Week 2: Math + Art
Although I'm a working photojournalist, I never formally received an art education past middle school, a part of the "de-geniusing" as mentioned by Buckminster Fuller. So to learn photography I took the analytic approach, seeing how exactly cameras and lenses work, what the numbers mean. I probably have an unnecessary amount of information on this, such as the meaning of aperture numbers (The f in f/4 refers to the focal length).
But note that this is all the technical bits of photography, analogous to Prof. Vesna's example of artists using computers. The more qualitative aspects, such as the difference in bokeh, why stand developing gives the look it does, and most importantly, composition, sees little connection to math. In effect, I've studied what makes art possible more than art itself.
Bridging the two and understanding the connection between math and art has become confusing over the years, as math and its related fields have grown more and more abstract and philosophically challenging. Henderson mentions "[s]hadows, mirrors, and virtual images were added to the four-dimensional vocabulary of the artist by Durchamp." However, none of these concepts are four-dimensional, both in the temporal and physical interpretations, or non-Euclidean.
Artists trying to depict the physical fourth dimension instead end up arriving at the Euclidean-temporal one instead or misrepresent it entirely. Dominguez's lithocronic super-lion, for example, would not have "extremely delicate and nuanced morphological characteristics" but instead be a giant, lion-colored blob. In fact, photography does exactly what Dominguez is describing: making a trace of the fourth dimension and projecting it onto a lower space, in this case ℝ2. The result is all those blurry pics of dogs we see on Twitter.
What, then, would be the best way to truly show the fourth dimension? One way is to sacrifice one dimension to be replaced with the fourth; Interstellar (2014) does this in the scenes inside a black hole. This has the advantage of physically showing the abstract fourth dimension at the expense of another.
Another way would be to manipulate the fourth dimension itself. Introducing a temporal element to any art piece immediately becomes an exercise in the fourth dimension. Abstract? Not really. But the fourth dimension, both temporal and physical, doesn't have to be abstract.
P.S. Seeing Flatland, I can't help but bring up the celebrated Carl Sagan and his excellent explanation of the fourth dimension.
1. Vesna, Victoria. Math Intro. YouTube, YouTube, 26 Mar. 2012, www.youtube.com/watch?v=eHiL9iskUWM.
2. "Rotating a Hypercube." Union College Department of Mathematics. http://www.math.union.edu/~dpvc/talks/2000-11-22.funchal/hcube-rotation.html
3. Henderson, Linda Dalrymple. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” Leonardo, vol. 17, no. 3, 1984, p. 205-10., doi:10.2307/1575193.
4. Interstellar. Directed by Christopher Nolan, Paramount Pictures, 5 Nov. 2014.
5. "The Edge of Forever." Cosmos: A Personal Voyage, written by Carl Sagan, Ann Druyan and Steven Soter, directed by Adrian Malone, PBS, 1980.
But note that this is all the technical bits of photography, analogous to Prof. Vesna's example of artists using computers. The more qualitative aspects, such as the difference in bokeh, why stand developing gives the look it does, and most importantly, composition, sees little connection to math. In effect, I've studied what makes art possible more than art itself.
 |
| How a rotating 4-dimensional tesseract would look in 3D, projected to a 2D computer screen. |
Artists trying to depict the physical fourth dimension instead end up arriving at the Euclidean-temporal one instead or misrepresent it entirely. Dominguez's lithocronic super-lion, for example, would not have "extremely delicate and nuanced morphological characteristics" but instead be a giant, lion-colored blob. In fact, photography does exactly what Dominguez is describing: making a trace of the fourth dimension and projecting it onto a lower space, in this case ℝ2. The result is all those blurry pics of dogs we see on Twitter.
What, then, would be the best way to truly show the fourth dimension? One way is to sacrifice one dimension to be replaced with the fourth; Interstellar (2014) does this in the scenes inside a black hole. This has the advantage of physically showing the abstract fourth dimension at the expense of another.
 |
| The tesseract, with a physical temporal dimension, in Interstellar. |
P.S. Seeing Flatland, I can't help but bring up the celebrated Carl Sagan and his excellent explanation of the fourth dimension.
1. Vesna, Victoria. Math Intro. YouTube, YouTube, 26 Mar. 2012, www.youtube.com/watch?v=eHiL9iskUWM.
2. "Rotating a Hypercube." Union College Department of Mathematics. http://www.math.union.edu/~dpvc/talks/2000-11-22.funchal/hcube-rotation.html
3. Henderson, Linda Dalrymple. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” Leonardo, vol. 17, no. 3, 1984, p. 205-10., doi:10.2307/1575193.
4. Interstellar. Directed by Christopher Nolan, Paramount Pictures, 5 Nov. 2014.
5. "The Edge of Forever." Cosmos: A Personal Voyage, written by Carl Sagan, Ann Druyan and Steven Soter, directed by Adrian Malone, PBS, 1980.
after reading the articles, it never occurred to me that photography is actually art in the 4th dimension! I think it is really interesting that you were able to make that connection. I think this also goes back to the idea that artists were trying to figure out ways to replicate what we see with our naked eye on a 2D canvas.
ReplyDeleteI find it really cool how you attempt to figure out how artists portray the 4th dimension. I am friends with a math major, and he too has tried to draw out the 4th dimension through art. While he used geometry to depict his idea of the 4th dimension, I did not realize that it could also be depicted with time or with removing a different dimension. Those examples you show are quite inspiring.
ReplyDelete