Theoretical Contribution How we conceptualize climate change: Revealing the force-dynamic structure underlying stock-flow reasoning Kurt Stocker1 and Joachim Funke2 1University of Zürich, Switzerland; 2Heidelberg University, Germany How people understand the fundamental dynamics of stock and flow (SF) is an important basic theoretical ques- tion with many practical applications. Such dynamics can be found, for example, in monitoring one’s own private bank account (income versus expenditures), the state of a birthday party (guests coming versus leaving), or in the context of climate change (CO2 emissions versus absorp- tion). Understanding these dynamics helps in managing everyday life and in controlling behavior in an appropriate way (e.g., stopping expenditures when the balance of a bank account approaches zero). In this paper, we present a universal frame for understanding stock-flow reasoning in terms of the theory of force dynamics. This deep-level analysis is then applied to two different presentation for- mats of SF tasks in the context of climate change. We can explain why in a coordinate-graphic presentation misun- derstandings occur (so called “SF failure”), whereas in a verbal presentation a better understanding is found. We end up with recommendations for presentation formats that we predict will help people to better understand SF dynamics. Better public SF understanding might in turn also enhance corresponding public action – such as en- hancing pro-environmental actions in relation to climate change. Keywords: force dynamics, stock-flow reasoning, climate change, causation, presentation format, dynamic problems The dynamics of stock and flow represent a fundamental,abstract principle of nature: incoming objects are ac- cumulated in a stock that keeps these objects for a certain period of time before they leave the stock by an outflow process. This abstract process description can be applied to species in a certain region (e.g., a given stock of birds has births as inflows and deaths as outflows), to the customers in a warehouse (e.g., a certain number of customers are at a given point in time in the store, new customers enter as inflows and satisfied customers leave as outflows), or to the daily food intake of persons (the current body weight representing the stock). One stock-flow dynamics is of special interest for the survival of most species on planet earth: the greenhouse gases, especially the carbon dioxide (CO2) emissions that contribute to global warming. Concerning CO2 emissions into the atmosphere, a certain amount of emissions is added as inflow to the given stock in the atmosphere, the outflow dissolves mostly in the oceans or by means of photosyn- thesis. For more than 50 years, the balance between in- and outflow seems to be disturbed by extreme increases of greenhouse gas emissions due to human activities (Inter- governmental Panel on Climate Change [IPCC], 2013). Understanding such stock-flow (SF) processes is of great importance when one wants to control a given system (not only to beware a bathtub from overflow). Therefore, it is alarming to hear about the “SF failure” that has been reported repeatedly (Cronin, Gonzalez, & Sterman, 2009; Sterman & Sweeney, 2002, 2007): “Results from the exper- iments reported here demonstrate an important and per- vasive problem in human reasoning: our inability to un- derstand stocks and flows, that is, the process by which the flows into and out of a stock accumulate over time” (Cronin et al., 2009, p. 128). Within the context of the climate change debate, the SF failure has important implications for the presentation of results (like those from the IPCC-reports) and for the pos- sible implementation of educative measurements (Clayton et al., 2016). A deeper understanding of the SF failure seems therefore necessary particularly because recent work from Fischer, Degen, and Funke (2015) suggests that the SF failure might be an effect of the type of representation, i.e., how the information about stock and flow is presented to the participants. Our paper offers an explanation of the representation effects found by Fischer and colleagues in terms of a more fundamental analysis of SF reasoning processes. This analysis fleshes out the underlying causal structure that is inherent to SF reasoning. Specifically, we (in section A) show for the first time how an SF problem (using atmospheric CO2 accumula- tion as an example) can be described in terms of force dynamics, a prominent theory of causal cognition (e.g., Stocker, 2014; Talmy, 2000). Moreover, we examine (in sections B–D) how well scientific presentation formats com- prising coordinate systems and graphs, verbal formats, and pictorial-schematic formats of presenting an SF problem (exemplified by atmospheric CO2 accumulation) represent the force-dynamic structure underlying basic SF reasoning. Our central argument is: the better the formats represent the underlying force-dynamic structure of the SF problem, the better people can understand it. Finally (in section E) the implications of these differences of how well the under- lying force-dynamic structure of SF CO2 accumulation is represented in these different formats are discussed. Corresponding author: Kurt Stocker, University of Zurich, Department of Psychology, Neuropsychology, Binzmühlestrasse 14, PO Box 25, CH-8050 Zürich, Switzerland, e-mail: kurt.stocker@gess.ethz.ch 10.11588/jddm.2019.1.51357 JDDM | 2019 | Volume 5 | Article 1 | 1 mailto:kurt.stocker@gess.ethz.ch https://doi.org/10.11588/jddm.2019.1.51357 Stocker & Funke: Understanding climate change A. The force-dynamic structure of conceptualizing stock-flow CO2 accumulation A most basic SF system consists of one inflow, one out- flow, and one stock (Sterman & Sweeney, 2002, 2007; Fis- cher et al., 2015). In this section the basic force-dynamic structure underlying SF reasoning is exemplified with at- mospheric CO2 level. People often prefer to make use of the underlying causal structure to understand SF reason- ing (Brehmer, 1976; Fischer et al., 2015; Garcia-Retamero, Wallin, & Dieckmann, 2007; Gonzalez, 2004). As a starting point to reveal the basic causal – force-dynamic – structure of atmospheric CO2 level SF relations, consider the fol- lowing two sentences adapted from Fischer and colleagues (2015, p. 13). These sentences highlight the basic causal relations involved in increase and decrease of atmospheric CO2 level: (1) Examples of informal causal verbalizations of SF reasoning (exemplified with atmospheric CO2 level) a. CO2 emissions are caused by the burning of fossil fuels and increase atmospheric CO2 concentration. b. CO2 absorptions are caused by forests and oceans and decrease atmospheric CO2 concen- tration. Naturally, the stock will increase if the inflow is greater than the outflow, decrease if the outflow is greater than the inflow, and remain constant if there is an equal amount of in- and outflow. If one puts these increase/decrease SF reasoning mechanisms into a slightly formalized verbal for- mat, one notices that causality is involved at two different hierarchical levels: (2) The basic causal structure of SF reasoning in slightly formalized verbal format (exemplified with atmo- spheric CO2 level) a. The burning of fossil fuels causeslevel-1 atmo- spheric CO2 concentration to increase. b. Absorption mechanisms of forests and oceans causelevel-1 atmospheric CO2 concentration to decrease. c. Larger increase of atmospheric CO2 concentra- tion [increase which is causedlevel-1 by the burning of fossil fuels] than decrease of at- mospheric CO2 concentration [decrease which is causedlevel-1 by absorption mechanisms of forests and oceans] causeslevel-2 atmospheric CO2 concentration to increase. d. Larger decrease of atmospheric CO2 concentra- tion [decrease which is causedlevel-1 by absorp- tion mechanisms of forests and oceans] than in- crease of atmospheric CO2 concentration [in- crease which is causedlevel-1 the burning of fos- sil fuels] causeslevel-2 atmospheric CO2 concen- tration to decrease. e. Equal increase of atmospheric CO2 concentra- tion [increase which is causedlevel-1 by the burning of fossil fuels] and decrease of at- mospheric CO2 concentration [decrease which is causedlevel-1 by absorption mechanisms of forests and oceans] causeslevel-2 atmospheric CO2 concentration to remain constant. Taking (2c) as an example, we can notice the embedded causal hierarchy that is underlying basic SF reasoning: in order to capture basic SF reasoning in a full-fledged way, one must not only understand the causes of the increase and decrease (here termed level-1-causality), but one must also understand that the relationship between increase and decrease (e.g., increase is higher than decrease) of course also has causal consequences (here termed level-2-causality; e.g., increase is higher than decrease causes stock to rise). Abstracting away from (2), we can also outline the generic causal structure of SF reasoning: (3) The generic causal structure of SF reasoning in slightly formalized verbalized format a. A causeslevel-1 stock to increase. b. B causeslevel-1 stock to decrease. c. Larger amounts of inflow [inflow which is causedlevel-1 by A] than outflow [outflow which is causedlevel-1 by B] causelevel-2 stock to in- crease. d. Larger amounts of outflow [outflow which is causedlevel-1 by B] than inflow [inflow which is causedlevel-1 by A] causeslevel-2 stock to de- crease. e. Equal amounts inflow [inflow which is causedlevel-1 by A] and outflow [outflow which is causedlevel-1 by B] causelevel-2 the stock to remain constant. What are the basic mental elements (basic building blocks) that make up SF reasoning? The conceptualization of cause and effect has long been treated (and often still is) as if cause and effect are themselves conceptual primitives – two conceptual “atoms” that do not consist of still further smaller elements (e.g. Goldvarg & Johnson-Laird, 2001; Pearl, 2000; Spirtes, Glymour, & Scheines, 2000). How- ever, with the advent of the theory of force dynamics – a by now prominent theory of causal cognition that has ini- tially been proposed by Talmy (e.g., Stocker, 2014; Talmy, 2000) – it has been possible to demonstrate that cause and effect can be described as consisting of still smaller concep- tual elements (see below). In analogy, cause and effect are more like conceptual “molecules” that consist of conceptual “atoms”, rather than being atoms themselves. That causation represents force-dynamic thinking pat- terns has also been supported by experimental findings (Barbey & Wolff, 2007; Wolff, 2003, 2007; Wolff & Song, 2003). Stocker (2014) has offered a substantial revision of the original force-dynamic account as developed by Talmy (1985, 1988, 2000). This revision makes it possible that force dynamics can be applied to all causation, no matter how concrete or abstract the entities that are involved in the causation are (with the framework developed by Talmy it was not clear, how force dynamics could be applied for certain abstract entities). This modern version of force dy- namics is called elementary force dynamics (Stocker, 2014) because it places a strong emphasis on identifying the el- ements (conceptual primitives) that make up a cause and the elements that make up an effect. First we introduce the basics of elementary force dynamics with a classic example from Talmy. Then we will demonstrate how elementary force dynamics can also be used to describe basic “elemen- tary” SF reasoning, using atmospheric CO2 accumulation as an example. 10.11588/jddm.2019.1.51357 JDDM | 2019 | Volume 5 | Article 1 | 2 https://doi.org/10.11588/jddm.2019.1.51357 Stocker & Funke: Understanding climate change A.1. Force dynamics: General elements of the theory Both classic force dynamics (Talmy, 2000) and elemen- tary force dynamics (Stocker, 2014) involve the assump- tion that mental representation of causation involves the conceptualization of two opposed entities that are engaged in a force interaction. All general elements of the force- dynamic theory explained in this section stem from the- oretical cognitive-linguistic work (Stocker, 2014; Talmy, 2000). For a linguistic exemplification, consider the fol- lowing sentence adapted from Talmy (2000, p. 416): (4) The ball started rolling because of the wind. In a force-dynamic terms, the ball functions as the ago- nist (Ago).1 In elementary force dynamics (Stocker, 2014), Ago is a cognitive entity which can take on any given state or action. In (4) Ago is the ball, which initially takes on the state-value stationariness (if there were no wind, the ball would not be moving). The opposed conceptualized force entity is referred to as the antagonist (Ant) in force- dynamic theory. In (4) the wind takes on the Ant func- tion. In elementary force dynamics, Ant is always concep- tualized as attempting to impose a state or action onto Ago that is different from the outset action or state of Ago. Thus, when Ago is initially associated with station- ariness, Ant will by definition try to impose a value or state other than stationariness. Hence in (4) the wind car- ries a different force value than the ball: Ant carries the force value motion, trying to impose this onto the inert ball. The resultant (effect) of a force-dynamic interaction always relates to Ago. The resultant depends on which of the force entities – Ago or Ant – is conceptualized as being stronger. In causation types that can be phrased with because (of), as in (4), Ant is always conceptualized as being stronger.2 Consequently, in (4) the force of Ant (the wind’s motion force) is stronger than force of Ago (the ball’s inert force). Thus, the ball is conceptualized as having been moved by the wind. Stocker (2014) has intro- duced a specific formal system to describe force-dynamic interactions (which is an abstraction of Talmy’s original force-dynamic diagramming system). For a force-dynamic interaction underlying the linguistic use of words like “be- cause” or “caused” (formally termed CAUSE or successful causation), the notational system looks as follows: (5) C: Ago-x, Ant-xdiff(++) → E: Ago-xdiff C stands for cause and E for effect. In elementary force dynamics, Ago can initially be associated with any given state or action value (value “x”). In contrast, Ant’s value must by definition be a state or action value that differs from x (“xdiff” where diff stands for different). Ant at- tempts to impose its different value onto Ago. As Ant’s force is stronger than Ago’s force in because (“++” stands for stronger3), the effect E is that Ago has to take on the different force value of Ant (→ E: Ago-xdiff). The content of (4) is force-dynamically distributed as follows (following notational convention, the content of (4) is added to the force-dynamic formula of (5) in underlined subscript): (6) C: Agoball-xstationariness, Antwind-xdiffmotion(++) → E: Agoball-xdiffmotion (6) reads: the cause C involves conceptualizing the ball in the function of Ago with the initial state value (x) of being stationary. Ago is weaker than Ant (the wind). Ant is conceptualized as imposing the different value (xdiff) of motion onto Ago (the ball). As Ant’s imposing motion is conceptualized as being the stronger (++) force than Ago’s inert force, the cognized effect E is indeed that the wind (Ant) causes the ball (Ago) to move. A.2. Force dynamics applied to stock-flow reasoning As a novel contribution to the study of stock-flow reason- ing, it is now shown that the force-dynamic elements in (5) readily offer themselves to capture the basic causal mech- anisms that are at work in stock-flow reasoning. (7) lays out all the force-dynamic elements that are involved in SF reasoning – exemplified in relation to how people concep- tualize climate change (the details of (7) will become clear as the analysis proceeds). (7) The force-dynamic elements of SF reasoning (exem- plified with atmospheric CO2 level) a. Agonist (Ago): stock (atmospheric CO2 level) b. Antagonist1 (Ant1): stock increaser (burning of fossil fuels) c. Antagonist2 (Ant2): stock “decreaser” (absorp- tion mechanisms of forests and oceans) d. x-state: at a certain level e. xdiff-action1: increase level f. xdiff-action2: decrease level g. xdiff-action3: remain level h. stronger than (++) i. larger than (>) j. equal to (=) Looking at (7), we may note that it is proposed that the stock can always be conceptualized as Ago (7a; atmo- spheric CO2 level), and the forces that increase or decrease the stock always as Ant (7b–c; the burning of fossil fuels as an atmospheric-CO2-level increaser, and absorption mech- anisms of forests and oceans as an atmospheric-CO2-level “decreaser”). The initial conceptualized state of Ago (at- mospheric CO2 level) before the intervention of Ant is al- ways to be at a certain level (7d). Force interaction that results in increase, decrease or no increase/decrease of the stock (of atmospheric CO2 level) always involves Ant try- ing to intervene with Ago’s state (7e–g), and depending on whether Ago or Ant is conceptualized as stronger (7h), the end result relates to either a change of stock amount – more increase than decrease or more decrease than increase (7i) – or no change of stock amount (7j). It is now shown how the elements of (7) can capture level-1 causality and 1Talmy (2000) borrowed the terms agonist and antagonist from physiology, where these terms stand for members of specific op- posed muscle pairs. In force dynamics, these terms are used in a different sense than in physiology (see Stocker, 2014). 2Ant is always stronger than Ago when the causal relationship can be phrased with words such as “caused”, “because”, “there- fore”, and the like. There are other forms where Ago is stronger then Ant, e.g. in „The ball did not roll despite the wind” (see Stocker, 2014). 3Talmy (2000) uses the symbol “+” to represent the force- dynamic meaning stronger than. However, since this symbol is already used in mathematics as a symbol to represent the meaning plus and since a few basic mathematical symbols (>, =) will later on in this article be used in a force-dynamic context, we use “++” to represent the force-dynamic meaning stronger than so as to avoid potential confusion with the mathematical meaning plus. 10.11588/jddm.2019.1.51357 JDDM | 2019 | Volume 5 | Article 1 | 3 https://doi.org/10.11588/jddm.2019.1.51357 Stocker & Funke: Understanding climate change level-2 causality in their conceptual entirety. (8a) and (8b) represent force-dynamic reformulations of the slightly for- malized verbal formats of (2a) and (2b), respectively (they represent level-1 causality). (8) Level-1 causality of SF reasoning in force-dynamic format exemplified with atmospheric CO2 level a. C: Agoatmospheric CO2-concentration-xat-a-certain-level, Antburning of fossil fuels-xdiffincrease level (++) → E: Agoatmospheric CO2-concentration-xdiffincrease level Verbalized: The burning of fossil fuels causeslevel1 atmospheric CO2 concentration to increase. Abbreviation: EMISSION-CAUSES-CO2-INCREASE b. C: Agoatmospheric CO2-concentration-xat-a-certain-level, Antforests and oceans-xdiffdecrease level (++) → E: Agoatmospheric CO2-concentration-xdiffdecrease level Verbalized: Absorption mechanisms of forests and oceans causelevel1 atmospheric CO2 concentration to decrease. Abbreviation: ABSORPTION-CAUSES-CO2-DECREASE (8a) suggests that the atmospheric CO2 concentration is force-dynamically conceptualized as Ago. Naturally, be- fore any CO2 concentration increasing or decreasing force interferes, the CO2 concentration is conceptualized as be- ing at a certain level – thus “at a certain level” functions as the x-value of Ago. In (8a), the role of Ant is taken on by the burning of fossil fuels. Recall that in elemen- tary force dynamics, Ant is by definition conceptualized as having a value different from the one of Ago which it tries to impose onto Ago. Here, Ant carries within it the force value (xdiff) of increasing Ago’s (CO2 concentration’s) initial state of remaining at a certain level. The burning- of-fossil-fuel’s (Ant’s) force of increasing the CO2 concen- tration is conceptualized as being stronger (++) than the CO2 concentration’s basic state of remaining at a certain level. All this – cognizing the CO2 concentration’s (Ago’s) initial state (the state before any forces act upon Ago) as being at a certain level and cognizing a stronger Ant force that imposes an increasing-level force onto Ago – repre- sents the force-dynamic cause C. Thus, given that Ant is conceptualized as being stronger than Ago, the cognized ef- fect E is indeed that the burning of fossil fuels (Ant) causes the CO2 concentration (Ago) to rise. As will be seen, the whole force-dynamic conceptualization of (8a) will become part of still larger force-dynamic conceptualizations in SF reasoning. In relation to this, it will be convenient, if we can abbreviate (8a). Thus an abbreviation is already in- troduced: EMISSION-CAUSES-CO2-INCREASE (please recall that this abbreviation stands for the entire force- dynamic structure (8a)). Force-dynamically (8b) reads very similarly to (8a) as it is only some content values that change. The Ago at the outset is the same in (8b) as in (8a): the cause (C) again involves cognizing the CO2 concentration’s (Ago’s) initial state (the state before any forces act upon Ago) as being at a certain level. But this time Ago’s initial state is conceptualized as being intervened by a different Ant: this time the forest and ocean absorption mechanisms function as Ant and as such Ant is carrying within it the force to decrease Ago’s initial state of remaining at a certain level. As Ant is again stronger (++) than Ago, the conceptu- alized effect (E) is this time that CO2 concentration de- creases. Formally (8b) is abbreviated to: ABSORPTION- CAUSES-CO2-DECREASE (please recall that this abbre- viation stands for the entire force-dynamic structure (8b)). As already shown in (2), the basic causal structure of SF reasoning involves a two-level causal hierarchy. So far, we have examined level-1 causality from a force-dynamic view- point. Level-2 causality now involves force-dynamically to conceptualize atmospheric CO2 increase with the follow- ing formulation for (2c), where CO2 increase is larger than decrease: (9) Level-2 causality (increase > decrease) of SF reasoning in force-dynamic format exemplified with increasing atmospheric CO2 level (with abbreviations) C: Agoatmospheric CO2-concentration-xat-a-certain-level, Ant: [EMISSION-CAUSES-CO2-INCREASE > ABSORPTION-CAUSES-CO2-DECREASE] xdiffincrease level (++) → E: Agoatmospheric CO2-concentration-xdiffincrease level Verbalized: Larger increase of atmospheric CO2 concentration [increase which is causedlevel1 by the burning of fossil fuels] than decrease of atmospheric CO2 concentration [decrease which is causedlevel1 by absorption mechanisms of forests and oceans] causeslevel2 atmospheric CO2 concentration to increase. Thus, Ago in (9) is still (as in all other examples) the atmospheric CO2 concentration. The role of Ant is now force-dynamically complex: Ant now stands for “increase is higher than decrease” (where increase and decrease them- selves also have a cause, as captured by the formal ab- breviations; the larger-than relation is represented with the standard mathematical symbol for this, >). This se- mantically complex Ant (increase > decrease) naturally carries within it the force of increasing Ago’s (CO2 con- centration’s) initial state of remaining at a certain level. Thus, given that Ant is conceptualized as being stronger than Ago, the cognized effect E is that increase > decrease causes the CO2 concentration (Ago) to rise. The two re- maining SF level-2-causality possibilities (CO2 decrease or CO2 remaining constant) can be formally captured in very similar ways to (9): (10) Level-2 causality (decrease > increase; increase = decrease) of SF reasoning in force-dynamic format exemplified with decreasing and constant atmospheric CO2 level a. C: Agoatmospheric CO2-concentration-xat-a-certain-level, Ant: [ABSORPTION-CAUSES-CO2-DECREASE > EMISSION-CAUSES-CO2- INCREASE]xdiffdecrease level (++) → E: Agoatmospheric CO2-concentration-xdiffdecrease level Verbalized: Larger decrease of atmospheric CO2 concentration [decrease which is causedlevel1 by absorption mechanisms of forests and oceans] than increase of atmospheric CO2 concentration [increase which is causedlevel1 10.11588/jddm.2019.1.51357 JDDM | 2019 | Volume 5 | Article 1 | 4 https://doi.org/10.11588/jddm.2019.1.51357 Stocker & Funke: Understanding climate change by the burning of fossil fuels] causeslevel2 atmospheric CO2 concentration to decrease. b. C: Agoatmospheric CO2-concentration-xat-a-certain-level, Ant: [EMISSION-CAUSES-CO2-INCREASE = ABSORPTION-CAUSES-CO2-DECREASE] xdiffremain level (++) → E: Agoatmospheric CO2-concentration-xdiffremain level Verbalized: Equal increase of atmospheric CO2 concentration [increase which is causedlevel1 by the burning of fossil fuels] and decrease of atmospheric CO2 concentration [decrease which is causedlevel1 by absorption mechanisms of forests and oceans] causeslevel2 atmospheric CO2 concentration to remain constant. Thus, in (10a) the complex Ant represents the relation- ship decrease > increase which imposes the force onto Ago (atmospheric CO2 level) of decreasing CO2 level, and in (10b) Ant represents the relationship increase = decrease which imposes the force onto Ago (atmospheric CO2 level) of keeping the CO2 level at a constant level. In sum, in this section it has been shown how the force- dynamic elements of (7) can fully flesh out the complex causal mechanisms that underlie SF reasoning. In the fol- lowing sections, different presentation formats for stock- flow CO2 accumulation will be investigated to see how well they represent (3), 2-level causality, and (7), the ba- sic causal elements of SF reasoning. We will argue that the better the presentation format for stock-flow reason- ing represents the underlying force-dynamic structure, the better people can understand stock-flow reasoning (in the following sections exemplified with CO2 accumulation). B. Pictorial-schematic presentation format for stock-flow CO2 accumulation As Fischer and colleagues write: The structure of SF systems is often explained by a bathtub analogy: The water level (stock) in a bathtub increases if the inflow of water through the faucet exceeds the outflow through the drain; the water level drops if the outflow exceeds the inflow (2015, p. 2). This bathtub analogy readily lends itself to a pictorial- schematic presentation format for SF CO2 accumulation. Thus, in order to investigate how well a pictorial bath- tub analogy of SF reasoning can represent the underlying force-dynamic structure, we have devised such a pictorial- schematic presentation (see Figure 1). This is how we in- tuitively would present the bathtub analogy in a pictorial- schematic presentation format; future studies would have to determine if there is an optimal way of how to repre- sent the bathtub analogy for climate change in a pictorial- schematic format. All pictorial-schematic elements of stock-flow CO2 ac- cumulation in Figure 1 have their ready analogues to po- tential water increase or decrease in a bathtub: instead of an increasing, decreasing, or constant water level in a bathtub container, we have an increasing, decreasing, or constant CO2 level in an “atmosphere container”; in- stead of water entering and leaving a bathtub, we now have CO2 “entering and leaving” the atmosphere; instead of larger/smaller amounts of inflow and outflow of water, we have larger/smaller amounts of inflow and outflow of CO2 (larger/smaller amounts of in- and outflow are de- picted by smaller and larger arrows, respectively). As a basic guide to analyze the causal force-dynamic content of Figure 1 we first use (3). This will allow us to check whether the pictorial-schematic representation of SF reasoning in Figure 1 explicitly represents two-level causal- ity. Then (7) – the force-dynamic elements of SF reasoning – will be used as a force-dynamic check to examine whether a pictorial bathtub analogy of SF reasoning (Figure 1) can represent all force-dynamic elements that are involved in basic SF reasoning. As examined in (3), SF level-1 causality involves the two basic causal relationships. First in level-1 causality (3a), A (i.e., Ant1) increases the stock (Ago). Figure 1(a–c) depicts this with an arrow pointing into the stock (labeled “CO2 IN (EMISSION: burning of fossil fuels)”), suggesting CO2 in- crease in the atmosphere. Second in level-1 causality (3b), B (i.e., Ant2) decreases the stock (Ago). Figure 1(a–c) de- picts this with an arrow pointing out of the atmosphere (labeled “CO2 OUT (ABSORPTION: forests, oceans)”), suggesting CO2 “leaving” the atmosphere. As also examined in (3), SF level-2 causality involves three basic causal relationships: (3c) increase > decrease causes stock increase; (3d) decrease > increase causes stock decrease; and (3e) increase = decrease causes stock to re- main constant. In Figure 1, the > and = relationships are captured by the different sizes of both solid-line arrows. Thus, for instance, if (depicting (3a)) the inward-pointing arrow is larger than the outward-pointing arrow, then it can be deduced that this results in CO2 increase (symbol- ized with the upward-pointing dotted arrow). Force-dynamically we may furthermore note that Fig- ure 1 depicts all ten force-dynamic elements that are in- volved in basic SF reasoning (cf. with (7)): (11) The force-dynamic elements of SF reasoning in the pictorial bathtub-analogy format (exemplified with at- mospheric CO2 level) a. Ago: stock (here CO2 level) is pictorial- schematically represented by a dotted line sym- bolizing the CO2 level which is complemented by the verbal label CO2 level b. Ant1: stock increaser (emission) is pictorial- schematically represented by an inward-pointing arrow which is complemented with the verbal la- bels CO2 IN and EMISSION: burning of fossil fuels c. Ant2: stock “decreaser” (absorption) is pictorial-schematically represented by an outward-pointing arrow which is comple- mented by the verbal labels CO2 OUT and ABSORPTION: forests, oceans d. x-state: being at a certain given level; pictorial- schematically represented by the horizontal ori- entation of the dotted CO2 level line and by adding the verbal label level next to the verbal label CO2 e. xdiff-action1: increase level is pictorial- schematically represented by the dotted upward arrow which is complemented with the verbal label increase f. xdiff-action2: decrease level is pictorial- schematically represented by the dotted downward arrow which is complemented with the written label decrease 10.11588/jddm.2019.1.51357 JDDM | 2019 | Volume 5 | Article 1 | 5 https://doi.org/10.11588/jddm.2019.1.51357 Stocker & Funke: Understanding climate change Figure 1. Pictorial-schematic presentation format for stock-flow CO2 accumulation (based on the bathtub analogy). (a) More CO2 gets in the atmosphere (symbolized by the larger inward-pointing arrow) than out (smaller outward-pointing arrow), resulting in CO2 increase (upward-pointing arrow). (b) More CO2 leaves the atmosphere (larger outward-pointing arrow) than comes in (smaller inward-pointing arrow), resulting in CO2 decrease (downward-pointing arrow). (c) The same amount of CO2 enters and leaves the atmosphere (symbolized by equal-sized inward- and outward-pointing arrows), resulting in a CO2 concentration that remains constant (symbolized by a horizontal non-pointed strip). g. xdiff-action3: remain level is pictorial- schematically represented by the dotted horizontal non-pointed strip complemented with the written label constant h. stronger than (++): is pictorial-schematically represented by placing the larger flow arrow to the stronger force entity and the smaller flow arrow to the weaker force entity (the force- relationship itself has no additional verbal la- bel; it is thus only symbolized by symbolically suggesting that stronger = larger and weaker = smaller). i. larger than (>): is (similar to h) pictorial- schematically represented by placing the larger flow arrow to the larger flow quantity and the smaller flow arrow to the smaller flow quantity j. equal to (=): is pictorial-schematically repre- sented by placing equally-sized flow arrows to the inflow and outflow quantities Summing up the analysis of Figure 1, one can notice that the pictorial-schematic presentation format for stock-flow reasoning together with its complementing verbal labels depicts the causal structure of SF reasoning about CO2 level in the atmosphere in its entirety: it depicts both levels of the causality hierarchy (level-1 and level-2 causality, cf. (3)) as well as all force-dynamic elements that make up basic SF reasoning (cf. (7)). C. Verbal presentation format for stock-flow CO2 accumulation Consider the following verbal format (from Fischer et al., 2015) that is used to assess the understanding of lay peo- ple’s SF understanding in the context of climate change: 12) Verbal presentation format for stock-flow CO2 accu- mulation CO2 emissions are caused by the burning of fossil fuels and lead to an increase of atmospheric CO2 concen- tration. CO2 absorptions are caused by forests and oceans and decrease atmospheric CO2 concentration. CO2 emissions are currently twice as high as CO2 ab- sorptions. Imagine that emissions were reduced by 30%: How would the atmospheric CO2 concentration react? a. Atmospheric CO2 concentration would increase. b. Atmospheric CO2 concentration would decrease c. Atmospheric CO2 concentration would remain constant. This format yielded high understanding of SF problems: the majority of the participants correctly inferred that as long as there is more CO2 increase than decrease (which is what the scenario above suggests), CO2 level rises. Let it now be examined how extensively (12) covers the under- lying causal (force-dynamic) structure of basic SF reason- ing. As with the pictorial-schematic format of the bathtub analogy which was examined in the previous section, first (3) serves again as a guide to analyze if both levels of the causality hierarchy (level-1 and level-2 causality) are rep- resented; and then (7) is again used to see how extensively force-dynamic elements are represented. The SF level-1 causal relation (3a) is clearly covered in (12) with the sentence “CO2 emissions are caused by the burning of fossil fuels and lead to an increase of atmo- spheric CO2 concentration”. SF level-1 causal relation (3b) is also covered: “CO2 absorptions are caused by forests and oceans and decrease atmospheric CO2 concentration”. In (12), the level-2-causality relationship (3c) increase > decrease is covered by the two sentences “CO2 emissions are currently twice as high as CO2 absorptions. Imagine that emissions were reduced by 30%” as well, of course, as by the corresponding correct answer “Atmospheric CO2 concentration would increase”. The causal thinking that is behind the other two theoretically possible basic rela- tionships – (3d: decrease > increase) and (3e: increase = decrease)– are covered by the (wrong) answers “Atmo- spheric CO2 concentration would decrease” and “Atmo- spheric CO2 concentration would remain constant”, respec- tively. In (12), how extensively are the force-dynamic elements that are involved in basic SF reasoning (cf. with (7)) rep- 10.11588/jddm.2019.1.51357 JDDM | 2019 | Volume 5 | Article 1 | 6 https://doi.org/10.11588/jddm.2019.1.51357 Stocker & Funke: Understanding climate change Figure 2. Coordinate-graphic presentation format for stock-flow CO2 accumulation. The graph plots time on the x-axis and hypothesized amounts of atmospheric CO2 in giga-tons on the y-axis. The predicted emission and absorption curves are plotted. resented? This is shown in (13). If force-dynamic elements are missing, then this will be symbolized with “—” and “n.a.” stands for not applicable. (13) The force-dynamic elements of SF reasoning in verbal format (exemplified with atmospheric CO2 level) a. Ago: “CO2 concentration” b. Ant1: “burning of fossil fuels” c. Ant2: “forests and oceans” d. x-state: — (xat a certain level has to be inferred) e. xdiff-action1: “CO2 concentration would in- crease” f. xdiff-action2: “CO2 concentration would de- crease” g. xdiff-action3: “concentration would remain con- stant” h. stronger than (++): n.a. i. larger-than (>): n.a j. equal-to (=): n.a. Hence, we may note that (12) explicitly represents al- most all force-dynamic elements that are involved in basic SF reasoning. What is not explicitly expressed in (12) is that Ago’s (the CO2 concentration’s) state is conceptual- ized as being initially at a certain level (before any inter- vention takes place). However, given the high SF under- standing that (12) has produced (Fischer et al., 2015), one may perhaps assume that the omission of this piece of in- formation can easily be inferred. That relational informa- tion such as increase > decrease (13h–j) is not represented in (12), lies in the nature of the task. After all, the very nature of this task is for the participants to infer relevant relational information, such as increase > decrease, from the other given information. In sum, in this section it has been shown that causal force-dynamic structure of SF reasoning about atmospheric CO2 level is almost captured in its entirety by the verbal presentation format of Fischer and colleagues (2015) and that the one force-dynamic value missing – the x-state at a certain level – can probably be easily inferred. D. Coordinate-graphic presentation format for stock-flow CO2 accumulation Figure 2 (as used in Fischer et al., 2015) shows one of the most common forms of how to represent stock-flow CO2 accumulation in studies on understanding SF phenomena: a coordinate-graphic presentation format based on stan- dard scientific representation norms (plotting a relation of two variables on an x- and y-axis). It is now examined how well the coordinate-graphic presentation format for stock- flow CO2 accumulation represents the underlying causal structure of SF reasoning. We may note that the graphic presentation of Figure 2 does neither depict level-1 causality (3a) nor level-1 causal- ity (3b). Hence, neither the actual causal interplay be- tween emission and CO2 increase (how more emission leads to more CO2) nor between absorption and CO2 decrease (how more absorption leads to less CO2) is depicted in the coordinate-graphic presentation. Similarly, one also does not find level-2 causality rela- tionships directly represented in the graph of Figure 2. Only part of the relationship (3c) “increase > decrease causes stock increase” can be logically inferred; for instance for 2050, by noticing that emission is still higher on the y-axis than absorption (this, of course, allows to infer “in- crease > decrease”). However, the causal consequence of this (“causes stock to increase”) can no longer be inferred from the visual information given by the graph of Figure 2. Hence, while parts of level-2 causality can be logically in- ferred by inspecting the visual information in the graph, the actual causal consequences cannot be directly derived by solely inspecting the visual information in the graph. Finally, we turn to the question: how extensively are the force-dynamic elements that are involved in basic SF reasoning (cf. with (7)) represented in Figure 2? (14) The force-dynamic elements of SF reasoning in the coordinate-graphic format (exemplified with atmo- spheric CO2 level) a. Ago: “CO2 in giga tons” b. Ant1: the plotted line labeled “Emission” c. Ant2: the plotted line labeled “Absorption” d. x-state: — (xat a certain level has to be inferred) e. xdiff-action1: — (in accompanying text only) 10.11588/jddm.2019.1.51357 JDDM | 2019 | Volume 5 | Article 1 | 7 https://doi.org/10.11588/jddm.2019.1.51357 Stocker & Funke: Understanding climate change Figure 3. Pictorial-schematic presentation format for stock-flow CO2 accumulation where increase/decrease/constancy has to be inferred. Could be combined with a verbal format. f. xdiff-action2: — (in accompanying text only) g. xdiff-action3: — (in accompanying text only) h. stronger than (++): n.a. i. larger-than (>):(++): n.a j. equal-to (=): n.a. The force-dynamic analysis of the graph in (14) is sum- marized quickly: the force-dynamic interaction between the Ago and the Ant is not represented because the action- values of the Antagonists (the powers that lead to increase, decrease, or constancy) are not represented in the graph. Therefore, none of the actual causal interplay between at- mospheric CO2 level and emission/absorption that leads to CO2 increase is graphically displayed. While the coordinate-graphic presentation format (14) displays the underlying causal relationships only marginally, it of course does display information that the pictorial-schematic presentation format (Figure 2) and the verbal presentation format (12) does not display: predic- tions of how levels of emission and absorption develop over time. Such information is of course vital and indispens- able, also for the public. Thus, what might be at hand in order to optimize public understanding of climate change (cf. Introduction) is a synthesis of the coordinate-graphic, the verbal, and the pictorial-schematic format (see Discus- sion). E. Discussion In this article two main endeavors were undertaken. First, we developed a force-dynamic account of stock- flow reasoning and showed that our new theoretical approach to stock-flow reasoning can explain all basic cognitive aspects that are involved in stock-flow rea- soning. Second, we carried out an analysis in terms of this new force-dynamic account for stock-flow reason- ing in relation to three different modes of presentation of CO2 accumulation: (a) the pictorial-schematic for- mat of the bathtub analogy (as shown in Figure 1), (b) the verbal format (as shown in (12) and (13)), and (c) the coordinate-graphic format (as shown in (14) and in Figure 2). Force-dynamic theory explains why (b) pro- duces better understanding than (c) because the neces- sary force-dynamic elements for a correct understand- ing are only present in (b). Thus, our force-dynamic account has the theoretical power to explain the em- pirical finding of Fischer and colleagues (2015) that a verbal format of stock-flow reasoning produces a bet- ter understanding than what studies using coordinate- graphic format (Cronin, Gonzalez, & Sterman, 2009; Sterman & Sweeney, 2002, 2007) have found. Additionally, – as a new empirical question – we can also turn to the question how the bath-tube-analogy- based pictorial-schematic presentation format could be used to enhance understanding of SF reasoning (including understanding the SF reasoning about cli- mate change). So far (in section B) we have only shown (see Figure 2) pictorial-schematic presentation formats that “give away” whether there will be stock increase, decrease, or constancy (because the pur- pose was to identify the underlying causal and force- dynamic structure and not to present ways how SF rea- soning abilities might be tested). However, any investi- gation into basic SF reasoning skills must of course not give away what has been termed level-2 causality in this paper (increase > decrease causes stock increase; decrease > increase causes stock decrease; and increase = decrease causes stock to remain constant) – because it is just the correctness of these inferences that usually are tested when investigating how well people perform in SF reasoning (Cronin, Gonzalez, & Sterman, 2009; Fischer et al., 2015; Sterman & Sweeney, 2002, 2007). Figure 3 gives one example of a pictorial-schematic presentation format for stock-flow CO2 accumulation that does not give away level-2 causality. The pictorial-schematic format in Figure 3 could for instance be combined with the verbal format of Fis- cher and colleagues (2015), with (12), to assess basic understanding of SF reasoning skills. Answering the questions in (12), participants in corresponding stud- ies could use a graph among the lines of Figure 3 to think their answers through. As participants would be reading the addition (“twice as high”) and subtrac- tion (“reduced by 30%”) information, they might for instance inspect the graph and might mentally project 10.11588/jddm.2019.1.51357 JDDM | 2019 | Volume 5 | Article 1 | 8 https://doi.org/10.11588/jddm.2019.1.51357 Stocker & Funke: Understanding climate change Figure 4. Pictorial-schematic complementation of the coordinate-graphic presentation format for stock-flow CO2 accumulation. Further- more, this combined format could also be presented together with an additional coordinate graph that shows the real, actual increase over the years. corresponding higher and lower levels of CO2 levels into the picture. Such a visual aid could possibly lead to still higher understanding of SF reasoning about cli- mate change. Schematic visual information – like the one in Figure 3 that highlights more spatial relations than actual visual content – might indeed assist rea- soning skills. People for instance do better in logical reasoning when little or no imagery is required, but when the problem can be cognized with a clear spatial layout (Knauff, 2013). Finally: what could be done to counteract so called “SF failure” – the widespread wrong interpretations of SF problems that involve emission/absorption co- ordinate graphs (Cronin, Gonzalez, & Sterman, 2009; Sterman & Sweeney, 2002, 2007)? This is a very important question, as such coordinate graphs fea- ture prominently in official reports about global warm- ing (e.g., Intergovernmental Panel on Climate Change [IPCC], 2013). A simple attempt to counteract SF fail- ure would be to add a pictorial-schematic presentation format of Figure 1 to the coordinate-graphic presenta- tion format of Figure 3. A text that could be added to Fig. 1 is for instance: “2050. Still CO2 increase. As long as there is more CO2 emission than absorption, there is CO2 increase”. This is represented in Figure 4. As shown in Figure 4, bringing together different presentation formats (coordinate, pictorial-schematic, which could furthermore be accompanied by verbal) could form a powerful synthesis that could possibly help a) researchers to more adequately assess basic stock-flow reasoning skills, and b) the public to better understand reasoning about climate change. Together with coordinate graphs showing the real increase over the years, this synthesis would allow representing fu- ture predictions of emission and absorption develop- ments (SF coordinate format), while at the same time making the underlying force-dynamic (causal) struc- ture transparent (SF verbal and pictorial-schematic format). Given the “relentless rise of carbon dioxide” (as NASA puts it4), and given the dangers that come with it for our planet, we should not too easily accept the “SF failure” of people as a scientific fact. Quite the opposite: we have offered a theoretical (force-dynamic) interpretation of an empirical finding (of Fischer and colleagues, 2015) that makes a strong case that – as long as the presentation formats for SF reasoning rep- resents force-dynamic causal thinking patterns – peo- ple actually show large SF competence. SF competence might be a much more promising basis than SF fail- ure to promote pro-environmental behavior among the human species in order to protect our planet. Declaration of conflicting interests: The authors de- clare that the research was conducted in the absence of any commercial or financial relationships that could be constructed as a potential conflict of interest. Author contributions: The authors contributed equally to this work. Handling editor: Andreas Fischer Copyright: This work is licensed under a Creative Com- mons Attribution-NonCommercial-NoDerivatives 4.0 In- ternational License. Citation: Stocker, K., & Funke, J. (2018). How we conceptualize climate change: Revealing the force-dynamic structure underlying stock-flow reason- ing. Journal of Dynamic Decision Making, 5, 1. doi:10.11588/jddm.2019.1.51357 Received: 24 Aug 2018 Accepted: 03 May 2019 Published: 07 May 2019 4 https://climate.nasa.gov/climate_resources/24/ 10.11588/jddm.2019.1.51357 JDDM | 2019 | Volume 5 | Article 1 | 9 https://doi.org/10.11588/jddm.2019.1.51357 https://climate.nasa.gov/climate_resources/24/ https://doi.org/10.11588/jddm.2019.1.51357 Stocker & Funke: Understanding climate change References Barbey, A. K., & Wolff, P. (2007). Learning causal structure from reasoning. In Proceedings of the 29th Annual Conference of the Cognitive Science Society (pp. 713–718). Nashville, TN: Erlbaum. Brehmer, B. (1976). 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