The Art of Math
Posted by carmennge on April 10, 2007
by Carmen Nge
Helaman Ferguson, Harriet Brisson, Thomas Banchoff, George Francis, Anatolii Fomenko—unlike Leonardo Da Vinci, these names are not household in the rarefied sphere of art. But like Da Vinci, the five share something atypical among artists: they are also mathematicians. From algorithms to geometry, these mathematicians whose work encompass a wide arena beyond lay understanding, live and breathe a field of knowledge that is also, surprisingly, steeped in aesthetics.
In their highly segregated fields of science and arts, our young über -specialists of compartmentalized knowledge departments are largely ignorant of a long tradition where experts in science, mathematics and the arts work in tandem, feeding off of each other in a mutually enriching environment. Within art history, the documented collaboration of Da Vinci and mathematician Luca Pacioli, as well as the influence of mathematician-physicist Henri Poincaré on Picasso, illustrate the symbiosis of two presumably divergent fields.
Malaysian Dr Rajinder Jit Singh, 41, is the personification of such a symbiosis. Currently living and working as a microchip designer and electronics engineer in Singapore, Rajinder is a modern Renaissance man. Confessing to a love for studying, he has amassed an impressive array of degrees—from a PhD in Engineering Mathematics to an MBA from the US, this soft-spoken baritone is also completing a postgraduate degree in Philosophy of Art at the National University of Singapore.
Rajinder’s psyche is a fusion of math and art; his apprehension of reality manifests in equations and algorisms: “I can’t get away from equations; I like my equations. Some equations I like better than others. I do a lot of curve fitting in my head. I think of points and I think of how they would fit in 3D or 4D. Is it quadratic? What power would it be?
“I think about variables with coefficients, for example E=mc². C² is a coefficient, a weight to anything. [For instance] every sentence has a weight to each word. If you want to write an equation for the sentence you are speaking, the emphasis would be the weight. I am thinking about a weight to our lives: the ratios that you use in calculating or putting together a decision as to what you want to have for dinner. There are many different variables but there are also many different weights. Through computation you can come to a value of those weights.”
If life could be distilled into a set of equations, then what about art? Rajinder’s art is antonymous to the linear perspective painters of the Renaissance: Filippo Brunelleschi, Lorenzo Ghiberti, Piero della Francesca, among others, who used mathematical equations to calculate depth, proportion and scale for their paintings. These luminaries saw math as a tool for artistic precision, resulting in a desired verisimilitude. Unlike them, Rajinder incorporates actual mathematical equations into his paintings.
“I use math equations in my art without there being meaning to them,” he explains. “I separate the meaning away from it [the equation].” In one of his newest work, Bin Bags, Rajinder inserts an equation based on the entanglement phenomena in physics. Even though a lay viewer would not be able to relate to it mathematically, this does not bother him in the least.
“I’m using the equation as it is, conceptually, because I think it’s pretty. I think it is pretty because I also understand what it is because I’ve read a lot about it. And I’ve used it before. I actually think the combination of symbols is quite pretty. This is not mathematical. It is about the aesthetics of [the equation].” He likens his work to that of Justin Mullins’ mathematical photography: taking beautiful equations from mathematics, framing them with captions explaining their context and meaning, and calling it art. The only difference is Rajinder’s equations are sans mathematical meaning and reproduced on a two-dimensional expressionist palate.
In many ways, Rajinder’s work invites us to reflect on the definition and parameters of beauty. Can mathematics, expressed in an equation sitting in swirls and swathes of colour, be elevated to art? Does the equation need to be mathematically sound before it can be transformed into a thing of beauty? Does our definition of art change when mathematics enters the equation?
Nurturing a love for math even as a child, Rajinder was drawn to what he terms “the preciseness and formality of math. I also like when the answers are correct, you knew. There’s a good feeling about it. Like a little buzz at the back of your head,” he smiles.
Yet, mathematical precision is never far removed from visual accuracy. As Rajinder puts it: “When I was doing my PhD, we used circles and lines as instruments to explain what we were trying to do. Even then it had to look “right”. The word “right” is weird here but I don’t know how exactly to explain it.”
According to Rajinder, Henri Poincaré says that all good mathematicians have a “delicate sieve”.
“When you are proving something or writing a math equation, you have an eye for it. Its complexity, its simplicity. When you’re doing that, you know when you’re correct, when you’re doing it ‘right’. That’s what Poincaré meant by ‘delicate sieve’. In my opinion, everybody has this ability even though Poincaré says only some do. It comes through practice and just through being familiar.”
This idea of the ‘delicate sieve’ closely approximates the idea of there being great artists with talent and bad ones without. What makes an artist great? Is it the monetary value of his works? Or does it have to do with something less concrete and more emotional, less predictive and more organic—a matter of taste? Who decides? Is taste arbitrary?
As Rajinder puts it: “One person’s good art will be another person’s bad art. Any distinction that you make through your senses, will necessarily be cultural, among other things. When you look at something and say this is better than the other, as soon as you make that decision, all your experiences, your whole history comes into play.”
Who can dictate which piece of artwork is valuable and why? One thing is certain: art is also about connection, an ephemeral but nonetheless significant communion between artist and his artwork, between artwork and viewer, and ultimately—though indirectly—between artist and viewer. Rajinder is testament to this simple logic.
“When I put the equation on my canvas, people react to that equation. Bereft of its meaning, when you see an integration sign, when people see it, it brings them back to their school days. With the mixture of that, along with the character of the painting, I am trying to build a dialectic, a contrast of emotion. I am trying to get a reaction and that reaction comes from several different aspects of the painting. The equation arises separate from its meaning. I am writing an equation in a piece of art. What is it doing there? By putting it on a canvas in a gallery I’m also questioning it.”
To question mathematics is to question the basis of its truth, its objectivity. Perhaps it is easier to question art because its foundations are subjective; interpretations can be challenged because they change. As do value. But how does one question math?
“Mathematicians look at the universe [in terms of] the whole grand unified theory—rules that guide the universe and our lives,” Rajinder concedes. Yet, he believes there exists a postmodern symptom in mathematics too, a symptom that rejects any notion of a grand theory of the universe.
“One person that I’ve read a lot about is Kurt Gödel,” Rajinder explains. “He did something that shocked mathematicians in the last century. Gödel said that if you have a system of rules that you develop and if these rules are all consistent and not contradictory, then there is no way you can conclusively prove the system is correct. Math is centered on proof—where we think we are completely correct all the time—but Gödel is saying that there is no way that that is possible.
“Gödel was saying something similar to the principle of uncertainty in quantum mechanics: that the person who is measuring is as important as the thing that is being measured. Math doesn’t like it when subjectivity comes into the equation. How can you bring the scientist or observer into it? It is a whole science based on objectivity, where you can conclusively predict. Otherwise it is not a conclusive statement and you can’t actually call it math.”
Rajinder likens visual art’s subjectivity to Gödel’s deconstruction of math’s inviolability. For Rajinder, Gödel brings us closer to what the former considers to be art. “At the end of the day, you perceive your reality based on your own experiences, based on who you are. That’s why I think art is so wonderful because it allows different people to have different interpretations,” Rajinder says.
But as a math practitioner, doesn’t the rigid and rule-bound nature of math cramp his artistic style?
“I have seen myself evolve. Many years of precise formal math, being very, very careful about how you write each symbol and how everything is put together because you cannot make a mistake. And now, the whole art thing kinda releases me. It’s a mark that I make. I could paint something that I do not want to make sense. I deliberately go out of my way not to be linear or formal. I feel that has opened up a different kind of understanding; it really opens up different ways of thinking if you do it long enough.”
For Rajinder, art also enables transcendence. An Indian of Punjabi origin, Rajinder has called many places home: Ipoh, as a boy; then Belfast, Ireland, where he received a higher education and spent a total of 15 years; and finally, Singapore, his place of residence for the past 11 years. But he feels at home nowhere and his abstract expressionist pieces reflect his fluid, transnational past and present. Wayang kulit characters and Indian men and women find their way into his many sketchbooks but so do samurai figures—hardly indicative of a nostalgia for his Malaysian roots.
“When I come back to Malaysia, I feel foreign. When I am in Singapore, I feel foreign and when I’m in Ireland, I definitely feel foreign. Why don’t I belong? I kinda want to belong somewhere but then I belong everywhere.”
While Rajinder is cognizant of the pressure to inject local colour into his work, to imbue his paintings with a more local identity—the sort of hometown boy-made-good, can-do Malaysian spirit—he elects not to subscribe to it. “It’s very difficult,” he admits. “If I try, it will be contrived. I just have to be me. I hope that who I am will come together in what I am doing. I cannot draw something that is foreign to me. I will never draw the Merlion,” he laughs. By the same token, neither will he draw a bomoh or a bunch of bananas. “Geometrical shapes, that’s what I do,” he says, matter-of-factly.
This article was published in Off The Edge magazine, May 2007 issue