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Vieira da Silva O jogo de xadrez 1943

Picture – The idea of Viera da Silva’s art as a kind of code to be decoded comes across most clearly in The Chess Game – “O jogo de Xadrez” (above, Oil on Canvas, 1943). […] The checkered pattern of the chessboard extends beyond the table not only to the players themselves but also to the very landscape itself […] … Vieira da Silva would have loved The Matrix films […] (more).

Last night I decided to do something new. To play and broadcast live on Twitter, two chess games, blindfold. A 1st one with white pieces, another playing black. For that, I have chosen Chess Titans (link) has my contender,  a computer program most people can also access and try out over their PC’s. Chess Titans is a computer chess game developed by Oberon Games and vastly included in Windows Vista and Windows 7.  While broadcasting the game live, I added some of my thoughts while playing both games. Even if in brief, that was what I was feeling at the moment: what I was planning, and in what adversary menaces I mostly decided to spent my time.

For those reasons, what follows are those on-the-fly live comments, uncut, made at each moment, while I was thinking. No extra analysis is included here today. It will be more interesting for those who will read me on the future, I guess. This could give a precise idea what happened each time I have made a move, how I react it to some computer moves, and how some of my errors happened as you will see. How my mind went in one direction, or several, depending on the position. Those comments are highlighted by brackets () below, and were twitted live as they arrived to me. Besides, two subsequent comment brackets do not mean two subsequent twitter live chess thinking comments. Sometimes, several minutes have passed between those different thoughts.

As a final note, Chess Titans played each move in around 15-35 seconds, and in difficult positions, rarely, up to 2-3 minutes (I have chosen to play against the maximum level, 10). Playing blindfold, I have spent around 3-4 minutes for regular moves, like exchanging pieces, tweeting, etc, and mostly around 10-15 minutes for some positions, in quite difficult combinatorial patterns. First game playing white, endured 1h and a half (lost it) ,while the second almost 4h and 30 minutes within 58 moves. Here they are:

Game (1) Vitorino Ramos vs. Chess Titans level max.=10 [Sicilian] (LIVE on Twitter 23:00 GMT – 00:24 GMT, Dec. 20, 2012) Duration: 1h 24m.

1. e4, c5 2. c3, Nf6 3. Qc2, e5 4. Ne2, d5 5. exd5, Qxd5 (hmm … 6. d4 or 6.Ng3) 6. d4, Nc6 (7. c4 8. d5 but feeling problems later with his Nb4, Qa4+, Bd7!) 7. dxe5, Nxe5 8. Nf4, Qd7 9. Na3 (for 10. Bb5!), 9. …, Qe7 (was expecting 9. … a6) (10. Be3 seems too bad. Maybe 10. Be2 or Qe2. Or the line 10. Bb5+, Bd7, BxB, Nexd7+, Be3, Ng4 hmm … then Nd5!! ok … 10. Bb5+) 10. Bb5+, Bd7 11. 0-0, (better than BxB+ I guess cause of a future Ng4 by him), 11. …, g5

Vitorino Ramos vs. Chess Titans level max.=10 after 11. ..., g5

Chess diagram – crucial position after his 11. …, g5 move. White (me) to play.

(too risky maybe 12. Re1, gxN, Bxf4, Nf6-g4, f3 difficult for me to compute the rest) (12. Re1, gxN, Bxf4, Nf6-g4, f3, … hmm … Nexf3+ ?!!!)
(how about h3; 12. Re1, gxN, Bxf4, Nf6-g4, h3) (hmm???? 12. Re1, gxN, Bxf4, Nf6-g4, h3, Nxf2, Kxf2, Neg4+ ~ hmm) (we also have intermediate variants like, Bxb5, Nxb5, Q moves and gains one tempo by attacking the Knight on b5) (ok, no prob, here I go. This will be bloody …)

12. Re1 12. …, Nf3+ (Oooohhh NO!!!! damn, calculated this more ahead, not now. So stupid) 13. gxf3, Qxe1+ 14. Kg2, gxf4 (now he has Rg8++) (Bxf4 for Rg8+, Bg3 he has QxRa1, bad, bad) 15. Bxd7+, Nxd7 (h3 is an escape now for my King) (16. Rb1, Rg8+, Kh3, Qf1+, Kh4, Be7+ and I think I’m lost) (k, let’s sacrifice the Rook in a1) 16. Bxf4, Qxa1 (at least I have some counter-game now) 17. Qe4+, Be7 (Bd6 will not work due to Rg8+ followed by Qf1+ I guess…, damn, should have played 17. Qe2+!!) (Nb5 menacing Nc7+ or Nd6+ does not work either. Follows Rg8+, Kh3, Qf1+ and Q takes Nb5) (and for Qxb7 he has the robust Rb8 answer) (…. k, the end. Give up. Chess Titans level 10 won 1st game – 2nd game follows) 0-1

After two big blunders on the first game above (the bad 12. Re1 instead of a normal 12. Nd3 – check 1st diagram above -, and 17. Qe4+ instead of 17. Qe2+, since controlling f1 was crucial)  the second game did not started well also. After 6 moves I was already losing 1 pawn. Yet, still did manage to open the game and get the initiative a few moves later (around 14. …, Re8+). I feel OK with open and highly combinatorial games as these (normally it’s when I play better), but I forgot one simple fact: I was playing blindfold. Four and an half hours later I guess I’m happy to have managed to drawn a quite interesting and complex game, playing black pieces. What a long and stressful headache. Here:

Game (2) Chess Titans level max.=10 vs. Vitorino Ramos [English opening] (LIVE on Twitter 00:45 GMT – 05:12 GMT, Dec. 20, 2012) Duration: 4h 27m.

1. c4, e5 (English) 2. Nc3, f5 3. g3, c6 4. e4, fxe4 5. Qh5+ (that 4. …, fxe4 was too bad from me. Childish error. Did not see the typical Qh5+ trap, g6, Qxe5+ followed by QxRh8. It should have been 4. …, d6) 5, …, Ke7 6. Qxe5+, Kf7 7. Be2, Qf6 8. Qxe4, Bc5 9. Nf3, Nh6 10. d4 (hmm prepares Ng5+ ??!) 10. …, Bb4 11. Bg5, Qf5 12. Qxf5+, Nxf5 13. Bd3, d6 14. a3, Re8+ 15. Be2, Bxc3+ 16. bxc3, h6 17. Bd2, g5 18. h4, g4 19. Nh2, h5 20. Bf4, b5 21. cxb5, cxb5 22. f3, Bb7 23. Rf1, gxf3 24. Nxf3, Nd7 25. Kd1, a6 26. Ng1, Kg6 27. Re1, Rac8 28. a4 (hmm … Bxh5+ is dangerous if I move the rock in column c, like 28. …, Rxc3), 28. …, Nf6 29. axb5, axb5, 30. Ra7, Bc6 (did calculate Ba8 and Bd5 but hmm, I need d5 for my knight. His bishop on f4 must die) 31. Bd3, Nd5 32. Ne2

Chess Titans level max.=10 vs. Vitorino Ramos after his 32. Ne2 move

Chess diagram – position after his 32. Ne2 move. Black (me) to play. I’m 1 pawn down but with the initiative.

(I can’t take on c3 right? Nxc3, Nxc3, Bf3+, and then he goes back with Knight to e2, gee…) (hard position to mentally calculate) (32. …, b4 ?????) (damn, let me simplify all this…) 32. …, Ra8 33. Rxa8, Rxa8 34. Bxd6 (geee, that 31. Bd3 was so well played) 34. …, Ra1+ (will try to drawn him with successive pressure and checks, I guess) 35. Kd2, Ra2+ 36. Kc1 (yep, he prepares to play Bb1, I guess) 36. …, Nde3 37. Nf4+, Kf7 38. Nxh5, Ra1+ 39. Bb1 (only move for him. If not I change the rocks in e1 with time and then  his bishop on d6) 39. …, Be4

Chess Titans level max.=10 vs. Vitorino Ramos after my 39. ..., Be4

Chess diagram – position after my 39. …, Be4 move, pinning b2. White (computer) to play. I’m now 3 pawns down.

(Pinning. Guess this would end with 2 knights and 1 pawn against 1 knight and 4 pawns!!) 40. Kb2, Rxb1+ 41. Rxb1, Bxb1 42. Kxb1, Nxd6 43. Nf4 …

Chess Titans level max.=10 vs. Vitorino Ramos after his 43. Nf4 move

Chess diagram – position after his 43. Nf4 move. Black to play. Now I must stop two different white pawn clusters, on each side. Hard final.

(must be careful, now) (I guess I will do the obvious) (hmm, does not work, 43 …. Ne4 44. Ne2!) (wait, then King on f6, f5, g4 pressing g3) (k, here I go) 43. …, Ne4 44. Ne2, (now, I must think of my pawn on b5, hmm) (he has Ka2, a3 etc) (I have Nc4-d6, hope this helps, … here I go) 44. …, Kf6 45. Kb2, Kf5 46. h5 (?????!!!) 46. …, Kg5 47. h6 (?? He wants my King outside the centre, is that it? … I must take it) 47. …, Kxh6 48. Kb3 (yep, now I have problems on the other side) 48. …, Nd6 49. Kb4 (now my aim will be to arrive on f3 with my King) 49. …, Kg5 50. Kc5, Nec4 (freezing everything!) 51. d5 (hmm, I get it, he wants to reach Kd4 and Kd3. Anyway, I will go for the one in g3) 51. …, Kg4 52. Kc6

(what?????? he is just waiting) (hmm … wait, makes some sense. If 52…, Kf3 then 53. Nd4+, Kxg3 54. Nxb5, Nxb5 55. Kxb5 and I would have 1 knight against 2 pawns and my King far away) (hmm, hard call) (52…, Kf3 or not 52…, Kf3 ??!!!) (Kf3 followed by Ke3 and Kd3 etc does not work also, I think) (… hmm, wait, it might if he does not go Kc5, Kd4. If he goes I will the other way around by Kf4, Ke5)

52. …, Kf3 53. Nd4+, Kxg3 54. Kc5, Kf4 55. Nxb5, Ke5 (and it’s a drawn, I guess) 56. Kb4, Nxb5 57. Kxc4 57. …, Nxc3 ( if he goes 58. d6 then 58. …, Nd5! 59. d7, Nb6+ followed by Nxd7!!) 58. Kxc3, Kxd5 ½½ (uuuufff, managing to draw blindfold, is a good result I guess :)

One of my conclusions: never play blindfold again in a open and highly combinatorial position, namely when you have a pair of knights. That, could make you dizzy and sick. Another (among, many others): never live tweet chess again. You will loose a lot of dumb followers (which turns-out to be healthy) and simultaneously attract all kinds of weirdos, and guru-like spam on-line marketeers. Vieira da Silva was right. It extends beyond the table. Like lake ripples when a stone is thrown.

Figure – Brain wave patterns (gamma-waves above 40 Hz). Gamma waves – 40 hz above – these are use for higher mental activity such as for problem solving, consciousness, fear. Beta waves – 13-39 Hz – these are for active thinking and active concentration, paranoia, cognition and arousal. Alpha waves – 7-13 Hz – these are for pre-sleep and pre-wake drowsiness and for relaxation. Theta waves – 4-7 Hz – these are for deep meditation, relaxation, dreams and rapid eye movement (REM) sleep. Delta waves – 4 Hz and below are for loss of body awareness and deep dreamless sleep (source: Medical School, link).

Figure – Subcritical Turing bifurcation: formation of a hexagonal pattern from noisy initial conditions in the two-component reaction-diffusion system of Fitzhugh-Nagumo type. From left to rigth:a) Noisy initial conditions at t = 0. b) State of the system at t = 10. c) Almost converged state at t = 100. (source link)

Figure – Other patterns found in the above two-component reaction-diffusion system of Fitzhugh-Nagumo type. From left to rigth: a) Rotating spiral.b) Target pattern. c) Stationary localized pulse (dissipative soliton). (source link)

When an activator-inhibitor system undergoes a change of parameters, one may pass from conditions under which a homogeneous ground state is stable to conditions under which it is linearly unstable. The corresponding bifurcation may be either a Hopf bifurcation to a globally oscillating homogeneous state with a dominant wave number k=0 or a Turing bifurcation to a globally patterned state with a dominant finite wave number. The latter in two spatial dimensions typically leads to stripe or hexagonal patterns. [p.s. – a related lovely beach bay!.. state-phase diagram; Reaction-Diffusion by the Gray-Scott model: Pearson’s Parameterization (link) ]

Video – “BIG BANG BIG BOOM”: an unscientific point of view on the beginning and evolution of life … and how it could probably end. Direction and animation by BLU / production and distribution by / sountrack by Andrea Martignoni.

[…] It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically, unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading. […], A. M. Turing, “The Chemical Basis of Morphogenesis“, in Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, Vol. 237, No. 641. (Aug. 14, 1952), pp. 37-72. (link)

It is not the strongest of the species that survives, nor the most intelligent that survives. It is the one that is the most adaptable to change“. Charles Darwin (On the Origin of Species, Nov. 1859)

During the Victorian era where high prudery and morality were constant, it would be hard to imagine seeing Charles Darwin wearing a Scottish-kilt. In fact, men’s formal clothing was less colourful than it was in the previous century, while women’s tight-fitting jersey dresses of the 1880s covered the body, leaving little to the imagination (source). There is however, one beautiful – as in strict sense of delighting the senses for exciting intellectual or emotional admiration – reason, I think he should have done it (!), regardless the  obvious bearing consequences of a severe Victorian society. Surprisingly, some how, that reason is linked to cheetahs chasing gazelles, among many other things…

As the image of Charles Darwin wearing a kilt, you will probably find these awkward too, but when a cheetah chases a gazelle, banded tartan Scottish-kilt woven textile like patterns soon start to pop-up everywhere. Not at the ground terrain level, of course. Instead, they appear as a phenotype-like map between your present and the past. You may think that this banded tartans will have no significance for your life, but do mind this: crying babies do it all the time with their mommy’s and fathers, companies do it with other companies in their regular business, people commuting in large cities do it over large highways, human language, literature and culture does it, friends do it, PC virus and anti-virus software do it, birds singing do it also, … and even full countries at war do it.

One extreme example is the Cold War, where for the first time on our Human history, co-evolutionary arms-race raised to unprecedented levels. Co-Evolution is indeed the right common key-word for all these phenomena, while large white banded strips punctuated by tiny black ones (bottom-left woven kilt above), would be the perfect correspondent tartan pattern for the case of the Cold War example mentioned. But among these, there is of course, much more Scottish-kilt like patterns we could find. Ideas, like over this TV ad above, co-evolve too. Here, the marketeer decided to co-evolve with a previous popular famous meme image: Sharon Stone crossing his legs at the 1992 ‘Basic Instinctmovie. In fact, there is an authentic plethora of different possible behavioural patterns. Like a fingerprint (associated with different Gaelic clans), each of these patterns correspond to a lineage of current versus ancestral strategies, trying to solve a specific problem, or achieving one precise goal. But as the strategic landscape is dynamically changing all the time, a good question is, how can we visualize it. And, above all, what vital information and knowledge could we retrieve from this evolutionary Scottish-kilts maps.

Fig. – The frontispiece drawing to the English edition of Ernst Haeckel‘s Evolution of Man (trans. 1903) presents a skull labelled “Australian Negro” as an intervening evolutionary stage between the “Mediterranean” skull and those of the lower primates (from the 1891 ed. of the Anthropogenie).

In nature, organisms and species coexist in an ecosystem, where each species has its own place or niche in the system. The environment contains a limited number and amount of resources, and the various species must compete for access to those resources, where successive adaptations in one group put pressure on another group to catch up (e.g., the coupled phenomena of speed in the cheetah and evasive agility in the gazelle). Through these interactions, species grow and change, each influencing the others evolutionary development [7]. This process of bi-adaptive relationship (in some cases can also assume a form of cooperation and mutualism) or reciprocal adaptation is know as Co-evolution, i.e. the evolution of two or more competing populations with coupled fitness.

The phenomena has several interesting features that may potentially enhance the adaptive power of artificial evolution [7], or  other types of bio-inspired learning systems. In particular, competing populations may reciprocally drive one another to increasing levels of complexity by producing an evolutionary “arms race”, where each group may become bigger, faster, more lethal, more intelligent, etc. Co-Evolution can then happen either between a learner (e.g., single population) and its environment (i.e. based on competitions among individuals in the population) or between learning species (two populations evolving), where the fitness of individuals is based on their behaviour in the context of the individuals of the other population [7]. This latter type of co-evolutionary search is often described as “host-parasite”, or “predator-prey” co-evolution. A good example and application of co-evolutionary learning include the pioneering work by Hillis in 1990 [1] on sorting networks.

It can occur at multiple levels of biology: it can be as microscopic as correlated mutations between amino acids in a protein, or as macroscopic as co-varying traits between different species in an environment. Being biological Co-Evolution, in a broad sense, “the change of a biological object triggered by the change of a related object” [2], his visualization however, could be profoundly hard. In fact, attempting to define and monitor “progress” in the context of Co-Evolutionary systems can be a somewhat nightmarish experience , as stated in [4]. It’s exactly here where Scottish-kilts come into play.

In 1995 [3], two researchers had a simple, yet powerful idea. In order to monitor the dynamics of artificial competitive co-evolutionary systems between two populations, Dave Cliff and Geoffrey Miller [3,4,5] proposed evaluating the performance of an individual from the current population in a series of trials against opponents from all previous generations. while visualizing the results as 2D grids of shaded cells or pixels: qualitative patterns in the shading can thus indicate different classes of co-evolutionary dynamic. Since their technique involves pitting a Current Individual (CI) against Ancestral Opponents (AO), they referred to the visualizations as CIAO plots (fig. above [3]).

Important Co-Evolutionary dynamics such as limited evolutionary memory, “Red Queen” effects or intransitive dominance cycling, will then be revealed like a fingerprint as certain qualitative patterns. Dominance cycling, for instance, it’s a major factor on Co-Evolution, wish could appear or not, during the entire co-evolutionary process. Imagine, for instance, 3 individuals (A,B,C) or strategies. Like over the well known “Rock, Paper, Scissors” game, strategy B could beat strategy A, strategy C could beat B, and strategy A could beat C, over and over in an eternal cycling, where only “arms race” specialized learning will emerge, at the cost of a limited learning generalization against a possible fourth individual-strategy D. If you play poker, you certainly know what I am talking about, since 2 poker players are constantly trying to broke this behavioural cycle, or entering it, depending on their so-far success.

Above (left and right figures – [3]), two idealised typical CIAO plot patterns can be observed, where darker shading denotes higher scores. On the left figure, however, co-evolutionary intransitive dominance cycling is a constant, where current elites (population A elites) score highly against population B opponents from 3, 8 and 13 generations ago, but not so well against generations in between. On the other hand (right figure), the behavioural pattern is completely different: over here we do observe limited evolutionary memory, where the current elites do well against opponents from 3,4 and 5 generations ago, but much less well against more distant ancestral opponents.

For to win one hundred victories in one hundred battles is not the acme of skill. To subdue the enemy without fighting is the acme of skill.” ~ Sun Tzu

Of course, in increasingly complex real-world situations Scottish-kilt like CIAO plots are much noisy than this (fig. above -[7]) where banded tartans could be less prominent, while the same could happen in irregular dominance cycling as elegantly showed by Cartlidge and Bullock in 2004 [6]. Above, some of my own experiences can be observed (submitted work). Over here I decided to co-evolve a AI agent strategy to play against a pool of 15 different strategies (6 of those confronts are presented above), and as a result, 6 different behavioural patterns emerged between them. All in all, the full spectrum of co-evolving dynamics could be observed, from the “Red Queen” effect, till alternate dominant cycles, and limited or long evolutionary memory. Even if some dynamics seem counter-productive in one-by-one confronts, in fact, all of these dynamics are useful in some way, as when you play Poker or the “Rock, Paper, Scissors” game. A typical confront between game memory (exploitation) and the ability to generalize (exploration). Where against precise opponents limited evolutionary memory was found, the same effect produced dominant cycles or long evolutionary memory against other strategies. The idea of course, is not to co-evolve a super-strategy to win all one-by-one battles (something that would be rather impossible; e.g. No free Lunch Theorem) but instead to win the whole round-robin tournament, by being highly adaptive and/or exaptive.

So next time you see someone wearing a banded tartan Scottish-kilt do remind yourself that, while getting trapped in traffic, that precise pattern could be the result of your long year co-evolved strategies to find the quickest way home, while confronting other commuters doing the same. And that, somewhere, somehow, Charles Darwin is envying your observations…


[1] W. Daniel Hillis (1990), “Co-Evolving Parasites improve Simulated Evolution as an Optimization Procedure”, Physica D, Vol. 42, pp. 228-234 (later in, C. Langton et al. (Eds.) (1992), Procs. Artificial Life II, Addison-Welsey, pp. 313-324).

[2] Yip et al.; Patel, P; Kim, PM; Engelman, DM; McDermott, D; Gerstein, M (2008). “An integrated system for studying residue Coevolution in Proteins“. Bioinformatics 24 (2): 290-292. doi:10.1093/bioinformatics/btm584. PMID 18056067.

[3] Dave Cliff, Geoffrey F. Miller, (1995), “Tracking the Red Queen: Methods for measuring co-evolutionary progress in open-ended simulations“. In F. Moran, A. Moreno, J. J. Merelo, & P. Cachon (Eds.), Advances in artificial life: Proceedings of the Third European Conference on Artificial Life (pp. 200-218). Berlin: Springer-Verlag.

[4] Dave Cliff, Geoffrey F. Miller, (2006), “Visualizing Co-Evolution with CIAO plots“, Artificial Life, 12(2), 199-202

[5] Dave Cliff, Geoffrey F. Miller (1996). “Co-evolution of pursuit and evasion II: Simulation methods and results“. In P. Maes, M. J. Mataric, J.-A. Meyer, J. Pollack, & S. W. Wilson (Eds.), From Animals to Animats 4: Proceedings of the Fourth International Conference on Simulation of Adaptive Behavior (pp. 506-515). Cambridge, MA: MIT Press.

[6] Cartlidge, J. and Bullock S., (2004), “Unpicking Tartan CIAO plots: Understanding irregular Co-Evolutionary Cycling“, Adaptive Behavior Journal, 12: 69-92, 2004.

[7] Ramos, Vitorino, (2007), “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), Lisbon, PORTUGAL. May 31, 2007.

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

@ViRAms on Twitter


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