Tag Archives: mathematical ideas

The Geometry of Art and Life

Hermetic Library fellow T Polyphilus reviews The Geometry of Art and Life by Matila Ghyka:

Matila Ghyka's The Geometry of Art and Life

 

This book is a genuine math book, not a mere popularization of mathematical ideas. Despite the fact that it has only 174 pages, of which 80 are dedicated to illustrative plates, full appreciation requires a slow “read” of formulas, equations, and tables — especially in the first half of the book, which treats the mathematical features of key proportions and the features of regular plane and solid figures. I was especially fascinated by the extensive discussion of Archimedean solids, which were new to me. The later chapters address the prevalence of such mathematical patterns in biological and artistic phenomena.

With respect to the “geometry of life” (which is treated before art in the book, contrary to the sequence in the title), this book shows its mid-20th-century age by being ignorant of fractal dimension and non-linear self-similarity. The mathematics of natural forms was revolutionized just one generation later than this book’s issuance. The later discoveries of Benoit Mandelbrot and others were greatly facilitated by automated computing. Still, Ghyka’s chapter on the topic is a concise summation of the earlier state of knowledge, and these concepts were not invalidated by fractal geometry.

The most significant portion of the “geometry of art” addresses the use of proportional canons in classical and gothic architecture, as rediscovered by modern scholars. Ghyka endorses a theory of the “transmission of geometrical symbols and plans” which implicates the ancient mysteries and asserts a continuity through medieval stonemasons to modern secret societies. There is no mention, however, of the further participation of isopsephy in the classical schemes. (For that, see David Fideler’s Jesus Christ, Sun of God.) The final chapter discusses conscious and unconscious applications of “symphonic symmetry” in modern art.

I enjoyed this little volume hugely, and I recommend it to anyone who shares my interests in mathematics, morphogenesis, and mysticism. [via]

 

 

The Hermetic Library Reading Room is an imaginary and speculative future reification of the library in the physical world, a place to experience a cabinet of curiosities offering a confabulation of curation, context and community that engages, archives and encourages a living Western Esoteric Tradition. If you would like to contribute to the Hermetic Library Reading Room, consider supporting the library or contact the librarian.

A Concise History of Mathematics

Hermetic Library fellow T Polyphilus reviews A Concise History of Mathematics by Dirk J Struik:

Dirk J Struik's A Concise History of Mathematics

 

This volume delivers on its promise: an efficient, digestible history of mathematics up to (but excluding) the 20th century. The focus is unsurprisingly on the Western world. Although there are efforts (expanded in this 1967 revised edition) to take non-European mathematics into account in the sections on ancient and medieval periods, there is no recognition of any accomplishments outside of Europe in the modern era.

Since the book is rather short, it is prudently supported with a considerable bibliographic apparatus. A general bibliography constitutes the bulk of the introduction, and a more topical bibliography is appended to each of the eight chronological chapters. A full index of names helps make the volume useful for reference.

I have not had any formal study of mathematics since my undergraduate days, although I like to challenge myself periodically by reading math books that exceed my training. This one actually qualifies. Although it is primarily a history book, it constantly alludes to mathematical topics far in advance of what an accomplished college freshman calculus student is likely to have encountered. Even so, the book remained intelligible to me for the most part.

Author Struik goes some way toward offering ideas about how social and political circumstances impacted the development of mathematical ideas and techniques. He also remarks historical parallels in particular schools and periods of activity. The prose is fairly dry, but an effort is made to communicate the personalities of key mathematicians.

This read has sufficiently stoked my mathematical enthusiasm that I will be reading some actual math texts quite soon. [via]

 

 

The Hermetic Library Reading Room is an imaginary and speculative future reification of the library in the physical world, a place to experience a cabinet of curiosities offering a confabulation of curation, context and community that engages, archives and encourages a living Western Esoteric Tradition. If you would like to contribute to the Hermetic Library Reading Room, consider supporting the library or contact the librarian.