Geometry of Shadows

Back in my university days my favourite part of Descriptive Geometry (although I basically slept through the course, I still managed to pass the exam with flying colours) was its application for construction of projected shadows and perspective. Shadows provide a great deal of nuances and undertones both in painting and photography, with the former being superior to the latter in terms of subtlety, thus creating atmospheres and moods.

In photography, which is essentially recording patterns of light, shade, and colour (while painting is the individual’s interpretation of these patterns, hence its unparalleled subtlety), "highlights" and "shadows" are the brightest and darkest parts of a scene or image. The challenge for a photographer is to adjust photographic exposure (unless you want special effects) so that the film or sensor, which has limited dynamic range, records detail without clipping the shadows and highlights.

Geometry of shadows. Wicker chair
(© 2012 LightColourShade. All rights reserved)

Cast shadows convey the following three separate pieces of information:
1. The angle of incidence of the light rays
2. The shape of the object casting the shadow
3. The topography of the surface where the shadow is cast

Geometry of shadows. Wicker chair close-up
(© 2012 LightColourShade. All rights reserved)

Transparent shadows create especially beautiful effects since they preserve part of the object’s colour. The following images, for instance, have the feel of old frescos, or so it seems to me.

Geometry of shadows. Glass vase
(© 2012 LightColourShade. All rights reserved)

The shadows of unseen objects put me in mind of Plato’s Allegory of the Cave, an imaginable scenario in which a group of people is chained in a cave all their lives, facing a blank wall and watching shadows projected on the wall by things passing in front of a light source behind them.
All they can do is ascribe forms to these shadows that are as close as they get to seeing reality.
The philosopher, according to Plato is like a prisoner who is freed from the cave and comes to understand that the shadows on the wall are not the reality itself but its reflection, as he can perceive the true form of reality rather than the mere shadows seen by the prisoners. Therefore, what prisoners conceive as real is in fact an illusion.
In a way, these shots illustrate the point of the allegory — looking at these shadows, we can only get an approximate idea of the nature of the objects that cast them.

Sandglass and ancient vases. Time
(© 2012 LightColourShade. All rights reserved)

As an aside, following this train of thought even further I find a kind of abstract (and rather simplistic) similarity between the allegory and the holographic principle in its larger sense that suggests that the entire universe can be envisioned as a two-dimensional information structure (hologram) "painted" or “projected” on the cosmological horizon (maximal limit of perception, but not an actual boundary), such that the three dimensions we observe are only an effective description at macroscopic scales and low energies.
And in the case of a black hole, the informational content of all the objects which have fallen into the hole can be entirely contained in surface fluctuations (“flickering shadows”) of the event horizon.

Geometry of shadows. Flower pots and railing
(© 2012 LightColourShade. All rights reserved)