Let me begin with a doff of the hat to the Math and Science Gene (MSG). He has marched tirelessly through countless generations of my family, far, far back into the cobwebbed recesses of ancestral lore and memory. He has worked hard, ceaselessly, relentlessly, without ever skipping a single progeny of my clan. To be sure, there were some dangerously close brushes with the Lunatic Gene (LG) (known in polite circles as the Quirky Gene), but the MSG always prevailed, always managed to nudge the LG, that over-ambitious and irreverent upstart, aside. In a daring attempt at a coup, the Slothful Gene once ventured to sabotage an entire sub-branch of my family, but the MSG pulled them out of that potential morass, that almost-blight on the family name, by sheer force of will.
And then, I came along. And as I did, the MSG skidded to a gentle halt. He stretched back against my branch of the family tree, and yawned. He pondered the many brilliant mathematicians, physicists, engineers and doctors he had brought forth. A small smile tickled the edges of his mouth as he remembered all the prizes, the awards, the accolades that had been heaped upon this family, all thanks to his single-handed efforts. The MSG began to droop as the sun rose higher in the sky. He felt tired. Exhausted. He needed a break from this relentless slogging. There was a whisper of a wind, and the LG appeared in front of him. The MSG looked at him without the usual irritation. He had been an exceedingly pesky neighbor all these years, had tried encroaching on his property more times than he could count. Today, however, he looked at him with a benevolent smile. The LG was taken aback.
“What’s the matter, old chap, you don’t look too good,” the LG said, his nasal voice grating on the MSG’s nerves just a little.
“I’m tired,” confessed the MSG. “I really need a break”.
The LG could not believe his ears.
“Yes, you do look a bit worse for the wear”, he said, trying not to sound too eager. “Perhaps if you skip this one” (nodding perfunctorily towards me, at the pinprick stage of development), “you can come roaring back stronger than ever with the next generation. Come on, it’s just one person! After all these centuries, surely they won’t mind if you took a break with one person!”
The MSG looked tempted. His defenses, weak to begin with, began to crumble. It was true; a break would do him good. He was beginning to get a bit worn at the edges, all those stray genes from other communities (what a battle that had been!) were beginning to take their toll. Whispers from the latest interloper, the Management Gene, told him of the need to “regroup” and “reassess his priorities”. He began to feel a bit resentful. He had been taken for granted all these centuries, but if he vanished in one person, it would shake them up and make them miss him and think longingly of him. Yes! He would do it. He would take a break. And I would be the casualty of his decision.
The LG watched the MSG with ill-concealed eagerness. “So, you’ve decided, then?” he asked. “Can I move into your spot?”
A tremendous feeling of relief washed over the MSG, now that he had made his decision. He felt relaxed and expansively generous. “Sure,” he exclaimed, waving his hand at the LG, “You are most welcome.” A long-dormant and firmly suppressed streak of mischief stirred awake in him. “And while you’re moving in why don’t you invite your friend the Slothful Gene?”
So the LG moved into me, and employed his entire arsenal of traits, the nature and composition of which I will leave to your imagination. The Slothful Gene settled in very nicely as well, having found an exceedingly hospitable environment in me.
And yes, the MSG, well-rested and rejuvenated, did come roaring back in the next generation. My two children, I am told, excel in Mathematics.
All this serves as a preamble and an apology for the incoherent nature of what is to follow: an attempt to explain the mathematics and the science of the kolam.
All over Tamil Nadu – urban or rural, at the homes of the poor or rich, highly-educated or illiterate, an almost identical ritual takes place early every morning. The threshold of the home is swept, washed clean with a sprinkling of water, and, with a handful of white powdered rice (or more commonly these days, stone), a beautiful pattern is drawn out by hand. It is always done by a woman, and is a wonderful way to showcase her artistry, skill and imagination. The kolam may be a small, simple, hastily drawn lotus, or a plain and straightforward six-pronged star, but on festival days, particularly Pongal, the displays are mind-boggling in their colorfulness, complexity and size.
I love my early morning walks when I am in Madras, delight in watching the ritual of kolam drawing outside the homes around where I live. It is heart-warming to see that in this age of hustle and bustle, of high-tech gadgets and instant meals, people still take the time and effort to create these works of art.
However (and this is where the lack of the MSG is going to drag me down) kolams are so much more than pretty drawings. They are a cultural and artistic expression of a whole array of mathematical ideas and concepts (yes, mathematical). Kolams have symmetry, patterned repetition, closed continuous curves and curve families, all of which have applications and meaning in mathematics and computer science. With their impeccably logical building up of patterns – their algorithmic nature - they have attracted the attention of computer scientists who have used kolams to study picture languages.
Kolams come in a variety of styles (which the computer scientists have taken to calling “kolam families”). Many begin with a grid of dots, which serve as the skeletal structure for the kolam. Lines are drawn, connecting the dots or around them, very often in a single, continuous curve. (An aside: the continuous curve is supposedly symbolic of the never-ending cycle of birth, fertility, death, continuity and eternity). The finished product is a symmetrical kolam. Kolams come in a variety of symmetries – horizontal, vertical and rotational.
A leader in the study of the mathematical properties of kolams was Dr. Gift Siromoney of Madras Christian College, who, along with his team, has done some fascinating work on these lines. He was a pioneer in the study of kolam designs as part of the analysis and understanding of picture languages. The study of picture languages is closely related to formal language theory, which has been used by computer scientists in the study and development of programming languages. Picture languages use sets of basic units, and study the syntactic rules for combining these units. Using the rules of syntax for a specific kolam family, a computer can mechanically generate new kolam patterns. Gift Siromoney and his group of scientists and mathematicians used these picture languages to describe and create kolam families. They created a language that produced strings of symbols, which could then be translated into pictures (kolams).
Array languages are another technique used for the mathematical and computational study of kolams, particularly those using dots. These include Siromoney Matrix Grammars and Kolam Array Grammars. These arrays can be used to describe and create kolams of various shapes. I also recall reading that Fibonacci numbers can be used to construct and design the dot structures and patterns of kolams. Fibonacci numbers are a sequence where the first two numbers are 0 and 1, and the subsequent numbers in the sequence equal the sum of the previous two numbers.
The next time you go for an early morning stroll, take a minute to watch the kolams being drawn, to see mathematician-artists make science and art come alive before your eyes. This is a tradition that goes back at least 300 years. May it live forever, and not just in the innards of a computer!
The article "The Kolam Tradition" by Martha Ascher, published in the American Scientist, January-February 2002, was my lifeline while writing this.
As special word of thanks to my father, who made me aware of the mathematical underpinnings of kolams; and, in the interest of maintaining domestic peace and harmony, I must mention my mother, a kolam artiste extraordinaire, and gold medal winning physicist.