Saturday

As is well known, in the last quaestio of the Latin Optice (1706), Newton emphasized a similarity between the methods to be followed in mathematics and those to be followed in natural philosophy.  The English version is familiar: 

 As in Mathematicks so in Natural Philosophy (in physica) the investigation of difficult things by the method of Analysis ought ever to precede the method of Composition (methodus synthetica). 

It is not my purpose to discuss this famous, often studied, and difficult to interpret passage. Actually, I will have little to say about it. Yet, opening my talk with this quotation allows me to address a question. Which methods was Newton referring to, having a contemporary reader in mind who apparently needed few explanations on the meaning of the terms “analysis” and “synthesis”? It seems that Newton was using a terminology familiar to his readers. Indeed, analysis, or resolution, and synthesis, or composition, are terms that occur frequently in early-modern mathematical texts. Thus, my purpose is to sketch a lexical and conceptual history –  to echo the title of one of Nico Bertoloni Meli’s recent books –  of analysis and synthesis in early-modern European mathematics.

Greek and Roman pharmacological texts written in the first centuries of the Common Era depict pharmaceutical adulteration as a common phenomenon, one against which methods of product authentication and methods of fraud detection, at times complex, had been developed. They also describe the motives of those who allegedly committed fraud, merchants whose interest in drugs is solely pecuniary. While there is no reason to doubt that pharmaceutical fraud occurred in antiquity, the seemingly noble motives of those who denounced the fraud have been taken at face value and not questioned as much as they should. 

In this paper, I examine passages drawn from the writings of Dioscorides, Pliny the Elder, and Galen to explore their motives in describing fraud and ways to prevent it. I will show that these authors’ ability to access the highest quality of drugs was grounded in their pre-existing social privilege, but that social privilege does not guarantee authority. I will argue that these elite authors used the theme of fraud to bolster their own authority, one that never granted, but always contested.

Thomas Willis, in his 1659 On Fermentation (trans. 1681), compared the invisible structures of nature to a tiny army. The "little Bodies or Atoms" "seems as an Army of Soldiers placed in their Ranks, who now draw into close Order, now open their Files and Ranks, now turn to the left, now to the right hand, as is diversely shown in the exercising of Tacticks, or the Art Military." In several works, Johann Daniel Major, professor of medicine at the University of Kiel, developed Willis's metaphor of natural tactics much further as a way to think about the regular orders, movements and reactions of nature. Natural tactics appeared both on a visible level, as in the constantly shifting, yet re-emerging V pattern of geese in flight, as well as on a chemical level that could only be revealed through synthesis and analysis. Major called the latter level the Gigantomachia, the fabled war of the giants, that is, the true battle of the giants “within nature herself.” Armies of acids and bases clashed with great uproar, before joining together in treaties, embracing each other tightly. But alliances were made to be broken. This view of natural tactics inspired Major's use of hyphenated classificatory categories, which identified natural bodies as compositions of smaller cohorts of material, as well his ground-breaking Tactica Conclavium (tactics of chambers), an early museology that deployed the Kunstkammer as a battleground of experimental research.