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[…] Ao contrário de muitos sistemas tecnológicos actuais como aqueles que são produzidos através da codificação de algoritmos feitos por empresas de software ditas state-of-the-art, ‘algoritmos em receita’, que se organizam através de comandos hierárquicos exteriores e estranhos em grande parte ao seu próprio caractér (incompativeis à simulação e modelização computacional de fenómenos largamente complexos e não-lineares, como a de um bando de aves em vôo, até à da propagação do El Niño pelo planeta, entre outros tantos exemplos necessários à vida em sociedade), está-se agora verdadeiramente a caminhar para a construção de novos sistemas artificiais, que se auto-organizam, tais como os naturais, através dos seus próprios processos internos, e esses desenvolvimentos estão simultâneamente a permitir conhecer mais sobre a própria natureza da Natureza […],

in V. Ramos, “Dois Caminhos divergiam na Floresta, e eu – eu tomei o menos viajado, e essa fez toda a diferença (*)”, palestra apresentada em “Horizontes da Física“, Univ. de Aveiro, Centro Cultural e de Congressos de Aveiro, Março 2007. (*) Tradução livre de “Two roads diverged in a wood, and I – I took the one less travelled by, And that has made all the difference“, Robert Frost (1874-1963), Mountain Interval, 1920.

___________ § ___________

The other day, I decided to pick 23 books from my own library. These are books which anyone could read. Even those who are not working in Science  could understand them, and that’s probably the second best feature they have in common. So by order of appearance here they are: Ernst Haeckel “Art Forms in Nature”, Dana Ballard “An Intro to Natural Computation”, Brian Goodwin “How the Leopard changed its Spots”, Camazine et al “Self-Organization in Biological Systems”, David Gale “Tracking the Automatic Ant”, Douglas Hofstadter “Godel Escher Bach”, Fortner Meyer “Number by colors”, George Dyson “Darwin among the Machines”, Herbert Simon “Sciences of the Artificial”, Ian Stewart “Nature’s Numbers”, John Barrow “The Constants of Nature”, John Holland “Emergence”, John Holland “Hidden Order”, Kevin Kelly “Out of Control”, Marvin Minsky “The Society of Mind”, Maturana and Varela “El Arbol del Conocimiento”, Peter Bentley “Digital Biology”, Peter Coveney and Roger Highfield “Frontiers of Complexity”, Richard Dawkins “Climbing Mount Improbable”, Steven Johnson “Emergence”, Steven Levy “Artificial Life”, Steven Strogatz “Sync”, Stuart Kauffman “At Home in the Universe”, and William Bartram “The search for Nature’s Design”.

Leave you also with a recent short film piece (above) inspired on numbers, geometry and nature, by Cristóbal Vila (Eterea studios, Zaragoza, Spain). The movie depicts among other concepts, Fibonacci series, Golden Ratio, Delaunay, Voronoi tesselations … (music by Wim Mertens, … of course); if you are really interested on Nature’s Nature and his ‘mysteries‘, forget the horrible Dan Brown’s “Da Vinci Code”. This is it. These are some of the books that really matter:

Fig. – Zeus turns ants into Men thus populating the Island of Aegina, his nymph above right next to the eagle (this lovely 17th century drawing was sent by a friend, Isabel Figueiredo). Some sources also say Zeus turned himself into an eagle before doing this.

According to the Greek mythology the island was inhabited when Zeus had a romantic interlude with the nymph Aegina there and had a son, Aecaus (later, grandfather of Achilles). Zeus, at the request of Aecaus populated the island so Aecaus would have subjects in his kingdom (source). Those inhabitants were entitled Myrmidons:

“These were men created from ants on the island of Aegina, in the reign of Aeacus, Achille’s grandfather, and they were Achilles’ followers in the Trojan War. Not only were they thrifty and industrious, as one would suppose from their origin, but they were also brave. They were changed into men from ants because of one of Hera’s attacks of jealousy. She was angry because Zeus loved Aegina, the maiden for whom the island was named, and whose son, Aeacus, became its king. Hera sent a fearful pertinence which destroyed the people by thousands. It seemed that no one would be left alive. Aeacus climbed to the lofty temple of Zeus and prayed to him, reminding him that he was his son and the son of a woman the god had loved. As he spoke he saw a troop of busy ants. “Oh Father,” he cried, “make these creatures a people for me, as numerous as they, and fill my empty city.” A peal of thunder seemed to answer him and that night he dreamed that he saw the ants being transformed into human shape. […] So Aegina was repopulated from an ant hill and its people were called Myrmidons after the ant (myrmex) from which they had sprang.” (Hamilton, Edith, Mythology, Warner Books, New York, 1969)

Aegina is the 2nd closest island to Athens after Salamina at the Saronic Gulf, with 86 square Kms and a current population of 12000 people. The island is home to one of the most beautiful temples of late Archaic Greece, the temple of Aphaia. A volcanic island with plains of respectable fertility to the northern and southern parts. Aegina is also where the famous pistachio nuts can be  found alongside the other main produce of the island, grain, vines, almonds and olives. The southern end of the island is rocky and barren. The highest peak of the island is Mt. Oros.

On November 7, 1940, “Galloping Gertie” went down. Due to strong lateral winds, his miscalculated resonant frequency achieved a critical level, and while experiencing a strong phase transition, the third longest suspension span bridge in the world collapsed, just 4 months after being built. The Tacoma Narrows Bridge stretched like a steel ribbon across Puget Sound river and soon became famous as the most dramatic failure in bridge engineering history. When Galloping Gertie splashed into Puget Sound, it created ripple effects across the nation and around the world mainly due to this footage (above). The event changed forever how engineers design suspension bridges. In fact, Gertie‘s failure led to the safer suspension spans we use today. These 356 seconds under chaotic regimes were precious…

Relax, enjoy the music, and wide open your eyes as never before…

Video -“Sand, sand, pile of sand” by Robert Proch (2009) – Impression without an idea, about trying to catch one (music by Pinkfreud).

Complex Adaptive Systems (CAS) are dynamic developing systems which arrange themselves according to external influences and to their own inner current state. If you are familiar with Conway’s “Game of Life“, you have an example of such a system. Complex adaptive systems arrange themselves around one or more critical factors (like in a sandpile, for example, where the pile will rearrange itself when you drop additional sand grains onto it). The theory behind these systems is related to chaos theory, but the systems are said to be “on the edge of chaos“, because they have the ability to adjust themselves (around the critical factors), unlike truly chaotic systems. One interesting thing with CA-systems is that they can suddenly rearrange themselves rather violently or criticality. Like in a sandpile which has a grain added to it, which topples onto other grains, which in turn topple onto other grains, etc. In physics, the Bak-Tang-Wiesenfeld sandpile model is the first discovered example of a dynamical system displaying self-organized criticality and is named after Per Bak [1] [2] [3], Chao Tang [1] [2] and Kurt Wiesenfeld [1] [2]. While running the model, you soon then have an avalanche effect and signatures produced equivalent to those found in nature. In fact, many phenomena in daily life are complex adaptive systems, like weather, traffic, earthquakes, eco-systems, or the stock market, and many of them share this precise 1/f noise pattern. As our brains.

[1] Per Bak, Chao Tang and Kurt Wiesenfeld (1987). “Self-organized criticality: an explanation of 1/f noise“. Physical Review Letters 59: pp. 381-384.
[2] Per Bak, Chao Tang and Kurt Wiesenfeld (1988). “Self-organized criticality“. Physical Review A 38: pp. 364-374.
[3] Per Bak (1996). How Nature Works: The Science of Self-Organized Criticality. New York: Copernicus. ISBN 0-387-94791-4.

[...] People should learn how to play Lego with their minds. Concepts are building bricks [...] V. Ramos, 2002.

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