The Rise and Fall of the “Personal Equation” in American and British Medicine, 1855–1952

Abstract

Originating within astronomy as a technical term in the first half of the 18th century, the term "personal equation" spread into a litany of other fields including medicine, where it was used widely and variously from the late 19th century to the middle of the 20th century. We explore the personal equation in the medical literatures of the United States and Britain through a systematic analysis of over 700 articles in four prominent medical journals in conjunction with additional relevant source materials. After tracing the term's dispersion from astronomy into medically allied fields, we examine its striking polysemy while using its rich usage as a lens to examine prevailing tensions within contemporary American and British medicine. Stretching from patient and clinician variability to observer variability and error, the personal equation's various meanings reflect debates about the art and science of medical care that persist into the present day. Perspectives in Biology and Medicine M edicine today, as both art and science, embodies a split personality. The ensuing tension-between individualized consideration, experience, and judgment on the one hand, and standardization, objective evidence, and guidelines on the other-plays out in the simultaneous aspirations of the medical humanities and evidence-based medicine, and in a host of other telling terms and movements. This is not a new tension, however. We turn in this paper to the critical but complex history of the term "personal equation" as both reflective and generative of this tension on both sides of the Atlantic during a formative period in medicine from the mid-19th through the mid-20th centuries. The term was featured in almost every realm of medical practice, entering prominent medical dictionaries, books, journal articles, orations, and conference proceedings. 1 In clinical, laboratory, and research settings, medical authors at various times considered the personal equation to be worthy of consideration, study, admiration, dread, cultivation, and control. The tension it reflected and engendered remains long after the term has been discarded. As we consider the language we mobilize and are influenced by today (including terms like "personalized medicine"), it is instructive to dig down into the complex manner by which terms can be introduced, invoked, and even discarded by an evolving and ever-complex profession. Historians of medicine have largely ignored the "personal equation," while historians of science have principally associated it with the disciplines of astronomy and psychology, leading one observer to claim that the personal equation was rarely used outside of these disciplines (Olesko 2003). In recent years, Jimena Canales (2009) has revised the standard account of the personal equation in the history of science by showing the wide disciplinary breadth of usage of the term (in fields ranging from anthropology to physics and mathematics), opening up the history of the personal equation in a way that has yet to be built upon in the history of ...

Insights from full-text analyses of the Journal of the American Medical Association and the New England Journal of Medicine

“…Methodologically, it may be noted that one of us had previously manually traced the rise and fall of the term ‘personal equation’ in the medical literature from 1850 to 1950 as a complex, multi-faceted term at times signifying individual patient or clinician variability, at other times signifying observer bias. The rise and fall of ‘personal equation’ through the present bigram computation ( Figure 3a ) conforms well to the NEJM analysis conducted previously through examination of each instance of the term recognized by the NEJM ’s own full-text search tool ( Brinkmann et al, 2019 ).…”

The ‘personal equation’ as observer bias, and proposed methods to contain it in Anglo-American medicine

“…It offset observer bias by blinding clinician-evaluators as to which remedy they had in fact employed in each case, while the variability of the patients and their treatments was offset by the random allocation of patients to various treatment groups, as each investigator was given five boxes with one of the two remedies being studied, and five with the other. As we have noted previously, 2 Hewlett's 32 use of the term personal equation and the actions associated with it served as a bridge to 20th-century attempts to add blinding to random allocation as key features of fair comparisons in assessing the effects of treatment.…”

“…1 We have elsewhere described the complexities of the use of the term in Anglo-American medicine between the mid-19th and mid-20th centuries, which reflected evolving concerns over the perceived art and science of medicine. 2 A principal use of the term 'personal equation' reflected concern about observer bias. It thus serves as a useful marker for examining the variety of methods invoked to reduce or remove bias and so promote fair assessments.…”