A prescient peripheral viewpoint

(click on image to enlarge)

Giverny

Watercolour and crayon sketch

©2013 Charlene Brown

The mid-19^th century invention of the camera lead to both an examination of Euclid’s assumptions about space, and science’s hold on the paradigms of art. 

And more specifically, after a few years, on the hold of the Academy des Beaux Arts on the artists of the time. Their rules of perfection and suitable content resulted in the rejection of the paintings of a new movement whom the Academy called Impressionists – and they weren’t smiling when they called them that, claiming that their paintings were merely illogical impressions of art, rather than the real thing with proper perspective.

In the 20^th century, these ‘impressionistic’ visualizations came to be regarded by scholars (clearly not members of the Academy des Beaux Arts) as prescient to Einstein’s Special Theory of Relativity, of all things. I will work through that concept as soon as I can…

Euclid and Newton get together outside Paris

(click on image to enlarge)

Versailles

Watercolour sketch

©2013 Charlene Brown

In the Age of Enlightenment – corresponding approximately to the late 17^th to early19^th centuries – the great thinkers of the time began to challenge ideas grounded in tradition and faith, and advance knowledge through what became know as The Scientific Method.

René Descartes (1596-1650) a French philosopher, after whom the Cartesian Coordinate System was named, united algebraic principles and visual space in developing analytic geometry.

The definitive jardin à la française, Versailles, begun in 1710, was said to be have been laid out as homage to Euclid’s postulates and the strict mathematics of Newton’s principles.

This period also featured extraordinary realism in painting... Perhaps I should have found a protractor and done this sketch 'properly.'

A significant Renaissance concept

(click on image to enlarge)

Ballooning over the Masai Mara

Watercolour and Photoshop™

©1996 Charlene Brown

The hot air balloon is not the concept I’m talking about here… although Leonardo daVinci probably had such a thing in his vast repertoire of ideas.

Rather, I’m using this Photoshopped painting to illustrate Renaissance artists’ understanding of the concept of infinity and the use of vanishing points and the visualization of depth using shadows.

This seems to have preceded by hundreds of years the realization by scientists such as Descartes that space is infinite.

Incidentally, I had some difficulty determining the directions of the sensational early-morning shadows in composing this picture using the dozens of photographs I’d taken from the balloon. They were a little easier to figure out after I realized that they all extended toward a vanishing point at eye level. And because we were in a balloon, eye-level was slightly above the horizon…

Our last night in Paris

(click on image to enlarge)

La Défense

Watercolour and crayon

©2013 Charlene Brown

On the last night of our Road Scholar Intergenerational Program in Paris, we went to the top of the Arc de Triomphe to watch the Eiffel Tower sparkling, and I made a video of the show… on purpose, unlike most of the videos I make with my digital camera. 
Turns out I’m not the first person to think of this – Google ‘Eiffel Tower sparkling Youtube’ and you will find almost 200,000 entries.  Mine turned out reasonably well, but I think it’s safe to say most of the versions on Youtube are better. So, if you want to see what it’s all about, please look there.

Then I decided to take advantage of our unique position to take some regular pictures in various other directions, including the view I’ve painted here, looking up the Ave de la Grande Armée and Ave Charles de Gaulle to La Défense. 
Begun in 1958, La Défense is Europe’s largest purpose-built business district, featuring many skyscrapers and La Grande Arche, a twentieth century version of the Arc de Triomphe (and at 110 metres, twice as high as the original).  It has been suggested that La Grande Arche could be a hypercube, or tesseract, projected on a 3-dimensional world, such as I talked about in my July 24 blog post… but I decided not to get my mind in a knot trying to think that through again!

The Classic Period (cont')

(click on image to enlarge)

Alexandria Serapeum
Computer painting
Charlene Brown

This painting of the Temple of Serapis at Alexandria doesn’t actually exist except on my computer.

A little background... After Alexander the Great conquered Egypt in the 4th century BCE, a combined Hellenistic-Egyptian god in human form, equivalent to the very popular Apis, was introduced to reconcile the two belief systems. An impressive temple was built (apparently vaulted in lodestone) that housed a colossal wood and iron statue of Serapis “which was neither supported on a base, nor attached to the wall by any brackets, but remained suspended.”

Later Christians considered this engineering feat diabolical trickery and the temple was ordered destroyed in the 4th century CE. This miraculously suspended statue of Sirapis may not have actually existed, which would account for its absence in the list of the Seven Wonders of the World…

The Classic Period - a great era for both art and science

(click on image to enlarge)

Carthage overlaid with Phoenician alphabet

Photograph and Photoshop®

©2009 Charlene Brown

This computer painting combines photographs of the Punic ruins at Carthage and a bas relief of the Phoenician alphabet on a stone plaque at the Bardo museum in Tunis. 

The alphabet has been described as civilization’s first abstract art. The Greeks added vowels to it and created a visual communications breakthrough in the same remarkable ‘Classic Period’ that they solidified the spatial concepts of Euclidean geometry.  And they named the ‘Seven Wonders of the World’ – works of art as much as science – and almost all of them Greek, while they were at it!

Visualizing n dimensions

(click on image to enlarge)

4D object + its 3D shadow

Watercolour and crayon

©2013 Charlene Brown

In devising a geometry of  more than three dimensions, mathematicians have determined that a four-dimensional cube would consist of eight cubes, just as a three-dimensional cube is made up of six squares. The hypercube (also called a tesseract) in Salvador Dali’s ‘Crucifixion’  has been suggested as an ‘aesthetically pleasing’ visualization of this concept… I don’t think so.

When I referred to the difficulty most people, including most geniuses, have in visualizing more than the usual four dimensions, in my blog post on Cubism on June 19, I wasn’t specifically referring to Dali, but now I am. I prefer my interpretation in 4D object + its 3D shadow.  The required eight cubes are aligned along the four extended diagonals of the purple cube, the four blue ones on the diagonals projecting out the back four corners of the cube and the orange ones on those emerging out the front.  Just as a three-dimensional object casts a two-dimensional shadow, a four-dimensional object casts a three-dimensional shadow, in this case the purple cube.

How to illustrate a physics textbook

(click on image to enlarge)

Glacier on a staircase

Watercolour, crayon and gouache

©2013 Charlene Brown

Marcel Duchamp intended his famous Nude Descending a Staircase to be “an expression of time and space through the abstract presentation of motion.” 

Duchamp’s masterpiece was initially rejected by both the Cubists and the Futurists, with one critic dismissing it as ‘an explosion in a shingle factory.’ This startling turn of phrase seemed like a good guideline for generating an ‘abstract presentation of motion’ – in this case the disappearance of a glacier over the hundred-year period from 1910 to 2010  as previously illustrated on 1150 Words.