Mathematics as sign. Writing, imagining, counting (Q2716311)

Mathematics is many things: the science of number and space; the study of pattern; an indispensable tool of technology and commerce; the methodological bedrock of the physical sciences; an endless source of recreational mind games; the ancient pursuit of absolute truth; a paradigm of logical reasoning; the most abstract of all intellectual disciplines. Two features of mathematics stand out. One is the collection of objects it deals with -- numbers, functions, graphs, spaces, categories, etc. -- that seem to be totally unaffected by space, history, or time. Do they really exist? If they do, where are they? Since our universe changes - and so does everything in it - mathematical objects must exist somewhere else. The second feature of mathematics is the language it uses: special notations, symbols, signs and diagrams. NEWLINENEWLINENEWLINEIn this book, the author challenges the widespread belief in the extra-human origins of mathematics and the understanding of mathematics as either a purely mental activity or a formal game of manipulating symbols. Instead, he argues that mathematics is a vast and unique man-made imagination machine controlled by writing and language. The book addresses both aspects -- mental and linguistic -- of this machine. The opening essay, ``Towards a Semiotics of Mathematics'' sets out the underlying semiotic model. According to this model, mathematics constitutes a kind of waking dream or thought experiment in which a proxy of the self is propelled around imagined worlds that are conjured into intersubjective being through signs. NEWLINENEWLINENEWLINEThe three themes present on all pages of the book are mathematical writing, imagining and counting: that is, the sense in which mathematics is a vast writing machine; how, in light of this sense, the activities of mathematical imagining and writing are interwoven; and what, in particular, are the ramifications of this interweaving for thinking -- or, rather rethinking -- the status of the all-too-familiar things known as whole numbers. NEWLINENEWLINENEWLINEOther essays in this book explore the status of the signs and the nature of mathematical symbols, how mathematical ideograms and diagrams differ from each other and from written words, the probable fate of the real number continuum and calculus in the digital era, the manner in which Platonic and Aristotelean metaphysics are enshrined in the contemporary mathematical infinitude of endless counting, and the possibility of creating a new conception of the sequence of whole numbers based on what the author calls non-Euclidean counting. NEWLINENEWLINENEWLINEWhom is the book for? One can argue that it is neither for mathematicians nor for semioticians. If the semiotic approach to mathematics can be made to yield theorems and be acceptable to mathematicians, then it is unlikely to deliver the kind of exterior view of mathematics it promises. If it does not engender theorems, then mathematicians will be little interested in its project of redescribing their subject. With readers in semiotics the principal obstacle is getting them sufficiently behind the mathematical spectacle to make sense of the project without losing them in the stage machinery. The presence of technical discussion is kept to an absolute minimum; but a certain dissatisfaction could present itself: the sheer semiotic skimpiness of the picture it offers. Having said that -- the book is recommended to all interested in either mathematics or semiotics. With a little effort -- invested in learning basic concepts and notions of either mathematics or semiotics -- arguments and ideas presented in the book should not be hard to follow.