Abstract
That modern quantitative economics and population health share an origin in seventeenth-century political arithmetic is well documented. This article argues for something further: that the mathematical affordances of selected phenomena helped shape the historical development of both sciences, and that this selection operates even when the resulting measurements are accurate. Tracing the history from John Graunt’s analysis of the London Bills of Mortality and William Petty’s Down Survey of Ireland, through eighteenth-century medical arithmetic and life tables, to Chadwick, Farr, Snow, national income accounting, psychiatric classification, and the Global Burden of Disease, it treats macroeconomics and public health as multimaterial and multisymbolic ways of governing and enhancing life in the mesocosm. It proposes that complex living processes have mixed recursivity, combining recursive aspects that answer back to how they are engaged with nonrecursive aspects that do not, and that every mathematical model of such a process, including models of responsiveness and feedback, works by isolating the nonrecursive aspects. Recursive processes as such cannot be modelled mathematically. Economics and epidemiology have each rediscovered this limit in their own terms. The article shows how mathematical representations became consequential through material interventions, and why breakdown, which leaves nonrecursive marks, has been systematically privileged over healing, which is recursive coordination that leaves none.
I. Introduction: Two Sciences, One Mathematical Selection
In 1662 a London haberdasher named John Graunt published a short book with a long title, Natural and Political Observations Mentioned in a Following Index, and Made upon the Bills of Mortality. For decades the parish clerks of London had compiled weekly counts of burials and christenings, and from 1629 the printed bills had also reported a cause for each death. Graunt gathered the bills of more than half a century, arranged them into tables, and found in them what no single entry contained: that more boys were born than girls, that the city grew by migration from the countryside more than by its own births, that plague years could be traced in the movement of christenings as well as burials, and that many causes of death recurred with striking steadiness from one year to the next (Graunt 1662). The book is a founding text of demography and epidemiology. It is equally a founding text of political arithmetic, the programme of numerical government from which important strands of quantitative economics descend, and Graunt’s friend William Petty, a physician and land surveyor, took its methods into the calculation of national wealth.
That the early mathematical study of population health and the early mathematical study of national wealth formed one connected undertaking is well documented (McCormick 2009; Rusnock 2002). The claim of this article is a different one. It holds that the mathematical affordances of particular phenomena helped decide which phenomena became central to both sciences, and that this selection operates before any particular measurement is made and persists even when every measurement is accurate. Land could be measured, deaths counted, transactions recorded, and populations estimated. The ongoing activities through which people kept well, cared for one another, healed, adapted to hardship, and sustained their households produced no equivalent numerical objects. Those activities were never unknowable or simply ignored, since physicians, midwives, householders, and parish officers knew a great deal about them, but they were placed at a systematic disadvantage within a form of knowledge whose authority was growing.
Three connected processes are traced. The first is historical selection: certain phenomena became privileged objects of investigation partly because they were mathematically tractable. The second is ontological substitution: the measurable properties and recorded counterparts of living processes came to stand for the processes themselves. The third is institutional reinforcement: what could be quantified became increasingly important to governments, economic institutions, medicine, and public health, which reinforced the original selection.
Underneath all three lies an ontological thesis about what mathematics can reach. A process is recursive when its subsequent course is altered by how it is engaged, so that it answers back. Mathematics is a nonrecursive symbolic system, and a recursive process as such cannot be modelled mathematically. Complex living processes, however, are rarely recursive in every respect. They have mixed recursivity: they combine recursive aspects with aspects that do not answer back to their engagement, such as the duration of an incubation period, the area of a field, or the fact of a death once it has occurred. The hypothesis developed here is that every mathematical model of a complex living process, including models that represent feedback, learning, and responsiveness, works by isolating its nonrecursive aspects. Prediction does the same with the future. A future is mixed, partly settled and partly open, and forecasting succeeds where it latches onto what is already settled. Mathematical selection, on this account, is the historical form taken by a constraint that is ontological.
These processes are best understood by treating political arithmetic, and the economics and public health that grew from it, as ways of governing and enhancing life that work through particular mediations. Living Value Theory distinguishes five irreducible mediations through which living beings coordinate with their worlds: multisensorial embodiment, multispecies being-with, multiversal dwelling, multimateriality, and multisymbolization. The first three, the zoetic mediations, are shared by all living beings. The last two, the poietic mediations, deposit coordination into durable things and durable signs, and so extend it across distance, delay, and scale; in the cumulative forms on which states depend, they are distinctively human. Survey chains and maps, registers and printed bills, coins and ledgers, drains and water mains, lancets and vaccines, tables and indices: the government of populations has always been multimaterial and multisymbolic at once. Its symbolic instruments decide what becomes known, and its material instruments change what happens in kitchens, streets, and bodies. The strongest cases in the history that follows are those in which mathematical representations became consequential through material interventions, and the relation between the two poietic mediations turns out to be central to the argument.
One qualification is essential. Economics and public health did not originate in the seventeenth century, since traditions of political economy, medicine, sanitation, quarantine, and collective care long preceded political arithmetic. The claim is that their modern quantitative forms share important institutional and intellectual origins, and that their later development reproduces related forms of selective legibility. The Global Burden of Disease (GBD) appears at the end of the story as its contemporary culmination, but the argument begins three and a half centuries earlier.
II. The Seventeenth Century: The Birth of Political Arithmetic
A. Before political arithmetic: from encounter to entry
Counting people and property was old. Rulers had long kept records of taxation, landholding, and military obligation, and in England parish registers of baptisms, marriages, and burials had been required since 1538. The novelty of the seventeenth century lay elsewhere, in the attempt to turn accumulated administrative records into systematic numerical knowledge about populations and territories.
London’s Bills of Mortality grew out of plague. From the sixteenth century the city’s parishes reported their burials so that the court, the city authorities, and anyone with the means to leave could judge when an epidemic was rising. The causes of death were supplied by the searchers of the dead, women appointed by each parish, usually elderly, who had no medical training and learned their work through long experience of illness and death in a city where both were common (Newton 2012). A searcher was called to the house, viewed the body, asked those present what had happened, and reported a cause to the parish clerk, who passed the week’s figures to the Company of Parish Clerks for printing. Graunt knew how this worked and how it could fail. He observed that the searchers, “after the mist of a cup of ale and the bribe of a two-groat fee”, could not be relied upon to distinguish one wasting disease from another, and that families had reasons to hide some causes altogether (Graunt 1662).
The process deserves close description, because it shows from the very beginning the transformation on which all later population statistics depend. A death occurred within a living history of kin, neighbours, illnesses, food, and household arrangements. The searcher’s visit was a recursive encounter: she looked, asked, listened, and weighed what she was told against what she saw, against the categories she knew, and perhaps against a coin. What left the house was a word: “consumption”, “teeth”, “aged”, “rickets”. Once entered and printed, that word no longer changed in response to anything the family later learned or anything a physician might have said. Graunt’s mathematics became possible because the records had become nonrecursive deposits. Their stability belonged to the record. The lives and deaths behind them had been as responsive and as tangled as any.
B. John Graunt and the selection of countable disease
Graunt’s achievement had three parts. He assembled large numbers of recorded events into a single mathematical field, extending across decades and parishes. He identified patterns available from no individual encounter, including the sex ratio at birth and the steadiness of many causes of death. And he examined the reliability of the categories through which deaths had been classified.
The third achievement matters most here. Graunt distinguished causes that were clearly identifiable and unlikely to be confused with other conditions, among which he named smallpox and rickets, from causes that were ambiguous and perhaps conjoined with or produced by other conditions, among which he named “teeth” and old age (Graunt 1662; Newton 2012). The ambiguity of the second group has been confirmed by later research. “Teeth” referred to infants who died while their milk teeth were erupting, usually between about six and eighteen months, and their deaths were probably caused by diarrhoeal disease and fevers. “Aged” depended on searchers who guessed a person’s age from appearance and rounded it to the nearest five years (Newton 2012). Even Graunt’s confidence in rickets now looks misplaced. Searchers probably recognised the outward deformities of rickets in children who died of respiratory infections, and the later decline of rickets as a recorded cause need not track any equivalent decline in the condition itself (Newton 2012).
Graunt could count the entries in every category with equal ease. Whether the entries in a category corresponded to comparable pathological events was another question, and he asked it. The distinction between the countability of records and their fit with the underlying illness was present at the birth of population statistics, raised by its founder from inside his own tables. The selection that this article traces was never simply imposed on seventeenth-century medicine from outside; its practitioners were already confronting the uneven mathematical affordances of the phenomena they studied, and the history of what could be counted was already part of the history of what became visible as disease.
C. William Petty: physician, surveyor, political arithmetician
William Petty is the key figure in this history, because in him the medical, territorial, and economic strands were not yet separate. He studied medicine in the Netherlands and Paris, took his Oxford doctorate in physic in 1650, became professor of anatomy, and in 1652 left Oxford to serve as physician-general to the Cromwellian army in Ireland. There he directed the Down Survey, helped found the Royal Society, and over the following decades wrote the treatises on taxes, money, Ireland, and national wealth that later economists claimed as their prehistory (McCormick 2009). Ted McCormick has shown that these activities belonged to one programme. Political arithmetic was a project of government and social engineering, aimed at making territories, populations, and resources knowable so that they could be managed, and it was much broader than an early version of economics.
Petty stated the programme’s method in the preface to Political Arithmetick. Instead of using only comparative and superlative words and intellectual arguments, he would express himself “in Terms of Number, Weight, or Measure; to use only Arguments of Sense, and to consider only such Causes, as have visible Foundations in Nature; leaving those that depend upon the mutable Minds, Opinions, Appetites, and Passions of particular Men, to the Consideration of others” (Petty 1690). The sentence is usually quoted for its first half. Its second half is more revealing. Petty set minds, opinions, appetites, and passions aside without calling them unimportant, because they were mutable, because they answered back, and he kept for his arithmetic the causes that did not answer back. In the vocabulary used here, he explicitly selected what could be engaged as nonrecursive and left the recursive to others. It is hard to find a clearer statement of mathematical selection at the origin of a science.
The same programme reached directly into the valuation of life. In Verbum Sapienti, written in 1665 and published in 1691, Petty estimated the wealth of England and included its people in the reckoning: “If 6 Millions of People be worth 417 millions of pounds Sterling, then each head is worth 69l.” From this he drew a conclusion about plague. A hundred thousand deaths above the ordinary number, he calculated, amounted to a loss of nearly seven million pounds to the kingdom, and he asked how well seventy thousand pounds might have been spent to prevent this “Centuple loss” (Petty 1691). In a plan for London two years later he set the cost of protective measures against the expected loss from the next epidemic and arrived at a ratio of about one to eighty-four. Here, in the 1660s, the arithmetic of health and the arithmetic of wealth were joined in a single operation: lives valued as national stock, disease as its depletion, and prevention as an investment whose return could be computed. The cost-effectiveness reasoning of twentieth-century health economics has an ancestor of exactly this form.
D. The Down Survey: mathematical fit and colonial power
The Down Survey of Ireland, completed in 1656, shows the multimaterial side of political arithmetic and its entanglement with power. To measure the forfeited lands that the Commonwealth intended to distribute among soldiers and creditors, Petty engaged about a thousand men, many of them soldiers, trained them in the use of chains and simple instruments, and mapped barony after barony in roughly thirteen months (McCormick 2009). The survey made land available as mapped boundaries, measured areas, and comparable parcels. It was a remarkable technical achievement, and land area affords such treatment well. A field has extension that does not alter in response to being surveyed; areas can be added, divided, and compared; two parcels of equal area are equal in a respect that matters for sowing, rent, and tax. The chain, the compass, and the map were multimaterial instruments well fitted to that property.
The survey was also an instrument of conquest. Its maps served the Cromwellian redistribution of Irish land, and Petty himself acquired large estates through it. In later writings he proposed schemes for moving and “transmuting” populations that treated people with the same arithmetic as acres (McCormick 2009). Two processes must therefore be kept apart. The first concerns mathematical fit: land area really does afford measurement. The second concerns institutional appropriation: the measurements entered a political order in which land could be confiscated, allocated, transferred, and taxed, and in which the people living on it were displaced. The accuracy of the measurements did not establish the legitimacy of the project. The land may have been measured well while the uses of the measurements were devastating for the living worlds of those who had farmed it. The distinction between mathematical fit and the value of mathematical application, which recurs throughout this history, appears here in its starkest early form.
E. Political arithmetic as common ancestor
Graunt’s tables of births and deaths and Petty’s estimates of wealth and productive capacity belonged to one intellectual movement. The population could be treated at once as a collection of lives subject to disease and death and as a resource for taxation, labour, military strength, and national prosperity. The future divisions between economics, demography, epidemiology, and public administration did not yet exist. The emerging mathematical representation of society was simultaneously medical, economic, administrative, and political, and it worked through both poietic mediations: chains, maps, registers, and printed bills on one side, tables, estimates, and valuations on the other. Quantitative economics and population medicine did more than develop similar methods: their earliest objects were constituted through overlapping practices of numerical representation, and those practices selected, from the start, the aspects of life that did not answer back to being counted.
III. The Eighteenth Century: Population, Probability, and Medical Arithmetic
A. From recorded events to national estimates
In the decades after Petty, political arithmetic became more ambitious. Ian Hacking has shown how probability emerged as a mathematical idea in these same decades, and how, a century and a half later, an avalanche of printed numbers made statistical regularity appear as a property of society itself (Hacking 1975, 1990). Gregory King compiled, in 1696, a table of the ranks, families, incomes, and expenditures of the whole English population, and Charles Davenant defined political arithmetic as “the art of reasoning by figures upon things relating to government” (Davenant 1698). In Prussia, Johann Peter Süssmilch read the regularities of births and deaths as evidence of a divine order in human affairs (Süssmilch 1741). What had been scattered administrative record was becoming a field of systematic comparison across nations and decades. It was not yet modern economics or modern epidemiology, but a shared project of understanding population and wealth through numbers, in which the same estimates served questions about health, taxation, and the strength of states.
B. Medical arithmetic and the decision of what to count
Andrea Rusnock’s Vital Accounts reconstructs how, in eighteenth-century England and France, physicians and political arithmeticians made births, deaths, diseases, environments, and medical interventions objects of numerical inquiry (Rusnock 2002). In the 1720s James Jurin, secretary of the Royal Society, collected reports from correspondents in order to compare the proportion of people who died of naturally acquired smallpox with the proportion who died after inoculation, and published the results year by year. Others compiled parish registers, weather diaries, and hospital returns to relate mortality to seasons, places, and practices. Rusnock emphasises that deciding what to count and deciding how to count were closely connected activities, and that the numbers which resulted were achievements of correspondence, standardisation, and persuasion.
Living Value Theory adds a question about the phenomena themselves. Smallpox suited Jurin’s arithmetic for identifiable reasons. Its eruption was visible and distinctive, its course was short, and the event that mattered, death or survival, was bounded and datable. Inoculation was an act performed at a known moment with known material, a lancet carrying matter from a pustule. The comparison worked because both the disease and the intervention possessed the discreteness and separability that counting requires. The fevers, fluxes, and declines that filled the bills resisted the same treatment, and they were correspondingly harder to bring into medical arithmetic at all.
C. Bernoulli, d’Alembert, and the mathematical comparison of lives
In 1760 Daniel Bernoulli presented to the Paris Academy of Sciences a mathematical analysis of smallpox mortality, published in 1766, which estimated that universal inoculation would raise life expectancy at birth by about three years (Bernoulli 1766). It was a substantial achievement and an early model of what a population-level intervention might accomplish. It also provoked a revealing objection from Jean le Rond d’Alembert, who questioned whether a gain in average life expectancy settled anything for a particular person deciding whether to be inoculated (d’Alembert 1761). Inoculation carried an immediate risk of death, small but concentrated in the weeks after the procedure, while its benefit was spread across a lifetime and might arrive decades later. A rational individual, d’Alembert suggested, might reasonably weigh a near danger more heavily than a distant gain, and the calculus of averages offered no way to adjudicate between them.
The dispute concerned more than mathematical assumptions. It concerned whether population-level gains could be interpreted as sufficient grounds for decisions taken by living beings who face risk in time, with their own attachments, fears, and horizons. The aggregate result was informative, and its implications for particular lives were not thereby established. The distinction between a calculable population benefit and the living consequences of an intervention was already being contested in the eighteenth century, in a form that anticipates later debates about cost-effectiveness and burden.
D. Life tables and the joint mathematisation of health and money
The same regularities that revealed patterns in mortality made it possible to calculate financial obligations. Edmond Halley’s 1693 table of mortality, built from the births and burials of Breslau, carried in its title the purpose of ascertaining “the Price of Annuities upon Lives” (Halley 1693). Abraham de Moivre developed the mathematics of annuities in the following decades, and in 1762 the Equitable Society in London began to sell life assurance priced from mortality tables. Pensions, annuities, insurance, and the estimation of future public obligations came to rest on the same tables that physicians used to compare places and diseases.
Death and financial value are different things, but mortality regularities became a common mathematical infrastructure supporting both medical and economic institutions, and the infrastructure was itself multimaterial as well as symbolic: ledgers, printed tables, policy documents, and the offices that kept them. Population statistics could provide valuable knowledge about disease and prevention, and they also enabled the valuation of lives through actuarial and administrative calculation. The mathematical achievement did not settle the purposes for which it would be used.
IV. The Nineteenth Century: Political Economy Becomes Public Health
A. Industrial cities and the cost of sickness
Industrial Britain made the questions of political arithmetic urgent. Cities grew faster than their housing, water, and drainage; fever, cholera, and consumption killed on a scale that alarmed the propertied classes; and the New Poor Law of 1834 made the cost of sickness, widowhood, and orphanhood a direct charge on local rates. Public health was inseparable from questions about productivity, poor relief, and the cost of maintaining a labouring population. Edwin Chadwick, secretary to the Poor Law Commissioners, stood at the junction of these concerns.
B. Chadwick’s sanitary report: health as calculation
Chadwick’s Report on the Sanitary Condition of the Labouring Population of Great Britain of 1842 is perhaps the strongest historical evidence for the shared orientation. It combined local medical reports, descriptions of courts, cellars, and cesspools, and mortality statistics, and it gave a whole section to the pecuniary burdens created by the neglect of sanitary measures: the costs of preventable sickness and premature death, of lost working capacity, and of the widows and orphans whose support fell on the poor rates (Chadwick 1842). These economic considerations were central to the argument for intervention. The report made illness governable partly by demonstrating its costs, and the numerical demonstration of ill health and the numerical demonstration of its economic consequences reinforced each other. It is a nineteenth-century prototype of reasoning later formalised in health economics.
Its best-known figures show both the power and the fragility of the method. Chadwick reported that the average age at death of labourers in Manchester was about seventeen, while that of gentry in Rutland was fifty-two (Chadwick 1842; Hanley 2002). The contrast was politically devastating. It was also statistically compromised, as William Farr and F. G. P. Neison pointed out, because an average age at death computed from deaths alone depends heavily on infant mortality and on the age structure of the population, so that a young and growing town will show a low figure even if its adults live long (Hanley 2002). James Hanley has argued that Chadwick’s measure was no worse than the crude death rates other statisticians used, which faced related objections (Hanley 2002). The episode is revealing in either case. A number with weak inferential fit can carry enormous persuasive force, and its force does not depend on its fit.
Chadwick’s remedy was multimaterial. He proposed what he described as an arterial and venous system for towns: constant supplies of piped water, and narrow glazed earthenware sewers flushed by that water to carry refuse away. The justification was multisymbolic, the intervention material, and the success, where it came, consisted in events that ceased to happen.
C. William Farr and vital statistics
The civil registration of births, marriages, and deaths in England and Wales began in 1837, and from 1839 William Farr, as compiler of abstracts at the General Register Office, turned the new records into a national system of vital statistics. Farr argued from the outset that “the advantages of a uniform statistical nomenclature, however imperfect, are so obvious” that its absence from the bills was surprising, and he devised a nosology for classifying causes of death, compared mortality across districts, occupations, and social conditions, and helped to found the international effort to standardise causes of death that eventually produced the International Classification of Diseases (Farr 1839). He also extended Petty’s valuation of people, estimating the economic value of a labouring man from his expected future earnings net of his maintenance (Farr 1853).
Farr’s comparisons supported investigations of disease, environment, and occupation that were enormously important to public health. Their basic objects nonetheless remained registered occurrences organised through administrative classifications. A death becomes a record; the record becomes part of a distribution; the distribution becomes evidence about the health of a population. Each transition is an operation whose fit with the preceding object must be examined, and statistical success at one transition does not remove the ontological differences between the living event, its record, and the population-level inference.
D. John Snow and the success of mathematical public health
It is essential to include a case in which quantification illuminated a cause of mortality decisively, and John Snow’s work on cholera provides it. In the second edition of On the Mode of Communication of Cholera, published in 1855, Snow compared households supplied by the Southwark and Vauxhall Company, which drew its water from the Thames in a reach contaminated by London’s sewage, with households supplied by the Lambeth Company, which in 1852 had moved its intake upstream. In the first seven weeks of the 1854 epidemic, he found, there were 315 cholera deaths for every ten thousand houses supplied by Southwark and Vauxhall, and 37 for every ten thousand supplied by Lambeth (Snow 1855).
Here mathematical comparison did what it should. It identified a relevant difference, supported causal inference, and provided a basis for intervention. The comparison worked for identifiable reasons. Cholera deaths were acute, distinctive, and datable. The exposure was a material fact about each house, and it was largely independent of what the households believed or did. The decisive condition was multimaterial. The pipes of the two companies had been laid through the same streets, so that, as Snow observed, a single house often had a supply different from those on either side, and households of every class and occupation were divided between the two waters without having chosen. The river belonged to dwelling, the conditions of the planet that no one had made; the pipes belonged to multimateriality; and the intermixing of the pipes created a comparison that no investigator could have designed. Snow’s arithmetic read a natural experiment that infrastructure had already performed.
Even here, the mortality comparison provided no account of the experiences, care arrangements, and household consequences of cholera. That limitation did not weaken the investigation; it established the scope of what the mathematics could legitimately reveal.
E. A shared logic consolidated
Chadwick, Farr, and Snow together established the authority of numerical comparison in identifying problems of health and justifying intervention, in the same decades that saw the expansion of economic statistics, insurance calculation, and quantitative administration. Mathematical public health was never confined to pathological states. It was deeply concerned with prevention, sanitation, and the conditions under which disease did not occur, and its greatest achievements were multimaterial: drains, water mains, housing regulation, and later vaccination. The historical bias therefore cannot be described as an exclusion of prevention, and the more precise claim is that the value of preventive work was most readily established through changes in measurable outcomes: fewer deaths, fewer cases, lower expenditure, preserved working capacity. A process that prevented illness acquired authority through the statistically identifiable illness that did not occur. That is the more fundamental selection, because it means that prevention was valued in the currency of the events it suppressed, while the coordination that sustained health from day to day remained without a currency of its own.
V. The Selection Becomes Institutionalised
A. Economic statistics: from measurable objects to national prosperity
The line from political arithmetic to national income accounting runs through King and Davenant to the twentieth century. In the 1930s Simon Kuznets in the United States and Colin Clark in Britain constructed estimates of national income that summed a vastly heterogeneous economy into standardised flows of production, income, and expenditure, and after the Second World War the United Nations System of National Accounts made such estimates the common language of economic government (Kuznets 1934; Clark 1937; United Nations 1953). Kuznets warned at the outset that “the welfare of a nation can, therefore, scarcely be inferred from a measurement of national income” (Kuznets 1934). The warning was as candid as it was ineffective.
What enters the accounts depends on what becomes available through their operations, chiefly market transactions and the incomes and outputs associated with them. Arthur Cecil Pigou noticed the consequence early: if a man married his housekeeper, the national dividend would fall, although nothing in the household had changed except the absence of a wage (Pigou 1920). Unpaid care, household coordination, subsistence production, and the many forms of sustaining living conditions do not enter the account through the same operations as paid work, and feminist economists have shown how much of what sustains life thereby disappears from the representation of prosperity (Waring 1988). None of this shows that such activities lack value; what it shows is that a mathematical apparatus built for particular measurable processes was extended into claims about national prosperity, and that what it could not register acquired a weaker institutional existence. Macroeconomic government works overwhelmingly through multisymbolic instruments, accounts, interest rates, money supply, and fiscal balances, which act on multimaterial production and, through it, on the living conditions of entire populations.
B. Medicine and its standardised objects
In medicine, pathological anatomy, laboratory science, and bacteriology made many properties of bodies and illnesses measurable for the first time. The identification of the tubercle bacillus in 1882, and of other pathogens in the same decades, made it possible to distinguish certain infectious diseases through identifiable biological agents, and international lists of causes of death, adopted from 1893, standardised the categories in which deaths were recorded across nations. This was a major expansion of knowledge. It also made disease identifiable through increasingly standardised objects, and the question this history raises is whether the measurable pathological entity acquired greater authority than the much wider living process of ill health within which it occurred.
C. Psychiatry: when classification makes a process tractable
Psychiatric illness did not enter medicine late because it was difficult to quantify. Asylums kept registers of admissions, diagnoses, and discharges from the early nineteenth century, and national statistics of insanity followed. The United States census of 1840 counted the “insane and idiotic” for the first time, and its results appeared to show that free Black people in the Northern states were afflicted at many times the rate of enslaved people in the South, a finding quickly used in defence of slavery. Edward Jarvis showed in 1844 that the figures were riddled with errors, including towns credited with more insane Black residents than they had Black residents of any kind (Jarvis 1844). In Heidelberg, Emil Kraepelin followed the courses of his patients on index cards and built his diagnostic categories from the regularities they displayed, and in 1918 American asylum physicians published a Statistical Manual for the Use of Institutions for the Insane, a classification devised so that institutions could report comparable numbers (American Medico-Psychological Association and National Committee for Mental Hygiene 1918).
These episodes reveal something important. Psychiatric statistics were possible even when their categories corresponded uncertainly to the phenomena being classified. Institutional records could count admissions, diagnoses, and treatments, but the counts did not establish that the underlying experiences formed discrete, universally equivalent disease entities. When a living process does not readily afford the operations a discipline requires, institutions may construct classifications that make it tractable anyway, and the resulting numerical objects can be extraordinarily stable while the experiences that produced them remain heterogeneous. The process is not unique to psychiatry, but psychiatric classification makes it unusually visible, and the 1840 census shows how quickly such numbers can be taken up for purposes that have nothing to do with the lives they claim to count.
D. How far the selection reaches
A shared origin does not by itself show that mathematical tractability shaped which objects became prominent. The stronger claim needs evidence of a specific kind, and the history supplies four kinds of it.
The first is explicit choice by the founders of a practice. Petty’s preface states the criterion outright: causes with visible foundations in nature for the arithmetician, the mutable minds and passions of particular men for others. The second is the design of categories for the sake of counting, with their imperfection openly accepted. Farr’s insistence that the advantages of a uniform statistical nomenclature, “however imperfect”, were obvious set the terms for the classification of death that led, through Bertillon’s international list of 1893, to the rule adopted in the sixth revision of 1948 that every death must be assigned a single underlying cause (Farr 1839). A death has many causes, often unfolding over years; the rule exists because tabulation requires each death to fall into one column. The third is the justification of an account’s boundaries by tractability. The System of National Accounts excludes own-account household services such as cooking, cleaning, and childcare from the production boundary, and among its reasons is that, because such services are rarely sold, there are no suitable market prices with which to value them (United Nations et al. 2009, para. 6.29). The exclusion is stated as a consequence of what can be valued, and what cannot be valued drops out of the national product. The fourth is the redesign of a field’s categories to satisfy statistical reliability. The Statistical Manual of 1918 was built so that asylums could report comparable figures, and the third edition of the Diagnostic and Statistical Manual of Mental Disorders in 1980 replaced descriptive accounts of disorders with explicit operational criteria whose explicit aim was agreement between raters (American Psychiatric Association 1980). Critics argued that the revision bought reliability, which can be counted, at the expense of validity, which cannot (Kirk and Kutchins 1992).
The selection was never total, and the counter-cases matter. Cholera was prominent long before anyone counted it well, because its epidemics were terrifying and visible; the sanitary movement acted on a miasmatic theory that was largely wrong, and its pipes and drains worked anyway. Accurate numbers could also be ignored. Jarvis’s corrections of the 1840 census did not stop its figures on insanity from being cited in defence of slavery. Fear, money, theory, and power shaped prominence alongside tractability. The claim defended here is therefore one of differential prominence: tractability acted as a persistent selection pressure, operating through the design of categories and accounts, so that over time the countable aspects of life accumulated evidence, institutions, and resources faster than the aspects that could not be counted. That pressure was strongest where categories and accounts were deliberately shaped to be countable, and the four kinds of evidence above show that this happened at every stage, from Petty’s preface to the reliability revolution in psychiatry.
E. Divergence conceals the common inheritance
By the twentieth century, economics and medicine possessed specialised methods, professional institutions, and literatures that rarely met. Their shared origin in political arithmetic became hard to see. The orientation persisted on both sides. Economics continued to privilege what enters recognisable accounts of production, income, transaction, and expenditure; medical statistics continued to privilege identifiable conditions, measurable impairments, recorded events, and population distributions. Neither discipline studies only these things, but these remain especially compatible with each discipline’s most authoritative mathematical techniques, and so they continue to attract evidence, funding, careers, and interventions. The convergence of the two orientations reflects a common inheritance embedded in separate institutions.
VI. The Ontology of Mathematical Selection
A. Why recursive processes cannot be modelled mathematically
Mathematics is a nonrecursive symbolic system. Its objects and operations do not alter in response to being engaged: a function returns the same value for the same argument however often it is evaluated, and a rule, once written, does not revise itself because someone has read it. A process is recursive when its subsequent course is altered by how it is engaged, so that the engagement becomes part of what happens next. A recursive process as such cannot be modelled mathematically, because any model is itself a nonrecursive deposit, and a nonrecursive deposit cannot answer back. This is an ontological limit, and no increase in mathematical sophistication, computing power, or data removes it.
The obvious objection is that mathematics models responsiveness all the time. Epidemic models represent people becoming infected and recovering; population models represent predators responding to the abundance of prey; control theory represents systems that correct their own deviations; game theory represents players responding to one another; agent-based simulations represent agents that adapt; machine learning systems update their parameters in response to data. Each of these, examined closely, represents responsiveness through a fixed specification of how the response works: a contact rate, a response function, a payoff matrix, a decision rule, an update procedure. The specification is itself nonrecursive. It models a recursive process exactly as long as the process continues to respond in the way the specification prescribes, which is to say exactly as long as the relevant aspect of the process behaves nonrecursively with respect to the model. When the living beings involved change how they respond, including in response to the model itself, the model does not follow. Its parameters must be re-estimated or its structure rewritten by the people who use it. Even a learning algorithm learns only by a procedure fixed in advance. The recursion is always located in the modellers and the modelled, and never in the model.
Nonrecursivity is the condition for direct mathematical fit, but it does not guarantee predictability or stability. The weather is nonrecursive, since the atmosphere does not respond to forecasts, and it is nonetheless predictable only over short horizons because of its sensitivity to initial conditions. Properties such as discreteness, continuity, invariance, equivalence, and separability then determine which operations fit a given nonrecursive aspect. The point concerns what mathematics can reach at all. Where a process answers back, mathematics can reach only what in it does not.
B. Mixed recursivity
Complex living processes are rarely recursive in every respect. They have mixed recursivity, combining recursive aspects with nonrecursive ones. Recursivity admits no degrees: a given aspect either answers back to its engagement or it does not. What varies from process to process is the composition, which aspects are which, and how much of the outcome of interest each carries over a given period.
An epidemic is a clear case. The replication of a pathogen within a host, the distribution of incubation periods, and the probability of transmission per contact under given physical conditions do not respond to how the epidemic is described: the virus does not read the forecast. The patterns of contact between people, their decisions to seek care, their compliance with advice, and the policies of governments respond continuously to what people know, fear, and are told, including what the models say. Epidemic models are reliable to the extent that the quantity of interest is carried by the nonrecursive aspects over the period being modelled. Early in an outbreak, before behaviour has changed, they can perform well; once people and governments respond, the contact parameters that the model held fixed begin to move.
The same structure governs prediction. A future is mixed: some of it is already settled and some of it remains open to what living beings will do. Forecasting succeeds where it latches onto what is settled. Demographic projections illustrate this precisely. The number of people who will be sixty years old in 2050 can be projected with considerable confidence, because they have already been born and the projection depends chiefly on mortality, which changes slowly. The number of children who will be born in 2050 cannot, because it depends on decisions not yet taken by people who are themselves not yet adults, and fertility assumptions are notoriously the weakest element of every population projection. Pension systems, health services, and fiscal planning rest on exactly this asymmetry. Prediction isolates the nonrecursive aspects of the future just as modelling isolates the nonrecursive aspects of a process, and both are reliable to the extent that what they isolate carries what matters.
The hypothesis can now be stated in full. Complex living processes have mixed recursivity, and whatever mathematical models are used to describe them isolate their nonrecursive aspects. Mathematical selection is the historical consequence. Where institutions came to rely on mathematical representation, the nonrecursive aspects of life, the deaths, areas, payments, lesions, and test results, were the aspects that could be brought into their instruments, and so they were the aspects that accumulated knowledge and authority. Petty’s preface records the moment of choice: the arithmetician takes the causes that do not answer back, and leaves the mutable minds, opinions, appetites, and passions to others.
C. What economics discovered about itself
Economics has repeatedly encountered this limit in its own terms. In 1928 Oskar Morgenstern argued that economic forecasting by quantitative methods was impossible, and illustrated the problem with Sherlock Holmes fleeing Professor Moriarty: if each could perfectly foresee the other’s response to his own foresight, their choices would dissolve into an endless regress (Morgenstern 1928). Robert Merton described the self-fulfilling prophecy, in which a false definition of a situation produces the behaviour that makes it true, with the run on a sound bank as his example (Merton 1948). Charles Goodhart observed that any statistical regularity tends to collapse once pressure is placed on it for control purposes (Goodhart 1975). And Robert Lucas showed that the parameters of econometric models are not invariant to policy, because the people whose behaviour the parameters summarise change that behaviour when policy changes; models estimated on past data will therefore mislead whenever they are used to evaluate new policies (Lucas 1976).
Each of these is a discovery of recursivity from inside the discipline. The response to the Lucas critique is equally revealing. Macroeconomics sought “deep” structural parameters, preferences and technology, that could be assumed invariant to policy, and rebuilt its models on them. That is to say, it looked for nonrecursive aspects beneath the recursive surface and isolated them again. The strategy is the only one available to mathematics, and its success is bounded by the extent to which the deep parameters really do not answer back. When they too move, in financial crises, in shifts of expectation, in changes of what people take to be normal, the models fail in the way the ontology predicts.
D. What epidemiology discovered
Mathematical epidemiology followed the same path. Ronald Ross’s equations for malaria and the model published by William Kermack and Anderson McKendrick in 1927 represented transmission through fixed rates of biting, contact, and recovery (Ross 1911; Kermack and McKendrick 1927). Their power, which is real, comes from the nonrecursive aspects they isolate. Their limit appears whenever behaviour becomes the decisive factor. In March 2020 the Imperial College COVID-19 Response Team estimated that an unmitigated epidemic would cause around half a million deaths in Great Britain (Ferguson et al. 2020). The projection helped bring about the interventions that ensured it would never be tested. A forecast of this kind is consequential precisely because it enters the recursive process it describes, and that entry is exactly what the model cannot contain. The model was a nonrecursive deposit; the government, the public, and the epidemic responded to it. Without implying that the model was wrong, the episode shows that its conditional statement, if contact rates remain as they are, isolated a nonrecursive aspect that the living process, once informed, refused to keep.
E. Selection without distortion
Mathematical selection does not require distortion. Counting deaths need not misrepresent them; measuring blood oxygen saturation need not misrepresent the property measured; calculating the area of a field can be entirely appropriate. A model that isolates the nonrecursive aspects of a process can describe those aspects accurately. The selection operates because success with such aspects encourages the extension of measurement to others, because institutions come to prefer objects that fit their existing techniques, and because the recursive aspects, which no model can contain, are then treated as noise, residue, or context. This can happen when every individual measurement is accurate. A science can be accurate about the phenomena it measures while remaining systematically selective about which phenomena it recognises as important. That proposition locates the problem of quantification earlier than the usual debates about the validity of indicators, at the prior selection of the objects that indicators are built for.
F. Four stages of mathematical selection
The history suggests a recurring process in four stages. First, certain aspects of living become identifiable as bounded events, states, or quantities: a death, a parcel of land, a payment, an infection. These are, almost always, the nonrecursive aspects of mixed processes, or the nonrecursive traces that recursive processes leave behind. Second, these aspects acquire durable symbolic counterparts through records, classifications, and measurements: an entry in a bill, a map, a ledger line, a test result. Third, the symbolic counterparts become amenable to increasingly sophisticated mathematical operations, from Graunt’s ratios to life tables, national accounts, and statistical models. Fourth, institutions organise resources, interventions, and definitions of success around the resulting indicators. The process reinforces itself. The more successfully a phenomenon is measured, the more evidence accumulates around it, and that evidence supports new investigations, professional specialisations, funding systems, and interventions. The recursive aspects of the same processes remain underdeveloped as objects of knowledge, because they cannot enter the infrastructure at all.
G. Persistence is not nonrecursivity
It is tempting to suppose that diseases become prominent objects of institutional attention when they do not resolve through the body’s own restorative processes, and persistence may contribute to that prominence. But persistence is a different property from nonrecursivity. Tuberculosis infection may be contained by the immune system for long periods. Malaria infections can clear without treatment in some circumstances, particularly in people with acquired immunity. HIV ordinarily persists without antiretroviral therapy, although host responses vary. Pathogens are responsive organisms, and their persistence may depend precisely on their interactions with immune responses. What a disease programme counts are the nonrecursive aspects of these mixed processes: a positive test, a notified case, a death, a dose dispensed. The historical hypothesis can be stated more precisely: conditions whose decisive aspects can be identified, recorded, and addressed by standardised intervention may be especially well suited to the construction of durable disease programmes, of the kind that came to dominate global health in the late twentieth century. That hypothesis should be investigated case by case.
VII. Things and Signs: The Two Poietic Mediations in the Government of Life
A. Three couplings
The strongest cases in this history show mathematical representations becoming consequential through material interventions. The relation between the two poietic mediations is therefore no side issue. It takes at least three forms.
The first coupling runs from things to signs. Material arrangements determine which symbols can be produced and how well they fit. Petty’s chains and compasses made acreage available as a number; the searcher’s visit to the house, with its body, its witnesses, and its coins, produced the word that entered the bill; standardised instruments, from the thermometer to the rapid diagnostic test, decide what can be recorded and compared. Snow’s comparison is the clearest case. The intermixed pipes of two water companies had already sorted the households of south London into two groups without regard to class, occupation, or belief, and the infrastructure had thereby performed an experiment that Snow’s arithmetic could read. The fit of his numbers was made possible by the material world before any number was written.
The second coupling runs from signs to things. Symbolic representations become consequential when they direct material change. The maps of the Down Survey became confiscations, boundaries, and estates. Chadwick’s statistics became sewers and water mains. Life tables became annuities, insurance policies, and pension funds, contracts written on paper and backed by money. Farr’s tables became arguments for drainage and housing regulation. Petty’s ratio of one to eighty-four was an argument for pest houses and quarantine. In each case the number travelled from where it was produced to where decisions were made, and returned as pipes, fences, or payments to the places where life was lived.
The third coupling runs from things to living coordination. Material interventions, once successful, descend into ordinary life and cease to call attention to themselves. Water runs from a tap without anyone thinking of Chadwick; a vaccinated child does not experience the disease she has not caught; a well-drained street is simply a street. The success of such interventions is a return of coordination to the first level of recursivity, where life proceeds without articulation, and that silence generates no records. Signs are needed to justify the intervention, but once it works, the only symbolic trace of its value is the absence of events it has suppressed.
B. Portable signs, local things
The two poietic mediations differ in a way that matters for government. Signs are portable and persistent. Bills, tables, accounts, rankings, and indices travel to ministries, banks, and boards far from the lives they record, accumulate over decades, and acquire authority in places where those lives are never encountered. Things are local. A drain works in one street, a water main in one district, a clinic in one town. The consequence is that material interventions are judged, where decisions are made, almost entirely through the signs that represent them. A sewer that prevents disease is assessed by the deaths that did not occur, a vaccination programme by the cases that were averted, a clinic by its throughput.
The Broad Street pump shows the asymmetry in miniature. At Snow’s urging the parish authorities removed the pump’s handle on 8 September 1854. The act was material, local, and immediate. Snow himself acknowledged that the outbreak was already declining when the handle was removed, so that the intervention’s effect on that epidemic could not be demonstrated in numbers (Snow 1855). The handle became the emblem of epidemiology, but the evidence that carried scientific weight was the comparison of the water companies, which the material world had arranged and the arithmetic could read.
C. Money and macroeconomic government
Money is the poietic hybrid on which macroeconomic government rests. It has always been multimaterial and multisymbolic at once, from Petty’s coins, whose debasement and circulation he analysed, to the ledger entries, central bank reserves, and payment systems of the present, which remain material records held in vaults and on servers even as their derivational distance from metal has grown. Macroeconomics governs almost entirely through this hybrid and through the accounts that represent it: interest rates, money supply, fiscal balances, national product. Its instruments act on multimaterial production, on factories, harvests, houses, and supply chains, and through them on the living conditions of entire populations, but it encounters those conditions only in the form its accounts can register. Public health has always had a second anchor in material interventions whose effects can be felt in the mesocosm, in cleaner streets, fewer funerals, and children who grow. Macroeconomics has a weaker anchor of this kind, which is why the selection described here is more nearly complete in economics, where what the national accounts do not register has scarcely any institutional existence.
D. Consequences for selection
The three couplings explain how mathematical selection becomes material. Signs decide, in the currency of what they can register, which material interventions are made; material interventions, once successful, return coordination to silence; and silence gives the signs nothing further to register. Interventions with legible outcomes are favoured whatever their wider consequences, while interventions that sustain coordination without producing countable changes are starved. The danger is greatest where the material anchor is weakest, and where the recursive aspects of a process, the care, trust, and adaptation through which people keep well, are the aspects that carry most of what matters.
VIII. Breakdown and Healing
A. The corpse as teacher
Medicine’s privileging of recordable breakdown over the coordination that maintains and restores health has a history, and its foundations were laid in the same decades as Chadwick’s statistics. The clinical medicine that took shape in Paris around 1800 located disease in lesions that could be seen in the body after death. Xavier Bichat’s injunction to open up a few corpses, so that the darkness left by observation of the living would be dispelled, became the programme of pathological anatomy, and Michel Foucault showed how it reorganised medical knowledge around the visible lesion and the dead body (Foucault 1973). A lesion found at autopsy is a nonrecursive trace par excellence. It no longer responds to anything, and it can be described, compared, and counted. The living processes of compensation and repair that had held the patient together until death left no comparable trace.
B. Hospitals, friendly societies, and the record of sickness
Institutional records reinforced the same orientation. Hospital registers recorded patients as admitted and then as discharged cured, relieved, or dead, so that healing appeared only as a category of exit. When morbidity first became countable on a large scale in Britain, it was through the sickness records of friendly societies, mutual insurance associations whose members claimed benefits for days of incapacity. James Riley’s reconstruction of these records shows how much they reveal about the health of working men during the mortality decline (Riley 1997). It also shows the form in which sickness entered the record: as a claim, a period during which a man could not work. Health appeared as the absence of claims. The coordination through which members stayed at work, recovered without claiming, or were nursed by their families entered the books only by not appearing in them.
C. Healing as a nuisance parameter
The older medical traditions had a name for the body’s own restorative coordination, the vis medicatrix naturae, the healing power of nature, and Hippocratic and Galenic physicians organised their practice around supporting it. Modern evaluation turned it into a quantity to be subtracted. In a controlled trial, recovery that occurs without the intervention appears as the improvement in the control group, together with regression to the mean and the placebo response, and the effect of the intervention is what remains after this baseline has been removed. The trial is a powerful instrument, and the subtraction is its strength. But the body’s own healing enters its mathematics only as a nuisance parameter, the background against which a countable effect can be detected. The structure follows from the ontology. An intervention is a discrete act, administered at a known time in a known dose, and can be treated as a nonrecursive variable; endogenous healing is recursive coordination, altering in relation to its own ongoing state and to everything around it, and can be represented only by its aggregate outcome in those who received nothing.
D. The fracture and the silence of the organs
A bone fracture shows the contrast between breakdown and healing at its simplest. A fracture is a comparatively distinct event with clearly measurable anatomical properties, visible on an image as a line. Many fractures are never recorded: people without access to imaging, or with minor breaks, may recover without seeking care, and fractures enter health statistics chiefly when they are treated. A system that depends on clinical records therefore registers treated fractures more readily than all the fractures occurring in a population. The deeper point concerns healing. Bone repair is an ongoing biological coordination that often proceeds without any clinical intervention, and the restoration of function involves compensation, adaptation, and the reorganisation of everyday life around a temporary incapacity. Union, when it is recorded, is recorded as a radiographic criterion, a second nonrecursive mark that closes the episode opened by the first. Restoration of health is not the numerical reversal of a pathological event. The Global Burden of Disease includes fractures and models their durations, and its enumeration of them is a real achievement; it does not amount to a representation of healing as living coordination.
Georges Canguilhem gave this insight its classic form. Quoting the surgeon René Leriche, he described health as life lived in the silence of the organs, and he understood it as a capacity to tolerate variation and to institute new norms, in contrast to a pathological state, which narrows the range of norms a living being can sustain (Canguilhem 1989). Living Value Theory places that silence at the first level of recursivity, where coordination proceeds without calling attention to itself. Healing tends towards that silence, and silence generates no records. Breakdown leaves nonrecursive marks: the lesion, the fracture line, the claim, the death. Healing is recursive coordination and leaves none. Misfit leaves symbolic traces, and fit leaves none.
E. A burden of disease and no burden of health
The World Health Organization’s constitution of 1948 defined health as a state of complete physical, mental, and social well-being and not merely the absence of disease or infirmity (WHO 1948). The statistics through which health was governed in the following decades remained statistics of death and disease, and the most ambitious health metric of the late twentieth century was named, accurately, the burden of disease. Even measures of healthy life expectancy are computed by subtracting the estimated prevalence of disease and disability from years of life. Health appears in these metrics as a remainder.
This is the counterpart in health of the economic problem of unpaid care, and it may be the most distinctive consequence of mathematical selection. In both cases, ongoing value-sustaining coordination remains largely invisible while its failure generates recognisable events and costs. In both, the reason is the same: the coordination is recursive, its failures leave nonrecursive marks, and mathematics can reach only the marks.
IX. The Global Burden of Disease: A Universal Mathematics of Ill Health
A. The World Bank reunites the two arithmetics
The World Bank’s World Development Report 1993: Investing in Health is the moment at which the two strands of political arithmetic were formally reunited (World Bank 1993). The report introduced the disability-adjusted life year, which combined years of life lost through premature death with years lived with disability, weighted for severity, into a single measure of health loss. Combined with estimates of the costs of interventions, expressed as dollars per DALY averted, it allowed the Bank to rank interventions and to design an essential package of services for low-income countries. Population illness became a standardised numerical burden; interventions became comparable in terms of cost and estimated benefit; health priorities could be represented within an apparatus of calculation that was simultaneously medical and economic. Petty’s ratio of one to eighty-four between the cost of plague measures and the loss they would prevent has a direct descendant in the cost-effectiveness tables of 1993. A DALY is a unit of health time, and monetary cost-effectiveness analysis is a further operation performed with it, but the two were designed to work together.
B. The GBD challenges its inheritance
The GBD did more than continue the old selection. By moving beyond mortality, it revealed health losses that earlier statistical systems had neglected. The original estimates attributed about a tenth of all health loss worldwide in 1990 to neuropsychiatric conditions, placed unipolar major depression among the leading causes of disability, and projected that it would rise further (Murray and Lopez 1996). This challenged representations of population health centred on death and infectious disease, and it gave advocates for mental health a powerful argument. In this respect the GBD represents an effort to overcome the bias inherited from political arithmetic.
It does so by creating new mathematically tractable objects: standardised health states, disability weights, durations, and modelled population estimates. That produces the central tension. The GBD expands what medicine can count while retaining the assumption that heterogeneous forms of ill health can be compared through a common unit, and it brings into its arithmetic precisely the kinds of condition, such as depression, whose mixed recursivity is most pronounced. What it counts for depression are the nonrecursive aspects that an instrument can fix: a score above a threshold, a diagnosis entered, a health state matched to a weight. The recursive aspects of distress, which change with how it is recognised, named, and responded to, are the aspects the unit cannot contain.
C. The problem is what counts establish
It would be a mistake to conclude that the GBD should count fewer illnesses. The more interesting problem is what its counts are allowed to establish. A disability estimate may illuminate an important problem and also leave much of that problem’s living significance outside the mathematical account. Both statements can be true. The relevant question is whether the GBD’s mathematical successes are being extended beyond their ontological fit. The estimates themselves are second-order deposits, assembled from vital registration, household surveys, hospital records, published studies, and verbal autopsies, in which trained interviewers ask relatives about the symptoms and circumstances that preceded a death so that a probable cause can be assigned. The verbal autopsy is the searcher of the dead in modern form, and the problems Graunt identified, of identifiable and ambiguous causes, of conditions conjoined with others, of what a visitor to the house can and cannot discern, have not disappeared. Ethnographic research on the production of the estimates shows how apparently unified figures are built from heterogeneous observations, classifications, models, and institutional judgements, and how they move between the World Bank, the World Health Organization, and the Institute for Health Metrics and Evaluation (Tichenor and Sridhar 2019; Gaudillière and Gasnier 2020). And the GBD remains, as its name says, a burden of disease: a vast and sophisticated accounting of breakdown, in which the coordination that keeps people well appears only as the losses it has prevented.
X. Conclusion: The Mathematical Selection of Living Value
Political arithmetic, far from discovering a world already organised as a complete set of measurable quantities, selected aspects of the world that were amenable to mathematical description and built powerful forms of knowledge around them, in a programme that from the start joined the arithmetic of health to the arithmetic of wealth. Those forms of knowledge produced remarkable achievements. They made mortality patterns visible, identified causes of disease, justified sanitation and prevention, and enabled increasingly sophisticated investigations of population health. They also established an enduring tendency to privilege the measurable aspects of living processes over forms of coordination that yielded no comparable objects. Economics came to represent prosperity through accounts of production and exchange; public health came to represent the health of populations through registered events, classified conditions, and measurable outcomes. The GBD inherited both the achievements and the limitations.
The selection has an ontological root. Complex living processes have mixed recursivity, and mathematics, being nonrecursive, can reach only their nonrecursive aspects. Every model of responsiveness isolates a fixed specification of how response works; every forecast isolates what in the future is already settled. Economics discovered the limit as the Lucas critique and Goodhart’s law, epidemiology as the forecast that changes the behaviour it forecasts. Where institutions governed through mathematics, the nonrecursive aspects of life were the aspects their instruments could hold, and breakdown, which leaves nonrecursive marks, was privileged over healing, which leaves none. Macroeconomics and public health govern and enhance life through things and signs. Their material instruments can return coordination to silence, and their symbolic instruments decide, in the currency of what they can register, which material instruments are made.
The greatest bias of mathematical inquiry may lie earlier than any error of calculation or inaccurate measurement, at the point when the properties that make something mathematically tractable also make it more likely to become an object of scientific knowledge, institutional intervention, and political concern. The histories of economics and public health show how this selection can become embedded in entire disciplines while every measurement they make remains accurate. The question is therefore whether mathematics describes ill health correctly, and also whether the mathematical selection of illness has shaped what medicine and government recognise as health and disease in the first place.
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