This is the second of a three-part exploration of the BBC documentary series The Code.
Part 1 – Part 2 – Part 3

Shapes are related to numbers (examined in the first programme) in that they express regular numerical patterns of angles. A shape is a numerical pattern made “real”, three-dimensional and interactive. This episode explored some fascinating concepts behind the fundamental, shape-based laws that make up our reality.

The section on honeycomb and bubbles was interesting as a first expression of this expression of numerical values in a real-world setting. The idea that 120 degree angles seem so ubiquitous in nature was interesting, as it seems to provide such a strong framework for “engineering” such as beehives. The explanation that this is simply the most efficient use of the material and requires the least energy only increases the wonder that these structures can be so beautiful and regular. The Force is built in patterns, as the programme went on to reveal later. These are some very distinct and familiar examples of that.

As a quick aside, I was astounded to learn that soap bubbles are thinner than a wavelength of light, and about 20,000 times thinner than a human hair. These beautiful insubstantial objects are something most of us have enjoyed since childhood, but to realise they are quite so ephemeral but resilient enough to drift through our world is a remarkable thing to consider.

So, the economy in nature described by the spherical formation of bubbles and the inherent “laziness” with which nature forms angles and shapes whilst trying to conserve energy and surface tension has real-world applications, such as the modelling of the Munich Olympic Stadium. It was fascinating to think such models could be created through such an elegant and simple method as soap bubbles and wet string, in the days before computer modelling made such calculations easy. The stadium itself was very beautiful and perhaps this is because it is a direct expression of a seemingly fundamental natural law; our eyes are attuned to their beauty, much like that found in the work of Jackson Pollock, discussed shortly.

One of the most interesting sections of the episode dealt with the five Platonic solids, five symmetrical objects Plato believed could describe the makeup of the entire universe. This is remarkable not just in that he was to an extent correct (because cell structures and the atomic structure of elements does indeed follow a similar conventional set of shape-based rules, something finally discovered over a thousand years after Plato’s postulation in the Timaeus), but that he would bhave reached his conclusion from a philosophical, a priori approach to reality. I’m struck time and again when learning about Plato by what a truly remarkable figure he was, and what a truly unique mind he had.

The difficulty in creating a “perfect” snowflake was another very interesting point in this programme. Because reality isn’t a vacuum, or a bubble, but a chaotic meeting-place of many opposing and competing forces, natural objects are created with a degree of “imprecision”, much like trying to draw a circle sat in the back of a moving car is likely to result in anything but a circle. How true of our path that what we think of as perfect in isolation is impractical int he real world; that what “perfection” looks like in a living system is something beautiful in its imperfection. As Jedi we live “in the world”. Our code can seem crystalline and perfect, objectively; however there is no objective view on reality and thus our code will be interpreted and applied differently given the situation.

I’d never heard the theory of Pollock’s paintings before, that they are beautiful specifically because they describe types of fractals, meaning smaller sections of the picture are indistinguishable from larger sections. I’ve had an interest in fractals since I was a child, watching a programme on my old Atari ST which modelled the Mandelbrot set and “fell” into it, on an endless loop. What then appeared a simple interesting optical illusion, I’ve since come to realise is a fundamental element of the structure of reality, just as De Sautoy describes here. How Pollock “tapped into” this fundamental structure is anyone’s guess, but the fact remains; his art is beautiful because it describes something structural about our reality, just as honeycomb and the Giant’s Causeway do.

Thinking back to the core of this lesson and the idea of coincidence, I think fractals provide an interesting model of how this could work. A fractal shows that one pattern can repeat itself endlessly, on smaller and smaller scales. Coincidence seems to describe a “structure” to reality in which certain things emerge seemingly from chaos. So perhaps this is the best model for coincidence; that irrespective of the scale we use, how wide or narrow a view we take, certain things will always emerge from the disorder life presents itself as. That although we sometimes have a hard time discerning it, beneath the confluence of forces and elements which make it almost impossible for the “perfect snowflake” to appear, there is indeed a perfect snowflake, describing 120 degree angles and an underlying fact of nature.

Further still, computer modelling shows that “fractalisation” of simple models can make realistic looking landscapes and terrain. This implies that at its heart, the very earth we stand on expresses some form of fractalisation; if a fractal model looks real, so too must reality look like a fractal model and express some of the same values. This suggests that at its core, all reality is an expression of simple shapes, repeated, scaled and miniaturised from an overarching structure.

Reality as ever smaller expressions of a large, single thing. Very Jedi.