Why don't all trees have the same number of branches and leavesIJ It's no secret that we're still trying to guess our way around how life began and dinosaurs disappeared and how humans evolved. Just as we're wondering at the intriguing and humbling discovery of Pi
A few years back, I was lucky enough to find myself sitting under a gigantic silk cotton tree in a pristine dense rainforest in Indonesia. This really was ‘the’ forest I had read about and imagined a hundred times; it was one of the last homes of the Orangutan. We were exploring the forest hoping to see some wild orangutans and had stopped to catch our breath. As we waited and breathed in the cool and damp air, feeling completely insignificant in comparison to the towering presence of nature all around us, the sheer volume of diversity hit me like a hammer. Every inch of the forest seemed to have life sprouting from it. Giant ants, leeches, butterflies, beetles, insects that crawled, flew and slithered, were all busy getting on with what they do. Why was there so much diversity in natureIJ An earthworm turns the soil and is food to other creatures. Why then did nature need to create more insects and bugs that seem to perform primarily the same functionIJ Why couldn’t all trees have the same colour and shaped leaf or there be only one kind of butterflyIJ After a little digging and research I found the answer wasn’t a simple one; in fact, the question itself was more philosophical than I had intended it to be. I was literally questioning the reason for creation, for the existence of life itself. Scientists and mathematicians across the globe have been trying to answer this question and have along the way formed many theories and made thrilling discoveries.
Nature can seem random, and it is probable that the randomness itself adds the variety and diversity to it. Waves rise, ebb and crash in an endless cycle that’s existed since the first ocean formed. Each wave is unique and no two waves will ever crash in exactly the same spot and in the same way, yet there is a natural rhythm and an order to it. To explain the unpredictability of nature scientists proposed the chaos theory to find an underlying pattern to all the ‘randomness’ in nature. The chaos theory stated that under certain conditions, patterns can be found in seemingly random, erratic and turbulent processes. Quite unlike what it sounds like, the chaos theory emphasised order rather than the inherent irregularities of a system. In the 70s, Benoit Mandelbrot added his Fractal Theory to this and revealed that rough fractals are easily found in nature. He found that there were patterns and shapes in nature that displayed a self similar structure over and extended but finite scale. Good examples of this are trees which begin as ‘Y’ shape and continue building onto this structure with more ‘Y’ shapes forming a final structure made of little ‘replicas’ of its original self. look at a cauliflower or a head of broccoli if you get the chance, and you’ll see they’re actually made up of little versions of themselves.
The discovery of mathematics within self-similar shapes had existed for centuries, but to discover it was a natural phenomenon opened up a world of possibilities. Suddenly the world seemed full of naturally occurring fractals — rivers, lightning, clouds, snowflakes, mountain ranges, fault lines, the cardiovascular system, coral reefs — the list goes on and on . With fractals seemingly ingrained into so many things it was natural to assume that there must be a reason behind this. What is quite clear is that fractals make ‘design sense’ by maximising the volume and space that is available or pre defined. In the case of a tree more branches would typically mean more leaves and more options to absorb sunlight which it needs to make food. At this point the original question returns, So why don’t all trees then have the same number of branches and leavesIJ It’s no secret we’re still trying to guess our way around how life began and dinosaurs disappeared and how humans evolved, but a very intriguing and humbling discovery was that of Pi.
We’ve all studied it in school and tried to memorise as many decimal points after 3.14 as we could. I wish what we had learnt in school wasn’t only that Pi is the ratio between the circumference and diameter of a circle and is one of the most ancient numbers known to man, but the fact that it is found through out nature, almost like a secret code for creation. From the sun to the moon, rainbows and rivers, ripples in water, the pupil of the eye and the spiral of the DNA double helix, The golden ratio of Pi is embedded into almost everything. Professor Hans-Henrik Stolum of Cambridge University decided to calculate the ratio between the actual distance of a river from beginning to end and the distance as the crow flies. The meandering ratio of a river differs as rivers that flow relatively straight from their source to the mouth, would have a smaller ratio when compared to a river with many loops and turns. Not surprisingly after all that Pi has revealed, the average meandering ratio of all rivers irrespective of how much they meander is also Pi!
Sounds amazing, but the best part is yet to come. Pi is known as a transcendental number. In simpler terms it has never been ever calculated completely and can’t be expressed as a finite number. There is still no real explanation for this and all rational methods and technology are still to fully describe Pi. In 1991, the Chudnovsky brothers calculated Pi to two billion two hundred and sixty million three hundred and twenty one thousand three hundred and sixty three digits. The most recent attempt at calculating was this year itself and was stopped at 10 trillion decimal places! Pi to this day still remains uncalculated and holds its mystery.
The numbers that appear after the decimal point in Pi seem to have no apparent pattern, order, rule or reason and seem to emerge almost randomly, a little like magicIJ Perhaps, we are able to make sense upto a certain value in our world of maths and formulae, but maybe the key lies in beyond what we can calculate. Maybe randomness is the secret code to life — unpredictable, mysterious and infinite, quietly tying all of nature and us in an invisible equation. Perhaps it’s not too far-fetched to think that all life on our planet is not only connected but drawn with the same ink.
(The writer is a wildlife film-maker)