Hidden Patterns in Nature

A collaboration with artist Sabrina Basten, for her project 'my space, your space, our space: my space'

Hidden Patterns in Nature: how we reveal them, how we keep them hidden, or how we create them.

Our understanding of Nature is limited by the constrains of our preconceptions of the World, but both evolve together since we are born: we learn more the more flexible our minds become. This process also occurs along history: we will see some examples of drastic changes in our understanding of things connected to breakthroughs in our geometrical models. (It is hard to determine what came first, though). We will talk about fractals, exotic structures that we suddenly find everywhere: from remote galaxies to Earth landscapes, clouds and vegetation; even in artistic works, like Pollock's. A big risk exists all the time: that we tend to project these structures and models that we build in our mind into the World around us, conferring them existence. Like that, our models become frozen, static, and we suffer from a new period of partial blindness.

Presentation summary

"...no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex, as the whole was to start with. That, I think, is the secret of the Universe." - Isaac Asimov.

Sure you can. Take the spherical geometry. For a long time we though the Earth was flat because our Euclidean notions were enough to describe local effects, but the shortest distance between Amsterdam and Antananarivo is not a straight line. You have to go along a curve to get from one point to the other. You may argue that this is because tunnels are expensive, but that does not change the practical conclusion: in fact, we describe our living place, the surface of the Earth, using a spherical geometry better than a flat one. A more exotic family of geometries is generated if you let any line have infinite parallel lines through an external point: hyperbolic geometries, that we use now for example to understand certain natural patterns. All these geometries reveal new possibilities of describing the world, and we were blind to them for centuries because we thought one model was enough. The real nature of space is not for mathematical reasoning to settle, but for Physics to measure. (Even in Physics there is not one truth, but at most a few a practical answers to the questions we have right now). Different experiments confirm Einstein's predictions that space is curved, not "flat", so having these alternative geometries to describe it has become very handy. There are many phenomena around us that are clearly non geometrical. Can we find also patterns in there? Take molds, a type of fungi. Molds look like quite chaotic to us (by chaotic people normally mean "random"), growing without a determined shape. But all living creatures are made of cells that eat, metabolize, reproduce and repair themselves, fight invaders, work in teams to do very complex tasks, and even die at a scheduled moment. Most of these activities are programmed inside the cells themselves, and many cells acting together build up larger structures, like molds or humans. Although molds grow on dead organic matter everywhere, their presence is only visible when they grow in colonies, in an interconnected network of branched filaments. Also plants are composed of parts that are repeated: think of the branches of a tree or the leaves of a fern. The case of the romanesco is probably the most impressive one. This kind of broccoli is an awesome natural example of a mathematical structure called "fractal": something in which any of the parts looks like the whole. Fractals were studied systematically only in the 20th century, starting with the works of Mandelbrot. This mathematician gives name to a set of numbers with remarkable graphical properties. It does not matter how much you zoom in, you always find the same structures with little variations (see http://fract.al).