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**The mangle of practice: time, agency, and science.**
*(English)*
Zbl 0834.01019

London: Univ. of Chicago Press. xiv, 281 p. (1995).

The author’s theory of how science, technology, and society interact to produce the things they produce, centers on his concept of “the mangle”. As an overall scheme, the mangle provides a view of science “as an evolving field of human and material agencies reciprocally engaged in a play of resistance and accommodation in which the former seeks to capture the latter” (p. 23). Given a concern with such a general dialectic it is not surprising that the author concludes the book by speculating about his product as a “theory of everything”. The mangle appears in various guises in the book as it is applied in examples from physics and technology (the bubble chamber, the hunting of the quark, and computer-controlled machine tools) and mathematics.

The mathematical example is that of William Rowan Hamilton and the problems giving rise to quaternions as, respectively, the human agent and the concepts that correspond to the “material agencies” in the author’s physical examples. Quaternions have been a favorite example of philosophers and sociologists of science because Hamilton conveniently documented his progress and explicitly linked his mathematics to a philosophical point of view (algebra as the science of pure time).

Refreshingly the author adheres closely to the documentary evidence and concludes that Hamilton was primarily guided by the mathematics of the problem. Thus, contrary to D. Bloor’s analysis in [Hamilton and Peacock on the essence of algebra, pp. 202-232 in Social History of Nineteenth Century Mathematics, H. Mehrtens, H. Bos, and I. Schneider (eds.) (BirkhĂ¤user, Boston, 1981)], the author believes that in his mathematical practice Hamilton “was struggling through dialectics of resistance and accommodation, reacting as best he could to the exigencies of technical practice, without much regard to or help from any a priori intuitions of the inner meanings of the symbols he was manipulating” (p. 155). To the extent that the mangle concept facilitates comparison between Hamilton’s discovery and the other endeavors analyzed by example in this book – “the development of experimental apparatus, the production of facts, the creation of theory, and the interrelation of machines and social organization” (from the back cover) – it appears to be a useful concept.

The mathematical example is that of William Rowan Hamilton and the problems giving rise to quaternions as, respectively, the human agent and the concepts that correspond to the “material agencies” in the author’s physical examples. Quaternions have been a favorite example of philosophers and sociologists of science because Hamilton conveniently documented his progress and explicitly linked his mathematics to a philosophical point of view (algebra as the science of pure time).

Refreshingly the author adheres closely to the documentary evidence and concludes that Hamilton was primarily guided by the mathematics of the problem. Thus, contrary to D. Bloor’s analysis in [Hamilton and Peacock on the essence of algebra, pp. 202-232 in Social History of Nineteenth Century Mathematics, H. Mehrtens, H. Bos, and I. Schneider (eds.) (BirkhĂ¤user, Boston, 1981)], the author believes that in his mathematical practice Hamilton “was struggling through dialectics of resistance and accommodation, reacting as best he could to the exigencies of technical practice, without much regard to or help from any a priori intuitions of the inner meanings of the symbols he was manipulating” (p. 155). To the extent that the mangle concept facilitates comparison between Hamilton’s discovery and the other endeavors analyzed by example in this book – “the development of experimental apparatus, the production of facts, the creation of theory, and the interrelation of machines and social organization” (from the back cover) – it appears to be a useful concept.

Reviewer: A.C.Lewis (Hamilton)

### MSC:

01A80 | Sociology (and profession) of mathematics |