The everyday life of the 21st century is deeply marked by numerical rankings.footnote^{1} From creditworthiness to the international ‘ease of doing business’ index, from five-star reviews of films or restaurants to the ‘impact factor’ of scholarly journals, they not only serve to describe and evaluate the world, but also in some respects help to change it. Evaluative lists as such are nothing new, of course; they have existed since Antiquity. The ‘canons’ of exemplary works compiled by Hellenistic philologists were of this type; but these depended largely upon critical-aesthetic evaluations. Vice versa, purely commercial lists—bestsellers, top tens and so forth—made no pretence of establishing artistic value. Operating in the medium of the digit, the specific authority that rankings have assumed today derives from their claim to be the result of numerically established worth. What are the origins of this type of valuation? In which domains did it first emerge? The answers lead to an epoch and a field of knowledge not normally associated with rankings: the 18th-century critics of European art and literature, who developed quantitative models of *comparatio*.

In classical rhetoric, *comparatio *or *syncrisis *is evaluation by means of comparison: it is an agonistic method in which persons, positions or objects are contrasted, with the intention of establishing an axiology of comparison. As such, it is a form of criticism whose contrastive oppositions also open up cognitive opportunities. Practices of *comparatio *have therefore been considered a key moment in the ‘pre-history’ of comparative studies. What has been largely overlooked, however, is the fact that a ‘new’ practice of *comparatio *established itself between 1700 and 1800, which employed quantitative procedures but was no longer content with merely contrasting two objects. For the first time, a quantifying system established itself as an aesthetic model, its numerical processes of argumentation and evidence production serving to guide the evaluative work of *comparatio*.

It was in Paris in 1708 that the art connoisseur and collector Roger de Piles (1635–1709) published the first numerically based aesthetic ranking. De Piles had served as secretary at the French Embassies in Venice, Spain and Portugal, and travelled widely in northern Europe—Germany, Austria, the Netherlands—collecting art works for Louis xiv. He played a leading role (as a *rubeniste*) in 17th-century aesthetic debates on line and colour, Poussin versus Rubens, classical proportion or ‘modern’ brushstroke. De Piles’s ‘Scale of Painters’ appeared as an appendix to his final treatise on painting, *Cours de peinture par principes*. Here he listed, alphabetically, the fifty-seven ‘best-known’ painters and awarded them numerical values according to a four-part categorical apparatus—composition, drawing, colour, expression—which also underpinned his analytical description of images (Figure 1). The painters could achieve a maximum of 20 points in each category. Thus, Titian gets a mere 6 for expression, but 18 for colour and 15 for drawing, or line. Rubens is weaker on drawing, but notably stronger on composition, colour and expression. The fact that de Piles did not aggregate the individual scores into an overall figure does not mean he did not intend for this to be done. Rather, he explained, the Scale is expressly designed so that, ‘by gathering all the parts found in the Works of each Painter, one can judge the weight of the whole.’footnote^{2}

De Piles’s contemporaries—for instance, Jean-Baptiste Dubos (1670–1742), author of *Critical Reflections on Poetry and Painting *(1719) and secretary of the Académie Française—praised the ‘Scale of Painters’. It became the pattern that guided the critical rankings devised by Enlightenment thinkers over the course of the 18th century. Diplomat that he was, de Piles remarked that his attempt had been made ‘more to amuse myself than to win others to my views’.footnote^{3} French mathematicians of the mid-18th century took it more seriously. Foremost among them was Jean Jacques d’Ortous de Mairan (1678–1771), editor of the *Journal des sçavans*, whose interests spanned the natural sciences, from the geometrical measurement of seasonal variation in the obliquity of the Sun’s rays to the *aurora borealis *and the circadian rhythms of plants. As he explained in his ‘Remarks on the Scale of Painters’ (1755), de Mairan understood de Piles’s tabulation as a project of critical-aesthetic calculus, part of a larger scientific project of the mathematization of knowledge. Pascal, Fermat and Gombaud, the ‘Chevalier de Méré’, had already applied the ‘spirit of calculus’ to games of chance—laying the basis for what would later be known as probability theory. Other contemporary mathematicians aimed to go further, applying it to ‘policy matters, medicine, morality’—even to ‘the great art of conjecture’.

Following de Piles, but improving upon his mathematics, de Mairan hoped to apply ‘geometric’ principles to objects hitherto ‘subordinated to taste’.footnote^{4} He accepted de Piles’s categories—composition, drawing, colour, expression—but argued that the total merit of each artist should be seen as the product of the multiplication of their individual qualities, rather than the sum of their addition. This required that no artist be given a zero in any category: de Piles had airily given several artists ‘0’ for expression, but de Mairan corrected this to 3. In his revised version of the table, the multiplied totals of the individual values are then reduced by three decimal points, for easier comparison with what their sum would have been (Figure 2).