IEEE Annals of the History of Computing Volume 16 Number 4 -- Reviews
Original Publication Date: 1994-Dec-01
Included in the Prior Art Database: 2005-Oct-07
Software Patent Institute
Abstract[ This record covers Pages 88 to 89 ] Reviews
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PEGGY A. KIDWELL, EDITOR
The Reviews department includes reviews of publications, films, audioand videotapes, and exhibits relating to the history of computing. Full-length studies of technical, economic, business, social, and institutional aspects or other works of interest to Annals readers are briefly noted, with appropriate bibliographic information. Colleagues are encouraged to recommend works they wish to review and to suggest titles to the Reviews editor.
John Barrow, Pi in the Sky: Counting, Thinking, and Being, Clarendon Press, Oxford, UK, 1992, 317 pp., 1 9.95.
This review was to have begun with a short homily on puns as a comment on the title of the volume being reviewed. However, criticism, explicit or otherwise, of this subject in the Annals may not be wise since an article on the history of the lambda calculus that appeared a few years ago began with the statement that "Kleene-ness is next to Godelness."~ So let us just say that however we may feel about the use of puns in formal writing, the use of one as the title of this book should not deter the prospective reader.
Pi in the Sky gets its title from the Platonic view that mathematics is a form of objective numerical truth. In the words of the author in the last chapter, which is a long discussion of the realist or Platonic view of mathematics:
There is an ocean of mathematical truth lying undiscovered around us: we explore it, discovering new parts of its limitless territory. This expanse of mathematical truth exists independently of mathematicians. It would exist even if there were no mathematicians at all -- and, indeed, once it did, and one day perhaps it will do so again. Mathematics consists of a body of discoveries about an independent reality made up of things like numbers, sets, shapes, and so forth. "Pi" really is in the sky.
This book is a development of an argument begun in the last chapter. "Is 'pi' really in the sky," of the author's recent Theories of Ever thing.2 A summary of much of the material in the book is given in his more recent article in the New Scientist.3
Most of the book is devoted to a very readable account of the several views of mathematics that have been held by mathematicians and users of mathematics: the logistic view that mathematics is an extension of logic, the intuitionist view that mathematics includes only those results that may be derived from basic axioms in a finite number of steps, the formalist view that mathematics consists of all possible deductions from all possible sets of consistent axioms...