should be sent to Dedre Gentner, Psychology Department, Northwestern University, 2029 Sheridan Road, Evanston, IL 60208. E-mail: firstname.lastname@example.org
We investigated the understanding of causal systems categories—categories defined by common causal structure rather than by common domain content—among college students. We asked students who were either novices or experts in the physical sciences to sort descriptions of real-world phenomena that varied in their causal structure (e.g., negative feedback vs. causal chain) and in their content domain (e.g., economics vs. biology). Our hypothesis was that there would be a shift from domain-based sorting to causal sorting with increasing expertise in the relevant domains. This prediction was borne out: The novice groups sorted primarily by domain and the expert group sorted by causal category. These results suggest that science training facilitates insight about causal structures.
Our focus here is different. We ask whether and to what extent people possess an abstract understanding of causal structure that allows recognition of common causal structures across disparate domains. For example, does understanding one positive feedback system—say audio feedback in an acoustic system—allow recognition of positive feedback in a different domain, such as a pricing bubble in economics? Or to put it another way, what sort of experience is necessary in order for someone to see these two phenomena as sharing important causal structure?
In this paper, we examine the representation and use of causal system categories, of which positive feedback systems is an example. Causal systems categories are defined by possessing common causal structure, irrespective of the particular domain. For example, the phenomena of population growth, economic bubbles, electronic audio feedback, and melting polar ice caps are all governed by positive feedback: a causal structure in which (for example) an event X positively influences another event Y, which in turn positively influences X, producing a cycle of increasing magnitude of effect in which the output becomes more and more extreme. There may be many more events than just two, but the principle is the same. Another causal category is a causal chain, in which an event X influences Y, which in turn influences Z.
First, given the centrality of causal relations in human cognition, it may be that adults in general have an abstract understanding of causal system commonalities, and that they view multiple phenomena with the same structure as comprising a class. However, a second, equally plausible alternative is that people focus on causal patterns within a given domain and fail to perceive general patterns of causal structure across domains. After all, the causal learning literature shows that even seemingly simple causal structures like causal chains can be quite difficult to learn (Steyvers et al., 2003). Given the complexity of many causal phenomena—such as the feedback structures involved in global warming or diabetes—it could well be that people’s causal reasoning remains chiefly at a domain-specific level.
The third possibility is that people begin with domain-specific causal models, but that with increasing education and experience, people can come to see abstract domain-general causal patterns. This third possibility gains credence from research on conceptual development. There is considerable evidence that relational information is acquired later than concrete featural information. For example, when asked to interpret the comparison “A cloud is like a sponge,” 4–5-year-old children focus on common concrete properties, such as “both are round and fluffy” while adults and older children focus on relational commonalities, such as “both store water and then give it back to you” (Gentner, 1988). In the same vein, when asked to reenact a story with new characters, 6-year-olds rely heavily on perceptual similarities among the characters, whereas 9-year-olds can map the plot structure even to very different characters (Gentner & Toupin, 1986).
In adults, a similar relational shift pattern also occurs with increases in domain knowledge. For example, Shafto and Coley (2003) found that while novices sorted fish by similarity of appearance, commercial fisherman grouped them according to behavioral and causal/ecological relations (see also, Medin et al., 2006; Proffitt, Coley, & Medin, 2000). Chi, Feltovich, and Glaser (1981) found that when expert and novice physics students were asked to sort physics problems, experts sorted the problems according to common principles (e.g., conservation of energy), which define the abstract structure of the problem, whereas novices sorted based on concrete similarities (e.g., problems containing ramps). Likewise, novice chemistry students classify chemical reactions in terms of concrete features of chemical reactions, such as whether a reaction produces water, whereas experts classify reactions by common chemical mechanisms, such as acid–base reactions (Stains & Talanquer, 2008). Analogously, we predicted that a shift from focusing on concrete domain properties to the more abstract causal relational structures would occur in the way people organize causal phenomena.
In the current experiment, we examined five causal system categories (see Fig. 1). The first is a common effect structure, a causal structure in which many factors influence one effect. The level of CO2 in the atmosphere is a product of fossil fuel burning, plant photosynthesis, and CO2 absorption in oceans. Heart disease is caused by genetics, smoking, high blood cholesterol, high blood pressure, and obesity. A common cause structure is one in which a single cause has multiple effects. For example, an allergic reaction can cause multiple effects, including inflammation, rash, asthmatic reactions, and sneezing. Another example, from economics, is that the unemployment rate has causal effects on a number of phenomena, including the crime rate, suicide rate, general health conditions, and GDP.
The third causal structure, defined above, is a positive feedback structure—often described as a “vicious cycle.” In a positive feedback structure, the output is “fed back” in such a way as to magnify the input. This in turn produces a greater output, resulting in a cycle of increasing magnitude of effect. For example, increased global temperatures cause polar ice to melt. Whereas ice reflects sunlight well, water absorbs more sunlight, which means that the earth warms faster. This in turn causes more polar ice to melt. Economic bubbles work in a similar way. People buy stocks or property because they assume the prices will increase. The buying itself causes the prices to increase, which causes yet more buying, and so on. Negative feedback is a causal structure in which the output of the structure is fed back in such a way as to reduce the input. If the input is increased, the resulting output will also increase, and this will act to reduce the subsequent input. This results in a cycle that stabilizes the system. For example, in the domain of biology, humans regulate temperature by perspiring when they are too warm. When the body has cooled enough, it stops perspiring. Similarly, in the domain of economics, the Federal Reserve regulates the economy by raising, lowering, or keeping constant the interest rate. If the economy is slow, the FED will lower interest rates to stimulate borrowing and economic activity. If the economy is growing too fast, the FED will raise interest rates to encourage saving.
The last structure is a causal chain—a structure wherein an event A influences an event B, which in turn influences C, etc. The chain can be of any length; the sequential nature is the chain’s defining characteristic. For example, we can understand the way petroleum prices affect the price of consumer goods as a causal chain: the price of gas affects the price of transportation of goods, which affects the price of goods sold in stores. Another example of a causal chain, from neurobiology, is that synaptic transmission requires a series of steps, including an action potential, release of neurotransmitter, and binding on the postsynaptic neuron.
Our interest here is in whether people organize their knowledge of causal phenomena according to these kinds of causal categories. To investigate this, we set up a design in which people could sort phenomena such as those described above either by domain content or by causal category. We created 25 descriptions of phenomena, organized into a 5 × 5 matrix defined by crossing the five causal categories just described with five content domains: biology, environmental science, economics, electrical engineering, and mechanical engineering (Fig. 1; see online supplement for full stimuli). Then we asked college students to sort the phenomena into categories, as described below. Our questions are (1) whether people will chose to sort by domain or by causal structure; and (2) whether their preferred organization will be influenced by expertise.
The participants were drawn from four populations of Northwestern University students differing in their expertise in physical science. Three groups were students majoring in different social sciences: economics, sociology, and psychology. The fourth group was made up of students majoring in the physical sciences, primarily physics majors and students in the Integrated Science Program. Many of the physical science students, particularly those in the Integrated Science Program, had been trained in multiple sciences. Thus, in addition to broader knowledge of the physical sciences, they had another possible advantage: Their course work in different physical sciences could have encouraged them to compare and abstract across domains.
For our four populations, we have two predictions and an open question. The psychology and sociology students were considered to be novices for purposes of the study, as their expertise does not match any of the five domains of phenomena used in the stimuli. We predicted these students would sort chiefly by content domain. At the other extreme, the physical science students served as the expert group. Because of their training in multiple relevant content domains, we expected that they would sort largely by causal category. The economics majors were chosen because they have experience in one of the content domains used in the study. If expertise in one domain is sufficient to recognize and use cross-domain commonalities in organizing causal phenomena, then the economics majors should show more causal-category sorting than the psychology and sociology majors.
Forty-four undergraduate students from Northwestern University were recruited from four populations: introductory psychology students (12), sociology majors (9), economics majors (11), and physical science students (primarily physics and Integrated Science Program majors) (12). The psychology students participated in exchange for course credit. The other three populations were compensated for their participation.1
1.2. Materials calibration
The 25 phenomena descriptions varied orthogonally on two dimensions, causal system and content domain (see Fig. 1 and Table 1). By the nature of the design, passages coming from the same domain should share more semantic similarities than did those from the same causal system. To confirm this, we use Latent Semantic Analysis (LSA)—a mathematical method for inducing the degree of relatedness between words in a large body of text on the basis of their contextual co-occurrence patterns—to generate pair-wise relatedness scores for the descriptions (Landauer & Kintsch, 2006).
Table 1. Examples of two seed cards, each showing one domain match and one causal systems match
Seed Card: (Environmental Science, Common Effect)
Many processes are responsible for the level of CO2 in the atmosphere such as fossil fuel burning, plant photosynthesis, and CO2 absorption in oceans. When making public policy decisions about environmental issues, we must keep in mind the many complex factors that influence the level of CO2 in the atmosphere.
Same Causal System Match: (Biology, Common Effect)
In the process of global warming, as the temperature of the earth rises, polar ice begins to melt. Water absorbs more heat from sunlight than ice. Consequently, as ice is turned into water, the temperature of the earth begins to rise even faster, which in turn leads to increased ice-melt.
Aside from genetics, the four main factors which increase the risk of heart disease are smoking, high blood cholesterol, high blood pressure, and obesity. Doctors advise people with any one, or a combination of these risk factors to improve their health to mitigate the risk of heart attack.
A thermostat works by measuring temperature and turning on or off a furnace or air conditioner to reach a desired temperature. If the temperature is too cold, the thermostat will turn on the furnace until it becomes warm enough. Likewise, the thermostat on an air conditioner turns on when the house is too warm.
Same-Domain Match: (Elect. Engineering, Common Cause)
Same Causal System Match: (Economics, Negative Feedback)
Internet routers work by distributing a data signal to multiple devices If the router is turned off, then all the computers loose signal. However, the functioning of one individual computer does not affect the functioning of other computers. Thus, if one computer is turned off, all the others still get the data signal from the router.
The Federal Reserve has the ability to raise or lower the interest rates depending on the current state of the economy. If the economy is slow, the FED will lower interest rates to stimulate borrowing and economic activity. Raising interest rates will slow the economy by increasing the cost of borrowing.
For each of the 25 phenomena, we calculated the mean LSA relatedness ratings to other cards within the same domain (M = 0.21, SD = 0.08), within the same causal system category (M = 0.10, SD = 0.04), and with neither of those relations (M = 0.08, SD = 0.02). Pairwise t-tests revealed that pairs of descriptions from the same domain had significantly higher relatedness ratings than pairs that shared the same causal system, t(24) = 5.59, p < .01, and pairs that shared neither t(24) = 7.22, p < .01. Additionally, the within causal system pairs had marginally higher relatedness ratings than the no relation pairs, t(24) = 2.10, p = .05. Thus, as intended, the overall semantic relatedness is high for items from the same domain, but not for items that share causal structure.
Each of the 25 phenomena was printed on a file card, and five cards (the grayed cells in Fig. 1) were designated as “seed cards.” Participants were told that they were to sort descriptions of real-world phenomena into categories that “go together.” On the table before them there were five columns headed by the seed cards, plus one column labeled “Other.” Participants were asked first to read the seed cards, and then to sort the remaining 20 cards into the columns “based on how well the description on the card goes with the initial card” already in the column. They could also place a card into the “Other” column if they did not think it fitted with any of the seed cards.
Because our goal was to pit the two sorting strategies (content domain and causal system) against one another, the seed cards were chosen to be equally applicable to either strategy. Specifically, the five seed cards each differed from one another both in content domain and in causal category. Thus, the columns could be taken to represent five different domains or five different causal systems, or some mixture of the two.
The 20 cards to be sorted were arranged in a semi-random order such that two cards from the same domain were never in immediate sequence, with half the participants receiving the reverse order. There was no time limit; participants were told that they could work with the cards in any order and were allowed to rearrange previously sorted cards.
Each of the 20 cards (one “sorting”) was coded according to whether it matched the seed card in its column by content domain or by causal system. On average, across all groups, 5.75 (SD = 2.61) of the 20 cards either were placed in the “other” column or failed to match their seed card by either domain or causal system. This average was consistent for all four groups and there was no main effect of group in a one-way anova, F(3,44) < 1. Since we were primarily interested in the cards sorted by domain or causal system, these cards were ignored in the following analyses.
Out of the cards that a given participant sorted either by domain or by causal structure, we looked at the percentage that were sorted by causal structure. On average, the physical science students sorted 61% of these cards (SD = 39%) by causal structure. However, for the other two groups, the percentage of cards sorted by causal structure was smaller: M = 34%, SD = 33% for the psychology and sociology students, M = 36%, SD = 33% for the economics students. A t-test did not find a difference between the group of psychology and sociology students versus the economics students, t(30) < 1. Therefore, we considered psychology, sociology, and economics students as a group (social science students) for further analyses. Importantly the physical science students sorted significantly more cards by causal structure than the combined social science group, M = 35%, SD = 32%, t(42) = 2.25, p = .03
To better understand the dominant sorting strategy used by participants of different groups, hierarchical cluster analysis (HCA) was performed based on a pairwise co-occurrence matrix per group (how many times participants sorted each pair of cards together). The HCA used the Euclidean squared distance metric and the between groups linkage agglomeration method. One benefit of the HCA analysis compared to the previous analysis was that the previous analysis only identified whether a card was sorted with a same-domain seed or with a same-causal-system seed. The HCA analysis looks at all of the relationships between the 20 sorted cards, ignoring the seed cards.
For the physical science students, HCA revealed five identifiable clusters of phenomena, closely matching the five causal system categories (Fig. 2; cards with the same letter of the alphabet share the same causal structure category). Three cards were not generally sorted by causal structure. The card E1 (a chain-environmental science card) was generally sorted in the positive feedback group (C), particularly with the card C1 (a positive feedback-environmental science card). Both of these cards were about global warming. Likewise, A4 was sorted with E4, and E2 with A2. Thus, it appears that high domain relatedness may have overridden the dominant strategy of sorting by causal systems. In contrast, the HCA dendrograms for the social science students (Fig. 3; cards with the same number share the same domain), revealed that the social science students sorted primarily by common domain, with the domains of mechanical and electrical engineering somewhat conflated.
To further probe into the basis for students’ sorting decisions, we computed the LSA relatedness scores for the co-sorted cards. The mean LSA score for the co-sorted clusters for the combined social science group (M = .17, SD = .04) was nonsignificantly higher than that of the physical science group (M = .14, SD = .05), t(42) = 1.93, p = .06. It is possible that the social science students relied in part on local semantic connections between terms from the same content domain.
The same patterns of causation occur across different domains. Our question is whether and to what degree people perceive these abstract causal structures. Specifically, we asked whether there are novice-expert differences in the degree to which students perceive the common causal structure underlying different phenomena, as assessed by their sorting behavior in a task that allows sorting either by causal system or by content domain. We predicted that experts (physical science students) would show more causal sorting than novices (psychology and sociology students). This prediction was confirmed: Psychology and sociology students sorted primarily by content domain, and physical science students sorted primarily by causal system. Additionally, we asked whether economics students would pattern with the other social science students or with the physical science students. They behaved as the other social science students did, sorting primarily by content domain. Hierarchical Cluster Analysis provided additional support for the hypothesis: HCA revealed clusters based on the domains for the combined social science group (including economics), and clusters based on causal systems for the physical science students.
Having an abstract understanding of causality, as described here, might confer a number of advantages. Previous research (Steyvers, Tenenbaum, Wagenmakers, & Blum 2003) has found significant individual differences in peoples’ ability to learn causal structures in a bottom-up statistical fashion. It is possible that some of these differences stem from differences in people’s abstract understanding of how different classes of causal structures function (see also Fernbach & Sloman, 2009). Another advantage of having an abstract understanding of causal structures is that it might help people interpret scientific evidence. For example, after learning that two variables are correlated, people with an abstract understanding of how different types of causal structures can produce a correlation between two variables might be more likely to search for a common cause instead of simply concluding that there must be a direct causal relation between the two variables.
Why did the physical science students, but not the social science students, sort causally? The most obvious explanation, as noted in the introduction, rests on differences in domain knowledge—specifically, in differences in the number of domains with which students were familiar. The physical science students typically had training in four of the five relevant domains—mechanical engineering, biology, electrical engineering, and environmental science. In contrast, economics students had training in only one of the domains (economics), and psychology/sociology students in none of them. Domain experience might plausibly lead to a better articulation of general causal patterns within the domain. So perhaps the difference results simply from knowledge of more individual domains.
Another possibility is that social science students could have perceived the causal commonalties, but simply considered the domain-level commonalities more important. After all, reasoning well within a domain is important, and nothing about the task communicated that domain sorting was “wrong.” However, a follow-up study (Goldwater & Gentner, unpublished data) suggests that there were real differences in the perception of causal systems. In this study, social science students were given two opportunities to sort and were asked to use a different strategy for the second. Consistent with the current findings, the majority of the students were domain sorters, but some sorted causally to a fair degree. These better causal sorters went on to sort quite well by domain for their second sort. In contrast, the domain sorters did not adopt a causal strategy for their second sort. This suggests that the ability to perceive domain-level commonalities is widely available, but that perceiving common causal systems is not. While this does not mean that causal sorting is necessarily the “right” answer, it does suggest it is a skill that does not come for free.
What led the physical science students to show greater awareness of causal systems? We speculate that this difference was not simply a matter of greater domain expertise in multiple disciplines. Rather, it seems likely that the physical science students (particularly the Integrated Science students) had also acquired a stock of cross-domain abstractions. That is, their multidisciplinary experience had provided them with opportunities to compare across different domains and to extract general patterns such as positive feedback and common-cause. These abstractions might then leap readily to mind as a natural way to organize phenomena in a sorting task. One indication that this might be the case is that the physical science students were more likely to produce causal sorts of economics phenomena than were the other groups, including the economists. Out of 4 economics cards to sort, the physical science students sorted on average 1.37 of them causally, in contrast to only 0.73 for the economics students (and 0.78 for the combined social science group). This suggests that the physical science students had formed abstract causal categories and were able to classify new phenomena from economics into those categories.
Developmental research shows that relational categories are slow to be acquired, relative to entity categories (Gentner, 2005). Further, earlier stages of learning are characterized by a focus on within-domain surface similarities; the ability to recognize relational structures across different situations emerges later (see Gentner & Rattermann, 1991; Doumas, Hummel, & Sandhofer, 2008 for reviews). There is also considerable evidence that analogical comparison promotes learning relational categories (Christie & Gentner, 2010; Gentner, Anggoro, & Klibanoff, 2011; Goldwater & Markman, 2011). Thus, one explanation for the difference between physical science students and the other groups is that the physical science students had many opportunities to compare across domains and had thereby abstracted a rich stock of causal abstractions.
An understanding of causal systems is crucial to explaining and predicting complex phenomena, both in the natural world and in social and economic spheres. The present work shows large differences in the ability to perceive common causal patterns across domains. Future work should reveal how people come to learn these causal patterns and to perceive abstract causal systems categories.
No demographics were retained for the introductory psychology students. Out of 9 sociology majors, 6 were double-majors in other fields, including political science (2), communication studies, legal studies, psychology, and a major called Mathematical Methods in the Social Sciences. Out of the 11 economics majors, 7 were double majors in other fields, including math, music, international studies, electrical, biomedical, and industrial engineering, and Mathematical Methods in the Social Sciences. Out of the 12 physical science students, 4 were obtaining triple majors, 5 were double majors, and 3 were obtaining one major. Their majors were in the following fields: inter-disciplinary Science Program (8), physics (6), math (5), chemistry (3), biology (2), and classics (1).
This research was supported by Office of Naval Research grant N00014-92-J-1098 awarded to the second author. We are grateful to the Similarity and Analogy group at Northwestern University for many discussions of these issues, and to Kathleen Braun for help with the research and analyses.