1 And if clinical medicine, which Michel Foucault gave birth to at the crossroads of sensualist doctrine and anatomo-pathological [1] practice, had eluded its link to the numerical method, wouldn’t its history, which was already traversed by accidents, diverted and delayed by multiple discourses, take on a new meaning? While the clinic is today drowned under the influence of statistical and probabilistic methods, it is undoubtedly reckless to dare to put forward the idea that these two currents maintain a historical relationship. The analysis of this history, which has been rewritten and commented on many times, could suffer from the tension that arises from this family quarrel – especially when it becomes the reason for an ideological struggle.

2 But if one happens to venture into the bibliographical labyrinth, with a certain retreat with regard to canonical readings, in order to get as close as possible to exposed archives, it is striking to see how much the clinic and the numerical method are linked beyond the conflict that feeds their respective desire for truth [2]: the one aspiring to truth through the singular intuition of the sick body, the other through comparison and analogy between cases. In such a way that modern medicine has long hesitated between a medicine of phenomena and a medicine of cases (in series). Thus, to understand the construction and historical origin of the numerical method, without the clinical action in principle of the accumulation of reports and the construction of evidence, is inane.

A Foucauldian Omission

3 The bifrons of modern medicine therefore requires questioning an experience that is both qualitative and quantitative, and that is differentiated over time. [3] In fact, before the power of large numbers enthroned the numerical method as a majority theoretical practice, the latter was undermined by the power of the great names of nineteenth-century medicine. It is therefore surprising that Foucault, whose project was to raise the foundation of our clinic, [4] did not leave any room in his work for an analysis of the numerical method, and that he stops precisely where the duplication occurs –at the moment of the crisis in fevers. [5] Thus, in order to return to the double birth of the clinic, we must deconstruct the postulate that made nineteenth-century medicine “a hidden statistic” [6].

4 Although the reason for this concealment lies, above all, in the contempt in which the numerical method was held by medical historiography at the end of the nineteenth century, [7] the contemporary reader too often imagines deciphering its palimpsests in the text itself of Foucault. They wrongly believe that they are unmasking a falsification in the reduction of the probabilistic part of the clinic to the semiotics of the medical gaze. Henri Ey exhuming this “error” from the conjecture of the ancients; [8] Steeves Demazeux suspecting it in the erasure of the symptom under the Saussurian sign. [9] Victims, at bottom, of what they denounce: the one gives in to anachronism by Hippocratism, the other by a semiotic analogy. [10] By considering that the Birth participates in an occultation of history, one falsely puts Foucault on trial, who nevertheless, like a good archivist, closes his discourse precisely where the numerical method comes to duplicate the clinic of a numerical syntax. It should also be remembered that Foucault does not use a structuralist [11] approach to describe the passage from one discursivity to another—from the nosologies of the Classical Age to the modern medical gaze—but rather epistemological history. [12]

5 In Birth, the “semeiotic” [13] description of the clinic thus takes up the elements of the medical textbooks of the time [14] combined with the philosophy of Condillac – for whom the sign is the expression of a sensation. [15] It does not affix the Saussurean method to clinical language. Foucault’s archaeological method [16] uses the archive to extract the semantics of a practice of auscultation, which was that of the first clinicians. What is undoubtedly disconcerting is the fact that Birth initiates the analysis of a process of differentiation of medical experience that exceeds Foucault’s own time frame (approximately from 1770 to 1832). For this very reason, it is more a work of philosophy than of history. Hence, the analysis of the change of scale and reference point of the medical gaze, probing a body becoming ill, opens a process transforming itself in the seizure of lesions, from the tissue towards the molecular. The semantic link identified by Foucault, between the symptom and the sign thus gradually found itself confronting computational syntax, which gave a numerical turn to medical evidence. [17]

6 In such a way that the birth of the clinic is not unified. The clinic is multiple. It is arranged as an experiment always to be redone according to methods and discourses. It multiplies the theoretical practice in an act attentive to the variations of the pathological in the grip of a technological becoming of medical sciences. Although the differentiation in time of this double birth of the clinic has not been analyzed by Foucault, it is important to remember that he did not succumb to structuralism as is too often believed, nor did he lock the clinic in the tomb of Bichat and Laennec. On the contrary, he underlined a point of emergence immanent to the sick body and to the medical gaze, by which the data are formed from an intuition without number towards a computation without intuition in a semantic analogy always to be remade between the phenomenon and the case.

The Numerical Critique of Doctrines

7 In order to understand the features of this duplication, it is necessary, first of all, to reveal the historical link that unites the clinic of Bichat and Laennec with the numerical method in the confrontation of a common enemy. To do so, it is necessary to specify that the numerical method emerged from the opposition of the clinic to the doctrines of Pinel and Broussais during the Crisis in Fevers. On the one hand, Pinel’s nosography multiplied the types of fever according to the symptoms, omitting the characteristic sign: temperature. [18] On the other hand, Broussais’s physiologism considered inflammations under the universal principle of the irritability of the organs, and sought to calm them down by antiphlogistics such as leeches and bloodletting.

8 In the face of this, the clinic questioned the symptoms and lesions on the living and the dead in order to define the characteristic features of fevers as well as a therapy adapted to the singularity of the case. Pierre Louis, an illustrious disciple of Laennec, accumulated a large amount of anatomo-pathological data in his department at the Hôpital de la Charité. However, he had the brilliant idea of arranging them in numerical tables. By numerical comparison and analogy, Louis thus demonstrated that Pinel’s classification was inaccurate. All kinds of fevers were in fact related to only one: typhoid fever. [19]The multiplicity of secondary symptoms, such as ataxia or dysphagia, had deceived the great Pinel.

9 By quantifying anatomo-pathology, Louis considered a new way to study fevers. The specificity of typhoid fever left no doubt as to its contagious nature, its long duration, the immunization that is established after a single contamination and the age group that it reaches, namely 15-20 years. Except, this set of facts was in opposition to Broussais’s conception, who compared the said disease to acute inflammatory diseases. For Louis, inflammation was not the primary cause of the disease. It was secondary and manifested itself at an advanced stage. This aroused the wrath of Broussais, who devoted a large part of the fourth volume of his Examens to the criticism of Louis’s numerical method. [20]

10 At the time when the theoretical confrontation with Broussais broke out, the latter’s theoretical practice was undermined by Louis. It should be remembered that at the beginning of the nineteenth century, Broussais’s physiologism had a dominant influence on medical theoretical practice. The most emblematic gesture of this practice was none other than bloodletting in the treatment of inflammations. [21] This therapeutic consideration marks the introduction of bloodletting performed coup sur coup in the treatment of pneumonia. Supported by the theory of irritability, which postulates that “life is sustained only by excitation” [22], Broussais normalizes the act of bloodletting under the aegis of a physiological principle. The immediate effect of bloodletting, characterized by a reduction in irritation, suggests a real access to the morbid principle through the perception of the phenomenon. Except, although the inflammation disappears, the patient is not necessarily cured.

11

In 1824-1827, a controversy had arisen around bloodletting and blood emissions of various kinds; the opponents of physiology had had the idea of exploiting against him (Broussais), in particular, the administrative statistics of deaths recorded in his own department of the Val-de-Grâce; the controversy that had ensued for years in various medical journals had not failed to fix for a long time the general attention on the surprises, the powers, and the delights of this art of making numbers speak. [23]

12 In the course of this controversy against the negligence of bloodletting, Louis drew up, as early as 1828, tables referencing the cures and deaths of patients with pneumonia treated by bloodletting performed coup sur coup in his department. [24] Louis’s goal was more to establish a definitive conjecture regarding the treatment of pneumonia than to discredit Broussais’s theory. He thus highlighted that in his department, the risk of dying from bloodletting was 44% when it was carried out in the first four days of the illness. Whereas the risk drops to 25% when bloodletting is performed from the fifth day onwards, i.e. at an advanced stage of the disease. [25] Bloodletting is not abolished but regulated according to the assessment of the risk of death.

13 Against the dogmatic perspective of Broussais, Louis thus developed a strictly empirical approach that allowed for the regulation of the medical procedure according to its results. In this sense, the numerical method intends to anticipate the risks in an objective way in order to arrange the therapeutic aim. From an epistemological point of view, it is in this sense quite relevant to see in Louis’s work on bloodletting something like the premises of Evidence-Based Medicine. [26] Indeed, we find in it the idea of basing the theoretical practice of medicine on the figures provided by clinical research.

14 But what the numerical method of the nineteenth century lacked in order to achieve the status of science was simply to be accepted within the scientific community of the time. Only through the standardization of numerical practice could research data acquire the status of scientific evidence. In Louis’s time, this was not the case. The numerical method was sidelined. It worked in the margins of the clinic on numerical data that are not accepted as evidence. These data had no weight in the face of the doctrines and the observed states of affairs, because they did not fit into the criteria for the objectification of pathologies. Large numbers are no match for the factual power of the big names in medicine.

The Quarrel of Probabilities

15 Obviously, Louis’s position goes against the grain of his own clinical tradition, which sees in theoretical silence at the patient’s bed the promise of safe treatment. Whereas, for the latter, without the adjustment of therapeutic practices by figures, one sinks irremediably into ignorance of the facts. Convinced by the relevance of this numerical precept, a famous surgeon of the time, Jean Civiale, affirmed together with Louis the importance of large numbers against big names. To promote his innovative technique of crushing urinary stones, called lithotripsy, he compared the success of his operations quantitatively to those of cystotomy and other methods of treating urinary stones. His use of numbers to guide therapy earned him considerable opposition. The status of the evidence he put forward was questioned. Yet his work was as brilliant as it was innovative.

16 In defense of lithotripsy, Civiale mobilized an immense collection of data arranged in statistical tables, thanks to the assistance of the Ministers of Public Instruction, Foreign Affairs, and the Administration of Paris Hospitals. The numerical data he compared came from about fifteen countries, thirteen departments of France and four Parisian hospitals. [27] According to Civiale, “statistics” was “the only way to arrive at a solution” [28]. However, as early as 1833, his results were criticized, raising doubts about their authenticity: “Mr. Civiale claims that there are only numerous facts that can lead to the solution of the important problem […] What should we think of the accuracy of the documents […]?” [29] One then wonders if the figures do not falsify the facts.

17 Four years later, a dispute over the numerical method took place at the Académie royale de médecine. [30] Against Louis’s doctrine, Risueño d’Amador’s Mémoire sur le calcul de probabilités became a source of discord. It highlights the anachronistic aspect of the numerical method. [31] Louis is considered in discontinuity with the history of medicine. His translation of the disease into numbers is opposed to all the theoretical foundations that gave rise to the certainty of therapy. It is important to understand how iconoclastic this undertaking was in the nineteenth century. It opposed the experience of the Hippocratic centuries and reduced the medical art to statistical management –administration of life and death. Against this, physiologists and sensualists alike joined forces to reaffirm the place of improvisation and talent in medicine. [32]

18 For the sensualists, relying on statistics is tantamount to detaching oneself from the degrees of certainty of the clinical method. François Joseph Double in his Observations sur l’application du calcul à la thérapeutique refused to leave the methodological place of the medical art to mathematics. Against the numerical posture, he highlights the fact that the variability of the pathological cannot be resolved in the universality of the law of large numbers. [33] Double thus confronts the numerical method with the aporia of variability. Disease can only be grasped qualitatively because quantification erases the singularity and the unpredictable movements of the pathological in the quotient. It is a progressive temporal variation that affects the irritability of the organs; it cannot be reduced to constants and average variables. The numerical method erases in its calculations the qualitative singularity of the pathological.

The Principles of Medical Experience

19 Against this supposed aporia of variability, Jules Gavarret, a great connoisseur of Laplace’s and Poisson’s calculations, noted how “the members of this learned society had only a very imperfect idea of the use of calculus in medicine” [34]. In order to obtain fruitful therapeutic results, it was necessary, according to him, not only to establish case statistics but above all to reinforce medical judgments by the principles of probability calculation. In this sense, he extended the work of Laplace, who considered that “the entire system of human knowledge is related to the theory of probabilities” [35], by applying it to medicine. According to Gavarret, medical reasoning must itself be enveloped by mathematical formalism. The structure of probabilities is thus displaced in medical judgment. To establish this, Gavarret faces three difficulties: 1) the comparability of facts; 2) the importance of large numbers of data; 3) the oscillations influencing the result. [36]

20 Gavarret begins by demonstrating that facts in medicine refer to facts with variable chance. The latter differ from constant chance facts by the change in conditions. In a constant chance draw the number of tickets in a box does not change, whereas in a variable chance draw the number of tickets changes. It is therefore necessary to calculate the variations so as to relate the facts to the possible causes: “It suffices that during the duration of the tests no disturbance occurs in the set of causes which govern them; these causes, moreover, being able to be combined in a thousand different ways from one particular case to another” [37].

21 The first principle therefore appears in the experimental restriction of possible causes. It is necessarily accompanied by the second, which implies the accumulation of data to reduce the importance of relative differences and to highlight the determining causes of the observed phenomena: “In the search for the laws of manifestation of events with variable chance, it is by hundreds that the observations must enter into the statistics, so that the a posteriori conditions offer some guarantee and merit some confidence” [38]. The principle of the generalization of laws can only be established from the repetition of the experiment. The accumulation of data becomes a condition of possibility for experimental medicine. Without it, no inference can be made to thwart the randomness of events.

22 Finally, using Poisson’s calculations of errors, Gavarret mathematically highlights the possibility of specifying the results in a way that takes into account the oscillations of judgment: “One will always have the means of knowing within what limits of possible error a conclusion a posteriori is understood, and consequently one will avoid giving as absolute a proposition which is true only within certain known limits of oscillation” [39]. The limits of oscillation reduce the margins of error of the experiment to specify the observed phenomena. The observation is corrected by applying the calculation of probabilities to reasoning.

23 For Gavarret, these three probabilistic principles of experience make it possible to considerably solidify the numerical method, whose primary defect stems from a lack of transcendence – the absence of categories of judgment. “It is precisely in order to go beyond these limits, to acquire more extensive knowledge of these relationships, that the calculation of probabilities can become a very valuable instrument” [40]. By placing the calculation of probabilities on an empirical and transcendental level, Gavarret thought he would resolve disagreements and perfect medicine. This was not the case, as his method was so alien to the eyes of his contemporaries. This approach did not fit in with the idea of clinical talent and sagacity proper to the physician, nor with the search for the laws of nature promoted by positivism.

The Cultural Rejection of the Numerical Method in France

24 In popular culture, Louis took on the traits of Dr. Griffon – a frightening character from Eugène Sue’s novel The Mysteries of Paris. In an iconic passage of the book, Louis’s practice is criticized for its experimental coldness: Dr. Griffon considers only disease and science, never the patient and their suffering. The contemporary reader will undoubtedly be surprised to read through this novelistic description – which at the time was frightening – a draft of the way randomized clinical trials work:

25

[T]he doctor wished to convince himself of the comparative effect of some new and hazardous treatment, in order to be able to deduce consequences favourable to such or such system, he took a certain number of patients,
Treated these according to the new system,
Those by the ancient method ;
Under some circumstances, he abandoned others to the care of nature,
After which he counted the survivers.
These terrible experiments were, truly, a human sacrifice on the altar of science.
Dr. Griffon did not seem to think of this. In the eyes of this prince of science (as they phrase it) the patients of his hospital were only subjects for study and experiment.” [41]

26 It is interesting to see the fate of Louis’s numerical experiments in modern literature. In the nineteenth century, it was a monstrous medical act, considered a sacrifice on the altar of science. The numerical method was, as we can see, rejected by popular culture. It was in no way an ethical practice. According to the literary rejection and the terrifying illustrations of Dr. Griffon by Hyppolite Lavoignat, Jean-Adolphe Beaucé and Gustave Staal, the numerical method and its proponents were horrifying because of their theoretical coldness. The people, as well as the scientific community, did not see in it a medicine based on evidence but a medicine based on the sacrifice of a quota of quantified deaths.

27 Within the scientific community, the reception was all the more heated as it claimed to reveal the elements of a pseudo-science in the work of numerists. Whether in the writings of the most illustrious positivists such as Auguste Comte or Claude Bernard, the statistics and probabilities of the physicians who resorted to the numerical method were constantly set aside from the truth of science. Their results were never considered true and valid for either theory or medical practice. It was believed that it was impossible to establish laws and to constitute proofs through the numerical processing of clinical data.

28 For Auguste Comte, “such a method, if it is permitted to give it such a name, would really be nothing other than absolute empiricism, disguised under frivolous mathematical appearances” [42]. The numerical method did not correspond in any way to the method of experimental medicine, which alone could succeed in revealing physiological laws in an absolute manner. Claude Bernard’s Introduction à la médecine expérimentale is symptomatic of the legacy of this rejection of the numerical method in nineteenth-century French medicine.

29 Whether on a theoretical or practical level, the law of large numbers cannot be the basis of medicine. At the theoretical level: “Statistics […] can never yield scientific truth, and therefore cannot establish any final scientific method” [43]. At the practical level: “But physicians have nothing to do with what is called the law of large numbers, a law which, according to a great mathematician’s expression, is always true in general and false in particular” [44]. For Claude Bernard, medical judgment had to be based on the knowledge of certain biological laws and the objective measurement of their disturbances. As for practice, it could only be based on experience in the observation of symptoms and clinical signs.

Conclusion

30 As Jacques Piquemal points out, the place given to the numerical method in France at the end of the nineteenth century and the beginning of the twentieth century is that of a historical oversight: “Whether individual or collective, oversights, as we know, are rarely accidental, and the analysis of the conditions that made them possible can lead to a better understanding of a biographical episode here, or a historical movement there. Is it necessary to say this, in particular, of the persistent oblivion that has affected, in France, even the program and the work of the Parisian physicians of the first half of the nineteenth century who advocated statistics as a fundamental method of research?” [45]

31 The French context deliberately forgot the importance of the numerical method because of its epistemological marginality. Outside the realm of clinical and experimental medicine, the memory of Louis and the numerists faded in the history of nineteenth-century medicine, only to recently become a distant echo of Evidence-Based Medicine. Thus, numerists are a historical singularity that it is important for the historians of science to study today by detaching themselves from the theoretical presupposition of linear continuity.

32 For numerists [numéristes] are “true monsters”. As François Delaporte wrote: “In relation to a discipline that deals with truth, monsters appear in the space of a wild exteriority […] But because the true monster appears in a wild exteriority, contrary to the etymology of the word, it goes unnoticed: we do not see it, we do not hear it, we do not talk about it” [46]. In this historical silence, it is the multiple displacements of this forgotten tradition that can inform us about its legacy in the present. Jacques Piquemal has already emphasized the displacement of the numerical method in North American medicine. He wrote on this subject: “Louis had just found a second homeland, and even – if the theoretical foundation of an attitude were to count more than its de facto geographical and historical origin – his true homeland” [47]. It is true that Louis’s thinking helped to found modern medicine in the United States. [48]

33 In fact, a whole international network for the dissemination of clinical data was born from the Société Médicale d’Observation. Joined by more than twenty associate members, the said Société moved Louis’s thinking in time and space. Several organizations expanded the network. Henry Igersoll Bowditch founded in 1846 the Boston Society for Medical Observation on the model of the Société Médicale d’Observation, chaired by Louis from Paris, in order to extend numerical studies in Massachusetts. The objective was always to enrich the network of quantified clinical data allowing to characterize pathologies and to define adequate treatments.

34 In Great Britain, William Farr, who had followed Louis’s teachings in Paris, was put in charge of collecting statistical data on British mortality at the General Register Office in 1836. He perfected the collection of mortality data by creating a statistical nosology that he presented to the International Statistical Congress in 1855. The said nosological classification allowed the referencing of diseases within the General Register Office from 1856 onwards. It served as a basis for the drafting of Jacques Bertillon’s Classification Internationale des Maladies, which was adopted in 1901 by twenty countries.

35 This is of course only a small part of the influence of the numerical school. Louis’s network extended from metropolitan France to overseas, including England, the United States, as well as Switzerland and Mexico. The epistemological anachronism of the numerical method may find a partial explanation here through its progressive deterritorialization. Basically, were the numerists not excluded from the space and time of the Parisian clinic because their practices and theories implicitly invited the formation of a community in the epistemological space of a wild exteriority? It is indeed likely to believe this, as the numerical method is part of a global history that has yet to be written.