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].

On form and formation…

Painting – Paul Klee, detail from “U struji sest pragova“, 1929.

“Nous avons une notion palpable de la métamorphose de la chenille. Nous, certainement, mais non la chenille.” ~ Edgar Allan Poe / “Le principe de l´evolution est beaucoup plus rapide en informatique que chez le bipède.” ~ Jean Dion / “Let chaos storm!… Let cloud shapes swarm!… I wait for form.” ~ Robert Frost

[…] In his notebooks the painter Paul Klee repeatedly insisted, and demonstrated by example, that the processes of genesis and growth that give rise to forms in the world we inhabit are more important than the forms themselves. ‘Form is the end, death’, he wrote. ‘Form-giving is movement, action. Form-giving is life’ (Klee 1973: 269). This, in turn, lay at the heart of his celebrated ‘Creative Credo’ of 1920: ‘Art does not reproduce the visible but makes visible’ (Klee 1961: 76). It does not, in other words, seek to replicate finished forms that are already settled, whether as images in the mind or as objects in the world. It seeks, rather, to join with those very forces that bring form into being. Thus the line grows from a point that has been set in motion, as the plant grows from its seed. Taking their cue from Klee, philosophers Gilles Deleuze and Félix Guattari argue that the essential relation, in a world of life, is not between matter and form, or between substance and attributes, but between materials and forces (Deleuze and Guattari 2004: 377). It is about the way in which materials of all sorts, with various and variable properties, and enlivened by the forces of the Cosmos, mix and meld with one another in the generation of things. And what they seek to overcome in their rhetoric is the lingering influence of a way of thinking about things, and about how they are made and used, that has been around in the western world for the past two millennia and more. It goes back to Aristotle. To create any thing, Aristotle reasoned, you have to bring together form (morphe) and matter (hyle). In the subsequent history of western thought, this hylomorphic model of creation became ever more deeply embedded. But it also became increasingly unbalanced. Form came to be seen as imposed, by an agent with a particular end or goal in mind, while matter – thus rendered passive and inert – was that which was imposed upon. […], in Tim Ingold, “Bringing Things to Life: Creative Entanglements in a World of Materials“, University of Aberdeen, July 2010 – Original version (April 2008 ) presented at ‘Vital Signs: Researching Real Life’, 9 September 2008, University of Manchester. (pdf link)

On Life, aLife and Death

Fig. – Knight, Death and the Devil (1513). This is one of three metal engravings by Albrecht Dürer in a series called Meisterstiche (since I have started this blog, I have also chosen a woodcut engraving done by Dürer, – his Rhinoceros – for several reasons, one being that it appeared in Europe for the fisrt time trough Lisbon in 1515). The others are Melancholia I and Saint Jerome in His Study. The engraving is dated 1513, two hundred years after the dissolution of the Knights Templar in 1313. We see a skull in the bottom left corner; the night in full armour (shining armor?) carries a lance; behing him is a pig-snouted horned devil and he is passing Death on his pale horse, who is carrying an hourglass. Under the knight’s horse runs a long-haired retriever, a hunting dog. Dürer called this picture Reuter, which is, Rider. (source).

“Every evil leaves a sorrow in the memory, until the supreme evil, death,
wipes out all memories together with all life“. Leonardo da Vinci.

Carlos Gershenson (Complexes blog), some days ago just uploaded a short (5 pp.) philosophical essay about life, death and artificial life (*) (aLife), which I vividly recommend. He starts his “What Does Artificial Life Tell Us About Death?” with this precise Leonardo’s quote (above). Among other passages it’s interesting to see how different notions of death are deduced from a limited set of different notions of life (in many situations, opposing terms could be used to define each other). Carlos points us out to six currents, or lines of thought:

• If we consider life as self-production (Varela et al., 1974; Maturana and Varela, 1980, 1987; Luisi, 1998), then death will the the loss of that self-production ability.
• If we consider life as what is common to all living beings (De Duve, 2003, p. 8), then death implies the termination of that commonality, distinguishing it from other living beings.
• If we consider life as computation (Hopfield, 1994), then death will be the end (halting?) of that computing process.
• If we consider life as supple adaptation (Bedau, 1998), death implies the loss of that adaptation.
• If we consider life as a self-reproducing system capable of at least one thermodynamic work cycle (Kauffman, 2000, p. 4), death will occur when the system will be unable to perform thermodynamic work.
• If we consider life as information (a system) that produces more of its own information than that produced by its environment (Gershenson, 2007), then death will occur when the environment will produce more information than that produced by the system.

I was aware of Kauffman’s “blender thought experiment”, however Gershenson adds much more into it. A variation. He goes on like this. Nice reading:

[…] Focussing on our understanding of death, this will depend necessarily on our understanding of life, and vice versa. Throughout history there have been several explanations to both life and death, and it seems unfeasible that a consensus will be reached. Thus, we are faced with multiple notions of life, which imply different notions of death. However, generally speaking, if we describe life as a process, death can be understood as the irreversible termination of that process. The general notion of life as a process or organization (Langton, 1989; Sterelny and Griffiths, 1999; Korzeniewski, 2001) has expelled vitalism from scientific worldviews. Moreover, there are advantages in describing living systems from a functional perspective, e.g. it makes the notion of life independent of its implementation. This is crucial for artificial life. Also, we know that there is a constant flow of matter and energy in living systems, i.e. their physical components can change while the identity of the organism is preserved. In this respect, one can make a variation of Kauffman’s “blender thought experiment” (Kauffman, 2000): if you put a macroscopic living system in a blender and press “on”, after some seconds you will have the same molecules that the living system had. However, the organization of the living system is destroyed in the blending. Thus, life is an organizational aspect of living systems, not so much a physical aspect. Death occurs when this organization is lost. […]

(*) even if, I do not recommend this Wikipedia entry. Extremely poor.