What’s in a number?

“What is this society in which a written, printed, mathematical form has greater credence, in case of doubt, than anything else: common sense, the senses other than vision, political authority, tradition, and even the scriptures?”
-    Latour (1986:23)

So often have I been told when describing achievements in a CV that ‘mere descriptions’ are not enough and that I need to ‘put a number on it’. So often when reporting how well my team played in a football match, have I been asked, well how many goals did they score, or how many corners did they concede. So often when applying to academic institutions have the detailed personal statements depicting my skills and fit been relegated as simply additional information to the much preferred method of selection which is a mark obtained in a test. So often does it boil down to a number. So why is this the case, and as the question by Latour above asks, what is this society in which numbers are valued and trusted so highly above all else? Through a critical examination of three different but related ways of seeing numbers, I argue here that there is much more qualitative ‘stuff’ hidden in numbers than that which is revealed in their use, and it is this clever omission of ‘stuff’ by those that deploy numbers that allows them greater credence than all of our other senses.

Numbers as ‘immutable mobiles’

One way of looking at numbers is as ‘immutable mobiles’. The term was coined by Latour (1986) and was used to describe things that are made to be easily transportable without changing the inherent characteristics of those things. The most powerful example he gives is that of the printing press. The printing press allowed ideas which were previously changed and modified from person to person to be spread across the world without distortion. These ideas are made more accurate “just as a consequence of more mobilization and more immutability” (Latour 1986:11). It is much easier to transport an idea to the other side of the world without distortion of that original idea if it is permanently printed on paper.

If there is a scale of immutability and mobility, then numbers are certainly on the top end. Latour argues that “…everything, no matter where it comes from, can be converted into diagrams and numbers, and combinations of numbers and tables can be used which are still easier to handle than words or silhouettes (Dagognet, 1973)” (Latour 1986:20). Here, then, we see can see that numbers are seen as much more valuable in terms of disseminating undistorted ideas than words on a page. I do not take any issue with this reasoning. It seems logical enough that it is easier to work with the number 71, than it is with a three paragraph description of the structure and content of an essay which is of first class quality. It also seems logical that it is easier to compare a mark of 71 with a mark of 65, than it is to compare a three paragraph description of a first class essay and the same of an upper second class essay. However, ease of use does not mean that it is closer to the truth or more objective. In fact, ‘ease of use’ most often hides the major assumptions and issues which make it appear so easy in the first place.

So, it is perfectly reasonable to grant ‘easiness’ to numbers, to see that numbers allow many comparisons to be made without much effort at all. But it is not reasonable to say that they are more accurate (Latour 1986:11). Going back to the example of essay marks reveals how much ‘stuff’ is concealed in a number and how making comparisons based on just a number leads to severely distorted conclusions and a satisfaction with incomparable comparisons. Graduate schools often compare students’ scores on their MPhils as if every institution and country’s grades were perfectly interchangeable. In reality, a 71 from a British university is not comparable with most other country’s systems of grading. In fact, a 71 from one British university is often not even comparable with a 71 from another university. For example, a 71 at the University of Oxford is classed as a Distinction at Masters level, whereas it is only awarded a pass at the University of Cambridge, and these are two institutions that are perhaps more comparable than most. Although the actual number may be an immutable mobile, the meaning behind the number most certainly is not. To use another of Latour’s terms, numbers can thus be seen as black boxes – something that “contains that which no longer needs to be considered, those things whose contents have become a matter of indifference” (Callon and Latour 1981:285).

The idea of being a black box is implicitly present in Latour’s list of the advantages of immutable mobiles. Although Latour is specifically listing the advantages of ‘paper-work’ in this article, the same points can also be extrapolated to discuss the case of numbers. Of particular note is the third advantage of flatness. Latour explains that “there is nothing you can dominate as easily as a flat surface of a few square meters; there is nothing hidden or convoluted, no shadows, no “double entendre”(Latour 1986:18). This seems to be a very naïve statement when referring to words on a page, and even more so when extended to describing numbers on a page. In making things flat, people hide all sorts of complexities and omit the assumptions behind them. The numbers become reified as ‘objective truth’ by those who take the flatness of the paper literally to be the flatness of the truth, and all sorts of consequential action can ensue.

Let me give a rather mundane example of the consequences of hidden assumption using the recent Bodleian Library survey about user satisfaction. One of the questions was about how quiet the library workspace was, and whether enough effort was made to ensure that there was a silent space available. The required response was a number on a Likert scale ranging from 1 (very noisy) to 10 (silent). I put down a 5 for my home library (the Sainsbury library at the Said Business School) since group work is allowed and there is usually a steady murmur of noise. Looking at how the question was framed, it is safe to say that a 5 will be viewed as negative, and as something that requires change (that more effort needs to be made to ensure a quiet workspace). However, 5 is perhaps the best score that I could have given in terms of satisfaction – I really dislike silent libraries and need there to be a steady stream of incomprehensible noise to feel comfortable enough to work. The consequences that are likely to ensue, if enough people put similar views, is that the library will make more of an effort to make it a quieter place to study, which is the opposite action to the one suggested by my answer. Whilst this is a relatively trivial example, we do not need to go too far to find examples with much more serious consequences.

Numbers as artefacts created by those who use them

In their book ‘Health and Efficiency’, Ashmore, Mulkay and Pinch (1989) discuss the Quality Adjusted Life Year (QALY) – a concept invented by health economists to attempt to apply a metric to the subjective characteristic that is the quality of life. The measure itself, as well as the numbers it produces, has been a source of much controversy and confusion. In fact, the authors devote a whole chapter to clippings of newspaper articles which explained what QALYs are in a number of different and contradictory ways. For some, the QALY is simply a type of scale, for others it is the basis of cost benefit analysis, and for others still it is the basis for choosing life or death. The numbers that are derived from the formula behind the QALY, are at once made into im/moral and un/ethical numbers with powers that were once reserved only for (the) God(s).

However, the apparent inventor of the QALY, Professor Alan Williams of York University, argues that the QALY is a “simple, versatile measure of success which incorporates both life expectancy and quality of life and which reflects the values and ethics of the community served (Scotsman 3 Dec 87)” (Ashmore et al. 1989:63). By giving a single number to the quality of life, Williams sought to make the choice between different types of treatments and operations much more efficient. Rather than rely on “peoples’ subjective judgements”, the QALY allows decision making to occur based on an “objective index” (Ashmore et al. 1989:98). However, as Ashmore et al. rightly argue, in trying to provide a solution to the health manager’s problem, Williams has managed to change the very nature of the problem itself. Rather than being a measure of someone’s relative gain from an operation in comparison with someone else’s, “the benefit to be gained from, say, coronary artery surgery becomes the number of QALYs it generates and nothing else” (Ashmore et al. 1989:91).

Once the intricacies and complexities involved in understanding the quality of life are subsumed under a single number, it takes on an ontological identity of its own. It is no longer an accurate picture of the thing it was created to represent, but wields its own power to make everything else behave in ways which conform to that number. For instance, Another one of the articles quoted by Ashmore et al.  (1989:64) is from the Guardian on the 5^th November 1986 and states that “LATE 20^th century man, it seems, engages in the pursuit not of happiness but of QALYs”. This shows how the number can come to displace the thing that it initially purported to measure, and becomes a self-reinforcing measure of itself only. By changing the way the quality of life debate is framed by including the QALY figures, by writing reports on the different QALYs earned by different types of operations and by framing budgeting decisions based on QALYs, the numbers become a powerful entity in and of themselves which can be used by those who create them to serve their own agendas. As such, numbers can be potent tools for people who need to persuade people to take certain (in)action.

Numbers as political tools of power

Helen Verran (2012:112) argues that “Modernity itself seems to be afflicted with an ongoing blindness when it comes to the social functioning of number”. Her account of numbers is perhaps the most political and philosophical.

“…in articulating the social functioning of number, I treat it as a material-semiotic device. This is a quite different way of framing numbers than treating them as either universal abstractions or as culturally relative social constructions. It keeps both numbers and those who use them as present in the here and now…this way of thinking about numbers makes them as inseparable from the practices in which enumerated material entities come to life, and as semiotically agential (Verran 2001). It recognises that the workings of numbers are deeply embedded and constitutive of the real.”
       -    (Verran 2012:112)

From the quote above, it is clear that Verran distances herself from treating numbers as either ‘universal abstractions’ or as ‘culturally relative social constructions’. Her preferred view of numbers is seeing them as embedded in the present and as inseparable from the practices in which they are brought into being. I agree with this view of numbers, however this makes it much more difficult to see numbers as immutable mobiles. In fact, their ‘mobility’ is severely restricted if numbers are only to be understood in the present practices in which they are constructed and used. Seeing numbers in this way also greatly reduces (and rightly so) their apparent claim to comparability; it means that a 71 from Cambridge will be seen as a 71 from Cambridge, and a 71 from Oxford as a 71 from Oxford – the two cannot be seen as interchangeable, because they are not so.

Furthermore, Verran argues that measuring things changes the nature of what it is that is being measures. Much like the findings of Goodhart (1975) and Campbell (1976) who found that once something is measured or quantified, the thing being measured changes and transforms, Verran (2012:15) argues that by the end of the 1930s, GNP had become the one true measure of the economy – it meant that new writings, theories, policies and interventions were created just to keep enacting this number. These policies were upholding the number, creating it, refining it and manipulating it. It was once created to describe something much more complex, but now has become the end in itself. GNP is the ‘thing’ that is aspired to now – not the wellbeing of the economy, but the production of an ever greater GNP value and rank within the GNP ordering.

If such numbers and measures do not really measure what they set out to measure, then why are there so many numbers still ruling policy decisions? For Verran, that is because numbers are potent political and cultural agents. This is perhaps because they are very easily treated as immutable mobiles which can black box a huge amount of complexity as well as hide a number of assumptions on which the number is created. Numbers can anchor the mind into certain lines of thought more so than qualitative descriptions, even if the thing being quantified is not really quantifiable. For example, Verran focusses on the numbers involved in an advertisement poster about the carbon emissions in Australia. She explains that Nature should not be quantified; to do so would be to detract from the aesthetics of it. Nature has value in and of itself without the need to attribute a quantitative value to it, but the makers of the poster have applied some unknown algorithm to Nature which allows them to make claims such as “$434 – 811 million: The estimated value Australian households are willing to pay for a 1% improvement in the health of the Great Barrier Reef” (we are told this is calculated using Net Present Value over 5 years using a 10% discount rate).

If we go back to Latour for a moment, he argues that if you want to convince someone of something “you have to invent objects which have the properties of being mobile but also immutable, presentable, readable and combinable with one another”  (Latour 1986:6). Using a figure like the one on the Australian poster does just this. It gives a figure that is readable, presentable and is combinable with other figures. Most of all, however, it gives a quantity that is very easily comparable. But what is hidden in this estimated value? First of all, it is an assumption that the Net Present Value is a reasonable measure of ascertaining the value of something in the future, and that a 10% discount rate is reasonable. Second of all, it assumes that both the reader and the people surveyed to come up with this figure all understand a “1% improvement in the health of the Great Barrier Reef” equally. Third, did every household in Australia say that they were willing to pay money to save 1% of the Great Barrier Reef? What of those households that actually demanded compensation because trying to achieve a 1% health benefit came at a larger personal cost to them and their businesses? The list could go on ad nauseam but the point is clear: there are endless assumptions and frameworks hidden in numbers which often go unquestioned.

The reason why numbers are regularly preferred over qualities, or why, for instance there is always a hint of disparagement at qualitative methods, is not because numbers are inherently more objective and rigorous, or because they are closer to the truth, but rather because numbers are very good at masking the subjectivities that are present in creating them in the first place. They are very easily turned into immutable mobiles, which, as we have seen above give them the advantage of being able to be disseminated without distortion, and they are, fundamentally, much ‘easier’ than qualitative descriptions and narratives. They are much easier to use in justifications for policies, in comparisons between different candidates applying to a school, in ranking which country is financially ‘better’ than the others, and so on.

Whilst I agree that numbers are immutable mobiles, this is only at face value. When you scratch beneath the surface, you find that numbers are very much mutable if they are to be mobile. Taking numbers out of context makes them meaningless and thus open to whoever wants to interpret them for their own uses. The answer to the question of ‘What’s in a number?’, then, is pretty much anything you want there to be to serve your purpose of the day.

References:

Ashmore, Malcolm, M. J. Mulkay, and T. J. Pinch. 1989. Health and efficiency: A sociology of health economics. Milton Keynes England and Philadelphia: Open University Press.

Callon, Michel, and Bruno Latour. 1981. “Unscrewing the big Leviathan: how actors macro-structure reality and how sociologists help them to do so.” Pp. 277–303 in Advances in social theory and methodology: Toward an integration of micro- and macro-sociologies. London: Routledge & Kegan Pau.

Campbell, Donald. 1976. Assessing the Impact of Planned Social Change. Hanover New Hampshire.

Goodhart, Charles. 1975. “Problems of Monetary Management: The U.K. Experience.” Papers in Monetary Economics (Reserve Bank of Australia) 1.

Latour, Bruno. 1986. “Visualization and Cognition: Thinking with Eyes and Hands.” Knowledge and Society: Studies in the Sociology of Culture Past and Present 6:1–40.

Verran, Helen. 2012. “Number.” Pp. 110–125 in Inventive Methods: The Happening of the Social, edited by Dr Celia Lury and Nina Wakeford. London and New York: Routledge Retrieved November 26, 2012.

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