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The Arts and Mathematics Are Sometimes Close Relations

UK's National Gallery Uses Geometric Artistry - Fabio Alessandro Locati
From the Geometry of Innocence to Mondrian’s abstracts to Mozart’s Effect to Minimalist music & painting, the arts owe a debt to the science of mathematics.

Maths is popularly thought definite, absolute and provably true, while art is the exact opposite, often defying logic. However, there are few certain realities, and some of the greatest works of art have drawn on mathematics to demonstrate that.

Geometry as Artistic Fundamental

Albert Einstein said: In so far as statements of geometry speak about reality, they’re not certain, and in so far as they are certain, they don’t speak about reality.’ Geometry is the essence in architecture and design, but is also a powerful image-maker.

The Geometry of Innocence is a book (2001) by US photographer Schles, about which Library Journal says: ‘his critical eye brought him to the extreme (e.g., police helicopters, operating rooms, death row) as well as the everyday (e.g., birthday parties, weddings, construction sites). From each, he extracts strangely humanizing views to address his apprehension with the ragged, noisy isolation of the modern urban experience. The result is a calamitous and visceral journey through a kinetic, disturbing, vibrant America’.

It is also the title of an abstract watercolour painting by Mark Ari; and The Geometry of Innocence Flesh on the Bone: The Body as Souvenir in Beatrice Grimshaw’s Travel Writing by Clare McCottera from the Department of Languages & Literature, University of Ulster, Northern Ireland, published in Journal of Tourism and Cultural Change.

There is also Bob Dylan’s Tombstone Blues: The geometry of innocence flesh on the bone/ Causes Galileo’s math book to get thrown/ At Delilah who sits worthlessly alone/ But the tears on her cheeks are from laughter.

The Mozart Effect & Music/Maths Links

Statistician Jeffrey Rosenthal from Toronto University writing in +plus magazine, said: ‘The astronomer Galileo Galilei observed in 1623 that the universe “is written in the language of mathematics”, and it’s remarkable the extent to which science and society are governed by mathematical ideas. It is perhaps even more surprising that music, with all its passion and emotion, is also based upon mathematical relationships. Such musical notions as octaves, chords, scales, and keys can be demystified and understood logically using simple mathematics’.

Dave Rusin, Associate Professor of Mathematics at Northern Illinois University, studies mathematics/music interplay. For example, as to why there are 12 tones in an octave, Rusin says it’s to do with the nature of sound and human perception of it. He refers to the ‘Mozart Effect’, which claims exposure to early classical music early in life can lead to improved performance in test scores, spatial visualisation and abstract reasoning, all of which feature in arts creativity.

He considers mathematical proofs set to music, sharp and flat, tuning & interval patterns, the shape of instruments like the harp, defining musical styles mathematically, beat frequency & trigonometry, and sums of series, which would support the reasoning that music theorists often use maths to understand music.

Ancient Chinese, Egyptian and Mesopotamian people studied mathematical principles of sound, while the ancient Greek Pythagoreans investigated musical scales in terms of harmony arising from numbers. It’s this harmony that is fundamental to music theory and artistic creation. Some teachers argue that maths is a language, and if that is understood, then it’s part in artistic endeavour is clear.

Other Branches of Learning Are Fundamental in Music

Abstract algebra can analyze music. ‘Rhyme’ and ‘rhythm’ are from same root; musical terms like ‘metre’ (linked to measure) reflect historical links with music, astronomy and physics. Music is extended by a plan of its musical form, as is architecture, taking account of function/purpose, repetition and order and pleasing artistic perception.

Sound experiments from historical traditions/cultures continue, often fusing styles. Either harmonious or discordant, regular/non regular pitches, frequencies, scales, rhythms, traditional orchestras, minimalist materials, eastern instruments, African sounds, Arabic or oriental variations, voices, even junk as in the work of Stomp: the rich variety of musical lifeblood demonstrates how the arts has absorbed scientific underpinning of music, and how the arts feed off one another.

Technology to amplify and record sound has long been around, but nowadays can twist, distort and change perception. Airbrushing photography, adding people to a scene who have been dead for years, is not not just a touch of postmodernism, but a genuine attempt to push arts’ boundaries, using every device yet known to man.

The Mathematics of Art

Traditionally painting employs mathematical techniques. Most artists, including Picasso are fine draughtsman. According to Math Central at University of Regina, people who like maths want to see patterns, angles and perspective, like Degas employed. Da Vinci’s Mona Lisa is drawn on what is known as the golden ratio: 1:0.618, aesthetically pleasing and reflecting the proportion of the human body. His painting has golden rectangles throughout, as does his The Last Supper.

M.C. Escher produced mathematically challenging artwork, as stated by Math Central, ‘His polytypes cannot be constructed in the real world, but can be described using maths’. Ascending and Descending is a staircase of mathematical impossibility, but the drawing makes it seem real.

Math Central says: ‘In art, mathematics is not always visible, unless you are looking for it. But there is much symmetry, geometry, and measurement involved in creating beautiful art. Perhaps math and art are quite intricately linked’.

First published on Suite 101, 4 August 2010.

Photo: UK’s National Gallery Uses Geometric Artistry – Fabio Alessandro Locati

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