Book Review: iv Mathematics and Art: A Cultural History

Mathematics + Art

As a reader fascinated by the connections between knowledge and the disciplines in which it is placed, it was encouraging to note reference to "Psychophysics" (p.136) the title of a book by Fechner. This is discussed under Suprematism with the development of tools for experimental psychology and evolving consciousness. The early 1900s was a time a search for higher consciousness and not just invention but new invention, made-up words for poetry, as art strove to shed light on the mind reaching for a "transrational" level of reasoning. It seems little has changed as many artists still seek the spiritual and Absolute in their work.

Reading of psychophysics is reinforcement for me of the many disciplinary bridges of which the book presents one. In Hodges' model you often find yourself traversing psychosocial, socioeconomic, physicopolitical, psychopolitical, psychosomatic and other bridges. This book demonstrates how in the four domains (plus spiritual) of Hodges' model, art and mathematics are interchangeable with respect to mind - body (reality), the objective and subjective. There are bound to be many writings that might follow on Malevich's Black Square, his icon to the secular age. I have wondered about Hodges' model as a culturally neutral, inert space, if there can ever be such a thing. Free will and probability provides a bridge of even greater span (for me 'here') in social physics (p.145). Using mathematics to understand human behaviour. What would Quetelet make of big data today and the often 'lively' debates between psychology and psychiatry?

Chapter 4 Formalism includes a definition:

"Today we use the word "formalism" to name both the mathematical and the artistic impulse to isolate form (abstract structure), but the term has a different origin in the two fields." (p.153).

Flatland is a marvellous book (plate 4-2, p.157) as is Gamwell's outline of the perception of space: Helmholtz's learned geometry. (p.156). Key mathematicians and their work feature here; Peano, Frege, Cantor and how consistency entails existence (p.161). Language introduces noise as much as when spoken it needs air as a medium. The focus on language, meaning and poetry with resort to made up words and pictograms to analyse rhythmic patterns is fascinating. There is this too:

"The task of artists who work with paint is to provide graphic symbols for the units of our mental processes. . . . The artist's task would be to provide a special sign for each type of space. Each sign must be simple and clearly distinguishable from all the rest. It might be possible to resort to the use of color, and to designate M with dark blue, B with green." (p.171). Khlebnikov.

The book prompts you to read further: Bohm and the interpretation of Hilbert's thought, "meaning-free" and "meaningless" begs further study.

In mathematics humanity has sought to understand not just the discipline but our place in the Cosmos. In chapter 5 (pp.196-223) we learn of Leibniz's project to invent the first artificial language.

More to follow ...

individual

|

INTERPERSONAL : SCIENCES

humanistic ----------------------------------------------- mechanistic

SOCIOLOGY : POLITICAL

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group - population

	Continuous phenomena: 24 hr air temperature
	Discontinuous phenomena: Bank deposit (p.134)

Lynn Gamwell (2016) Mathematics and Art: A Cultural History. Princeton, New Jersey: Princeton University Press. ISBN: 9780691165288. p.283.

(Thanks to PUP and John Wiley for the review copy.)