The featured image is a visualization of the routing paths through a portion of the Internet. As the Internet is now the means, the tool, the depository of data and the projection wall for our collective knowledge, we can easily see it as a collective brain. The connections and pathways can be easily imagined as the pathways of neurons and synapses in this global brain. But this is not the only parallel; the neuron connections can also parallel the structures shown by our cities viewed from aboard the space station, or the images of the deep space in the visible universe – it seems that, the larger the diversity of scales, the more similarity we find. Science names this repetition of patterns from the micro to the macro scale fractality, which is a fundamental property of our universe. A fractal is “an object whose parts, at infinitely many levels of magnification, appear geometrically similar to the whole.“
Fractality is only one example of universality of patterns and systems; as the common trait of many fractals is self-similarity, there is a whole world of scale-free complex networks that suggest common self-organization dynamics. The complex networks are self-repeating patterns on all length scales. At human scale we can observe real-life systems like the world-wide web, biological and social networks – we are part of all three. As we are also part of the universe. As the universe is part of us.
One of the most common patterns of self-similarity is the spiral. We see spirals everywhere; besides being a beautiful shape, a spiral is a truly efficient form. The marvelous curves are not only nature’s way to organize space efficiently, but they also convey energy and motion.
When we analyse the geometry of a spiral we realize that it is possibly the most simple mathematic pattern that occurs in nature at all levels, from the tracks made by atomic particles (this is how far “small” we can see) to chemical reactions (Belousov-Zhabotinsky reaction) to bacteria-growth patterns, to crystals (bismuth), to clouds, to turbulence in water and air, to weather patterns on distant planets, to galaxies and nebula; we see curves in a wave, in the shells and snails, in animals’ tails and horns, in flowers, and plants. We can hear because of such a spiral – cochlea.
Mathematics is our way to translate the universe into numbers.Numbers are only what we use to organize quantitative information. If we analyse the spiral, it is always the repetition of the same ratio, the so called “Golden Number”, 1.61803399, represented as the Greek letter Phi. Along time it has been called a number of names, all of them containing “golden” or “divine” as adjective: Golden Ratio, Golden Proportion, Golden Mean, Golden Section, suggestive of how people can be fascinated and awed by the “divine” intelligence of the universe: it is also known as the “Divine Proportion” and the “Divine Section”.
The Golden Ratio is generated by a specific, easy to calculate sequence of numbers: starting from zero, then one and two, each number is to be additioned to the one before it:
zero, one + one = two, two +one =three, three + two = five, and so on, to infinity.
The potentially infinite series, called Fibonnaci after the nickname of the Italian matematician who first published a book on the series, is now well known in the mainstream of pop culture. A Fibonacci Spiral is a logarithmic spiral with a growth factor of phi, or a rectangle with sides in the ratio of 1 : φ – the Golden Rectangle, or the Golden Spiral, widely used in arts and architecture. Throughout history, but particularly in the Renaissance art with Leonardo da Vinci and his peers, many artists and architects proportioned their works according to the Golden Ratio – which explains why, innately, we find their works aesthetically pleasing (what about this inclination we commonly share, that of liking and loving, of disliking or hating the same things – as much as we would like to deny it, there are more similarities among us to unite, than are differences to separate us).
As we are all webbed within our human society, we are already one example of a complex system, and there is a whole hierarchy of systems inside us – fractality. Human society is itself being webbed in the larger system of life on the planet, as the planet is also part of its solar system, itself part of … .
It is undeniable, and today more obvious than ever, that we are intricate, irreplaceable parts embedded in ever larger complex systems; we cannot hold ourselves apart from the laws of a universe ruled by self-organizing processes. This is our place in the order of Being. This is our Identity. This is our Right. This is our Responsibility.
Man has instinctively complied to the laws dictated by nature, first by imitating nature, and now through understanding nature, realizing that he is nature itself, that nature’s intelligence is man’s intelligence. Everything that our mind perceives and is aware of is the universe looking at itself. Since the numbers are everywhere, everything is part of a pattern. The same patterns that are outside us, in the infinite universe, are also inside us. We reflect on them, as they reflect on us: we, as individuals, are holograms within the holographic universe: images within images. Life itself is a Fractal. The initial question: “What is our place inside the universe?” is gradually finding its answer; in as much as it is hard to believe it, this is, however, the true answer.