DynaPsych Table of Contents

On Dynamics of Affective Liquids

On Dynamics of Affective Liquids

Andrew Adamatzky

Faculty of Computing, Engineering and Mathematical Sciences
University of the West of England
Coldharbour Lane, Bristol BS16 1QY United Kingdom


We design a toylike and somewhere speculative model of emotional interactions based on a paradigm of artificial chemistry. Four basic emotional states - happiness, anger, confusion and sadness - are studied as different types of molecules, or reagents, which constitute an affective liquid. The computational study of integral dynamic of emotion-reagents in well-stirred reactors demonstrates a rich spectrum of the affective liquids development: irregular oscillations of happiness, sadness and anger; domination of happiness, sadness or confusion; short-term outbursts of confusion and happiness and many more phenomena. Results of the study will contribute to a theory of collective emotions and be applied in practice - design of emotional robot controllers and simulation of artificial societies.

1  Introduction

Why are we looking for a minimalist representation of interacting emotions in a context of artificial life? First, cognition rests on emotions [18,6,10,31] - emotions form a primary, fast, component of an intelligent response to an external stimulus, while beliefs constitute the secondary, or slow, component [14,18]; all machines now can be intelligent just few if any emotional. We need a new generation of emotional robots, that do not simply express but also experience and communicate emotions to their fellow robots and humans [27,8,33]. Second, emotions rather than knowledge govern behaviour of crowds - crowds are better in feelings than in reasoning [24,22,29]; artificial societies still lack natural emotions.

What is the best way to study dynamic of nonlinear processes in societies of emotional entities? Automata networks, esp. cellular automata, are proved to be feasible models of artificial societies, and quite useful complements to conventional logical systems and software agents [5,16,15,13]. However, sometimes automaton models are difficult to interpret and some aspects of their dynamic are too far from real world. An artificial chemistry approach - well cultivated in a context of nonlinear media computing [4], evolution of collective mentality [3], universal computation and robotics [11] - helps us to preserve simplicity of automaton simulation and enrich our models with specific of interaction. The chemical paradigm as applied in theory of computation employs molecules that represent computational processes participating in reaction kinetic [17]. A molecule corresponds to a symbolic representation of an operator, the molecule's behaviour is the operator's action, a chemical reaction is an evaluation of the functional application; collision of two molecules may be seen as a production rule or a relation [17].

In the paper we consider basic emotions as interacting molecules and study concentration dynamic of these affective liquids for various reaction schemes. A chemistry of emotion is defined in the Sect. 2. Dynamic of well-stirred solutions of anger, happiness and confusion is studied in the Sect. 3. In the Sect. 4 we show what happens in affective liquid when sadness is added. The Sect. 5 is conclusive.

2  Designing chemistry of emotions

Why chemistry of emotions? Subjects of emotions are discrete, so one could think about emotions as molecules. Emotions spread in collectives by contagion, possibly through imitation and facial mimicry that cause an affective feedback from facial receptors and neurons [19,20]. ``The precipitating stimuli arise from one individual, act upon ... one or more other individuals, and yield corresponding or complementary emotions ... in these individuals" [20]. This means emotions diffuse. Do they react? Yes, subjects in some emotional states more probably change their emotions when encounter subjects in other emotional states [25,20,26]. ``It is happy people who are most receptive to others and most likely to catch their moods; the unhappy seem relatively oblivious to other' feelings and to contagion" [20]. A real life emotional interaction usually depends on the emotions' strength, context of emotional interaction as well as a vector of relationships between subjects of emotions - ``Angry faces sometimes stimulate fear as well as anger; another's fear may put us at ease" [20].

What are basic reagents of affective solutions? There are myriads of so-called ``basic" emotional states, that vary from one publication to another. The classification depends rather on scientists' personal preferences and their academic school. In this paper we selected four emotional states: happiness (H), sadness (S), anger (A) and confusion (C). This set is not complete however could be used to roughly characterize somebody's state of mood. Also, these four emotions (together with disgust and fear) are proved to be culture-independent emotions [14], which is important for universal models.

A scheme of emotion interaction is very simple. Let i and j be subjects of emotions, emotion careers, persons, or molecules. The subjects take their states, si and sj, from the set E = { H, S, A, C } in the discrete time: for t N sit, sjt E. The subjects move in a physical space, and collide with each other. When collided they update their emotional states: sit+dt = f(sit,sjt). This method of binary interaction of mental states is already proved to be productive [1,2,3]. We consider the states H, S, A or C as four different types of abstract molecules. When two molecules collide they undergo transformation and change their types. That is the collided molecules react one with another. A reaction between the molecules X and Y is seen as { f(X,Y), f(Y,X) } { Z1, Z2 }, or in more conventional form: X + Y Z1 + Z2, where X, Y, Z1, Z2 E. The system is conservative, number of entities is constant.

It is really easy to simulate well-stirred reactors in automaton collectives, as we did in [1,2]; however, for this particular paper we have chosen Chemical Kinetics Simulator (CKS, IBM Corporation, 1996) [9], to make results more chemically-realistic and truly portable. The CKS works on principles of discrete stochastic simulation and portrays a stirred chemical reactor, as a system of discrete particles, where each particle represents a certain amount of reagents; an interaction of reagent pools is simulated via interaction of particles [9]. Using the simulator we investigated behaviour of well-stirred reactors for all possible mixtures of happiness (H), sadness (S), anger (A) and confusion (C). In all experiments discussed in the paper reagents, presented in initial mixture, have the same concentrations (not all reagents may be included in the initial mixture however).

3  Anger, happiness and confusion

To start with we consider a basic model of anger, happiness and confusion. Let persons be sensible, polite and particular about social sense of their emotions. When a happy person meets an angry one they both become confused because the emotional state of each one is opposite to his counterpart's emotion: Anne blushed a second time, and turned aside under the pretext of taking her pen from her desk again, but in reality to conceal her confusion from her son. ``Really, Philip," she said, ``you seem to discover expressions for the purpose of embarrassing me, and your anger blinds you while it alarms me; reflect a little" [12]. Both anger and happiness could infect confusion. A confused person becomes happy (angry) when he encounters a happy (angry) person.

Thus, we have three following reactions:
H + A 2 C
H + C 2 H
A + C 2 A
From the reactions (1) we see that confusion catalyses production of anger and happiness. Moreover, the confusion is produced when anger and happiness react to each other. All three reagents can be kept in a single-reagent solutions.



Figure 1: Concentration dynamic in the model (1). (a) Irregular oscillations of concentrations. (b) Vanishing of two species and dominance of the only one.

We studied dynamic of the reaction system (1) in various initial conditions and found that each possible scenario fits one of three following modes. If we prepare a mixture of three reagents, in equal concentrations, and pour the mixture in a well-stirred reactor we observe chaotic-like oscillations of the reagent concentrations (Fig. 1, a).

If anger (happiness) is mixed with happiness (anger) such that one of the reagents has slightly smaller concentration than another one, the reagent with initially higher concentration, will dominate the reactor (Fig. 1, b). In such experiments one can also observe temporary production of confusion, which concentration grows for a short time and then vanishes (Fig. 1, b).

And finally, if we mix anger and happiness in equal concentrations, both reagents coexists in the system; the confusion is generated as well and joins two initially present reagents in their low amplitude oscillations.

Now we slightly modify the reactions (1). Namely, we assume, possibly a little bit artificially but nevertheless reasonably, that when a happy person meets a confused person, the happy person remains happy while the confused person becomes angry. In real life it may look like somebody is confused and disoriented and the other guy seems to be making fun of him. Therefore, that who confused infuriates. The following example reflects rather incompatibility of personal contexts: Why are you jealous of the sudden reveries which overtake me in the midst of our happiness? Why show the pretty anger of a petted woman when silence grasps me?[7].

We could consider a situation when an angry person encounters a confused one. The angry becomes happy, when he sees the confused, and the confused person again becomes preoccupied with the anger. This may be explained by a counter-mimicry, which is usually observed in a situation of hostility or competitions [23].

When two confused persons gather together they may change their moods to either happiness or anger, thus the reaction A + C H + A is incorporated in the model:
H + A 2 C
H + C H + A
A + C H + A
2 C H + A
There happiness catalyses transformation of confusion to anger. The anger in its turn facilitates transformation of confusion to happiness. Two former reactions of the scheme (2) may be written in a more convenient form representing a process of association-dissociation: H + A ↔ 2 C.



Figure 2: Dynamic of reagent concentrations in the model (2). (a) Development of a mixture of happiness and confusion. (b) Domination of confusion during development of mixture of happiness, anger and confusion.

Both happiness and anger are stable in their pure form. A confusion is not. The confusion dissociates into anger and happiness, thus its concentration decreases while concentrations of happiness and anger grow. Eventually, the system, started its evolution in a solution of pure confusion, reaches an equilibrium, where the confusion prevails and the happiness and anger are present in smaller concentrations.

Actually, for all other initial mixtures of the happiness, anger and confusion the reactor finishes its evolution in the state of highest confusion and low concentrations of anger and happiness. Nevertheless, some transient phenomena are remarkable. Thus, e.g. let us mix either happiness with the confusion or the anger with the confusion. Then during some short period of reactor's development the confusion deteriorates while the other two species increase their presence. The situation reverses soon and the final distribution of reagents reaches its typical mode, shown in (Fig. 2, b).

If anger is mixed with happiness the confusion is produced. Thus again the confusion starts to prevail in the reactor. A difference between concentration of confusion and other emotional states becomes even more visible when one mixes the three reagents altogether (Fig. 2, c).

4  Happiness, anger, confusion and sadness

A sadness, being of commonly recognized states of human mood, could make a valuable addition to our model. So, in this section we consider three models of interaction of happiness, anger, confusion and sadness.

When a happy person meets a sad one the happy may become confused, e.g. the person feels guilty of being happy when another is confused. The sad could get angry if he is upset that somebody can be happy when he is sad. When the happy and the angry contact each other they both turn to confusion. The happy person confuses and the confused enrages in the result of their meeting. What is about interaction of sadness and confusion? We could offer the following scenario: the sad becomes angry and the confused does not change his mood. Thus we get the system of four reaction:
H + S C + A
H + A 2 C
H + C C + A
S + C A + C

As one can find from the scheme (3) all four reagents are stable in single-reagent solutions. The anger and sadness do not interact with the confusion.



Figure 3: Concentration dynamic in mixtures of happiness, anger, sadness and confusion. (a) Production of confusion and anger in the mixture of happiness and sadness. (b) Development of the mixture of sadness and anger.

Concentrations of happiness and sadness decreases to zero in all mixtures that include happiness and sadness. The happiness and sadness vanish and the confusion prevails in mixtures for all initial combinations of the reagents. The anger also increases in concentration in the reactor, if it is present there initially, hence the anger only in few cases increases up to the level of confusion. Two typical examples of reagent dynamic are shown in Fig. 3, where concentration dynamic of the initial solutions of happiness and sadness (Fig. 3, a), and anger and sadness (Fig. 3, b) are illustrated.

World looks pretty sad in the model (3). Let us make it a bit happy. First of all, we assume that the happy and sad persons become confused when encounter one another. The happy changes his states because ``it is a shame to be happy when somebody is sad". The sad confuses because he may feel his happiness inappropriate for the situation. There are dozens of real-life instances of the reaction H + S 2 C, e.g. ... They are gay without knowing any very sufficient reason for being so, and when sadness is, as it were, proposed to them, things fall away from under their feet, they are helpless and find no stay [30]. Secondly, the happy turns sad when he confront the angry and the angry himself goes confused seeing the happy. Thirdly, a confused person could be easily infected with happiness and be confused by the angry one; both sad and angry develop confusion contacting each other. These assumptions are reflected in the following reaction set:
H + S 2 C
H + A S + C
H + C 2 H
S + A 2 C
A + C 2 A
All four reagents are stable in their pure forms. The confusion does not interact with the sadness. Also, the reaction scheme (4) is symmetric in relation to anger and happiness. These two reagents ``consume" the confusion and they produce the confusion when interact with sadness. The anger and happiness generate the sadness and confusion when react with each other. Therefore, we could expect some kind of bifurcation in development of reaction mixture - this in the experiments.



Figure 4: Concentration dynamic in the model (4). (a) Domination of happiness in a mixture of happiness and sadness. (b) Development of mixture of happiness, confusion and anger.

When one mixes happiness (anger) with sadness the happiness (anger) grows in concentration. Then we observe domination of the happiness (anger), decline of the sadness and short-time explosion followed by subsequent decline of the confusion (Fig. 4, a).

Quite obviously entire confusion is transformed to the happiness (anger) in the mixture that includes the happiness (anger). In mixtures of happiness (anger) with sadness and confusion both sadness and confusion declines and the pure happiness (anger) is developed in the reactor. The situation becomes even more interesting in mixtures of happiness, confusion and anger (Fig. 4, b); happiness, sadness and anger; or mixture of all four reagents. There we observe outgrowth of either happiness or anger. Which of these two reagents dominates is determined by chaotic dynamic of molecular ensembles, and each of the reagents can be dominating with the same probability.

Finally, we are making subjects very sensible. We leave interaction of confusion with anger and happiness as they were in the model (4) but assume the sadness is stable when interacts with happiness and anger. The happy and angry persons are confused when meet a sad person. A reaction between anger and sadness could be derived from the following quotation: - Ah, Wilfred, Wilfred!'' he exclaimed in a lower tone, ``couldst thou have ruled thine unreasonable passion, thy father had not been left in his age like the solitary oak ...'' The reflection seemed to conjure into sadness his irritated feelings [32]. The angry and the sad are transformed to the sad and confused, respectively, in the result of their binary reaction; the complete set of reactions looks therefore as follows:
H + S S + C
H + A S + C
H + C 2 H
S + A S + C
A + C 2 A
All reagents are stable in single-reagent solutions. Sadness does not interact with confusion. When happiness (anger) is mixed with confusion, concentration of the confusion tends to zero while the happiness (anger) increases in its concentration and stabilizes after that.

The confusion and sadness are produced in initial mixture of happiness and anger, eventually both happiness and anger deteriorate and the reactor becomes filled with sadness and confusion. The only anger survives in mixtures of sadness, confusion and anger. A reactor filled with one of the following mixtures : (i) happiness, sadness and anger; (ii) sadness and anger; (iii) happiness and sadness; (iv) happiness, confusion and anger; (v) happiness, sadness, confusion and anger, finishes its development in a state where only confusion and sadness are present.



Figure 5: Concentration dynamic in the model (5). (a) Development of mixture of happiness and sadness. (b) Emergence of oscillation dynamic in mixture of sadness, confusion and happiness.

Three types of reaction mixtures are more interesting than those previously discussed. Thus, if we mix happiness (anger) and sadness we find that the sadness does not change its concentration whatsoever; the happiness gradually vanishes and the confusion gradually increases until its concentration becomes equal to the concentration of sadness (see the example of transition in Fig. 5, a). Concentrations of sadness and happiness oscillate in the mixture of sadness, confusion and happiness, and concentration of sadness does not change (Fig. 5, b). The reason for the oscillation is very simple. Considering the reactions H + S S + C and H + C 2H we find that concentration of sadness should not actually change, while dynamic of happiness and confusion is described by the equations:

[d(xH)/dt]=xH xC and [d(xC)/dt]=-xH xC.

5  Discussion

We demonstrated that artificial-chemistry-based approach bears a great potential for minimalist nevertheless realistic representation of nonlinear dynamic of emotions in collectives. In the study we deliberately, possibly provocatively, chosen oversimplified schemes to illustrate varieties of integral dynamic of affective mixtures. Some interesting types of reactions have not been considered, e.g., a single-reagent auto-catalytic loop C 2C: And so with a new sorrow I sorrowed for my sorrow and was wasted with a twofold sadness [35]. Further research could be advanced in the following directions. Firstly, one could enrich typology of abstract molecules to include dozens of recognized emotional states. Secondly, real-life verifications of basic types of reactions between emotion-molecules could be provided, e.g. transformations Anger  { Disgust, Fear }, Fear  Disgust, and Sadness  Sadness are experimentally observed [36]. Thirdly, we can incorporate a spatial component in the models to analyze diffusion and reaction of emotions in thin-layer reactors. In this context more careful defining of emotional contagion may be useful: a conventional ``emotional contagion" usually means spreading of a mood in initially emotionless collective. This is a diffusion. The diffusion coefficients for each type of emotion can be derived from experiments with real persons: e.g. we know that happy faces are recognized quicker than sad faces [36], i.e. happiness diffuses faster than sadness. Basing on the results on accuracy of facial expressions decoding [21] we could suggest the following diffusion coefficients: chappiness=0.87, canger=0.45, cdisgust=0.43 and csadness=0.75. Also emotions usually interact with other emotions when spread in the collective. This is a reaction. A reaction-diffusion paradigm will be exploited in full details later.


Adamatzky A. Space-time dynamic of normalized doxatons Chaos, Solitons and Fractals 12 (2001) 1629-1656.

Adamatzky A. Pathology of collective doxa. Automata models Applied Math. Comput. 122 (2001) 195-228.

Adamatzky A. Chemistry of belief Kybernetes 30 (2001) 1199-1208.

Adamatzky A. Computing in nonlinear media and automata collectives (Institute of Physics Publishing, 2001).

Axelrod R. The complexity of cooperation (Princeton University Press, 1997).

Bates J. The role of emotions in believable agents Comm. ACM 37 (1994) 122-125.

Balzac, Honore de The Lily of the Valley (The Gutenberg Project, 1998; ftp://ibiblio.org/pub/docs/books/gutenberg/etext98/tlotv10.txt).

Breazeal C. and Scassellati B. How to build robots that make friends and influence people Proc.IRO99 (Kyonjiu, Korea), 1999; http://citeseer.nj.nec.com/breazeal99how.html

Chemical Kinetics Simulator 1.01, IBM's Almaden Research Centre. http://www.almaden.ibm.com/st/msim/ckspage.html

Chalmers D. The Consciousness Mind: In Search of a Fundamental Theory (Oxford University Press, 1996).

Dittrich P. Artificial Chemistries, Tutorial held at the Europ. Conf. Artif. Life 1999 (Lausanne, Switzerland); http://ls11-www.cs.uni-dortmund.de/achem

Dumas, Alexandre Ten Years Later (The Gutenberg Project, 1998; ftp://ibiblio.org/pub/docs/books/gutenberg/etext98/2musk10.txt)

Dyer M.G. Emotions and their computations: three computer models Cognition and Emotion 1 (1987) 323-347.

Eckman P. Are there basic emotions? Psychol. Review 99 (1992) 550-553.

El-Nasr M.S., Yen J. and Ioerger T. FLAME - Fuzzy logic adaptive model of emotions Int. J. Autonom. Agents and Multi-Agent Syst. 3 (2000) 1-39.

Epstein J.M. and Axtell R. Growing artificial societies (Brooking Institution Press, 1996)

Fontata W. and Buss L.W. The barrier of objects: from dynamical systems to bounded organizations, SFI Working Paper, 96-05-035, 1996.

Goleman D. Emotional Intelligence (Bloomsbury Publishing, 1996).

Hatfield E., Cacioppo J.T. and Rapson R.L. Primitive emotional contagion Rev. Personal and Social Psych. 14 (1992) 151-177.

Hatfield E., Cacioppo J.T. and Rapson R.L. Emotional Contagion (Cambridge University Press, 1994).

Hess U. and Blairy S. Facial mimicry and emotional contagion to dynamic emotional facial expressions and their influence on decoding accuracy Int. J. Psychophysiology 40 (2001) 129-141.

Graumann C.F. and Moscovici S. (Editors) Changing Conceptions of Crowd Mind and Behaviour (Springer-Verlag, 1985).

Lanzetta J.T. and Englis B.G. Expectations of cooperation and competition and their effects on observers' vicarious emotional responses J. Pers. Soc. Psychol. 33 (1989) 354-370.

Le Bon G. The Crowd: A Study of the Popular Mind (Traders Press, 1994).

Levy D. and Nail P.R. Contagion: A theoretical and empirical review and reconceptualization Social and General Psych. Monogr. 119 (1993) 183-235.

Marsden P. Memetics and social contagion: two sides of the same coine J. of Memetics 2 (1998).

McCarthy J. Ascribing mental qualities to machines (1979) http://www-formal.stanford.edu/jmc/

McDougall W. The Group Mind (Knickerbocker Press, 1920).

McPhail C. The myth of the madding crowd (Aldine de Gruyter, 1991).

Meynell A.K. The Children (The Gutenberg Project, 2000; ftp://ibiblio.org/pub/docs/books/gutenberg/etext99/chldn10.txt).

Picard R.W. Affective Computing (MIT Press, 1997).

Sir Walter Scott Ivanhoe, Chapter III. (The Gutenberg Project, 1993; ftp://ibiblio.org/pub/docs/books/gutenberg/etext93/ivnho13.txt).

Scheeff M., Pinto J., Rahardja K., Snibbe S. and Tow R. Experiences with Sparky, a social robot Proc. Workshop Interact. Robotics in Entertain. (Pittsburgh, 2000); http://citeseer.nj.nec.com/428152.html

Smelser N.J. Theory of Collective Behaviour (The Free Press, 1962).

Saint Augustine The Confessions of,, Book 9, Chpt. XII. (Transl. by E.B. Pusey) (The Gutenberg Project, 2002) ftp://ibiblio.org/pub/docs/books/gutenberg/etext02/tcosa10.txt

Wild B., Erb M. and Bartels M. Are emotions contagious? Evoked emotions while viewing emotionally expressive faces: quality, quantity, time course and gender differences Psychiatry Research 102 (2001) 109-124.

File translated from TEX by TTH, version 3.13.
On 3 Oct 2002, 11:32.