Schunn, C. D., & Vera, A. H. (1995). Causality and the categorization of objects and events. Thinking & Reasoning, 1(3), 237-284.

 

 

 

 

 

Causality and the Categorization of Objects and Events

Christian D. Schunn

Carnegie Mellon University

 

Alonso H. Vera

The University of Hong Kong

 

 

 

 

 

Author Note:

Christian Schunn, Department of Psychology; Alonso Vera, Centre for Cognitive Science and Department of Psychology.

Part of the studies reported here were done in collaboration with Frank Keil at Cornell University as part of the second author's thesis. Part of these studies were also presented at the 1992 Annual Meeting of the Society for Philosophy and Psychology. Work on these studies was supported by graduate fellowships from NSERC and FCAR to the first author, and an NIMH grant to Frank Keil. We would like to thank Steve Ritter, Marsha Lovett, Rosemary Stevenson, and Ken Gilhooly for their helpful comments on the manuscript, and members of the Siegler and Anderson research groups for their insights.

Correspondence regarding this manuscript should be addressed to Christian Schunn, Department of Psychology, MSN 3F5, George Mason University, Fairfax, VA 22030-4444.

Electronic mail may be sent to schunn@gmu.edu.

 

Abstract

Two series of experiments investigating the nature of category structure are presented. The studies focused on object categories and event categories. It was found that, for both objects and events, property centrality (a rating of how important the property is to the category) is not entirely predicted by property typicality (how frequently the object or event possesses that property). By contrasting conditions in which adult subjects rank-ordered properties according to various criteria, it was found that causal theories about the role of the properties in the categories strongly predicted property centrality, although recognitional and definitional factors did play some role. This relationship held for both familiar and newly acquired categories. Recent empirical work on the attribution of causal relationships to sequences of events is reviewed. The evidence from both the past work and the current studies indicates humans do indeed have causal theories which they use to categorize objects and events.

 

Causality And The Categorization

Of Objects And Events

What are the cognitive mechanisms that serve to organize our representations of category concepts? The organization might follow probabilistic cues in the environment, or it might be more actively structured by our mental constructs. Probabilistic cues in the environment are certainly quick and easy to use for rapid identification of familiar instances. They are also readily available to our senses. On the other hand, they can be misleading and memory intensive. We will argue that while probabilistic cues are relevant to category structure, causal theories about the world are generally the more powerful mechanism in the acquisition and use of category concepts, regardless of the domain. We review evidence from the psychological literature on the role of causal theories in object and event categorization and present new results supporting the position that causal relations are primary in the acquisition and use of category concepts.

There is a relatively long history of work in psychology attempting to understand the cognitive processes involved in the categorization of objects. For example, much work has gone into understanding people's concepts of artifacts, biological kinds, natural kinds, and so on. In this research, both theory-based and probabilistic-based views of category structure have been proposed (e.g., Anderson, 1990; Murphy & Medin, 1985). There has also been a significant amount of research looking at how people understand events. This research has focused on the interrelations among temporal, perceptual and statistical features of events. Similar to the research on objects, both theory-based and probabilistic-based views of event perception and causal attribution have been proposed (e.g., Bullock, Gelman, & Baillargeon, 1982; Shultz & Kestenbaum, 1985).

However, the possible commonalties between object and event categorization have not been significantly investigated. It is not unreasonable to hypothesize that similar cognitive processes might be involved in both domains of categorization. This paper presents a series of studies on the nature of object categorization. This is followed by a detailed discussion of research on the categorization of events and a set of studies which investigates the processes which underlie event categorization. The results will show that there are significant commonalties between the mechanism involved in the categorization of objects and events.

Categorization Of Objects

Objects can be seen as categorizable using two different organizational mechanisms: probabilistic cues and domain-level theories. A number of probabilistic theories (e.g., Rosch, 1973; Rosch & Mervis, 1975; Nosofsky, 1988; Anderson, 1990) have been put forward in order to explain how people form concepts based on the clustering of features in the world. They all are based on notions of similarity: objects with similar sets of features are grouped together. These types of theories are probabilistic in the sense that no one feature is considered to be necessary nor sufficient to determine class inclusion. Proponents of this general view argue that people form prototypes by first abstracting the most central features of categories and then comparing novel objects to these.

The main argument against probabilistic views has been that concepts are not simply sums of independent features. Categorization must rely on more than just similarity among features. Otherwise, how might such features be selected from the indefinitely large number available for comparison (cf. Quine, 1960)? Probabilistic views provide no way of selecting among features in order to draw category distinctions. Furthermore, organizing and integrating constraints of some sorts must be present in order for concepts to serve as adequate inductive bases.

In order to address the insufficiency of probabilistic accounts, Murphy and Medin (1985) proposed that theories structure peoples' concepts. They argued that there are domain-level explanations which organize concepts above and beyond the structure afforded by probabilistic mechanisms. We will refer to this as the theory-based view. The term "theory", as they use it, has a narrower definition than that found in conventional scientific usage. In the natural sciences, theories are usually conceived of as very general and abstract sets of rules which describe a particular domain and allow predictions to be made with respect to that domain. What Murphy and Medin mean by "theory" is a little more constrained since it refers specifically to certain kinds of mental entities. Theories, in this sense, are mental representations of relations between features which embody explanations about their co-occurrence.

Unlike the Roschean view where the relations between features are understood to be purely probabilistic, Murphy and Medin suggested that causal aspects of these relations must also be represented in order for the relations to be useful in categorization. Causal relations between features allow people to categorize objects according to family resemblance (Rosch, 1973) and other higher order relations, whereas treatment of features as independent entities (or even as correlated entities) does not yield such categorization (Medin, Wattenmaker & Hampson, 1987).

The distinction between the centrality and typicality of properties was first demonstrated by Medin and Shoben (1988). They found a dissociation between the frequency of property-category correlation and the centrality of the property to its category. The effect they found was that properties that are rated as being equally highly correlated with instances of a category were not equal in terms of importance to the category as judged by subjects. For example, the property of curvedness was equally associated with both bananas and boomerangs (near 100% in both cases). Nevertheless, when asked, subjects indicated that being curved was more important for being a boomerang than for being a banana.

Unfortunately, their study did not pursue the question of why the same property is rated as being more important to one category than another. Indeed, empirically investigating centrality ratings can be a challenging task. There may be any number of factors influencing ratings of centrality. For example, people’s centrality judgments might be based on their beliefs about how categories are used to label objects (i.e., perhaps trying to adhere to something like scientific convention), or on how important particular properties are for perceptual recognition and distinguishing an object as a member of a category. Furthermore, since such factors need not be present in isolation, it is possible that they may co-exist in the process of categorization. Testing the correlation of these factors, as individual variables, with centrality is therefore likely to be a poor test of underlying concept structure. Multiple factors need to be contrasted together in order to determine which of them best predict(s) centrality.

In the studies that follow, we consider three potential factors. First, centrality may derive from beliefs about social convention. If so, then curvedness would be central to boomerangs because curvedness is generally considered part of the definition of a boomerang. Second, it may be that centrality derives from beliefs about relevance of particular properties for object recognition. That is, curvedness may be central to boomerangs because curvedness is very useful and salient in the recognition of boomerangs. Third, centrality may derive from beliefs about the causal or functional relevance of the properties. For example, curvedness may be central to boomerangs because it is believed to be causally important to the function of a boomerang. The studies presented here evaluate the role of these factors in determining property centrality.

Investigations of the basis of our centrality evaluations are further complicated by potential domain-dependence issues. Different factors may determine property centrality for different kinds of objects. For example, functional relevance may be important for artifact concepts, like ‘hammer’, whereas object recognition may be more important for biological kind concepts, like ‘dog’. Consequently, the studies that follow considered artifacts and biological kinds separately. This allowed us to directly address the issue of domain-specific constraints.

Another difficulty in investigating what drives centrality ratings is that it is unclear what might be a good measure of property centrality. As an example, one option is to have subjects rate the centrality of properties for objects by considering objects with that property dimension absent rather than set to a particular alternative value. It is possible that manipulating properties in this way overly biases people's ratings towards raw typicality evaluations since objects with missing dimensions are very atypical (e.g., a dog with an unknown number of legs). By contrast, having subjects consider a specific value for a property may carry too much arbitrariness, since different values may produce very different ratings (e.g., a three-legged dog vs. a one-legged dog). Furthermore, allowing the experimenter to chose the particular values may lead to outcomes biased towards the experimenter’s theoretical stance. A third option is to simply negate the property (e.g., a dog that does not have four legs). A potential advantage of this method is that it does not explicitly bias the subjects towards any particular theoretical stance. On the other hand, it potentially introduces some ambiguity into subjects' interpretation of negated properties.

Another potentially problematic point is the choice of object properties. For any given object, the list of potential properties is infinite. Moreover, the method of property selection is critically important for the study since it could easily be biased toward the experimenters' particular theoretical bent. For example, choosing the properties that are most important for object recognition will bias the centrality ratings towards emphasizing object recognition. An alternative is to have subjects generate the properties. This method is less likely to produce a theoretically biased set of properties, and it is less likely to generate properties which subjects might consider unnatural or strange. It should also be noted that a large group of subjects is not necessary for property generation as long as subjects produce a fairly similar and consistent set of properties.

Conceptual structure has proven to be remarkably difficult to study, as was seen in the above discussion of methodological issues. With these issues in mind, we address two central theoretical questions. First, are there domain-level theories that structure our mental representations of categories, and, if so, what is their nature? In particular, are our categories structured by beliefs about social convention, beliefs about the importance of features for object recognition, or theories about property functional/causal relevance? The evidence presented here indicates that causal/functional theories structure our concepts across domains. Second, does the centrality/typicality dissociation effect require years of experience with a particular category or does it occur even when new categories are learned? This will be tested by contrasting object categories which subjects know little about with categories with which they are well familiar. The results will show that novel categories are quickly organized according to domain-level theories.

Experiment 1a

The goal of these studies was to investigate the relationships that adults perceive as existing among object properties. The first step was therefore to generate a set of independently derived properties with which to compare probabilistic and theory-based explanations of concept structure. Since the goal was to evaluate not only the structure of people's existing concepts, but also how individuals organize information about novel objects, two methods were used to generate properties. For unfamiliar objects, subjects were asked to read stories describing a wide variety of aspects of each object, including historical information. The stories were generated from encyclopedia entries. For the familiar objects, subjects were simply asked to generate properties for the category, but were given no additional information.

Method

Subjects. Ten Cornell University undergraduate students participated in individual sessions for course credit.

Procedure. Two kinds of objects were used: biological kinds and artifacts. Half of each kind were familiar to subjects and the other half were unfamiliar to them. There were four conditions: 2 (familiar, unfamiliar) x 2 (biological kinds, artifacts). Twelve objects were used in the study (see Table 1). There were three objects in each of the four conditions. Each object had its properties generated by all ten subjects. In the unfamiliar condition, subjects were given a story-like description of the object. They were instructed to "Read the story carefully. Then, on the response form following the story, write as many properties as you can about the thing you read. Try to generate at least 25 properties." These stories were taken from encyclopedia entries. The biological kind stories were about six pages in length and the artifact stories were about three pages. Appendix C presents two of the stories–one artifact and one biological kind.

In the familiar condition subjects were given the following instructions: "This is a simple study to find out the properties and attributes that people feel are common to and characteristic of different kinds of ordinary everyday things. There are six common objects on the following pages. Write as many properties as you can think of for each of them. Spend about 2 minutes on each object." Subjects were given no additional information about the objects.

 

Table 1. Objects used as stimuli in Experiment 1.

Object type

Objects

Biological Kinds

 

Familiar

cats, pigeons, mice

Unfamiliar

milkweed bugs, fleas, tobacco hornworms

Artifacts

 

Familiar

lawn mowers, cars, toilets

Unfamiliar

blast furnaces, routers, governors

 

Results

The subjects in this study provided a very consistent set of properties for each object. We decided not to increase the n since the goal of getting a typical set of subject-generated properties had been achieved. The procedure yielded a large set of properties for each object. The task was then to distill a subset of properties for each object to be used for subsequent experiments. Within each set of properties, some were mentioned quite frequently (i.e., by all the 10 subjects), whereas others were mentioned much less often. We determined the most natural cut off point in the frequencies of mention for each group of objects. Consequently, the conditions do not have the same number of properties per object. Each of the unfamiliar biological kinds has 8 properties, unfamiliar artifacts 7 properties, and familiar biological kinds and artifacts 6 properties each. Across all four conditions, only those properties mentioned by at least half of the subjects were used. However, the average frequency of mention was much higher than 50% for most of the objects, particularly in the unfamiliar condition. Overall, subjects mentioned fewer properties in the familiar condition. This was probably due to the fact that the subjects in the familiar condition spent less time on each object–as they were instructed–than the subjects in the unfamiliar condition. The instructions for the unfamiliar condition asked subjects to generate at least 25 properties whereas, for the familiar condition, subjects were asked to spend 2 minutes on each object. Although subjects in the familiar condition ended up generating fewer properties for each object than those in the unfamiliar condition, there were enough properties for each object to allow us to select a subset shared by most of the subjects. Table 2 presents the set of properties selected for some of the objects. The complete set is given in Appendix A.

 

Table 2. Examples of the frequently-generated properties.

Object

Features

Cats

fur, tails, four legs, meow, purr, claws

Fleas

resilin, coiled penis, have combs, jump high, good at finding hosts, flattened hard bodies, survive long time, very active

Cars

four wheels, engines, steering wheels, seats, use fuel, expensive

Routers

versatile, different size bits, 2-3 hp, bit shape variable, cut fancy edges, toggle switch, raisable motor

 

Discussion

The goal of Experiment 1a was simply to generate a set of properties that subjects typically thought of as properties of these objects. It is clear that this procedure for generating properties did not generate all the possible properties for each object. It might also be the case that it did not generate the most central properties for each of the objects. However, the purpose of this manipulation was to generate a set of features that subjects typically considered to be part of the objects in question, rather than selecting the features a priori. It was not essential to select the most central properties. As long as the features ranged in centrality, the role of the domain-level theories in category structure could then be tested.

Experiment 1b

The centrality effect found by Medin and Shoben seems to indicate that properties which are equally correlated with two objects (e.g. green with money and grass) are not necessarily equally central in people's concepts of the two objects. However, their study has a number of problems which make it difficult to interpret the results. They negated properties by replacing the adjectives with roughly equivalent but incorrect alternatives (e.g. they replaced pink for green resulting in "pink grass" and "pink money"). They treated adjectives as values of superordinate classes (e.g. color in the above example). This may not seem problematic at first, but a significant difficulty arises when one attempts to negate adjectives in this way. Any adjective has more than one opposite. For example, what is the negation of "light"? It could be "heavy", or "weightless", or perhaps "dark"? This problem quickly becomes compounded if there is more than one adjective. For example, is the opposite of "long black tail" "tail-less", "short black tail", "long white tail", or any combination of these?

A formal approach to this problem has been to suggest that a proposition has, not one, but a set of possible antonyms (Katz, 1972). If this is correct, then it is clearly problematic that Medin and Shoben selected antonyms without accounting for their choices among the set of possibilities. In the studies reported here, it was decided to circumvent selecting among a set of potential antonyms by avoiding them altogether. Each property was negated without giving any extra information. This procedure is discussed in detail in the Methods section below.

Another problem with Medin and Shoben's study is that they did not control the categories they compared. They compared the same property for nominal kinds (e.g., money) and biological kinds (e.g., grass). They also included comparisons between artifacts and biological kinds. It is consequently difficult to ascertain whether the results they found were due to subjects' genuine intuitions, or simply to subjects’ confusion at being asked to compare objects of fundamentally different types.

Given that Experiment 1a yielded a set of properties that was mentioned with roughly equal frequency, it was decided to assess the relative centrality of the properties with respect to each object. The centrality effect found by Medin and Shoben might thus be established while avoiding the difficulties in their study.

Method

Subjects. Eight Cornell University undergraduate students participated in individual sessions for course credit.

Procedure. To obtain property centrality ratings, a property-negation methodology was used. For each of the objects, subjects were asked to imagine a new object with all the same properties as the standard/familiar object except one. Subjects were then asked to make category membership rating judgments for these counterfactual instances. For example, subjects were asked "Suppose you could change just one property of pigeons so that they did not have feathers. How good a pigeon would it be? That is, how good or bad would it then be as an example of its category? How different a kind of thing is it from pigeons? How much does removing this property change your concept of it?" These questions were asked for each property of each object. The same five questions were repeated in each case, merely substituting the appropriate object and property names (and making appropriate grammatical adjustments). Although five questions were asked for each property, subjects responded with only one centrality judgment for each property, reflecting the overall importance of that property to the object category. The subjects made their judgments using a 7-point scale ranging from "very good example of the category" to "very bad example of the category". For the familiar objects, subjects simply rated each of the property negation cases. For the unfamiliar objects, subjects read the story for each object prior to making their judgments. Subjects rated all twelve objects in random order.

Results

To remove individual biases toward using the bottom or top portion of the scale, centrality ratings for each subject were converted to z-scores. The centrality measure for each property was the negation of the mean z-score, such that higher scores were more central. Property centrality ranged from 1.3 to -1.3. Table 3 presents the two most central properties for a subset of the objects (Appendix A presents the complete set).

Table 3. Examples of the two most central object features.

Object

Features

Cats

have fur, have four legs

Fleas

have combs, good at finding hosts

Cars

have engines, have seats

Routers

are versatile, bit shape is variable

 

While there was a range in the centrality of the properties generated by the subjects, this range was not attributable to differences in property generatability. Figure 1 compares the mean centrality rating for properties with their frequency of mention. The figure shows a lack of relationship between centrality and frequency of mention in Experiment 1a. Spearman rank correlations between frequency of mention and centrality ratings were not significant for any of the objects confirming that our measure of centrality was not a consequence of frequency of mention.

 

Figure 1. Comparison of frequency of mention and rated centrality for the properties of objects.

 

Discussion

The goal of Experiment 1b was to obtain centrality ratings for each of the objects. It was predicted that these property centrality ratings would not be a simple function of property typicality, as measured by property frequency of mention in this case. Experiment 1b succeeded in establishing which properties are consistently considered more important to each of the categories. Furthermore, it demonstrated that property centrality was not a simple consequence of the frequency of mention of the property. The use of frequency of mention, however, provides a weak test of the dissociation of typicality from centrality. Frequency of mention is several steps removed from property typicality. A more direct measure of property typicality may show a stronger relationship with property centrality. In this study, a very restricted range of frequency of mention was used, thereby weakening any potential effects. Consequently, the frequency of mention of properties is not used as a measure of typicality in the experiments that follow.

Experiment 1c

Does typicality account for our measure of centrality? There were two main goals of Experiment 1c. The first was to test whether the measure of centrality developed in Experiment 1b still dissociates from typicality when a stronger measure of typicality is used. Second, we wanted to develop a good measure of typicality against which the independent effects of domain-level theories could be tested.

To test the effects of typicality, two measures of property frequency were developed. In both conditions, subjects were asked to estimate how often the objects have each of the properties. For the first measure, subjects were asked to consider only the instances that they had personally seen. For the second measure, subjects were asked to consider all instances of the object in the world. The two measures were used to test whether actual experienced frequency or perceived frequency were related to property centrality. That is, it may be that subjects believed their own experience to be highly idiosyncratic, and based category membership decisions based on theories of property frequency. For example, a person may own a three-legged dog and see this three-legged dog with great frequency, and yet still know that three-legged dogs are atypical.

Methods

Subjects. Twelve Carnegie Mellon University undergraduate students participated in group sessions for course credit.

Procedure. There were two conditions corresponding to the two measures of typicality. In the All condition, subjects were asked to rate each feature on the proportion of all objects of that type that have feature. For example, subjects were asked to "indicate what proportion of all cats have fur". In the Seen condition, subjects were asked to rate each feature on the proportion of objects of that type that they had seen that have the feature. For example, subjects were asked to "indicate what proportion of cats that you have seen had fur". Subjects in both conditions made their judgment using a 7 point scale ranging from "none" to "all".

Since the frequency-judging task required familiarity with the objects, the frequency judgments could only be made for the familiar objects. Six subjects were randomly assigned to each condition. Each subject rated all six objects using a particular criterion. The objects were presented in random order for each subject.

Results

The two property frequency measures correlated highly with one another (r=.86, n=36). Furthermore, the two measures of frequency correlated with other measures (from Experiments 1a, 1b, and 1d) in similar ways. Therefore, we collapsed the two measures into one property frequency measure, called Frequency.

Frequency proved to be quite predictive of Centrality (r=.63). To investigate how well Frequency predicted the most central properties, we tabulated the overlap between the properties which were the most central to an object and the properties which were more frequently present for an object. For each object, properties were divided into three categories along both the Frequency and Centrality dimensions: First-highest property, Second-highest property, and the Rest. Table 4 presents the contingency between the Frequency and Centrality dimensions for the 36 properties of the familiar objects (see table 4). This table highlights two important facts about the relationship between Frequency and Centrality. On the one hand, Frequency and Centrality are correlated, since the majority of the first and second-most central properties are also the first or second-most frequent properties (this was true of all of the familiar biological kind objects). On the other hand, Frequency cannot be the only determinant of the most central properties because none of the most frequent properties are the most central ones.

 

Table 4. Contingency between property frequency and property centrality for objects.

 

Frequency

Centrality

First

Second

Rest

First

0

5

1

Second

4

0

2

Rest

2

1

21

 

Discussion

Experiment 1c had two goals: 1) to develop a better measure of typicality, and 2) to establish some dissociation between typicality and centrality. While Frequency was fairly predictive of centrality, there was some indication of a typicality/centrality dissociation. In fact, the dissociation was a little stronger than one might have expected a priori. Nevertheless, whether the dissociation is actually this strong, or whether factors such as ceiling effects artificially inflated it, the magnitude of the dissociation is not relevant to our current thesis. The result of interest is simply that there is some suggestion of dissociation, for which we seek to find a cause.

Given the high intercorrelations of the two frequency measures and the strong correlations with centrality, it is likely that we have found a reliable measure of typicality. Furthermore, given the strong correlation with centrality, this combined Frequency measure provides a strong benchmark against which domain-theory effects can be measured.

Experiment 1d

What sorts of factors lead subjects to selecting the properties they do as most central? There are at least three commonly raised alternative explanations for centrality ratings. The goal of Experiment 1d is to contrast these three views. First, features considered most central may simply be those that would be most important for identifying the object in everyday sorts of encounters with it. The findings reported in Experiment 1c suggest that property frequency for a given category is related to conceptual centrality. This indirectly suggests that those properties used most in "quick and dirty" recognition may be the most central ones. Nevertheless, this needs to be assessed more directly.

A second explanation of why certain properties are evaluated as being more central might be that subjects think those properties are the most "taxonomically" relevant (i.e. if a scientist or expert were attempting to categorize the object). People may prefer properties that are somehow important to the "definition" of the category. A third possibility is that certain properties are more central as a consequence of their direct role in the causal functioning of the object. That is, humans organize information according to causal theories and, as a result, properties which are causally more important are evaluated as being more central to the concept.

To test these hypotheses, three conditions were developed. Subjects in each of the three groups were given a different set of instructions in which they were asked to rank the properties according to an explicit criterion corresponding to each possible explanation. Properties found to be central to the category in Experiment 1b should consistently appear at the top of the ranking for that condition which best accounts for the centrality ratings. Each of the conditions can be tested for independent contributions by regressing the ranking scores against centrality scores.

Method

Subjects. Twenty-four Cornell University and twenty-four Carnegie Mellon University students took part in group sessions for course credit.

Procedure. Subjects were asked to rank the properties for the six familiar and six unfamiliar objects. For the unfamiliar objects, the subjects read the story before ranking its properties. For the familiar objects, subjects read only the six properties. The twelve objects were presented in random order and the properties were randomized for each.

There were three conditions with sixteen subjects in each condition. The three conditions differed only in the instructions given for ranking the properties. In the first condition, subjects were instructed to rank order the properties in terms of their importance to recognizing what kind of thing the object is. This was the Recognition condition. The instructions were as follows "For each object, rank order the statements below it by considering which of the stated properties would be more important if you were trying to determine whether a given object belonged to that category."

In the second condition, subjects were asked to rank the properties according to their relevance for a scientist or expert trying to categorize the object. This was termed the Definition condition. The instructions were as follows "For each object, rank order the statements below it by considering which of the stated properties would be more important for a scientist or expert who was trying to determine what it was. For example, if it is an animal, which properties are most important for a scientist to distinguish it from other similar species. Rank order the properties given in terms of how important they would be for a scientist trying to correctly classify the species. Or, if it is an artifact, which properties are most important for an expert to distinguish it from other similar artifacts. Rank order the properties given in terms of how important they would be to an expert trying to determine what kind of artifact it is."

In the third condition, subjects were asked to order the properties in terms of their role in the functional/biological success of the object. This was termed the Function condition. The instructions were as follows "For each object, rank order the statements below it by considering which of the stated properties would be more important for the thing to be successful at what it is. For example, if it is an animal, which properties are most important for it to survive as a species. Rank order the properties given in terms of how important they would be for the species to be a successful one. Or, if it is an artifact, which properties are most important for it to be functionally useful. Rank order the properties given in terms of how important they would be for the artifact to be a useful one."

Results and Discussion

Since it was only possible to obtain frequency ratings for the familiar objects, any of the following analyses which contain frequency as a factor are on the familiar objects only. All other statistics are on the entire set of objects unless otherwise stated.

Aggregate correlational analyses. To assess the overall predictiveness for centrality of the three ranking conditions, we regressed mean centrality rating for each property against the mean item rankings in each of the three ranking conditions: Definition, Recognition, and Function. Simple linear regressions were used since there did not appear to be any obvious non-linearities (i.e., residuals appeared to be normally distributed, and curvilinear trends were not statistically significant). All three ranking conditions were significantly associated with Centrality (r=.44, r=.59, and r=.61 respectively, p's<.001). Although not greater by much, Function had the highest correlation with Centrality of the three ranking conditions.

Since Frequency was also correlated strongly with the three ranking scores (r=-.5, r=-.5, and r=-.53 respectively, p's<.001) and with Centrality (r=.63), it may have been the case that the correlation between one or more of the ranking scores with Centrality was at least partially mediated by differences in frequency estimates. However, with Frequency partialled out, Function continued to have the highest partial correlation with Centrality (r=.39, r=.44, and r=.48 for the Definition, Recognition, and Function conditions respectively, p's<.001).

Since Definition and Recognition scores were strongly correlated with Function scores (r=.69 and r=.61 respectively), it may be that the associations between Definition and Recognition with Centrality are mediated by the strong correlations with Function. To test whether Definition and Recognition had independent predictiveness of Centrality independent of Function, the Definition and Recognition scores were regressed against Centrality in two different ways: once with the effects of Function partialled out, and once with the effects of both Function and Frequency partialled out. With Function partialled out, Recognition had a significant partial correlation with Centrality (r=.35, p<.01), whereas Definition did not (r=.03, p>.5). With both Function and Frequency partialled out, Definition and Recognition had small nonsignificant partial correlations with Centrality (r=.09, p>.5, and r=.18, p>.2 respectively). Therefore, it seems that while Definition did not have any independent predictive value for Centrality, Recognition may have had small independent predictive value for Centrality.

Object kind correlational analyses. We also wanted to assess whether this pattern occurred for all of the objects individually, or whether the overall pattern was an artifact of averaging across very different patterns. That is, it may have been that Definition was the best predictor of Centrality for some objects, Recognition was the best predictor of Centrality for other objects, and only because Function was the second best predictor in all cases did Function become the best predictor overall. It was not possible to accurately parcel out which factors were independent predictors for each object since there were too few data points and high colinearity among the potential factors. Instead the analyses were conducted separately on the four object types: unfamiliar artifacts, unfamiliar biological kinds, familiar artifacts, and familiar biological kinds. However, even for these groupings, there were too few data points to conduct very reliable multiple regression analyses given the high colinearity among the factors. Therefore, the analyses below should be considered as primarily exploratory.

For unfamiliar artifacts and unfamiliar biological kinds, both Recognition and Function proved to have independent predictive value (p’s<.001 for biological kinds, and p’s<.05 for artifacts), whereas Definition did not (p>.5 for biological kinds and p>.1, in the wrong direction, for artifacts). For familiar biological kinds, Frequency and Definition had strong independent predictive value (p’s<.05), whereas Function had a weaker independent predictive value (p<.1), and Recognition had no independent predictive value (p’s>.3). For familiar artifacts, both Recognition and Function were strongly correlated with Centrality (p’s<.001). However, since the two factors where strongly correlated (r=.95), it was not possible to determine whether the factors contributed independently of the other. Neither Definition nor Frequency had independent predictive value for the familiar artifacts (p’s>.2). In sum, for unfamiliar objects there are both Function and Recognition components to centrality, whereas for familiar objects the picture is less clear with Function being the only potentially common element to both types of familiar objects (see table 5).

Table 5. Independent predictors of centrality for each object kind.

Object type

Independent predictors of centrality

Biological Kinds

 

Familiar

Definition (.7), Frequency (.63), Function (.57)

Unfamiliar

Recognition (.72), Function (.7)

Artifacts

 

Familiar

Recognition (.76), Function (.72)

Unfamiliar

Recognition (.58), Function (.58)

Note. Overall correlations with centrality are presented in brackets. 

Most-central property analyses. In the aggregate and object kind correlational analyses, Frequency and Function were often independent predictors of Centrality. However, it was unclear whether Function was an important predictor of the most central properties. That is, it may be that the most central properties were solely predicted by other factors, and Function predicts the ordering of the less central properties. Since, in previous analyses (see table 4), it was determined that Frequency was likely not the only determinant of the most central property, the other ranking conditions may be good predictors of the most central property.

To test which of the three ranking conditions best predicted the most central property, a 3 (Condition) x 2 (Familiarity) X 2 (Kind) ANOVA was computed on the ranking data for the two most central properties of each object. Since Frequency was not measured for the unfamiliar objects, it was not added into the analysis. The main effect of condition was significant (F(2,45)=14.3, p<.0001). Figure 2 presents the mean rank of the most central property in each condition. Post-hoc tests revealed that the ranks were significantly lower in the Function condition than either the Definition or Recognition conditions (Bonferroni/Dunn t(45)=5.35, p<.0001, and t(45)=2.71, p<.01 respectively).

Figure 2. The mean rank (and standard error) in each condition of the two most central properties of objects

 

There was no interaction of Kind with Condition (F(2,45)<1), nor was there a Kind by Familiarity by Condition interaction (F(2,45)=1.28, p>.25). There was a marginal interaction of Familiarity by Condition (F(2,45)=1.72, p<.2). Figure 3 presents the mean rank in each condition for familiar and unfamiliar objects. For both familiar and unfamiliar objects, Function was more predictive of the most central properties than the other two ranking conditions (p<.05, and p<.01 respectively). One might also note that the mean ranks were lower for the unfamiliar objects, possibly because there was more noise in either the centrality ratings or the ranking data for the unfamiliar objects.

Figure 3. Mean rank of the two most central properties for familiar and unfamiliar objects.  

 

An alternative explanation for the greater predictive value of Function over Definition and Recognition is that subjects found the instructions for the Definition and Recognition questions more difficult to achieve than the instructions for the Function condition. This potential greater amount of noise in the Definition and Recognition measures may have reduced their predictive value. An ANOVA computed on the subject intercorrelations was significant (F(2,357)=14.3, p<.0001). The mean subject intercorrelations within the Definition, Recognition and Function conditions were .21, .25, and .31 respectively. The mean subject intercorrelation within the Function condition was significantly higher than those of the Definition and Recognition conditions (Bonferroni/Dunn t(357)=3.47, p<.01, and t(357)=5.24, p<.05 respectively). These differences support this alternative explanation.

To address with this alternative explanation, the mean intercorrelation with all of the other subjects in their condition for each of the subjects was calculated. Those subjects in the Definition and Recognition conditions with mean intercorrelations within a standard deviation of zero were removed from the data set (i.e., those subjects whose rankings had little in common with the rest of the subjects). This procedure removed three subjects from the Definition condition, and three subjects from the Recognition condition. The resulting mean correlations for the three correlations were r=.28, r=.3, and r=.31 respectively. The differences were not significant (F(2,273)=1.87, p>.15).

With these six subjects removed, the 3 (Condition) x 2 (Familiarity) X 2 (Kind) ANOVA on the ranking data for the two most central properties of each object was recomputed. The removal of these six subjects did not effect the main effect for condition, nor any of the other interactions of familiarity or kind with condition. Therefore, it is unlikely that the differences in the predictive value of the ranking data were caused by differences in understanding of the instructions across conditions.

General Discussion

The goal of Experiment 1d was to determine what factors predict property centrality. Four potential predictors were contrasted: Frequency, Definition, Recognition, & Function. Function was overall a better predictor of property centrality than the other potential predictors. This suggests that what makes a property more central to a concept is partially dependent upon its causal/functional role within that concept. Furthermore, Function was the most predictive of the most central properties for both familiar and unfamiliar objects, although it was a better predictor in the familiar case.

The conclusions from these studies would have been more difficult to interpret had the direction of the effect of object Familiarity been reversed. If this had been the case, then there would have been reason to suspect that the unfamiliar object tasks were capturing something other than the basic organization of concepts. That is, if the Function condition had shown lower (i.e. more central) rankings of the properties in the unfamiliar condition, then it may have been argued that the association between the Function condition and centrality was due to factors other than the way humans' concepts are organized. For example, it may have been claimed that the stories were such that they unnaturally led subjects to organize the properties in a causal/functional way. However, since the directionality of the relation was such that the Function condition does even better for the familiar objects, this possibility can be discounted.

The results suggest that the centrality/typicality dissociation effect is primarily due to an organization of information in terms of causal/functional priority. Properties which are more causally/functionally significant to objects are more central to peoples' concepts of those objects. It is important to note, however, that the other two conditions were not bad as predictors of centrality, indicating that these two factors influence centrality as well. Furthermore, as expected from the large numbers of successful probabilistic models of categorization, typicality was a good predictor of centrality.

The findings of Experiment 1 are congruent with the position that objects can be organized into categories of similar functions (e.g., Nelson, 1974). However, the findings of Experiment 1 go beyond this claim, arguing that, even for objects with no obvious function (e.g., natural kinds), causal theories can shape category structure. Further research is necessary to investigate whether the role of causal theories is as important in other kinds of object categories with no clear function such as nominal kinds (e.g., uncle, two, island).

The results suggest that there is more to category structure than would be predicted by the probabilistic structure of the environment. However, it may be that there are higher level probabilistic structures which are the source of the causal theories. That is, if causal theories are themselves determined by probabilistic features of the environment, then, although indirectly, concept structure is actually purely determined by probabilistic features.

While the structure of causal theories for objects has not been studied in detail, the structure of causal theories for events has been the subject of many psychological investigations. We present a brief review of this literature with two goals in mind. First, we wish to establish that peoples’ causal theories are not based upon simple probabilistic models of the environment. Second, we wish to demonstrate that event categories are structured by causal theories, as were object categories. Having achieved these two goals, we will then have established that concept structure, at least for event concepts, cannot be entirely determined by probabilistic features, either directly or indirectly–true causal theories must play a role.

 

Causal Attribution In Events

What exactly is causality in events, and how do humans perceive it? Most philosophers who have ever thought about the nature of scientific explanation or the way humans see the world have had an opinion on the role of causality in these problems. Here we have chosen to contrast the views of Hume and Kant as they clearly represent (and antedate) each side of the probabilistic/theoretical debate. Hume (1739/1960) argued that although causality is not directly verifiable by empirical means, humans can perceive causal relations when certain conditions are present. Hume suggested that humans make use of certain regularities in the world as indicators of causal relationships.

Psychologists have investigated these regularities and found evidence that people do, in fact, use them. Hume's regularities (and the psychological research that supports them) are 1) the temporal priority cue which specifies that an effect will not be attributed to a cause that began after the effect (Shultz & Mendelson, 1975; Kun, 1978; Bullock & Gelman, 1979; Shultz, Altmann & Asselin, 1986); 2) the temporal contiguity cue which specifies that an effect is attributed to a cause with which it overlaps in time (Mendelson & Shultz, 1976; Siegler & Liebert, 1974); 3) the spatial contiguity cue which specifies that an effect is attributed to a cause that makes spatial contact with the effect (Bullock, Gelman & Baillargeon, 1982) 4) the covariation cue which specifies that an effect is attributed to the cause with which it covaries most consistently (Shultz & Mendelson, 1975); and 5) the similarity cue which specifies that an effect is attributed to a particular cause when they are structurally similar to one another (Shultz & Ravinsky, 1977). The psychological evidence for the use of such cues in causal inference is significant, supporting Hume's argument that they are crucial to our understanding of events.

In contrast, Kant (1781/1921) argued that there is more to the attribution of causation than these five cues and proposed that people can obtain direct knowledge about how one event produces another. More recent work (e.g., Bunge, 1979; Harre & Madden, 1975) has adopted and extended Kant's generative approach arguing that some sort of transmission between materials and events must be observed to occur to produce or change the other -- the cause generates the effect. For example, a heavy falling object transmits force to the object that it breaks or a fire transmits heat to the object it burns. Thus, generative principles based on this kind of knowledge allow people to make attributions about the causality of events beyond and perhaps even in disagreement with Hume's criteria. Kant claimed that we are equipped with an innate understanding of causation which allows us to make causal attributions as we do.

Psychologists have found considerable evidence for the use of generative explanations in causal attribution (see Shultz & Kestenbaum, 1985 for a review). For example, in one experiment, Shultz (1982) presented children with a lit candle and two electric blowers to either side of the candle. A three-sided piece of Plexiglas shielded the candle from the blowers. One blower was turned on (see figure 4a). Five seconds later, the second blower was turned on, and the shield was turned so that the opening faced the first blower (see figure 4b). The children attributed the cause of the candle going out to the first blower even though the onset of the second blower was temporally more contiguous, indicating that children were able to use knowledge beyond the basic Humean cues. Moreover, Shultz replicated these results with children in the West African bush suggesting that the results were not due to familiarity with the particular items used in the experiment. These results support the view that children have a causal model which overrides the Humean cues that are simultaneously available.

Figure 4. A diagram of the blower apparatus used by Shultz (1982).

 

Anderson (1990) described an experiment in which there were two distinct causal models that can account for the same effect. The effect was a latch opening on the top of a box and a ball rising from the resulting opening. Subjects in the experiment saw one of two different alternative events preceding the effect: a ball being dropped in a different hole of the box, or a weight being dropped on the box. In the first case, the experimental setup promoted a projectile model (see figure 5). In the second case, the setup promoted a vibratory wave model (see figure 6). The experiment also varied the delay time between cause and effect. For the projectile model condition, subjects thought the dropped ball was the more likely cause of the effect when the two events were separated by an appropriate period of time for the ball to cover the necessary distance (from one hole to the other inside the box). On the other hand, for the vibratory wave model condition, subjects thought the weight was a more likely cause when both events were as close in time as possible. Thus, Anderson argues, only the vibratory wave model induced subjects to use the temporal contiguity cue. Separate causal models corresponding to the different modes of causal transmission put varying emphasis on the Humean cues.

 

Figure 5. A simplified version of the projectile model display from Anderson (1990).

 

Figure 6. A simplified version of the wave model display from Anderson (1990).

 

While it does seem to be the case that cues are emphasized differently within each causal model, there are also circumstances where, for a given causal model, a cue which the model emphasizes is in conflict with other causal knowledge. For example while the model of transmission of wind from the blower to the candle surely emphasizes temporal contiguity, it seems that the blocking of the second blower was a much more important factor (Shultz 1982). As a consequence of these and subsequent findings, Shultz and Kestenbaum (1985) argue that the constraints imposed by theories of causal transmission are much stronger than Humean cues in determining causal attribution. Thus, returning to the probabilistic cues vs. causal theories debate, we see that while both probabilistic cues and causal theories of the world shape our interpretation of causation in events, it is truly causal theories that underlie the process.

Putting the results of our studies on the categorization of objects together with the findings on the structure of causal attribution for events, it seems likely that the causal theories that shape object category structure are truly theories, and not simple derivatives of probabilistic features of the environment. However, this line of reasoning is dependent upon an important untested assumption–that events and objects are similarly structured. That is, we do not have direct evidence for the structure of causal theories for objects, nor do we have direct evidence for the structure of event categories. It is unclear whether these causal theories are used in the structuring of event categories. For example, while people may use causal theories to understand how a thunderstorm works, it is unclear whether they use these causal theories to decide whether an event is a thunderstorm. To address this issue, we conducted a set of studies on the category structure of events.

 

Categorization Of Events

Our research has addressed the category structure of objects. However, it is unclear whether other kinds of categories are structured by similar factors. That is, is the role of domain-level causal/functional theories unique to object categories? The investigation of event category structure is also an opportunity to assess the generality of the objects category structure findings.

If event categories are structured by domain-level theories, what is the form of these domain-level theories? Moreover, the role of causal theories become less clear in more complex and socially-defined events (e.g., a birthday party). In these cases, typicality or social convention may be the only factors determining category structure. To investigate what drives property centrality in events, a set of studies and analyses similar to those conducted for objects were conducted for events.

A range of event types were used. They were grouped into four types (formal, physical, informal short, and informal long), reflecting commonsense expectations about how different degrees of definitional components, social convention, or simple physical causality might effect how the events are structured. For example, one might expect that physical events, like thunderstorms, are more likely to be structured by causal theories than more socially-defined events since the causality is more obvious for such physical events. In contrast, one might expect formal events, like weddings, to be more definitional in nature, since the definitional components (e.g., bride and groom) were obvious. Moreover, one might expect that shorter events would be easier to structure with causal theories, whereas longer events would be simply structured by typicality. Alternatively, if event categories are similar to object categories, then all of the event categories should be primarily structured by typicality and causal/functional domain-level theories.

Experiment 2a

The goal of these studies was to investigate the factors underlying adults’ perception of event properties. The first step was therefore to generate a set of independently derived properties with which to compare probabilistic and theory-based explanations of concept structure. Unlike Experiment 1, all of the event categories were familiar. Subjects were simply asked to generate properties for each of the event categories.

Method

Subjects. Eight Carnegie Mellon University undergraduate students participated in individual sessions for course credit.

Procedure. Sixteen events were used. The events were grouped into four event types, with four events per event type (see Table 6). Each event had its properties generated by all eight subjects. They were given the following instructions: "This is a simple study to find out the properties and attributes that people feel are common to and characteristic of different kinds of ordinary everyday events. There are a number common events on the following pages. Write as many properties as you can think of for each of them. Try to generate at least ten properties for each. Spend about 2 minutes on each event." Subjects were given no additional information about the objects.

Table 6. Events used as stimuli in Experiment 2.

Event type

Events

Formal

birthday party, birth, election, wedding

Physical

car accident, haircut, cold, thunderstorm

Informal short

making coffee, using a MAC machine, making photocopies, a phone call

Informal long

breakfast at a diner, getting dressed to go out, shopping, taking a final exam

Note. MAC is the local term for an Automated Teller Machine (ATM).

Results

From the data, a set of properties was selected for each event to be used for the subsequent experiments. For each event, all properties that were generated by at least 50% of the subjects were selected. Consequently, each event has a different number of properties, ranging from 6 properties to 10 properties. The event types did not differ significantly in number of properties per event. Table 7 presents the set of properties selected for some of the events (Appendix B presents the complete set).

 

Table 7. Examples of the frequently-generated properties.

Event

Features

Birthday Party

cake, presents, friends, candles, singing, games, party hats

Car accident

damage to car, upset people, noise, insurance co., broken glass, police, ambulance, injured people

Making coffee

water, coffee aroma, coffee maker, filter, mug, morning, milk, coffee beans, grinder

Breakfast at a diner

bill, eat, waitresses, coffee, eggs or omelet, toast

 

Discussion

As with Experiment 1a, it is possible that this procedure for generating properties did not generate the most central properties for all of the events. For example, subjects did not mention the birthday boy/girl as a property for birthday parties. However, the purpose of this experiment was to generate features that subjects typically considered as part of the events in question. Therefore, it was necessary to have the subjects, rather than the experimenter, choose the features. Furthermore, it was not necessarily important to select the most central properties. As long as the features ranged in centrality, the role of the domain-level theories in category structure could be tested.

Experiment 2b

Once a set of properties was determined for each event (i.e., those that were most frequently mentioned by subjects), a separate group of subjects was used to obtain a measure of the centrality of each property to the event in question. That is, subjects were asked to evaluate the importance of each of the properties to the category. To obtain centrality judgments for each property, the same procedure was used as in Experiment 1b. That is, the properties were simply negated.

Method

Subjects. Twelve Carnegie Mellon University undergraduate students participated in individual sessions for course credit.

Procedure. Subjects were asked to imagine a new event with all the same properties except one. For example, subjects were asked "Suppose you could change just one property of a thunderstorm so that you didn't get wet. How good an example of a thunderstorm would it be? That is, how good or bad would it then be as an example of its category? How different a kind of thing is it from thunderstorms? How much does removing this property change your concept of it?" They made their judgment using a 7-point scale ranging from "very good example of the category" to "very bad example of the category". Subjects rated all sixteen events in random order.

Results and Discussion

As was done for object centrality ratings, event centrality ratings for each subject were converted to z-scores. The centrality measure for each property was the negation of the mean z-score. The centrality measure of the features ranged from 1.3 to -1.2. Table 8 presents the two most central features for a subset of the objects (Appendix B presents the complete set).

 

Table 8. Examples of the two most central object features.

Object

Features

Birthday Party

friends, cake

Car accident

noise, upset people

Making coffee

water, coffee beans

Breakfast at a diner

eat, eggs or omelet

 

Experiment 2b established which properties are consistently considered more important to each of the categories. It is possible, however, that the property centrality effect found for events is simply a consequence of property typicality. No typicality/centrality dissociation was established in Experiment 2b, since typicality had not yet been measured. Experiment 2c was conducted to measure the typicality of the event properties.

Experiment 2c

Can typicality account for our measure of centrality? There were two main goals of Experiment 2c. First, there was a goal to test whether the measure of centrality developed in Experiment 2b dissociates from typicality. Second, there was a goal to develop a good measure of typicality against which the independent effects of domain-level theories could be tested. To test the effects of typicality, two measures of property frequency were developed, similar to those used in Experiment 1c. As with objects, it was felt that frequency of mention is a poor measure of typicality for event properties. Instead, direct ratings of feature frequencies were used.

Methods

Subjects. Twelve Carnegie Mellon University undergraduate students participated in group sessions for course credit.

Procedure. The same two conditions were used as in Experiment 1c, corresponding to the two kinds of typicality measures. In the All condition, subjects were asked to rate for each feature what proportion of all events of that type had that feature. For example, subjects were asked to "indicate what proportion of all birthday parties have cake". In the Seen condition, subjects were asked to rate for each feature what proportion of events of that type that they had seen had that feature. For example, subjects were asked to "indicate what proportion of birthday parties that you have seen had cake". Subjects in both conditions made their judgment using a 7 point scale ranging from "none" to "all".

Six subjects were randomly assigned to each condition. Each subject rated all sixteen events using one of the two criteria. The events were presented in a random order for each subject.

Results and Discussion

As with objects, the two property frequency measures for events correlated highly with one another (r=.87, n=118). Furthermore, the two measures of frequency correlated with centrality, and the Definition, Recognition, and Function measures developed in Experiment 2d, in similar ways. Therefore, the two measures were collapsed into one property frequency measure, called Frequency.

Frequency proved to be fairly predictive of Centrality (r=.70). To investigate how well Frequency predicted the most central properties, we tabulated the overlap between the two most central properties and the two most typical properties (see table 9). Half of the most central properties were not the most frequently present property, and half of the most frequent properties were not the most central properties. Furthermore, 31% (5 of 16) of the most frequent properties were neither the most central nor the second-most central properties. Therefore, it is likely that frequency is not the only factor determining which properties are most central.

Table 9. Contingency between property frequency and property centrality for events.

 

Frequency

Centrality

First

Second

Rest

First

8

4

4

Second

3

6

7

Rest

5

6

75

 

 

The goal of Experiment 2c was twofold: 1) to develop a good measure of typicality for events; and 2) to determine whether property centrality dissociates from property typicality for events as it does for objects. While Frequency was fairly predictive of centrality, there was some indication of a typicality/centrality dissociation. Also, given the high intercorrelations of the two frequency measures and the strong correlations with centrality, it is likely that we have found a reliable measure of typicality. Furthermore, given the strong correlation with centrality, this combined Frequency measure provides a strong benchmark against which other potential determinants of centrality can be measured.

Experiment 2d

What sorts of factors lead subjects to select the properties they did as most central? The goal of Experiment 2d is to address this question. As with objects, there are three commonly raised alternative explanations for event feature centrality ratings. Features considered most central may simply be those that would be most important for identifying the event in everyday sorts of encounters with it (as is suggested by the findings of Experiment 2c). A second explanation might be that people believe the most "taxonomically" relevant (i.e. if an expert were attempting to categorize the event) are the most central properties. A third possibility is that certain properties are more central as a consequence of their direct role in the causation of the event. That is, humans organize information according to causal theories and, as a result, properties which are causally more important are evaluated as being more central to the event.

To test these three hypotheses, three conditions were developed, similar to Experiment 1d. That is, subjects in the three conditions were asked to rank the properties given an explicit criterion corresponding to each possible explanation. However, the exact description of the criteria had to be altered slightly to fit the nature of events. As with Experiment 1d, properties found to be central to the category should consistently appear at the top of the ranking for that condition which best accounts for the centrality ratings. Furthermore, each of the conditions can be tested for independent contributions by regressing the ranking scores against centrality scores.

Method

Subjects. Twenty-four Carnegie Mellon University undergraduate students took part in group sessions for course credit.

Procedure. Subjects were asked to rank the properties for the sixteen events. The sixteen objects were presented in random order and the properties were randomized for each.

There were three conditions with eight subjects randomly assigned to each condition. The three conditions differed only in the instructions given for ranking the properties. In the first condition, subjects were instructed to rank order the properties in terms of their importance to recognizing what kind of thing the event is. This was the Recognition condition. The instructions were as follows: "For each event, rank order the statements below it by considering which of the stated properties would be more important if you were trying to determine whether a specific situation belonged to that category of events. For example, you see a situation and you are trying to determine whether or not it is a car accident. Which properties are most important for you to distinguish it from other similar types of events?"

In the second condition, subjects were asked to rank the properties according to their relevance for a scientist or expert trying to categorize the event. This was termed the Definition condition. The instructions were as follows: "For each event rank order the statements below it by considering which of the stated properties would be more important for a scientist or expert who was trying to determine what it was. For example, an expert is observing a situation and is trying to determine whether or not it is a car accident. Which properties are most important for an expert to know that it is that type of event? Rank order the properties given in terms of how important they would be for an expert trying to correctly classify the event."

In the third condition, subjects were asked to order the properties in terms of their causal role in the functional success of the event. This was termed the Function condition. The instructions were as follows: "For each event, rank order the statements below it by considering which of the stated properties would be more important for the event to occur. For example, if it is a car accident, which properties are most important for it to occur? Rank order the properties given in terms of how important they would be for the event to happen." A fairly general form of the instructions was taken such that it would apply equally well to all the events, and such that the subjects were not biased towards a particular causal interpretation.

Results and Discussion

Aggregate correlational analyses. To assess the overall predictiveness for centrality of the three ranking conditions, we regressed mean centrality rating for each property against the mean item rankings in each of the three ranking conditions: Definition, Recognition, and Function. Simple linear regressions were used for all of the analyses since there were almost no obvious non-linearities. The two non-linearities that were found (between Function and Centrality, and between Frequency and Centrality) were very small, and occurred only at the very low end of the Centrality scale.

All three ranking conditions were significantly associated with Centrality (r=.38, r=.48, and r=.59 respectively, p's<.0001). As with objects, Function had the highest correlation with Centrality of the three ranking conditions. Furthermore, with Frequency partialled out, Function continued to have the highest partial correlation with Centrality (r=.25, r=.34, and r=.46 respectively, p's<.001).

Since Definition and Recognition scores were strongly correlated with Function scores (r=.84 and r=.87 respectively), it may be that the associations between Definition and Recognition with Centrality are mediated by the strong correlations with Function. To test whether Definition and Recognition had independent predictiveness of Centrality independent of Function, the Definition and Recognition scores were regressed against Centrality in two different ways: once with the effects of Function partialled out, and once with the effects of both Function and Frequency partialled out. With either Function alone or both Frequency and Function partialled out, Definition and Recognition had small negative partial correlations with Centrality. Therefore, it seems that Definition and Recognition do not have independent predictive value for Centrality.

An alternative explanation for the greater predictive value of Function and Frequency over Definition and Recognition is that subjects found our instructions for the Definition and Recognition questions more confusing than the instructions for the Function and Frequency conditions, and the greater amount of noise in the Definition and Recognition measures reduced their predictive value. However, the mean subject intercorrelation within each of the conditions did not differ significantly (F(3,116)=1.76, p>.15), with the mean subject intercorrelation for each of the conditions varying from r=.48 to r=.54, suggesting that subjects found the instructions for all of the conditions equally informative/confusing.

Event kind correlational analyses. We also wanted to assess whether this pattern occurred for all of the events individually, or whether the overall pattern was an artifact of averaging across very different patterns. That is, it may have been that Definition was the best predictor of Centrality for some events, Recognition was the best predictor of Centrality for other events, and only because Function was the second best predictor in all cases did Function become the best predictor overall. It was not possible to accurately parcel out which factors were independent predictors for each event since there were too few data points and high colinearity among the potential factors. Instead the analyses were conducted separately on the four event types: Physical, Formal, Informal/Short, and Informal/Long.

In three of the four cases, Frequency and Function were the only significant independent predictors of Centrality (p’s<.01, except for Function in the Informal/Long case, p<.05). In the case of Formal events (e.g., weddings or elections), while Frequency again proved to be an important predictor of Centrality (p<.01), it was not possible to determine whether Function, Recognition, or both were additional independent predictors because of strong colinearity problems (r=.93). In sum, Function and Frequency tended to be the best predictors both overall and within each of the event types (see table 10).

Table 10. Independent predictors of centrality for each event type.

Event type

Independent predictors of centrality

Physical

Frequency (.8), Function (.74)

Formal

Frequency (.69), Function (.54) / Recognition (.53)

Informal/Short

Frequency (.69), Function (.59)

Informal/Long

Frequency (.66), Function (.46)

Note. Overall correlations with centrality are presented in brackets.

 

Most-central property analyses. From the preceding analyses, Frequency and Function were often the only independent predictors of Centrality. However, it was unclear whether Function was an important predictor of the most central properties. That is, it may be that the most central properties were solely predicted by other factors, and Function predicts the ordering of the less central properties. While, in previous analyses (see table 9), it was determined that Frequency was not the determinant of the most central property, the other ranking conditions may be good predictors of the most central property.

To test which of the three ranking conditions best predicted the most central property, a 3 (Condition) x 4 (Event Type) ANOVA was computed on the ranking data for the most central property of each event. The main effect of condition was significant (F(2,21)=6.3, p<.008). Figure 7 presents the mean rank of the most central property in each condition. Post-hoc tests revealed that the ranks were significantly lower in the Function condition than either the Definition or Recognition conditions (Bonferroni/Dunn t(21)=3.52, p<.002, and t(21)=2.08, p<.05 respectively).

Figure 7. The mean rank (and standard error) in each condition of the most central properties of events.

The interaction of condition with event type (F(30,315)<1) was not significant. Figure 8, which presents the mean rank in each condition for each event type, reveals that the function condition is the best predictor of the most central property of all four event types. When the means for each of the particular events were examined, it was found that for 12 of the 16 events the Function condition was most predictive (lowest mean rank) of the most central property, whereas the Recognition and Definition condition were each most predictive in only two cases (although not significantly better than Function in any of these four cases).

 

Figure 8. Mean rank of the most central properties for each event type.

 

General Discussion

The goal of Experiment 2d was to determine what factors predict property centrality for events. As with objects, four potential predictors were contrasted: Frequency, Definition, Recognition, and Function. Overall, Frequency and Function proved to be the best predictors of property centrality. These relationships held within each of the event types as well. Thus, as was found with objects, what makes a property central to an event concept is partially dependent upon its functional role within that concept.

Comparing the results of Experiments 1 and 2, it was generally true that the Function condition played a stronger and more consistent predictive role for events than for objects. Similarly, Frequency played a more consistently predictive role for events than for objects, whereas Recognition was a more consistent predictor for objects. Thus, while there are some important similarities between the structure of events and objects, there are also some general differences. It is, of course, possible that these differences were due to sampling more broadly from object category types than event category types. However, it is difficult to objectively compare the breadth of categories chosen across these two very different classes of categories. Future research will determine whether these findings will prove to be general to all classes of events and objects.

Several non-probabilistic factors have been found to play an important role in our mental representations of object and event categories. This is supported by the finding that a number of theory-level factors (most often causal/functional factors) were independent predictors of centrality over and above the effects of typicality, and by the finding that properties considered most central tend to be those that are most causally /functionally significant to the category.

Furthermore, it has been demonstrated that the causal theories which constrain the relevant properties of the concepts we already have are also critically involved when new concepts are formed. This was supported by the strong predictiveness for centrality of the Function condition (where properties were ranked according to causal/functional criteria) for both familiar and unfamiliar categories.

These studies show that the centrality of particular properties is not purely a consequence of the frequency-based features of the environment. It is a consequence of several other factors, especially the way humans see the properties in relation to the causal powers of the category members. Furthermore, as demonstrated by earlier work on causal attribution for events, this causal attribution is based upon true causal theories rather than just probabilistic cues to causality–at least for event categories.

In some cases, it was found that the definition and recognition factors were also independent predictors of category structure. Further research is required to determine precisely the conditions under which the various factors play a role in categorization, and whether there are any interactions among these factors. It is possible that these other factors will play larger roles for properties and categories for which no strong causal theories exist (e.g., the category of superstitious beliefs).

In this research, we have assumed a context-independent definition of categories. That is, it is assumed that categories exist independent of the current context, and their structure is consistent across contexts. However, we acknowledge the existence of context-dependent effects on category structure, and we do not see the research on context-dependent effects as being inconsistent with our findings. For example, Barsalou (1982) has shown that context can affect the salience of properties, and Roth and Shoben (1983) have shown that context can also affect the concept definition. Typically, these demonstrations of the biasing affects of context involve highlighting the functional properties of the object for the functional needs of the particular context. Thus, it is likely that the context-dependent factors of categories are driven to an even greater extent by causal/functional theories.

Methodologically, the studies presented here do not represent the final word on these issues. The task of determining the structure of categories is a difficult one, and must be approached from multiple methodologies. The research presented here relied on many measures which could have been reasonably constructed in several other ways, none of which are perfect measures. For example, in our studies, only commonly generated features were used, and centrality judgments were obtained using a property negation counterfactual. Both of these methodological choices are open to various criticisms. However, these methodologies were deemed the best first step. Further research using other methodologies should be conducted to assess the generalizability of our findings.

On a related point, it is unclear that we have chosen the best characterization of typicality. It is not that our measure of typicality is in doubt–the two measures of typicality used in both experiments produced very self-consistent results. Rather, it is the way in which this measure was used that is potentially problematic. In our analyses, we tested the simple linear regressions of typicality against centrality. It may be that there are much stronger higher-order relations between typicality and centrality that were not properly assessed by the regression analyses. For example, it may be statistical patterns of properties relative to immediate superordinates that determine centrality rather than overall frequency that determine centrality. This possibility is much more difficult to test, since the set of possible statistical relationships is infinite. Furthermore, since true causal relations underlie these higher-order statistical relationships, it is unclear whether typicality is always separable from causal/functional factors.

There are two further methodological issues worth noting. First, the results of the experiments reported in this paper were not based on large numbers of subjects–between eight and sixteen subjects per condition were used throughout. N's of this size would have been problematic if we had not found statistically significant results. However, the presence of consistent and statistically significant patterns of data suggest that 1) our N’s allowed statistical tests of sufficient power; and 2) the effects found are quite robust. Moreover, while some of the experiments did not involve large subject numbers, subjects were typically asked to generate ratings for multiple stimuli–twelve objects in the first set of experiments and sixteen events in the second set of experiments. Thus, the repeated measures design of these studies contributed to their statistical power. Finally, the fact that consistent results were found across the two sets of experiments involving different sets of subjects suggests that the results are not attributable to cognitive processes idiosyncratic to a set of unrepresentative subjects.

The second additional methodological issue turns on the use of essentially correlational methods in our experimental analyses. Although some of our experiments involved experimental manipulations, all of our statistical analyses were correlational in nature. As a result, the correlations between property centrality ratings and property causal/functional rankings have multiple interpretations: 1) centrality is determined by causal/functional theories (as we have argued); 2) causal/functional theories are determined by centrality; or 3) centrality and causal/functional theories do not influence each other, and are determined by some third factor. The second possibility, although very interesting if it were true, seems quite implausible: it is completely unclear how centrality could have such a large impact on causal theories, especially for novel objects. The fact that the correlations between centrality and causal/functional rankings held up even when the other factors (i.e., frequency of occurrence, frequency of mention, definitional rankings, recognitional rankings) were partialled out suggests that the third factor explanation is also unlikely. Moreover, the literature on causal attribution for events supports the view that causal theories for events are not a simple consequence of probabilistic features of the environment (e.g., property frequency). Thus, although correlational analyses were used, the relationship found between property centrality and causal/functional relevance does not seem to allow alternative causal interpretation.

In this paper, we have investigated several potential determinants of category structure. We have found that, in general, beliefs about the causal/functional relevance of a property to a category plays an important role in category structure. Furthermore, we have found that other factors also play a role, albeit a weaker one, in category structure. For example, the property’s frequency of association with a category, the value of the property for recognizing a member of the category, and the role of the property in conventional definitions of the category all have been found to play a role in the structure of some categories. Our results also make some preliminary suggestions for which category types the various factors play a role. Consequently, our results provide a more detailed account for the centrality /typicality dissociations previously reported in the literature (e.g., Medin & Shoben, 1988; Murphy & Medin, 1985). Finally, the work presented here has extended our understanding of the commonalties underlying the representations of object and event categories. What remains is to see how these commonalties might extend to other category types.

References

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Medin, D. L., Wattenmaker, W. D., & Hampson, S. (1987). Family resemblance, concept cohesiveness, and category construction. Cognitive Psychology, 19, 242-279.

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Appendix A

Properties and their Centrality Ratings for the Four Types of Objects

Table A1. Properties and their Centrality Ratings for Each Unfamiliar Biological Kind.

Centrality

Property

 

MILKWEED BUGS

+1.269*

Milkweed bugs' poison sickens predators, so that predators will often vomit after eating them and avoid eating them thereafter.

+1.097*

Milkweed bugs color markings serve as survival mechanisms in that they warn predators that they are poisonous.

+0.147

Milkweed bugs feed by sucking food through a straw-like beak.

+0.062

Milkweed bugs drink a lot of water from dew and sap in order to soften food before they can suck it up with their beaks.

-0.365

The milkweed bugs' ovaries develop fully only in the presence of males and, in fact, they only achieve full development after mating.

-0.643

There are two types of milkweed bugs: large and small.

-0.695

Frequent mating shortens life span for both male and female milkweed bugs, so that virgins live almost twice as long as non-virgins.

-0.873

Milkweed bugs' mating lasts from under an hour up to 10 hours in order to achieve maximum egg production.

  

FLEAS

+0.598*

Fleas are very good at finding a host animal quickly.

+0.526*

Most fleas have combs around their heads that enable them to stay attached to their prey.

+0.47

Fleas have flattened hard bodies.

+0.192

When stimulated, some species of fleas can jump once every second for 3 days.

-0.062

Fleas have resilin, an elastic material, in their back legs.

-0.17

A flea can jump as high as 8 inches and as far as 13 inches.

-0.362

Some fleas can survive as long as a year without feeding on blood.

-1.192

The male flea has a coiled penis that is half as long as its body.

 

TOBACCO HORNWORMS

+1.234*

The nicotine in the tobacco plants is poisonous to most organisms, but passes through the tobacco hornworm harmlessly.

+0.537*

Some species of tobacco hornworm eat tomato plants and other species eat tobacco plants.

+0.111

Tobacco hornworms are a major crop pest.

-0.16

During the last molting before the pupal stage, tobacco hornworms are bigger and eat much more so that they are difficult to detect until then.

-0.334

Tobacco hornworms choose what they eat by taste, but they will feed on other things if their 'tasters' are removed.

-0.337

Tobacco hornworms are green with patterns of pale lines.

-0.518

Tobacco hornworms never form a cocoon during their development.

-0.533

Tobacco hornworms are blue from the color of their bile, but they acquire yellow pigment from the plants they eat, so that together the two pigments make them green.

Note. * two most central properties for each object.

 

Table A2. Properties and their Centrality Ratings for Each Unfamiliar Artifact.

Centrality

Property

 

ROUTERS

+0.61*

Routers are very versatile tools.

+0.522*

The shape of the bit determines the shape of the cut made into the wood.

+0.497

Routers can be used to cut fancy edges.

+0.283

The router's motor can be raised or lowered to adjust depth of cut.

+0.279

There are many different size bits available for routers.

-0.918

The routers' power is typically 2 hp to 3 hp.

-1.271

Routers have toggle or trigger on/off switches.

 

GOVERNORS

+0.792*

When speed increases, the balls fly out, and fuel supply is decreased.

+0.718*

A governor is a device for maintaining the speed of a machine relatively constant.

+0.041

Governors depend on centrifugal force.

-0.11

Governors have a pair of rotating masses.

-0.236

Governors are very sensitive to small changes in speed.

-0.556

Governors regulate speed by regulating fuel supply.

-0.648

Governors are typically used for controlling engines and turbines.

 

BLAST FURNACES

+0.923*

Gravity feed is used to keep raw materials flowing from the top to the bottom.

+0.71*

Preheated air is blasted into the blast furnace.

+0.306

Blast furnaces have tuyeres which are water cooled pipes.

+0.147

Blast furnaces are tapered toward the top.

-0.297

The shaft of the blast furnace is brick-lined.

-0.504

Coke has replaced charcoal as fuel in blast furnaces.

-1.284

The term "furnace" is derived from the Latin fornax.

Note. * two most central properties for each object.

 

Table A3. Properties and their Centrality Ratings for Each Familiar Biological Kind.

Centrality

Property

 

CATS

+0.778*

Cats have fur.

+0.547*

Cats have four legs.

+0.14

Cats meow.

-0.116

Cats purr.

-0.497

Cats have tails.

-0.851

Cats have claws.

 

PIGEONS

+0.628*

Pigeons have wings.

+0.612*

Pigeons have feathers.

+0.392

Pigeons fly.

-0.429

Pigeons are gray.

-0.555

Pigeons coo.

-0.648

Pigeons live in big cities.

 

MICE

+0.545*

Mice are furry.

+0.479*

Mice are small.

+0.077

Mice move very fast.

+0.019

Mice are food for other animals such as cats and birds of prey.

-0.507

Mice have long tails.

-0.613

Mice are dirty and smelly.

Note. * two most central properties for each object.

 

Table A4. Properties and their Centrality Ratings for Each Familiar Artifact.

Centrality

Property

 

CARS

+0.622*

Cars have engines.

+0.606*

Cars have seats.

+0.155

Cars have four wheels.

-0.022

Cars have steering wheels.

-0.597

Cars use fuel.

-0.764

Cars are expensive.

 

TOILETS

+0.84*

Toilets remove waste.

+0.273*

Toilets have seats.

+0.224

Toilets flush.

+0.206

Toilets have water.

-0.618

Toilets have a handle.

-0.925

Toilets are typically white.

 

POWER LAWN MOWERS

+0.636*

Power lawn mowers have a blade.

+0.407*

Power lawn mowers have a handle.

+0.396

Power lawn mowers have wheels.

-0.169

Power lawn mowers use gas or electricity.

-0.433

Power lawn mowers are loud.

-0.786

Power lawn mowers are dangerous.

Note. * two most central properties for each object.

 

Appendix B

Properties and their Centrality Ratings of Each of the Four Types of Events

 

Table B1. Properties and their Centrality Ratings for Each Formal Event.

Centrality

Property

 

Centrality

Property

 

BIRTHDAY PARTY

 

 

ELECTION

1.026*

friends

 

.875*

booths

.010

cake

 

.821

candidates

-.021

presents

 

-.173

republicans

-.062

singing

 

-.512

mudslinging

-.253

candles

 

-.755

democrats

-.716

games

 

-.803

TV ads

-1.057

party hats

 

 

WEDDING

 

BIRTHS

 

1.006*

groom

1.334*

mother

 

.913

bride

1.051

baby

 

.303

relatives

.368

pain

 

.150

rings

.351

crying

 

.078

cake

.308

father

 

.009

priest

-.180

doctor

 

-.093

gifts

-.195

hospital

 

-.426

throw bouquet

 

 

 

-.440

drinking

Note. * most central property for each event.

 

Table B2. Properties and their Centrality Ratings for Each Physical Event.

Centrality

Property

 

Centrality

Property

 

CAR ACCIDENT

 

 

GETTING A HAIRCUT

.841*

noise

 

.919*

scissors

.617

upset people

 

.358

barber

.608

damage to car

 

.255

use comb or brush

.057

insurance co.

 

.180

style hair

.030

police

 

-.582

pay

-.373

broken glass

 

-.741

wash hair

-.434

injured people

 

 

HAVING A COLD

-.763

ambulance

 

.250*

sniffling

 

THUNDERSTORM

 

.208

sore throat

1.147*

thunder

 

-.063

coughing

.666

rain

 

-.109

sneezing

.541

lightning

 

-.155

headache

.263

get wet

 

-.194

medicine

-.634

summertime

 

-.228

trouble sleeping

-.764

electrical problems

 

-.606

fever

 

 

 

-.773

soup

 

 

 

-1.048

aspirin

Note. * most central property for each event.

 

Table B3. Properties and their Centrality Ratings for Each Informal/Short Event.

Centrality

Property

 

Centrality

Property

 

MAKING COFFEE

 

 

A PHONE CALL

.913*

water

 

1.036*

use a phone

.485

coffee beans

 

.960

phone number

.217

coffee aroma

 

.746

talk

.002

coffee maker

 

.106

dial

-.147

filter

 

-.825

busy signal

-.192

mug

 

-1.081

answering machine

-.865

grinder

 

 

USING A MAC MACHINE

-.923

morning

 

1.049*

withdrawals

-1.164

milk

 

.875

add/take money

 

MAKING PHOTOCOPIES

 

.872

use PIN number

1.006*

paper

 

.268

MAC card

.868

photocopier

 

.041

get receipt

-.415

select options

 

-.253

check balance

-.918

change/copy card

 

-.686

bank

-.964

copier problems

 

-.708

beeping noises

-.984

do stapling

 

-.750

make deposit

 

 

 

-1.164

wallet

Note. * most central property for each event.

 

Table B4. Properties and their Centrality Ratings for Each Informal/Long Event.

Centrality

Property

 

Centrality

Property

 

GROCERY SHOPPING

 

 

TAKING A FINAL EXAM

.439*

money

 

.405*

studying

.172

aisles

 

.216

writing

-.077

carts

 

.084

stress

-.197

checkout lines

 

-.285

test booklets

-.202

bags

 

-.408

pencils

-1.076

shopping list

 

-1.006

review sessions

 

BREAKFAST AT A DINER

 

 

GETTING DRESSED TO GO OUT

1.209*

eat

 

.808*

shower

.448

eggs or omelet

 

.748

shoes

.424

bill

 

.671

look in mirror

.326

waitresses

 

.164

socks

.159

coffee

 

.162

fix hair

.054

toast

 

-.316

shave

 

 

 

-.342

tie

 

 

 

-.539

cologne/perfume

 

 

 

-.677

iron clothes

 

 

 

-1.131

coat

Note. * most central property for each event.

 

Appendix C

Two examples of the stories of unfamiliar biological kind and artifact objects

FLEAS

Fleas are only moderately discriminating in their tastes. Each of the about 1,500 species of fleas tends to have a favored host mammal or bird, but will in many cases take advantage of any convenient source of blood. There is the so-called human flea, suitably called Pulex irritans (the Romans thought fleas arose from dust, and the word "pulex" is said to be derived from pulvis, the word for dust). But the human flea is believed to have originally been a pest of pigs. (The human body louse can survive only on people and pigs; do these insects sense some subtle kinship?) People are more often bitten by cat, dog, rat or chicken fleas. But, of course, in our sanitized Western world it is uncommon to be bitten by a flea at all.

Fleas are tough-bodied creatures, as anyone can confirm who has tried to crush one in his fingers. Their bodies are so flattened from side to side that one wonders where there is space for all their internal organs. The compressed body is, of course, marvelously suited for slipping between the hairs or feathers of their hosts in their search for blood. Perhaps the most striking features of the fleas is the presence of rows of thick spines, forming "combs," chiefly on the head and just behind the head. Each species of flea has its own particular arrangement of these combs, evidently depending upon the kind of animal it normally attacks. Often the distance between the comb-spines is closely correlated with the diameter and density of the hairs of the host animal. Fleas that attack bats have especially strong combs, enabling them to cling to their hosts while they are in flight. The porcupine flea is said to have the largest combs of all. But some fleas have no combs, chiefly those that bury themselves in the skin and cannot be easily removed. Scratching, grooming, and preening are the major defenses of mammals and birds against fleas, lice and other parasites, and the combs and claws of these insects play a major role in preventing dislodgement.

The jumping abilities of fleas also invite our admiration. Fleas are reported to be capable of a broad jump of thirteen inches and a high jump of eight inches. Given the size of the flea, this seems incredible, and it is to some extent. However, all insects appear to have prodigious strength, a result of the fact that as any animal increases in size, its weight increases at a far more rapid rate than its size and strength. The numerous short muscles of insects, attached to an external skeleton, also render them capable of seemingly great feats of strength. The hind legs of fleas are unusually large and strongly musculated. Not only do fleas excel at the art of jumping, but they are able to jump repeatedly. An oriental rat flea, if stimulated by the presence of other fleas, will jump an average of once a second for as long as three days! The muscles of the hind legs show little evidence of fatigue, and the leg movements are made much more automatic by the presence of a pocket of resilin at the base of the leg. Resilin in a natural rubber capable of storing and releasing energy by contracting and stretching, producing a rebound somewhat like that of a good rubber ball. When a flea is about to jump, its hind legs are "cocked" by pulling them up so that the major joint is against a ridge on the body. This compresses the resilin. When the leg is suddenly extended, it snaps from the catch and at the same time permits the resilin to expand, providing the extra bounce.

One of the advantages of using energy stored in an elastic structure is that it is relatively independent of temperature. Insects, in general, move slowly when it is cold, but fleas that can move at all can take advantage of the elastic bounce. Bird fleas, for instance, have been seen leaping about on snow in the Alps. Rabbit fleas can be frozen at about 32 degrees Fahrenheit for several months, and when returned to normal temperatures will jump about within a few minutes, prepared to gorge themselves as soon as they can find a source of blood.

Fleas locate a food source by leaping about until they find a cue telling them a host is near. The cue may be a specific odor or an increased concentration of carbon dioxide. Evidently they also respond to vibrations. Fleas occurring in the nests of certain rodents respond to the tread of a man and may actually pursue him for some distance. Since fleas are generally able to live for weeks apart from a host and without food, they can build up a considerable appetite. That is why persons entering houses that have been empty for some time are sometimes bitten voraciously; the former owners of the house had pets, and their fleas have been waiting patiently for the new owners. Some starved fleas have been known to live for over a year.

Fleas are remarkably efficient at finding a host. One researcher released 270 marked rabbit fleas in a meadow of 2,000 square yards, and within a few days nearly half of them had found a rabbit. Another researcher collected 48,996 fleas from 143 ground squirrels, and within three days most of the squirrels had been reinfested with about equal numbers of fleas.

Fleas will bite over and over again if given a chance. Their mouths are supplied with swordlike blades that lacerate the skin. An anticoagulant is pumped into the wound, and the blood is drawn into the digestive tract by a muscular pump. Blood is imbibed rapidly, and much of it passes through the body and dribbles from the anus. This apparently sloppy manner of feeding reflects the fact that the fleas extract certain nutrients that occur in blood only in small quantities, ridding themselves of the surplus, which falls into the nest where the fleas' larvae live. The rather wormlike larvae feed on scraps in the nest, including dribblings from the adult fleas. The adults in a sense "feed their babies" with fecal matter that is mostly blood. Eventually the larvae spin silken cocoons in which they transform into adults. When they emerge they must first jump on to a suitable host animal, where they feed and may ride about for some long time before receiving the appropriate cues that induce mating.

When fleas are "in the mating mood," the males release their short antennae from the grooves in which they are usually held and hold them erect. Then they slip beneath the female and use their antennae to grasp her from below. The sex organs of the male are so complex that for many years no one could figure out exactly how they worked. Some of the details were discovered by quick-freezing copulating fleas and then dissecting them and studying them under high magnification. Among the spines and hooks that serve to grasp the female is a delicate structure looking somewhat like a feather duster. Evidently this serves to titillate the female; or perhaps it serves to detect a subtle odor emanating from her. The penis is a large structure, often half as long as the male's body, but coiled like a watch spring within it. When erected the major part serves as a guide for a shaft that penetrates as far as the female's genital pouch, where it locks in place and itself serves as a guide for a slender, flexible rod that extends to the sperm receptacle, deep inside her abdomen. Here the sperm are discharged, and stored until released to fertilize the eggs as they are laid.

ROUTERS

Of all the portable electric power tools found in a typical woodworking shop, the router is arguably the most versatile. Some of the most common uses include cutting cabinet joints; shaping decorative edges; milling moldings and carving signs and plaques. The router consists of a high-speed electric motor, a base, two handle knobs, and bits (cutting tools). When fitted with anyone of the hundreds of bits available, the router's capacity is almost endless. The motor has a chuck for securing the bit so that it protrudes beyond the base. The depth of the cut made by the bit into the wood is adjusted by raising or lowering the motor in the base. The bottom of the base, a circular plate with a central opening for the bits, provides a flat, low-friction surface for the router to slide on.

Some bits have noncutting pilot pins that extend below the cutting edges and control the sidewise depth of the cut when the router is working on the side of a board. The bits have a straight shank and three or four cutting edges shaped to suit the work being done. The shapes of some of the bits can best be described by considering their silhouettes. For example, to cut a beveled edge on a table, or a V groove, a silhouette of the rotating cutter would have a V shape; to cut a semicircular groove the silhouette would be a semicircle with the diameter perpendicular to the shank; to cut a beaded (rounded) edge on a table the silhouette would be a rectangle with quarter circles cut from the lower corners. The cutter rotates very rapidly, and the base of the machine is constructed so that the cutter can be guided over the work by the operator, who holds the handle knobs. The router is a versatile power tool that in addition to its usefulness in cabinet work can do many ordinary household jobs, such as cutting fancy edges for shelving, grooves for storm windows and weather stripping, circles and ovals with smooth edges, and round corners on work of all types. The electric router and its bench-mounted analog, the spindle shaper, have largely displaced hand routers either pushed like a plane or pulled like a drawknife, formerly used by woodworkers for cutting grooves and shaping edges.

Most routers have a simple toggle ON/OFF switch while others have a more convenient trigger switch. Routers come in various sizes with respect to power and are rated according to chuck capacity and horsepower - typically ranging from 2 hp to 3 hp. Most routers have a 4 inch chuck. Larger routers accept bits with 2 inch in-diameter shanks. For general woodworking, a 1-hp router with a 4 inch chuck is adequate. However, if you're using a router primarily as a shaper in a router table, then consider a 3 hp router with a 2 inch chuck. When changing a router bit, always unplug the tool and - in most cases - remove the base. Some routers come with two wrenches. One is used to hold the motor's shaft from turning and the other wrench loosens or tightens the chuck. Other routers have a convenient shaft-lock button. When depressed, the button keeps the shaft from turning so that only one wrench is needed to remove a bit. After installing a bit, check to be sure it's held securely before starting the router.


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