Chapters 2 and 3 on proportion and infinity and chapter 7 on symmetry concern foundational topics in mathematics and also the arts. From antiquity through to modern day the ideas are interwoven within and across personalities, history and the development of thought and a never ending quest for knowledge and meaning.
The diagrams in chapter 2 work very well illustrating the literal transformation of the representation of 3D space on a 2D plane. Linear perspective then presented it own challenge for artists, the human figure correctly proportioned against architecture that can dominate space, as intended, but on a canvas?
I have long laboured the point that in Hodges' model, it takes physical and emotional labour to put the patient (person, carer, student, ...) at the center of the model. In art, Alberti suggested putting the vanishing point in the center of a painting to achieve an overall symmetry (p.81). We realise of course that comprehensive, non-judgemental, person-centredness also relies on political labour too.
In chapter 3 on infinity, the 'frightening' aspect of the concept is highlighted from the outset in the work of Cantor, even before discussing rational and irrational numbers. As much as we clearly seek to reduce phenomena, it is fascinating; the human drive to unify, synthesize and discern some higher Absolute order. The existence of free will was subject to question (C. 19th) and is still debated today, with probability calculations and quantum mechanical additions. Although we might understand a concept in a certain disciplinary context, the conjunction of disciplines (art and mathematics) and the meaning of terms abstract and objective (and hence subjective) are instantly and usefully perturbed. That's what I enjoyed about reading this.
In the first post on Gamwell's book I suggested the (oh so real!) mystery of mathematics for me. The book could have been a challenge in terms of explaining complex mathematics, but this 'tome' rewards rather than confounds the reader.
In chapter 3 you will find 'set theory' and Cantor's Actual infinity. At the risk of contradicting myself, aleph-zero, aleph-null et al. are worth (require) re-reading. Gamwell provides the titles of other key texts, some dating to the earliest writings and with some background. Gamwell refers to friar Giodano Bruno and the plurality of worlds, another very early reference to SETI. A reminder of a book to pick up again, with Leopardi Giacomo in the Zibaldone: infinity, (other) beings and nihilism too?
Like you perhaps, I have seen this engraving many times:
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Camille Flammarion:
L'atmosphère météorologie populaire.
Paris 1888 |
As if often the case, there is more to this than meets the eye.
Thanks to Gamwell (p.126) I can see Hodges' model not only as "the place where four roads meet" but:
"In this nineteenth-century popular science on meteorology, an anonymous engraver depicted a medieval cleric who, like Bruno, imagined that beyond the fixed stars on the dome of the heaven were other suns, other worlds, and, according to a vision of the Hebrew prophet Ezekiel, a spirit-filled chariot with "a wheel intersecting a wheel" (shown in the upper left-hand corner) that could magically roll in four directions...".
individual
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INTERPERSONAL : SCIENCES
humanistic ----------------------------------------------- mechanistic
SOCIOLOGY : POLITICAL
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group - population
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Cantor's real number axis, he called "the continuum", it is dense. p.123.
statistics
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STATISTICUS
(Latin: 'of the state') p.120.
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More to follow ...
Lynn Gamwell (2016)
Mathematics and Art: A Cultural History. Princeton, New Jersey: Princeton University Press. ISBN: 9780691165288. p.283.
(Thank you to PUP and I must add John Wiley for the review copy - more to follow.)
Source image:
Camille Flammarion: L'atmosphère météorologie populaire. Paris 1888.
https://www.researchgate.net/publication/267625072_Feasibility_of_Parallaxes_with_CoRoT
orcid.org/0000-0002-0192-8965
