I still remember when I first read about fractal mathematics. The sheer wonder of it made the hairs on the back of my neck stand up. I have a profound feeling that even now, many years after this image entranced people who understood its significance, it has yet to fulfill what it is destined to one day achieve: reach a critical mass of understanding that will become an immensely powerful conceptual weapon.
You see, the picture above may well illustrate a fundamental truth that humanity has yet to fully grasp. That struggle is symbolised by many of the arguments that sceptics encounter, arguments that maintain a refusal to see life, the universe and everything in anything but lofty, 'un-knowable' concepts. Be it doctrine or simply uneducated 'common-sense', we humans seem to find it difficult to imagine how such a complex and 'miraculous' thing as life, or the universe, could possibly come about "by chance". Perhaps it is the relic of religions hold on our language that it is hard to describe such wonders without recourse to misleading connotations? Maybe it is merely a limitation of our evolution that we have not developed the necessary capabilities to see beyond what our environment has decried as 'need-to-know'? Either way, through the combined efforts of un-indoctrinated minds or freaks-of-nature, we now have at our disposal the cumulative insights necessary to really start conceiving the impossible.
This picture represents such an insight. This picture is generated by the simple equation Z = Z2 + C. All one has to do is repeat the equation over and over, using the answer each time as the starting point for the next iteration. And yet this picture is infinitely complex, generating complex pattern after pattern the further you zoom in. How can this be so?
It goes against all intuition that complexity can come from simplicity. And yet we now see that it is common throughout nature. This is surely the most exciting and significant philosophical discovery of the 20th century, if not of all time. As a concept, it beautifully and utterly destroys the need for a creator of any sort and yet, more than that, it also probes deep into the question of Free Will and determinism.
You see, complexity theory, together with chaos theory, tells us that with any reiterative process (as cause and effect surely is), time is all that is needed for complex structures to form unpredictably. You would have to know the exact position and velocity of every known particle (which quantum theory says is impossible anyhow) down to an infinite degree of accuracy in order to predict far into the future, clearly impossible. On a smaller scale, it means that by viewing ourselves as agents in a complex system, we can have faith that even though free will in the strict sense is an illusion, our destiny is not manifest or pre-ordained. This knowledge in and of itself is extremely valuable, since though it tells us our will is but a small cog shaped by iterative processes involving other cogs, it still comes under own own individual jurisdiction if you will. We have responsibility, through our awareness of our own part in shaping others and our ability of empathy and foresight, to shape how we effect the future as best we can.
Mandelbrot's discovery of this concept of complexity from simplicity has contributed to giving me vast peace of mind, as it has many others. His contribution to the world will only grow as more people come to realise its significance.