Geometry in art

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Greetings, all, and thank you, Walt, for inviting me to post here. I hope you find my take on the mathematical arts interesting enough to read and respond to my posts!

Since I’m a believer in the importance of context, let me say that I’m posting this from Brussels, Belgium, where I happen to be for a meeting. This afternoon I caught a major exhibition of the arts of the first Russian Avant Garde, held at Bozar, the Center for Fine Arts in Brussels. Why am I reporting this on a site devoted to mathematics, I hear you cry? Well, I think a typical pure mathematician would be struck by the geometrical nature of cubist, futurist or constructivist art, and particularly that of the Russians who are the focus of this exhibit. The cubists sought to reveal an object from all perspectives simultaneously, the futurists to capture the dynanism of machines and the colours of metals, and the constructivists to distill visual art to its essential and abstract forms and colours.

Indeed, our typical mathematician would not be mistaken in seeing geometry in this art. In the last decades of the 19th century and the early years of the 20th, there was widespread public interest in the ideas which had recently revolutionized geometry — non-Euclidean geometry, David Hilbert’s axiomatization of geometry (1899), and ideas of “the fourth dimension”. Two of the leading artists of this period, Kazimir Malevich and Piet Mondrian, both sought to represent these new ideas from geometry in their art, and said so explicitly.

If this topic interests you, there is some further reading below.

I’ll have more to say on Hilbert and the intellectual trouble that his axiomatization of geometry caused the philosopher Gottlob Frege in a later post.

References:

M. Dabrowski [1992]: Malevich and Mondrian: nonobjective form as the expression of the “absolute'”, pp. 145-168, in: G. H. Roman and V. H. Marquardt (Editors): The Avant-Garde Frontier: Russia Meets the West, 1910-1930. University Press of Florida, Gainesville, FL, USA.

L. D. Henderson [1983]: The Fourth Dimension and Non-Euclidean Geometry in Modern Art. Princeton University Press, Princeton, NJ, USA.

D. Hilbert [1899]: Grundlagen der Geometrie. pp. 3-92, in: Festschrift zur Feier der Enthullung des Gauss-Weber-Denkmals in Gottingen. Teubner, Leipzig, Germany. (Translated by E. J. Townsend as, “Foundations of Geometry”, Open Court, Chicago, IL, USA. 1910.)

The Humble Bumblebee

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Something that’s always annoyed me is the story about how scientists have shown that bumblebees can’t fly. Everytime I hear the story, it’s always told with the same “stupid scientists” tone.

I see, via Cosmic Variance that scientists have finally found out how they manage the trick. (Interestingly, someone in the comments suggests that the original research showed not that bumblebees couldn’t fly, but that they couldn’t glide, which in fact they can’t.)

Wikipedia policy change?

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I’ve learned to take all media articles about internet phenomena with a grain of salt, but this article from news.com, Growing Pains for Wikipedia, claims that Wikipedia is changing its policy so that anonymous users cannot create new pages (they can still edit existing pages). While practically speaking it’s a small change, it’s a big change in Wikipedia philosophy. The online encyclopedia has always prided itself in the ability of anyone to edit, with the notion that making participation as easy as possible will attract more and higher quality editing.

Bishop quote

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Eric Schechter’s Handbook of Analysis and Its Foundations has a cool quote from constructivist mathematician Errett Bishop:

Mathematics belongs to man, not to God. We are not interested in properties of the positive integers that have no descriptive meaning for finite man. When a man proves a positive integer to exist, he should show how to find it. If God has mathematics of his own that needs to be done, let him do it himself.