Philippe Campillo, PhD
Associate Professor, University of Lille, France
|Portrait of Borelli by Pierre-Roch Vigneron
Public Domain via Wikimedia Commons
Iatromathematics, also known as iatromechanics or iatrophysics, is above all a designation applied to a school of thought or to a sect of physicians. It claims to be able to subject all living phenomena to the rigors of computation, explaining all laws of physiology in terms of mechanical forces and by expressing all capacities through mathematical formulas.
The initiatory events that promoted the emergence of the iatromathematical discipline can be reduced to just a few main factors. Originally, its history was associated with that of iatrochemistry, a medical doctrine of the seventeenth century whose main representative was Franz de le Boë, also known as Sylvius (1614-1672). This discipline’s approach consisted of explaining all living functions, whether healthy or diseased, by chemical processes, such as fermentation, distillation, volatilization, alkalinity, effervescence, etc.
As iatromechanics was seen in a favorable light by the luminaries of the day, from the end of the seventeenth century, it progressively succeeded iatrochemistry over the course of a century. It was particularly through the investigations by Santorio Santorio (1561-1636), who had tried to accurately measure body temperature and pulse, that the application of measurements and calculations to functioning of the body gained momentum. Documentation of the process of blood flow, as conceived by William Harvey (1578-1657), boosted this way of thinking, thus equating the vascular system to a hydraulic machine for which the driving force or the quantity of propelled and circulating fluid can be calculated.
Similarly, the spread of René Descartes’s philosophy (1596-1650) was one of main causes of associating medicine with mathematics. He explained physiological phenomena of the body by referring to the structure and the movement of atoms. Physiology became a part of mathematics since the laws governing the movement of these atoms could be determined and calculated just like the movements of any other machine.
In Italy science and the liberty to think were given free reign. As the cradle of natural history, it was there that science was molded to comply with the rigorous laws of mathematics. Scientists could only oppose scholastic speculations by arming themselves with experimental physics, for which Galileo Galilei (1564-1642) deserves particular acknowledgement. Through the genius of his great discoveries in physics, mechanics, astronomy, architecture, and other sciences, he inspired many Italian scholars to fully embrace the study of natural sciences and experimental physics.
Towards the middle of the seventeenth century a group of Galileo’s disciples sought to develop his philosophy, cultivate experimental mechanics, and apply it to all of nature. The Accademia del Cimento (Academy of Experimentation) was founded in Florence in 1657 by Leopoldo de’ Medici and the Grand Duke of Tuscany, Ferdinando II de’ Medici, and became the main society for scientific knowledge that used Galileo’s experimental methodology in Europe. The members of this society performed many experiments, mainly in thermometry, barometry, and pneumatics using locally contrived instruments. Giovanni Alfonso Borelli, the leader of the iatromathematics discipline, trained in this academy for about ten years, where he was taught how to unite mathematics and experimental physics with the art of healing. Along with doctor and naturalist Marcello Malpighi (1628-1694), the two dissected numerous animals in order to understand anatomy.
The young Borelli, born in Naples on January 28, 1608, was under the tutelage of the Dominican monk Tommaso Campanella (1568-1639) and then Benedetto Castelli (1577-1643), a disciple of Galileo, in Pisa. For most of his life he taught at the famous chairs of Italy, in Florence and Pisa in particular (Figure 1). Yet the most original contributions of this mathematician consist of the implementation of mathematical theories and the laws of statistics regarding the constitution and functioning of living organisms and the application of hydraulics in physiology, particularly for understanding locomotion.
Before Borelli, scientists had barely examined the mechanics of muscular movement. Those who had tried to study it were engrossed in writing primarily about superfluous aspects. Concerned by this lack of rigor, he applied his thorough knowledge of mathematics to body mechanics to measure muscular forces and assess the powers of “machines” and “systems.” It should be noted that he was one of the first to make use of mathematics to understand the laws of animal use.
Borelli compiled most of his studies on living organisms in the “De Motu Animalium,” which became the highlight of his life’s work. It was published postmortem in 1680, perhaps out of fear of the views of the reigning religious inquisitor. Indeed, at that time, the Catholic Church oversaw cultural and ideological life, as well determining what written materials were sanctioned for wider distribution.
The book summarizes all the knowledge accumulated during his productive career. A career that was dedicated to teaching applied mathematics in the foremost Italian universities to promote understanding of, amongst many things, movements of living creatures, and indirectly a better understanding of life. 
|A mechanical configuration of balance. Table 10 from the book, De Motu animalium (1680). Courtesy of Collection BIU Health Medicine, Open Licence|
In this book he developed these iatromathematic concepts. It is composed of two parts: one devoted to external movements and the other to internal movements. The first volume consists of 23 chapters and 224 proposals and focuses on the mechanical action of muscles as they act on the movement of bone segments, generating locomotion such as walking, running, jumping, flying, and also swimming. He shows that the mechanics of bone movement are akin to a system of levers (e.g. support, length of the segment, the resistance, and force) for which the muscles represent the powers. He also refers to the notion that the very oblique insertion mode of these powers, such as being closer to the center of movement than to the resistance, results in an enormous loss of strength. He strived to calculate and quantify the power developed during various actions, such as balancing a load on one’s back, walking, running, jumping, etc. (Figure 2).
The second part analyzes the laws governing the functioning of major physiological systems. Divided into 22 chapters and 233 proposals, it focuses essentially on the physiology of the heart, lungs, and other organs. Borelli calculated cardiac output and described the contraction of the cardiac muscle in detail. He developed specific measuring instruments—a spirometer in particular—to determine the various volumes of the thoracic cavity. He noted that blood circulation is linked to the dimensions of the cross-sectional area of blood vessels.
Despite the lack of accuracy of the calculations, the first part of the work on the movement of animals represents an epistemological stage in the history of sciences of biomechanics, as well as for medicine. It is true that Borelli developed his mechanical explanations for all functions of the body to a point of excess, and the evaluations that he made in regard to the strength of various organs rests entirely on arbitrary assumptions. Yet these ideas contributed to more daring opinions being corrected, to the deduction of proposals, and to the development of less erroneous theories.
By adhering to the views of iatromechanics, Borelli, who was a strong supporter of the rigor of mathematical demonstrations, wished to achieve a rational understanding of the nature of humans, the mechanisms of life, of disease, and of death. For this method alone, his approach has merit as it provided a precedent, generating interest and encouraging critical assessment for the centuries that would follow him, while also participating indirectly in the development of biomechanics, physiology, as well as medicine. 
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Philippe Campillo after a thesis obtained in 1998 at Montpellier University in STAPS (Science and Technology of Physical and Sports Activities) on the biomechanical analysis of specific sport movements, he completed a second doctoral graduate level at Lille University in the discipline “Epistemology, history of science and technology”, on the theme: the history of the theories of locomotion. His perspectives and research interests are: analysis and optimization of motor performance / history and epistemology of science and biomechanics of locomotion.