Simplicity Effects in the Experience of Near-Miss Jean-Louis Dessalles (dessalles

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

Near-miss experiences are one of the main sources of intense emotions. Despite people"s consistency when judging nearmiss situations and when communicating about them, there is no integrated theoretical account of the phenomenon. In particular, individuals" reaction to near-miss situations is not correctly predicted by rationality-based or probability-based optimization. The present study suggests that emotional intensity in the case of near-miss is in part predicted by Simplicity Theory.

The Near-Miss Experience

People are emotionally responsive to situations in which some benefit was within reach, but has nevertheless been missed. Near-miss (or near-hit) experiences are one of the main sources of strong emotion. The 1000001 th customer in a store may feel frustrated when the person in front of her gets his shopping cart reimbursed. Failing an entrance examination by only a few points may spoil entire lives. In June 1995, Tim O'Brien shot himself in the head in despair, after he (mistakenly) believed he had lost out on a £2.7m National Lottery jackpot because he had forgotten to renew his ticket. The missed opportunity is not always as evident as in these examples: individuals sometimes make up an alternative situation to compare their actual fate with, e.g. when thinking in retrospect [START_REF] Teigen | When a small difference makes a big difference -Counterfactual thinking and luck[END_REF].

In studies about reasoning, feelings generated by nearmisses are considered to introduce irrational bias [START_REF] Wohl | The effects of near wins and near losses on self-perceived personal luck and subsequent gambling behavior[END_REF][START_REF] Dillon | The near-miss bias in decision making[END_REF]. If rational agents are supposed to rely on objective probability only, then human sensitivity to near-misses indeed reveals a gross departure from rationality. Though the present study confirms the relative irrelevance of probability, we still suppose that the near-miss experience obeys definite laws.

One of the most remarkable characteristics of near-misses is the human ability to recognize them and to extract all relevant parameters that contribute to making the situation emotional. In particular, though the missed situation has often no objective character (as it did not occur), its closeness to the actual situation is treated as objective by people [START_REF] Kahneman | Propensities and counterfactuals: The loser that almost won[END_REF]. Since they are easily recognized, near-miss situations populate spontaneous conversations, as individuals systematically urge to share such emotional experiences [START_REF] Rimé | Le partage social des émotions[END_REF].

In near-misses, the actual situation is compared to a counterfactual one. The counterfactual alternative may be preferable or worse. The former case is associated with bad luck, while the latter generates feelings of good luck. In the present paper, we deal with bad luck situations exclusively. The symmetrical case can however be easily derived.

In a previous study [START_REF] Dessalles | Emotion in good luck and bad luck: predictions from simplicity theory[END_REF], the problem has been explored qualitatively in relation to Simplicity Theory. Participants were proposed short stories and were given the possibility to choose some parameter so as to make emotion maximum. For instance, Lucas had to lace up his shoes at 100m/200m/400m from the station, and then missed the train by five seconds. In this kind of story, a majority of participants choose the shortest distance, as predicted by the theory. The present paper offers two significant improvements. First, we concentrate on bare near-miss (i.e. without considering possible mutable causes of the failure, as in the Lucas story). Experiments are thus made simpler and more systematic thanks to a change of modality: we use graphical representations of the missing events and then we vary probability or distance to the target. The second improvement concerns the implementation of the theory, which is done more rigorously.

In the next section, we mention the various factors that are known to influence near-miss emotion intensity, though they have not been included in a coherent theory yet. Then several experiments will be described that explore the role of the complexity (or simplicity) of outcomes. Then we give a short summary of simplicity theory and evaluate its predictions in near-miss situations.

Determining Factors

A variety of parameters have been found to control emotion intensity in the case of near-miss. The most obvious factor is the difference in "utility" v between the actual situation s 1 and the counterfactual s 2 [START_REF] Teigen | When a small difference makes a big difference -Counterfactual thinking and luck[END_REF]. Another acknowledged (but ill-defined) factor is the spatial or temporal "closeness" D to the counterfactual [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]. [START_REF] Teigen | When a small difference makes a big difference -Counterfactual thinking and luck[END_REF] represents these effects through the formula: L = v / D, where L stands for emotion intensity. For some authors, the low probability of the actual event is crucial [START_REF] Rescher | Luck: The brilliant randomness of everyday life[END_REF]. Other factors include controllability [START_REF] Roese | Counterfactual thinking[END_REF] and the mutability (i.e. modifiability) 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].

We designed a first test to confirm that the "rational" approach, based exclusively on utility and probability, is unable to predict emotional judgment. Participants were asked to rank emotion in three similar situations where a young man broke his leg while on a one-week skiing holiday. A"s accident occurred the first day, on the very first run; in case of B, it occurred the third day, at 14h30; for C, it occurred the last day of the week, on the very last run. We may consider that the probability of each accident was equal. Utility, however, is different: v(A) < v(B) < v(C), since C and, to lesser extent, B, could still enjoy their holiday. If utility was the sole factor, B should be thought to be significantly more disappointed than C. Figure 1 shows average reversed emotion rankings (from 3: most maddening, to 1: least maddening) attributed to A, B and C. We can see that the results contradict the prediction based on pure utility. C"s situation is judged as emotional as B"s (54% judged it less maddening, but 46% found it more maddening). For nearly half of the participants, the singularity of the temporal location of C"s accident (the very last run) as opposed to B"s (one run among many) more than compensates for the difference in utility. This result is consistent with Teigen"s formula L = v / D, as the "distance" to the counterfactual (if only C had stopped skiing one run earlier) is minimal for C. Our experiments will show, however, that v and D are often not the only parameters involved.

We tested various lottery situations in which an individual is supposed to have missed the opportunity of winning 1000 €. The near-miss situations we tested are depicted on figures 2-4. Red areas are winning regions (note that figures 2-e, 3-d and 4-b are not really near-misses). In each case, the "objective" probability of the outcome is evenly distributed over the whole line or plane.

v is fixed (players were supposed to win 1000 € if the dot had landed in a red region). The way emotion varies is not controlled by the "objective" winning probability, at least in figures 2 and 4 where that probability is kept constant. It is not entirely controlled by D either, contrary to Teigen"s claim, as evidenced by the fact that emotion may significantly vary between figures 2-c and 2-d.

Experimental Results

Participants (number = 89) were asked to rank the disappointment of losers in various uniform lottery situations. They were shown slides corresponding to figures 2-4 during approximately 1.5 min. In these tests, the dot moved continuously before stopping at its landing site. Each participant was asked to write down different ranks for each test, from 1 (mostly infuriating) to 5 or 6 (least disappointment). These experiments show that probability alone cannot explain emotion ranking, as the winning probability is kept constant in figures 2 and 4, or would make wrong predictions (e.g. in figures 3-c and 3-e where emotion is high despite opposite probabilities). More generally, most 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]. The experimental results show that distance to target is not fully relevant either, as judgments for figures 2-c and 4-c show.

We consider now what simplicity theory can possibly bring to the analysis of the problem.

Simplicity and Probability

Simplicity is a fundamental cognitive principle [START_REF] Chater | The search for simplicity: A fundamental cognitive principle?[END_REF]. For instance, it explains how human brains reconstruct hidden shapes (figure 8).

The description complexity C(s) of a situation s (or Komogorov complexity) is defined as the size of its (current) best summary. The partially hidden square in figure 8 is simply defined as an invariant of a rotation group, a description that no alternative shape can beat (out of any specific context). Complexity theory [START_REF] Solomonoff | Complexity-based induction systems: Comparisons and convergence theorems[END_REF] states that probability is given by:

p a (s) = 2 -C w (s)
(1) C w (s) is the generation complexity of s, i.e. the minimal amount of information that the "world" requires to generate s. This definition presupposes that s is designated in advance. In most real life situations, this is not the case. Individuals determine probability after the fact. Simplicity theory (Dessalles, 2008) takes the ex post determination of s into account by comparing C w (s) to the complexity C(s) of describing s. Unexpectedness U, for any situation s, is the difference between its generation complexity C w and the complexity C of its description.

U(s) = C w (s) -C(s) (2)
To be unexpected, situations must be out of the ordinary, i.e. they must be abnormally simple (C smaller than C w ). For instance, a lottery draw such as 1-2-3-4-5-6 would be highly unexpected whereas a typical draw would not (what Solomonoff"s formula does not predict).

The main claim of Simplicity Theory (ST) is that unexpectedness translates into subjective probability through the following expression.

p(s) = 2 -U(s)

(3)

The difference (in bits) between generation complexity and description complexity, if regarded as successive flips of coin, measures probability. Improbable situations are situations that seem "too" simple, i.e. easy to describe and hard to generate. Equations ( 1) and (3) coincide only when s is fully determined (C(s) = 0) before considering its probability (e.g. when one"s own combination is drawn in a lottery). Note that ST"s definition of probability only considers singular events and never sets of alternatives (contrary to standard probability theory).

The notion of unexpectedness explains a variety of phenomena (Dessalles, 2008a;www.simplicitytheory.org). Let"s mention a few.

-Rarity: rare situations are felt improbable, but only if the feature that makes them rare is simple enough (a phenomenon that standard probability theory ignores).

-Closeness: events locations, if drawn uniformly, are felt improbable when the location happens to be simple (egocentrically close or close to a simple landmark).

-Exceptions: exceptional situations are considered improbable, but only if the feature that makes them exceptional is simple enough.

-Coincidences: The unexpected character of coincidences is also due to simplicity (Dessalles, 2008b). If s 1 and s 2 are the two coinciding events, then the complexity of the joint event can be assessed: C(s 1 &s 2 ) < C(s 1 ) + C(s 2 |s 1 ). Consequently, U(s 1 &s 2 ) > C w (s 1 ) + C w (s 2 ) -C(s 1 ) -C(s 2 |s 1 ). If both events are not unexpected separately and have similar generation complexity, we get: U(s 1 &s 2 ) > C w (s 1 ) -C(s 2 |s 1 ). Unexpectedness may be large if the analogy between s 1 and s 2 is strong (which means that the knowledge of s 1 allows to spare in the description of s 2 ).

ST"s definition of probability can be used to describe aspects of the near-miss subjective experience.

Simplicity and Near Miss

Let"s consider the near-miss situation of figure 9, where the colored zone is the winning one. The actual outcome is s 1 . It might be compared with a standard (i.e. mostly complex) loosing situation s 1s , or with a standard winning situation s 2s or with the closest winning situation s 2 .

Figure 9: One dimensional near-miss.

The probability of loosing in the lottery is assessed by:

U(s 1s ) = C w (s 1s ) -C(s 1s ) (4)
The generation complexity of any landing site s is:

C w (s) = log(L/a) (5)
Logarithms are in base 2 (see appendix for indications about how complexity is computed). This formula reflects the fact that the draw is uniform over the whole strip. On a discrete lottery strip, a is the size of a unitary cell; on a continuous line, it would be the length of the minimal distinguishable landing site. In complexity terms, C w (s) is the amount of information (in bits) that the "world machine" needs to produce the event (see www.simplicitytheory.org).

Complexity C(s) is the minimal amount of information needed to designate s unambiguously. Since s 1s is a typical position in the losing range, its complexity (see appendix) is: C(s 1s ) = log(l 1 /a). We get:

U 1s = U(s 1s ) = log (L/l 1 ) (6)
This value is equal, on a logarithmic scale, to the standard ratio of extensional probabilities, though it has been established by considering the complexity of one individual event only. Similarly, we have for a standard winning location:

U 2s = U(s 2s ) = log (L/l 2 ) (7)
Simplicity theory allows different computations for U(s 1 ). One computation is the straightforward one, given by ( 6). U(s 1 ) can be also evaluated by comparison with a counterfactual winning situation s 2 :

C w (s 2 ) = C w (s 1 ) + C w (s 2 |s 1 ) C(s 2 ) < C(s 1 ) + C(s 2 |s 1 )
This writing presupposes that s 2 is (fictitiously) generated in two steps, through s 1 . The inequality comes from the fact that any constraint in the computation of complexity may give a suboptimal result. The minimal value of C(s 2 ) is obtained when s 2 is the closest winning position, in which case C(s 2 |s 1 ) = 0 (s 2 can be determined unambiguously from s 1 ). We get:

U(s 1 ) > U(s 2 ) -C w (s 2 |s 1 ) (8)
C w (s 2 |s 1 ) measures the smallest amount of information that should be given to the "world" (here, the lottery machine) for it to produce s 2 instead of s 1 . Normally, C w (s 2 |s 1 ) = C w (s 2 ), as the lottery has no memory. In the case of the near-miss experience, individuals allow themselves to "cheat" with the world (as the normal world does not allow giving such a bit of a boost), as if they could alter the course of events in retrospect. The value of C w (s 2 |s 1 ) measures the amplitude of "almost" in the expression "I almost won". It implements the "distance" D postulated by [START_REF] Teigen | When a small difference makes a big difference -Counterfactual thinking and luck[END_REF]. Our definition, however, is more abstract than mere physical distance (sitting next to a lottery winner doesn"t necessarily provide a feeling of near-miss!). In the situation depicted in figure 9, we have:

C w (s 2 |s 1 ) = 1 + log(/a)
In that "cheating" mode, we need 1 bit to "tell" the world to move the landing site to the right instead of to the left and log(/a) to designate the amplitude of the move. On the other hand, the complexity of s 2 is negligible, as it is a remarkable location. We may consider C(s 2 ) = 0 (see appendix). Finally:

U 2 = U(s 1 ) > log (L/) -1 (9)
We examine now whether the three expressions Us 1 , Us 2 , U 2 are of any help to account for the specific cases of figures 2-4.

Simplicity Effects

The main difficulty in applying ST to near-miss situations comes from the fact that we ignore how probability controls emotion. We may assume that emotional intensity is an increasing function of unexpectedness.

A first result is the ability of ST to explain the emotional value of situations depicted in figures 2-d and 4-d. Formula (9) gives a high value for U(s 1 ), as the missed position is both close to the actual outcome and remarkably simple. In the five situations of figure 2, a=1, L=48, l 1 =32, l 2 =16 and   l 2 /2. If we apply (9) to situation 2-b, we get

L  s 1 s 2 l 1 l 2 s 2s  s 1s
U 2 = log (48) -1 = 4.6. In situation 2-d, the landing site is blocked at one end of the strip, so we spare the direction bit in the instruction given to the world, and U 2 = 5.6. In terms of probabilities, loosing that way is equivalent to hitting a target location designated in advance.

In the two-dimensional situation of figure 4-a, the generation complexity of a draw is C w (s) = log (S/a 2 ), where S is the area of the rectangle. We also have for a standard winning location: C(s 2s ) = log (l 2 2 /a 2 ), where l 2 is the size of the winning square. For the counterfactual winning position s 2 , we have: C(s 2 ) = log (4l 2 /a), as s 2 must be located along the perimeter of the winning zone. The complexity of cheating is now: C w (s 2 |s 1 ) = 2 + log (/a) (the two additional bits are used to select the "cheating" direction from four possibilities). Finally:

U 2 > log (S/(4l 2 )) -2 -log  (10)
In the experiments of figure 4, S = 10×8,  = 0.25 (or more) and l 2 = 4 or 2. We get U 2 = 2.3 for situation 4-a and U 2  7.3 for situation 4-d. The difference comes from the fact that s 2 is a remarkable point (see appendix) that does not require to be located on the perimeter of the winning zone. Moreover, the world has only two directions available for correcting its "mistake", instead of four.

Formula (9) also explains the influence of the distance to the target, and thus the systematic preference of 2-b over 2-a over 2-e, and of 4-a over 4-f over 4-b. The formula does more: it accounts for the fact that the counterfactual location s 2 is closest to s 1 , a fact that most models merely take as granted.

Finally, formula (9) explains why situation 2-b dominates 2-c and why situation 4-a dominates 4-c. When the winning region is split, the complexity of the counterfactual s 2 increases, by two bits in 2-c and by one bit in 4-c. Unexpectedness is thus diminished in both cases, and emotion is less intense. This is a situation in which subjective probability (as predicted by (3)) changes, while extensional probability does not.

Unfortunately, formula ( 9) is silent about preferences in figure 3 and it makes two wrong predictions. It wrongly predicts that 2-a should be more emotional than 2-c and that 4-e should be more emotional than 4-c (note that the experimental difference between 4-e and 4-c is not statistically significant). The subjective feeling given informally by some participants is that in 2-c and 4-c, it was "harder" to avoid the winning regions and thus that they are more disappointed. Formulas ( 6) and ( 7) may explain these phenomena by providing an estimate of prior probabilities. When the winning region is broken down into four pieces, the complexity of a standard winning region s 2s is increased: we need to designate a way of distinguishing the pieces (see appendix). Note that the two additional bits necessary to find the relevant piece are spared when searching into it, as it is four times smaller. But C(s 2s ) gets globally increased and, according to formula (7), winning seems less unexpected and losing appears less probable. Conversely, in a situation like 4-e, the loosing region becomes simpler, making the standard loosing position more complex (s 1s can be almost anywhere) and thus making U(s 1s ) smaller than in 4-c. This may explain why the emotion attached to 4-e is relatively downgraded.

Discussion

This study investigates a phenomenon which, despite its importance in the generation of intense emotions in daily life, resists adequate modeling. In particular, probabilistic models (including Bayesian models) do not provide acceptable explanations.

Simplicity theory does not account for all observed phenomena, but explains for some of them. The principal missing ingredient is the link between probability, as defined by unexpectedness through (3) and emotional intensity. We merely assumed that emotional intensity is an increasing value of unexpectedness. However, we do not know how to integrate prior probabilities, given by ( 6) and ( 7), with the amplitude of near-miss given by ( 9).

The role of prior probabilities is manifest in the situations of figure 3. It is correlated with the fact that extreme values of priors in 3-c and 3-e are felt mostly emotional. However, as evidenced by the large standard deviation in figure 6-e, some participants consider situation 3-e as poorly emotional, as the prior winning probability is very low. We tried to manipulate experimental settings to favor prior probability vs. counterfactual thinking. We proposed a version of the experiment in which dots dynamically appeared at random locations before stopping at the nearmiss position, instead of moving continuously as in the preceding experiments. The hope was to make people more aware of U 1s and U 2s , as both situations of failures and of success could be observed just before the test began. A comparison of figure 7 and figure 10 shows the consistency of participants" behavior, but fails to show any effect of the prompting. For some aspects of the near-miss experience, we must perhaps make additional assumptions. In the case of figures 3-c and 3-e, we see that individuals declare equally strong emotions (figure 6) with some indication that 3-c would be even more emotional. Unexpectedness is, however, stronger in 3-e. A possible explanation is that losses provoke more intense emotions than gains [START_REF] Kahneman | Prospect theory: An analysis of decision under risk[END_REF].

We are still confident that the near-miss experience obeys definite laws that are in part to be discovered. The aim was to show that simplicity, rather than extensional probability, is the main aspect through which our minds compute emotional intensity. What is at stake is not only the elucidation of an important phenomenon that controls many of our daily emotions. It is also to connect it to a general theoretical framework, Simplicity Theory, which has been developed independently and makes strong predictions in various other domains. One expected outcome of these studies will be to show that emotional judgment is not blurred by a variety of independent biases, but obeys general laws in which simplicity play a central role.

Figure 1 :

 1 Figure 1: The ski story (102 participants; bars indicate standard deviation).

Figure 2 :

 2 Figure 2: One-dimensional lottery.

Figure 3 :

 3 Figure 3: One-dimensional lottery, variable probabilities.

Figure 4 :

 4 Figure 4: Two-dimensional lottery. Figures 5, 6, 7 show experimental results for the situations illustrated in figures 2, 3 and 4 respectively. Bars show inverted emotional ranks, ordered from most emotional to least emotional. Segments in grey indicate standard deviation.

Figure 7 :

 7 Figure 5: Experiment of figure 2 (89 participants).

Figure 8 :

 8 Figure 8: Hidden shapes are the least complex ones.

  Figure 10: Experiment of figure 4 with random prompting (89 participants).

Acknowledments

This study is supported by a grant from the "Chaire Modélisation des Imaginaires, Innovation et Création".

Appendix

Complexity is still regarded as unknowable by many scholars, as it cannot be computed in an "objective" way. This prejudice is not justified in cognitive science [START_REF] Chater | The search for simplicity: A fundamental cognitive principle?[END_REF]. Simple codes can approach minimal description. For a list, we can use a positional code.

-0 1 00 01 10 11 000 001 010 … Note that the first element requires no additional information (once the list is designated). Such codes are not self-delimited. Self-delimitation is irrelevant here, as we are concerned with the minimal description of individual objects. The preceding code can be easily extended to sets of lists (as below) or trees, by using positional code on a branch and switching bits at nodes. The lists may contain structures, operations or even represent short-term memory.

The preceding code can be adapted to assign simple representations to remarkable points. For instance, on a bounded list, endpoints are simpler than middle points.

-0 00 01 000 001 010 110 101 100 10 1 This explains why remarkable points such as frontiers are less complex than "normal" points.

With this code, elements of a list of size N are coded with log 2 N bits on average.


Eric Bonabeau
email: bonabeau@santafe.edu

Jean-Louis Dessalles
email: dessalles@enst.fr

Detection and emergence

Keywords: detection, emergence, models, complexity, organization levels Résumé détection, émergence, modèles, complexité, niveaux d'organisation

Two different conceptions of emergence are reconciled as two instances of the phenomenon of detection. In the process of comparing these two conceptions, we find that the notions of complexity and detection allow us to form a unified definition of emergence that clearly delineates the role of the observer.

Introduction

Emergence is obviously an ill-defined concept, which has been given many, apparently incompatible, definitions (Bonabeau et al., 1995a). Some of them refer to levels of organization (Lewes, 1874). Emerging properties would be relevant only to the upper level, even if they are grounded in the lower level. Other definitions refer to self-organization [START_REF] Varela | The embodied mind[END_REF], to entropy changes [START_REF] Kauffman | Requirements for evolvability in complex systems: Orderly dynamics and frozen components[END_REF], to non-linearity (Langton, 1990), to deviations from predicted behavior [START_REF] Rosen | Anticipatory Systems[END_REF][START_REF] Cariani | Adaptivity and emergence in organisms and devices[END_REF] or from symmetry [START_REF] Palmer | Broken ergodicity[END_REF]. Other definitions are closely related to the concept of complexity (Bonabeau et al., 1995a(Bonabeau et al., , 1995b;;[START_REF] Cariani | Adaptivity and emergence in organisms and devices[END_REF][START_REF] Kampis | Self-Modifying Systems in Biology and Cognitive Science[END_REF]. Among all these definitions, some are presented as more "objective" than others which refer explicitly to an observer (Bonabeau et al., 1995b).

We propose here a conceptual framework, based on the notion of detection, in which all these definitions of emergence may be compared. We first consider well-accepted characterizations of emergence, which refer to levels of organization and to model changes. Then we show that emergence is related to complexity shifts. Lastly, we propose to focus on the observer, rather on the emerging system, in order to show that all characterizations of emergence are implicitly connected to the notion of detection.

Defining emergence

Emergence is foremost an intuitive phenomenon. An easy way to illustrate this idea is to consider scale changes. When walking in the streets of a European city, an observer may not detect its fractal structure, whereas an aerial or satellite photograph of the city would reveal it. Another example in the same vein involves patterns of vegetation aggregation [START_REF] Dayong | Detection of spatial pattern in desert shrub populations: a comment[END_REF]: the spatial pattern of desert shrubs may display a combination of smallscale regularity (generated through competition among individuals) and large-scale aggregation (due to the clustered seedling establishment resulting from limited seed dispersal). When looking at these patterns on either a large or a small scale, one will miss the global organization which requires, to be understood, that both scales are simultaneously taken into account. Classical statistics, indeed, will tend to confound smallscale regularity with large-scale aggregation. Yet another example from ecology comes from the fractal dimension of forests [START_REF] Sugihara | Applications of fractals in ecology[END_REF]: the fractal dimension of deciduous forest patterns in Mississippi (Natchez Quadrangle) has been measured by plotting the logarithm of the patch perimeter against the patch area. A discontinuity is discovered in the fractal dimension, indicating a shift in dimension from D=1.2 to D=1.5, at area scales of about 60-70 ha. Since native forests in this region have recently been converted into agricultural use, this shift in dimension may result from human activities. Small forest areas (<60 ha) are indeed relatively smoother than larger areas (>70 ha). This is due to the fact that human disturbances dominate at small scales, making forest patterns smoother, while natural processes, such as geology or the distribution of soil types, continue to dominate at larger scales [START_REF] Sugihara | Applications of fractals in ecology[END_REF]. If this interpretation is correct, the scale at which the dimension shift takes place should increase with the expansion of human disturbances. Once again, here, if the system is observed over an insufficient number of scales, the effect of human activities cannot be detected. Another example from neurobiology [START_REF] Swindale | A model for the formation of ocular dominance stripes[END_REF] illustrates the same idea from a slightly different viewpoint: among the patterns of ocular dominance in the visual cortex of monkeys, stripes of righteye dominance alternate with stripes of left-eye dominance, covering the cortex like the coat of a zebra. For an observer studying the level of synapses, these patterns cannot be detected, whereas looking at 2D cuts of the cortex over scales of the order of a few hundreds of µm allows to detect these patterns, which, as many models suggest, result from short-range activation and long-range inhibition among synapses.

In all these examples, some relevant phenomenon remains hidden if the observer looks at the wrong scales. Such phenomena emerge when the observer begins to consider the correct scale. It seems that "objective" notions like shifts in fractal dimension make the presence of an observer unnecessary. We will suggest that is only an illusion, and that the concept of emergence is much better captured through a sound analysis of the observer's structure, if we accept to generalize the observer's role.

A classical attempt to give a general definition of emergence consists in considering levels. According to this view, there is emergence whenever a "phenomenon" appears at a level L h out of constituents and processes defined and taking place at a lower level L l , and when the properties of L h are "difficult" or impossible to deduce from the properties of the constituent units and processes of L l . Let us name this type of emergence "emergence of higher-level structures" (EHS). We may distinguish two cases: (i) a structure appears at L h in the course of time through the natural dynamics of the system, or (ii) the "structure" was potentially there before, but it was not actualized in L h until some observational tool was available. The first case (i) refers, for example, to self-organizing systems in physics, chemistry or biology [START_REF] Nicolis | Exploring Complexity: An Introduction[END_REF], whereas (ii) refers, for instance, to the above mentioned example of the fractal structure of a city, which becomes apparent only with appropriate tools (large-scale observations, such as satellite observations). Note that the very notions of "structure" and "phenomenon" are still quite ambiguous here.

Another conception of emergence is called emergence-relative-to-a-model (ERM) [START_REF] Cariani | Adaptivity and emergence in organisms and devices[END_REF][START_REF] Rosen | Fundamentals of measurement and representation of natural systems[END_REF][START_REF] Rosen | Anticipatory Systems[END_REF]. For the supporters of ERM, there is emergence when a natural system's behavior can no longer be explained by a model of that system (it deviates or "bifurcates" from the predictions of the model), and requires a new model. According to [START_REF] Pattee | Artificial Life[END_REF], theories like fractals, catastrophe theory, dissipative structures, symmetrybreaking instabilities and chaotic dynamics do not convey the full essence of emergence, esp. of biological emergence, since such formal models are unable to produce entirely novel structures. They are doomed to deviate from the behavior of the actual system. In order to keep up with the system's behavior, the modeler either has to (i) find new relationships between existing variables (syntactic emergence), or (ii) find new observables associated with the natural system which can be transformed into variables for modeling purposes (semantic emergence).

We can easily show that both approaches, EHS and ERM, implicitly involve an observer. The existence of an emerging structure in L h is only possible if it can be detected at that level thanks to some observational tool. Similarly, the connection, through observables, between the model and the emerging phenomenon looks like the relationship between the observer and the observed system. In what follows, we use the notion of complexity to better formalize this link between levels, models, observer and emergence.

Complexifying emergence

Emergence and complexity do indeed share a lot of common features. Before attempting to present a unified picture of EHS and ERM, let us briefly introduce the notion of complexity. Complexity is a relative concept, which depends both on the task at hand and on the tools available to achieve this task [START_REF] Bennett | How to define complexity in physics, and Why, in Complexity, Entropy and the Physics of Information[END_REF]Bonabeau, 1993;[START_REF] Crutchfield | Computation at the onset of chaos[END_REF][START_REF] Grassberger | Problems in quantifying self-organized complexity[END_REF][START_REF] Kampis | Self-Modifying Systems in Biology and Cognitive Science[END_REF]. A first idea of complexity is given by entropy, which measures the lack of information of a given observer about a system. A more elaborate approach to complexity consists in evaluating the length of the shortest algorithm which is able to reconstruct the observed system (Kolmogorov-Chaitin-Solomonoff algorithmic complexity). The notion of complexity can be refined to take into account the internal structure perceived in the system. Given a set of tools considered as structuring elements, there are some aspects of the system that can be explained (or compressed) by means of these tools, and there are some aspects of the object that cannot be understood using these tools. Such tools may be Turing machines, as in the standard definition of algorithmic complexity, or more generally any device able to give a concise description of some part of the observed system. The relative complexity C(S/T) of a system S with respect to a set of tools T can be interpreted as "the difficulty of decomposing S when T is used as a structuring element (i.e. what is explainable by T) + what is not decomposable by means of this structuring element (i.e. what is not explainable by T and remains to be explained otherwise)".

Emergence can be advantageously described in this kind of framework. Like complexity, it is not an absolute notion. It is relative to the tools that one may use to observe the system to be characterized. Emergence can then be defined with respect to the same tools used to define the complexity of a system. It occurs when an object or phenomenon cannot be detected or understood with a given set of tools but can be detected or understood by allowing some additional tools. For some reason (dynamic evolution of the system or changes in the set of observational tools) a new apprehension of the system becomes possible that offers a shorter overall description, and hence a smaller relative complexity. Emergence is thus associated with a decrease of the relative complexity. For instance, when observational tools are characterized by a perceptive "diameter", as was the case in our example about the perception of fractal structures, emerging structures correspond to shifts in relative complexity which, in this case, takes the form of K dcomplexity [START_REF] Chaitin | Toward a mathematical definition of life, in The maximum entropy formalism[END_REF].

We will examine now how this unifying description applies to EHS and ERM. This will require the introduction of the notion of detection.

Detecting emergence

The notion of detector is very basic: any device which gives a binary response to its input. Intuitively, since emergence is an all-or-nothing phenomenon, it must correspond to some detector becoming active. This very simple idea has interesting consequences for the characterization of emergence.

It is possible to define the relative complexity of a system with respect to a set of detectors. The relative complexity of a system observed through a set of detectors at a given moment will be measured by the complexity of active detectors + the complexity of the relations between these detectors. More precisely, the relative complexity should be written C(S / D,T), where D is a set of detectors and T a set of available tools that allow to compute a description of structures detected through D. This constitutes a new formulation of the notion of relative complexity, the only difference being that the distinction between observational tools and description tools is now made explicit.

We can now characterize emergence. Let us consider that a given detector, D k , becomes active at time t+t. At time t, D k is inactive. Taking D k into account at time t does not change the relative complexity:

C t (S / T, D 1 , ..., ,D k-1 , D k ) = C t (S / T, D 1 , ...,D k-1 )
(1)

At time t+t, D k becomes activated. Normally, an increase of complexity should ensue, since the description of the system performed with T becomes a priori longer. Emergence occurs when the contrary happens:

C t+t (S / T, D 1 , ..., ,D k-1 , D k ) < C t (S / T, D 1 , ...,D k-1 )= C t (2)
This is possible if the activity of some of the D i is redundant with the activity of D k . The D i can thus be omitted in the description, and the result may be a smaller relative complexity.

We can now reconsider EHS and ERM in this framework. Levels of organization can be described as resulting from a hierarchical structure of the set of detectors (Bonabeau et al., 1995b). A detector of level n receives inputs from detectors of level n1 only. To borrow an example from linguistics, the ontological hierarchy soundphonemewordphrasesentence can be shown to result from a set of appropriate linguistic devices that we can describe as nested detectors. We detect the occurrence of a sentence after having detected its phrasal constituents, and not directly from the presence of words nor from its bare acoustic form. Many perceptual or computational devices exhibit this hierarchical detecting structure. When a detector becomes active in such a hierarchy, the active detectors from the lower level that are connected to it can be omitted from the description. When we recognize a word, we can forget the phonemes that compose it and that were detected in the first place (this is only an approximation when the input is noisy: erroneous phonemes should remain in an exhaustive description of the linguistic structure).

EHS fits naturally in our definition of emergence. If D k is a detector of level n, then all active detectors of level n1 which are connected to D k become redundant. There are such detectors, since D k did not become active by magic. As a consequence, relative complexity automatically decreases and emergence necessarily occurs whenever an n-detector is activated while only (n1)-detectors were previously active. The activation or availability of an n-detector systematically enables the building of a more compact -and therefore less complex -model that takes advantage of regularities and redundancy at the lower level. Emergence is thus a characteristic feature of detection hierarchies.

Note that emergence may occur at level n=1. The lower level, L 0 in this case, consists of analog sensors. Even between two genuine levels (n1) and n, analog properties among (n1)-detectors (e.g. neighborhood, in the visual system) may be involved in the computation of the n-detector's output. In such case, these analog properties are lost at level n, they cannot be recovered from the mere observation of the n-detector activity.

We will now consider ERM and show that it is a special case of EHS. A situation of ERM presupposes three successive periods: (T1) the behavior of the modeled system is correctly predicted; (T2) it departs from the predicted behavior (bifurcation); (T3) a new model emerges, thanks to the introduction of a new observable (semantic emergence) or of a new combinatorial ability (syntactic emergence). From a complexity viewpoint, a bifurcation leads to an increase in relative complexity, because one must back up to a lower level description in terms of available observables. In this respect, the introduction of a valid model of the system in T3 offers a higher-level description, which restores a concise description. This looks very much like EHS. To formalize this analogy, let us notice that a bifurcation is a binary event. This suggests that the model should be considered itself as a detector. As we will see, if we take this idea seriously, then several aspects of emergence become clearer and ERM and EHS can be unified.

Conceptualizing emergence

The prototypic idea of detector is a binary device receiving its input from analog sensors or from other detectors through hardwired circuitry. This is probably how low-level detectors like edge detectors are implemented in visual perception. We suggest that more complex devices involved in language understanding or in scientific modeling can legitimately be considered as detectors too.

For instance, Chomsky's grammars correspond to well-formalized detectors. They recognize languages as subsets of all possible strings of symbols. They can be implemented in automata: a finite-state automaton will detect strings of a regular language, a pushdown automaton will detect strings of a context-free language, a linear bounded automaton recognizes strings of a context-sensitive language. These automata perform an actual detection. However, detection is already present, conceptually, in the grammar itself.

Similarly, the use of spatial or temporal correlation functions can help discover, say, periodic features in space or time. The fact that these correlations are implemented in actual devices or remain mathematical abstractions is not relevant. If the mathematical model is able to predict some periodicity, it acts as a detector, a conceptual one. Kepler's laws can also appear as a conceptual detector: they can predict whether the trajectory of a cosmic object will be elliptic. The detecting abilities of these models are obvious in case of failure, what we called a bifurcation. If a combination of periodic signals fails to be periodic, or if the comet's trajectory is neither elliptic nor hyperbolic, then the model is able to "raise a flag" to signal that something goes wrong.

Such models rely on observables (arrays of coordinates, data like body masses, etc.) and compute predictions. In case of bifurcation, either new observables must be found (higher sampling rate, presence of other celestial bodies) or new computations must be made available (e.g. Eintein's formula instead of Newton's laws). As already mentioned, the former case may lead to semantic emergence, the latter to syntactic emergence. It is important to note that such emergence, ERM, consists in the restoration of an appropriate (conceptual) detector. The analogy with EHS is now clear: at period T2, the system is described only through the available observables, which belong to a lower level L l (continuous observables should be considered rather as sensors than as detectors). At period T3, a new valid model is available. It behaves as an activated detector of higher level L h , receiving its input from L l .

Syntactic ERM is nothing but the setting-up of a new high-level detector which becomes activated. Semantic ERM consists in introducing a new low-level detector or sensor (observable), which leads to the emergent activation of a high-level detector. In semantic ERM, the system's relative complexity is increased not only by the bifurcation, but also by the introduction of a further relevant variable. The dimension of the phase space increases so that the system's behavior is harder and longer to describe with the available tools. It is only thanks to the re-activation of the model that the complexity diminishes, leading to an emergent phenomenon. The mere mention of a nominal trajectory may for instance replace a whole set of previously unexplained arrays of coordinates.

By considering that scientific models play the role of conceptual detectors, we see that ERM is a special case of EHS. Conversely, the existence of complex detectors in ERM, like grammars or scientific models, that require sometimes heavy computations, draws the attention to the fact that in EHS, the computational cost of detectors has to be taken into account to evaluate complexity. The high-level detector which is responsible for the occurrence of emergence makes the description of the system simpler, by extracting various types of symmetry and redundancy. There is a cost, however: the cost of detection, which can be defined as the size of the recognition device (we do not consider the depth of computation here (Bennet, 1990)). By becoming aware of the existence of complex detectors, we may consider that low-level detectors too should be included in the computation of relative complexity. This may not be an easy task, since the notion of detection complexity is not always easily quantifiable.

Conclusion: emergence and cognition

By introducing the notion of detection, first to characterize organization levels, then to describe the behavior of scientific models in case of "bifurcation", we could offer an unified picture of emergence, embracing both emergence of higher-level structures (EHS) and emergence relative to a model (ERM). Emergence has been characterized by the activation of a high-level detector, with the effect of decreasing relative complexity.

This way of presenting emergence leads to an unexpected situation. Many attempts have been made in the literature to describe emergence in an "objective" way, i.e. in an observer-independent way. Levels of organization, phase spaces, complexity and models are thought to be more or less independent from the observer. In this paper, this picture has been completely inverted. Levels of organization are not out there, but result from the observer's perceptive structure which is organized as a detection hierarchy. Phase spaces are drawn in coordinates which are the problem's observables. These observables are the observer's low-level sensors (if continuous) or detectors (if binary). They are not intrinsic to the system itself. Similarly, complexity has been presented as observer-dependent: relative complexity makes an explicit reference to available detectors and combinatorial tools. Even models have been presented as detectors. They are not part of the system. They are conceptual tools, and as such they are observer-dependent. The model may change without affecting the system itself in any way. What remains at the end is a scenario of emergence which takes place entirely on the observer's side. This result should not be considered as negative. What we name "observer" here may indeed refer to abstract entities like computational devices, grammars or scientific models, and are as such idealized observers. It is important to note, however, that emergence does not lie in the system itself. Nothing would emerge anywhere in the absence of human observers and of their conceptual constructions.

The study of emergence, somewhat unexpectedly, tells us something important about human cognition. The fact that perceptual emergence be possible at all reveals that binary events take place in our mind, and that they occur at different levels. In other words, some aspects of cognition must be structured as detection hierarchies. Furthermore, this is not only true for perception, but also for linguistic processing and conceptual thinking (Bonabeau et al., 1995b). This result should be taken into account in the discussions about the nature of cognitive processing (van Gelder, to appear).


Jean-Louis Dessalles
email: dessalles@enst.fr

Laleh Ghadakpour

Semantic abilities evolved as well

The evolutionary story proposed in the target paper makes no difference between semantic representations underlying language and more general cognitive representations, at work in perception and action, which humans share with apes and probably other mammals. Though semantic representations supporting language are grounded in perception, some of them, specifically predicative structures, should rather be considered a distinctive feature of human communication system. Any evolutionary scenario about language should explain how human minds evolved to form the kind of thoughts that are communicated through language.

In his attempt to explain the presence of language in our lineage, M. Arbib makes generous assumptions about pre-hominid cognition and yet the transition to language remains enigmatic. One of the most challenging issues about language is why human beings, like bees, but unlike other primates, spend much time and energy in referential communication [START_REF] Dessalles | Aux origines du langage : une histoire naturelle de la parole, Hermès. JEAN-LOUIS DESSALLES & LALEH GHADAKPOUR, Object Recognition Is Not Predication (commentary on "The Neural Basis of Predicate-Argument Structure[END_REF]. The most blatantly unsupported presupposition in the target paper is the author"s belief in some general biological urge to transmit skills and useful information to unrelated conspecifics, which nonhuman primate species, due to some cognitive limitations, would have been unable to satisfy. The author"s concern is thus limited to finding some cognitive bifurcations that merely enabled human communication.

Even on this ground, the scenario imagined by M. Arbib seems unnecessarily intricate. In a first step, our ancestors are supposed to master a pantomime-like analog code, relying on imitation capabilities. Then, in a second step, their followers developed the ability to associate conventional holistic signs to frequently encountered scenes. In a last non-biological step, some sapiens invented compositional languages. The most obvious problem with this scenario is that the middle, conventional step undermines any necessity for the initial, imitative stage. Why did not hominids associate conventional signs with frequent situations in the first place? Association is intrinsically reversible, and does not require any complex mirroring machinery to serve as a code. Moreover, conventional signs are claimed to fulfil a disambiguation purpose. Why didn"t we evolve more powerful analog imitating abilities, instead of regressing to mere holistic signalling?

Our strongest scepticism concerns the fact that the cognitive bifurcations postulated by M. Arbib do not affect semantic abilities. Because of their various cognitive skills, apes and hominids are generously granted with the same semantic representations as modern sapiens: they are supposed to recognise, decompose and assemble cognitive schemas, the kind of schemas that they are able to imitate. Such abilities appear both too rich and too poor to account for the evolutionary emergence of language.

Monkey brains are claimed to host hierarchical predicative structures such as GRASP(LEO,RAISIN). The purpose of a language evolution scenario is thus merely to explain how "the ability to communicate in a way that reflects these structures" could develop. However, predicative structures are relevant to language, and not to perception (DESSALLES & GHADAKPOUR 2003). Though our brain is able to simultaneously detect a variety of complex perceptive structures in some given visual scenery, predicative structures like GRASP(LEO,RAISIN) are constructed for communicative purposes from the perceived scene rather than being a mere translation of it. One obvious reason is that we can systematically express the negative version of a predicative structure, e.g. "Leo doesn"t grasp the raisin", while there is no perceptive meaning corresponding to the negation of a visual scene (what would be the negative version of Picasso"s Guernica?). If semantic representations could be translated indifferently into language or into actions, as the author assumes, we would expect something like negative actions, as there are negative sentences. But this does not exist.

Our claim is that the ability to form predicative representations is part of the language faculty, and that action-oriented perceptive representations, as rich as they may be, are not what language communicates in the first place. Arbib"s proposal that some actions like grasping or running can be directly communicated through mimetic gestures would be attractive if the mechanism could be extrapolated to the whole range of communicable objects, relations and judgements. But there is no natural imitation of an object like raisin. Drawings on paper, on cave walls or in the air are too conventionalised to be a direct translation of semantic representations. Similarly, while language offers words for relations, imitation can only attempt to show instantiated situations. Contrary to spoken or signed phrases, mimetic performances for "on the ground", "on the table", "on my hand" bear no systematic resemblance. This is unexpected if semantic relations are supposed to shape our perceptions and actions. The same can be said of judgements like "a huge raisin" or "a huge tree", which we would be bound to imitate in a systematic manner if something like HUGE(X) was represented in our mind regardless of any communication.

Predicative structures lie neither in scenes nor in gestures. Though some authors see in perceptive mechanisms interesting prerequisites for predicate formation [START_REF] James R Hurford | The Neural Basis of Predicate-Argument Structure[END_REF], genuine predicates cannot be reduced to perceptive structures (DESSALLES & GHADAKPOUR 2003). They are constructed to be communicated. When a raisin is predicated as huge, it is not merely perceived as such. It is contrasted with the speaker"s prototypic raisin, and the adjective "huge" happens to be the closest word associated with that contrast [START_REF] Laleh Ghadakpour | Le système conceptuel, à l'interface entre le langage, le raisonnement et l'espace qualitatif : vers un modèle de représentations éphémères[END_REF]. During this contrasting procedure, a large number of perceptive details of the scene are ignored. Predicates appear to be cognitive constructs, which exist for one main purpose: language. They are much poorer than perceptive representations, but they can bear propositional attitudes like assertion, disbelief, worry, etc. [START_REF] Dessalles | Aux origines du langage : une histoire naturelle de la parole, Hermès. JEAN-LOUIS DESSALLES & LALEH GHADAKPOUR, Object Recognition Is Not Predication (commentary on "The Neural Basis of Predicate-Argument Structure[END_REF].

The purpose of human communication is not to create an accurate copy of a scene in the addressee"s mind through some iconic or symbolic code. Language is not a poor substitute for video reporting. Most scenes are too rich and the expressive powers of language are too narrow and to slow. Moreover, the reason why addressees would be interested in comprehensive descriptions of scenes is still missing. Arbib is certainly right to try to ground the expressiveness of language in perception and in action. A sound scenario of the evolutionary emergence of language, though, would not strive to explain how hominids managed to make accurate descriptions, be it through pantomime or through words. Such a scenario should rather explain why and how our ancestors got minds able to form predicative structures, and to express them through compositional languages.