The 20th century may come to be remembered as the penultimate grasp for prosperity, a blind progression that plunged its offspring into misery. New ideas, technologies, and politics exploded, but the tumultuous death of viable ideological alternatives has perhaps become its most enduring legacy. While the collapse of the Communist state can hardly be considered a tragedy, the abolition of Marxism as the basis for a just society is an oversight.
A lot of criticism has been levelled at deterministic models of society. They are not only dangerous but misleading. The self-contained destruction of capital, as identified by Marx, proved to be untrue, and his prophecies of a bright communist future failed to materialise. Radical revolutions may have succeeded in overthrowing systems, but strict adherence to rhetoric rendered them incapable of building truly socialist societies.
Mathematicians, meanwhile, were running into similar problems of rigidity. Classical geometry often failed to account for the chaotic nature of reality. On the other side of the ideological divide, Benoit Mandelbrot, a mathematician, was working on the coastline paradox. It states that the smaller the measuring instrument, the longer the coast. To deal with the problem, he developed a new field of mathematics: fractal geometry.
Fractals are never-ending patterns of intense complexity. No matter how far you zoom in, they continue. They occur all around us: in clouds, the shapes of leaves, trees, snowflakes, and coastlines. A key feature of fractals is their self-repetition. They continue to repeat themselves through all scales. It is seemingly a key feature of unfolding nature.
In 1980, Benoit’s work on fractals led to the discovery of the Mandelbrot Set. It was very much the lovechild of unbridled capital and modernity. In theory, it could have been discovered at any time in history, but it first appeared on the printout of an IBM supercomputer. The formula is simple: Z= Z2 + C, but its application was revolutionary. Each input either shrinks to zero or shoots off to infinity. By repeating the calculation and plotting the numbers on a chart, a pattern begins to emerge. While, in theory, this could be done by hand, it requires millions upon millions of iterations. The introduction of computing power made it possible to visualise the result, a pattern that has often been referred to as the thumbprint of God.
This infinite pattern seems to be an uneasy parallel to society. The way it grows and moves, the subtle cascade of order running through an organic chaos. We also seem to organise ourselves into little islands of familiarity; even in the unknown, we recognise something of humanity.
I wonder what endlessness means now we are confronted with an end that seems to be growing closer. It often feels like the problems we face are amounting to the unsurpassable. If we are to approach, as we must, the issues resulting from society's intricate connections, it might be fruitful to dream in visual modes. We might not be able to use formulas or functions, but perhaps this type of thinking might reveal something new. Instead of discarding theory, maybe another angle, one that accepts the infinite complexity and unpredictability of life, might reveal tools for a brighter future.