Arrow phobia and change trajectories
Newton is out
Nowadays, Newtonian is a dirty word in social science. More than a decade ago, Robert Chambers compared the epistemic paradigms of neo-Newtonian practice and adaptive pluralism. Chambers defined neo-Newtonian practices as those ‘processes, procedures, roles and behaviour which emphasise standardisation, routines and regularities in response to or assuming predictabilities.’ For complexity aficionados, these are all dirty words.
Brian Castelliani and Lasse Gerrits recently published the Atlas of Social Complexity which includes a chapter on Revisiting Complex Causality. They wrote an interesting blog to introduce the chapter in which they make the case that:
‘The standard scientific imagination tends to render causality as a linear vector, as if social life were a giant billiard table of variables, each bouncing off the next. But for those of us working in the complexity sciences, this simply will not do.’
“Much of social science is still working with a Newtonian imagination of cause preceding effect. Yet, as any student of systems theory knows, life rarely moves in straight lines. Feedback loops are not exceptions but the rule.”
Castelliani and Gerrits illustrate the diagrammatic dilemma thus:
But, are we really contained within the standard scientific imagination in the social sciences? I think many complexity scholars and practitioners might well disagree with this narrow characterisation. I don’t know exactly how Castelliani and Gerrits have defined these words, but let me give it a try with some quite widely-accepted definitions:
Linear: ‘A linear process is one in which, if a change in any variable at some initial time produces a change in the same or some other variable at some later time, twice as large a change at the same initial time will produce twice as large a change at the same later time… A nonlinear process is simply one that is not completely linear (Lorenz, 2024).’
Vector: ‘A quantity that has both magnitude and direction (Britanica, n.d.).’
Variable: ‘A variable can represent anything whose values change over a set of units (King, Keohane, and Verba, 1994: 51).’
Feedback loop: ‘When outputs of a system are routed back as inputs as part of a chain of cause and effect that forms a circuit or loop (Ford, 2010; see also Meadows, 1998).’
This supposed Newtonian imagination seems, to me, to be a straw man. As I discussed in response to Toby Lowe, there’s a conflation here of linear and sequential, and unidirectional. Castelliani and Gerrits rightly point out that ‘consequences [can] feed back into causes.’ This does not, however, mean that there is not a temporal sequence to this causal process (what they term a trajectory). To argue that consequences also affect causes does not mean that the cause did not precede the primary effect, nor that causes and effects necessarily ‘co-occur,’ as Castelliani and Gerrits suggest. Me writing this blog did not co-occur, did it? It simply means that the effect can, in turn, affect the agent (or agents) or contextual factor (or configuration of factors) for the subsequent causal process. Or, in other words, long causal chains tend to have positive or negative feedback loops, and thus as they put it, ‘cases evolve, bifurcate, and diverge.’ This is not a circle (or closed circuit), it’s a sequential and adaptive trajectory which is not wholly unidirectional.
Furthermore, (potentially) causal arrows in diagrams like theories of change rarely, if ever, imply specific quantities and a proportional relationship (i.e., linear dosage effect) between inputs and outputs (or outcomes). By referring to a “linear vector,” Castelliani and Gerrits seem to be making the case that proportionality and quantities go together. It’s possible they mean vector as a pathogen host (the Xs in their diagram might be metaphorical hosts considered as interventions), but with the use of the term linear and reference to Newtonian mechanics, there is some implicit reference to direction and magnitude of inputs.
Castelliani and Gerrits don’t specifically mention theories of change, but as they refer to ‘a giant billiard table of variables, each bouncing off the next’ there is an implicit critique of theories of change. Unfortunately, they do not discuss generative causation in their blog (perhaps they do in the chapter itself). But, I assume they also see problems in theories of change in the same way that Lowe or Patton does. I’ve probably seen hundreds, if not thousands, of theories of change, and I’ve literally never seen a theory of change defined in strictly linear dosage effect terms which assume a proportional relationship between an independent variable and a dependent variable. This doesn’t, of course, mean such models don’t exist, but I think they are extremely rare if they do. So, I cannot help but view this kind of critique as potentially epistemically confused, a straw man, or at least, attacking the wrong man.
In his critique of a book with questionably epistemically pluralistic views on complexity and evaluation, Patton argued against theories of change (and theory-based methods in general) by suggesting ‘if you are in the search for causal mechanisms (realist or otherwise), you are in a complicated not complexity mind-set.’ Yet, complexity scholars and evaluators actually disagree on the degrees of (un)knowability, (un)certainty, and (un)predictability. Some complexity scholars take a view of radical (and absolute) uncertainty, arguing that the domain of complexity is not just unknown (to cite Donald Rumsfeld) but unknowable (Snowden, 2002; Zimmerman et al. 2011; Patton, 2011, 2015).
Snowden (2023) points out that ‘in a complex system, you don’t have linear relationships between cause and effect which means you have inherent uncertainty.’ Inherent uncertainty is not, in fact, equivalent to totally unknowable. It seems more accurate, to me, to suggest that complexity is about “looking through a glass darkly,” to cite St Paul, not looking into a void where nothing is perceptible or intelligible. Snowden himself refers to complexity as “looking through a glass darkly,” and he even cites Corinthians, but then immediate attaches this to the view that there is ‘no linear material causality.’ Again, who is arguing that causation is necessarily a proportional relationship between the quantities of independent and dependent variables?
Generative causation which underpins realist evaluation does not express ‘linear relationships between cause and effect’ in this sense. Nor do any other generative-inspired methods. So, it strikes me that Snowden and Patton (and, by omission, Castelliani and Gerrits) inappropriately conflate experimental or statistical approaches to causality with generative ones (see Stern et al. 2012 for a discussion). As Gill Westhorp argues, in realist evaluation:
‘Any outcome will be a result of many causes and any action or change in a system may have many consequences. If causation itself is not simple and linear, evaluation approaches that treat causation as being simple and linear will be inadequate.’
This is almost identical to Boulton et al. (2015) who argue in Embracing Complexity that what matters most is to ‘consider the interplay between interventions (complex or not) and contexts.’
Alternatively, if what is meant by “linear” is, in fact, sequential, I would argue that Castelliani and Gerrits have potentially even greater contradictions to address.
Time’s arrow isn’t straight
Castelliani and Gerrits argue that:
‘To take social complexity seriously is to take time seriously. Not clock time, but lived time. Not fixed intervals, but trajectories. Cases evolve, bifurcate, and diverge.’
I mostly agree with this, or I think I do, if I understand them correctly. We could even refer back to thermodynamics and space time. I wrote a blog on time where I cited Carlo Rovelli’s The Order of Time where he noted that:
‘The arrow of time appears only where there is heat… every time a difference is manifested between the past and the future, heat is involved.’
Time’s arrow seems to flow from the past to the future, and appears to be constant, but it actually passes faster in some places (mountains) than others (sea level). Hence, our knowledge and indeed our perspective on time is, in fact, situated and positional. Castelliani and Gerrits would seem to agree with me on this. Yet, situated perspective does not mean that we must let go of causality.
This strikes me as a kind of causal arrow phobia. Arrows do not necessarily imply attribution, they are not always of equivalent width or density, or comparable degrees of certainty, or probative value of evidence as warrants for the strength of the arrow. They have somehow been reified, by some, as if they expressed an invariant law of nature. They are not. I think we have become misled by the poverty of our diagrammatic representation.
Certainly, there may be times, perhaps as we cross the edge of chaos, when we can make no sense of the entangled interdependencies of emergent phenomena, and the velocity of change is so fast that our little human brains cannot meaningfully make sense what is happening (i.e., radical ontological confusion where you may make inappropriate epistemic choices). Under such circumstances, it’s probably unwise to use the C word of causation. But, I’m not sure we often cross that rubicon in social science. The threshold is invariably poorly defined and tends to come down to individuals’ personal perspective of a particular degree of confusion. It seems unlikely we will ever get to a consensus. And maybe we should’t even strive to do so.
Methodological implications
Either way, there are some important methodological implications for Castelliani and Gerrits because elsewhere in the book they recommend trajectory-based QCA. This adaptation of QCA is very interesting because QCA was originally time-agnostic and cannot account for the fact that individual cases develop over time. It’s a really interesting adaptation of what is a highly restrictive method based on set-theoretic causal logic (which, I should point out, is also not circular). Trajectory-based QCA attempts to address this limitation of chronological or ordered unfolding over time.
In Lasse Gerrits and Sofia Paligarin’s explanation for the Centre for the Evaluation of Complexity across the Nexus (CECAN), they refer to the importance of the temporal order of conditions, and the sequences of events. Now, does this not mean that prior temporal conditions precede effects? Is it not likely that they also have at least some relationship to those effects? Viewing conditions as time sequences and as structured and ordered sequences of events in trajectory-based QCA surely means they are not circular (and the word circular is nowhere to be seen in Gerrits and Paligarin’s article). You can’t have clearly bounded timespans of event sequences if something is formally circular.
Is this the same flawed Newtonian imagination, or do we perhaps need to disentangle a linear process from a configurational sequence of factors which combine, evolve, and transmute over time? Particularly when we look at long causal chains or scaling processes, the very objects we’re studying may well evolve. And this is usually due to the interaction between whatever the thing was and its new context. These typically combine to produce something new. But, this does not mean that there isn’t a time sequence to that scaling, or indeed there isn’t path dependence to the process. Causes don’t simply disappear, even if they may dissipate.
Castelliani and Gerrits argue that ‘causality must be approached as a pluralistic, creative, and often contradictory terrain.’ I fully agree, and wish this is what they had argued more extensively in their blog. In a special issue of Evaluation on complexity, Barbrook-Johnson et al. (2021 including Castelliani) outlined a wide variety of complexity-appropriate methods discussed in the evaluation literature: Agent-based Modelling; Case Studies; Causal Loop Diagrams; System Dynamics; Process Tracing; Qualitative Comparative Analysis, and; Social Network Analysis.
So, let’s have an open discussion about a whole array of other causal approaches and their epistemic and ethical strengths and limitations.
