Not in chaos, at the λ=0.273 vicinity of it

Photo – “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].

Simulacra and Simulation

According to Baudrillard, Simulacra are copies that depict things that either had no reality to begin with, or that no longer have an original. While, Simulation is the imitation of the operation of a real-world process or system over time. “Simulacres et Simulation” is a 1981 philosophical treatise by Jean Baudrillard seeking to interrogate the relationship among reality, symbols, and society:

[…] Simulacra and Simulation is most known for its discussion of symbols, signs, and how they relate to contemporaneity (simultaneous existences). Baudrillard claims that our current society has replaced all reality and meaning with symbols and signs, and that human experience is of a simulation of reality. Moreover, these simulacra are not merely mediations of reality, nor even deceptive mediations of reality; they are not based in a reality nor do they hide a reality, they simply hide that anything like reality is relevant to our current understanding of our lives. The simulacra that Baudrillard refers to are the significations and symbolism of culture and media that construct perceived reality, the acquired understanding by which our lives and shared existence is and are rendered legible; Baudrillard believed that society has become so saturated with these simulacra and our lives so saturated with the constructs of society that all meaning was being rendered meaningless by being infinitely mutable. Baudrillard called this phenomenon the “precession of simulacra”. […] (from Wikipedia)

“Simulacra and Simulation” is definitely one of my best summer holiday readings I had this year. There are several connections to areas like Collective Intelligence and Perception, even Self-Organization as the dynamic and entangled use of symbols and signals, are recurrent on all these areas. Questions like the territory (cultural habitats) and metamorphose are also aborded. The book is an interesting source of new questions and thinking about our digital society, for people working on related areas such as Digital Media, Computer Simulation, Information Theory, Information and Entropy, Augmented Reality, Social Computation and related paradigms. I have read it in English for free [PDF] from a Georgetown Univ. link, here.