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52
On Not Muddling Lunches and Flights: Narrating a
Number, Qualculation, and Ontologising Troubles
Ingmar Lippert
Bureau for Troubles: Post-natural histories and futures, Museum for Natural History Berlin, Germany/
lippert@ems-research.org
Abstract
Calculating and making public carbon footprints is becoming self-evident for multinational
corporations. Drawing on ethnographic data I narrate of the calculative routine practices involved
in that process. The narration shows how routine yet sophisticated mathematical transformations
are involved in retrieving salient information, and second that mathematical consistency is readily
interrupted by ‘dirty data’. Such interruptions call for opportunistic data management in devising
work-arounds, which eect enough mathematical coherence for the number to hold together.
Foregrounding an episode of calculative data retrieval, interruption and work-around contrivance,
I employ it to make a comparative reading of two STS analytics, arguing: whereas Callon and Law’s
(2005) analytic technique of qualculation reveals the episode of data management and work around
contrivance as a teleologically oriented process that manages to bridge mathematical inconsistency,
Verran’s technique of ontologising troubles enables us to recognise how a number-as-network
congures its particular kind of certainty and coherence, how it sticks.
Keywords: calculation, number, ontics, ontology, qualculation, empirical philosophy
Introduction
Number studies thrive in Science and Technol-
ogy Studies (STS). STS has raised a range of ques-
tions challenging numbers and calculation. These
include how chance got quantied and politically
employed (Hacking, 1990; Desrosières, 2002), how
accuracy gets constructed (MacKenzie, 1990),
how trust in numbers is playing out in society,
technology and economy (Porter, 1995) or how
equivalences are achieved (Espeland and Stevens,
1998; MacKenzie, 2009a). The concerns here are
not about numbers as output of some calcula-
tion, but rather about how numbers and calcula-
tions are employed in practices that constitute
science, technology, economy—such as knowing
epistemic objects (Knorr Cetina, 2002), distrib-
uting resources and accountabilities (Strathern,
2000), constructing economic agents (MacKenzie,
2009b), setting prices (Fourcade, 2011) or dening
baselines (Ureta, 2017).
The eld of actor-network theory (ANT) has
been highly instrumental in STS for studying
material and semiotic entities as relational
networks (Latour and Woolgar, 1986; Latour, 1987;
Law, 1992, 2009). ANT studies of numbers and
calculations have opened up how accounting
numbers congure action at a distance (Robson,
Article Science & Technology Studies 31(4)
53
Lippert
1992), how markets get materialised (Callon,
1998; Callon and Muniesa, 2005) or how collat-
eral realities get enacted in presenting quanti-
cations (Law, 2012). In the latter cases, numbers
and calculations, too, are analysed as compo-
nents of semiotic and materials relations that
congure science, technology, economy. ANT’s
power to open up entities as relational networks,
however, has not been deployed to open up
specic numbers, numbering or calculations. Two
notable exceptions are Verran’s (2001) work on
doing numbers in routinised practices and Callon
and Law’s (2005) proposal to study calculations as
interwoven with judgement, using the neologism
of qualculation.1 Callon’s (1986) concern with
numbers can be traced back to his work on
scallops and their conservation at St Brieuc Bay,
Law readily shares how he learned it from Callon
(personal communication), whilst Verran (2001),
disconcerted by her experiences of learning and
teaching numbers and basic concepts like length
in Nigeria, set about delving to the insides of
numbers.
The subfield which this paper operates in,
then, is the use of ANT to open up the networks
within numbers or calculations. How to use ANT to
explore this opening? A number of ANT authors
point us to ANT not as a consistent body of theory
but rather as something akin to a toolkit (Latour,
1996, 1999, 2005; Law, 2009; Verran, 2007b).
I wonder, then, whether the tools to open up
numbers and calculations are equivalent, lend
themselves to the same kind of work. And, I
suppose, this concern and question is relevant to
others who want to understand, master or even
deploy the toolbox of ANT to open up numbers.
The research question of this paper then is narrow
and has a methodological form: how do the two
analytical framings, qualculation and Verran’s take
on numbers, dier, complement or work against
each other? This question matters not only for
enriching our understanding of the ANT toolkit’s
inner compatibilities and frictions, but also to
the larger task in STS of spelling out the nuances
between some of its analytics.
The question, and the research to address it, is
novel in that it positions the reader to engage in a
comparative methodological exercise. This means
that this paper focuses on studying how the two
analytics work, in analytic practice. In short, this
paper presents a study of two ANT techniques.
Both these techniques are key for ethnographic
investigations of a number-as-network. To study
number-as-network this paper employs a method
of empirical philosophy, narrating a number.
What both analytical approaches share is that
enumerated concepts, results of calculative and
quantifying relations, have ‘insides’. This follows
from a core claim of the ontological commitment
in ANT to the mattering of material, bodily and
semiotic practices (Verran, 2001; Callon and Law,
2005; Law, 2009): doing numbers or calculations
enacts not only the known but also the knowers.
The argument pursued here is that both
analytics narrate and analyse numbers/calcula-
tions dierently, foregrounding dierent relations,
elements or eects of the insides. This means that
the objective is to show that both approaches
lend themselves easily to make dierent points.
This does not rule out that both approaches
could be mobilised to say what the respective
other is saying, too. The point I want to draw out
is that each approach makes some things easier
and other things more dicult to explicate. And,
unsurprisingly, both approaches have not been
very explicit about what they tend to fore- or
background. So, the contribution to STS which I
pursue is to show how these two ANT approaches,
though similar, are also dierent, and not easily
substitutable against each other.
The empirical ethnographic material that I draw
on in narrating a number deserves an introduc-
tion as much as the choice to use precisely this
material. The domain in which the number/calcu-
lations I am interested in have been practiced,
is the eld of carbon numbers and economics
(Callon, 2009; MacKenzie, 2009a; Lohmann, 2009;
Lovell and MacKenzie, 2011; Ehrenstein and
Muniesa, 2013; Vesty et al., 2015; Lippert, 2016).
Specically, I turn to carbon accounting and book-
keeping, numbering and data practice. This ties in
with an analytical trajectory that investigates how
environments are known and come into being
through data, information, algorithms, simula-
tions, databases and reporting—congured into
situated practices of environmental manage-
ment and sustainability governance (Elichirigoity,
1999; Waterton, 2002; Fortun, 2004; Ellis et al.,
54
Science & Technology Studies 31(4)
2007; Millerand and Bowker, 2009; Edwards, 2010;
Gabrys, 2016; Lippert et al., 2015; Blok et al., 2016).
I studied carbon accounting in a financial
service provider, one of the globally 50 largest
companies (by revenue). This was an ethnography
conducted across 20 months, studying the multi-
national’s environmental management work with
a focus on their material and semiotic practices
through which they achieved their global carbon
footprint.2 Opening up numbers of carbon
accounting involves addressing their indetermi-
nacies and certainties.
To open up number-as-network, I tell a story of
a number, which has been congured, inter alia by
myself, the corporation’s sustainability accounting
database, a subsidiary’s chief operations ocer
(COO) and a worker who put environmental
numbers together for him. The worker, Nick,
gures key in my narrating. Most relevant for the
present paper, Nick was a novice—rst-time user/
practitioner—of doing environmental data for the
company. Studying a novice promises to disclose
the frictions and work involved in doing numbers
(cf. Suchman, 2007: 122). Neither Nick nor his
boss, the ocer, were concerned with explaining
or theorising numbers, data and calculations,
not with experimentation for making carbon
markets work (Callon, 2009). Still, my narration
of the number includes a calculation. And this
calculation was highly eective as a machine that
made the corporate carbon accounting exercise
proceed, a machine that made things work,
enriching the voluntary carbon market, rather
than standing in the way (on machines and their
working, see also Lippert, 2011; Neyland, 2018, in
this special issue).
Next, I oer some notes on methodology and
transparency. Then I turn to the core: I narrate a
number in a way such that the two analytics can be
deployed; subsequently I introduce the qualcula-
tion analytics, putting it into practice by analysing
a calculation. Then I present the Verranian
analytics and use it to ontologise a number’s
troubles. Finally, I draw together my conclusions
in terms of the two analytical approaches dier-
ently oriented capacities to foreground specic
workings within numbers or calculations.
Methodology
This paper is grounded in an ethnography. The
workers I studied knew I researched them; and I
was employed to support the company in opti-
mising their environmental accounting database.
To pr ote ct inf orman ts, I render names anony -
mous, numbers imprecise and convert currencies
into EUR.3
This paper’s methodology takes the form of
empirical philosophy, rather than of systematic
qualitative data analysis. Following the purpose
of the present special issue—interrogating
recent innovations in STS analytics of numbers
and numbering (Lippert and Verran, 2018)—
for my analysis I have constructed an empirical
story that serves to interrogate STS analytics. The
narration, or story, here is not shaped to meet
specific sociological and ethnographic criteria.
Storytelling serves here to allow the reader relate
and attend to key empirical detail, strengthening
my ability to respond to the troubles I identify in
and around Nick’s calculation (on response-ability,
see Haraway, 2016; on storytelling as relational
practice Kenney, 2015: 758–759). The story is not
narrated to privilege a particular explanation,
attempting, drawing on Benjamin (2006), even to
keep it free from explanation. This choice of meth-
odology suces to draw out the generativities
and limitations of particular STS analytics.
The empirical story I present is bundled with
inferences that draw out the signicance of some
of the relating that shaped the calculation or took
place within the latter. To be able to analyse the
practical, epistemic and ontological work in doing
the calculation, I use the mathematical genre as
a device: I employ mathematical denominations
and equations that the numbering and calculation
practice explicitly referenced or implicitly postu-
lated. Using the mathematical genre stays true to
some of the forms of rationality that I identify in
Nick’s practice.
A concern with accurate description or
grounded theorising would shift the focus away
from the kind of empirical philosophy I undertake.
The evidence presented within the empirical
story may be understood as serving a part-whole
generalisation (Winthereik and Verran, 2012)—
the kind of numbering and calculation I analyse
is part of the company’s global carbon footprint
55
and involved in relations to governments and
investors, i.e. global political economy. One limita-
tion of the kind of empirical philosophy I conduct
is that this paper in isolation cannot make
claims about the majority of calculations I have
studied. The empirical story in this paper, if read
in isolation, must be understood as an artefact of
being written to serve the methodologically inter-
ested interrogation of the two ANT analytics.
For the purpose of comparative methodolog-
ical analysis, I oer an interested presentation and
deployment of both approaches, mediated by a
partial reading of both, Verran (2001) and Callon
and Law (2005). Whilst this constitutes another
limitation of this methodology, an exhaustive
review of the authors and their approaches is
beyond the scope of this paper and not needed
for the purpose of the comparative exercise. To
respond to the research question, it suces to
identify differences between both approaches
that are salient to the empirically grounded data
and inferences that I narrate.
Narrating a number
The multinational’s accounting database, acces-
sible as a Lotus-Notes based application in the
corporate intranet, included forms, suitable called
‘task forms’, which subsidiary environmental
agents were tasked to ll (as an illustration, view
the form for reporting water consumption, Figure
1). I wanted to learn about the ways data gets con-
structed. My own boss at the headquarters (HQ)
allowed me to travel to a Western Asian subsidi-
ary, study their environmental data practices, and
she tasked me to support subsidiary sta. So, o
I went, arrived in the megacity, housing the mul-
tinational’s regional sub-HQ. On my second day
Lippert
Figure 1. ‘Task’: General form for environmental data entry (this screenshot documents Nick’s form use to report
2008 drinking water consumption; for the respective analysis, see Lippert (2016); Source: Lippert, 2013: 81)
56
Article
in the city, after a bus tour on a hot summer day,
through the Eastern parts of the city, and then into
the better neighbourhoods, nally I arrived at the
modern steel-glass block. I entered the building,
was asked whom I wanted to see, and after some
back and forth was led to the subsidiary’s COO.
He occupied a large oce, with a glossy wooden
desk and several square metres of windows at the
top of the building.
Early in our meeting Nick Xi joined us and
presented a list of numbers to hiss boss, the COO.
Later on I learned: Nick was the oce site’s head
engineer, a novice in environmental accounting.
Nick had been asked to retrospectively collect the
2008 environmental data that the HQ was seeking.
Subsequently, Nick showed me around at the site,
and, eventually, we went to his oce, located in
the building’s windowless basement. His work
space was neighbouring round six other desks.
Nick and I soon got to work in depth, me doing
participating observation and helping him out,
clarifying things when he had questions, and Nick
drawing together various environmental data. We
worked, and worked, and, let me fast forward, to
the next day of working with Nick, he sitting on his
red chair, and me at his beige desk on this Friday
afternoon, directly after lunch, between 2–4pm,
in spring 2009. His desk was set up with two land
line telephones, a computer screen, mouse and
keyboard.
Nick picked up the phone to ask a colleague
about the distances travelled by staff of his
company. In the conversation he learned about
the costs incurred in the prior year for domestic
flights, 168,078 EUR. This phone conversation
made him laugh and smile. His work equipment
included a paper, to note the numbers and to
conduct some simple calculations, like additions,
multiplications and divisions. He next divided the
ight cost number by 230 EUR, an average cost of
each ight, and multiplied the result with 500 kilo-
metres, an average distance crossed with domestic
ights. With the result of this calculation ready, he
turned to his computer and entered the result in
the ‘task’ form for reporting the distances travelled
on short-haul ights. At this point I intervened,
suggesting to Nick to also briey describe in the
form’s comment eld how he had calculated the
estimation. He hesitated, but then agreed.
Five inferences bring out the richness of Nick’s
calculating, mixing the ethnographic with the
mathematical genre. Nick mobilised the total cost
fact for the calculation. Where did this fact come
from? Picking up the phone, Nick had called a
colleague and received the cost fact on domestic
ights for the subsidiary. This is not trivial. And this
is the rst inference. While for this particular case
he managed to ‘immediately’ access such a cost
fact for the totality of the subsidiary, with other
environmental indicators he had to struggle more.
For instance, Nick was also to report his subsidi-
ary’s water consumption data. Yet, some of his
subsidiary sites did (or could) neither fully report
water costs nor the consumed amounts. So, Nick
extrapolated the available site-specic consump-
tion facts to the scale of the subsidiary, with calcu-
lations, materially supported by spreadsheets, pen
and paper. Luckily, for calculating ight distances,
Nick was equipped with an already complete fact;
no need to extrapolate towards the total costs at
subsidiary level: at the end of his phone call, thus,
he laughed and smiled.
Knowing that the organisation had paid
168,078 EUR for domestic flights did not tell
him how many kilometres have been bridged,
however. Nick reconstructed the cost fact corre-
sponding to a particular mathematical form, my
second inference: as the sum of several individual
ights, totalling n ights, each with a cost, cn. He
eectively exploded one number into many.
Unfortunately, Nick had not received information,
at this point in time, about each ight’s associ-
ated costs, c1 to cn; all the individual costs were
as unknown to him as the number (n) of and
distances (d1 to dn) travelled with flights. From
observing Nick exploding the total cost fact and
transforming it into the cognitive form, shown
in Equation 1, I infer, thirdly, that this cognitive
understanding inspired Nick to use a mathemati-
cal routine, well known to him, that would allow
ignoring all these unknowns. Thus, Nick expli-
cated assumptions about these individual ights,
specifying each ight in two dimensions, in terms
of estimated average values: one for the cost,
57
, and one of the distance of an individual ight,
. For instance: ‘I assume, on average a domes-
tic ight bridges a distance of 500 kilometres and
costs 230 EUR.’ Mathematically, he postulated
=230 EUR and
=500 km. To be even more
explicit, these assumptions implied:
as well as
And, Nick knew what he was searching for: the
total distance travelled by short-haul ights, sum
of all the ights’ distances,
. My fourth infer-
ence is then: making such assumptions, when
equipped with the total cost and searching for
the total distance travelled, presented Nick with a
clean structure of statements (illustrated by Table
1), l ea vi ng o nl y on e un kn ow n el e me nt , th e qu an ti -
er x for the data type total ight distance in km.
Nick treated this frame of triples with only
one unknown as mathematically exploitable, my
fth inference. He identied the two repeating
units, km and EUR. Dividing the average distance
travelled per ight by the the average cost of a
ight, and multiplying the result with the total
cost fact, Nick could cancel out the two EUR units,
resulting in a data point with the unit km.
This is the corresponding mathematical form:
In a dierently plain language, for the qualitative
STS scholar:
And this is the calculation:
Despite the more or less overwhelming math-
ematical richness, Nick swiftly and seemingly
routinely solved the problem of the missing
data point and entered it in the short-haul ight
accounting form.
Entering data into the environmental database
was part of a routine of what the headquarters
(HQ) called ‘environmental data collection’ in the
company. The collected data was reviewed at
the HQ, checked for inconsistences or obvious
errors, followed by possible corrections. All the
unique data points, indicating the consump-
tion of water, electricity and paper as well as the
distances travelled and the amounts of waste
disposed, were multiplied with specic factors
that converted each data point into the amount
of carbon emissions (CO2e) resulting from the
respective consumption.4 For example, according
to standard conversion factors, short-haul ights
cause higher emissions, per kilometre, than long-
Lippert
Table 1. Structure of statements.
Knowledge status Framed triples of data Math.
Quantier Unit Data type
Partial xkm total ight distance
∑
=1
Complete
500
168,078
230
km
EUR
EUR
average ight distance
total ight costs
average ight costs
¯
∑
=1
¯
,
,
.
.
58
Science & Technology Studies 31(4)
Figure 2. ‘Employee footprint’, extract from the corporation’s Sustainable Development Report (Source: Lippert,
2013: 206).
distance ights.5 The amounts of emissions were
then summed up into a carbon footprint reported
on a balance-sheet, for each subsidiary as well
as for the global operations of the multinational.
This footprint was communicated to stakeholders,
including auditors, partners, investors govern-
ments and civil society organisations, for instance
in the form of relating last year’s (2008) average
carbon footprint per employee to the target of
emission reduction in the future (2015), as illus-
trated in Figure 2.
59
Later the afternoon, Nick received an email
that contained a spreadsheet. The latter detailed
which cost items have been part of the account
for domestic ights. The list included diverse items
such as ights, restaurant visits, trips by boat and
taxi and visa fees. He called out: The list includes
lunch! Despite the skilled mathematical routine, it
seemed clear the data could not be used. And so
it proved.
Before the workday ended, Nick and I went
to see Nick’s boss. In this meeting we talked
through a range of uncertain issues (that are not
at the centre of this story), which Nick and I had
encountered. In his reaction, the boss made one
point very clear: he demanded Nick to only report
facts; no insecure estimations! A few days later the
comment Nick had originally added to the ight
data had disappeared; and the distance itself had
decreased to 60 percent of the distance Nick had
calculated earlier.
What has happened, to summarise, is that Nick
was tasked to report short-haul ight data. This
data did not exist. So he contrived a work around,
employing mathematical routines to retrieve the
data he was to report. This work around contriv-
ance drew on domestic flights’ cost data and
Nick used his calculation’s output as input to the
short-haul ight reporting form. Yet, later, Nick
realised that his mathematical ‘trick’ for recovering
distances from the domestic ight data would not
work well because the cost gures included other
costs that go along with sta taking ights—like
buying lunch during the journey! The data was
dirty! Eventually, Nick’s subsidiary had reported
a lower gure. I was not there to observe how
precisely this has been derived but I suppose that
Nick withdrew the ‘non-flight’ cost items from
the total cost fact of the domestic ights sum
(data cleaning). And I know that Nick’s subsidiary
did not posses distance data. Thus I infer he was
otherwise going through the same series of math-
ematical assumptions and calculations. Closing
o, as instructed he did neither draw attention
to this ‘internal adjustment’ nor the assumptions
in the short-haul ight reporting form. For the
purposes of this paper, I end my narration here—
though of course the story continues, elsewhere.
It is this episode in the ‘doing of this number’ that
serves the purpose of comparing STS number
Lippert
analytics. And, thus, I turn now to analysing this
episode.
Qualculation
This section re-presents the qualculation
approach, deploys it to re-narrate numbers, math-
ematical forms and a calculation and, at the end,
draws out what I discern from this deployment
about the qualculation approach in practice. I
argue that the qualculation approach lends itself
to foregrounding how a calculation achieves a
form that eects connection, in this case securing
quantitative calculability despite mathematical
inconsistencies.
Borrowing the notion qualculation from Frank
Cochoy,6 Callon and Law (2005: 718, 722) argue
for dismantling the dichotomy between the calcu-
lative and the noncalculative, instead positing
both as mutually constitutive: the very distinc-
tion dissolves when we consider a boundary as
achieving both, one side and its Other. Positively
speaking, they use the notion qualculation to
suggest that calculation and judgment are inter-
woven. This interwoven character comes to the
foreground in their thinking of calculation as a
‘three-stage process’. This process can be read and
deployed as a robust instrument, as evidenced in
this special issue by Gorur (2018), Holtrop (2018)
and Neyland (2018). In this section I primarily
focus on this qualculation process as an analytic
instrument and deploy it, subsequently analysing
what the instrument foregrounds.
First, the relevant entities are sorted out, detached,
and displayed within a single space. Note that
the space may come in a wide variety of forms
or shapes: a sheet of paper, a spreadsheet, a
supermarket shelf, or a court of law—all of
these and many more are possibilities. Second,
those entities are manipulated and transformed.
Relations are created between them, again in a
range of forms and shapes: movements up and
down lines; from one place to another; scrolling;
pushing a trolley; summing up the evidence. And,
third, a result is extracted. A new entity is produced.
A ranking, a sum, a decision. A judgment. A
calculation. And this new entity corresponds
precisely to—is nothing other than—the relations
and manipulations that have been performed
along the way. (Callon and Law, 2005: 719)
60
My partial reading of Callon and Law elabo-
rates this three-stage process. Core to the rst
stage is the existence of entities that are disen-
tangled from other relations, rearranged and by
that ordered to t a space. In that respect, the
rst stage needs to be considered as performing
a relational and categorical shift: the entities’
connections are severed and they come to t into
the boxes of specic sorts. Within this space, in
the second stage, these entities are rearranged by
positioning them into new relationships between
each other. The authors address these relational
changes as manipulations and transformations
of the entities themselves. In the nal stage, out
of these rearranged entities, a statement is drawn
(‘the result’). They plausibilise their generalisation
by referring to several versions of such spaces and
transformations: For the supermarket and the
trolley, consider Lave (1988) and Cochoy (2008),
for the court of law Latour (2009) and for sheets of
paper and spreadsheets Lippert (2015).
Callon and Law (2005) specify their model in
several ways. I identify two larger points. First, they
clarify that the entities, ‘objects’, are manipulated
‘within a single spatiotemporal frame’ (Callon and
Law, 2005: 719). True to post-ANT considerations,
they suggest that the entities do not preexist their
framing. The framing shapes the object; making
entities t the box, the order, constitutes new
entities. In short, with Mol (2002), the framing
enacts its objects. And framing comes with
overows, all that which does not t in (Callon
1998). Qualculation as enacting new entities
means also that the practice of qualculating is
both, material and semiotic. For that they point to,
inter alia, ‘paper and pencil; the benches in a court
of law; a system for tallying arrivals and depar-
tures’ (Callon and Law, 2005: 719). Each of these
frames and framings comes with specic spatiality
and temporality; their shapes and topologies are
potentially indenite. Enacting any particular form
takes time, is work, is an achievement. The eort
consists of disentangling entities from others,
removing and adding relations.
Second, I propose, Callon and Law (2005) model
qualculation as intentional action—between the
lines. In a summarising sentence, they suggest
that qualculations “are all about arraying and
manipulating entities in a space in order to achieve
an outcome, a conclusion” (Callon and Law, 2005:
719, emphasis added). Thus, qualculations come
with a purpose, i.e. a telos; they are practices for
the purpose of producing their result. When
the two authors turn to addressing the modes
and practices of achieving non-qualculability,7
they engage with Quaker worship and agapè as
“strateg[ies] of calculative rarefaction” (Callon and
Law, 2005: 723). Common to both are intentional
practices of being passionate. “The Quakers have
a set of material and discursive practices for disen-
tangling from qualculability. For losing them-
selves in the passionate” (Callon and Law, 2005:
722, emphasis added). The disentanglement is
purposefully produced in material and discursive
practices. This analysis of resisting qualculability
resonates, for the authors, with Power’s (1999)
take on accountability in ‘audit society’. Making
accountability is work, and so is making unac-
countability (Callon and Law 2005, 725; see also
Gorur, 2018, in this special issue). Achieving unac-
countability is tough. I read their model of (non)
qualculation, then, as purposeful action, in which
actors or strategies are directed towards results,
using resources to achieve these results. Whilst
their analysis is not limiting qualculation to inten-
tional action, all their cases involve intentional
actors, trying to achieve particular (un)account-
abilities and (non)qualculabilities.
To put the instrument of qualculation into
action, I distil from the prior discussion the
following questions: by which configuration
of material and discursive practices do actors
achieve what kind of simultaneously qualcula-
tive and non-qualculative space? How has Nick
actually managed to produce this agencement
which we tend to refer to as calculation? What
do we grasp by analysing this as a mathematical
operation? Conceptualising this set of relations,
this movement of signs, as a mathematical oce
operation suggests that all the entities involved in
it are unproblematic; we grasp it as a rule-following
method, an implementation of the rules of multi-
plication and division. This understanding misses
the practical point of the operation: it was not
about solving a mathematical problem but about
bringing into reality an entity that before had not
existed. Thus, Nick’s practice had a transformative
character: it altered the form of how these entities
existed; he assembled them in a shared plane in
Science & Technology Studies 31(4)
61
which he conducted the operation. This transfor-
mative movement deserves spelling out.
In what follow, I map the three stages by Callon
and Law onto my narration of Nick’s calculation
and numbers. According to qualculation’s first
stage, Nick had to initially sort out and detach
some entities that he could work with. The total
cost fact, which he had received, was already of a
sort that he could employ well. This, however, was
not self-evident. In the cases of several other envi-
ronmental key performance indicators, Nick had
not received total cost facts, but had to construct
those.
Yet, whilst Nick was able to employ the total
cost fact, in isolation the fact did not suce. Nick
next created further statements that eectively
reconstructed the total cost fact via a mathemat-
ical form: as the sum of several individual ights.
This reconceptualisation expanded the possibility
for calculability. He could now make assump-
tions about these individual ights—he dened
the average cost and distance travelled per ight.
The postulations depicted in Equation 2 and
Equation 3 mean that Nick judged his assump-
tion of the two averages,
and
, to be su-
ciently equivalent with the real ights costs and
distances (textbook mathematics, in contrast,
would require some form of signier like standard
deviation to specify the degree of equivalence).
Nick’s judgement was relevant to bridge the gap
between the dierent sources of information, the
phone call’s provision of the total costs versus
his own experience of ights. In this moment he
used situated judgement about these relations,
I presume his local knowledge of distances and
ight costs in the subsidiary’s region of operations,
rather than documented traces that might have
established a link between the averages and the
individual ights’ distance/cost facts. These inter-
woven judgements, bridging the gap across the
two dierent kinds of sources, are by no means
self-evident. Politics and economics, in particular
cost-benet analysis, recognise the signicance of
this kind of treatment, calling it commensuration
(see Adorno and Horkheimer, 2006: 13–14; Porter,
1995: Ch. 4; Patterson, 1998): “Commensuration
transforms qualities into quantities, dierence into
magnitude.” (Espeland and Stevens, 1998: 316)
And the accounting database form made clear
what he was working towards: the total distance
travelled, in km, for which he lacked the quanti-
er. Thus, at the outset, here, we can identify four
statements (one given fact, two assumptions and
one searched for result, the partial statement).
He had, thus, disentangled the total cost fact and
the body of ights these costs represented into
four statements and drew all these statements
together. With Callon and Law (2005: 719) we can
think of his practices as sorting out and detaching
these statements from the wide range of data
held by nancial accountants and of the possible
assumptions he could have made. They call this
process qualculation, underlining the involvement
of judgment and qualication with quantication
and calculation. The qualication here consists
precisely in performing these statements and
relations as appropriate rather than others. Not
only could the assumptions have been dierent
(such as specifying the average distance or costs
with other quantiers) but also could have the
statement structure been alternatively congured
(in fact, below, I introduce how Nick later chal-
lenged the structure himself). The selection, thus,
of precisely these statements created and preg-
ured a space in which the subsequent calculation
had to take place.
Now that the relevant entities are enacted and
detached from another, they need to be “displayed
within a single space” (Callon and Law, 2005: 719)
to conclude qualculation’s rst stage; the space of
these four statements needed to be transformed
to perform in two ways: rst, the space needed
to allow for calculation and, second, the calcula-
tion’s results needed to t the material structure
of the company’s environmental database, i.e.
its data entry form (cf. Figure 1). Thus, again, the
accounting form guided Nick in how he worked.
This form required the total distance travelled by
short-haul ights to be represented with specic
qualiers and quantiers: these included, rst, the
quantitative ‘value’ of the ight distance (i.e. the
number) and the ‘unit’ (kilometres), second a ‘value’
and a ‘unit’ of corresponding costs and, optionally,
a qualitative ‘comment’ on this particular data set.
A possible inscription structure that prepares this
list for calculability is to reimagine/rewrite the
statements as triples. The calculation which Nick
eventually performed, thus, corresponded to a
three-fold structured space, depictable as a table
(illustrated by Table 1). This space is marked with
Lippert
62
a boundary of in/exclusion: to be excluded were
the traces of the statements’ sources. The fact that
some statements were assumptions got lost in the
framing—Nick was focused on the numbers.
With this rst stage of organising qualities and
quantities, Nick achieved new entities: once in
the table, ights and costs existed in the shape
of numbers, units and categories. The table itself
framed these shapes in particular ways. The
qualities of framing extend from the design of
the data entry form to Nick’s preparation of data
for that form. Thus, the entities drawn together
by Nick were transformed and changed shape;
the resulting objects did not preexist their
framing. Those qualities that did not t in, are the
overows that Callon (1998) addresses: making
things calculable means framing them and that
necessarily implies that some things do not t the
frame and ow over the frame.8 The boundary-
drawing performs a qualication of how numbers
are present in this space. Nick’s employment of
the framed triples (in Table 1) shows that he is
precisely not just dealing with hypothetical, in an
undeconstructed sense, ‘numbers’ but with inter-
woven qualities, categories and units. The triples
do not prepare some ‘calculation’ (in an undecon-
structed sense) but a much more specic qualcu-
lation.
This selection, positioning and framing allows
for the second stage in the qualculation process
model: to actually informationally treat the four
statements in relation to each other. Nick related
the costs of all ights to the average cost of a
single ight. This means he treated these kinds
of costs as being of an equivalent quality. And he
handled the average distance of a single ight as
qualitatively non-distinct from the sought for total
distance travelled. In both relations, he treated the
two statements related as quantitatively dierent,
rather than qualitatively. Nick achieved quite
simple arithmetic relating—an ongoing relation—
that took the form presented in Equation 6. Stage
two of the qualculation instrument, points us,
thus, to the calculative machinery, the central
component of the equation:
Without structuring triples in this way the
information would have been dierent. In this
mathematical form, the entities of the table are
rearranged so that they appear simultaneously
qualitatively and quantitatively compatible,
thus, calculatively relatable. Now, consider Nick’s
judgement that his structure of treatment was
apt. This is a key qualication, underwriting the
calculative machinery, a second commensurating
move.
Finally, in the third stage of the qualculation
process, the arithmetic practice mathematically
related the three framed triples, shown in the
middle column of Table 1. These three triples
were solved for the one remaining unknown
with Equation 7, producing a result, 365,387 km,
eectively a fourth triple: a) the value/quantier
365,387, b) the unit km and c) the category total
ight distance. This result was, importantly, tech-
nically compatible with the accounting short-haul
ight reporting form’s eld for numeric input, and
its option to select km as a unit, and this is a point
I come back to. To summarise, Nick related the
triples that he heaved into this space in a way that
allowed him to produce a result for the unknown
slot. With this calculation he produced the fact,
the very data which he was to report. Nick, thus
reported through the database environmental
data that he rst had to bring into existence in a
thoroughly qualculative performance.
This story of qualculation nearly gets slightly
messed up when we consider the spreadsheet
that Nick received in the afternoon. Some of its
elements threatened to undermine the calcula-
bility, which Nick had so routinely achieved and
we have so painstakingly adumbrated. Nick made
judgement about these troubling entities of the
spreadsheet. I never did learn what precisely
happened subsequently. I can only report that,
eventually, this Western Asian subsidiary reported
a smaller sum; the total distance crossed by means
of short-haul ights was reduced. Nick eectively
managed to avert the threat to calculability: he
delivered a result to the headquarters. Yet, the
spreadsheet did not detail the distances travelled
by each domestic ight, d1 to dn.
Zooming out, one further calculative-quali-
fying move comes in light. Lingering between the
lines so far, Nick’s task was to ll the form for the
Science & Technology Studies 31(4)
63
indicator short-haul ights, y. Following Callon
and Law (2005: 719) ‘[t]hings have to qualify
before they can enter a process of qualcula-
tion’. Nick’s qualculative practice performed the
domestic ight cost data, x, which he received,
and subsequently employed in his arithmetics, as
qualifying for the short-haul ight travel account.
Nick, practicing this qualculation, could be cer-
tain that his work of slipping and connecting
was organisationally appreciated—contrasting
with Coopmans’ (2018) analysis of the trouble of
workers who have not been managing to solve
a disconnect through clever numbering. Nick
employed his judgement and calculative rou-
tines making x t the form of y, even if this nal
slippage in reference was collateral, a ‘collateral
reality’ (Law, 2012) of inserting the quantier for
the domestic ight data in the form for short-haul
ights.
The mathematical tension here did not concern
Nick. Whilst multiple interpretations are possible,
Nick situationally judged well, that his achieve-
ment of connecting sources to the data form
would not generate organisational tensions but,
rather, comfort (on comfort, see Pentland, 1993).
What do we learn about the instrument of
qualculation? By way of rethinking Nick’s work
as qualculating, we overcome the misleading
dichotomy between calculation and judgement.
In actual practice they overlap. This is no news
to accounting scholars (e.g. Pentland, 1993;
Robson, 1992). The point was not only to demon-
strate a case of qualculation. I am concerned with
analysing the apparent ease of a calculation—of a
class that was not at all exceptional, but was and
is exercised, constantly, ubiquitously. Defamiliar-
ising such a calculation is a hard case.
The qualculation approach is generative in
that Callon and Law’s (2005) take translates the
hard defamiliarisation task into a quite simply
procedure, consisting of the three stages.
These were quite straight forward to apply. This
approach allowed us to identify the entities
employed by Nick and helps us see their satura-
tion with politics: at several moments other quali-
ers and quantiers, other structures and moves
of relating them, could have been opted for. Qual-
culation, then, seemingly oers an instrument for
analytically narrating; we get a well-tellable story
in which even the challenge to calculability even-
tually disappears when the qualculation’s telos is
realised in the reporting of a result to the HQ.
Core to this style of qualculation analysis is
that it generates a story of Nick as intentionally
treating the data in a way to achieve a number
that can be plugged into9 the multinational’s
central environmental database. Nick had started
out with one determinate entity, the total cost
fact, and rapidly conjured up further claims that
turned into certainties in their tabular formation
and were enrolled in the equation form to solve
for his target not-yet-determined number, the
total distance travelled by short-haul flights. I
applied the qualculation analytics and found it
to guide me in narrating of progressively more
determinacy along the stages towards the result
that Nick achieved. Determination, then, charac-
terises both what I analysed and how I analysed it.
Indeterminacy is rst solved, and when new inde-
terminacies cropped up in the form of unwelcome
content of the spreadsheet, these were overcome.
In sum, Callon and Law’s (2005) approach is gener-
ative of a story of a directed chain of enactments
with the clear target of dissolving indeterminacy:
the solute of indeterminacy changes its visibility,
rendered invisible in the fact delivered to the HQ.
Callon and Law’s (2005) qualculation approach
congures a narration that conveys how (non)
qualculability is achieved and secured. The qualcu-
lation instrument is generative of foregrounding
how connections are made, relations established,
in order—intentionally—to effect either qual-
culability or non-qualculability. Callon and Law
are ttingly quite concerned with dierentiating
strategies to achieve these. This instruments’ focus
on strategies to achieve either, qualculability or
non-qualculability, establishes simultaneously a
dichotomy—collateral damage?
The approach does not encourage me to
analyse and attend to the fascinating fastidious-
ness and assiduousness of Nick, his practices of
Lippert
64
making things very clear, reading the spread-
sheet in detail, cleaning up data, indicating how
he got to his fact in a comment and deleting it,
attending to some of the data troubles. Maybe
because these are not central to his practices’
telos, securing qualculability? But they seem to
be important elements in shaping these calcula-
tions and the mode of qualculability. Yet, these
are neither about (non)qualculability nor the
measurable degrees thereof. Whilst the authors,
Callon and Law, surely have capacity to engage
with these elements, their three-stage approach
of qualculation and the strategies for achieving
(non)qualculability do not lend themselves to
open up these elements. In fact, Callon and Law
(2005: 724–725) position qualculation as Other to
the space of (pre)trust, care and agapè.
How then did these elements matter? I suspect
these are about qualities of relations of account-
ability and I am disconcerted about their (missing)
relevance in the qualculation analytics’ study of
the incremental crystallisation of the reported
data on short-haul ights as certain.
Ontologising troubles
Nick did not voice troubles, but my narration does.
Does it matter that Nick oered a comment, like
in the centre section of Figure 1, deleted it and
cleaned up the data? In introducing this section’s
deployment of Verranian analytics, and with
Verran (2001), clearly, yes, it does. It does matter
because the comments’ explication of how Nick
had calculated the result as well as the sorting
out of inappropriate elements, i.e. data cleaning,
involve commitments to, or explications of, what
these data are. So Nick had faced ontological
troubles which he engaged with by deleting the
comment and cleaning data. Verran (2001) would
point to Science and an African Logic, Mr. Ojo and
herself, ontologising troubles in the classroom.
In turning to Verran’s work, I am not renarrating
what the qualculation analytics was able to scruti-
nise. Instead, I deploy her work to attend to how
it comes that the mathematical inconsistency,
troubles, in the work achieved did not shatter
Nick’s qualculation. I argue that Nick ontologically
accomplished a calculation that achieved a cong-
uration of certainties, in plural(!), that suciently
cohered, allowing the result to stick. Cohering
elements contribute to amassing certainty,
despite mathematical inconsistency. This section
brings forward, and then alter-ontologises, the
troubles in Nick’s work. Ontologising, then, is
the instrument I draw from Verran. To continue,
I initially introduce Verran’s take on ontology as
practice and subsequently deploy it to analyse a
subset of relations of the number-as-network.10 I
close this section with a reection about the way
Verranian (re)ontologising foregrounds elements
and relations in enumerated entities.
Practicing a form of juxtapositioning that does
not privilege Western or Scientific standards,
Verran oers a form of empirical philosophy that
draws on engagement with both indigenous
community as well as western science and techno-
science. To start in the middle, consider her book’s
end in which she calls for “telling of the rituals
and the coparticipants, human and nonhuman,
living and nonliving, in microworlds, as reliable
ways of managing complexity” (Verran, 2001:
238). In order to narrate and ontologise Nick’s, or
my, troubles, we need a sense of her notions of
microworlds and ritual.
I consider counting objects like books a
repeated routine performance. Verran (2001) calls
such performances microworlds, or micro-worlds
(Verran, 2002), based on Rouse’s (1987) work on
laboratories. She species microworlds as mate-
rially and semiotically configured time-places
featuring routinising practices of interrogation,
naming and tracking, eecting the boundaries
of stu, rather than passively reading preexisting
entities. In such a microworld, the exclusion of
irrelevant complexity is similarly routine. Microw-
orlds produce realness. She highlights the reoc-
curring character of microworlds, repeatedness,
routine and ritual, with her concept of clotting.
“An object clots when the repetitions and routines
of its generating microworld become a ritual.”
(Verran, 2001: 162) The repetitions and re-perfor-
mances in ritual-like ways pre-figure and pre-
script and, thus, stabilise their objects, gradually
and relationally coagulating the objects and its
shape. Normally, the case of counting routines is
safely ignored, leaving the material and semiotic
processes of clotting specific numbers often
invisible (Verran, 2007a: 37–38).
Science & Technology Studies 31(4)
65
She develops these considerations in Science
and an African Logic and proposes that in the very
practices of counting an object not only is the
number performed but the object too. Following
her approach, the pure matter of, say, books when
we count them is not antecedent to the action but
is brought into reality in that very performance.
Face your distributed bookshelves; any count is an
outcome of relational practice involving nonliving
participants, e.g. paper and digital entities, living
like ourselves, counting some entities as books, a
multi-volume work as 1 book, excluding others.
Being certain of the count emerges within doing
counting, that is in the acting within a relationally
congured situation. The bookshelves in my study
room surely can be assessed as complex; but more
importantly, the narration of the number at the
core of this paper clearly shows the simultaneous
simplicity and complexity within Nick’s qualcula-
tion.
More importantly than the degree of
complexity—numbers, numbering and how
certainty is embedded within them appears, in
the Verranian approach, as an eect of particular
situated relating. Drawing on her work amongst
Yoruba children learning calculating, she
proposes: “Certainty of numbers is an outcome
of the routines by which they are constituted in
collective acting” (Verran, 1999: 150).
Her approach does not limit itself to numbers,
but explores more widely what, and how, things
are. This she calls ontological investigation (Verran,
1998) or empirical ontology (Verran, 2005). Core
to this approach is to “refuse any and all a priori
separations” in relational practices, characterising
Verran’s (2005: 42, her emphases) take as monist,
whilst narrating things, society and nature as
eected in those practices.
Core to the instrument of ontologising is the
analytical division of labour between two narra-
tions:
• Ontic narrations refer to ‘the level of entities’
existence or being’ (Verran, 2007a: 34), i.e.
realness, where entities are to be understood
as actor-network s, that are accomplished,
performed in material-semiotic practices that
include our practices’ (not necessarily explicit)
commitments to these entities being there.11
• Ontologic narrations are characterised by
explicitly explaining, studying or theorising
what is and the metaphysical commitments
to what is; this ontology is materially-semioti-
cally performed and, thus, may shape reality-
making.12 Ontologising, however, does not
necessarily determine its object, the reality
being enacted.
To d epl oy t his in str um ent , I na rr ate t wo dis con -
certments that the qualculation instrument did
not easily allow me to story. Firstly, I turn to clean-
ing data, and, secondly, to the comment.
Lunch! Whilst the qualculation approach was
able to register that data cleaning took place, I
sense a richness in the moment of Nick receiving
the spreadsheet and recognising the range of
non-flights inscribed into the domestic flights
account. Nick calling out ‘lunch!’ only made sense
in relation to the spreadsheet that included a line,
implying that some lunch cost had been part of
the accumulated ight costs. In this evocation,
then, Nick indexes the spreadsheet’s lunch line.
This specic line troubled Nick. Lunch was out of
place. This implies that Nick was committed to the
sort of things that would be correctly listed in the
spreadsheet. He was concerned about the wrong
entity being in the list. This means, Nick was able
to draw a border between dierent categories,
marking some as not tting with the category of
ights. Lunch was easy. Taxi costs more dicult,
because they were clearly part of the overarching
key performance indicator ‘travel’, of which ‘short-
haul ights’ have been part. Evidently Nick was
exercising a logic of what ights are. Lunches are
not ights.
With Verran we can call Nick’s practice of
storying lunch as not being a member of the
category ight as doing ontology. Nick ontolo-
gised ights. Lunch in the ight account troubled
his ontology. Interestingly, before Nick got the
spreadsheet, he was not troubled by the lunch
line yet. That is because he was enacting the
ights dierently then, with a dierent ontology,
an untroubled one. The ight data, before the
spreadsheet, were practiced as pure ights. Flight
data after the spreadsheet was impure. His ontolo-
gising had shifted.
Nick must have noted then that the ight data
body he was working with was dierent from what
Lippert
66
he felt committed to. He had been doing a reality
all along, ritually, over the many steps I narrated
above, an ontic practice, that was committed
to including the original domestic ights’ total
costs in deriving the total distance travelled by
short-haul ights. So, whilst his practices were
committed to enacting short-haul ights all along,
after reading the spreadsheet, he nuanced his
allegiance, his commitment.
Cleaning data, eventually eecting a smaller
total distance fact, was enacting then a dierent
ontology, to which his practice was committed,
a smaller x inserted into the form of short-haul
ights. In this ontology lunches are not ights, and
routinely x equals y, as an ontic eect, domestic
ight data remains slipped into the account for
short-haul ights.
In the microworld of Nick ‘gathering’ data and
entering that into the central database’s forms,
numbers were part of clotting several data sets,
just like the short-haul ights. These clots have
been stabilised. That we assess the short-haul
ight fact as being erroneous does not (seem to)
aect that this subsidiary’s 2008 data has been
maintained and employed by the corporation for
many years. To my knowledge, the multi-authored,
with Nick as a core author, clot continues to be
enacted as part of the historic, this subsidiary’s
baseline, data of environmental impacts.
Now, on to the second disconcertment. When
Nick had rst entered the result of his calculation I
had asked him to enter a comment on his calcula-
tion in the data entry form. He then had described
in the comment eld how he had gotten to the
total distance fact (to illustrate, see the comment
section in the entry form, Figure 1). By oering
this comment he oered a trace of what his fact
meant, eectively telling a story about what his
number was. Simultaneously, this established the
fact as troubled because it was not a straightfor-
ward fact, speaking securely for itself. I suggest
this kind of storying work can be considered an
ontological practice because it explains what the
number of the total distance crossed by means of
short-haul ights consisted of.
In the conversation with Nick’s boss, Nick was
told to only report facts; no insecure estimations.
In tension with this demand, his comment did
point to the two estimations involved in the calcu-
Science & Technology Studies 31(4)
lations, the average distances and costs,
and
, qualifying the total distance fact as a calcu-
lated estimate, not securely signalling factishness.
The explication of trouble got, thus, troubled, and
troublingly the trouble got hidden: a few days
later the comment was deleted. The numbers
without comment showed no trace of their history
anymore, no contingency, no trouble.
What did deleting the comment do to
emissions? A data set that came with a comment
was signalled to the database user at the head-
quarters and prompted them to review that data
set. Trouble! This algorithmic function served
to support the system in achieving account-
ability. It was considered necessary by the system
designers because the company recognised that
sometimes numbers required some explanation;
numbers did not always tell all relevant stories on
their own. Comments, thus, enriched the ontology
of environmental data, by serving as unstructured
metadata. Without comments, those data users
who had no direct contact to the agent-entering-
data had less chance to actually learn about
some of the considerations around the numbers
reported. Yet a dierent form of trouble. Simulta-
neously, no comments also meant that superiors
were less likely getting back to the bookkeeper
to inquire about the data reported. Less of this
trouble, at last. Both effects altered account-
ability—however, in dierent ways. In a Strather-
nian/Harawaynian twist, we could voice: it matters
what troubles trouble troubles.
I understand the information reportable in
comments as a partial account of the modality of
the numbers and units reported in a form. Such
modality was co-constitutive of the numbers.
Bookkeepers were responsible for the data
they entered. For the bookkeeper, deleting the
comment also implied that they alone carried
the possibility for responding to questions on
data. Providing a comment extended respon-
sibility materially to the database. The data set
could respond directly to questions. A response-
able data set was also a risk, however, because
it could answer to questions without the book-
keepers’ control. Deleting a comment made the
data less accountable and reciprocally reduced
the risk of having taken the work situation out
of the worker’s control. No risk that the data set
67
would speak against the bookkeeper, no risk that
the comment would raise undesired concerns or
questions about the number’s straightforward
story.
This shows that oering the comment quali-
tatively enriched ontologising the commented
data and the reality of ight distance; and second,
that opening up the ontological shape of what
the data supposedly represents emerges as a risk.
Without comment, ontologising for actors (other
than Nick) was much more speculative—deni-
tively dierently grounded, if not less grounded—
for they only encountered a straightforward
fact, no detour via uniquely authored metadata,
con-text. No signier of trouble.
This seemingly straightforward fact was
enrolable with less friction in a range of ontolo-
gies. Precisely because the numbers were not
accompanied by explicit stories, the numbers lost
their ability to resist arbitrary stories that would
refer to the fact. Whilst the straightforward fact
appears intuitively more certain, it emerges in my
analysis as rather indeterminising.
Verran’s instrument of ontologising and
attending to ontological practice helps fore-
grounding the range of potential stories about
what is the case, the range of storying reality,
how troubles trouble. This analysis in terms of
ontologising troubles indexes a complicated
space of responsibilities and accountabilities. I
propose that Nick’s data submission mattered in
two key ways. (1) Nick seemed to care for giving a
good (enough) account of the ights. For that he
edited the data after having received the spread-
sheet that had included, in his reading, non-ight
costs, indexing his data sources ‘better’, cleaning
up data. This qualication work involved onto-
logical considerations by Nick about what was
not to count as short-haul ight costs, such as
lunch costs. However, his explicit ontologising did
not range into reasoning how domestic ights
mapped onto the company’s denition of short-
haul ights. Thus, his routine calculation approach
to translating domestic into short-haul flights
remained stable. Ontics does not determine
ontology. (2) Further, he wanted to complete
the data submission without problems—and
his boss had troubled the friction caused by
qualifying data as estimated. Correspondingly,
Lippert
deleting modalities became a solution. These two
ways were not overly coherently aligned to one
another. None of the actants involved dominated
the relations around the data submission with
a singular strategy. Much rather, this work space
needs to be understood as ordering in multiple
ways—situated doings that were both materi-
ally-semiotically ordered and in which actants
enacted a non-deterministic order of the ight
fact. Precisely because the comment got deleted
the resulting data was interpretable in more ways.
The matter of the reported total short-haul
ight distance of Nick’s subsidiary, thus, was not
precise and stable. By way of staging the ight
fact as simple, his ‘simple’ practice eected ight-
matter with less stable meanings and as a less
xed reference point compared to to upholding
his indexing comment. Indeterminacy multiplies.
The simplicity allowed more readings of and,
thus, workings with the numbers. Removing the
grounding of ontologies multiplies the space of
narrative possibilities. Thus, the configuration
of bookkeepers, the central database and head-
quarter sta achieved a world of ight matter
that was loose, connectable to all kinds of other
entities, and not explicitly referring to the multiple
material-semiotic doings in which practices and
entities were ordered and performing order.
I turn now to analysing this narration of the
ontological signicance of providing and deleting
the comment as well as of cleaning up data. It has
deployed a Verranian attention to actors (re)doing
and not-doing ontology, generating a space of
multiple stories of how the comment-in-relation
mattered. This instrument of re- and alter-ontolo-
gising foregrounds relations and congurations of
accountabilities, certainties and indeterminacies.
Deploying Verran’s ontology in this way
performs ontologising ethnomethodologically.
Using ontology involves a form of accounting.
And these accounts can come with a range of
temporal orientations. An ontological enactment
may attempt to pregure some practices; and in
the very moment of ontic practice (e.g. Nick doing
ight data, rst-time-reading the spreadsheet),
ontological reection about these practices may
take place (lunches are not ights); and doing
ontology may as well relate back in time to oer
a retrospective retelling about reality that, of
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Science & Technology Studies 31(4)
course, joins in shaping the present. With respect
to versions of the past, I am reminded of the retro-
spective telling of plans, that always diers from
situated actions, simultaneously oering a new
account of reality-making joining in semiotic
recongurations (Suchman, 2007). The realness
eected in some material-semiotic practice may
be recongured in material change and semiotic
shifts over time—as in when a number sign that
was accomplished to signify a specic reality is
read dierently, through another ontology. The
ability for retrospective retelling and rereading
allows the Verranian instrument of ontologising to
account for members’ storying of realness where
members’ own stories may gloss over, sidetrack
from or even highlight relations between signs—
such as categories, units, number words and
rules—or logics of how these should relate.
Ontologies of reality multiply because it is not
an antecedent reality that determines how the
reality is theorised, but ontologies are enacted in
time-places, and tomorrow’s ontology might be
as dierent from the current as the ontology of a
dierently positioned actant in the present.
Following this consideration of troubles and
multiplicity, I suggest that we can consider the
use of this analytics as yielding several political
troubles: in this analysis of narrating a number-
as-network, I opened up the politics of undoing
modalities of claims and the trickiness of what
it means to get the job done. Contrasting the
troubles with the punctualising (Law, 1992) char-
acteristics of technologies of, say, policy recom-
mendation bullet points for evidence-based
governance, Verran’s analytics is generative of
stories of so rich realness that explodes punctu-
alisation attempts, rendering her analytics rather
compatible with anti-hierarchical politics, such
as workplace resistance in the midst of global
environmental accounting. Spelling out an ever-
dynamic partial and situated realness-in-the-
making is unlikely to travel well in the universe of
evidence discourse—hegemonic policy circles.
My Verranian-inected account of a number’s
metadata contrasts with the ease in which Nick’s
numbers could circulate within the company
and plug into the multinational’s global carbon
accounting. Deleting the comment altered qual-
culability not in degrees but in kind, rendering
the carbon accounting machinery more smooth,
removing merely a tiny obstacle to it running well.
This Western Asian subsidiary’s short-haul ight
distance number became part of not-so-earthly
machines of references in emission trading. Nick’s
practice did not only eect collateral realness,
but collateral certainty, too. Above we had iden-
tied that Nick was positioned to be certain that
his slippery commensuration of domestic ights
with short-haul ights would be organisationally
appreciated. By attending to the space of storying
around the comment the Verranian analytics fore-
grounds how certainty that the reported fact is
straightforward is conjured up.
The corporation, too, was positioned through
the enactment of the total short-haul flight
distance to be certain that these short-haul
ights existed. Whilst conjuring up out of costs
a quantity for short-haul ights, these ights are
enacted along the way as much as the certainty
that they exist at least in so far that they do not
resist their enactment. And deleting the comment
helped reduce resistance. For the user, whether
in the corporation’s HQ, its civil society or regula-
tory counterparts, the situation appears straight-
forward: “I read short-haul ights, I include them
in my assessment, therefore I can be certain they
exist.” Certainly, we are encountering here the
multiplicity of certainty.
Conclusion
Narrating a number opens up possibilities for
analysis that reveals worlds in the process of being
made. This paper presented ‘narrating a number’
as a method of empirical philosophy. Narrating a
number is generative of a narration that includes
description and inferences. Here, the descrip-
tion is ethnographically derived. Description and
inferences together ontologise the number. This
method allows investigating the number-as-net-
work. Narrating a number, then, shows what is
inside the number, what it is made up of, how it
coheres and relates.
This paper conducted a two-fold exercise.
First, it narrated and analytically renarrated a
number, and its constituting calculative practices,
explicating worlds being made—the case here
shaping the world presumed in environmental
69
Lippert
economics—emissions. Assembling emissions
secures the demand basic to carbon markets.
Second, it analysed how two analytical approaches
within the eld of actor-network theory—Verran’s
(2001) take on ontology and Callon and Law’s
(2005) three-stage process of qualculation—dier,
complement or work against each other.
With their shared commitment to reality
emerging in material-semiotic relating, both
analytics are well positioned to agree with, or
complement, each other. Comparing them
indicates three sets of results.
First, as analysing numbers and calculations is
discursively positioned in relation to competing
formalist discourse, such as mathematics, it is
relevant to note that both qualculation as much
as Verran’s empirical ontology allow for inconsist-
ency to be part of numbering and calculating.
While in qualculation analytics inconsistency
may be encountered, its mattering is second to
the achievement of (non)qualculability and their
respective securing of a result or the impossi-
bility to draw out results. Verranian ontologising
turns to how reals emerge, encourages attention
to elements and practices, independently of
how coherent they appear, and this may result
in attending to entities and relations which the
qualculation take does not need to generate a
neat qualculation narration. Thus, whilst I nd
the commitment to material-semiotic relating
shaping objects and worlds to be shared by both
analytical approaches, what the approaches invite
attention to is not equivalent.
Second, what these analytics foreground,
is methodologically differently configured. In
narrating a qualculation, I nd myself positioned
to reconstruct a quite linear temporality, preg-
ured by this analytics’ three-stage process. Verran’s
ontologising invites narrating of ongoing relating.
The latter can be quite disorienting, but also gener-
ative in turning to practices’ multiple relations of
accountability, backwards, forwards and sideways
in time. The (non)qualculability attention appears
as a focussing apparatus, singularising concern:
which of either form of qualculability is achieved?
Verranian ontologising, in contrast, appears as
an instrument that guides puzzling, exploring
troubling, maybe well described with Haraway’s
(2016) quest to ‘stay with the trouble’.
This leads to the third point: While narrating a
number through the qualculation analytics, I am
repeatedly provoked (as some of the reviewers,
too) to feel consternated: x = y, this can’t be!
This approach seems to invite a form of external
critique, In contrast, in ontologising troubles, I
identify a form of infracritique, attending to collec-
tive accomplishment, multispecies co-authoring
and wonder. Verran might call this exploring
disconcertment.
I conclude that these two analytics oer useful
instruments, and that both of the analytics’ instru-
ments are not equivalent in that they do not fore-
ground and guide attention equivalently. Thus,
declaring the use of the ANT toolbox to open up
numbers is not suciently specic, for it matters
with which commitments the scholars prepares
and analyses the material.
Venturing into prescriptive number analytics
methodology, I suggest as criteria for narrating
number: The narration needs to take a form such
that a number’s worlding, relating, ontic and onto-
logical commitments can be analysed, as much
as the frictions, gaps or disconnects between
material, epistemic or logical entities or relations
as well as the directedness of calculative processes
or their meandering and swaying in social-mate-
rial space.
Along this narrative analysis, a final point
crystallises—on numbers. Narrating a number
explodes the number, for the number’s inside is
relating in multiple ways to outsides. The inside/
outside dichotomy starts to collapse. Instead
of presuming where the boundary of a number
is, it seems now apt to analyse the boundary-
making of how numbers are made to, or seek to,
be dierent to non-numberly space. We can also
follow how numbers are enacted, singled out, or
qualculative relations. Maybe provoked by qualcu-
lation’s thesis that quantication and judgement
are interwoven, and sensitised by Verranian
attending to ongoing relations by heterogeneous
co-participants, number is denaturalised as much
as pushed to the analytic margin: relations of
qualifying need as much as attention as relations
of quantifying. Yet, even more focus needs to be
redirected to the multiple relations of connecting
and disconnecting, relations of account-abili-
ties and response-abilities in networks that are
70
Science & Technology Studies 31(4)
glossed with a shorthand as ‘number’. Such redi-
rection of concern in numbers studies might be
called ‘after numbers’, for here we study what is
within the number-as-network as much as, in a
dierent topology, behind number signs.
Acknowledgements
This paper would not have been possible without
the conversations with Helen Verran for which I am
deeply thankful. I am grateful to Lucy Suchman
and Christoph Lau for motivating me to pursue
the underlying project of this paper and in par-
ticular to Niklas Hartmann for scrutinising Helen
Verran’s thought with me. An early version of the
argument, but with the core material, was first
presented at the Asia-Pacic Science, Technology
& Society Network Conference, in July 2013, and
later discussed as part of a joint work-in-progress
seminar with Catelijne Coopmans at Tembusu
College, National University of Singapore, in Octo-
ber 2013. I thank Catelijne Coopmans for thinking
together, working through the twinship of our
contributions to this SI. I also thank Casper Bruun
Jensen, John Law, Adrian Mackenzie, Franz Krause,
Lydia Stiebitz and Cornelius Lippert for their gen-
erous critique and encouragement as well as to
the participants of STS seminars at Lancaster Uni-
versity, in June 2014, and at the Technologies in
Practice Group (IT University of Copenhagen), in
October 2016, for their generative comments on
earlier drafts of this paper. Three reviewers and
Estrid Sørensen oered very helpful critiques that
heavily informed the revisions of the paper.
71
Lippert
References
Adorno TW and Horkheimer M (2006) Dialektik der Aufklärung: Philosophische Fragmente. 16th ed. Frankfurt
am Main: Fischer.
Asdal K (2008) Enacting things through numbers: Taking nature into account/ing. Geoforum 39(1): 123–132.
Benjamin W (2006) The Storyteller: Reections on the Works of Nikolai Leskov. In: Hale DJ (ed) The novel: an
anthology of criticism and theory, 1900-2000. Malden: Blackwell Publishing, pp. 361–378.
Blok A, Nakazora M and Winthereik BR (2016) Infrastructing Environments. Sciene as Culture 25(1): 1–22.
Callon M (1986) Some elements of a sociology of translation: domestication of the scallops and the
shermen of St Brieuc Bay. In: Law J (ed) Power, Action, and Belief: A New Sociology of Knowledge? London:
Routledge & Kegan Paul, pp.196–223.
Callon M (1998) An essay on framing and overowing: economic externalities revisited by sociology. In:
Callon M (ed) The Laws of the Markets. Oxford, Malden: Blackwell Publishers/The Sociological Review, pp.
244–269.
Callon M (2009) Civilizing markets: Carbon trading between in vitro and in vivo experiments. Accounting,
Organizations and Society, 34: 535–548.
Callon M and Law J (2005) On qualculation, agency, and otherness. Environment and Planning D: Society and
Space 23(5): 717–733.
Callon M and Muniesa F (2005) Peripheral Vision: Economic Markets as Calculative Collective Devices. Organ-
ization Studies, 26(8): 1229–1250.
Cochoy F (2008) Calculation, qualculation, calqulation: shopping cart arithmetic, equipped cognition and
the clustered consumer. Marketing Theory 8(1): 15–44.
Coopmans C (2018) Respect for Numbers: Lively Forms and Accountable Engaging in Multiple Registers of
STS. Science & Technology Studies 31(4): 109-126.
Desrosières A (2002) The politics of large numbers: A history of statistical reasoning. Cambridge, MA and
London: Harvard University Press.
Edwards PN (2010) A Vast Machine: Computer Models, Climate Data, and the Politics of Global Warming.
Cambridge, MA and London: The MIT Press.
Ehrenstein V and Muniesa F (2013) The Conditional Sink: Counterfactual Display in the Valuation of a Carbon
Osetting Reforestation Project. Valuation Studies 1(2): 161–188.
Elichirigoity F (1999) Planet management: Limits to growth, computer simulation, and the emergence of global
spaces. Evanston: Northwestern University Press.
Ellis R, Pacha M and Waterton C (2007) Assembling Nature: The Social and Political Lives of Biodiversity
Software. Lancaster University, UK. Brochure. Available at: http://eprints.lancs.ac.uk/33750/1/FINAL._
LANCS_COMPUTER_%284732%29_%285%29.pdf (accessed 22.10.2018).
Espeland WN and Stevens ML (1998) Commensuration as a Social Process. Annual Review of Sociology 24:
313–3 43.
Fortun K (2004) From Bhopal to the informating of environmentalism: Risk communication in historical
perspective. Osiris: 283–296.
Fourcade (2011) Price and Prejudice: On Economics, and the Enchantment/Disenchantment of Nature. In:
Beckert J and Aspers P (eds) The Worth of Goods: Valuation and Pricing in the Economy. Oxford: Oxford
University Press, pp. 41–62.
Gabrys J (2016) Program Earth: Environmental Sensing Technology and the Making of a Computational Planet.
Minneapolis: University of Minnesota Press.
72
Science & Technology Studies 31(4)
Gorur R (2018) Escaping Numbers? Intimate Accounting, Informed Publics and the Uncertain Assemblages
of Authority and Non-Authority. Science & Technology Studies 31(4): 89-108.
Hacking I (1990) The Taming of Chance. Ideas in Context. Cambridge: Cambridge University Press.
Haraway DJ (2016) Staying with the Trouble: Making Kin in the Chthulucene. Durham: Duke University Press.
Holtrop T (2018) 6.15%: Taking Numbers at Interface Value. Science & Technology Studies 31(4): 75-88.
Kenney M (2015) Counting, accounting, and accountability: Helen Verran’s relational empiricism. Social
Studies of Science, 45(5): 749–771
Knorr Cetina K (2002) Wissenskulturen: Ein Vergleich naturwissenschaftlicher Wissensformen. Frankfurt am
Main: Suhrkamp.
Latour B (1987). Science in Action: How to Follow Scientists and Engineers Through Society. Cambridge: Harvard
University Press.
Latour B (1996) On actor-network theory: a few clarications. Soziale Welt: 369–381.
Latour B (1999) On recalling ANT. In: Law J and Hassard J (eds) Actor Network Theory and after. The Socio-
logical Review. Oxford, Malden: Blackwell, pp. 15–25.
Latour B (2005) Reassembling the social: An introduction to actor-network-theory. Oxford: Oxford University
Press.
Latour B (2009) The making of law: an ethnography of the Conseil d’État. Cambridge: Polity.
Latour B and Woolgar S (1986). Laboratory life: The construction of scientic facts. Princeton, New Jersey:
Princeton University Press.
Lave J (1988) Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge: Cambridge
University Press.
Law J (1992) Notes on the Theory of the Actor-Network: Ordering, Strategy, an Heterogeneity. Systems
Practice 5(4): 379–393.
Law J (2009) Actor Network Theory and Material Semiotics. In: Turner BS (ed) The New Blackwell Companion
to Social Theory. Chichester: Blackwell, pp. 141–158.
Law J (2012) Collateral realities. In Baert P and Rubio FD (eds) The Politics of Knowledge. London and New
York: Routledge, pp. 156–178.
Lippert I (2011) Extended Carbon Cognition as a Machine. Computational Culture (1). Available at: http://
computationalculture.net/article/extended-carbon-cognition (accessed 4.11.2018).
Lippert I (2012) Carbon Dioxide. In: Zimring CA and Rathje WL (eds) Encyclopedia of Consumption and Waste:
The Social Science of Garbage. Los Angeles: Sage Publications, pp.105–118.
Lippert I (2013) Enacting Environments: An Ethnography of the Digitalisation and Naturalisation of Emissions.
PhD thesis, Augsburg University, Philosophisch-Sozialwissenschaftliche Fakultät. Available at: https://nbn-
resolving.org/urn:nbn:de:bvb:384-opus4-21997 (accessed 4.11.2018).
Lippert I (2014) Studying Recongurations of Discourse: Tracing the Stability and Materiality of ‘Sustain-
ability/Carbon’. Journal for Discourse Studies — Zeitschrift für Diskursforschung 2(1): 32–54.
Lippert I (2015) Environment as Datascape: Enacting Emission Realities in Corporate Carbon Accounting.
Geoforum (66): 126–135.
Lippert I (2016) Failing the market, failing deliberative democracy: How scaling up corporate carbon
reporting proliferates information asymmetries. Big Data & Society (July–December).
Lippert I, Krause F and Hartmann NK (2015) Environmental Management as Situated Practice. Geoforum
(66): 107–114.
73
Lippert
Lippert I and Verran H (2018) After Numbers? Innovations in Science and Technology Studies’ Analytics of
Numbers and Numbering. Science & Technology Studies 31(4): 2–12.
Lohmann L (2009) Toward a dierent debate in environmental accounting: The cases of carbon and cost-
benet. Accounting, Organizations and Society 34 (April–May): 499–534.
Lovell H and MacKenzie D (2011) Accounting for Carbon: The Role of Accounting Professional Organisations
in Governing Climate Change. Antipode 43(3): 704–730.
MacKenzie D (1990) Inventing accuracy: A historical sociology of nuclear missile guidance systems. Cambridge,
MA: MIT Press.
MacKenzie D (2009a) Making things the same: Gases, emission rights and the politics of carbon markets.
Accounting, Organizations and Society 34 (April–May): 440–455.
MacKenzie D (2009b) Material Markets: How Economic Agents are Constructed. Oxford: Oxford University
Press.
Millerand F and Bowker GC (2009) Metadata Standards: Trajectories and Enactment in the Life of an
Ontology. In: Lampland M and Star SL (eds) Standards and their stories: How quantifying, classifying, and
formalizing practices shape everyday life, Ithaca: Cornell University Press, pp. 149–167.
Mol A (2002) The Body Multiple: Ontology in Medical Practice. Durham and London: Duke University Press.
Neyland D (2018) Something and Nothing: On Algorithmic Deletion, Accountability and Value. Science &
Technology Studies 31(4): 13-29.
Patterson M (1998) Commensuration and theories of value in ecological economics. Ecological Economics
25(1): 105–125.
Pentland BT (1993) Getting comfortable with the numbers: auditing and the micro-production of macro-
order. Accounting, Organizations and Society 18(7-8): 605–620.
Porter TM (1995) Trust in Numbers: The Pursuit of Objectivity in Science and Public Life. Princeton, New Jersey:
Princeton University Press.
Power M (1999) The Audit Society: Rituals of Verication. Oxford: Oxford University Press.
Robson K (1992) Accounting numbers as “inscription”: Action at a distance and the development of
accounting. Accounting, Organizations and Society 17(7): 685–708.
Rouse J (1987) Knowledge and power: Toward a political philosophy of science. Ithaca, NY: Cornell University
Press.
Strathern M (2000) The Tyranny of Transparency. British Educational Research Journal 26(3): 309–321.
Strathern M (2005) Externalities in comparative guise. Chap. 3 In: Barry A and Slater D (eds) The technological
economy. London and New York: Taylor & Francis, pp. 66–83.
Suchman L (2007) Human-machine Recongurations: Plans and Situated Action. 2nd ed. New York: Cambridge
University Press.
Ureta S (2017) Baselining pollution: producing ‘natural soil’ for an environmental risk assessment exercise in
Chile. Journal of Environmental Policy & Planning 20(3): 342–355.
Verran H (1998) Re-Imagining land ownership in Australia. Postcoloniocal Studies 1(2): 237–54.
Verran H (1999) Staying true to the laughter in Nigerian classrooms. In: Law J and Hassard J (eds) Actor
Network Theory and after. The Sociological Review. Oxford, Malden: Blackwell, pp. 136–155.
Verran H (2001) Science and an African Logic. Chicago and London: University of Chicago Press.
Verran H (2002) A Postcolonial Moment in Science Studies: Alternative Firing Regimes of Environmental
Scientists and Aboriginal Landowners. Social Studies of Science 32: 729–762.
74
Science & Technology Studies 31(4)
Verran H (2005) On Seeing the Generative Possibilities of Dalit neo-Buddhist Thought. Social epistemology
19(1): 33–48.
Verran H (2007a) Metaphysics and learning. Learning Inquiry 1(1): 31–39.
Verran H (2007b) The educational value of explicit non-coherence. In: Kritt DW and Winegar LT (eds)
Education and technology: Critical perspectives, possible future. Lanham, Maryland: Lexington Book, pp.
101–124.
Verran H (2009) Natural Resource Management’s ‘Nature’ and Its Politics. Communication, Politics & Culture
42(1): 3–18.
Verran H and Christie M (2007) Using/designing digital technologies of representation in aboriginal
Australian knowledge practices. Human Technology 3(2): 214–227.
Vesty G, Telgenkamp A and Rosce P (2015) Creating Numbers: Carbon and Capital Investment. Accounting,
Auditing & Accountability Journal 28(3): 302–324.
Waterton C (2002) From Field to Fantasy: Classifying Nature, Constructing Europe. Social Studies of Science
32(2): 177–204.
Winthereik BR and Verran H (2012). Ethnographic Stories as Generalizations that Intervene. Science Studies
25(1): 37–51.
Notes
1 Asdal’s (2008) work, too, is relevant for ANT takes to open up numbers. However, in this paper, I want to
focus on ethnographic, rather than historiographic, approaches.
2 The narration that I pursue here is not shaped to reconstruct a case of carbon management accounting.
I do present such a case, explore it in the political and economic context, including relationships to
stakeholders and standardisers—e.g., GRI reporting demands, the WBCSD, a global nature conservation
NGO—elsewhere (see Lippert 2013, 2015, 2016).
3 Detailed methodological outlines of the study and its generalisations are available (Lippert 2014).
4 On the relations between the concepts of carbon, CO2 , and CO2e, see Lippert (2012).
5 The conversion factors dier because in short-haul ights the emissions resulting from take-o and
airport infrastructure relative to the emissions by a plane ying in ‘parallel’ to earth’s surface is larger
than in long-haul ights (326g versus 180g per kilometre) (see Lippert 2013: 101).
6 Cochoy introduced the notion in 2002, see Cochoy (2008).
7 Gorur’s (2018) contribution to this issue further nuances and enriches Callon and Law’s (2005) take on
non-qualculability.
8 Economists refer to this move as externalisation. More specically, however, I identify a form of internal
externality: the project of internalising environmental consumption facts folds into itself the externalisa-
tion of the statuses of these particular environments (cf. Strathern 2005).
9 On plug-ins, see Latour (2005).
10 For a more elaborate re-reading and contextualisation of Verran’s work, consider Kenney’s (2015) contri-
bution.
11 See Verran 1999: n.16; 2001: 116–118; 2005: 42; 2007a: 36.
12 See Verran 1999: n.16; 2001: 118; 2005: 42; 2007a: 34; 2009: 5, 17; Verran and Christie 2007.
