but also marked the first clear distinction between computer
programs—in the form of algebraic scripts—and information. This section would
not be complete without mentioning Augusta Ada Byron (1815–52)—later the
Countess of Lovelace—whose extensive descriptions of the Analytical Engine
not only made up for the absence of a finished product, but also, and more
importantly, fully grasped the implication of computation: its abstract qualities
which implied the exploitation of combinatorial logic and its application to
different type of problems.
The year 1890 was also an important year in the development of computation,
as calculating machines were utilized for the U.S census. This not only marked
the first “out-of-the-lab” use of computers but also the central position of the
National Bureau of Standards, an institution which would play a pivotal part in the
development of computers throughout the twentieth century: as we will see later,
the Bureau will also be responsible for the invention of the first digital scanners
and pattern recognition software. The technology utilized was still that of
perforated cards, which neatly suited the need to profile every American citizen:
the organization in rows and columns matched the various characteristics the
census aimed to map. The year 1890 marks not only an important step in our
short history, but also the powerful alignment of computers and bureaucracies
through quantitative analysis.

Introduction
9
Whereas the computing machines developed between 1850 and the end of the
Second World War were all analogue devices, the ENIAC (Electronic Numerical
Integrator and Calculator), completed on February 15, 1946, emerged as the first
electronic, general-purpose computer. Contrary to Vannevar Bush’s machines
developed from the 1920s until 1942, the ENIAC was digital and already built
on the architecture of modern computers that we still use. This iconic machine
was very different from the image of digital devices we are accustomed to: it
weighed 27 tons covering a surface of nearly 170 square meters. It consisted
of 17,468 vacuum tubes—among other parts—and was assembled through
about 5,000,000 hand-soldered joints needing an astonishing 175 kilowatts to
function. It nevertheless brought together the various, overlapping strands of
development that had been slowly converging since the seventeenth century,
and, at the same time, paved the way for the rapid diffusion of computation in
all aspects of society.
The final general configuration of modern computers was eventually designed
by John von Neumann (1903–57) whose homonymous architecture would devise
the fundamental structure of the modern computer as an arithmetic/logic unit—
processing information; a memory unit—later referred to as random-access
memory (RAM); and input and output units (von Neumann 1945). The idea of
dedicating separate computational units to the set of instructions contained in
the software from the data upon which they were operated allowed the machine
to operate much more smoothly and rapidly, a feature we still take advantage of.
The 1970s finally saw the last—for now—turn in the history of computers with
the emergence of the personal computer and the microprocessor. Computers
were no longer solely identified with colossal machines that required dedicated
spaces, but rather could be used at home and tinkered with in your own garage.
This transformation eventually made processing power no longer “static” but
rather portable: today roughly 75 percent of the microprocessors manufactured
are installed not on desktop computer but on portable machines like laptop,
embedding computation into the very fabric of cities and our daily life.
Brief history of CAD
It was the development of specialized pieces of software that marked the advent
of CAD tools. The invention of CAD should be seen as one of the products of the
conversion of the military technologies developed during the Second World War
to commercial uses as needed by the US government in order to capitalize on
the massive investments made. This decision had a profound effect on postwar

10
academic research. Tasked with transferring technologies conceived for very
specific purposes (e.g., ballistic calculations), software designers stripped these
tools down to their more general features in order to make them applicable to
as many problems as possible, including unforeseen ones. This would be a
common habit in software development which has only grown in time with more
accurate and faster client feedback and through “error reports” or forums.
CAD was also a necessity as computer-controlled machines—broadly
grouped as computer-aided manufacturing (CAM)—were also being developed.
These machines were operating on a numerical rather than manual basis; no
need for dials and levers to control them but rather an interface which also
operated on a numerical basis: the computer. It is within this context that the
DAC-1 by IBM and Sketchpad were designed. Sketchpad (1962)—the result of
Ivan Sutherland’s (1938–) research at MIT—not only marked a historic benchmark
for digital design but also exemplified how digital tools migrated from military
to civilian uses. The software was deliberately conceived as a generic interface
for design in order not to foreclose any potential area of application. However,
since his first presentation, Sutherland (2003) realized the design potential of
CAD; designing objects with a computer was “essentially different” from hand
drafting, he stated. The step-by-step formal logic of emerging software could
not have been fully exploited without also changing the way in which objects
were conceived. The ambition was for both design process and representation
to radically merge traditional practices with the advantages afforded by
computation. Just as the following two decades would be characterized by
many experiments developed within academia—which will occupy large parts
of the discussion in the book—CAD has also slowly been developed in the
corporate world. Here the emphasis was not so much on innovative design
methods or theories, but on efficiency, on streamlining the transmission of
information between design offices and building sites to make projects possible
and/or cheaper. Architecture practices rarely involved computers though, and,
as a result, CAD only began to penetrate the world of architecture in the 1980s
when software packages such as AutoDesk AutoCAD were first released.2
A
rare exception was American corporate practice Skidmore, Owings Merrill
(SOM), which not only acquired mainframe computers since the 1960s, but also
developed their own pieces of software to assist both design and construction.
During this period, however, other disciplines such as automobile, aeronautical,
and naval design were leading the way in the implementation of CAD. It is not a
coincidence that the term “computer graphics” was invented at Boeing by William
F. Fetter (1928–2002), for instance. Computer graphics would eventually branch
out to form the field of image visualization and animation, which found fertile

Introduction
11
ground in the movie industry.3
This is not an anecdotal matter as the very context
within which software packages developed would deeply impact its palette of
tools and general architecture. When later on architects started appropriating
some of these software packages they had to adapt them to fit the conventions
of architectural design. Cardoso Llach (2015, p. 143) usefully broadly divided
software for design into two categories: CAD solely relying on geometry and
its Euclidean origins; and simulation software based on forces and behaviors
inspired by Newtonian physics. Every Rhinoceros or Autodesk Maya user knows
all too well the frustration caused by respectively having to model architecture in
environments conceived for different disciplines: the default unit of engineering
design is millimeters, whereas in the animation industry scale does not have
physical implications. Likewise, it is not surprising that computer programs
conceived to design airplanes’ wings or animated movie characters did have
such advanced tools to construct and edit complex curves and surfaces. In all
the design fields mentioned, aerodynamics is not a matter of aesthetic caprice
but rather a necessity! However, much of both the criticism and fascination
for these tools have argued their position by using the most disparate fields
such as philosophy, aesthetic, or even psychology but very rarely computation
itself, with its intrinsic qualities. As the market demand grew so did the range of
bespoke digital tools to design architecture, with some architects such as Frank
Gehry, Peter Eisenman, or Bernard Cache going the extra mile and were directly
involved with software manufacturers to customize CAD tools.
Figure 0.2 The Computer Tree, ‘US Army Diagram’, (image in the public domain, copyright
expired).

12
Understanding both the evolution of computing and its application to design
is not only a key step to appreciate its cultural richness, but also crucial to deepen
architects’ understanding of what is at stake when designing with computers.
Notes
1. Encyclopaedia Britannica (1948), s.v. “
Jacquard, Joseph Marie” (Quoted in Goldstine
1972, p. 20).
2. Developed since the late 1970s, the first release of AutoCAD was demonstrated at the
COMDEX trade show in Las Vegas in November 1982. AutoCAD 1.0 December 1982.
Available at: http://autodesk.blogs.com/between_the_lines/ACAD_R1.html (Accessed
August 15, 2016).
3. This connection will be explored in the chapter on pixels.

Chapter 1
Database
Introduction
The use of databases is a central, essential element of any digital design. Any
CAD package designers routinely use, manage, and deploy data in order to
perform operations. This chapter not only deconstructs some of the processes
informing the architecture of databases; but, more importantly, also maps out
their cultural lineage and impact on the organization of design processes and
physical space. The task is undoubtedly vast and for this reason the chapter
extends onto the study of networks discussed in a different chapter: the former
traces the impact of data organization on form (physical structures), whereas the
latter analyzes the later applications of data to organize large territories, such as
cities and entire countries. Since the initial attempts to define and contextualize
the role of digital information as a cultural artifact, theoretical preoccupations
have been as important as technical progress; for instance, when introducing
these issues to a general audience, Ben-Ami Lipetz did not hesitate to state that
“the problem [of data retrieval] is largely an intellectual one, not simply one of
developing faster and less expensive machinery” (Lipetz 1966, p. 176).
A database is “a large collection of data items and links between them,
structured in a way that allows it to be accessed by a number of different
applications programs” (BCS Academy Glossary Working Party 2013, p. 90).
In general parlance, databases differ from archives, collections, lists, and the
like, as the term precisely identifies structured collection of data stored digitally.
Semantically,theyalsodivergefromhistoricalprecedents,astheyaresimplerdata
collections than, for instance, dictionaries or encyclopedias. Much of the semiotic
analysis of historical artifacts concerned with collecting data has been focusing
on the difficulties arising to unambiguously define both the individual elements—
primitives—of a list and the rules for their aggregation or combination—formulae.
This issue is not as crucial in the construction of a database as both primitives
and formulae are established a priori by the author. This will be true even a

14
database is connected to other ones or its primitives are actually variables. This
should not be seen as a negative characteristic; rather it circumscribes the range
of action of databases to a partial, more restricted, domain in contrast to the
global ambitions of validity of, for instance, the dictionary. Databases construct
their own “world” within which most of the problems highlighted can be resolved:
a feature often referred to as semantic ontology (Smith 2003).
Given the wide time span we will be covering in this chapter we will
unavoidably refer to both archives and collections as databases, or better proto-
databases. Key characteristics of databases are hierarchy (data structure) and
retrieval system (algorithm), which determine how we access them and how
they will be visualized. It is the latter that indicates that similar, if not altogether
identical, databases may appear to be radically different if their retrieval and
visualization protocols change. This is a particularly important point constituting
one of the key criteria to analyze the relation between databases and space.
By excluding that databases are just sheer accumulation of structured data—a
necessary but insufficient condition; we will concentrate on the curatorial role
that retrieval systems have to “spatialize” a collection of data on the flat confines
of a computer screen or in physical space. In the age of Google searches in
which very large datasets can be quickly aggregated and mined, data curation
becomes an evermore essential element to navigate the deluge of data. However,
rather than limiting it to the bi-dimensionality of screens, we also will concentrate
on its three-dimensional spatialization; that is, on how changes in the definition
of databases impacted architecture and the tools to design it. In fact we could
go as far as to say that design could be described as the art of organizing and
distributing matter and information in space. To design a building is a complex
and orchestrated act in which thousands of individual elements have to come
together in a coherent fashion. Vitruvius had already suggested that this ability to
coordinate and anticipate the result of such an operation was the essential skill
that differentiated architects from other design professions. This point is even
more poignant if we consider that most of these elements making a building
are not designed by architects themselves and their assembly is performed by
other professionals. This analogy could also hold true for designing with CAD, as
this process can be accomplished by combining architectural elements existing
both as textual and as graphic information, as it happens in Building Information
Modeling (BIM).1
Here too hierarchy of information plays a crucial role to
produce coherent designs accessible to the various professions participating in
the construction process.
Hierarchy and retrieval eventually provide the form for the database. Form
here should be understood to have both organizational and aesthetic qualities,

Database
15
whether the database contains abstract or visual information. These databases—
referred to as practical or “pragmatic” by Umberto Eco (1932–2016)—possess
three characteristics (2009, p. 45). First, they are referential, as they stand for
objects which are external to the database itself. Their type of external links set
can vary: items on databases are indexical, they stand for real objects or values
(e.g., the specific weight of steel in a software for structural analysis), while at
other times they are purely virtual (as in the case of mathematical operations
routinely carried out to perform specific tasks). Secondly, they are finite: their
limit is always known and fixed. This does not mean that databases cannot have
dynamic qualities—a key feature of digital databases which we will explore in the
chapter on parametrics—rather this means that at any given moment their form
is finite. Consequently, their final property establishes that they cannot be altered
without also changing any of the conditions forming them. There is nothing
incongruous in a database; its closed world does not tolerate blurry boundaries.
The combination of these three factors represents their form which defines the
aesthetics of the database. We should note in passing that the “introverted”
definition of database will contrast with the open, infrastructural definition of
networks which will be used later on. The relation between the content and
the form of a database is an active element which can be legitimately defined
as an act of design; all the examples dissected in the chapter will focus on
how these databases were designed and how they gave rise to abstract or
concrete spatial configurations. Finally, the retrieval logic of the database—the
element differentiating databases from other historical modes of structuring
information—gives rise to five types of spatial configurations according to their
degree of flexibility: hierarchical (arranging data in tree structure and parent/
child relations), network (close to the previous model but use “sets” to allow
children to have more than one parent as well as many-to-many relationships),
relational (based on a graph model of nodes and relationships), client/user
(in which multiple users can remotely and simultaneously access and retrieve
information), and object oriented (in which the objects in the database appear
as programming language) (Paul 2007, p. 96). Rather than emphasizing
technical differences, we should understand this categorization as an example
of combinatorial logic which greatly precedes the invention of databases and
constitutes their philosophical and aesthetic foundation.
Finally, to design a database always also involves issues of data compression.
As we will see, since the early experiments with memory theaters, organizing
information invariably also meant reducing it. Two elements here are relevant to
the discussion of the role of databases vis-à-vis digital design. First is the notion
of metadata—that is, data on data—forming a much reduced dataset used by

16
software to perform searches on the database itself. The second technique—
appearing as early as the sixteenth century—is cryptography, which allows
replacing symbols with other symbols to both reduce the database size and
protect data.
As mentioned, databases are at the core of computer software regardless
of whether the end user can interact with them. Some applications, however,
make list management an explicit feature. Parametric modelers such as
Grasshopper do provide a series of tools to manage lists of numbers which can
be associated to geometrical properties of objects. It is however with scripting
software (e.g., Processing) or languages that such tools acquire a more
prominent role, as users do not interact with a graphic interface but directly
manipulate the data structure. Out of the many scripting languages allowing
direct operations on databases, AUTOLISP deserves greater attention, as it
provided basic software architecture for AutoCAD. LISP was invented by John
McCarthy (1927–2011) in 1958 and is one of the oldest high-level programming
languages still in use. Its evolution into AUTOLISP was designed around the
organization and connection between numerical lists. AutoCAD employed it
between 1986 and 1995, as it gave the possibility to directly manipulate lists,
still an essential feature for modeling complex structures. These features
are also at the core of BIM, which makes the most direct use of databases;
pieces of software such as Revit adopt an object-oriented modeling allowing to
associate text-based information to building components such as doors and
windows. BIM models building parts as much as databases formatted in a
non-visual, text-based media: these lists can not only be interacted with by
various parties, but also be outputted separately from the actual drawings.
Such techniques should not be regarded as strictly technical procedures
bereft of aesthetic potential. Some examples of this are Marcel Duchamp’s
(1887–1968) decision to abandon painting to become a librarian at the Sainte
Genevieve Library in Paris conceiving art as the manipulation of data toward an
aesthetic objective, Le Corbusier’s (1887–1965) enthusiastic appreciation for the
Roneo filing system (Le Corbusier, 1987), or Buckminster Fuller’s (1895–1983)
Dymaxion Chronofiles, which all speak of architects’ interest in data organization
both as a cultural manifestation and as a design method.
When mapped onto architecture, the closest point of comparison is the
library. Libraries are an established building type to store and retrieve books;
and more recently, other types of media. The primary concern in the design of
a traditional library is the organization of books, an issue restaging the same
conversations on information hierarchy and access we just saw. Contrary to the
museum—also a type concerned with the organization of cultural artifacts—
the objects contained in a library are extremely consistent in form and physical

Database
17
properties, making organizational issues even more relevant. There are multiple
computing mechanisms at work in a library. The cataloging system operates on
the abstract level but it nevertheless has both cultural and physical connotations.
The way in which books are ordered reflects larger cosmologies: from the
spiraling, infinite Tower of Babel to more recent cataloging structures such
as the Dewey system2
according to which each item has a three-digit code
ranging from 000—philosophy—to 900—history and geography—reflecting an
imaginary journey from the heavens down to earth. In the library we can observe
how architecture can also present direct computational properties: the very spatial
layout adopted allows users to retrieve information, facilitate ad hoc connections
between disparate objects, and, more generally, produce an image of culture as
expressed through the medium of books. The recent addition of electronic media
has revamped discussions on both access to information and their public image
in the city. Among the many examples of libraries the recently completed Utrecht
University Library (2004) by Wiel Arets (1955–) and the Seattle Public Library
(2004) by the Office for Metropolitan Architecture (OMA) are exemplary outcomes
restaging this discussion. Wiel Arets distributed 4.2 million books in suspended
concrete volumes, each thematically organized, creating a very suggestive series
of in-between spaces and constructing a theatrical set of circulation spaces for
the user’s gaze to meander through. Koolhaas’ office conceived the library as an
extension of the public space of the city, which flows from the street directly into the
foyer and along the vertical ramp connecting the various levels of the library. Along
the same line we should also include the impressive data visualizations generated
by mining large datasets: the works of Lev Manovich, Brendan Dawes, Senseable
City Lab at MIT represent some of the most successful works in this area.
Ramon Llull’s wheels
Though first emerged in the work of the Greek Simonides and Aristotle, the first
systematic account of techniques to gather and retrieve data appeared in three
books: the Ad Herennium written by anonymous, Cicero’s De Oratore (55 BC),
and Quintilian’s Institutio Oratoria (AD 95). Ars memorativa—the sum of techniques
to artificially remember notions—was at the center of all three examples. Memory
was constructed by transforming notions into icons, which then were “placed” in
the rooms of imaginary buildings. By recalling how the rooms were furnished, one
could unfold the small units of information “stored” in each object to eventually
aggregate them all into a comprehensive narrative. Since these early examples, it is
possible to see how architecture—though only in its virtual form—played a central
role in the history of databases: it was an organizational as much as a generative
device to store and retrieve information. Architecture would provide the formal

18
structure to store notions regardless of their topic or meaning. Architecture would
provide the formal structure to store notions regardless of their topic or meaning. In
this sense we could say that architecture computed; icons ornated the walls of the
palaces whose structure allowed information to be “played back” to reconstruct
more articulate notions. Room layouts, luminosity, typological organization, etc. all
facilitated storing information in virtual building, reducing the amount of notions to
retain to memorize a complex event or concept. The use of architecture as retrieval
and computational system is clearly stated in the Ad Herennium (c.80 BC) when
the author states that “the places are very much like wax tablets or papyrus, the
images like the letters, the arrangement and the disposition of the images like the
script, the delivery is like the reading” (Yates 1966, p. 179).3
Similarities have been
drawn between the memory palaces and formal logic: the separation between
the layout of the architecture chosen (algorithm) and images populating it (data),
the semi-automatic properties of the device conceived, and the need to develop
techniques to compress the information stored.
An important precursor of the innovations that the Renaissance would diffuse
was Ramon Llull (Majorca 1232–c.1315). Born in Majorca on the border between
Christianity and Islam, Catalan Ramon Llull occupies an important place both
in the history of the organization of knowledge and that of proto-computational
thinking, as he introduced abstract and combinatorial logics which still play a
central role in the design of databases. His work is situated at the end of the Middle
Ages—between the end of the thirteenth and the beginning of the fourteenth
centuries—and in many respects anticipates themes and issues that will gain
popularity from the fifteenth up to the seventeenth century. His vast production was
a result of lifelong studies ranging from astronomy to medicine, to some very early
developments on electoral systems. Often met with either adulation or complete
rejection, Llull’s Ars Magna was a system to organize knowledge—referred to
as memory—to demonstrate to other religions the superiority of Christianity, an
aspect to keep in mind as we venture into more detailed descriptions of the Ars.
Llull invented a system based on a series of basic lists that could be
aggregated or combined by using a series of concentric wheels with letters
marked along the perimeter. (Probably inherited from the very Muslim culture he
was seeking to convert.) The random combinations of letters returned by each
spin of the wheel were encoded to give rise to philosophical statements answering
the fundamental metaphysical questions. At the basis of this construction were
the basic primitives: nine attributes of God called dignities: Bonitas, Magnitudo,
Eternitas, Potestas, Sapientia, Voluntas, Virtus, Veritas, and Gloria.4
Letters from
B to K were given to each attribute and eventually organized along the first
wheel. The Tabula Generalis established six groups of nine elements each and

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provided the general structure of the Ars: Principia assoluta (dignities), Principia
relativa, Quaestiones, Subjecta, Virtutes, and Vita. They combined through a
small machine in which three concentric circles literally computed combinations
in exceptionally large numbers (despite the outer wheel was static). The groups
were each associated to the nine-letter system, a fixed characteristic of Llull’s
Ars. By spinning the wheels, new configurations and possible new ideas were
generated: for instance, the letters representing dignities in the outer ring were
connected through figures to generate seventy-two combinations allowing
repetitions of a letter to occur. The Tabula Generalis allowed decoding the random
letters generated by the wheels: for instance, BC would translate as “Bonitas est
magna,” whereas CB would be “Magnitudo est bona.” At this level of the Ars
Magna both combinations were accepted: this apparently secondary detail would
have profound implications, as it allowed each primitive to be either a subject
or a predicate. Geometry also played a central part in formalizing this logic and
was clearly noticeable in the illustrations accompanying the description of the
first wheel: the perfect circle of the wheel, the square denoting the four elements,
and the triangle linking the dignities according to the ars relata which described
the types of relations between primitives and arched back to Aristotle’s De
memoria et reminiscentia (c.350 BC). Triangular geometry allowed Llull to devise,
perhaps for the first time, both binary and ternary relations between the nine
letters by applying his Principia relativa and three-letter combinations—named
chambers—were listed in the Tabula Generalis. Llull added a series of rules—a
sort of axiomatics formed by ten questions on religion and philosophy and their
respective answers—to discriminate between acceptable and unacceptable
statements generated through the wheels. Llull introduced here a tenth character,
the letter T as a purely syntactic element in each chamber. The position of T
altered how the ternary combination read: its role has been compared to that of
brackets in modern mathematical language, as it separated the combinations
into smaller entities to be “computed” independently to be then aggregated
(Crossley 2005). The letter T also changed the interpretation of the letter in the
group: each letter to the left of T must be interpreted from the list of dignities,
while the reader should have used the Principia relativa for letters to the right
of T. The letter T in Llull’s Ars represented one of the first examples of symbolic
logic with purely syntactical function. The table eventually listed 1680 four-letter
combinations divided in columns of twenty elements each.
As we have seen, the overall structure of the Ars was fixed, with constant
relations and recursive “loops” that allowed to move across the different scales
of being (Subjecta). Deus, Angelus, Coelum, Homo, Imaginativa, Sensitiva,
Vegetativa, Elementativa, and Instrumentativa were finally the nine primitives

20
(scales) of the universe; to each of them Llull applied his godly attributes.5
The
recursive logic of this system was also guaranteed by the very nature of the
geometrical figures chosen to measure it: a geometrical structure defined each
step or iteration and related to one another. This allowed the user to move up and
down the chain of being: from the sensible to the intelligible, from material reality
to the heavens, in what Llull himself called “Ascensu et Descensu Intellectus”
(ascending and descending intellect) and represented as a ladder.6
It is this
aspect that prompted Frances Yates to affirm that Llullian memory was first to
inject movement into memory, an absolute novelty compared to the previous
medieval and classical methods (Yates 1966, p. 178). Llullian recursion was
mostly a rhetorical device rather than a logical one, as its main aim was to
disseminate its author’s doctrine and religious beliefs: any random spin of
the wheel would confirm the validity and ultimate truth of Llull’s system and
metaphysics. This system was therefore only partially generative, as some of the
options were excluded in order not to compromise the coherence of any final
answer delivered by the wheels. The more one played with the wheels, the more
its logic became truer.
Besides the introduction of complex binary and ternary relations, Llull’s Ars was
also the first known example of use of parameters. Whereas in Aristotle primitives
had a fixed meaning, in Llull these slightly varied according to syntactical rules:
statements such as “Bonitas est magna” and “Magnitudo est bona” were only
possible if subjects and predicates could morph into each other. This was in turn only
possible if the meaning of letters from B to K varied changing the overall reading of
the letters in different combinations. The importance of variables and parametrics in
mathematics and digital design cannot possibly be overstated and will find a proper
formal definition only with François Viète (1540–1603) in the mid-sixteenth century.7
The combination of letters obtained by spinning the wheels was fundamentally
independent of their application to the Tabula: it was in this sense that Llull spoke
of “artificial memory,” a definition that was close to that of formal language. As
Yates noticed, the self-referential system conceived by Llull no longer needed to
heavily rely on spatial or visual metaphors—as classical and medieval memory
edifices had done up to that point—but rather on abstract symbols (letters) and
geometry (circles, squares, and triangles)(Yates 1966, pp. 176–77). This point
was also corroborated by the lack of visuals accompanying Llull’s rhetoric (his
treatise on astronomy made no use of visual material). Even when drawings
were employed, they lacked the figurative qualities so abundant in the classical
and medieval tradition; in fact, it may be more appropriate to refer to them as
diagrams, indicating geometrical relations between various categories through
careful annotations. The relevance of this point is twofold and far exceeds that

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of a mere philosophical dispute as, first, it marks a sharp departure from any
other medieval tradition—and will have a lasting influence on Renaissance and
baroque thinkers shaping the emergence of formal logic, which will play an
important role in defining the ideas and methods of computation.8
The efficacy of logical thinking to model either empirical phenomena or
theoretical ideas is an essential part of computational thinking and its ability
to legitimately represent them. This book touches upon this theme in several
chapters (parametrics, randomness, and networks), as it affects both how real
objects are translated into the logic of computational language and whether
logical steps can represent them. Llullian machines were purely computational
devices strictly calculating combinations regardless of inputs and outputs; they
literally were computers without peripherals (mouse, keyboard, or monitor).
However, the Ars was not an actual generative system, as not all statements
produced by the wheels were semantically acceptable: consequently it could
not yield “new” realities, rather only answer a limited number of fundamental
questions in many different ways. Its purpose was to convert whoever interacted
with it to Christianity and the very idea of “generating” new combinations also
presented a completely different and potentially undermining problem: that
of having conceived of a machine that could create new knowledge and be
consequently accused of heresy. Llull’s methods differed from classical ones
as they were not so much addressed to remembering notions, but rather to
remember “speculative matters which are far remote not only from the senses but
even from the imagination” (Yates 1966, p. 194). In other words, Llull’s method
concerned “how to remember, how to remember”—that is, recursive logic. The
power of logical abstract thinking resonates with that of modern computers,
which also have developed to abstract their operational logic to become
applicable to as many problems as possible. By abstracting its methods and
making them independent of individual applications, Llullism widened its domain
of applications to become an actual metaphysics. To witness an actual “open”
exploration of the unforeseen possibilities yielded by combinatorial logic, we
will have to wait until the fifteenth century when Pico della Mirandola (1463–94)
will venture into much more audacious exercises in “materialist permutations”
(Eco 2014, p. 414), freeing Llull’s work from its strictly theological and rhetorical
ambitions and paving the way for the logical work of Kircher and Leibniz.
Llull’s machine also reinforced the use of wheels as mechanical devices for
analogue computation; already present in the Antikythera orrery, wheels freely
spun in a continuous fashion. A whole plethora of machines would make use
of this device: from the first mechanical calculating machines by Pascal and
Leibniz, to Analytical Engine by Charles Babbage respectively completed in the

22
seventeenth and nineteenth centuries. Leibniz’s admiration for Llull persuaded
him to directly work on the Ars: Leibniz in fact calculated all the possible
combinations that Llull’s wheel actually allowed if no semantic rule was applied
to curtail them: the number he came up with was 17,804,320,388,674,561 (Eco
2014, p. 424). Finally, Llull indirectly influenced architects too: in 2003 architect
Daniel Libeskind (1946–) was inspired by the rotating devices in his design for
an artist studio in Palma—Llull’s birthplace—which he used as a metaphor for
connecting cosmology and architecture.
The cosmos in 49 squares9
L’Idea del Theatro written, apparently, in only seven days is Giulio Camillo
Delminio’s (1480–1544) main work which was only published posthumously
passing away in 1544 in Milan. The book constitutes one of the most
intriguing, enigmatic, and relevant precedents shaping the relation between
information and design. In this book Camillo described a project that had
occupied his entire life: the construction of a theater containing all the best
exemplars of the knowledge known at the time. Despite such a grand project,
Camillo would have found this description still rather underwhelming, as he
also referred to it as a library, a translating machine, and, most importantly,
a creative device. By the time he started dictating his memories he had
already spent several years in Venice—in which he became a close friend of
Titian (1488/90–1576), Lorenzo Lotto (c.1480–1556/7), and Sebastiano Serlio
(1475–c.1554) (Olivato 1971)—and France where François I—a great admirer
of the Italian Renaissance—invited him with the idea of finally constructing
the theater.10
In many ways, Camillo built on several of the precedents we
have already discussed—particularly Ramon Llull’ Ars—but this would not do
justice to his work and to the new elements he brought to the relation between
knowledge, memory, and creativity. The first of these elements was the range
of media through which Camillo’s system materialized: Camillo directly utilized
architecture—in the form of a classical theater—to organize and “compute” the
information stored. Contrary to previous examples, L’Idea is a complete work
of art including painting—201 drawings by Titian accompanied one edition of
the book11
—and machines. Camillo’s ideas had great traction—thanks to the
charismatic, almost mystical tone with which he illustrated his project—which
extended to architects too as Serlio was deeply influenced by it. The theater
was a physical place as much as a mental map, an externalization of the
cognitive and associative processes constantly at work in the brain; a notion
that still resonates with how we experience the World Wide Web.

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The basic organization adopted by Camillo was a grid divided into seven
columns and rows. Seven were the known planets of the universe occupying
each column; whereas each row—which Camillo refers to as “degrees or gates,
or distinctions”—described the mythical figures organizing knowledge from the
Heavens down to Earth. More precisely the 7 degrees are:
1 The seven Planets—sun excluded;
2 The Banquet—in which the oceans transport the “water of knowledge” in
which ideas and prime elements float;
3 The Niche—in which the Nymphs weave their fabrics and bees “combine” the
prime elements bringing them down into the natural world;
4 The Gorgons—the three mythical figures with only one eye representing the
three souls of men and, consequently, their internal dimension;
5 Pasifae—symbolizing the soul descending into the body;
6 Talaria—Mercury’s winged shoes—representing human actions on earth;
7 Prometheus—representing all the products of arts and sciences (Bolzoni
2015, p. 22).
Variedly combined these categories provided all the “places” to store the
knowledge of the theater, each marked by the insertion of a painting. The
combination of places and images added another layer of interpretation to
the theater, as the same image could have different meanings according to its
position. Providing the theater of a structure was not only a practical expedient
to give access to its inner workings, but it was also necessary to make all
knowledge easier to remember. Camillo was not just interested in cataloging
past and present ideas; the arrangement in columns and rows was also
instrumental to allow the “audience” of his theater to generate new works by
combing existing elements, also providing them with some guidance to place
potentially new images and words in the theater. The architecture of the theater
with rows and seats maintained a tension between both individual parts and
the whole—that is, how the celestial scales of the cosmos and earthly ones
are related, and between singular notions and multiple—that is, combinatorial
and complex—knowledge. Camillo was always adamant to point out the wealth
of materials contained in the theater. Numbers detailing the quantities of items
regularly punctuated his description: for instance, in his letter to Marc’Antonio
Flaminio, he boasted that his theater had “one hundred more images” than
Metrodoro di Scepsi’s (140–170 BC), whose system for ordering memory was
still based on the 360 degrees of the zodiac.12
As we progress through the Idea
more space is given to ever-longer lists enumerating every item that ought to be
included in the theater. The Theatro was a perfect device not only because of the

24
sheer quantity of knowledge it contained, but also because this knowledge was
indeed “perfect”; that is, directly derived from classical texts representing the
highest point in a specific area of inquiry.
The grid was then re-mapped onto the architecture of the classical theater as
already described by Vitruvius. However, there was a radical departure from the
model inherited: the spectators did not occupy the seats, but they were meant
to be on stage watching the spectacle of memory unfolding before their eyes.
Camillo was certainly interested in utilizing a converging geometry to enhance
the mesmerizing effect of images on memory and knowledge to impact on
the users of his theater, but the reason for this inversion seems to run deeper.
Camillo looked for a spatial type able to order his “database” while being able
to induce in the viewer the impression that what was displayed was the very
spectacle of the images stored in their brain. The powerful image which the
theater was meant to evoke was that of a “Magnam mentem extra nos” (Camillo
1587, p. 38)13
demanded a spatial structure able to give both a totalizing
impression and persuasiveness that allowed users to grasp its organization in
a single glance. Camillo referred to Socrates’ metaphor of an imaginary window
opening onto the human brain to illustrate how he understands his creation: the
possible confusion of all the images stored in the brain ideally seen all together
was counterbalanced by its structure organization, which brought legibility to
an otherwise cacophonic space. Camillo’s theater multiplied Socrates’ image
presenting itself as a theater with many windows: both an image and a place
where it would have been possible to both touch all the knowledge but see the
flickering spectacle of the brain unfolding (Bolzoni 2015, p. 38).
Replacing the seats of a traditional theater were small cabinets with three
tiers of drawers—organizing texts by subject ranging from heavens to earth—
covered by drawings announcing their content. The books in each drawer were
specially designed to enhance their visual qualities: images decorated the
covers, diagrams were inserted to show their content and structure, and finally
tabs were introduced to indicate the topics discussed. The works contained in
the theater directly came from the classical Greek and Latin tradition.
Camillo often described the Theatro not only as a repository of knowledge, an
externalized memory, he insisted that the Theatro was also a creative machine
that would educate its users to produce novel forms of artistic expression.
On the one hand, this could be achieved by only storing the great classics of
Latin literature which Camillo regarded as models to aspire to; on the other, the
classical world of Cicero was distant enough to that of Mannerist culture to avoid
direct comparisons which would have not been beneficial for either those who
used the theater or to the longevity of the knowledge stored in it. Camillo actually

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25
described how the Theatro would have worked as an engine for creative writing.
Besides the books and paintings composing its space, Camillo also mentioned
the introduction of machines to facilitate creativity, especially when the model to
draw inspiration from proved particularly challenging. Though never precisely
described, these machines could be imagined to have been dotted around the
theater, sitting next to the cabinets with drawers. In the Discorso in materia del
suo theatro (1552) Camillo talked of an “artificial wheel” which users would spin
in order to randomly shuffle chosen texts. The mechanism of these automata—
apparently depicted in drawings and models—could deconstruct a given text
into its constituent parts, revealing its rhetorical mechanisms; an artificial aid
supporting the creative process. This description closely echoed that of Llull’s
wheels, which had already gained popularity in the fifteenth century, through
the use of combinatory logic: new knowledge and creativity resided in the
ability, whether exercised by a human or not, to recompose existing elements.
What Camillo’s theater added to these long-standing conversations was not
so much a different logic, but rather an aesthetic dimension; the circle—the
geometry chosen to play with randomness—but also metaphor of a “whirlpool,”
a source—as Lina Bolzoni suggests (2015, pp. 70–71)—from which novel forms
emerge. This conception of creativity never really ceased to attract interest as
the works of Giordano Bruno in the sixteenth century and Leibniz a century later
will eventually become fundamental figures of the formal logic of computation.
The ambition to make the theater far more than a “simple” container for
knowledge opens up an important, and in many ways still contemporary, issue
on the relation between information and creativity. As mentioned, the theater
Figure 1.1 Reconstruction of Camillo’s Theatre by Frances Yates. In F. Yates, The Art of
Memory (1966). © The Warburg Institute.

26
only contained classical works—Petrarca and Virgilio from the vulgar tradition
and Aristotle and Plinio from the classical one—considered by Camillo the
highest point in their respective languages and, therefore, a reliable model
for inspiration. Several contemporaries—particularly Erasmus—dismissed his
positions as anachronistic, unable to reflect the very contemporary reality of
the time the theater was meant to be used. However, Camillo’s intentions were
different; as for the experiment in logical thinking we have already seen or are
about to, Camillo too was looking for a language of “primitives” that could return
the greatest variety and therefore value; that is, the most reliable and succinct
source of elements able to yield the greatest and most novel results (in logical
terms, the range of symbols yielding the highest number of combinations). This
operation first involved highlighting the deeper, invariant elements of knowledge
and rhetoric onto which the combinatorial game could have been performed.
In his Trattato dell’Imitazione (1544), Camillo noticed that all concepts existent
were more than 10,000 that can be hierarchically organized in “343 governors, of
which 49 are captains, and only 7 are princes” (1544, p. 173, quoted in Bolzoni
2012, p. 258). Having passed the test of time, these literary sources paradoxically
guaranteed users to be freer while performing their literary creations. The very
structure of the theater—as a combination of architecture and paintings—
provided the mechanisms to deconstruct the content of texts studied and give
rise to the very associative logic through which to mutate the lessons learned.
Once the elemental rhetorical figures had been revealed, the theater revealed
to the user a chain of associations to move from text to text causing the initial
ideas to morph and gain in originality. Camillo called it topica; a method which
we could broadly define as the syntax binding the vast material stored in the
theater, a logic causing the metamorphosis of ideas. The theater revealed itself
in all its grandiose richness, its detailed and rigorous structure allowing the user
to first dissect—almost anatomically in Camillo’s language—a specific author,
theme, etc., and then, through the topica, to revert the trajectory to link unique
observations back to universal themes, to timeless truths. Different from Llull or
Leibniz, Camillo did not fund his logic on purely numerical or algebraic terms,
rather on a more humanistic approach as the arts were used to dissect, structure,
and guide the user. The role of automata must be read in conjunction with the
logic of the topica: the role of machines here was not simply that of computing
a symbolic language.
The theater did produce almost “automatic” results through its accurate—
perfect, Camillo would have argued—map of knowledge and methods to
dissect and reorganize it. The definition of the theater as a closed system of
classical texts in which creativity emerged out recombining existing elements

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echoes with the “introverted” notion of databases in which novel constructs
result from aggregating, combining existing items. The model for creativity
presented through the Theatro also applies to digital databases: this is the
one in which the “new” is already present within the given set of elements,
somehow “hidden” within the endless combinations available, a virtual form to
actualize.
Its organization and iconography suggested vertiginous correlations between
images, moving from natural to mythical subjects, relating minute objects or
observations to vast themes so as to prompt the user to possibly create their
own images grounded on the classical tradition. Here the database was seen
as an aesthetic device: the implementation of logical protocols gave rise to
aesthetic effects. This is the most relevant part of Camillo’s work, one we are
also daily confronted with when we design through digital tools as we can clearly
notice the presence of a data structure and a retrieval mechanism. The ideas
posed here go beyond issues relate to the sheer ability to store large quantities
of data or devising efficient retrieval mechanisms; the focus is rather on what
images—we could say, metadata, in today’s digital parlance—are appropriate
to experience such collection of information and which elements can elicit
creativity. In this sense, Camillo is an important precedent to also understand
Aby Warburg’s (1866–1929) Mnemosyne Atlas started in the 1920s in which
visual material would come to completely replace the role that text had had in
organizing large collections of material.
Camillo had a profound effect on the artistic scene. Gian Paolo Lomazzo
(1538–92) constructed his Idea del Tempio della Pittura (1590) around seven
columns. But it was architecture to be even more profoundly affected because
of the close friendship between Camillo and Sebastiano Serlio. Camillo thought
that his theater would be applicable to not only literary works but also other types
of artistic production, such as paintings and architecture. The method of the
topics would have been as effective to dissect text as other types of media, such
as drawings and paintings; these too had deep rhetorical mechanisms to unveil
and appropriate. Serlio’s Seven Books of Architecture—whose first tome was
published in 1537—echoed Camillo’s theater in more than one way: first, the
use of the number seven to structure the work; it also proceeded from particular
to universal by deriving the primitives of his language from Vitruvius—custodian
of the classical tradition—to then recompose them according to the principles
of the aggregational logic (Carpo 2001, pp. 58–63). Although similar ideas were
also to be found in the Idea dell’eloquenza (1544), Serlio’s book was the first
architecture book to consciously couple the conceptual tenets put forward by
Camillo with the technological advancement of modern printing to inaugurate

28
the modern tradition of the architectural treatise accessible to a wider audience
(Carpo 2001). Finally Serlio’s treatise also supported a design method based
on ars combinatoria based on the idea that the architect must have been able
to correctly bring together and articulate elemental pieces whose legitimacy had
already been sanctioned by history.
The fascination with the theater was not only confined to Mannerist artists, but
also found renewed interest at the arrival of the internet, which also posed similar
questions regarding access to information and its relation to creativity. Several
recent installations celebrated the pre-digital character of Camillo’s databases.
For instance, Robert Edgar’s Memory Theatre One (1986)—programmed in
GraForth on Apple II—updated the model of the memory theater according to
1980s’ computer technology. Agnes Hegedüs (with Jeffrey Shaw) added virtual
reality to her Memory Theatre VR (1997) consisting of a virtual museum in the
shape of an eight-meter-diameter cylindrical space (Robert 1985). Despite
several centuries having gone by since Camillo’s work, these examples still
confirm how deep the relation between architecture and information is and how
they have influenced one another.
Leibniz and the Ars Combinatoria
German polymath Gottfried Wilhelm Leibniz (1646–1716) occupies a special
place in the history of computers having largely contributed to both the birth of
infinitesimal calculus and set the basis of formal logic through binary numeration.
We have already seen how Llull’s work influenced not only Leibniz’s thinking on
logic but also the design of his calculating machine. However, Leibniz’s work had
far greater implications for computation, as it moved the development of formal
logic further and virtually lay the foundation to coding as the “algebra of ideas”.
Since Dissertatio de art combinatoria (1666), Leibniz demonstrated his interest in
devising a universal language based on the simplest—i.e., the shortest—lexicon
to express the largest, perhaps even infinite, number of statements; an idea
that carried through his oeuvre and formed the basis of his most famous and
enigmatic work The Monadology (1714). Different from what we have examined
so far, Leibniz ventured outside the strict confines of science and sought to apply
his language to philosophy: symbolic logic—based on algebraic operations—
was developed and applied to thoughts rather than just numbers (at some point
in his life, Leibniz even tried to apply it to juridical cases) (Leibniz 1667). He
conceived it as the “alphabet for human thought” to which he eventually referred
to as characteristica universalis: a discipline separate from the actual act of
calculating (calculus ratiocinator), which he imagined to become more and more

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a mechanized activity. This separation was essential for both the development
of more sophisticated logical thinking and for the actual development of the
architecture of the modern computer. The basis of the characteristica should
have been rooted in real phenomena, but the power of this type of thinking
made immediately evident that “new realities” could have also been calculated
and logically inferred through mathematical operations. This brilliant observation
not only laid the foundations for computation but also opened up the possibility
to generate new numerical combinations. This intuition promised to invest
machines (proto-computers, in fact) with the potential to augment our cognitive
capabilities and imagine different cultural and even social realities; a promise
that still seems partially fulfilled today.
In defining his combinatorial logic, Leibniz developed his own symbols, out
of which the ⊕ deserves closer attention. This symbol signifies the aggregation
of two separate sets of statements, which can be combined according to a
series of predetermined rules. The second axiom of the Ars enigmatically states
that A⊕A = A. Contrary to algebraic mathematics in which 1 + 1 = 2, here we
are adding concepts rather than numbers and therefore adding a concept to
itself does not yield anything new. We have already seen how influential these
considerations have been in the history of computer and, in particular, in George
Boole’s work.
The task of expressing thoughts through algebraic notation proved more
complicated than expected as Leibniz realized that the problem was twofold:
on the one hand, to map out all the domains to be simulated by defining their
characteristics; on the other, to detect with univocal precision the primitives of
such language. The task of naming such primitives was replaced by the idea of
postulating them instead to concentrate all the efforts on the syntax of the logic to
compute them. The result was used by Leibniz to describe with mathematical—
algebraic, quantitative—precision qualitative phenomena: the characteristica
allowed “running calculations, obtaining exact results, based on symbols whose
meaning cannot be clearly and distinctively identified” (Eco 2014, p. 56). The
clear separation between describing a problem through logic and calculating it
is still an essential characteristic of how computers operate, but also—from the
point of view of the history of databases—provided a way forward to manage the
increasing number of notions and the unavoidable difficulties in defining them.
As we will discuss in greater depth in the chapter on randomness, symbolic
logic implicitly contains a wider range of application which is not strictly bound
by reality; it can also be used to test propositions, almost as a speculative
language for discoveries that, with the help of a calculating machine, take care
of its “inhumane quality” (Goldstine 1972, p. 9).

30
Aby Warburg’s Mnemosyne Atlas
The next historical fragment in this journey through the evolution of databases
takes us to the beginning of the twentieth century to investigate a particular
classificatory system whose methods to link and retrieve information have been
often seen as precursors of the modern hyperlink.14
To discuss this important
element of digital design we have to venture into the idiosyncratic world of Aby
Warburg. Abraham Moritz Warburg was part of one of the wealthiest German
families in the late nineteenth century; being private bankers, the Warburgs’
interests and fortunes extended far beyond Germany’s borders, as they
also had offices in London and New York. The story goes that Aby—the first
descendant—renounced his rights to take over the family business and passed
them on to his brother in exchange for financial backing to pursue his artistic
interests. Unencumbered by financial pressures, Warburg could devote himself
to studying antiquity—particularly Italian Renaissance—travelling the world,
and, most importantly for us, supporting his research by methodically collecting
books, objects, and images. In his native Hamburg, in 1933, Warburg managed
to open the Kulturwissenschaftliche Bibliothek Warburg, a library and research
institute whose layout reflected Warburg’s own cataloging system. The very
architecture of the institute was an embodiment of Warburg’s archival practice
as its four-story structure purposefully matched the division by media predicated
by Warburg: Image (on the ground level), Word, Orientation, and Practice (on the
top floor). The very classification system was also an ontological one that moved
from religious themes to applied ones as one walked up the building. None of
this original scheme survived in Hamburg: the rise of Nazism forced the institute
to quickly relocate in London, where it still operates.
Despite having produced a very limited number of papers and publications,
Warburg’s research was restless and unique, warranting its own classification
system in order to store and retrieve documents. It is still possible to explore
the vast card collection kept by Warburg; contrary to traditional systems, cards
were not annotated by bibliographical references but by theme, privileging their
content—and potential associations—over the individual piece of information.
The library too operated according to a complex and unique classification system
in which books were organized by theme, forming small clusters around specific
subjects. The very meaning of each book in this complex web directly depended
on its position within the library; again, architecture and, in this case, pieces
of furniture such as shelves computed the very information they contained. To
make matters more difficult, Warburg understood this relation to be dynamic and
constantly relocated books to reflect his latest ideas, or, in a more “generative”

Database
31
fashion, to test hypotheses. Whoever visits the Warburg Institute at University
College London can either enjoy—as I did—or despair in trying to navigate such
a unique system.
While working with his close assistant Fritz Saxl on a lecture on Schifanoia,
Warburg started brainstorming ideas by pinning different materials on large
black canvases. Besides the practical advantages of this way of working, the
two saw the potential to foreground a different methodology to carry out art
history studies. The project was given the name of Mnemosyne Atlas directly
linking it to classical culture—”Mnemosyne” is the Greek goddess of memory
the memory theaters of the Renaissance, and the format of the Atlas, a media
whose popularity had been growing in Germany since the second half of the
eighteenth century. Their ambition was to write a history of art without text; that
is, to utilize iconology, the study of images, their migration and metamorphosis
to trace cultural motifs through history. These mutating figures were termed
“dynamograms” and the methodology tracing their reappearances and
movement took the captivating name of “pathos formulas” to foreground the
importance of symbolism. It is in this very quality of the project that many
have seen the first incarnation of the digital hyperlink. By the time Warburg
passed away there were seventy-nine panels, each dedicated to a particular
symbolism traced in its mutations. As for the task of recording the content
of each composition, these panels were constantly changing; a feature
encouraged by the very media utilized. This journey involved collecting visual
material of radically different sources: Plate 79, for instance, was dedicated to
the theme of the Eucharist covering it both in time—with materials spanning
from the ninth century to 1929—and space—with iconography from Germany,
Japan, and Italy (Fig. 1.2). The panel featured—among other items—an image
of Rafael’s The Mass at Bolsena (1512) (part of the rooms he painted in the
Vatican), the Last Communion of St. Jerome (1494–95) by Sandro Botticelli, two
clippings from the Hamburger Fremdenblatt of 1929, and several photographs
of Saint Peter’s Square (probably taken from other publications). There was
no hierarchy between copies and originals as well as between high and low
cultural references or disciplines: Warburg combined Rafael and newspapers
clippings; some panels also featured sketches, genealogical trees, and maps.
The project took full advantage of the new media of the time—photography—to
rethink the idea of memory, and mnemonics, in the light of increasingly more
accessible images. As mentioned, the construction of the Atlas required not
only a cross-disciplinary approach, but also an ability to evaluate different types
of media which had not been available and that had to be invested with rigorous
examination. Likewise, chronological ordering was abandoned not only because

32
of the heterogeneous sources employed—fragments collected followed both a
diachronic and synchronic system—but also because the spatial arrangement
adopted was that of an open network: there was no starting or vantage point
through which to grasp an overall narrative. The meaning of each panel was
neither to be found in the individual fragments collated—as archetypes—
nor in the overall image the whole of the artifacts gave rise to; rather, what
mattered was not the origin of the material but the relations established by each
element (Agamben 2009, pp. 28–30). Contrary to other studies on iconology,
Warburg ventured beyond mere visual affinity between disparate fragments to
foreground the importance of their relationships. There was no a priori meaning
which the plates were to reinforce; fragments were proposed for their “found”
qualities, in the most objective fashion. The act of interpretation through writing
was seen as an additional layer superimposed to open up a conversation to
attribute more specific meanings to the material gathered. The Atlas was an
example of information management elevated to the level of philosophy, as it
Figure 1.2 Image of Plate 79 from the Mnemosyne series. © The Warburg Institute.

Database
33
was tasked to deliver both content and form; both of which were in a state of
flux, as relations between all the elements could be explored in different ways.
The overlay of text onto the images was at time employed to frame a field of
interpretation; this too could have been intended as temporary or permanent
part of the plates.
Warburg’s “retrieval system” went far beyond the examples we have seen so
far. The plates delivered an “open” set of materials revolving around a theme,
which was then arbitrarily “fixed” by Warburg when the accompanying text was
produced. The rigid logic of the memory theater had found a coherent new
paradigm to replace it: the Atlas was a pliable method, more uncertain and
complex. The arrangements of the plates were susceptible to alterations over
time (new objects could be added or removed) and necessitated an interpreter
to overlay a textual depth to the otherwise purely visual nature of each plate.
The image describing this type of database was no longer that of the tree or
circle; the relations between objects could no longer be imagined to be sitting
on a flat surface, but rather moving in a topological space regulated by the
strength of the connections linking the individual fragments, an ever-expanding
landscape dynamically changing according to the multiple relations established
by the objects in the database. This space did not have predetermined limits;
it could constantly grow or shrink without changing its nature. In principle,
any object could be connected to any other and changed at any time; in
experiencing each plate, one would have learned about connections as much
as content. Warburg’s plates mapped a network of relations as much as a
number of artifacts; any form of knowledge extracted would only have a “local”
value depending on the shape of the network at the time the interpretation
was produced, making any more general claim impossible. Pierre Rosenstiehl
(1933–) saw in this condition similarities to the world of computation when he
likened the navigation through a network to that of a “myopic algorithm” in
which any local description could only be valid as a hypothesis of its general
configuration; in other words, in a network we can only avail of speculative
thinking. The similarities of this way of thinking information and the organization
of the World Wide Web are striking: not only because of the dynamic nature of
internet surfing, but also because of the convergent nature of the web in which
disparate media such as sound, images, videos, and texts can be linked to
one another (Rosenstiehl 1979, cited in Eco 2014, pp. 64–65). The conceptual
armature to map and operate in such conditions found a mature formulation
when Gilles Deleuze and Felix Guattari compared such space to a rhizome
(1976). The impact of the internet on the arts goes well beyond the scope of
this work; however, it is compelling to recall how David Lynch used the complex

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something once of a friend of his—and it turned out—what did it turn out,
Pandolfini? an enormous prize, you know. How was a man to divine that?
There was nobody to speak up for it, and I don’t pretend to be a
connoisseur. By the way, if you have friends who want to sell anything, you
had better send them to Diana. She is the person. She could buy us all up
and never feel it. To see her so simple as she is, you would never suppose
that she was such a great lady at home.”
“Is she, then, a great lady at home?”
“As great as a princess in other places. You didn’t know? Well, I don’t
suppose it will make much difference to you, but that’s the truth. She is
what we call a great Squire in England. You know what that means?”
“Yes; I know what that means.” Pandolfini looked at him with a half-
smile, yet sigh. What difference could it make to him? He had never
thought of putting himself on a level with that beautiful princess, of
securing her to be his—his housewife, his chief possession. All that he had
thought of was the pleasure of being with her, looking at her, like poor
Snodgrass. Now here was something which put a still greater difference
between them, and removed her out of his sphere. Was it not an irony of
fate that before one woman only the doors of his heart should have flown
wide open? and that she should be so entirely out of his sphere? A slight
vague smile came upon his face, half at himself and his evil fortune—half
with a tremulous and painful pleasure that she should be so rich, so
magnificent, so secure of everything that was good. Whatever happened,
that was always well: that she should be a kind of queen, regnant, and safe
from all straits and contradictions of fortune in the outer world as well as in
the hearts that loved her. But he sighed. Why was it that the world was so
made that the beautiful was always beyond reach, that love must be never
more than a dream? He murmured over a verse or two of Leopardi, as he
went upon his way, with that smile and sigh.

“O natura, o natura,
Perchè non rendi poi,
Quel che prometti allor? perchè de tanto,
Inganni i figli tuoi.”
Nothing more pathetic or more poignant than that sense of tantalised
anguish and pleasure—supremest good held before the eyes, but ever
inaccessible, giving happiness and suffering together, without blame of any
one, or wrong, can be. And Pandolfini was not the kind of man who rails at
fortune. He went away melancholy along Arno: yet smiled while he sighed.
Somehow or other this passing and temporary life of the English visitors
in the foreign town had become too serious, too securely established and
certain with all of them, being as it really was an affair of a few weeks or
months at the utmost, and incapable of extension. Perhaps this was Diana’s
fault. Arriving in March, she had no more than six or seven weeks before
her, a mere temporary visit—but the temporary was uncongenial to her
nature. She established herself half unconsciously, involuntarily as if she
had been at home. She made her piano nobile in the old palace assume a
certain resemblance to herself, just as she, on the other hand, perhaps
unconsciously too, perhaps with a touch of that fine vanity which disguises
itself under the semblance of taste, suited herself to her dwelling-place, and
put her dress and all her surroundings into conformity with it. If Diana had
not had the kind of lofty beauty to which utter simplicity of toilet is
becoming, probably it might not have occurred to her to leave the new dress
from Paris, before which Mrs. Norton and Sophy had rendered homage,
hanging in her wardrobe, and put on the old velvet gown, which, as Sophy
indignantly remarked, “she had worn all last winter!” But this was what she
did: though in some lights the long sweeping folds of the velvet, which was
of a very dark Venetian blue, looked somewhat faded, at least in the eyes of
her friends. “I never thought Diana would be like that: wearing out her old
dresses, when she can afford to have as many new ones as she pleases!”
Sophy cried, almost weeping at the recollections of all M. Worth’s poufs
and plissés. “It does not matter for us,” Mrs. Norton added, with serious
vexation, “we know her and look up to her in any dress; but among
strangers!” Thus her friends were annoyed by her supposed frugality: and
perhaps Diana, if her French toilet had been more becoming to her, would
not have felt the necessity of conforming her dress to the style of those

great rooms, so pathetically faded, so noble and worn, and independent of
all meretricious decoration.
She did other things, which perhaps were less justifiable still, and which
excited the displeasure of another section of her friends. In a country
practically unconverted to the laws of political economy, she was but too
glad to forget them, and gave alms with a largeness and liberality which, I
suppose, is quite indefensible. She was even so misled as to allow the
shameless beggars about to come to her for weekly pensions, putting them
on their honour, and talking to them in friendly, if somewhat solemn Italian
—slow as Pandolfini’s English, and from the same cause. “Giving to all
those beggars,—I can’t imagine what Miss Trelawny can be thinking of,”
cried the rector; “surely she must know that she is helping to demoralise
them: destroying all the safeguards of society.” “So far as that goes, I don’t
think Diana will do them much harm; but I object to have the staircase
haunted by Peppino and Company,” said Mr. Hunstanton. “I must talk to
her, and you had better talk to her, Snodgrass. As for demoralising, you
know, they’re past that. I defy you to demoralise Peppino. You can’t blind a
man who has no eyes; can you, now?” But this will be enough to show that
Diana gave dissatisfaction on both sides: only Pandolfini and the curate
stood by with silent adoration, and thought everything she did and was, the
noblest and the fairest that ever were made visible to eyes of men.
It must be allowed, however, that neither the disapproval nor the
adoration affected Diana. She went on her way calmly, indifferent to what
was said, laughing, though gently, at Mr. Snodgrass’s serious remonstrance,
and at the half-crying appeal of Sophy. And everything seemed to conspire
around her to give the air of stability and everlastingness which seemed
natural to her life. She acquired for herself, without knowing it, a distinct
position, which was partly by her beauty, no doubt, partly even by her
height and dignity of person, and partly from the individuality about her,
and her modest indifference to ordinary rule. There is an immodest
indifference which gives distinction of a totally different kind; but Diana—
who did not come for pleasure as commonly so called, who appeared
seldom at public places, and whose enjoyment of her strange habitation was
that of an inhabitant, not of a tourist—Diana became known in Pisa as
scarcely ever forestiera had been before. Pandolfini felt that he could divine
why, believing, as was natural at once to a patriot and a lover, that his race
was quick to recognise supreme excellence, and that it was natural that all

who knew her should bow down before her. But anyhow, in her retirement,
in her quietness, she became known as if by an instinct of sympathy. The
beggars in the piazzas asked nothing of her, but blessed her with bold
extravagance as she passed. The people uncovered right and left. Quant’ è
bella! they said, with that unfeigned and heartfelt admiration which is pure
Italian, not loudly, to catch her ear, nor yet in whispers, as if they were
ashamed of it, but in their ordinary tones, all being natural, both the popular
worship and its object. The curate when he became aware of this grew red,
and clenched his fist, with an English impulse “to knock down the fellow;”
but Pandolfini, who knew better what it meant, followed her steps at a
distance with glowing eyes, and was proud and happy in the universal
homage. He quoted lines out of the “Vita Nuova” to his stupid faithful
companion. Not always to his listener’s edification. “How do you suppose I
can understand that stuff?” growled the Rev. William through the beard he
was growing, and the Italian ceased to throw about such pearls.
But it may be imagined what a thunderbolt fell into this peaceful little
society when there began to be consultations among the leaders of the party
about going away. “Our time will soon be up, you know,” Mr. Hunstanton
said one evening, rubbing his hands; “May is a very nice month to get home
in. A week or two in Switzerland; perhaps a week or two in London, if my
wife has good accounts of the children. That’s what I like. After May it’s
sultry here and uncomfortable, eh, Pandolfini? Off in November, home in
May, that’s my rule—and if you like to take it old style, you know, as they
do in Russia, so much the better. That’s my regular rule.”
“W—what?” said Mrs. Norton, who sometimes tried to persuade herself
that she was rather deaf, and would not hear anything that was unpleasant;
but she had scarcely self-possession for this little trick, being too much
aghast at the idea thus presented to her mind, which it seemed incredible
they should all have ignored till now.
Then there was a pause of universal dismay, for they had all enjoyed
themselves very much, and disliked the idea of breaking up. Mrs.
Hunstanton alone went on working placidly, and the murmur of Reginald’s
voice, who was playing patience at a table, and whispering the value of the
cards to himself, became suddenly audible. The impatience of the whole
company with Reginald cannot be described. “My dear boy,” said the rector
sharply (in a tone which meant You odious idiot!), “couldn’t you just count
as well if you did it to yourself?”

“What has the boy done?” said Mr. Hunstanton with surprise. “Yes; we
must bolt. I don’t know how that may affect your plans, Diana.”
“I have no plans,” she said. “I came here by the light of nature, because
you were all here——”
“And you will come away in the same manner,” said Mr. Hunstanton
briskly. Sophy turned round and transfixed him with her eyes, or would
have done so had his middle-aged composure been penetrable, or had he
seen her, which had something also to do with it. But he did not see her,
and, good man, was perfectly easy in his mind.
“Well, I confess I shall be sorry,” said the rector, “and so, I am sure, will
be my dear Bill. We have had a very agreeable visit, nice society, all
centring round the Church in the most delightful way, and so many
charming people! I shall be very sorry to think of breaking up.”
He stopped somewhat abruptly, with unexpected suddenness, and in the
silence, more audible still than Reginald’s whispering, came a sort of groan
from the burdened bosom of the curate, who stood behind-backs in his
usual place, and who had felt himself covered by his uncle’s speech. This
made everybody look up, and there was a faint titter from Reginald, by way
of revenge for the rector’s rebuke. It was Sophy who had the boldness to
take up this titter in the wild stinging of disappointment and dismay.
“Why should you feel it so much, Mr. Snodgrass?—what does it matter
to you? You will have to go home to the parish whether or not!” she cried.
“Sophy, hush, hush! Yes, dear Mr. Hunstanton, how pleasant it has
been!” said Mrs. Norton. “What a blow to us all to break it up! I should like
to stay here for ever, winter and summer. It would not be too hot for me.
For I can never be grateful enough to Italy,” she added, impressively, “for
restoring health to my dear child.”
This called the general attention to Sophy, whose blooming countenance,
a little flushed by vexation, looked very unlike any possible failure of
health. Sophy was as near crying as possible. She had to put force upon
herself to keep the tears out of her eyes.
“Let us not make ourselves miserable before the time,” said Diana. “It is
not May yet; there is a week of April left. Let us gather roses while we may,
and in good time here is Mrs. Winthrop and our musical people. Sophy,
come and help to get the songs out. We can talk of this another time.”

Sophy came, with a sullenness which no one had ever remarked in her
before. She made no reply to what Diana said, but pulled the music about
under pretence of arranging it. As she did so, with her back turned to the
rest of the company, Diana saw a few hot hail-drops of tears pattering down
among the songs. She put her hand kindly upon Sophy’s shoulder.
“Sophy, dear,” she said, “is it the thought of going away? is this what
you feel so much?”
“Oh, leave me alone, please! I have got a headache,” cried Sophy,
jerking away from her friend’s grasp.
Diana said nothing more. She was grieved and disturbed by this very
strange new development. She put down all the songs and music that were
likely to be wanted, and opened the piano, and greeted with her usual
dignified kindness the new people who came rustling in to the agitated
atmosphere. It did not seem agitated to them. Mrs. Winthrop came in all
smiles and flounces, and there was a gathering round the piano, and much
laughter and talk and consultation, as is customary on such occasions.
Diana herself did not sing except rarely. She helped to set the little company
going, over their madrigals and part-songs, and then she withdrew, with that
sensation of relief which is afforded to the mind of the mistress of a house
and chief entertainer by the happy consciousness of having set an
amusement going, by means of which her guests will manage to entertain
themselves for the rest of the night.

CHAPTER VIII.
AN EVENING PARTY.
Diana seated herself in her favourite place, in a great chair covered with
dark old velvet, which had got a bloom on it by dint of age, such as youth
sometimes has, like the duvet of a purple plum. Her own dress was made in
toned white, creamy and soft, not the brilliant white of snow, and of rich
silk, which fell in heavy splendid folds. But it was “old-fashioned” in its
cut, which Sophy had deeply deplored already, with a plain long skirt, “such
as was worn three years ago!” the girl had cried with vexation. A certain
weariness was about Diana as she laid her head back on the velvet,
weariness yet satisfaction in having settled all her people comfortably in the
way of amusing themselves, and being thus herself left free. Mr.
Hunstanton was talking with Colonel Winthrop, who was the husband of
the musical lady, and two other persons who did not care for music. Mrs.
Norton, who was not musical, except in the way of playing waltzes (of
which she knew three) and one old set of quadrilles, had taken pity upon
Reginald, and had gone to the side-table with him to play piquet, which was
more amusing than patience. Diana looked round her with a sigh of
comfort, feeling that all her guests were off her hands. The central group at
the piano was the brightest point. Mrs. Winthrop, who was a pretty young
woman, and acted as conductor, held the chief place, holding a pink
forefinger in the air instead of a baton, swaying her head, and tapping her
foot according to the measure. Around her were her troupe with their music,
among whom, most evident to Diana, was Mrs. Hunstanton, “putting in a
second,” as she had been adjured to do—and anxious to escape, Sophy
singing soprano, with the half-tearful, half-sullen look gradually melting
from her face under the charms of the madrigal; and over Sophy’s head,
holding his book high, the poor curate, who had been forced into it, and
who, with his mouth open, and his eyes wandering, added a powerful but
uncertain bass. The soft lights of the candles on the walls lighted them all
up, shining upon the lightness of their faces, and the dresses of the ladies, as
they stood grouped about the piano. Behind, Mr. Hunstanton’s darkly attired
group of men gave an agreeable balance to the picture.

In front of Diana there were but three figures. Mrs. Norton and Reginald,
with a table between them, covered with the glories of the coloured cards,
which were repeated in the rose-coloured ribbons of her cap; and standing
quite alone in front of the dim profundity of a great old mirror—Pandolfini.
He was the only one who was alone as she was, though not by design, like
Diana. The glass was so old and so dim that it almost shrouded him, giving
its background of mysterious reflection to make even his solid figure look
unreal. But one thing about him was very real, which was that his eyes were
fixed upon herself. It was an inadvertent moment, and Mr. Hunstanton’s
sudden announcement of approaching departure had brought a certain
agitation into the atmosphere. To Diana, who had taken root in the friendly
place, notwithstanding her consciousness that her stay could not be long,
the feeling was painful—but to Pandolfini it was like the crush of
overthrow. He had known it, he said to himself—of course he had known it
—but it had not appeared such an utter and miserable conclusion of all
hopes, and revolution in life. The room had contracted round him, and the
lights grown dim, just as he felt the firmament itself would contract, and the
sun grow dim to him, when she was gone—and he had forgotten himself.
He had not been able to talk, to join in what everybody was doing, so long
as this feeling that the earth had opened under his feet, ready to swallow
him up and all things, was foremost in his mind. He had had his full of
revolutions: he knew what they were, and how men could live through
them, and the vulgar placidity of every day overcome all the violence that
could be done in life. But here was a revolution which could not be got
over. Yes, yes, he said to himself drearily, as, under cover of the music and
the movement, he put himself thus behind-backs, and allowed his eyes to
rest upon Diana with a half-despairing intentness. Si! si! it could be got
over. If a man is hacked limb by limb he has to bear it, making no unseemly
outcries; but still the thought of what it would be, the going out of all sweet
lights and hopes, the settling down of darkness, the horror of something
taken away which could never be replaced, appalled his very soul. What an
irony it was, what a cruelty of fate! He had been well enough before,
contenting himself with his existence, thinking of no Diana, satisfied with
the life which had never known her. But now!—without knowing,
Pandolfini gazed at her out of the shadows with eyes that glowed and
burned, and with a longing and fixedness very startling to her pensive calm,
as suddenly she turned to him with a half-smile and met his look!

Diana drew a little back in her chair, swerved for a moment, so startled
that she did not know what to do or think. She felt a blush rising over her—
why she could not tell: a sort of self-consciousness seized upon her,
consciousness of herself as being gazed at, rather than of him who was
gazing. Why should he or any one look at her so? Then she recovered, with
a slight shake of her head to throw off the impression, and a confused laugh
at her own vanity (as she called it): and seeing nothing better to do,
beckoned to him to come to her. Pandolfini was not less confused than she.
His first thought was that he had betrayed himself, and that nothing was to
be done now but to face his fate with melancholy boldness, which becomes
the unfortunate. He had made up his mind before now in moments of peril
to sell his life dearly. If this unconscious queenly lady was to have his life
like a flower, at least she should be aware of what it was which was thrown
on her path for her delicate foot to tread on. A kind of tender fury came into
his mind. He went up to her slowly, almost solemnly, as a man might be
supposed to go to his death—not affecting to be indifferent to it, but ready
for whatever might befall.
Diana had called him: but she was confused, not knowing how she was
to speak to this man, who looked at her not as acquaintances look. In her
embarrassment she found nothing but the most banal of nothings to say.
“I cannot suppose you are not fond of music, Mr. Pandolfini.”
“Should I unite myself to the gentlemen, then? But neither does Miss
Trelawny—it is not that one does not love music.”
“I cannot answer for myself,” said Diana, gladly plunging into an
abstract subject. “I am fanciful—I think I like music only when it goes to
my heart.”
“What a pretty idiom is that!” said Pandolfini. “One loves everything
most when it touches there.” He had placed himself just a step behind her,
enough to make it difficult for her to see him, while he could see her
perfectly. It was an unfair advantage to take. “But music,” he added, “it has
other aims—the ear first, and the mind and the imagination.”
“There is my deficiency,” said Diana. “I only understand it in this way.
Other arts may instruct, or may inspire; but if music does not touch me,
move my feelings, I do not make anything of it. I do not understand it. This
is my deficiency.”

“I acknowledge no deficiency,” said the Italian in a low tone. The
excitement in his blood was subsiding a little, but still he wanted some
perfume to reach her from the myrtle-bow crushed on her path. And the
tone was one which answered her musical requirements, and went right to
her heart. Where had she heard that tone before? It was not the first time in
her life, as may be supposed; but it seemed a long time since, and the thrill
of recognition was also a thrill of alarm.
“We will not quarrel on this point,” she said, “especially as the present
performance is not one to call forth much feeling; but it makes people
happy, which is always something.”
“Happy?” said Pandolfini; “is it this then which in your English calls
itself happiness? Ah! pardon—the Italian is more rich. This is (perhaps) to
be amused—to be diverted—but happy—no. We keep that name for better
things. I, for instance,” he added once more, in so low a voice that she had
to stoop forward to hear him, “I might say so much—and, alas! it is for a
moment, for a breath, no more. But they, these gentlemen and ladies—they
divert themselves: the difference is great.”
“You must say ladies and gentlemen, Mr. Pandolfini,” said Diana, glad to
be able to escape from too grave an argument; “in English it is more
courteous to put us first.”
“Pardon,” he said, with the flush of ready shame, which every one feels
who has made a slip in a new language. “I thought it was used so. But in all
languages heaven goes before the earth. I ought to have known.”
Diana laughed, but he did not laugh. He was not without humour; but at
present he was in deadly earnest, incapable of seeing the lighter side. “At all
events, that is pure Italian,” she said. “Your compliments are delightful, Mr.
Pandolfini—so general that one ventures to accept them on account of all
the other women in the world. I wish one could believe it,” she added,
shaking her head.
“I do believe it,” he said once more, in his deepest tone.
“Ah! you speak too low: I cannot hear you—which is an English not an
Italian fault. But you are right to discriminate between happiness and
amusement. We do so too, but we are not sufficiently particular about our
words, and use the first that comes to hand.”
Then there was a pause, and this time it was he who began. “Is it true,”
he said, “that this is soon to come to an end?—that you are going away?”

“I suppose we must go, sooner or later. Not perhaps with the
Hunstantons; but people do not stay here for summer, do they? It is for
winter one comes here?”
“I am no judge,” he said gravely, with that seriousness, on the verge of
offence with which a man hears his own country criticised. “I have spent
many summers here. You shut yourself up behind the persianis all day; but
when evening comes—ah, Miss Trelawny! the night of summer that goes to
the heart, as you say. I have never been in your country. I cannot tell if
among the seas you can know. Ah, you smile! I am wrong; I can believe it.
England is no more sombre when you—such as you—live there; but in Italy
I would give—how much—a year! years—of my life that you might see
one summer night. The air it is balm; so soft, so warm, so cool, so dark. The
moon more lustrous than any day. And all the people out of doors. You who
love the people it would make you glad. Upon the stairs and in the
doorways, everywhere, all friendly, smiling, singing, feeling the air blow in
their faces. How it has made me happy!—But now,—now——”
“You ought to be more happy than ever, Mr. Pandolfini,” said Diana,
raising herself erect in her chair, turning round upon him with the courage
the situation demanded, yet unable to keep a tremor of sympathy out of her
voice, “now that your country has risen up again, and takes her place once
more among the best.”
“I thank you for saying so—yes, I should be more happy; but, ecco, Miss
Trelawny, we are not as we would. I have my senses, is it not true? I am not
a child to stretch out my hands for what is beyond reach? Yet also, alas! I
am that fool,—I am that child. My country?—I forget what I meant to say.”
“You are not well,” said Diana, troubled. “It is this hideous din. Oh no, I
meant this beautiful music. You will be better when it is over.”
“Nay,” he said, the moisture coming into his eyes. “I like it; it makes a
solitude. It might be that there was no one else in the world.”
All this was nothing. If Mr. Hunstanton had heard it, he would have said
that Pandolfini was in one of his queer moods, and would have divined
nothing of what lay below; but to most women this inference of adoration is
more seductive than the most violent protestations. Even Diana felt herself
yield a little to the charm. She had to make an effort to resist and escape
from this fascination.

“And happily, here we are at the end,” she said. “Listen—here comes the
last burst.”
“Will you tell me?” said poor Pandolfini, paying no attention to the
interruption; “it will be very kind. Will you tell me to my own self, à me
stesso, before you go away?”
“It will be your turn to pay us a visit in England,” she said, rising; and
she turned and looked at him with a smile which was very sweet and
friendly, though so calm. “Then I will show you my country as you have
shown me yours,” she added. How kind she was! almost affectionate,
confiding; looking at him as if he had been an old friend—she who had
known him a few weeks only. But, alas! the moon in the sky was not more
serene than Diana. She went forward to the singers, adding in the same
breath, “Is it over so soon? You have given us a very pleasant half-hour”
(was it by their singing?). “Won’t you take something, and begin again?”
“Tea is the worst thing for the voice,” said Mrs. Winthrop, “though I am
dying for a cup of tea. No more to-night, dear Miss Trelawny. I am sure we
have bored you quite enough: though it is amusing to those who sing, I am
always sorry for the audience. We must not try you any more.”
“I have liked it,” said Diana; and he thought she gave a humorous half-
glance towards himself, as if to indicate how it was that she had liked it. As
for Pandolfini, he could not bear the contact of the gay little crowd. He
went into one of the deep windows, and after a moment stole out into the
balcony outside. He was not calm. If Diana had liked this brief retirement
from her little world and its busy affairs only to plunge into them again—to
pour out tea for Mrs. Winthrop, and condole with the tenor on the cold
which affected his voice—the Italian was not so philosophical. His frame
quivered with all that he had said and all that he had not said. Had he
betrayed himself? In every other kind of sentiment two people are on easier
ground; but in love, except when they understand each other completely,
how are they ever to understand each other? A woman cannot be kind
without being more than kind, or a man make himself intelligible without
those last explanations which one way or another are final—knitting the
two together, or cutting them adrift for ever. Alas! there seemed no
likelihood with that calm Diana of any knitting together: and he would not
be cut adrift. No: he would take her at her word. He would be patient—nay,
passive, tenacious—as the English like a man to be. He would be silent,

resisting all temptation to speak even as he had spoken to-night. He would
give up the ways of his own race and take to hers, concealing every
sentiment; he would be reticent, self-controlled, everything that an Italian is
not by nature. He would take the benefit of every moment here, and enjoy
her society as if he did not love her. Yes; that is what he would do—take the
good of her, as if she were nothing to him but an acquaintance, and never
risk that subdued happiness by any revelation of deeper feeling. And then
when all was had that could be had here, he would do as she had said—he
would go to England, and there be happy, or at least a little happy, again.
And who could tell? If he could manage to be so wise as this, so self-
controlled, so English, who could tell what might happen? She might be in
some great danger from which he could rescue her; she might fall into some
great strait or misfortune in which he might be of use. He did not, perhaps,
immediately realise the drowning, or the fire, or the runaway horses which
might form the extremity which would be his opportunity, as a youth might
have done; but when a man is under the dominion of one of the primitive
emotions, does not that reverse the distinctions of youth and age?
It was the most youthful foolish notion, transparent as gossamer, which
thus sprang up within him, and which he cherished with such tenderness.
He stood on the balcony with his back turned to the world outside: the soft
infinite sky of a spring night, the dewy sense of moisture in the air, the
gleam of the Arno between its banks below, and the voices of the passers-
by, in which there was generally a dreamy attraction for him—all this was
of less importance to Pandolfini to-night than the lighted interior, with those
groups of careless forestieri laughing and carrying on their chatter under
that solemn cavalier of the Sogni, his own ancestor, who looked on so
gravely, seeing the Northern hordes come and go. A momentary contempt
and almost hatred for them seized Pandolfini, though he was an Anglomane.
What did they want here with their curiosity and their levity?
“Le case di Italia son fatte per noi,” he said to himself; then laughed at
himself for the doggerel, and so brought his mind down as well as he could
from these thoughts to the common platitudes, to Mr. Hunstanton, who
appealed to him about a discussion which had taken place in the Italian
parliament, and to Colonel Winthrop, who claimed his opinion as an
impartial person as to the relative intelligence of the English and
Americans. He stepped in from the balcony with a smile on his face, and
gave them his reply. His heart was thrilling and quivering with the effort,

but he made no sign. Was not this the first symptom that he had conquered
himself, that he was as strong as an Englishman, and had surmounted that
impatience of suffering, that desire for demonstration which is in the Italian
blood? Would she think so? or had she divined what he meant, or ever
thought enough about him to wonder? This was the most exciting question
of all.

CHAPTER IX.
WARNINGS AND CONSULTATIONS.
Mrs. Hunstanton lingered after the visitors had gone away. She made a
determined stand even against Mrs. Norton and Sophy, and outstayed them
in spite of all their efforts. She said, with something of that breathlessness
which betrays mental excitement, “I want to say a word to you, Diana. I
want to warn you. Spectators always see more than the chief actors, and I
have been a spectator all the evening. You must not play with edge-tools.”
“I play with edge-tools?” said Diana; “are there any in my way?”
“My dear,” said the elder lady, who was not addicted to phrases of
affection, “I wish I could let you have a peep from my point of view
without saying a word: but that is a thing which cannot be done. Diana—I
don’t know if you have observed it,—but poor Pandolfini——”
Involuntarily, unawares, Diana raised her hand to stop the warning with
which she had been threatened, and the colour rose in her face, flushing
over cheeks and forehead, to her great distress and shame. But what could
she do? Some women cannot help blushing, and those who are thus affected
generally consider it as the most foolish and unpleasant of personal
peculiarities. She tried to look unconscious, calmly indifferent, but the
effort was entirely destroyed by this odious blush.
“Mr. Pandolfini?” she said, with an attempt at cheerful light-heartedness.
“I hope it is not he who is your edge-tool. It does not seem to me a happy
simile.”
“Oh, Diana,” cried Mrs. Hunstanton, too eager to be careful, “don’t treat
a man’s happiness or misery so lightly! I never questioned you on such
subjects, but a woman does not come to your age without knowing
something of it. Don’t take his heart out of his hand and fling it to the dogs.
Don’t——”
“I?” cried Diana, aghast. She grew pale and then red again, and the tears
came to her eyes. “Am I such a monster? or is it only you who are
rhetorical? What have I to do with Mr. Pandolfini’s heart?”

“You cannot deceive me, Diana,” said her friend. “You blushed—you
know very well what I mean. Men may not see such things—but women,
they understand.”
“We have no right to speak of a gentleman we know so little—or at least
whom I know so little—in this way,” said Diana, very gravely. “It is an
injury to him. You are kind—you mean him well—but even with that we
have no right to discuss——”
“I don’t wish to discuss him, Diana. If there was any chance for him,
poor man—oh no, you need not shake your head; I know well enough there
is no chance for him; but don’t torture him at least,” cried Mrs. Hunstanton,
getting up hastily, “this I may say——”
“It is the thing you ought least to say,” Diana said, accepting her good-
night kiss perhaps more coldly than usual, for though she was perfectly
innocent, she dared not dispute the fact pointed out to her. “No, I am not
angry: but why should you accuse me so? Do I torture any one? You have
made me very uncomfortable. If it is true, I shall have to break up and leave
this nice place, which pleased me, and go back with you to England.”
“You are afraid of yourself,” cried Mrs. Hunstanton.
“I!”—— Diana did not say any more. Yes; she was too proud. It was not
like a woman to be so determined, so immovable: and yet a woman whose
colour went and came, whose eyes filled so quickly, who was so sensitive
and easily moved, could she be hard? Mrs. Hunstanton did not quite know
what she wished. She was a little proud of Diana—among all the girls who
married, the one unmarrying woman, placed upon a pedestal, a virgin
princess dispensing good things to all, and above the common weaknesses.
One such, once in a way, pleased her imagination and her esprit de corps.
And if Diana had willingly stepped down from her pedestal, a sense of
humiliation would have filled her friend’s mind. But then poor Pandolfini!
She was quick of wit and quick of speech, and would have been as ready as
anybody to turn upon him, and ask who was he that he should have the Una,
the peerless woman, he a penniless foreigner with nothing but a fine name?
Probably had Diana melted, all this wilful lady’s impatient soul would have
risen indignant at the idea of the English lady of the manor consenting to
turn herself into a Madame Pandolfini. But all the same, as Diana had no
such intention, her heart melted over the hopeless lover. Poor fellow! how
good he was, how kind, how friendly! It was hard that by a mere accident,

so to speak, because Diana had taken it into her head so suddenly to come
here, that his whole life should be ruined for him. How hard it was that such
things should be! As Mrs. Hunstanton went upstairs to her own floor she
could not help remembering with some virulence that it was that absurd
little Sophy’s sham cough which had brought Diana here, and done all the
mischief. Little ridiculous creature, whom Diana would spoil so, and raise
altogether out of her sphere! Mrs. Hunstanton was quite sure that it was
entirely Sophy’s fault (and her aunt’s: the aunt was on the whole, being
older, more ridiculous and more to be blamed than Sophy) that this
misfortune had happened; though after all, she added to herself, how could
Pandolfini expect that Diana was to be kept out of Italy, and shut up, so to
speak, in England on his account, lest he should come to harm? That was
out of the question too. Thus it will be seen the argument on her side was
inconsistent, and indeed contradictory, as most such arguments must always
be.
At the same time a very different sort of conversation was going on in
another room in this same Palazzo dei Sogni. As they went out, Mr.
Hunstanton had seized Pandolfini by the arm. “Come upstairs and smoke a
cigar with me: the night is young,” he said; “and there are lots of things I
want to talk to you about. Now there are so many ladies on hand, I never
see you. Come, you shall have some syrup or other, and I’ll have soda—and
something—and a friendly cigar. What a business it is to be overdone with
ladies! One never knows the comfort of a steady-going wife of one’s own—
that is acquainted with one’s tastes and never bothers one—till a lot of
women are let loose upon you. Diana there, Sophy here—a man does not
know if he is standing on his head or his heels.”
“Pah! you like it,” said the Italian with a smile.
“Do I? Well, I don’t know but what I do. I like something going on. I
like a little commotion and life, and I am rather fond, I confess, of helping
things forward, and acting a friend’s part when I can. Yes, I’m very glad to
be of use. You now, my dear fellow, if I could help you to a good wife.”
Pandolfini turned pale. Was it sacrilege this good easy Englishman was
talking? The idea seemed too profane, too terrible to be even contradicted.
He pretended not to have heard, and took up the “Galignani” which lay in
Mr. Hunstanton’s private room—the room where he was supposed to write
business letters, and do all his graver duties, but in which there was always

a limp novel in evidence, from the press of Michel Levy, or Baron
Tauchnitz, and where “Galignani” was the tutelary god.
“Sit down, and let us talk. You should come over to England, Pandolfini.
The change would do you good. I like change, for my part. What is the
good of staying for ever in one corner of the world, as if you were a
vegetable and had roots? We say it is a grievance that we have to leave
home every winter on Reginald’s account, and I suppose I grumble like
other people; but no doubt, on the whole, I like it. There’s the hunting—of
course one misses all that; but then I don’t hunt, so it matters less: change is
always agreeable. And then you have got used to our little society. One
abuses the women; but they are always pleasant enough. The worst is, one
has a little too much of them in the country. Well, not so constantly as here;
but they are our nearest neighbours, and toujours perdrix, you know.”
“Is it that you mean to persuade me to come, or not to come?” said
Pandolfini, laughing.
“My dear fellow, how can you doubt? Of course we shall be delighted to
see you, both I and my wife. We always feel together, she and I. Of course
you will think me an old fool and all that for speaking with so little
enthusiasm. I am past the age of les grandes passions; but a good wife is a
very good thing, I can tell you, Pandolfini. It is astonishing how many
worries a man is spared when he has somebody always by him who knows
his ways, and sees that he is comfortable. Many a great calamity is easier
put up with than having your tastes disregarded, and your customs broken
in upon.”
“This may be very true, my good Hunstanton, but why to me—why say
it to me? I have no—wife.” His voice changed a little, with a tone which
would have been very instructive to the lady spoken of, but which conveyed
no particular information to her husband. Mr. Hunstanton rubbed his hands:
then he took his cigar out of his mouth in his energy, and puffed a large
mouthful of smoke into his companion’s face.
“That is exactly the question—exactly the question. My dear fellow, that
is just what I wanted to say to you. You ought to have a wife.”
Pandolfini gave a quick look up into his friend’s eyes. What he thought
or hoped he might find there who can tell? Many things were possible to his
Italian ideas that no Englishman would have thought possible. From whom
might this suggestion come? His heart gave a wild leap upward, then sank

with a sudden plunge and chill. What a fool, what a miserable vain fool he
was! She to hold out a little finger, a corner of her handkerchief, to him or
any man! His eyes fell, and his heart; he shook his head.
“Come, come, Pandolfini! that is the way with all you foreign fellows.
You are as afraid of marriage as if it were purgatory. You have had full time
to have your fling surely. I don’t mean to insinuate anything against you. So
far as I know, you have always been the most irreproachable of men. But
supposing that you hadn’t, why, you have had time enough to have your
fling. How old are you, forty? Well, then, it is time to range yourself as the
French say. An English wife would be the making of you——”
“Hunstanton,” cried the Italian, “all this that you are saying is as
blasphemy. Is it to me you speak of ranging myself, of accepting
unwillingly marriage, of having an English wife offered to me like a piece
of useful furniture? It is that you do not know me—do not know anything
about me—notwithstanding buon amico, that you are my best friend.”
Mr. Hunstanton looked at him with complacent yet humorous eyes.
“Aha!” he said, “didn’t I divine it! I knew, of course, how the wind was
blowing. Bravo, Pandolfini! so you are hit, eh? I knew it, man! I saw it
sooner than you did yourself.”
Pandolfini looked at the light-hearted yet sympathetic Englishman with a
glow upon his dark face of more profound emotion than Mr. Hunstanton
knew anything about. He held out his hands in the fulness of his heart.
Instinct told him that this was not the man to whom to speak of Diana—
although the Englishman was fond of Diana too in his way. But his heart
melted to the friend who had divined his love. Mr. Hunstanton, too, was
touched by a confession so frank yet so silent. He got up and patted his
friend on the shoulder. “To be sure,” he said, his voice even trembling a
little, “you mustn’t have any shyness with an old man. I divined it all the
time.”
There was a little pause, during which this delightful and effusive
confidant resumed his seat. He kept silence by sheer force of the emotion
which he saw in the other’s face, though it was almost unintelligible to him.
Why should he take it so very seriously? Mr. Hunstanton was on the very
eve of bursting forth when Pandolfini himself began—
“But to what good? She is more young, more rich, more highly gifted
than I. What hope have I to win her! She with all the world at her feet! I—

nobody. Ah, it is not want of seeing. I see well—not what you say, my good
friend, but what all your poets have said. That is what a woman is—a
woman of the English. But, amico mio, do not let us deceive ourselves.
What hope is there for such a one as I?”
“Hope! why, every hope in the world,” cried the cheerful counsellor.
“Talk about the poets: what is it that Shakespeare says? Shakespeare, you
know, the very chief of them—
‘She is a woman, therefore to be wooed;
She is a woman, therefore to be won.’
Tut! why should you be discouraged. Don’t you know our proverb, that
‘Faint heart never won fair lady’? Cheer up, man, and try. You can but lose
at the worst, and then if you win——”
Pandolfini sat and looked at him with glowing eyes. He was gazing at
Hunstanton; but he seemed to see Diana: not as she had been that evening,
seated calmly, like a queen, in the centre of so many people who looked up
to her—but as she appeared when he saw her first, when she shone upon
him suddenly, with her black veil about her head, and when all the bells
chimed Diana. What a revelation that had been to him! he did not even
know her, nor did he know how, without knowing, he could be able to
divine her as he felt he had done. He fell into a musing, his eyes all alit with
the glow of passion and visionary happiness. He knew there was no hope
for him: who was he that she should descend from her heights, and take him
by the hand? The idea was too wonderful, too entrancing, to have any
possibility in it; but it brought such a gleam of happiness to his mind as
made him forget everything—even its folly. He paid no attention to
Hunstanton gazing at him,—the substantial Englishman became as a mist,
as a dream, to Pandolfini,—what he really saw was Diana, the revelation of
that new unthought-of face rising upon him suddenly out of dimness and
nothing! What a night that had been!—what a time of strange witchery ever
since! He did not know how it had passed, or what he had done in it—was it
not all Diana from beginning to end?
Mr. Hunstanton was kind. After a minute or two he saw that the look
which was apparently bent upon himself was a visionary gaze, seeing only
into some land of dreams. He broke up the fascination of that musing by a
hearty honest laugh, full of genuine enjoyment. “Are you so far gone as

that?” he cried; “then, upon my word, Pandolfini, some one must interfere.
If you are afraid to take it into your own hands, I’ll speak for you if you
like. You may be sure I am not afraid. It isn’t our English way: but I’ll do it
in a moment. Is that what you would like? We’re leaving soon, as I told
you, and there is not much time to lose.”
“Oh, my best friend!” cried the Italian, with sudden eagerness. Then he
paused. “No, Hunstanton, I dare not. Let me have the little time that
remains to me. I can at least do as does your curate. I understand him. He,
too, has not any hope; how should he, or I either? but I would not be sent
away from her: banished for the little time that remains. No! let me keep
what I have, lest I should get less and not more.”
“Stuff!” said Mr. Hunstanton. “The curate, Bill Snodgrass! that’s a
different case altogether. Look here now, Pandolfini: you are ridiculously
over-humble; there is no such difference as you suppose. Now, look here!
You have some confidence in me, I know, and if ever one man wished to
help another, I am that man. Will you leave the matter in my hands? Oh,
don’t you fear. I shan’t compromise you if things look badly. I’ll feel my
way. I shan’t go a step farther than I see allowable. You shan’t be banished,
and so forth. Though that’s all nonsense. Will you leave it to me?”
Pandolfini fixed his eyes this time really upon Hunstanton’s face. “You
are too honest to betray me,” he said, wistfully; “you would not ruin me by
over-boldness, by going too far.”
“Who? I? Of course I should not. I have plenty of prudence, though you
may not think so; besides, I know a few things which are not to be
communicated outside my wife’s chamber. Oh, trust to me,—I know what I
am doing! You don’t need to be afraid.”
“But I am,” said the other. “Hunstanton, Hunstanton, my good friend, let
things remain as they are. I have not the courage.”
“Stuff!” said Mr. Hunstanton, getting up and rubbing his hands. “I tell
you I know a thing or two. Betray what my wife tells me—never!—not if I
were drawn by wild horses; but I know what I know. You had better leave it
in my hands.”
Pandolfini searched the cheerful countenance before him with his eyes.
He watched those noddings of the head, those little emphatic gestures of
self-confidence and sincerity. Was it possible that this man could be in
Diana’s confidence? No: but then his wife: that was a different matter: was

it—could it be possible? He got up at last, and went to him with a certain
solemnity. “Hunstanton,” he said, “good friend, if you have the power to
say a word for me, to recommend me, to lay me most humble at her
feet,”—he paused, his voice quivering,—“then I will indeed put myself in
your hands.”
“That’s right—that is exactly what you ought to do. But you must not be
so tremendously humble,” said Mr. Hunstanton. “Yes, yes, my dear fellow,
I’ll undertake it; but don’t be down-hearted. If you are not as happy a fellow
as any in Christendom by this time to-morrow night——”
“You—think so? Dio mio! You—think so?” said the Italian. His heart
was too full to say any more. He wrung his friend’s hand, and snatched up
his hat and went away with scarcely another word, stumbling down the long
staircase, which was as black as night, his mind too distracted to think of
anything. As he passed Diana’s door the glimmer of light which showed
underneath stopped him, as if it had carried a message, a word of
encouragement. He stopped short in spite of himself, and a wild fancy
seized him. It was all he could do to keep himself from rushing into her
presence, confessing everything, asking—ah! what was it that he could ask?
Would she be but favourable—kind—nay, something more? Should he
make the plunge himself without waiting for Hunstanton, and if such an
unimaginable bliss could be, have it a day earlier? The impulse made him
giddy, so strong was it, turning his brain round and round; but as he stood
there, with his hand uplifted almost in the act of ringing the bell, Diana’s
factotum, all unaware of who was standing outside, came to the door within
and began to bar and bolt and shut up for the night. Pandolfini’s hand
dropped as if he had been shot. He turned and made his way, without once
pausing to take breath, into the open air beneath, on the side of Arno. The
lamps twinkled reflected in the water, the stars from the sky; there was a
quiver and tremor in the night itself, a little soft wistful melancholy breeze.
Might this be the last night for him, the end of all sweet and hopeful days?
or was it, could it be, only the tender beginning of a long heaven to come?

CHAPTER X.
THE TWO LITTLE WOMEN.
Mrs. Norton and her niece had received the tidings of the Hunstanton’s
approaching departure with consternation almost more profound, and
certainly more simple in its exhibition, than had been exhibited by any of
the other members of the party. Surprise, which at the first moment took the
form of angry petulance and offence, had been the manner in which it
showed itself in Sophy; and as her aunt lived only in her and her wishes, the
girl’s angry vexation resolved itself into a mixture of offence and
resignation in Mrs. Norton. She calmed her child and soothed her, and then
repeated Sophy’s sentiments in a more solid form. “My darling, you must
not blame Diana. Diana has been goodness itself. We never could have had
this pleasure at all but for her thoughtfulness,” she said, and then added: “I
think, however, that Diana might have managed to let us know delicately
what she meant—not forcing it upon us through the Hunstantons, if that is
what she wants us to know.” Sophy did not think whether Diana had or had
not taken this underhand way of warning them that it was time to depart;
but she was angry beyond measure and beyond reason. They both cried
over the thought, shedding hot tears. “Just when we know everybody and
are really enjoying ourselves!” said Sophy. “Oh! how are we ever, ever, to
put up with that nasty, windy Red House among the trees, with no society,
after all that we have had here?”
“Oh hush, my darling!” said Mrs. Norton; “this is what it is to be poor,
and to have to do as other people like. Those who are rich can please
themselves—it is only the poor who are shuffled about as other people like;
but we must remember that we should never have come at all if it had not
been for Diana.”
“Would it have been worse not to come at all than to be sent away now?”
said angry Sophy, at that height of irritated scepticism which would rather
not be, than submit to anything less than perfect satisfaction in being. Could
any one say they were ungrateful? Did not the ascription of praise to Diana
preface everything they said, or at least everything that the most reasonable
of them said? For as for Sophy, what was she more than a child? and a

child, when it is crossed, allows no wisdom or kindness even in God
Himself, who ought to know better than to expose it to suffering. They
made up their little plans together on the very morning after that
momentous night. They would go to Diana, and find out what her intentions
were—whether she meant them to go, whether they were to accompany her
wherever she might be going, or go back with the Hunstantons. “She must
at least see that it is reasonable we should know,” Mrs. Norton said, with a
dignified and restrained sense of injury—as one above making an open
complaint, whatever reason she might have. When it came to the moment of
going downstairs, Sophy indeed began to hesitate. She was afraid of Diana.
“I am sure you will talk to her better without me, dear auntie,” she said.
“When any one is cross I cannot bear it.”
“That is because you are too sensitive, my love,” said Mrs. Norton.
“Poor darling, who would be cross to you? and you are only afraid of Diana
because of the time when she was your governess,” she added, with a mild
sense of superiority as of one who never was, nor had in her family any one
who required to be a governess. But nevertheless, half by moral suasion
half by authority, Sophy was made to come and back up the elder lady by
her presence. They went downstairs slightly nervous it must be allowed.
They knew that they were braver behind backs than when Diana looked at
them with those large eyes of hers; but having made such a strenuous
resolution, they could not withdraw from it now. They found Diana taking
her morning coffee with a book before her, as is the use of lonely people,
and she received their visit quietly as a not unusual incident. She was not an
early riser—that was one of her weak points—and they were early risers;
and they naturally looked at each other with a glance of commentary and
gentle moral indignation at her late hours.
“You are so like a gentleman sitting there with your book,” said Sophy,
with a sense of pleasure in finding something to find fault with. Diana
closed the book and smiled.
“I suppose I should take that as a compliment,” she said, “for Sophy, I
know, has the highest opinion of gentlemen. Can one do better than copy
them? You have been up for hours, and have done a great many things
already, while I have been idling here.”
“Yes—but then we have no maid to do anything for us; and if we want to
have our things nice, we must get up early,” said Mrs. Norton. “We thought

most likely you would be at breakfast, and that we should be sure to see you
alone for a few minutes—you are always so much engaged now.”
“Am I? I thought I was generally at my friends’ disposal,” said Diana,
with a smile; and then there was a little pause. For even her smile when she
looked up at them expectant, perceiving something that was on their lips to
be said, alarmed the two little women. However, Mrs. Norton, feeling the
situation to be too serious for silence on her part, took courage and began—
“Diana—we don’t want to disturb you, dear. We know you are sure to do
what is best and kindest for everybody; but we should just like to know, if
you don’t mind, what your plans are——”
“My plans! I don’t think I have any plans,” said Diana, surprised, and
then she laughed and added, “To be sure, we can’t stay here all the summer,
can we? We are not at home, are we? That is what I always forget when I
get settled anywhere.”
“And not much wonder: for you can surround yourself with all kinds of
comforts,” said Mrs. Norton, looking round her wistfully. To be sure, the
third floor upstairs was not like the piano nobile: but she did not intend to
seem to make any injurious comparison. The idea was suggested however,
and Diana, who was very quick, took it up, and she coloured, and a pained
look came upon her face. This was the kind of reproach to which she was
most susceptible. It was as if she had been accused of making herself
comfortable at some one else’s expense.
“I hope you are not uncomfortable upstairs,” she said. “I thought the
house was the same all the way up—no difference but the stairs.”
“Oh no, Diana, dear!” cried Sophy. “Our drawing-room is not half so big
as this. It is divided into two. This part is auntie’s room in our apartment
——”
“But that does not matter a bit,” cried her aunt; “you must not think we
are anything but comfortable, and quite happy, Diana, and most grateful to
you.”
“Never mind about being grateful,” said Diana, “the comfort is much
more important.” She laughed and shook off her momentary offence. “If
there is anything I can do to secure that, you must tell me,” she said, kindly;
“the Hunstantons’ rooms perhaps might be better when they leave.”
“Oh!” cried both the appellants, with a common breathlessness. “That
was just what we meant to ask you about,” Mrs. Norton went on—Sophy,

so to speak, running behind the skirts of the elder and more skilful operator.
“We wanted to know if you thought—if you wished—what you think we
ought to do? We came with the Hunstantons; and Pisa is not a place to stay
in, in summer. But on the other hand, to go back to the Red House when
you were away, Diana——”
“Yes, I understand; but shall I be away? If Pisa is not a summer place, I
cannot stop in Pisa more than any one else.”
“But you can go where you like, dear. There are a great many other
places to go to. There is Florence, which you would like to see, and the
Bagni di Lucca; and there is Switzerland, Diana. You can do whatever you
please; but we can’t afford, can we, to do anything but go straight home?—
if you think we ought to go straight home.”
Diana looked from one to the other. There was a point in which she was
the foolishest of women. She liked to satisfy other people, to give them the
things they wanted. When she saw a secret coveting in anybody’s eyes,
instead of disapproving and reproving, the immediate thought in her mind
was how she could get them what they wanted. Perhaps this was a
temptation which she would not have felt had she always been Miss
Trelawny of the Chase, accustomed from her cradle to be better off than
other people, and feeling it natural. But the new power of giving, and of
gratifying those wishes which she remembered to have entertained herself
without being able to gratify them, was very pleasant to her, and she could
not resist it. She was not strong enough to deny herself in order to preserve
the independence of Sophy and Mrs. Norton. She looked from one to
another, and saw the suppressed eagerness in their eyes.
“And you would like to go to Florence too—and Lucca—and to go
home by Switzerland? Why not? It seems a very reasonable plan.”
“But we cannot afford it, Diana.”
“Oh, as for that, I can afford it. Don’t say anything,” said Diana. “Don’t
you see it would be no pleasure to me to go alone?—and evidently that is
the natural thing to do.”
“To be sure,” said Mrs. Norton, gravely. “It is not nice to travel alone:
but then the expense. How could I put you to so much expense? I don’t
think it would be quite—right. I don’t think——”
“As for the right and the wrong, I think we may take them in our own
hands,” said Diana, with a smile. “You must get the Bradshaw—that is what

you must do, and settle the routes. Of course, we must go by Switzerland.
And I had never thought of it! It is evident I want you to put things in my
head.”
“You are very kind, Diana. I am sure if I can be of use in any way to you
who are so good to us—and, of course, it would not be nice for you to
travel alone, I allow that: even for gentlemen, it cannot be so nice. But for a
lady, and so young as you are still——”
Diana laughed. She was half ashamed of herself for seeing so clearly
through this little air of reluctance and difficulty. “Evidently,” she said, “I
am too young to take care of myself. Any one who thinks differently does
me an injury. Then that is settled, is it not? It will be a great deal more
pleasant having your company. I never like to do anything alone.”
“Oh, Diana, what a darling you are! How good you always are!” cried
Sophy, throwing her arms round her friend. “And I am such a nasty little
thing! I thought you would not care a bit: that you would send us away with
the Hunstantons by that horrid long railway, and never think—— Oh, I am
so ashamed of myself! and you do love us, you do like to have us with you,
Diana, dear?”
“Do you expect me to make protestations?” said Diana, shaking herself
free with a little embarrassment, feeling compunctions on her own side that
she could not be more effusive. “I ought to have thought of it before, but it
did not occur to me. Yes, to be sure, we must see the snows. We have our
time in our own hands; we are not compelled to be at home by a certain day
like Mr. Hunstanton.”
“Oh, Mr. Hunstanton! he is so fussy, always interfering with everything
—what does it matter when he gets home? I am tired of Mr. Hunstanton!”
cried Sophy.
“You should not speak so rashly, my dear. Mr. Hunstanton has been very
kind. She has never liked us much. She has always been jealous of Diana’s
love for you, never seeing how natural it was: but Mr. Hunstanton has
always been kindness itself. Oh, I am sure she will make disagreeable
remarks now! She will say we don’t mind what expense we put Diana to. I
know exactly how she will look. But do not think anything of that—I do not
mind, Diana. Do not imagine that I would take the pleasure out of your
journey, dear, for anything any one could say——”

“And spoil our own pleasure, too, when Diana is so kind,” cried Sophy,
with frank delight. “Oh, do you think my old travelling-dress will do, aunt?
—or should I have another grey alpaca? Switzerland! I never, never thought
of such happiness: though indeed,” added the girl with a sigh, “I shall be
very, very sorry to leave Pisa, too. I have never been so happy as here.”
What was it that had made Sophy so happy? Diana looked at her with
some curiosity, patting her softly on the cheeks.
“So many parties,” said Sophy, “or at least as good as parties. We have
never been at home for a whole week. There has always been something
going on; and expeditions; and dances now and then. I have never been so
happy in all my life before.”
“Hush, hush, my darling! you would be just as happy at home. I hope my
Sophy does not want constant amusement to make her happy; but still it has
been very pleasant, and, of course, we could not hope to have so much in a
quiet country place.”
“And in England! where, as Colonel Winthrop says, the skies are always
grey, and the company bumpkins,” said Sophy, with the sublime contempt
of a traveller. What could Diana do but laugh as they played their little
pranks before her. They were as good as two little white mice in a cage.
“You had better look into that serious question of toilet,” she said, “and
quite make up your mind whether another grey alpaca is necessary; for if
we do go to Switzerland, there will be a great deal of travelling to do.”
“What shall you wear, Diana?” said Sophy, growing serious; “for you
know your merino that you came in will be too warm. I wish you would
think of that a little more. Yes, auntie, indeed I must speak. You know you
always say that Diana never does herself justice.”
“Do I?” cried Mrs. Norton, colouring a little, while Diana laughed with
great amusement “I am sure Diana always looks well whatever she puts on.
You have heard me say so a hundred times.”
“Don’t take any trouble on my account,” said Diana. “I shall find
something, never fear.”
“And we are wasting all your time,” said Mrs. Norton. “Sophy, we must
run away. If Diana has not the little things to do which we occupy ourselves
with, she has other matters to think of. Dear Diana! how can I ever say all I
think of your kindness! Nothing would make me accept it except the

thought that we can perhaps, in our little way, make it pleasanter for you
too.”
She was very strong on this subject to everybody to whom it was
mentioned afterwards. “Yes,” she said, “we are going to Switzerland. Dear
Diana does not like to travel alone; and, indeed, it is scarcely proper, for she
is still quite what is considered a young lady, you know—though, of course,
a very great deal older than my Sophy; and Diana has been so very kind to
us that I like to do all I can to be of use to her. Sophy will enjoy it too. Oh,
it is not at all disagreeable to me, I assure you,” she said, smiling with
gentle friendliness and resignation. The chaplain’s wife, if no other, thought
it was “so kind” of Mrs. Norton to go to Switzerland with Miss Trelawny.
“It took them all by surprise, I believe, and they had made their plans to go
home: but they are such good creatures, so unselfish! They have changed all
their arrangements rather than that Miss Trelawny should have the
annoyance of travelling alone.” This was repeated over and over again that
afternoon in the little church coterie at a choir practice, where there was
quite a flutter of admiration over the unselfishness of the two little ladies.
The glee-party was all there, with the exception of Mrs. Hunstanton, whose
absence, perhaps, was fortunate in the circumstances. As for Mrs. Norton,
she never departed from this ground even in her most private moments. “I
am so fond of Diana that nothing is a trouble,” she said, “she has always
been such a friend;” and then it got whispered round, to the great
admiration and surprise of everybody, that Miss Trelawny, though so great a
lady, had once been Sophy’s governess. What a wonderful thing it was!
everybody said; exactly like a romance in real life!
The Snodgrasses, who were also at the choir practice, heard, like the
rest, of Miss Trelawny’s plan, and the excitement of the information
brought the curate out of his corner. “I don’t really care about going to
Florence. I never did care,” he said hurriedly to his uncle. “Switzerland is
what I should like most.” The rector shook his head, and called his dear Bill
a goose; but yet, reflecting within himself that dear Bill was six feet high,
and a fine specimen of a man (though not perhaps what is generally called
handsome), and that Miss Trelawny had a fine fortune, and that
Perseverance was the thing which carried the day, Mr. Snodgrass thought
that perhaps, by chance, so to speak (if it were not an impious thing to
speak of Chance), he might direct his steps to Switzerland too. So that a
whole party of people were moved, and their intentions and destinations

changed, by the impatience and disappointment of Sophy Norton at the
prospect of an abrupt conclusion of her holiday. She thought herself, and
with justice, an insignificant little person, yet it was she who had made all
this commotion.
In the meantime Sophy’s own head was full of her wardrobe, to the
exclusion of other ideas. Should she have dresses enough for the summer?
should she want another grey alpaca? or could she get on with what she
had, with a new white frock, perhaps, and a dust-cloak? “There is nothing
looks so nice as white,” said Sophy, regarding her wardrobe with an
anxious pleasure. “In fine weather, my darling: but it always rains among
the mountains, and a white dress, or a cotton dress of any kind, looks poor
in bad weather.” This was a very serious question: for indeed she had a grey
alpaca already, which was too good yet to be taken merely for a travelling-
dress. It was the one which had been made up on the model of Diana’s
beautiful new silk from M. Worth’s. This was a very perplexing problem,
and one which gave them a great deal of trouble; but yet it was a happy
kind of care.
As for Diana, she had the faculty of putting aside the points that jarred in
her friends’ characters. She was aware that they were not perhaps so
unselfish as they took credit for being, and she could not but laugh softly
under her breath at Mrs. Norton’s solemn conviction that she “could be of
use” to Diana. But what then?—what did it matter after all? It would be
pleasant enough to go to Switzerland, and travelling alone was not very
pleasant. So far the Nortons were right. Diana feared (a little) the
innuendoes of Mrs. Hunstanton when she heard of the project; but
otherwise it amused her (she did not put it on any higher ground) to see
their pleasure, to indulge them with every luxury of a journey made en
prince. To have everything you can desire, without ever having to think of
the expense, how pleasant it was! How she would have liked it when she
was poor! She did not say to herself that she had been as independent as she
was poor, and would not have lightly taken such a pleasure at any one’s
hand. Why should she have remembered this? Sophy was not like her: and
after all, to make these two little women perfect, to reform their characters,
and mould them after her own model, was at once a hopeless proceeding
and one altogether out of her way.

CHAPTER XI.
THE PROPOSAL.
The rooms on the third floor of the Palazzo de Sogni were not like those
in Diana’s beautiful appartamento. The drawing-room, which was so
spacious and lofty in the piano nobile, was low, and divided into two; one
half of it was Mrs. Norton’s bedroom. In moments of excitement, and in the
early part of the day, the door of communication was sometimes left open,
though it was against all the English ideas of nicety and tidiness, in which
these little ladies were so strong, to leave a bedroom visible. But what else
could be done, when Sophy was seized with that anxiety about her toilet,
and the delightful sense of preparation for a further holiday whirled them
both out of their sober routine? Mrs. Norton had her excuse all ready if
anybody should call—that is, if any lady should call—for the thought of a
masculine foot crossing her threshold did not occur to her. “We have no
maid,” was what she would say, “and of course there are a great many
things which we must do ourselves. Fortunately, I am quite fond of
needlework, and Sophy is so clever, and has such taste. You would never
think that pretty dress was made at home? but I assure you it is all our own
work. The only thing is that we keep the bedroom door open, in order to
keep this one as tidy as possible.” Every visitor (being a lady) sympathised
and understood: and gentlemen, except the clergyman, never came. A
clergyman, by virtue of his profession, has more understanding on these
points—has he not?—than ordinary men; he is apt to understand how poor
ladies have to employ themselves when they have no maid; in short, he has
the feminine element so strongly developed as to be able to criticise without
rushing into mere ignorant censure, as probably a gentleman visitor of
another kind would have done. And no profane male foot ever crossed Mrs.
Norton’s threshold. They were at their ease therefore next morning, after
their interview with Diana, when they got up to the serious business of the
day. There was no hurry; but the work was agreeable, the excitement of
preparation agreeable, and then, to be sure, a hundred things might happen
to hasten their departure, and it was always best to be prepared. The door of
Mrs. Norton’s sanctuary was accordingly standing wide open, revealing not
only the Italian bed with its crackling high-piled mattress of turchino, but a

large wardrobe standing open with all kinds of dresses hung up inside. The
alpaca which was in question was spread out upon the sofa in the little
drawing-room, and formed the foreground to the picture. They were both
standing at a little distance contemplating it with anxious interest. Mrs.
Norton had her head on one side. Sophy had a pair of scissors in her hand.
It was almost the most difficult question that had ever come before them.
“It is very elaborately made,” said Mrs. Norton, doubtfully. “The
flounces would be very awkward in a travelling-dress. They are so heavy to
hold up, and they get so full of dust——”
“But, auntie, I have heard you say it made all the difference to a dress
when it was nicely made.”
“Yes, that is very true; but a travelling-dress ought to be simple—it never
ought to have a train, especially for a young person. You ought to be able to
jump out and in of carriages, and never think of your dress. Besides, that
would be so useful at home. You could wear it so nicely for Diana’s little
parties, or when she is alone——”
“Oh, auntie! I shall never care for these horried little parties again.”
“Hush, my darling! at least you must never talk like that. You will be
very glad of them, Sophy, when winter comes.”
Sophy shook her head: but the present matter was still more important.
“Something new would be better, no doubt,” she said, “for the evening—
one of those light silks that are almost as cheap as alpaca. When one has to
get a new thing, isn’t it better to have it for one’s best? whereas an alpaca is
never very much for a best dress, and would look nothing in the evening;
and making a new common dress is just as troublesome as making a
handsome one. And I might cut this a little shorter, or loop it up: and it
would look nice when we stayed anywhere for a few days. Diana will insist
on staying everywhere for a few days: I am sure she cannot really like
travelling: and this with my white frocks when it is very fine——”
“I see your heart is set upon a new silk.”
“No, indeed, auntie,” said Sophy, half offended. “The only thing is, what
should I do with two grey alpacas? If I were to take off the trimming here,
and change this flounce——”
“Run, Sophy, run! there is some one at the door. Filomena has no sense
—she will show them in at once.”

“What does it matter?” said Sophy. “It can only be Mrs. Hunstanton—I
don’t mind at all what she says. I should like her to know. She ought to be
cured of her interfering. It will let her see who Diana cares the most for. It
will show her——”
“Mr. Hunstanton!” cried Mrs. Norton, with almost a shriek. A
gentleman! and actually the bed visible, and all the things hanging up. She
made a dart at the door and shut it, then turned round breathless but bland.
“This is a pleasure!” she said; “but you find us in great disorder. I am so
sorry. We were just arranging a little against our journey.”
“What journey?” said Mr. Hunstanton. “Don’t apologise. I like to have a
finger in the pie. You shall have my advice with the greatest pleasure. But
what journey? Were you thinking really of returning with us? That would be
good news: though I think I have perhaps something to say that may make a
difference. Don’t take away the dress: I am a great authority about dress—
though my wife snubs me. Don’t take it away.”
“We are going with Diana,” said Mrs. Norton. “If we had been going
home there is nothing I should have liked so much as going with your party.
You were all so kind to us coming. But our first duty is to Diana. She has
never been abroad before—she thinks she would like to return by
Switzerland, and see as much as possible; and, of course, I could not let her
go alone. And Sophy will enjoy it—though, indeed,” said the little woman,
with a sigh, “it will not be unalloyed pleasure to me. My circumstances
were very different when I was there before. Still I must not be selfish; and,
of course, I could not let Diana go alone. After all her kindness to Sophy,
that would be too ungrateful—it is what I could not do——”
“Whew!” said Mr. Hunstanton under his breath: and then corrected
himself, and composed his countenance. “So you are going to Switzerland
with Diana. Ah-h!—with Diana! That is a new idea. Bless me! I wonder
what Diana will say to me if I spoil her trip for her? Mrs. Norton, I have
come to say something very important to you. It is not on my own account
exactly. I am come as an ambassador; as—plenipotentiary. I have got
something to say to you. Well, of course I don’t know what you will
answer; but it is not disagreeable. It is the sort of thing I have always heard
that ladies like to hear——”
Mrs. Norton looked with unfeigned amazement at the beaming
ambassador, whose enjoyment of his office there could, at least, be no doubt

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