The adaptive advantage of symbolic theft over sensorimotor toil

Paper presented at the Second International Conference on the Evolution of Language, London, April 1998. To appear in volume edited by C. Knight and J. Hurford


Angelo Cangelosi
Centre for Neural and Adaptive Systems
University of Plymouth (UK)

Stevan Harnad
Cognitive Science Centre
Department of Electronics and Computer Science
University of Southampton (UK)


Using neural nets to simulate learning and the genetic algorithm to simulate evolution in a toy world of mushrooms and mushroom-foragers, we create a competition between two ways of learning the same information. One way ("sensorimotor toil") acquires new categories through real-time trial and error experience, guided by corrective feedback.; the other way ("symbolic theft") acquires new categories from propositions made up strings of symbols describing the new category. In competition, symbolic theft always beats sensorimotor toil, and we conjecture that this is the basis of the adaptive advantage of language. Because of the symbol grounding problem, however, ground-level categories must still be learned by toil by all. The changes in internal representations that occur during the course of learning are analysed in terms of a compression of within-category distances and expansion of between-category that allows regions of similarity space to be separated, bounded and named, then allow the names to be combined and recombined to describe further categories, grounded in the existing ones. The compression/expansion effects, called "categorical perception" (CP), have previously been reported with categories acquired by sensorimotor toil; we show further CP effects induced by symbolic theft alone.

1. Language Evolution: A Martian Perspective

Whatever the adaptive advantage of language was, it was indisputably triumphant. If all our linguistic capabilities were subtracted from the repertoire of our species today, very little would be left. Not only would all the fruits of science, technology and culture vanish, but our development and socialisation would be arrested at a stage currently occupied only by our severely mentally retarded. Buried somewhere among all those undeniable benefits that we would lose with language there must be a clue to what its original bonus was, the competitive edge that set us inexorably on our unique evolutionary path, distinct from all the nonspeaking species (Harnad,Steklis & Lancaster 1976).

There has been no scarcity of conjectures as to what that competitive edge might have been: It helped us hunt; it helped us make tools; it helped us socialise. There is undoubtedly some merit in such speculations, but it is hard to imagine how to test them. Language is famously silent in the archeological and paleontological record, requiring interpreters to speak for it; but it is the validity of those very interpretations that is at issue.

Perhaps we need to take a step back, and look at our linguistic capacity from the proverbial Martian anthropologist's perspective: Human beings clearly become capable of doing many things in their world, and from what they can do, it can also be inferred that they know a lot about that world. Without too much loss of generality, the Martian could describe that knowledge as being about the kinds of things there are in the world, and what to do with them. In other words, the knowledge is knowledge of categories: objects, events, states, properties and actions.

Where do those categories come from? A Martian anthropologist with a sufficiently long-range database could not fail to notice that some of our categories we already have at birth or soon after, whereas others we acquire through our interactions with the world (Harnad 1976). By analogy with the concept of wealth, the Martian might describe the categories acquired through the efforts of a lifetime to be those that are "earned" through honest toil, whereas those that we are born with and hence not required to earn he might be tempted to regard as ill-gotten gains -- unless his database was really very long-range, in which case he would notice that even our inborn categories had to be earned through honest toil: not our own toil, nor even that of our ancestors, but that of a more complicated, collective phenomenon that our (ingenious) Martian anthropologist might want to call "evolution."

So, relieved that none of our categories were come by other than through honest toil, our Martian might take a close look at precisely what we did to earn those of them that we did not inherit. He would find that the way we earned our categories was through laborious, real-time trial and error, guided by corrective feedback from the consequences of sorting things correctly or incorrectly (Catania & Harnad 1988). As in many cases the basis for sorting things correctly was far from obvious, he would note that our honest toil was underwritten by a substantial inborn gift, that of eventually being able to find the basis for sorting things correctly, somehow. A brilliant cognitive theorist, our Martian would immediately deduce that in our heads there must be a very powerful device for learning to detect those critical features of things (projected onto our sensory surfaces) on the basis of which they can be categorised correctly (Harnad 1996b). Hence he would not be surprised that this laborious process takes time and effort -- time and effort he would call "acquiring categories by Sensorimotor Toil" (henceforth Toil).

Our Martian moralist would be surprised, however, indeed shocked, that the vast majority of our categories turn out not to be learned by Toil after all, even after discounting the ones we are born with. At first the Martian thinks that these unearned categories simply appear spontaneously; but upon closer inspection of his data he deduces that we must in fact be stealing them from one another somehow. For whenever there is evidence that one of us has acquired a new category without first having performed the prerequisite hours, weeks or years of Toil, in the labourious real-time cycle of trial, error and feedback, there is always a relatively brief vocal episode between that individual and another one who has either previously earned that category through sensorimotor Toil himself, or has himself had a very brief vocal encounter with yet another individual who has either… and so on.

Without blinking, Martian dubs this violation of his own planet's Protestant work ethic "the acquisition of categories by Theft," and immediately begins to search for the damage done to the victims of this heinous epistemic crime. To his surprise, however, he finds that (except in very rare cases, dubbed "plagiarism," in which the thief falsely claims to have acquired the stolen category through his own honest toil), category Theft seems to be largely a victimless crime.

Ever the brilliant cognitive theorist, our Martian would quickly discern that the mechanism underlying Theft must be related to the one underlying Toil, and that in principle it was all quite simple. The clue was in the vocal episode: All earthlings start with an initial repertoire of categories acquired by sensorimotor Toil (supplemented by some inborn ones); these categories are grounded by the internal mechanism that learns to detect their distinguishing features from their sensorimotor projections. These grounded categories are then assigned an arbitrary symbolic name (lately a vocal one, but long ago a gestural one, his database tells him [Steklis & Harnad 1976]). This name neither resembles the members of the category, nor their features, nor is it part of any instrumental action that one might perform on the members of the category. It is an arbitrary symbol, of a kind that our Martian theorist is already quite familiar with, from his knowledge of the eternal Platonic truths of logic and mathematics, valid everywhere in the Universe, which can all be encoded in formal symbolic notation.

When our Martian analyses more closely the brief vocal interactions that always seem to mediate Theft, he finds that they can always be construed in the form of a proposition that has been heard by the thief. A proposition is just a series of symbols that can be interpreted as making a claim that can be either true or false. The Martian knows that propositions can always be interpreted as statements about category membership. He quickly deduces that propositions make it possible to acquire new categories in the form of recombinations of old ones, as long as all the symbols for the old categories are already grounded in Toil (individual or evolutionary). He accordingly conjectures that the adaptive advantage of language is specifically the advantage of Symbolic Theft over Sensorimotor Toil, a victimless crime that allows knowledge to be acquired without the risks or costs of direct trial and error experience.

Can the adaptive advantage of Symbolic Theft over Sensorimotor Toil be demonstrated without the benefit of the Martian Anthropologist's evolutionary database (in which he can review at leisure the videotape of the real-time origins of language)? We will try to demonstrate them in a computer simulated "toy" world considerably more impoverished than the one studied by the Martian. It will be a world consisting of mushrooms and mushroom foragers who must learn what to do with which kind of mushroom in order to survive and reproduce (Parisi, Ceccone & Nolfi 1990; Cangelosi & Parisi 1998). But before we describe the simulation we must introduce some theoretical considerations that are too fallible to be attributed to our Martian theorist: One concerns a fundamental limitation on the acquisition of categories by Symbolic Theft (the symbol grounding problem) and the other concerns the mechanism underlying the acquisition of categories by Sensorimotor Toil (categorical perception).

1.1. The Symbol Grounding Problem. Just as the values of the tokens in a currency system cannot be based on still further tokens of currency in the system, on pain of infinite regress, needing instead to be grounded in something like a gold standard or some other material resource that has face-value, so the meanings of the tokens in a symbol system cannot be based on just further symbol-tokens in the system. This is called the symbol grounding problem (Harnad 1990). Our candidate for the face-valid groundwork of meaning is perceptual categories. The meanings of symbols can always be cashed into further symbols, but ultimately they must be cashed into something in the world that the symbols denote. Whatever it is inside a symbol system that allows it to pick out the things its symbols are about, on the basis of sensorimotor interactions with them (Harnad 1992; 1995), will ground those symbols; those grounded symbols can then be combined and recombined in higher-level symbolic transactions that inherit the meanings of the ground-level symbols. A simple example is "zebra," a higher-level symbol that can inherit its meaning from the symbols "striped" and "horse," provided "striped" and "horse" are either ground-level symbols, or grounded recursively in ground-level symbols by this same means (Harnad 1996a).

The key to this hierarchical system of inheritance is the fact that most if not all symbolic expressions can be construed as propositions about set (category) membership. Our Martian had immediately intuited this: The simplest proposition "P," which merely asserts that the truth-vale of P is true, is asserting that P belongs to the set of true propositions and not the set of false propositions. In the classical syllogism: "All men are Mortal. Socrates is a Man. Therefore Socrates is Mortal," it is again transparent that these are all propositions about category membership. It requires only a little more reflection to construe all the sentences in this paragraph in the same way, and even to redraw them as Venn Diagrams depicting set membership and inclusion. Perceptual categories are the "gold standard" for this network of abstractions that leads, bottom-up from "horse," "striped" and "zebra" all the wat to "goodness," "truth" and "beauty."

1.2. Categorical Perception. Can perceptual categories bear the weight of grounding an entire symbolic edifice of abstraction? Where the things in the world that our senses must categorise and assign a symbolic name obligingly sort themselves into disjunct, discrete categories that admit of no overlap or confusion, and our senses can duly detect and distinguish those categories, it does look as if the perceptual groundwork can bear the burden. But in regions of the world where there is anything approaching the "blooming, buzzing confusion" that William James wrote about, the world alone, and passive senses (or even active, moving, Gibsonian ones; Gibson 1979) are not enough. Here even an active sensorimotor system needs help in detecting the invariants in the sensorimotor interaction with the world that afford the ability to sort the subtler, more confusable things into their proper categories. Neural networks are natural candidates for the mechanism that can learn to detect the invariants in the sensorimotor flux that will eventually allow things to be sorted correctly (Harnad 1992, 1993). This is the process we have agreed to call Toil.

A sensorimotor system with human-scale category learning capacities must be a "plastic" (modifiable) one: Inside the system, the internal representations of categories must be able to change in such a way as to reliably sort themselves correctly. It is perhaps an oversimplification to think of these internal representations as being embedded in a great, multidimensional "similarity space," in which things sort themselves in terms of their distances from one another, but this simplification is behind the many regularities that have been revealed by the psychophysical method of multidimensional scaling (Livingston & Andrews 1995) which has been applied to category learning and representation in human subjects (Andrews, Livingston & Harnad 1998). What has been found is that during the course of category learning by what we have called sensorimotor Toil, the structure of internal similarity space changes in such a way as to "compress" the perceived differences between members of the same category and "expand" the differences between members of different categories, with the effect of separating categories in similarity space that were highly interconfusable prior to the Toil (Goldstone 1994; Pevtzow & Harnad 1997). This compression/separation in turn allows an all-or-none ("categorical") boundary to be placed between the regions of similarity space occupied by members of different categories, thereby allowing them to be assigned distinct symbolic names.

These compression/separation effect has come to be called "categorical perception" (CP) (Harnad 1987) and has been observed both with both inborn categories and learnt ones, in human subjects as well as in animals and in neural nets (Harnad, Hanson & Lubin 1991; 1995; Tijsseling & Harnad 1978). The neural nets offer the advantage that they give us an idea of what the functional role of CP might be, and it appears that CP occurs in the service of categorisation. It can be seen, for example, as changes in the "receptive fields" of hidden units in the supervised backpropagation nets that will be used in this study. What will be analysed for the first time here is how the CP "warping" of similarity space that occurs when categories are acquired by sensorimotor Toil is transferred and further warped when categories are acquired by Theft. Categorical perception induced by language can be seen as an instance of the Whorfian Hypothesis (Whorf 1964), according to which our language influences the way the world looks to us.

2. The mushroom world

Our simulations take place in a "mushroom world" (Cangelosi & Parisi, 1998; Harnad 1987) in which little virtual "organisms" forage among the mushrooms, learning what to do with them (eat or don't eat, mark or don't mark, return or don't return). The foragers feed, reproduce and die. Mushrooms with feature A (i.e. those with black spots on their tops, as illustrated in Figure 1) are to be eaten; mushrooms with feature B (i.e. a coloured stalk) are to have their location marked, and mushrooms with both features A and B (i.e. both black-spotted top and coloured stalk) are to be eaten, marked and returned to. All mushrooms also have three irrelevant features, C, D and E, which the foragers must learn to ignore.

Apart from being able to move around in the environment and to learn to categorise the mushrooms they encounter, the foragers also have the ability to vocalise. When they approach a mushroom, they emit a call associated with what they are about to do to that mushroom (EAT, MARK). Both the correct action pattern (eat, mark) and the correct call (EAT, MARK) are learned during the foragers' lifetime through supervised learning (Sensorimotor Toil). Under some conditions, the foragers also receive as input, over and above the features of the mushroom itself (+/-A, +/-B, +/-C, +/-D, +/-E), the call of another forager. This will be used to test the adaptive role of the Theft strategy. (Note, however, that except in special cases -- reported and analysed elsewhere (Cangelosi & Harnad, in preparation) -- in the present simulations the "thief" steals only the knowledge, not the mushroom.)

The foragers' world is a 2-dimensional (2D) grid of 400 cells (20x20). The environment contains 40 randomly located mushrooms. Mushrooms are grouped in four categories according to the presence/absence of features A and B: 00, A0, 0B, and AB (Figure 1). In each world there are 40 mushrooms: 10 instances of each of the four categories. Our ecological "interpretation" of the "marking" behavior is that it has two functions: Both the inedible 0B and the edible AB mushrooms have a toxin that is painful when inhaled, but digging into the earth ("marking") immediately after exposure blocks all negative effects. There is also a delayed contingency on the AB mushrooms only, which is that wherever they appear, many more mushrooms of the same kind will soon grow in their place. So with AB mushrooms it is adaptive to remember to return to the marked spots.

Figure 1: 2D world with one forager and the four samples of mushrooms. Mushroom feature A is the presence of black dots on the top; feature B is a coloured stalk. Mushroom position corresponds to the normalized relative angle between forager's orientation and the closest mushroom.


Feature A is the black-spotted top and feature B is the coloured stalk. Mushroom position is encoded as the normalized relative angle between the direction the forager is facing and the direction of the closest mushroom. In this simulation, the foraging is done by only one forager at a time. As it moves, the forager perceives only the closest mushroom. For each mushroom, the input to the forager consists of the 5 +/- features plus its location relative to the forager, expressed as the angle a, between its position and the direction the forager is facing. The angle is then normalized to the interval [0, 1]. The five visual features A, B, C, D, E are encoded in a binary localist representation consisting of five units each of which encodes the presence/absence of one feature. An A0 mushroom would be encoded as 10***, with 1 standing for the presence of feature A, 0 for the absence of feature B and *** being either 0 or 1 for the 3 irrelevant features, C, D, and E. 0B mushrooms are encoded as 01***, and AB as 11***. The calls that can be produced in the presence of the mushroom are also encoded in a localist binary system. There are 3 units for each of the three calls: 1** EAT, *1* MARK and **1 RETURN, so EAT+MARK+RETURN would be 111. Like the Calls, the three actions of eating, marking and returning are enocded localistically.

3. The Neural Network and Genetic Algorithm

The forager's neural network processes the sensory information about the closest mushroom and activates the output units corresponding to the movement, action and call patterns. The net has a feedforward architecture (Figure 2) with 8 input, 5 hidden and 8 output units. The first input unit encodes the angle to the closest mushroom. Five input units encode the visual features and three input units encode incoming calls (if any). Two output units encode the four possible movements (one step forward, turn 90 degrees right, turn 90 degrees left, or stay in place) in binary. Three action units encode the action patterns eat, mark, and return, and three call units encode the corresponding three calls, EAT, MARK, and RETURN.

Figure 2 - Neural network architecture.


A forager's lifetime lasts for 2000 actions (100 actions in 20 epochs, each of them sampling a different distribution of 40 mushrooms). For each epoch there are two spreads of activation, one for the action (movement and action/call) and one for an imitation task. The forager first produces a movement and an action/call output using the input information from the physical features of the mushroom. The forager's neural network then undergoes a cycle of learning based on the backpropagation algorithm (Rumelhart, Hinton, & Williams, 1986).

The net's action and call outputs are compared with what they should have been; this difference is then backpropagated so as to weaken incorrect connections and strengthen correct ones. In this way the forager learns to categorise the mushrooms by performing the correct action and call. In the second spread of activation the forager also learns to imitate the call. It receives as input only the correct call for that kind of mushroom, which it must imitate in its call output units. This learning is likewise supervised by backpropagation.

The population of foragers is also subject to selection and reproduction as generated by the genetic algorithm (Goldberg, 1990). The population size is 100 foragers and remains constant across generations. The initial population consists of 100 neural nets with a random weight matrix. During the forager's lifetime its individual fitness is computed according to a formula that assigns points for each time a forager reaches a mushroom and performs the right action on it (eat/mark/return) according to features A and B. At the beginning of its life, a forager does not become much fitter from the first mushrooms it encounters because it takes some time to learn to categorise them correctly. As errors decrease, the forager's fitness increases. At the end of their life-cycles, the 20 foragers with the highest fitness in each generation are selected and allowed to reproduce by engendering 5 offspring each. The new population of 100 (20x5) newborns is subject to random mutation of their initial connection weights for the motor behavior, as well as for the actions and calls (thick arrows in Figure 2); in other words there is neither any Lamarckian inheritance of learned weights nor any Baldwinian evolution of initial weights to set them closer to the final stage of the learning of 00, A0, 0B and AB categories. This selection cycle is repeated until the final generation.

4. Stage 1: Grounding Eat and Mark Directly Through Toil.

Two experimental conditions were compared: Toil and Theft. Foragers live for two life-stages of 2000 actions each. The first life-stage is identical for both populations: they all learn, through sensorimotor Toil, to eat mushrooms with feature A and to mark mushrooms with feature B. (AB mushrooms are accordingly both eaten and marked.) Return is not taught during the first life-stage. The input is always the mushroom's position and features, as shown in Table 1. In the second life-stage, foragers in the Toil condition go on to learn to return to AB mushrooms in the same way they had learned to eat and mark them through honest toil: trial and error supervised by the consequences of returning or not returning (Catania & Harnad 1988). In contrast, foragers in the Theft condition learn to return on the basis of hearing the vocalisation of the mushrooms' "names."
































Table 1 - Input and backpropagation for Toil and Theft learning and for imitation learning


We ran ten replications for each of the two conditions. In the first 200 generations, the foragers only live for the first life-stage. From generation 200 to generation 210 they live on for a second life-stage and must learn the return behavior. The first 200 generations are necessary to evolve and stabilize the ability to explore the world and to approach mushrooms. After the foragers are able to move in the 2D environment and to approach mushrooms, they learn the basic categories plus their names, EAT and MARK. The average fitness of the ten replications is shown in Figure 3. The populations that evolve in these 10 runs are the same ones that are then used in the Toil and Theft conditions from generations 200 to 210.


Figure 3 - Average fitness of the best 20 individuals in ten replications. Foragers lived one life-stage and only eating and marking was taught.


In the next runs, the second life-stage differs for the Toil and Theft groups: The Toil group learns to return and to vocalise RETURN on the basis of the feature input alone, as in the previous life-stage. Their input and supervision conditions are shown in Table 1. In the Theft condition the foragers rely on other foragers' calls to learn to return. They do not receive the feature input, only the vocalisation input.

Our hypothesis is that the Theft strategy is more adaptive (i.e. results in greater fitness and more mushroom collection) than the Toil strategy. To test this, we compare foragers' behavior for the two conditions statistically. For our purposes we count the number of AB mushrooms that are correctly returned to. The average of the best 20 foragers in all 10 replications is 54.7 AB mushrooms for Theft and 44.1 for Toil. That is, Thieves return to a higher number of AB mushrooms than Toilers. This means that learning to return from the grounded names EAT and MARK is more adaptive than learning it through direct toil on the physical features of the mushrooms. To compare the two conditions, we performed a repeated measures analysis of variance (MANOVA) on the 10 seeds. The dependent variables were the number of AB mushrooms collected at generation 210 averaged over the 20 fittest individuals in all 10 generations. The independent variable was Theft vs. Toil. The difference between the two conditions was significant [F(1,9)=136.7 p<0.0001]. Means and standard deviations are shown in Figure 4.

Figure 4 - Mean number of AB mushrooms correctly returned to in Toil and Theft simulations


5. Theft vs Toil: Simulating direct competition

A direct way to study the adaptive advantage of Theft over Toil is to see how they fare in competition against one another. We ran 10 competitive simulations, starting with the 10 populations from generation 200 of the previous runs. Foragers again live for two life-stages. In the first, all learn to eat and mark through Toil. In the second life-stage, the 100 foragers are randomly divided into 50 Thieves and 50 Toilers for the learning to return. There is no real on-line competition in our simulations because in each run, only one individual is tested in its world. The number of AB mushrooms to which a forager is able to return to will strongly affect its fitness. Direct competition occurs only at the end of the life cycle, in the selection of the fittest 20 to reproduce. Direct competition for scarce mushrooms has been studied separately in other simulations;1

1 In simulations conducted by Emma Smith (in prep.) and Gianni Valenti (in prep.) we have shown that when the scarcity of the mushrooms is varied, Theft beats Toil when there are plenty of mushrooms for everyone, but when the mushrooms are scarce and vocalising risks losing the mushroom to the Thief, Toil beats Theft and the foragers are mute. Further studies analysing kinship showed that under conditions of scarcity vocalising to relative only beats vocalising to everyone. Of course a mushroom world is too simple, and foraging categories are not the only ones that can benefit from Theft. The pattern may be different for categories related to danger, territory, mating, dominance, or instructing offspring.

in the present ecology, the assumption is that mushrooms are abundant and that the only fitness challenge is to emerge among the top 20 eaters/markers of the generation. Figure 5 shows the proportion of Thieves in the overall population of the 10 replications of Theft vs Toil (from generation 200 to 210). Even though Thieves are only 50% of the population at generation 201, they gradually come to outnumber Toilers, so that in less than 10 generations the whole population consists of Thieves.

Figure 5 - Proportion of Thieves in the 10 competitive simulations.


6. What Changes During Learning? Analysis of internal representations

In this section we compare the changes in the foragers' hidden-unit representations for the mushrooms to determine what it is that changes internally during Toil and Theft. The activations of the 5 hidden units are recorded during a test cycle in which the forager is exposed to all the mushrooms as input. We will report the analysis of a single case study using the network of the fittest individual in seed 8. These results are representative of the learning dynamics in all nets that successfully learned to categorise mushrooms.

We first used Principal Components Analysis (PCA) to display the network's internal states in two dimensions, thereby reducing the 5 activations to 2 factor scores. PCA, however, has the limitation that the different conditions cannot be compared directly because of differences in scale. For each PCA, factor scores are normalized to a distribution with a mean of 0 and a standard deviation of 1. Hence this analysis can only be used to compare internal representations within each condition, not between conditions.

Figure 6 - Similarity space for network with random weights. Factors are obtained after PCA on the activation values of the five hidden units.

Figure 7 - Similarity space for network that learned to eat, mark, and return by Toil.


Figure 6 and 7 show the effect of category learning (Toil) on the distances between the internal representations of the mushrooms in hidden unit similarity space. In Figure 6, prior to Toil, the four kinds of mushroom are not clearly distinguishable. During the course of learning the actions/calls eat-mark-return the representations form four separable clusters. We will now show how these representations can be used to analyse the effects of Toil and Theft learning on similarity space directly.

7. Categorical Perception Effects

The change in our networks' hidden-unit representations during the course of category learning can be analysed and understood in terms of learned "categorical perception" (CP) effects (Harnad 1987, Goldstone 1994; Andrews et al., 1998), i.e. the compression of within-category distances and the expansion of between-category distances. CP has already been demonstrated to occur with Toil learning (Harnad et al. 1991, 1995; Goldstone et al., 1996, Csato et al., submitted); we will now extend this to an examination of what happens to the internal representations with Theft learning.

To overcome the limitations of the previous analysis, we record the Euclidean distances between and within categories using the coordinates of the five hidden unit activations directly. At the end of each simulation, the 5 fittest foragers in each population are tested by giving them 40-mushroom samples as input. The hidden unit activations for each kind of mushroom are saved for three input conditions: (1) Features-only (only the 5-bit feature input); (2) Calls-only (only the 3-bit call input) and (3) Features+Calls (both types of input). The within-category distances are calculated as the mean squared Euclidean distances between each individual mushroom's coordinates and its category mean. There are four means, one for 00, A0, 0B, and AB respectively. Between-category distances are calculated as the distances between the category means.

Four learning conditions are used to analyse within-category and between-category distances for CP effects: (1) Pre-learning, for random-weight nets before learning; (2) No-return, for nets that were only taught to eat and to call EAT, and to mark and to call MARK, (3) Toil, for nets that also learned to return and to call RETURN with feature input, (4) and Theft for learning to return from calls alone. In every replication one mean was obtained for each of the 10 between- and within-category distances (4 within measures for each category, plus 6 between measures for all the possible pairings of the 4 categories) by averaging the distances derived from the 5 fittest foragers. These 10 mean distances were collected for each of the three input conditions. Because we have 10 replications, the 10 means for each distance can be used as dependent variables in two separate analyses of variance, one for within-category, the other for between-category distances. Our MANOVA for the within-category distances had two independent variables: LEARNING CONDITIONS with 3 levels (Pre, No, Toil) and CATEGORY TYPE with 4 levels (Eat, Mark, Return, Do-nothing)2.

2 We will use the names Eat, Mark, Return, and Do-nothing (i.e. non-A, non-B mushrooms) to refer to the four categories. Return categories could also be called Eat+Mark+Return because the Return category implies the co- occurrence of behaviours/calls Eat and Mark.

We used a repeated measures MANOVA because all levels of CATEGORY TYPE and LEARNING CONDITIONS involve repeated measures in the same set of nets. (We excluded the Theft condition in which the within-category distance is 0 because all ten samples of mushrooms use the same call input). The average within-category distances in the 4x3 conditions are shown in Table 2 and Figure 8.





















Table 2 - Table of means for the MANOVA of within-category distances

Figure 8 - Average within-category distances in the three conditions. The curve for Mark is not shown because it coincides with the curve for Eat.


The two main effects are statistically significant ( F(2,18)=917.6 and p<0.00001 for LEARNING and F(3,27)=18.8 and p<0.00001 for CATEGORY TYPE); the interaction is not significant. Using the post-hoc Duncan test with a significance threshold of p<.01 to compare the means for each independent variable, all the comparisons in the LEARNING condition were significant. That is, within-category distances decrease significantly from Pre-learning to No-return to Toil. The biggest decrease is between the (random) Pre-learning and all the post-learning nets (see Table 2 and Figure 8). In the four levels of CATEGORY TYPE, all means differ from each other except the Eat and Mark within-distances. That is, the within-category distance for Eat and Mark is the same, whereas the within distance of Do-nothing is the biggest and that of Return the smallest.

MANOVA for the between-category distances had two repeated variables: LEARNING CONDITIONS with 4 levels (Pre, No, Toil, Theft) and CATEGORY COMPARISONS with 4 levels (Eat Versus Mark, Eat vs Return, Eat vs Do-nothing, Return vs Do-nothing). The Mark vs Return and Mark vs Do-nothing comparisons are not included in the analysis because their means are very similar to the parallel comparisons Eat vs Return and Eat vs Do-nothing, respectively (Table 3). We then go on to generalize the results for the Eat vs Mark comparisons. The between-category distances for the 4x4 repeated measure design are shown in Table 3 and Figure 9.





















EAT « Do-nothing





MARK « Do-nothing





RETURN « Do-nothing





Table 3 - Table of means for the MANOVA of within-category distances

Figure 9 - Between-category distances in the four conditions. Return vs Mark and Mark vs Do-nothing are not shown because they are congruent with Return vs Eat and Eat vs Do-nothing respectively.

The two main effects are significant ( F(3,27)=3771.6 and p<0.00001 for LEARNING and F(3,27)=868.6 and p<0.00001 for COMPARISONS) as is their interaction (F(9,81)=75.7 and p<.00001). Duncan tests revealed, first, a significant difference distance between the Pre-learning nets and all the post-learning nets. (This expected effect only shows that any kind of systematic learning will increase between-category distances compared to random initial distances.) Comparing Toil vs Theft specifically, we see that all distances between Return and the other three categories are greater in the Theft nets. Learning Return by Theft has the effect of separating this category more from the others. The mean Return vs Eat, Return vs Mark, and Return vs Do-nothing differences, 1.25, 1.25 and 1.25, respectively, in the Theft nets, and 1.10, 1.12, and 1.52 in the Toil nets, were all significant. The Theft learning of Return caused the between-category distances not involving Return to decrease. [A last effect is that in all learning conditions the Eat vs Mark and Return vs Do-nothing distances are greater then the other pairs because the Hamming distances of their I/O codes is maximal (e.g. features A and B for Eat Vs Mark have this input contrast: 10 Vs 01).]

Figure 10 shows the change in the distances between the internal representations of the A (Eat only), B (Mark only), A&B (Eat & Mark & Return), and not-A&not-B (neither Mark nor Eat nor Return) Mushrooms. Prior to Toil, the circles, proportional to the within-category distances are large and the rectangle, proportional to the between-category distances is small. After Toil learning, the within-category differences shrink and the between-category distances expand.

Figure 11 then traces the between-category expansion to Theft Learning: The thin dashed rectangle is proportional to the between-category distances before learning (random). The thick dashed line is what they look like after Toil learning of Eat and Mark without Return; the thin continuous line is identical to Figure 9, that is, Toil learning of Eat and Mark, with Return, and the thick continuous line is for Theft learning of Return. Note the increased separation between A&B and not-A&not-B induced by Theft alone.

Figure 10 - 2D projections of between-category distances (quadrilateral sides) and within-category distances (circle radius) in the Pre-learning condition and after Toil learning of Eat, Mark,and Return. All distances except Eat vs Mark correspond to the actual Euclidean distances in 5 dimensional hidden unit space.

Figure 11 - 2D projections of the between-category distances (quadrilateral sides) in the four conditions. The distances, except Eat vs Mark, are comparable and reflect the actual Euclidean distances between categories. Note that the distances between Return and all the other categories (Return vs Eat, Return vs Mark, Return vs Do-nothing) are the highest in the Theft condition.


8. Conclusions

We have shown that a strategy of acquiring new categories by Symbolic Theft completely outperforms a strategy of acquiring them by Sensorimotor Toil as long as it is grounded in categories acquired by Toil. The internal mechanism that makes both kinds of category acquisition possible does so by "warping" internal similarity space so as to compress the representation of members of the same category and to separate the those of different categories. The warping occurs primarily in the service of Toil, but Theft not only inherits the warped similarity space but can warp it further. This warping of similarity space in the service of sensorimotor and symbolic learning is called categorical perception and can be interpreted as a form of Whorfian effect (Whorf 1964).

Can these results from a 3-bit toy world really cast light on the rich and complex phenomenon of the origin and adaptive value of natural language? This is really a question about whether such findings will "scale up" to human size in the real world. This scaling problem -- common to most fields of cognitive modeling where the tasks themselves tend not to be lifesize or to have face validity -- can only be solved by trying to scale up, introducing more and more of the real-world complexity and constraints into the model. This is how our own research programme will continue. For now, however, we wanted to enter our own toy candidate into the competition with the other toy models (tool-make, hunt-help, chit-chat, etc.) in the search for the provenance of our species’ most powerful and remarkable trait.


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