One of the best types of art appreciation course is a straight-up studio course in painting, drawing, or sculpture. Even a few lessons can provide a better grasp of the talent and discipline that go into the artwork we see in galleries and museums. But what about the contemporary art we see in movie theaters? More and more of what we see on the movie screen is computer-generated imagery (CGI), including entire films by the big animation studios such as Pixar, DreamWorks, and Industrial Light & Magic. Are there art appreciation lessons for this type of art?
It so happens there are. While a complete understanding requires a fairly advanced knowledge of mathematics and computer graphics, a good grasp of the basics requires only elementary mathematics and access to computer spreadsheet software. Annalisa Crannell and I devote a chapter to this in Viewpoints: Mathematical Perspective and Fractal Geometry in Art. One of my students, Tia, chose this medium for her final project. Although Tia was a biology major, you can see from the samples below that she was able to design a nice mathematical model of a lamp and lampshade, and use a spreadsheet to visualize them from any angle.
Part of a student’s final project
Tia’s project included multiple, hand-colored drawings made from scatter plots she generated in Microsoft Excel. This hybrid approach gives a good feel for the power of computers in 3-D imagery, without losing the connection between the relevant mathematics and the final artwork. The quality of her images underscores an important advantage of doing perspective by the numbers like this. Namely, it acts as a kind of safety net for people who lack talent or confidence in drawing, allowing them to make images that art majors would be equally proud of.
Marc Frantz holds a BFA in painting from the Herron School of Art and an MS in mathematics from Purdue University. He teaches mathematics at Indiana University, Bloomington where he is a research associate.
As a mathematician, I expect that people at parties will tell me that they’re no good at math. I’m used to my friends confessing their fears of my subject. I understand that many people think math is hard and scary. That’s why I was so eager to do something easy and approachable, like drawing, in my math classes. I figured Viewpoints: Mathematical Perspective and Fractal Geometry in Art would allow my students to learn geometry by doing art.
But to my great surprise, I found that it is the art, not the math, that makes people really nervous. As my coauthor Marc Frantz told me, most college graduates have a bit of math in college, and almost all have had a math class their senior year of high school. But few adults have had an art class since 6th grade. Sid’s drawing below is typical of what I see at the beginning of the semester in my course. My students enter college drawing like children, and they are understandably embarrassed by this.
Sid’s first drawing
Learning the mathematical “rules” for drawing opens up whole new possibilities. In this context, rules don’t stifle creativity; they allow for fuller expression. My math-and-art students flourished, and I was heartened, too. Few of my students ever want to see their final calculus exam after they turn it in, but almost all of my students show their parents photocopies they’ve made of the final drawings they’ve turned in to me. Sid’s final drawing, like so much of my students’ late-semester work, shows a mastery of space with hints of great things beyond the horizon. You can tell he’s not going to be afraid of anything.
Sid’s final drawing
Annalisa Crannell is professor of mathematics at Franklin & Marshall College. She is the coauthor of Writing Projects for Mathematics Courses.
Perspective artists at Franklin & Marshall College
In the photograph above, Annalisa Crannell’s students learn perspective by tracing what one student sees through the window from a fixed viewpoint. The window on the far left contains a color painting of the same subject—proof that the process really works. In grappling with perspective problems, our students have taught us a lot about creativity in math and art. On more than one occasion an art major (or an art professor in our workshops) has leapt to the blackboard to sketch a solution to a tricky problem in perspective, before many math majors made a mark on their papers. The artist might need help in proving the correctness of the solution, but it’s impressive that they guessed it so quickly. What’s their secret?
A key issue is the difference in the way people view, and even define, the concept of a mistake. In art it’s commonplace to begin a project with many rough sketches, most of which are drawn very quickly. Although most of these sketches differ markedly in design and quality from the end result, they are viewed, not as mistakes, but as a natural part of the process. That’s how the artists approach math problems in perspective: by making quick sketches and approximations, until the beauty and symmetry of a solution suggests its correctness.
All too often, math students are afraid to make a mark on their papers unless they’re sure it’s correct. This is ironic, because professional mathematicians work more like the artists do: by making quick, rough guesses about what ought to be true, then proving or improving or discarding the result. They call the guesses “conjectures” rather than “sketches,” but it’s the same idea. Wading in and making mistakes is part of the creative process in any field. That’s why Annalisa and I took the approach we did in Viewpoints: Mathematical Perspective and Fractal Geometry in Art—so that readers can learn not only what mathematicians do, but how they do it, and where the fun comes from.
Marc Frantz holds a BFA in painting from the Herron School of Art and an MS in mathematics from Purdue University. He teaches mathematics at Indiana University, Bloomington where he is a research associate.
When I started working with Marc Frantz on designing a course on the mathematics of art, I didn’t realize Marc would soon have me looking at the world in a whole new way—literally. Above you see Marc’s students looking through a window at buildings outside, directing their classmates to recreate the image of those buildings on the windows themselves. (Drafting tape is easily removable, for which the custodial crews thank us!)
I’m just a math geek, but over the past decade while we were writing Viewpoints: Mathematical Perspective and Fractal Geometry in Art, Marc and I have gotten to repeat the window taping exercise with an amazing list of 200 people. I’ve taped windows with mathematicians and artists, with chemists and geologists, with a minister and a motorcycle rider. One couple who came to our Pennsylvania-based workshop stuffed their dorm room here with shrubbery they’d take back to Ohio at the end of the week. Other instructors taught my student helpers to play a game called “Catch Phrase,” and it went viral that week.
The most enjoyable part of this project, though, has been seeing my students wrestle with simple-seeming questions (where do we draw the next fence post?) and come up with those Ah-HA! moments of insight. In our book you’ll see statements and theorems listed by number, but my students and I think of them as “Alex’s Theorem” and “Dierdre’s construction.” We all ought to get a chance to name a brilliant insight after ourselves or our friends, I think.
Annalisa Crannell is professor of mathematics at Franklin & Marshall College. She is the coauthor of Writing Projects for Mathematics Courses.
As reported by the BBC, an Oxford University residence hall has learned that one of its numerous religious paintings may be one of the Maestro’s originals. Needless to say, the painting has been relocated to the Ashmolean Museum until further notice. This is exciting news for the art world and for Renaissance scholars as the verdict is anxiously awaited.
For more on Michelangelo’s life and art, check out Michelangelo: A Life on Paper by Princeton professor Leonard Barkan.
If you give a damn about the local music scene, are interested in changing things and can afford to fork over 50 bills, this Friday night’s annual Midtown Business Association gala might house the elbows you should be rubbing. Not to mention the guest speaker: Elizabeth Currid, author of The Warhol Economy: How Fashion, Art and Music Drive New York City, who’ll speak about how we can transform all our city’s abandoned warehouses into acid-washed ingenuity engines for the socially abstract. Who’s game? (This Friday, July 15, from 5 to 9 p.m. at Harlow’s, 2708 J Street; $50; www.mbasac.com.)
This week’s book giveaway is for all the art lovers out there!
Kissing Architecture by Sylvia Lavin is the first book in a cutting-edge new series, POINT: Essays on Architecture. Kissing Architecture explores the mutual attraction between architecture and other forms of contemporary art. In this fresh, insightful, and beautifully illustrated book, renowned architectural critic and scholar Sylvia Lavin develops the concept of “kissing” to describe the growing intimacy between architecture and new types of art—particularly multimedia installations that take place in and on the surfaces of buildings—and to capture the sensual charge that is being designed and built into architectural surfaces and interior spaces today.
“In the most sober assessment I can offer, I find Sylvia Lavin’s Kissing Architecture to rank among the most original writings in contemporary art discourse I have ever read. Utterly disarming, it is wondrous, brilliant, innocent, naughty, trite, hilarious, fresh, weightless, and profound. Simply put, I am mad for it.”—Jeffrey M. Kipnis, Ohio State University
The random draw for this book with be Friday 7/1 at 11 am EST. Be sure to “Like” us on Facebook if you haven’t already to be entered to win!
Sylvia Lavin will be at Cornell University on April27th to speak about her new book, Kissing Architecture, as part of Cornell’s Department of Architecture Spring 2011 Lecture Series. Sylvia Lavin is professor and director of critical studies and M.A./Ph.D. programs at UCLA, is known for her scholarship and her criticism of contemporary architecture and design. This is an event you don’t want to miss!
“In the most sober assessment I can offer, I find Sylvia Lavin’s Kissing Architecture to rank among the most original writings in contemporary art discourse I have ever read. Utterly disarming, it is wondrous, brilliant, innocent, naughty, trite, hilarious, fresh, weightless, and profound. Simply put, I am mad for it.” -Jeffrey M. Kipnis, Ohio State University
Our friends over at Art Info put up a great post in honor of this snowy, topsy-turvy Friday. Without further ado, I give you “The 8 Greatest Pranks in Art History.” Mmm…lobster.
FACT: Chinese workers in the third century b.c. created seven thousand life-sized terracotta soldiers to guard the tomb of the First Emperor. In the eleventh century a.d., Chinese builders constructed a pagoda from as many as thirty thousand separately carved wooden pieces. In the seventeenth and eighteenth centuries, China exported more than a hundred million pieces of porcelain to the West. As these examples show, the Chinese throughout history have produced works of art in astonishing quantities–and have done so without sacrificing quality, affordability, or speed of manufacture.
Lothar Ledderose takes us on a remarkable tour of Chinese art and culture to explain how artists used complex systems of mass production to assemble extraordinary objects from standardized parts or modules. As he reveals, these systems have deep roots in Chinese thought–in the idea that the universe consists of ten thousand categories of things, for example–and reflect characteristically Chinese modes of social organization.
Ledderose begins with the modular system par excellence: Chinese script, an ancient system of fifty thousand characters produced from a repertoire of only about two hundred components. He shows how Chinese artists used related modular systems to create ritual bronzes, to produce the First Emperor’s terracotta army, and to develop the world’s first printing systems. He explores the dazzling variety of lacquerware and porcelain that the West found so seductive, and examines how works as diverse as imperial palaces and paintings of hell relied on elegant variation of standardized components. Ledderose explains that Chinese artists, unlike their Western counterparts, did not seek to reproduce individual objects of nature faithfully, but sought instead to mimic nature’s ability to produce limitless numbers of objects. He shows as well how modular patterns of thought run through Chinese ideas about personal freedom, China’s culture of bureaucracy, Chinese religion, and even the organization of Chinese restaurants. Originally presented as a series of Mellon lectures at the National Gallery of Art, Ten Thousand Things combines keen aesthetic and cultural insights with a rich variety of illustrations to make a profound statement about Chinese art and society.
This interview was taped at The Getty in Los Angeles when Andrei gave a lecture on The Poetry Lesson.
For more “Art Lessons” click over to The Getty’s site to view more interview segments on lessons like “Learning requires a blind path toward a labyrinth of bones” and “Laughter and silence as subversive tools for creativity”.
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