Understanding the‘ScientificRevolution’ 147
The question of innovation versus tradition was central to the major figures (and often the minor
ones) in sixteenth-century science. If one considered the scholastic tradition a barrier to science,
which of the Greeks did one call on to contest it? Copernicus claimed to be reviving an earlier
theory of Aristarchus, Galileo drew particularly on Archimedes, Kepler was influenced by Plato
and Pythagoras. In mathematics Aristotle was less important as a reference point, but the existence
of a third tradition, that of practical algebra with its disturbing Islamic parentage made for a three-
way contest; and many important textbooks start with explicit statements such as the above about
where their authors stand. In the apparently very different field of (English) literature, Stephen
Greenblatt^10 introduced the idea of ‘self-fashioning’, or what we might call the personal makeover,
as a distinctive feature of the century:
Self-fashioning is in effect the Renaissance version of these control mechanisms, the cultural system of meanings
that creates specific individuals by governing the passage from abstract potential to concrete historical embodiment.
Literature functions within this system in three interlocking ways; as a manifestation of the concrete behaviour of
its particular author, as itself the expression of the codes by which behavior is shaped, and as a reflection upon these
codes. (Greenblatt 1980, pp. 3–4)
If we stop confining the narrow application of the word ‘literature’ to the writing which is called
creative and allow the inclusion of algebra textbooks such as Viète’sAnalytic Art, Greenblatt’s
model provides a useful explanation of the projects of the new algebraists of the sixteenth and
early seventeenth centuries—Tartaglia, Cardano, Bombelli, Viète, Stevin, and Descartes. (It is of
course equally applicable to other scientists; Galileo notably was intensely aware, both as stylist
and as self-presenter, of models to be adapted and avoided; and much of what Feyerabend (1975)
presents as ‘propaganda’ could be looked at from this point of view.) The algebra texts actually solve
equations in the author’s favoured style (‘the concrete behavior of the particular author’), they
provide a model for others to imitate (‘the expression of the codes by which behavior is shaped’),
and, strikingly, they are given to programmatic statements which explain the author’s attitude to
the competing traditions and reasons for choosing a particular method or language (‘a reflection
upon these codes’). The statement which defines the author’s innovation is also a self-portrait as
the author would wish to be seen, as the extracts above show. And other aspects of Greenblatt’s
description of his self-fashioners apply easily to the mathematicians, in particular their social
mobility (p. 7) and their need of an ‘authority’ and of an opposing ‘alien’ (p. 9); as Greenblatt
points out (1980, pp. 3–4), ‘One man’s authority is another man’s alien’. However, the authorities
who shaped the mathematical discourse were (fortunately for them) unrelated to the great religious
controversies of the day, so long as the geometry of the universe was not involved. For Viète, as
his extract shows, the authorities were the ancient Greeks; while the aliens were the modern,
barbarous, and filthy (one presumes Muslim) corrupters of the ancient art.
Viète was a notable innovator who invented the first fully coherent algebraic notation (to be
superseded by the simpler version of Descartes, which we now use). His contradictory claims
(‘new, but in truth so old’) are characteristic of modernizers of the time; renewal, as is implied
in the term ‘renaissance’ has to be presented as rediscovery.^11 His book is hard to read, partly
because of the notation (it is almost easier to read the traditional language of algebra which the
Italians derived from the Arabs); and partly because he invented a new language of procedure,
borrowing words from the Greek to describe his methods in solving problems, a language which no
- The founding father of ‘new historicist’ criticism. See (1980).
- The same strategy has been used up to the twentieth century for example, by T. S. Eliot—and no doubt after.