You are currently browsing the tag archive for the ‘phase transitions’ tag.

Saramago Caos quote - Lisbon, Vitorino Ramos 2013Photo – “O caos é uma ordem por decifrar” (Portuguese), that is… “Chaos is an order yet to be deciphered“, a quote from the Nobel Prize in Literature (1998) José Saramago [Lisbon, V. Ramos, 2013].

In 1990 (*), on one of his now famous works, Christopher Langton (link) decided to ask an important question. In order for computation to emerge spontaneously and become an important factor in the dynamics of a system, the material substrate must support the primitive functions required for computation: the transmission, storage, and modification of information. He then asked: Under what conditions might we expect physical systems to support such computational primitives?

Naturally, the question is difficult to address directly. Instead, he decided to reformulate the question in the context of a class of formal abstractions of physical systems: cellular automata (CAs). First, he introduce cellular automata and a simple scheme for parametrising (lambda parameter, λ) the space of all possible CA rules. Then he applied this parametrisation scheme to the space of possible one-dimensional CAs in a qualitative survey of the different dynamical regimes existing in CA rule space and their relationship to one another.

By presenting a quantitative picture of these structural relationships, using data from an extensive survey of two-dimensional CAs, he finally review the observed relationships among dynamical regimes, discussing their implications for the more general question raised above.  Langton found out that for a 2-state, 1-r neighbourhood, 1D cellular automata the optimal λ value is close to 0.5. For a 2-state, Moore neighbourhood, 2D cellular automata, like Conway’s Life, the λ value is then 0.273.

We then find that by selecting an appropriate parametrisation of the space of CAs, one observes a phase transition between highly ordered and highly disordered dynamics, analogous to the phase transition between the solid and fluid states of matter. Furthermore, Langton observed that CAs exhibiting the most complex behaviour – both qualitatively and quantitatively- are found generically in the vicinity of this phase transition. Most importantly, he observed that CAs in the transition region have the greatest potential for the support of information storage, transmission, and modification, and therefore for the emergence of computation. He concludes:

(…) These observations suggest that  there is  a fundamental connection between phase transitions and computation, leading to the following hypothesis concerning the emergence of computation in  physical systems: Computation may emerge spontaneously and come to dominate the dynamics of physical systems when those systems are at or near a transition between their solid and fluid phases, especially in the vicinity of a second-order or “critical” transition. (…)

Moreover, we observe surprising similarities between the behaviours of computations and systems near phase transitions, finding analogs of computational complexity classes and the halting problem (Turing) within the phenomenology of phase transitions. Langton, concludes that there is a fundamental connection between computation and phase transitions, especially second-order or “critical” transitions, discussing some of the implications for our understanding of nature if such a connection is borne out.

The full paper (*), Christopher G. Langton. “Computation at the edge of chaos”. Physica D, 42, 1990, is available online, here [PDF].

Advertisements

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…

(image: Hundredth Monkey – graphic art design by Michael Paukner, 2009)

This phenomenon is considered to be due to critical mass. When a limited number of people know something in a new way, it remains the conscious property of only those people. The Hundredth Monkey Syndrome hypothesises that there is a point at which if only one more person tunes in to a new awareness, a field of “energy” is strengthened so that new awareness is picked up by almost everyone.

The Hundredth Monkey Effect was first introduced by biologist Lyall Watson in his 1980 book, ‘Lifetide.’ He reported that Japanese primatologists, who were studying Macaques monkeys in the wild in the 1950s, had stumbled upon a surprising phenomenon. Some anthropologist were studying the habits of monkeys on some islands in the ocean off the shores of Japan. They found one particularly smart little fellow, and taught it to wash its food before eating it. He learned to do this quite quickly. Soon the other monkeys in his family also began to wash their food before eating it. Later this behavior spread to other monkeys in the clan. About the time one hundred monkeys were washing their food prior to eating it, suddenly all the monkeys on all the islands, some thousands of miles away, began to wash their food before eating it. This surprising observation became known as the Hundredth Monkey Effect and has been repeatedly observed. This same phenomenon is true in humans as well. It is part of the reason we have trends in fashion, the economy, and politics, etc. Finally for those who wish for extra sources, Malcom Gladwell’s “The Tipping Point” book, will be a good start.  Other related books include Philip Ball’s “Critical Mass“. Here is a good review.

Poster design above was done by Michael Paukner, one of my favourite graphic and info design contemporary artists. Not only for the themes he chooses (for instance, his most recent work was about the Golden ratio and Leonardo’s Vitruvian man), but above all, by his incredible and powerful final design. Meanwhile and on purpose, I asked today my youngest son to draw a monkey on it’s own. He his 5 years old, and this is his drawing.

(image: António’s Monkey – 5 years old – click to enlarge, Jan. 2010)

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

@ViRAms on Twitter

Error: Twitter did not respond. Please wait a few minutes and refresh this page.

Archives

Blog Stats

  • 246,257 hits