The Golden Cauliflower
Math was never my favorite subject in school. I was more of a verbal person, stimulated to explore the stories of people, in all their genius and frailty. These stories helped to direct my choices about what to do, and who to be. Math seemed less applicable to the world I lived in. Until I saw the fractal cauliflower. Now I recognize the true power of math, to help us model the world around us, and to rediscover our true place among all life.
The basic territory of math is, of course, numbers, and numbers are very strange. Consider the sequence of numbers known as the “Fibonacci Sequence,” for the Italian mathemagician who brought it to the west (it was previously discovered in India (of course)).
Start with the first number: 1. Add 1 to 1, and you get two. So the Fibonacci Sequence begins: 1, 1, 2. Now, add the last two numbers in the sequence: 2+1 = 3. So 3 becomes part of the sequence. Now add the last two numbers in the sequence, again: 3+2 = 5. Now, 5+3 = 8. Extrapolating this pattern out produces this sequence of numbers (it goes on infinitely):
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597…
When you examine the relationship between each number in the sequence and the one that precedes it, a ratio emerges: approximately 1.618 over 1. (So, multiply 5 by 1.618 and you get ~8, multiply 8 by 1.618 and you get ~13, and so on.)
Okay, okay - enough with the math. But it was a worthwhile digression, because this math happens to describe an extremely important and common pattern of growth in biology: the golden ratio. The golden ratio is ~1.618 (the decimals go on forever, like pi), and we can find it in all kinds of places. Sunflower seedheads, attractive human faces, and the fractal patterns of river systems all exhibit the golden ratio. Using the golden ratio allows a living thing to grow indefinitely without changing its characteristics. These Romanesco “fractal cauliflowers,” in their mesmerizing beauty, boldly display the golden ratio in living, delicious action:
Here’s the point that the cauliflower teaches : the fibonacci sequence is one of the simplest things we can do with numbers, which are an invention of the human mind. And yet, it describes the fundamental pattern of life! To me, this shows the deepest truth we can learn: The truth that our minds themselves are yet another expression of living nature. We are not separate, we are a part of it all, blessed with the ability to see the patterns in things, and to appreciate beauty. So, thanks to these cauliflowers, I find it beautiful that we find the golden ratio beautiful. It feels beautiful to be part of nature, doesn't it?