Jean-Louis Dessalles

HAVE YOU ANYTHING UNEXPECTED TO SAY? THE HUMAN PROPENSITY TO COMMUNICATE SURPRISE AND ITS ROLE IN THE EMERGENCE OF LANGUAGE

Have you anything unexpected to say? The human propensity to communicate surprise and its role in the emergence of language

Jean-Louis Dessalles

Theoretical Context

Human language has several remarkable features. It is a massive phenomenon (M): human individuals are involved more than six hours a day in spontaneous language activities [START_REF] Mehl | The sounds of social life: A psychometric analysis of students' daily social environments and natural conversations[END_REF] and speak some 15 000 words on average during that time [START_REF] Mehl | Are women really more talkative than men?[END_REF]. Information is available in abundance, due to the existence of talkative individuals (T). Many conversations deal with futile matters that are unlikely to affect the participants' survival (F). Speakers do not (or loosely) discriminate who will hear what they say (D), and most interactions in a group are not one-to-one [START_REF] Dunbar | Size and structure of freely forming conversational groups[END_REF]. Many conversational topics are narratives, i.e. they report on some current or past unexpected event (U) [START_REF] Tannen | Conversational style -Analyzing talk among friends[END_REF][START_REF] Eggins | Analysing casual conversation[END_REF][START_REF] Norrick | Conversational narrative: storytelling in everyday talk[END_REF]; This behaviour: drawing attention to unexpected situations, is a human distinctive feature [START_REF] Tomasello | Why don't apes point?[END_REF]) that shows up early in childhood (Carpenter et al. 1998). Human beings learn and understand huge lexicons made of tens of thousands of words and set phrases (L). Most individuals willingly engage in conversational behaviour (W) with no noticeable difference between sexes (S) [START_REF] Mehl | Are women really more talkative than men?[END_REF]. And sharing conversational time strongly correlates with establishing and maintaining social bonds (B) [START_REF] Dunbar | Grooming, gossip, and the evolution of language[END_REF].

Usual accounts of altruistic behaviour are at odds with these facts. Kin selection [START_REF] Fitch | Evolving honest communication systems: Kin selection and 'mother tongues[END_REF] has problems with M, F, D, L, B. Reciprocal cooperation [START_REF] Nowak | Five rules for the evolution of cooperation[END_REF]) conflicts with T, F, D and indirect reciprocity [START_REF] Nowak | Evolution of indirect reciprocity[END_REF] conflicts, in addition, with W. Group selection [START_REF] Sober | Unto Others. The Evolution and Psychology of Unselfish Behavior[END_REF] conflicts with M, T, W, and in its warrior version [START_REF] Bowles | Group competition, reproductive leveling, and the evolution of human altruism[END_REF]) also with S. Though each of these theoretical difficulties should be discussed in more detail, we must observe that these traditional models of altruism cannot be straightforwardly applied to the case of human language. Moreover, none of them positively predicts any of the first seven facts in the above list.

Other accounts of costly behaviour include sexual selection [START_REF] Miller | The mating mind[END_REF] and Costly Signalling Theory (CST) [START_REF] Gintis | Costly Signaling and Cooperation[END_REF]. Sexual selection, when applied to language, is however incompatible with facts M, S and B. The case of CST will be examined in the next section.

We will first consider how CST can be applied to language. It requires that the quality advertised by speakers be specified. We then describe a study showing how the human mind detects and interprets unexpected events. We interpret the systematic communication of unexpected situations in our species (fact U above) as a way for individuals to advertise their ability to spot unexpectedness. This advertising behaviour makes sense within the CST framework if language emerged in the new context created by the use of artefacts to kill.

Can Costly Signalling Theory Account for Human Language?

CST [START_REF] Zahavi | The handicap principle[END_REF][START_REF] Gintis | Costly Signaling and Cooperation[END_REF] appears to be the most promising model to explain the above list of facts concerning spontaneous language, despite some initial beliefs about the contrary (Zahavi & Zahavi, 1997:222). In CST, individuals send signals, even if this involves a significant cost, to advertise a definite quality Q. They benefit from being perceived as possessing Q. In the social version of CST [START_REF] Dessalles | Coalition factor in the evolution of non-kin altruism[END_REF][START_REF] Gintis | Costly Signaling and Cooperation[END_REF], individuals establish social bonds based on Q. Social bonds are systematically beneficial to chosen signallers. They benefit followers as well, but only if the chosen partner really had Q, in other words if the signal was honest in the first place. CST shows that, under certain conditions, honest signals emerge and remain stable.

It is tempting to invoke CST to account for the existence of language, as it would correctly predict facts labelled T, D, W, B in our list. There are, however, several problems. One of them is that CST is apparently incompatible with M: the fact that everyone speaks, and speaks a lot. Within CST, signalling is competitive. This generates a threshold, below which it is not worthwhile signalling. The honesty of signals relies precisely on this fact: only high-quality individuals benefit from signalling, while the others have better time saving the cost, as they have little hope of return. We addressed this issue elsewhere [START_REF] Dessalles | Generalised signalling: a possible solution to the paradox of language[END_REF], by showing that when the competition is decentralized, even low-quality individuals benefit from signalling their true quality. The fact that social bonds imply spending time together [START_REF] Dunbar | Grooming, gossip, and the evolution of language[END_REF] is crucial in this respect: individuals must recruit their friends among individuals who available time left. This constraint creates a situation in which friends turn out to be matched by quality. In such situation, everyone benefits from signalling.

The major remaining problem concerning CST is that it leaves the advertised quality Q unspecified. The constraints are the following:

-Joining an individual with higher Q should bring more benefit to followers; -Cheating on Q should be difficult for signallers. Importantly, cost is not a necessary ingredient of CST! Cost might be borne by cheaters rather than signallers (Lachman et al. 2001), and in some cases cheating might simply be impossible, e.g. if recipients can check the validity of the signal. In the next sections, we explore the possibility that one prime quality advertised through language is the ability to notice unexpected states of affairs.

Unexpectedness in Language

Some 25% to 40% of language time is devoted to mentioning immediate or past events [START_REF] Eggins | Analysing casual conversation[END_REF][START_REF] Dessalles | La pertinence et ses origines cognitives -Nouvelles théories[END_REF], especially through conversational narratives [START_REF] Norrick | Conversational narrative: storytelling in everyday talk[END_REF]. To appear interesting to listeners, these events must appear unexpected, i.e. they must contrast with the listener's expectations about the world (see below for a more technical definition). We will show how this unique property of human communication can make sense within CST.

Unexpectedness can be given a formal definition. In their attempts to define randomness, mathematicians developed a concept known as Complexity (in the Kolmogorov sense). The complexity C of a situation is the minimal information needed to reconstruct it unambiguously. Though objective (i.e. observerindependent) complexity cannot be computed, observer-dependant C can be easily calculated in most concrete cases, as shown in table 1 (see www.unexpectedness.eu, or [START_REF] Dessalles | La pertinence et ses origines cognitives -Nouvelles théories[END_REF] for more details). Time distance t to the event log2(t/a) a is the typical duration of event.

Social relatedness log2 r r is the rank of the acquaintance in the observer's address or cell phone shortlist.

Celebrity log2 r r is the rank of the person in an ordered list (see note).

Feature f log2 r r is the rank of the notion in an ordered list (see note).

Note: ranked lists can be obtained through Web search engines, or through temporal ordering (events being ranked by elapsed time), or by experimenting with individuals' reaction times in recognition tasks. r is ideally the minimal rank obtained through such means.

Unexpectedness is defined as a complexity drop:

U = C w -C (1)
C w stands for the expected complexity, i.e. the minimal information needed for the known world to produce the situation. Table 2 shows the contribution of various parameters to unexpectedness (see www.unexpectedness.eu, or [START_REF] Dessalles | La pertinence et ses origines cognitives -Nouvelles théories[END_REF] for more details).

The claim is not that the human brain performs these computations formally. However, individuals seem to have clear intuitions about how these various parameters affect unexpectedness. For instance, they intuitively know that a fire breaking out next block is more unexpected, and thus more interesting to tell, than the same fire occurring five kilometres away. They intuitively know that coincidences are all the more unexpected, and thus interesting, as the two coincident facts share common features (making C(s 2 |s 1 ) smaller). And they know that it is highly unexpected to bump into one's neighbour P in a remote place L (e.g. a village in India), much more unexpected indeed than a mere encounter with some forgotten former colleague in the train station nearby (what the difference C(P) -C(L) captures). The study presented in the next section puts these intuitions to the test.

Time log2(T/t)

T is the typical distance in the past to similar events (estimated by the time distance to the last remembered instance).

Rarity log2(1/F) -C(f) F is the occurrence frequency of feature f. Atypicality 0.7 k 2 -C(f)
The situation lies at k standard deviations along feature f from its prototype.

Coincidence

C(s1) -C(s2|s1)

Conditional complexity C(s2|s1) measures the minimal information needed to reconstruct s2 from s1.

Encounter C(L) -C(P)

The observer bumps into P at location L.

Unexpectedness and Conversational Interest

A corpus of 18 short narratives was presented to 101 French participants (see [START_REF] Dimulescu | Understanding narrative interest: Some evidence on the role of unexpectedness[END_REF] for a detailed description of the experiment). For each story, participants had to choose among two options (randomly selected out of three possible values) the one that makes the story more interesting. The following stories (originally in French) illustrate, in turn, the influence of time distance, the role of atypicality, the importance of common features in coincidences, and the influence of social proximity (* signals when results are statistically significant p < .05).

 For a year, I had been thinking of changing my mobile phone at SFR (mobile operator). I finally decided to do so even if I had to pay a part because I did not have enough Red Square Points. I bought the new phone at 13:00. Participants altogether never preferred the least unexpected option (c). For 17 stories out of 18, the most unexpectedness option (a) was significantly ranked best. This is in perfect accordance with the major role played by unexpectedness in conversational interest. We now show that this role may owe its origin to our phylogeny.

Discussion

The human universal propensity to signalling unexpected events and the corresponding demand by listeners matches the CST prerequisite that it is used to display a social quality. What kind of quality? Candidates do not abound. There is one hypothesis, however, that seems to offer a consistent account.

It is a fact that at some point in our phylogeny, individuals started to use stones, sticks or weapons to kill at no risk (what chimpanzees do not do). This new behaviour dramatically transformed hominin politics [START_REF] Woodburn | Egalitarian societies[END_REF]Boehm 2000:177;[START_REF] Bingham | Human evolution and human history: A complete theory[END_REF]. If anyone can kill anyone at no risk, e.g. during sleep, to be on one's guard is not enough. Individuals must rely on friends' alertness. In this context, ideal friends are those who are best able to anticipate danger. Language would have emerged as a way to advertise this ability.

In most species, danger is easy to anticipate. The gazelle knows that lions are dangerous, and it knows what the safe distance is. Chimpanzee males know that wandering close to territorial limits puts their life at risk. The problem is significantly harder for hominins: danger may come from group mates who may strike anywhere anytime by surprise. How can the unexpected be anticipated?

The present account of the evolutionary emergence of language instantiates CST in the following way: individuals, through their conversational utterances, advertise their ability to surprise others. By preferring to join and remain close to the most talented individuals in this game, listeners increase their viability as they diminish the probability of being taken by surprise. In a context of easy killing, information replaces muscular strength as main asset for success. Male chimpanzees display their muscles, whereas human beings advertise their informational abilities through language. Note that, as required by CST, it is difficult to cheat on unexpectedness, as the unexpected character of reported events can be easily checked by listeners. This model accounts for all the facts listed at the beginning of this paper. In particular, noticing futile facts (F), such as the current date (09/09/09), can make a successful communicative act (in this example, the date is interesting, not because it is consequential, but merely because it is 'too' simple and thus unexpected). The model predicts that various levels of talkativeness will coexist (T); it predicts no discrimination of listeners (D), no sex difference (S), and of course a strong correlation between conversation and social closeness (B). It is, in addition, one of the few models that account for the existence of plethoric lexicons (L): the set of unexpected situations is by definition unbounded, and one must be potentially able to describe all of them, especially the rarest ones, with enough precision for their unexpected character to be correctly appraised.

In the hominin world in which riskless killing becomes possible, individuals secure their safety by choosing the right friends, those who are most able of keeping them informed of any unusual situation going on. This is the only way to prevent the danger of being taken by surprise. The initial emergence of language may be the consequence of this situation: individuals strive to display their ability to notice anything unexpected, as it is the best way, as predicted within the CST framework, to build efficient social networks.

  [---] I got a message from SFR: "Change your mobile, SFR offers you 15 000 Red Square Points." Options: (a) At 13:10; (b) At 14:00; (c) Two weeks later. Results: (a)/(b): 29/4* -(b)/(c): 28/6* -(a)/(c): 31/3*  Wednesday, the city of Amiens police seized [---] kg of heroin at number 13 rue Fafet. Options: (a) 10 -(b) 5 -(c) 2. Results: (a)/(b): 28/13* -(b)/(c): 20/11 -(a)/(c): 21/8*  I'd just bought a small Peugeot 106 ColorLine for 2000 euros. I had tried it the day before and it was very good. I turned the key, I started, I left the property of the former owner of the car when, coming from the left without looking, another [---] crashed into me. Options: (a) Peugeot 106 ColorLine -(b) Peugeot 106 -(c) Peugeot. Results: (a)/(b) 24/8* -(b)/(c) 32/4* -(a)/(c) 28/5*  Two weeks after my car had been stolen, the police informed me that a car that might be mine was for sale on the Internet. They showed me the ad. The phone number had been identified. It was the mobile phone number of [---]. Options: (a) my office colleague -(b) a colleague of my brother's -(c) someone of my neighbourhood. Results: (a)/(b) 25/6* -(b)/(c) 24/10* -(a)/(c) 26/7*

Table 1 :

 1 Complexity computations

	Parameter	C	Remark
	Distance d to the event	log2(d 2 /a)	a is the typical surface of the event.

Table 2 :

 2 Unexpectedness computations

	Parameter	U	Observation
	Distance	2 log2(D/d)	D is the typical distance to similar events (estimated by the distance to the last remembered instance).


Jean-Louis Dessalles
email: dessalles@telecom-paristech.fr

Emotion in Good Luck and Bad Luck: Predictions from Simplicity Theory

Keywords: Kolmogorov complexity, simplicity, emotion, luck, probability, unexpectedness

HAL is

Good Luck and Bad Luck

Situations spontaneously associated with good luck or bad luck are an important source of emotion. They are frequent in daily life: missing (or catching) the train by five seconds, forgetting one"s cell phone the very day one is late for an important appointment, finding a banknote on the ground, etc. They are heavily used in popular fiction, precisely to arouse emotion: the gun gets jammed just at the right (or bad) time, the heroine defuses the bomb just before it explodes, etc. Regarding oneself or someone else as lucky or unlucky on specific occasions may induce gratitude or guilt, and for those who downplay the role of chance, intense feelings of good or bad luck may strengthen supernatural beliefs (Teigen & Jensen, in press). Reasoning about good luck and bad luck may also significantly influence rational judgment [START_REF] Roese | Counterfactual thinking[END_REF][START_REF] Wohl | The effects of near wins and near losses on self-perceived personal luck and subsequent gambling behavior[END_REF].

The feeling of having good or bad luck is a clear-cut phenomenon. Different individuals have consistent views of which situations can be regarded as bad or good luck (what the present study will confirm). This ability therefore gives rise to a well-posed problem, worth investigating. Previous studies have identified various parameters that control the feeling of luck. These include physical or temporal closeness [START_REF] Kahneman | Propensities and counterfactuals: The loser that almost won[END_REF][START_REF] Teigen | Luck: The art of a near miss[END_REF][START_REF] Roese | Counterfactual thinking[END_REF][START_REF] Pritchard | The psychology and philosophy of luck[END_REF], deviation from norms and expectations [START_REF] Kahneman | Norm theory: Comparing reality to its alternatives[END_REF], mutability of causes [START_REF] Kahneman | Norm theory: Comparing reality to its alternatives[END_REF][START_REF] Byrne | Mental models and counterfactual thoughts about what might have been[END_REF][START_REF] Byrne | Précis of the Rational Imagination: How people create alternatives to reality[END_REF] and controllability [START_REF] Roese | Counterfactual thinking[END_REF].

Many authors have acknowledged the prime importance of counterfactuals in any situation that generates a strong feeling of good or bad luck. Individuals systematically go through thoughts such as "If only…" or "I almost…" when regarding situations as (un)lucky. The theoretical treatment of counterfactuals in general, and in emotional situations in particular, remains however complex, as a multitude of determining factors seem to be involved.

The purpose of the present study is to propose a new perspective on the phenomenon, imported from two other scientific domains. One is the study of narrative relevance (Dessalles 2008a). Spontaneous conversations are replete with stories about (un)lucky episodes, and the laws of interestingness seem to apply to them. The other import is the mathematical notion of complexity, which is involved in several important cognitive phenomena [START_REF] Chater | The search for simplicity: A fundamental cognitive principle?[END_REF]Chater & Vitányi, 2001).

After mentioning existing attempts to capture the good/bad luck phenomenon formally, I will briefly present the Simplicity Theory and its first predictions concerning our problem. I will then present a study that seems to corroborate those predictions. Then, I will consider situations in which individuals adopt causal thinking. The results and the scope of the theory will be discussed in a last section.

Formal accounts of luck

Various determining factors have been identified that control the intensity of luck. One of them is the low probability of the (un)lucky event s. According to Rescher (1995:211), the intensity of luck is given by L = E (1-p), where E measures the difference that the occurrence of s makes for the interests at stake, and p is its probability. This formula has two major drawbacks. First, contrary to intuition, it does not distinguish moderately unlikely outcomes from highly unlikely ones, as both would provide emotion roughly equal to u. Second, as pointed out by [START_REF] Teigen | When a small difference makes a big difference -Counterfactual thinking and luck[END_REF], it fails to capture the crucial presence of a counterfactual. As shown by Teigen in various studies, the amplitude of (un)luck is controlled by the "distance" to an alternative outcome that would have provided an emotional contrast. [START_REF] Teigen | When a small difference makes a big difference -Counterfactual thinking and luck[END_REF] represents these effects through the formula: L = u / D, where u is the difference in "utility" between the counterfactual s 2 and the actual situation s 1 , whereas D represents the "distance" between s 1 and s 2 .

This formula makes predictions that are much closer to observation, and thus represents a significant progress in comparison with Rescher"s initial proposal. It has, however, its limitations. First, the influence of low probability, as identified by Rescher, is lost. The problem is illustrated in figure 1, where the feeling of unluck after missing the winning sector (in color) in a wheel of fortune game is stronger in (b) than in (a). Second, the notion of "utility", imported from economics, does not account for situations of pure surprise ("I almost got six on all dice"). Third, the www.simplicitytheory.org notion of distance is not properly defined. Sitting next to a lottery winner doesn"t make you feel unlucky; you might however feel unlucky to have played her winning numbers, but a week too soon. Lastly, Teigen"s formula fails to capture one property of counterfactual s 2 that contributes to (un)luck, namely its simplicity. In figure 1(c), the winning sectors (in color) of the wheel of fortune occupy the same area as in (a) and the distance to the landing site is the same in both cases. Judgment of bad luck is, however, stronger in (a) than in (c). This phenomenon, due to the greater complexity of the counterfactual in (c), is not predicted by Teigen"s formula. We will propose an alternative account, based on Simplicity Theory. It can be formulated in an informal way:

(Un)lucky events are situations that occurred despite of simple, easily accessible alternatives.

Simplicity Theory

Simplicity Theory (ST) (formerly called "Complexity Drop Theory") has been developed to predict how people select events worth to tell. It has applications in the study of spontaneous conversations, of narratives, of news, and in the definition of subjective probability [START_REF] Dessalles | A structural model of intuitive probability[END_REF]2008a). ST"s main principle can be stated:

Interesting situations are those which are 'too' simple.

ST uses the notion of cognitive complexity, which is a slightly modified version of the mathematical notion know as Kolmogorov complexity.

The complexity C(s) of a situation s is the size of the ideal minimal description of s that is available to the observer.

(the last restriction is crucial for the notion to be useful in cognitive science). The concept is much less trivial than it seems at first sight, and has given rise to a growing literature since its definition in the years 1960.

ST uses two notions of complexity. The second notion is generation complexity. C w (s) is the minimal size of the parameters to be set for the 'world' w to generate situation s.

To compute C w (s) of a lottery draw, for instance, one adds up the descriptions of all drawn numbers, as the "world" (in this case, the lottery machine) had to "choose" them independently. Note that the notion refers, not to any objective world, but to the observer"s perception of the world. ST"s central notion is unexpectedness, noted U(s).

U(s) = C w (s) -C(s) (1)
A situation is unexpected if it is "too" simple, i.e. simpler to describe than to generate. In the lottery example, a "remarkable" lottery draw such as 22-23-24-25-26-27 is unexpected, since C is much smaller than C w . It only requires to instantiate 22 and to mention that it is a continuous series. C thus spares five instantiations by comparison with C w . Hence a strong feeling of unexpectedness if such a draw actually occurs [START_REF] Dessalles | A structural model of intuitive probability[END_REF]. This definition of unexpectedness accounts for various cognitive abilities, such as the perception of coincidences (Dessalles, 2008b) and of interestingness (Dessalles, 2008a;[START_REF] Dimulescu | Understanding narrative interest: Some evidence on the role of unexpectedness[END_REF] (see details on www.simplicitytheory.org). It is consistent with the observation that "contrast" (what we call unexpectedness) is more relevant than (standard) probability to explain surprise [START_REF] Teigen | Surprises: low probabilities or high contrasts?[END_REF].

Complexity is usually linked to probability p 0 thanks to the following formula p 0 =2 -C w0 , where w0 is a blank world [START_REF] Solomonoff | Complexity-based induction systems: Comparisons and convergence theorems[END_REF]. This formula is, however, unsatisfactory, as it assigns a virtually zero probability to most situations of daily life, as they depend on a huge quantity of parameters. If we replace the blank world w0 by the observer"s model w of the actual "world", we get p w = 2 -C w , which corresponds to the usual definition of "objective" probability. In a lottery, for instance, p w is the same for all draws. ST [START_REF] Dessalles | A structural model of intuitive probability[END_REF]) defines subjective probability p by subtracting cognitive complexity C from C w . We get:

p = 2 -U (2)
Hence the statement about unexpected events being "too" simple. In ST"s framework, the concept of probability is a derived notion and should be replaced by the notion of unexpectedness to account for many aspects of cognition.

To account for good luck and bad luck, we must say how emotion is related to simplicity (Dessalles, 2008a). Let"s call E(s) the (always positive) intensity of the emotional experience caused by situation s.

E(s) = E h (s) + U(s) (3) E h (s)
is the hypothetical emotional intensity attached to the occurrence of s. It corresponds to a not unexpected experience (when U = 0). In many cases, E h (s) = V(s), where V is a utility function. Events that were complex for the world to produce (C w large) arouse more intense emotion when they occur, as they are more unexpected. Using (2), (3) can be rewritten: e(s) = e h (s)/p(s), where e h and e stand for non-logarithmic emotions. The cognitive complexity C(s) decreases E(s) in (3). It acts like an emotional "tax" paid for considering the event.1

www.simplicitytheory.org

If s is not an event, but an anticipated situation, the expected emotion can be expressed using utility function V:

E h (s) = V(s) -U(s) (4)
The perspective of a situation that is complex for the world to produce (C w large) arouses less emotion. In the non-logarithmic domain, equation ( 4) reads e h (s) = v(s)p(s).

In causal reasoning, we suppose that expected emotion propagates through causal links (Dessalles 2008). If a known emotional situation s is believed to result from situation s', then E h (s) = E h (s'). Using conditional complexity, we may write:

U(s) = U(s') + C w (s|s') (5)
By adding E h (s) to both sides, we get:

E(s') = E(s) -C w (s|s') (6)

ST's Predictions

In the absence of any precise counterfactual, as when one"s house is struck by lightning, (3) provides a definition of luck, in line with [START_REF] Rescher | Luck: The brilliant randomness of everyday life[END_REF]:

L 1 = E h (s 1 ) + U(s 1 ) (7)
To assess the expected emotion E h (s 1 ) in such case, individuals may recall a known situation s of lightning on a house (or imagine it), and consider

E h (s 1 ) = E h (s) = L 1 (s) - U(s).
In wheel of fortune situations, the expected emotional intensity E h (s + ) of winning corresponds to landing on a winning site s + . The colored segment in figure 2 represents the winning sector in a linear version of the wheel of fortune. The complexity of landing on s + is C w (s + ) = log 2 l 0 . This is the number of bits required by the "world" to choose a landing position. According to (4), the maximum value of E h (s + ) is obtained for typical, i.e. maximally complex s + : C(s + ) = log 2 l 2 . This is the number of bits required to discriminate among all winning positions. We get:

max E h (s + ) = V(s + ) -log 2 l 0 /l 2
This corresponds to the classical expected utility in the non-logarithmic domain. When playing with a wheel of fortune, individuals acknowledge that the probability of landing in various sectors of the roulette is constant, but that landing close to a winning sector involves more intense bad luck [START_REF] Teigen | Luck: The art of a near miss[END_REF]. Let us considered a linear version of the problem (figure 2).

After the draw, possibly for (self-)narrative purposes, individuals pick the situation s that maximizes emotional intensity E(s). It may be the actual situation s 1 , as in (7), or a counterfactual one s 2 . Individuals are supposed to opt for the computation that gives the more intense emotion. In the counterfactual case, s 1 is seen as an intermediary step toward s 2 . ( 3) and ( 6) give a new value for E(s 1 ): E c (s 1 ) = E h (s 2 ) + U(s 2 ) -C wc (s 2 |s 1 ). Luck is measured by the emotional gap between both emotions for s 1 :

L 2 = E h (s 2 |s 1 ) + U(s 2 ) -C wc (s 2 |s 1 ) (8)
Conditional E h (s 2 |s 1 ) means that the expected emotional intensity is assessed using the actual emotional intensity of s 1 as baseline. The counterfactual nature of s 2 requires the introduction of a fictitious world wc that is able to keep a memory of s 1 to generate s 2 . The term C wc (s 2 |s 1 ) is the minimal price to pay for the "If…". It represents the size of the minimal parameter modifications that the observer can imagine for the "world" to have generated s 2 instead of s 1 .

In the case of figure 2, E h (s 2 |s 1 ) = V(s + ), and C wc (s 2 |s 1 ) = 1+ log 2 (+), which is the amount in bits needed to indicate the (non zero) targeting shift to the right toward s 2 . On the other hand, C w (s 2 ) = log 2 l 0 and C(s 2 ) = 1 + log 2 (1+) (one bit to choose the left edge of the winning region, plus the representation in bits of the (possibly null) shift to reach s 2 ). We get: L 2 = V(s + ) + log 2 l 0log 2 (+)(1+) -2. Taking  = 0 to maximize the intensity of unluck:

L 2 = V(s + ) + log 2 l 0 / -2 (9)
The experience of bad luck in this near miss experience is an increasing function of the missed opportunity V(s + ) and of the number l 0 of possibilities, and a decreasing function of the miss .

If the counterfactual is assessed against the expected emotion, here max E h (s + ), instead of s 1 , we get:

L 3 = V(s + ) + log 2 l 2 / -2 (10)
This model accounts for the fact that when s 2 is more complex, as in figure 1(c), the intensity of (un)luck is smaller. We have C(s 2 ) = log 2 k + 1 + log 2 (1+), where k is the number of winning regions. The intensity of luck is thus diminished by log 2 k.

The extension to the continuous case is straightforward (figure 3). We suppose that the space is bounded to the left but not to the right. If we call  the landing precision, then C w (s 2 ) = log 2 (l 0 /), as we need that number of bits to decide where to stop. 2 As previously, C wc (s 2 |s 1 ) = log 2 (+)/, and C(s 2 ) = log 2 (1+/). After taking the best choice  = 0, we get:

L 2 = V(s + ) + log 2 l 0 / -1 (11)
2 This supposes that there is a way to delimit numbers in the algorithm.

l 0  s 1 s 2  l 1 l 2
www.simplicitytheory.org (the one-bit difference with (9) comes from the fact that the winning region has only one edge). Equation ( 11) accounts for emotions described by the expression: "fall short of the goal". 9) and ( 11) define the intensity of luck, but not only. They predict what the counterfactual situation s 2 will be (what many models of counterfactual thinking omit to do). Individuals pick the alternative s 2 that realizes the best compromise between high emotion E(s 2 ) and low counterfactual complexity C wc (s 2 |s 1 ).

Nine Stories

The following experiment was conducted to validate the predictions of the model. We tested 61 participants who accepted to pass the test on a Web site (www.dessalles.fr/expe/histoires). All contacted individuals had a high level of academic education, though in domains different from psychology or language sciences (mainly students in engineering). Nine short stories were presented to them (see Table 1). Each involved two or three choices. Instructions invited participants to choose options that made emotion maximal. Some choices irrelevant to the present study (such as the age of the victim in story S9) have not been exploited. Answers given after less than 20 sec. of reading were automatically discarded (median answering time per story was 90 sec.), which leaves us with a minimum of 56 answers per story. Presentation order (stories and options) was randomized.

Table 1: Abridged translation of the stories (originals on www.dessalles.fr/expe/histoires). S1-René is a railway worker. He works at the border, at a place where signals must me manually transmitted between the two networks. There is single-track line at [9 (71*) / 23 (21) / 15 (7)] km from René"s post. That day, René forgot to send the signal as a train crossed the border. He eventually did, but [ten (59*) / fifty (21) / thirty (20)] seconds before that, another train had entered the single-track line. The collision killed one of the two drivers. As shown in Table 1, most results were significant and 19 of the 21 majority choices are congruent with the model"s predictions.

Analysis

Some results are commented now in the light of the theory.

Emotions: The intensity of the actual event, E(s 1 ), was tested in story S2 (Lucas"s waiting time), and in story S5 (duration of Florence"s lost experiment). Unsurprisingly, majority choices make E(s 1 ) maximal. In story S7, the third choice (number of points offered) influences E h (s 2 ): option "500",

l 0  s 1 s 2 
www.simplicitytheory.org which would lead to a smaller value of E h (s 2 ), was discarded by participants.

Counterfactual simplicity: In story S8, counterfactual s 2 corresponds to the invited girl (G) being involved in the accident ("it could have been her"). Both majority choices in S8 tend to make s 2 simpler, in agreement with equation ( 8).

Participants clearly preferred that the invited girl (G) be one among 2 (71%) instead of one among 5 (17%) or 30 (12%), thus making the minimal description of G smaller by log 2 n -1 in comparison with n = 5 and n = 30. Similarly, by choosing the closest location (200m (55%)) instead of 500m or 900m for the counterfactual accident, they saved bits on C(s 2 ) (log 2 (500/200) and log 2 (900/200)).

Duration before near miss: In story S7, participants judged important that the hero hesitated four months (76%) instead of two months or two weeks before buying her/his telephone. We are in a case of unbounded near miss, and as predicted by equation ( 11), participants preferred the largest value for L. The same phenomenon explains the strong preference for the fact that Michèle has been playing for 6 years (84%) in story S3 (in this case, the winning "sector" is s 1 and it is reached, but the computation is identical).

Proximity in near miss: Equation ( 11) predicts that emotion is maximum when one ends up close to the border between "winning" and "loosing" sectors ( small). Several stories represent near miss situations. In S1, the train accident would have been prevented if the signal had been sent k×10sec before (k = 1 preferred (59%)); In S4, the worker would not have been badly injured if the accident had occurred k days later (k = 1 preferred (75%)); in S7, the cost would have been saved if the purchase had been made k days later (k = 1 preferred (74%)); in S9, Helen would have died if her admission had been delayed by k×30min (k = 1 preferred (77%)).

Causal Thinking in Good or Bad Luck

When confronted with events they perceive as (un)lucky, people tend to construct causal explanations for why these events happened [START_REF] Pritchard | The psychology and philosophy of luck[END_REF]. Causal thinking may produce counterfactuals by negating causes of the actual event, but also by enabling conditions for the counterfactual [START_REF] Byrne | Précis of the Rational Imagination: How people create alternatives to reality[END_REF]. In what follows, we show how causal thinking can be accounted for within the ST framework.

Suppose that a cause s 3 can be found to explain s 1 . If we use (5) together with (7), we get:

L 1 = E h (s 1 ) + U(s 3 ) + C w (s 1 |s 3 ) (12)
This relation shows that unexpected causes (U(s 3 ) large) and materially complex causal links will tend to increase the feeling of (un)luck in the non-counterfactual case.

If s 4 is a counterfactual alternative to s 3 that would have led to s 2 , we can compute L 2 from s 3 . Using (8):

L 2 = E h (s 2 |s 3 ) + U(s 2 ) -C wc (s 2 |s 3 )
We may decompose C wc (s 2 |s 3 ):

L 2 = E h (s 2 |s 3 ) + U(s 2 ) -C w (s 2 |s 4 ) -C wc (s 4 |s 3 ) (13)
The term C wc (s 4 |s 3 ) measures the mutability of s 3 [START_REF] Byrne | Précis of the Rational Imagination: How people create alternatives to reality[END_REF]. Equation ( 13) can be used to find a cause that people will be likely to select as mutable. Let us check these predictions against the experimental results.

Cause simplicity: Relation (12) predicts that simple causes (C(s 3 ) small) will augment emotion since they are more unexpected. This is verified in story S5, where participants preferred the student responsible for the damage to be a neighbor"s son (67%) instead of more complex individuals. In story S6, they preferred the virus to have been mentioned in the media (52%), rather than in a medical journal or a medical record where it would have been more complex to discriminate. Story S9 was also designed to test causal simplicity. We expected participants to reject option "a retired couple", as these individuals would be more complex to discriminate than in the two other options ("a colleague teacher" and "a member of her bridge club"). However, participants did not show the expected preference (49% vs. 26%+25%).

Causal link complexity: Relation (12) predicts that materially complex causal links (C w (s 1 |s 3 ) large) are more unexpected and thus will augment emotion. Story S6 has been designed to check this point. Participants did prefer Magalie"s eventual success to go through a seven hour (79%) test to decide between 8 (66%) infectious agents, rather than easier alternatives.

Causal link simplicity: Relation (13) conversely predicts that in counterfactual thinking, simple causal links will be preferred (C w (s 2 |s 4 ) small). In story S1, participants chose the shortest distance between the railway worker"s faulty action and its effect (71%); in story S2, they preferred Lucas to lace up his shoe close to the station (71%). In both cases, the material simplicity of the causal link diminishes the counterfactual complexity from the cause ("if he had sent the signal…", "if Lucas had not paused to lace his shoe…") to the counterfactual effect. We failed to show the same effect in story S5, where we expected participants to chose the simpler causal mechanism ("broke all the boxes") instead of more complex ones ("broke a bottle of formalin"; "broke the nourishing device"). The probable reason is that a simple causal link is preferable if one adopts Florence"s counterfactual thinking, whereas a complex causal link is preferable if we only consider the newsworthiness of the story, what some participants seem to have done despite the instructions.

Discussion

The strong point of this study was to show the relevance of the notion of complexity in the study of the perception of luck. Many judgments about (un)lucky situations are not explained by variations of probability (even perceived probability) [START_REF] Teigen | Luck: The art of a near miss[END_REF]. However, they vary in a systematic way according to variations in complexity. We tried to connect people"s attitude toward luck with predictions from Simplicity Theory, with some positive results.

Another positive aspect of the study is to highlight several intervening factors that have gone unnoticed in previous studies, such as the simplicity of the counterfactual situation (story S8), the fact that proximity is measured on a relative scale (stories S3, S7), or the simplicity of causes (stories S5, S6). The model also provides quantitative laws, e.g. for the wheel of fortune near miss.

We had two negative results in the experiment (story 5, choice 2 and story 9, choice 1). Note, however, that both consist in qualitative choices, which are more prone to complex interpretations by participants. The failure in S5 is likely to result from the bad design of the story; the failure in story 9 remains a mystery (perhaps the association due to word "retired" being used twice is sufficient in rapid readers to make the rescuers seem simple).

In its current state, this theory of luck is not as simple as it should be. There are still some conceptual connections to be done that will make the link between equations and the processing of emotional intensities more transparent. The present account is meant as an attempt to depart from mere lists of factors and to outline an integrated model of the human ability to perceive luck in events.

The research, initiated in the recent years, on the cognitive role of descriptive complexity has already produced valuable results. The model presented in this paper is meant as a contribution to this enterprise. The sensitivity to complexity differences, which is central to ST, seems to be a general law, which applies across modalities and at all levels of abstraction. Its importance in the processing of some emotions that are involved in decision processes, such as the feeling of being (un)lucky after the occurrence of an event [START_REF] Loomes | Regret theory -An alternative theory of rational choice under uncertainty[END_REF], should encourage further investigation in this domain.

Figure 1 :

 1 Figure 1: Three examples of near miss

Figure 2 :

 2 Figure 2: Discrete bounded near miss

Figure 3 :

 3 Figure 3: Continuous unbounded near miss Equations (9) and (11) define the intensity of luck, but not only. They predict what the counterfactual situation s 2 will be (what many models of counterfactual thinking omit to do). Individuals pick the alternative s 2 that realizes the best compromise between high emotion E(s 2 ) and low counterfactual complexity C wc (s 2 |s 1 ).

S2-

  Lucas was heading for the metro station.At [30 (71*) / 100 (20) / 800 (9)] m from the station, he stopped to lace up his shoe. As he arrived on the platform, the doors of the train closed in front of him. He had to wait [25 (89*) / 15 (9) / 6 (2)] minutes for the next train. S3-Michèle has been playing lotto every week for [6 (84*) / 4 (11) / 2 (5)] years. On December [19 (70*) / 3 (18) / 12 (12)], she told [two (60*) / four (32) / three (9)] friends of hers that she would stop playing. They persuaded her to bet for the special Christmas draw, on December 26. She did and won 62 000 Euros. S4-Jacques was badly injured at his workplace by a defective machine on November 7. The defect had been previously notified and the machine was planned to be repaired on [November 8 (75*) / November 17 (12) / December 18 (12)]. S5-Florence works in a biology lab. Her two-[year (84*) / month (11) / week (5)] experiment on cell cultures was ruined by a student who knocked over a shelf. This broke [all boxes containing (35) / a bottle of formalin that fell on (45) / the automatic device nourishing (20)] the cell cultures. Florence was furious. She discovered that the student was the son of [her neighbor (67*) / her former PE teacher (15) / the piano teacher of her sister (18)]. S6-A young writer is admitted to Magalie"s emergency department at the hospital. Her condition deteriorates. [8 (66*) / 4 (21) / 6 (14)] infectious agents may explain the illness. Magalie sends samples to the lab and tests are conducted in parallel. It takes [seven (79*) / three (16) / five (5)] hours to get the result and the patient is saved at the last minute. Magalie remembers that she saw the name of the virus in [the media, as well-know singer recently died of it (52*) / the record of another patient (28) / a specialized journal (21)]. S7-For [four months (76*) / two months (21) / two weeks (3)] I was thinking of changing my cell phone. I eventually went to SFR Thursday at 1pm. I had to pay part of it because I was lacking 1000 points. [Thursday (74*) / Friday (21) / Tuesday (5)] evening, I received an offer: "change your phone, SFR offers you [1500 (55) / 4000 (38) / 500 (7*)] points". S8-Ms Tsuda"s daughter had invited [two friends (71*) / all girls in her class (17) / four friends (12)] to her house. One of them was late. She had left her own house long ago. Ms Tsuda walked toward the girl"s house and arrived at a level crossing, located at [200 (55*) / 500 (24) / 900 (21)] m from Ms Tsuda"s house. There was indeed an accident involving a young girl. It turned out that the invited girl was not involved and was late because of a detour caused by the accident. S9-Helen, retired teacher, fainted as she was walking in the woods. She was found by [a retired couple (49) / a colleague teacher (26) / a member of her bridge club (25)] who called the rescue team. Helen would not have survived if she had reached the hospital [half an hour (77*) / one hour (16) / one hour and a half (7)] later. Note: Choices irrelevant to the present study are not shown here. Numbers in parentheses indicate percentages. Asterisk indicates significance (p < 0.001). Underlined numbers indicate model predictions.

  Dessalles, J-L. (2010). Emotion in good luck and bad luck: predictions from simplicity theory. Proceedings of the 32nd Annual Conference of the Cognitive Science Society. Portland, OR: Cognitive Science Society. www.dessalles.fr/papiers/pap.cogni/Dessalles_10020801.pdf

In (2), U must remain positive. In (3), U may be negative, but E must be positive. These constraints can be used to define the relevance of events(Dessalles,

2008a).


Jean-Louis Dessalles
email: tel.33145817529jl@dessalles.fr

Reasoning as a lie detection device

The biological function of human reasoning abilities cannot be to improve shared knowledge. This is at best a side-effect. A more plausible function of argumentation, and thus of reasoning, is to advertise one's ability to detect lies and errors. Such selfish behavior is closer to what we should expect from a naturally selected competence.

I fully support HM & DS"s central claim that deliberative reasoning is a byproduct of argumentative competence. But if the function of reasoning is argumentation, what is the (biological) function of argumentation? According to HM & DS, argumentative reasoning improves "both in quantity and in epistemic quality the information humans are able to share", and thanks to it, "human communication is made more reliable and more potent".

If the biological function of reasoning is to achieve shared knowledge optimization (SKO), as suggested in the target article, then why do people show obvious limitations such as confirmation bias? HM & DS answer that information quality is optimized, not at the individual level, but at the group level. It would even be a good thing that individuals specialize on their (probably erroneous) line of reasoning, as long as argument exchange restores global information quality. The problem is that natural selection does not operate at the collective level. Shared knowledge belongs to the phenotype of no one.

How does the speaker benefit from uttering an argument? If the purpose is to correct or update her own earlier beliefs, why go public with it? And if it is to correct or update others" beliefs, what"s her advantage? HM & DS explanation for the existence of deliberative reasoning does not escape the general evolutionary paradox of communication: if it benefits listeners only, there should be no speakers; and if it benefits speakers only (e.g. by allowing manipulation), there should be no listeners. Invoking collective benefits does not offer an escape route if we wish to remain on firm Darwinian ground.

To solve the paradox, we must depart from (SKO). My proposal (Dessalles, 1998) is that human-like reasoning started with logical consistency checking (CC), and that humans used it as a lie detection device (LD). As a response to the risk of appearing self-contradicting, the ability to restore consistency (RC) through argumentation emerged. In this game, information quality is not what is at stake. The point for individuals is to advertise (AD) their ability to perform or resist (LD). This advertisement behavior makes sense within a costly signaling model of human communication (Dessalles, 2007;2008).

The main difference with HM & DS"s position comes from (AD). HM & DS are close to the (CC/RC) distinction when they speak of evaluation vs. production (of arguments). They fail, however, to see that these two faculties did not evolve for the sake of any form of public knowledge, but as signals. Individuals who can publicly signal lies or errors by naming inconsistencies (CC) get immediate social benefit (Dessalles 2007). Those who publicly restore consistency (RC) get social benefit as well, or regain their momentarily lost status.

Contrary to (SKO), the competitive nature of (AD) explains why reasoning is far from remaining a private activity: argumentation takes up the major part of the 16 000 words spoken daily on average (Mehl et al., 2007). Moreover, various observations by HM & DS make more sense within (AD) rather than (SKO), especially the fact that humans are better at finding inconsistencies in others" line of reasoning and at finding support for their own. Another argument in favor of (AD) is the futility of many conversational topics, which makes no sense from an (SKO) perspective. Yet another good example of the divergence between (AD) and (SKO) is offered by the BBS commentary system: commentators are of course concerned by the overall quality of scientific knowledge, but most of them are even more motivated by the urge to show their ability to point to some inconsistency in the target article. (SKO) would perhaps hold if contributors accepted that their name be omitted.

HM & DS strangely do not mention a fundamental common property between deliberative reasoning and argumentation. Both processes seem to consist in a sequential alternation between logical incompatibilities and attempts to resolve them. This property is concisely captured by the Conflict-Abduction-Negation procedure that describes argumentative processes (Dessalles, 2008). The sequential nature of argumentative reasoning supports the central claim of the target article, but it is at odds with any idea of knowledge optimization. Virtually all artificial reasoning devices (from chess players to planning programs) involve parallelism whenever possible (esp. in muti-option comparison). So-called Truth-maintenance systems and argumentation systems make use of graph representations that are not limited to sequential processing (e.g., Dung, 1995). In comparison, human argumentative reasoning is skewed. It is bound to start from a logical incompatibility, and then sequentially creeps forward through recursive attempts to solve the current incompatibility and then detect new ones. Such manifestly suboptimal procedure does not make sense if the aim is knowledge optimization. It makes perfect sense, however, in the (LD/AD) context.

The biological importance of informational capabilities is due to the particular political context of our species (Dessalles, 2007). In that context, information is not important as such; it is rather an excuse to show off informational capabilities, such as being the first to point to unexpected events. In the absence of a lie detection system, such communication is bound to checkable, almost immediate, events. The advent of consistency checking capabilities offered a new occasion for individuals to compete, by allowing them to advertise their lie and error detection capabilities. This new competition has side-effects, such as opening the possibility of communicating about past events that cannot be directly checked. Knowledge improvement also turns out to be a side-effect of reasoning and argumentation. When reasoning and producing arguments, speakers follow a more selfish agenda, which is to show off their competence for dealing with anomalies in information. This leaves us with the urgent question that any evolutionary account of reasoning must face: Why us and not other species? Why do other primates (apparently) lack deliberative reasoning abilities? HM & DS mention the fact, but do not address the issue, though in their view, (SKO) should be beneficial to any species. The usual way to evade the issue consists in invoking some deficiency that would affect all other species: lack of intelligence, lack of theory of mind (Sperber, 2000a), lack of cooperation. . . As suggested by Bickerton (2009), the plausible sequence of events is the opposite. Some new selection pressure created the need to signal new information to conspecifics; all other unique features of the human mind are consequences, rather than causes, of this fact. This is especially true of intelligence and reasoning abilities (Monod, 1970;Bickerton, 2009). The sequence of events could be as follows. Due to the advent of weapons that allow killing at no risk at some point in the hominin lineage (Woodburn, 1982), classical primate politics became obsolete. Information replaced muscular strength as a criterion for choosing allies. Individuals started signaling any unexpected event, as a way to advertise their ability to warn for danger. This form of communication was initially limited to checkable events. Then the ability to detect inconsistencies (and to name them) became a new asset (hypothesis LD), and was advertised as such (hypothesis AD). This opened the way for communication about past events that could not be directly checked. Further reasoning abilities (especially abduction) developed as a way to publicly restore previously jeopardized self-consistency (hypothesis CC). Virtually no evolutionary scenario of language makes communication advantageous both to speakers and listeners at each step (Dessalles, 2007;Bickerton, 2009). This one does. It provides an evolutionary account for HM & DS"s central claim that reasoning serves argumentative purposes. Contrary to HM & DS"s view, however, Reasoning is used in the first place to show off one's ability to spot lies and errors; reasoning abilities are then used to demonstrate one's ability to restore logical consistency.

I also agree with the fact that argumentation evolved as an anti-liar device. BUT:

If individuals are endowed with the ability to detect logical inconsistencies, it is:

-neither "to correct or update earlier beliefs" (otherwise, it would be absurd to go public with those inconsistencies) -nor to improve "small group cooperation […by] overcoming disagreements" (unless one relies on the shaky ground of group-selectionist accounts of language).

From the perspective of the signaling theory of language (Dessalles 2000/2007), we must split the (deliberative) reasoning ability into two:

-the ability to detect inconsistencies, to name them and to make them public -the ability to restore consistency HM & DS are close to this distinction, when they speak of production vs. evaluation. They fail, however, to see that these two faculties evolved, neither to improve the welfare of the group nor for the sake of any form of "thruth", but as signals.

Individuals who can publicly signal lies or errors by naming inconsistencies get immediate benefit (Dessalles 2000(Dessalles /2007)). Those who publicly restore consistency regain their momentarily lost status.

Evidence for the necessity of splitting deliberative reasoning into two signaling behaviors can be found in the following facts:

-deliberative reasoning is frequently public (when individuals are not alone, of course) -virtually all argumentative discussions involve sequential alternations between contradictions and attempts to resolve contradictions -even private deliberative reasoning is shown to involve the same sequential alternation, whereas all artificial reasoning devices (from chess players to planning programs) involve parallelism whenever possible (esp. in muti-option comparison).

Reference

Dessalles, J-L. (2000/2007). Why we talk -The evolutionary origins of language (English edition of 'Aux origines du langage', 2000). Oxford: Oxford University Press.

http://www.dessalles.fr/WWT/ My expertise on the subject:

-In the past decade, I have been repeatedly supporting the idea that (deliberative) reasoning is a by-product of argumentation and that argumentation evolved as an anti-liar device.

-I discussed that issue in a paper to appear in 2010 in Biology and philosophy -function of reasoning = maximize epistemic quality -people do it only for the sake of their own claims and to challenge others" claims "When a group has to solve a problem, it is much more efficient if each individual looks mostly for arguments supporting a given solution." "This joint dialogic approach is much more efficient than one where each individual on his or her own has to carefully examine all possible solutions" "It is not just opinions that may have to be defended: people may also have to put forward arguments to defend their decisions and actions, and they may reason proactively to that end. We want to argue that this is the main role of reasoning in decision making." "We view the evolution of reasoning as linked to that of human communication.

Reasoning, we have argued, allows communicators to produce arguments in order convince addressees who would not accept what they say on trust; it allows addressees to evaluate the soundness of these arguments and to accept valuable information that they would be suspicious of otherwise. Thus, thanks to reasoning, human communication is made more reliable and more potent."

"More realistically, individuals may develop some limited ability to distance themselves from their own opinion, to consider alternatives and thereby become more objective. Presumably this is what the 10% or so of people who pass the standard Wason selection task do. But this is an acquired skill, and involves exercising some imperfect control over a natural disposition that spontaneously pulls in a different direction."

  Symposium on J.-L. Dessalles's Why we Talk (OUP, 2007): Precis by J.-L. Dessalles, commentaries by E. Machery, F. Cowie, and J. Alexander, Replies by J.-L. Dessalles -My book (2000/2007) (see above) has two chapters on the topic -My recent book (La pertinence et ses origines cognitives, 2008) has two chapters on the topic "The function of an inferential process is to augment and correct the information available to cognitive system." Arguments = "representations of relationships between premises and conclusions." "Reasoning allows people to exchange arguments that, on the whole, make communication more reliable and hence more advantageous. The main function of reasoning, we claim, is argumentative" "[Reasoning] thus increases both in quantity and in epistemic quality the information humans are able to share" = "main function" "To avoid being victims of misinformation, receivers must therefore exercise some degree of what may be called "epistemic vigilance"" (Sperber et al., In press).

	"Communication plays an obvious role in human cooperation both in the setting of
	common goals and in the allocation of duties and rights."
	"The main function of reasoning is argumentative: reasoning has evolved and
	persisted mainly because it makes human communication more effective and
	advantageous."
	jld1998: "A possible conjecture is that our ability to check logical consistency
	evolved from the necessity to protect oneself against lies."
	Contradiction:


Jean Louis Dessalles
email: dessalles@enst.fr

Biomimetic Use of Genetic Algorithms

Genetic algorithms are considered as an original way to solve problems, probably because of their generality and of their "blind" nature. But GAs are also unusual since the features of many implementations (among all that could be thought of) are principally led by the biological metaphor, while efficiency measurements intervene only afterwards. We propose here to examine the relevance of these biomimetic aspects, by pointing out some fundamental similarities and divergences between GAs and the genome of living beings shaped by natural selection. One of the main differences comes from the fact that GAs rely principally on the so-called implicit parallelism, while giving to the mutation/selection mechanism the second role. Such differences could suggest new ways of employing GAs on complex problems, using complex codings and starting from nearly homogeneous populations.

GENES AND SCHEMATA AS THE UNITS OF SELECTION

A fundamental common feature between GAs and natural genetic systems comes from the fact that in both situations individuals are not what is selected.

In GAs, individuals are represented by their genome (most often a binary vector), and are evaluated so that only the best fitted ones have some chance to reproduce. The hope is that the GA will create individuals which will reach a maximum of the evaluation function. But this is not sufficient to make a GA: each pair of "parents" chosen among the best graded individuals enters a hybridation (crossover) in which genomes are mixed to give the genome of an offspring. This crossover is essential, as was shown by J. Holland. Without crossover we have random search, not GA. This requirement has many consequences for our purpose, as we will see after having compared it with its natural counterpart. Figure 1 shows an example which was especially designed to underline the added value of crossover. Individuals are "marked" according to the sum of the bits of their genome. Crossover allows the selected 1s to gather in the same individuals.

Figure 1. A genetic algorithm is asked to maximize the sum of 100 bits. The right histogram shows the result of 50 generations of 100 individuals: the whole population scores between 93 and 96. The left diagram shows the histogram resulting from 5000 random choices, which spreads between 34 and 66.

Crossover allows selection to operate not on individuals, but, as shown by J. Holland in 1968, on schemata (cf. [Goldberg 1989]). A schema is theoretically a partial specification of the genome, on which the observer is keeping an eye through generations. Practically, only schemata that are specified on a short length have some chance of survive after crossover. For the observer, only those schemata can pretend to be selection units . It would be indeed nonsense to say that the population as a whole is selected. And individuals are destroyed at each generation (if we except the so-called elitist models)! Only short schemata have a long enough life span so that, after some generations, some of them can be considered as selected by the observer.

J. Holland showed that at best n 3 different schemata were simultaneously present in a population of n individuals, and since schemata are selected when individuals are evaluated, he coined the term "implicit parallelism" ([Goldberg 1989]). But we must keep in mind that this counting of schemata is only valid for a random population.

This observation has to be compared with the ideas of Richard Dawkins, who pointed out that rigorously natural selection does not operate by selecting individuals, nor groups, but that it operates on genes (cf. [START_REF] Dawkins | The Extended Phenotype -The Gene as the Unit of Selection[END_REF][START_REF] Dawkins | The Extended Phenotype -The Gene as the Unit of Selection[END_REF]). When considered from the point of view of natural selection mechanisms, individuals are mere temporary arrangements of genes. Only genes can survive through generations. Genomic hybridation is thus an essential phenomenon. Crossover is well known for sexual beings, but it has been also observed among unicellulars which reproduce normally through division: it is the so-called conjugation, during which two individuals mix their genome, and by the way no longer exist as individuals. There are reasons (from genetics and chemistry) to think that, contrary to what is usually said, crossover is as old as DNA, and that it is widespread among all living beings, although it has not been observed in each case. We could hardly speak of species in the absence of genomic encounters.

Since selection in GAs operates on schemata, one can define an average fitness value for each schema. But some schemata have also a meaning given by the designer, and it is often interesting to relate meaning and fitness, as a way to "explain" the solutions calculated by the algorithm. As we will see, this may not be possible in the case of biomimetic GAs.

BIOMIMETIC CONSTRAINTS ON THE GENETIC CODE

Using GAs is an art which lies for the major part in the coding of the problem. The designer has to define the semantics of the genome, so that a "mark" can be assigned to each individual. But the designer has to face several problems: nonseparability -The "coding" of living beings is definitely complex. Natural selection operates on the phenotype of individuals, and the relation genome --> phenotype is very complicated (see for example [START_REF] Petit Claudine | Evolution: Génétique des populations, évolution moléculaire[END_REF]): genes have multiple effects on the phenotype (pleiotropy) and phenotypic characteristics are the result of the combined action of numerous genes. Furthermore high order genes have been discovered (e.g. genes which code for the repressor of the activator of another repressor, cf. [START_REF] Beardsley | La régulation des gènes[END_REF].

But why should the designer of a genetic algorithm choose a complex coding? An answer could be that a too simple coding often reveals a too simple problem, for which GAs may sometimes be superfluous. Since schemata are selection units, one may be led to consider sections of genome as independant units on which evaluation will operate. This was actually the case in the example of figure 1: each bit contributes to the global "mark" apart from the others. But this means that the problem, as far as it can be solved by such a GA, can be split into as many independent sub-problems as there are independently evaluated units.

However, interesting problems are often non-divisible (some problems may be separable, and GAs are precisely used to separate them, finding out independant schemata, but we are speaking here about complex problems that cannot be hoped to be separable). Schemata are indeed selection units, but they cannot be seen as fitness units if the problem is really complex, since the fitness of a given schema is necessarily highly dependent on the presence or absence of other schemata in the genome. In such a situation, the use of simple codings is unuseful . It may even be restricting, because it allows only a restricted exploration of the fitness landscape, as we will see. Complex codings, on the other hand, may be needed if we want the link genome  evaluation to be complex, as is the case for example when one uses second order schemata, i.e. schemata that modify the way other schemata are evaluated (e.g. a group of bits coding for the number of relevant bits in an other section of the genome).

continuity

-one may think conversely that if a complex coding was chosen to handle a complex problem (with no hope that this problem may be separable), then this coding may not follow the continuity principle. This principle claims that genomes which are close for the Hamming distance (number of elementary mutations needed to transform one into the other) should have most of the time about the same evaluations. This is what makes offspring viable and allows some tolerance to mutations. [START_REF] Manderick | State of the art in theoretical approaches to genetic algorithms[END_REF] measures this continuity with the autocorrelation of fitness when elementary mutations are performed. Unfortunately, it seems that the complex coding we are claiming from a biomimetic point of view has little chance to respect this continuity principle. If for instance a second order schema is even slightly mutated, then several other parts of genome will change meaning, and the global "mark" will be significantly changed.

So how can we explain that the natural system, which is so complex, is quite continuous? Part of the answer comes from the fact that genes are extended. Most of functional natural genes code for complex molecules, proteins. An elementary mutation will for instance change one aminoacid into another, which may eventually slightly change the chemical properties of the protein, e.g. diminishing its catalytic power or specificity. The effect will most probably go unnoticed, or will even be cancelled (more protein synthesis) at the level of individual fitness. The problem with many GA-codings is that they concentrate too much meaning on each bit. An "extended" coding should allow punctual mutations to have limited effects, and would thus allow complex codes, as required in biomimetic GAs, to be continuous.

preservation of semantics

The balance between these two requirements: complexity and continuity, appears thus to be quite difficult to be hold. But the designer must also grant the preservation of semantics through genetic macro-operators like inversion, translocations or duplications. Such transformations do occur in nature (very seldom for some of them). They allow completely new genes to be created, and "cooperating" genes to become closer and to constitute longer functional genes (polygenes). In GAs, a complete "gene from locus" separation creates two orders: a semantic order, which never changes, and a topological order which may change through macro-operators and which bears neighbourhood relations that are used during crossover. But such a de-correlation between meaning and position makes offspring very unlikely to be functional after crossover. In the natural counterpart, major changes may go unnoticed if they occur in non-coding regions of DNA. And genes or polygenes may sometimes change location with no consequence on their own functioning or the functioning of their genetic environment. This is made possible by the presence of signals within DNA (e.g. starting position for transcription) that make groups of genes quite independent. To sum up, macro-operators are biomimetic, but complete gene/locus separation is not. Biomimetic GAs should instead make use of signals to make absolute position in the genome less relevant.

The choice of the genetic coding is crucial when we design a genetic algorithm to process a given problem, but, if we follow the biological metaphor, it appears also very difficult, since the coding has to meet the requirements of contradictory constraints: complexity (to allow better exploration of nonseparable problems), continuity, preservation of semantics. Furthermore, such constraints upon the structure of codings may have consequences for the way we use GAs. They indicate that the classical way of using GAs is not very biomimetic, as we will see now.

COMPLEXITY IN THE CODING, NOT IN POPULATIONS

Classical genetic algorithms interbreed individuals that are completely different. In most applications, initial populations are indeed set up randomly. The GA is then considered to have completed its job when the population becomes nearly homogeneous. The end of convergence is sometimes handled differently because GAs become very slow: in a nearly homogeneous population, crossover looses its major role which is now played by mutation. New solutions are generated much more by the mutation/selection mechanism than by implicit parallelism.

However, nature shows us a quite different situation. Individuals that can be successfully crossed share at least 99% of their genome, and most differences are phenotypically neutral! This may contribute to explain why the tremendously complex coding from genotype to phenotype, with genes of high degree, remains compatible with the continuity principle even through crossover: offspring look like their parents because both parents are similar, and crossover creates few changes (quantitatively and qualitatively) when yielding new genomes. This questions the biomimetism of GAs as they are classically defined. If the coding is complex enough (as is required by biomimetism), then a random initial population will consist of individuals that are unlikely to give viable offspring when crossed, because offspring will have very low fitness or no meaning at all. Of course the genome of individuals processed by classical GAs could be compared to the 1% of the significantly variable genes of a natural population (less than 1000 genes for mammals). But even in case of a sudden environmental change, very few of the alleles on these variable loci may become evolutionary meaningful, contrary to what is expected with GAs.

Genetic algorithms thus appear to be most biomimetic when they seem least interesting, i.e. at the end of convergence, when the population tends to become nearly homogeneous, and when the role of mutation dominates the rearrangement due to crossover (figure 2). At this stage, implicit parallelism no longer exists.

Figure 2. This schema shows that the GA of figure 1 converges asymptotically. The mere redistribution due to crossover does not allow to reach optimum (all bits 1). Admittedly we have a probability of only [1 -(1 -1/2 100 ) 100 ]  10 -28 that one locus is 0 for all individuals in the initial population. But after the first generation, if 10% of the population reproduce, this probability reaches 0.1 . In the trial plotted above (elitist model), it seems that 4 loci remain 0 after 50 generations. If p m is the mutation probability, we have [1 -(1 -p m ) 4 ]  4.p m chances that a given individual gains a 1 on one of these loci during the next generation. On can estimate by 1/10p m the number of generations necessary to switch all four bits to 1. But increasing p m may be problematic, especially with a complex coding.

However what we want to suggest here is that the biomimetic use of genetic algorithms may be legitimate and could prove efficient in certain situations. Biomimetic GAs characteristics (as summarized in table 1) are legitimate because they bring the biological metaphor logically further. After all, GAs were not selected after a competition with all thinkable alternative algorithms. They were studied in the first place because of heuristic principles like "what performs well in nature should perform well in optimization". GAs, used biomimetically as proposed here, are of course less efficient. They lack the implicit parallelism put forward in most applications. However, they should appear as worth studying as well, if we can anticipate situations in which they could bring an added value, as may be the case with problems that cannot be formulated in terms accessible to usual methods.

Table 1 Main features of biomimetic genetic algorithms

BIOMIMETIC GAs ON COMPLEX PROBLEMS

Good solutions for a complex problem are unlikely to be simple. Biomimetic GAs may be an interesting way to discover good complex solutions.

To examine this point we can consider the interesting attempt of Lavalou [1990] who tried to apply genetic algorithms to a complex enough problem. His genetic algorithm handled genomes coding for short music pieces which were evaluated by a connectionist network. He decided to design a complex coding with genetically encoded musical operators. For instance, musical themes were transformed recursively using short patterns, and not only the patterns, but also the number of recursive transformations were determined by genes.

The idea we want to suggest here in order to promote biomimetic GAs is that if the problem to be solved is complex (think of a very "tortured" and multidimensional fitness landscape), classical GAs will not perform better than random search! Crossover between necessarily very different (because initially randomly determined) individuals will give intermediary offspring which are very unlikely to obtain a significantly better fitness: if the fitness landscape is complex enough, each individual of the initial population is isolated in a local fitness context in which the fitness value of a given locus depends on the values of many other loci. Specific mutational changes may bring a higher fitness, while different (and often contradictory) changes would benefit another individual placed in a very different fitness context. In such a situation, crossover does not play its role of gathering independent good solutions together as expected with implicit parallelism, but it produces individuals, located in totally new fitness contexts, that can be considered as random in these contexts. The populations processed by classical GAs through generations correspond in this case to a few thousands of random trials, and if the problem is really complex, a satisfactory solution has little chance to be obtained this way.

Biomimetic GAs theoretically escape from this difficulty since they operate on nearly homogeneous populations. The initial random choice that locates the entire population near a given location in the fitness landscape will then be slowly, but constantly, improved by the combined effect of mutations and crossover. This is the mutation/selection mechanism. Then comes another feature of biomimetic GAs into play: the complexity of coding.

Since the link labelled A in figure 3 is very simple in classical GAs, the reachable phenotypes will have a quite limited complexity (e.g. algorithmic  complex coding, with high order genes, in order to allow better exploration of non-separable problems  extended genes to allow quasi-continuous mutational changes  use of signals (instead of complete gene-locus separation) to allow macrooperators  nearly homogeneous populations, where the mutation/selection mechanism takes the major role over implicit parallelism in the search for new solutions complexity as defined in [START_REF] Chaitin | Algorithmic Information Theory[END_REF]]) because of a lack of combinatorial power. . This schema illustrates the importance of the genotype/phenotype distinction for biomimetic GAs. This separation allows codings (in A) to create a "wide" range of phenotypes by complex combinations.

There are many ways to make the link A complex. For instance Werner & Dyer [1992] designed a system in which evolving creatures learn to communicate. In this application, the genome of each creature codes for a small connectionist system (its phenotype) that controls the creature's behavior. But we may think that combinatorial codes (i.e. with high order genes), as suggested for biomimetic GAs, may yield even richer genotype --phenotype links.

If the coding leading from genes to phenotype is too simple (e.g. in the case of music, each note could be coded separately), then one can imagine that it is not an efficient way for the population to explore the landscape during its continuous walk (for instance a combinatorial coding of music pieces like the one chosen by Lavalou produces pieces of arbitrary length, what a trivial coding will never do). Simple codings do not have here the advantage of allowing a capture of parameters that are relevant to the problem (because the problem is not separable), and they may prove to be too limited in many complex applications.

POWER AND LIMITS OF BIOMIMETIC GAs

We may think of the genome of individuals processed by biomimetic GAs as a blueprint for a kind of machine (the phenotype of individuals). The mutation/selection mechanism has been invoked in very different contexts as a way to create complex systems (Darwin's natural selection theory, Burnet's clonal selection theory, synaptic selection theory of Edelman and Changeux, aspects of behavioral learning, and even cognition (see [START_REF] Jean-Pierre | Neuronal models of cognitive functions[END_REF]), etc.). Can a system like biomimetic GAs create phenotypes that become increasingly complex? Can we imagine they could reach the same creative power as their natural counterparts?

Even if they should prove to be an interesting way to explore very complex problems, there are fundamental reasons why GAs as we know them are also limited in their creative power (this is particularly relevant to research on Artificial Life, see [START_REF] David | Evolution as a Theme in Artificial Life: The Genesys/Tracker System[END_REF]).

The semantics of GAs lies for the major part, and often totally, outside the genes. If we consider again Lavalou's program, a 5 bit sequence contributing, say, to a musical pattern has no chance to have any influence on the recursivity depth. In other words, one cannot imagine any combination of mutations, anywhere in the genome, that could change the semantics of these five bits this way.

In living beings, on the other hand, the semantics of genes is controlled by the genome itself, and it may be changed by the mutation/selection mechanism. If we discover that 5 codons have an influence on eye color, one could theoretically imagine a group of mutations somewhere else in the genome that makes these 5 codons control this time tooth length! One can say that living beings are endosemantic entities, while GAs are exosemantic. The genome of living beings is the only known endosemantic system. If we define the "genetic envelope" of a GA as the set phenotypes that it can reach, then this enveloppe is predetermined (most of the time implicitly) by the designer of the genes --> phenotype coding. This may prevent us to expect too "miraculous" properties from GAs, even if they are biomimetic.

But GAs show quite impressive properties (generality, adaptation, learning capabilities when associated with classifiers,...). We tried to indicate here that, when used in a biomimetic way, they may be an interesting tool to explore very complex problems.

acknowledgments: I am grateful to Alain Grumbach, Irène Fournier and Olivier Hudry for having read an early version of this paper and for their fruitful remarks.

  Figure3. This schema illustrates the importance of the genotype/phenotype distinction for biomimetic GAs. This separation allows codings (in A) to create a "wide" range of phenotypes by complex combinations.