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].

The Hacker and the Ants

The Hacker and the Ants is a work of science fiction by Rudy Rucker published in 1994 by Avon Books. It was written while Rucker was working as a programmer at Autodesk, Inc., of Sausalito, California from 1988 to 1992. The main character is a transrealist interpretation of Rucker’s life in the 1970s (Rucker taught mathematics at the State University College at Geneseo, New York from 1972 to 1978. from Wikipedia). The plot follows:

(…) Jerzy Rugby is trying to create truly intelligent robots. While his actual life crumbles, Rugby toils in his virtual office, testing the robots online. Then, something goes wrong and zillions of computer virus ants invade the net. Rugby is the man wanted for the crime. He’s been set up to take a fall for a giant cyberconspiracy and he needs to figure out who — or what — is sabotaging the system in order to clear his name. Plunging deep into the virtual worlds of Antland of Fnoor to find some answers, Rugby confronts both electronic and all-too-real perils, facing death itself in a battle for his freedom. (…)

Alice’s move

“Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!” ~ The Red Queen, at “Through the looking-glass, and what Alice found there“, Charles Lutwidge Dogson, 1871.

Your move. Alice was suddenly found in a new strange world. And quickly needed to adapt. As C.L. Dogson (most known as Lewis Carroll) brilliantly puts it, all the running you can do, does not suffices at all. This is a world (Wonderland) with different “physical” laws or “societal norms”. Surprisingly, those patterns appear also to us quite familiar, here, on planet Earth. As an example, the quote above is mainly the paradigm for Biological Co-Evolution, in the form of the Red-Queen effect.

In Wonderland (1st book), Alice follows the white rabbit, which end-ups driving her on this strange habitat, where apparently “normal” “physical” laws do not apply. On this second book however, Alice now needs to overcome a series of great obstacles – structured as phases in a game of chess – in order to become a queen.  Though, as she moves on, several other enigmatic personages appear. Punctuated as well as surrounded by circular arguments and logical paradoxes, Alice must keep on, in order to found the “other side of the mirror“.

There are other funny parallel moves, also. The story goes on that Lewis Carroll gave a copy of “Alice in Wonderland” to Queen Victoria who then asked him in return to send her his next book as she fancied the first one. The joke is that the book was (!) … “An Elementary Treatise on Determinants, With Their Application to Simultaneous Linear Equations and Algebraic Equations (link)”. Lewis Carroll then went on to write a follow-on to Alice in Wonderland entitled “Through the Looking-Glass, and what Alice found there” that features a chess board on his first pages, and where chess was used to gave her, Queen Victoria, a glimpse on what Alice explored on this new world.

In fact, the diagram on the first pages contains not only the entire book chapters of this novel as well how Alice moved on. Where basically, each move, moves the reader to a new chapter (see below) representing it. The entire book could be found here in PDF format.  Besides the beauty and philosophical value of Dogson‘s novel on itself, and his repercussions on nowadays co-Evolution research as a metaphor, this is much probably the first “chess-literature” diagram ever composed. Now, of course, pieces are not white and black, but instead white and red (note that pieces in c1 – queen – and c6 – king – are white). Lewis Carroll novel, then goes on like this: White pawn (Alice) to play, and win in eleven moves.

However, in order to enter this world you must follow the “rules” of this new world. “Chess” in here is not normal, as Wonderland was not normal to Alice’s eyes. Remember: If you do all do run you could do, you will find yourself at the same place. Better if you could run twice as fast! First Lewis Carroll words on his second book (at the preface / PDF link above) advise us:

(…) As the chess-problem, given on a previous page, has puzzled some of my readers, it may be well to explain that it is correctly worked out, so far as the moves are concerned. The alternation of Red and White is perhaps not so strictly observed as it might be, and the ‘castling’ of the three Queens is merely a way of saying that they entered the palace; but the ‘check’ of the White King at move 6, the capture of the Red Knight at move 7, and the final ‘check-mate’ of the Red King, will be found, by any one who will take the trouble to set the pieces and play the moves as directed, to be strictly in accordance with the laws of the game. (…) Lewis Carroll, Christmas,1896.

Now, the solution, could be delivered in various format languages. But here is one I prefer. It was encoded on classic BASIC, running on a ZX Spectrum emulator. Here is an excerpt:

1750 LET t$=”11. Alice takes Red Queen & wins(checkmate)”: GO SUB 7000 (…)
9000 REM
9001 REM ** ZX SPECTRUM MANUAL Page 96 Chapter 14. **
9002 REM
9004 RESTORE 9000 (…)
9006 LET b=BIN 01111100: LET c=BIN 00111000: LET d=BIN 00010000
9010 FOR n=1 TO 6: READ p$: REM 6 pieces
9020 FOR f=0 TO 7: REM read piece into 8 bytes
9030 READ a: POKE USR p$+f,a
9040 NEXT f
9100 REM bishop
9110 DATA “b”,0,d,BIN 00101000,BIN 01000100
9120 DATA BIN 01101100,c,b,0
9130 REM king
9140 DATA “k”,0,d,c,d
9150 DATA c,BIN 01000100,c,0
9160 REM rook
9170 DATA “r”,0,BIN 01010100,b,c
9180 DATA c,b,b,0
9190 REM queen
9200 DATA “q”,0,BIN 01010100,BIN 00101000,d
9210 DATA BIN 01101100,b,b,0
9220 REM pawn
9230 DATA “p”,0,0,d,c
9240 DATA c,d,b,0
9250 REM knight
9260 DATA “n”,0,d,c,BIN 01111000
9270 DATA BIN 00011000,c,b,0

(…) full code on [link]

This is BASIC-ally Alice’s story …

Complex Systems and Alice in Wonderland

Video – Awesome choice by Tim Burton. It fits him like a glove. Here is the official Tim Burton’s Alice in Wonderland teaser trailer (just uploaded yesterday). Alice in Wonderland is directed by visionary director Tim Burton, of everything from Pee-Wee’s Big Adventure to Beetlejuice to Batman to Edward Scissor hands to Mars Attacks to Sleepy Hollow to Charlie and the Chocolate Factory to Sweeney Todd most recently. This is based on Lewis Carroll’s beloved series of books that were first published in 1865. Disney is bringing Tim Burton’s Alice in Wonderland to both digital 3D and 2D theaters everywhere on March 5th, 2010 early next year (more). Finally, just one personal thought. Soon, Tim Burton’s will stand for cinema, as what Jules Verne represented in literature.

In 1973, under several ongoing works on Co-Evolution and Evolutionary theory, L. van Alen proposed a new hypothesis: the Red Queen effect [1]. According to him, several different species will migth propably undergo and submit themselves to a continuous re-adapation [2,3], being it genetic or synaptic, only to end themselves at the point they started. A kind of arms races between species [4], potentially leading to specialization, as well as evolutionary Punctuated equilibria [5,6].

Van Alen chose the name “Red Queen” in allusion to the romance “Alice in Wonderland”, from Charles Lutwidge Dodgson (better known as Lewis Carroll) published in 1865. Over this country (Wonderland) it was usual to run as quick as you could, just to end yourself at the same place. The dialogs between Alice and the Red Queen are sintomatic:

[…] ‘Now! Now!’ cried the Queen. ‘Faster! Faster!’ And they went so fast that at last they seemed to skim through the air, hardly touching the ground with their feet, till suddenly, just as Alice was getting quite exhausted, they stopped, and she found herself sitting on the ground, breathless and giddy. The Queen propped her up against a tree, and said kindly, ‘You may rest a little, now. Alice looked round her in great surprise. ‘Why, I do believe we’ve been under this tree the whole time! Everything’s just as it was!’ ‘Of course it is,’ said the Queen. ‘What would you have it?’. ‘Well, in our country, said Alice, still panting a little, ‘you’d generally get to somewhere else – if you ran very fast for a long time as we’ve been doing.’ ‘A slow sort of country!’ said the Queen. ‘Now, here, I see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!‘ […]

Meanwhile, since 2007 (even much earlier!) I have taken Alice into my own arms. In fact, she is not heavy at all. If you feel you should keep running, some should, have a read on “Co-Cognition, Neural Ensembles and Self-Organization“, extended abstract for a seminar talk at ISR – Institute for Systems and Robotics, Technical Univ. of Lisbon (IST), May 31, 2007. Written at Granada University, Spain, 29 May 2007.

[1] van Alen, L. (1973), “A New Evolutionary Law“, Evolutionary Theory, 1, pp. 1-30.
[2] Cliff D., Miller G.F. (1995), “Tracking the Red Queen: Measurements of Adaptive Progress in Co-Evolutionary Simulations“, in F. Moran, A. Moreno, J.J. Merelo and P. Cachon (editors) Advances in Artificial Life: Proceedings of the Third European Conference on Artificial Life (ECAL95). Lecture Notes in Artificial Intelligence 929, Springer- Verlag, pp.200-218.
[3] Cliff D., Miller G.F. (1996), “Co-Evolution of Pursuit and Evasion II: Simulation Methods and Results“. In P. Maes et al. (Eds.), From Animals to Animats IV, Procs. of the Fourth Int. Conf. on Simulation of Adaptive Behaviour, MIT Press, pp. 506-515.
[4] Dawkins R., Krebs J.R. (1979), “Arms Races between and within Species“. In Procs. of the Royal Society of London: Biological Sciences, nº. 205, pp. 489-511.
[5] Eldredge, N., Gould, S. J., “Punctuated equilibria: an alternative to phyletic gradualism“. In: Models In Paleobiology (Ed. by T. J. M. Schopf), 1972.
[6] Gould, S. J., & Eldredge, N., “Punctuated equilibria: the tempo and mode of evolution reconsidered“. Paleobiology, 3, 115-151, 1977.

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.