Convergence, Divergence, and the Continuum of Field-Organizing Activities

So what are the possibilities for growing out green shoots from the seeds and roots of an ethical orientation to keeping the dialogue going? What kinds of fruits might be expected from cultivating a common ground for choosing discourse over violence? What are the consequences for practice of planting this seed in this ground?

The same participant in the conversation earlier this week at Convergence XV who spoke of the peace building processes taking place around the world also described a developmental context for these issues of mutual understanding. The work of Theo Dawson and her colleagues (Dawson, 2002a, 2002b, 2004; Dawson, Fischer, and Stein, 2006) is especially pertinent here. Their comparisons of multiple approaches to cognitive and moral development have provided clear and decisive theory, evidence, and instrumentation concerning the conceptual integrations that take place in the evolution of hierarchical complexity.

Conceptual integrations occur when previously tacit, unexamined, and assumed principles informing a sphere of operations are brought into conscious awareness and are transformed into explicit objects of new operations. Developmentally, this is the process of discovery that takes place from the earliest stages of life, in utero. Organisms of all kinds mature in a process of interaction with their environments. Young children at the “terrible two” stage, for instance, are realizing that anything they can detach from, whether by throwing or by denying (“No!”), is not part of them. Only a few months earlier, the same children will have been fascinated with their fingers and toes, realizing these are parts of their own bodies, often by putting them in their mouths.

There are as many opportunities for conceptual integrations between the ages of 21 to 99 as there are between birth and 21. Developmental differences in perspectives can make for riotously comic situations, and can also lead to conflicts, even when the participants agree on more than they disagree on. And so here we arrive at a position from which we can get a grip on how to integrate convergence and divergence in a common framework that follows from the prior post’s brief description of the ontological method’s three moments of reduction, application, and deconstruction.

Woolley and colleagues (Woolley, et al., 2010; Woolley and Fuchs, 2011) describe a continuum of five field-organizing activities categorizing the types of information needed for effective collective intelligence (Figure 1). Four of these five activities (defining, bounding, opening, and bridging) vary in the convergent versus divergent processes they bring to bear in collective thinking. Defining and bounding are convergent processes that inform judgment and decision making. These activities are especially important in the emergence of a new field or organization, when the object of interest and the methods of recognizing and producing it are in contention. Opening and bridging activities, in contrast, diverge from accepted definitions and transgress boundaries in the creative process of pushing into new areas. Undergirding the continuum as a whole is the fifth activity, grounding, which serves as a theory- and evidence-informed connection to meaningful and useful results.

There are instances in which defining and bounding activities have progressed to the point that the explanatory power of theory enables the calibration of test items from knowledge of the component parts included in those items. The efficiencies and cost reductions gained from computer-based item generation and administration are significant. Research in this area takes a variety of approaches; for more information, see Daniel and Embretson (2010), DeBoeck and Wilson (2004), Stenner, et al. (2013), and others.

The value of clear definitions and boundaries in this context stems in large part from the capacity to identify exceptions that prove (test) the rules, and that then also provide opportunities for opening and bridging. Kuhn (1961, p. 180; 1977, p. 205) noted that

To the extent that measurement and quantitative technique play an especially significant role in scientific discovery, they do so precisely because, by displaying significant anomaly, they tell scientists when and where to look for a new qualitative phenomenon.

Rasch (1960, p. 124) similarly understood that “Once a law has been established within a certain field then the law itself may serve as a tool for deciding whether or not added stimuli and/or objects belong to the original group.” Rasch gives the example of mechanical force applied to various masses with resulting accelerations, introducing idea that one of the instruments might exert magnetic as well as mechanical force, with noticeable effects on steel masses, but not on wooden masses. Rasch suggests that exploration of these anomalies may result in the discovery of other similar instruments that vary in the extent to which they also exert the new force, with the possible consequence of discovering a law of magnetic attraction.

There has been an intense interest in the assessment of divergent inconsistencies in measurement research and practice following in the wake of Rasch’s early work in psychological and social measurement (examples from a very large literature in this area include Karabatsos and Ulrich, 2002, and Smith and Plackner, 2009). Andrich, for instance, makes explicit reference to Kuhn (1961), saying, “…the function of a model for measurement…is to disclose anomalies, not merely to describe data” (Andrich, 2002, p. 352; also see Andrich, 1996, 2004, 2011). Typical software for applying Rasch models (Andrich, et al., 2013; Linacre, 2011, 2013; Wu, et al., 2007) thus accordingly provides many more qualitative numbers evaluating potential anomalies than quantitative measuring numbers. These qualitative numbers (digits that do not stand for something substantive that adds up in a constant unit) include uncertainty and confidence indicators that vary with sample size; mean square and standardized model fit statistics; and principal components analysis factor loadings and eigenvalues.

The opportunities for divergent openings onto new qualitative phenomena provided by data consistency evaluations are complemented in Rasch measurement by a variety of bridging activities. Different instruments intended to measure the same or closely related constructs may often be equated or co-calibrated, so they measure in a common unit (among many publications in this area, see Dawson, 2002a, 2004; Fisher, 1997; Fisher, et al., 1995; Massof and Ahmadian, 2007; Smith and Taylor, 2004). Similarly, the same instrument calibrated on different samples from the same population may exhibit consistent properties across those samples, offering further evidence of a potential for defining a common unit (Fisher, 1999).

Other opening and bridging activities include capacities (a) to drop items or questions from a test or survey, or to add them; (b) to adaptively administer subsets of custom-selected items from a large bank; and (c) to adjust measures for the leniency or severity of judges assigning ratings, all of which can be done, within the limits of the relevant definitions and boundaries, without compromising the unit of comparison. For methodological overviews, see Bond and Fox (2007), Wilson (2005), and others.

The various field-organizing activities spanning the range from convergence to divergence are implicated not only in research on collective thinking, but also in the history and philosophy of science. Galison and colleagues (Galison, 1997, 1999; Galison and Stump, 1996) closely examine positivist and antipositivist perspectives on the unity of science, finding their conclusions inconsistent with the evidence of history. A postpositivist perspective (Galison, 1999, p. 138), in contrast, finds “distinct communities and incommensurable beliefs” between and often within the areas of theory, experiment, and instrument-making. But instead of finding these communities “utterly condemned to passing one another without any possibility of significant interaction,” Galison (1999, p. 138) observes that “two groups can agree on rules of exchange even if they ascribe utterly different significance to the objects being exchanged; they may even disagree on the meaning of the exchange process itself.” In practice, “trading partners can hammer out a local coordination despite vast global differences.”

In accord with Woolley and colleagues’ work on convergent and divergent field-organizing activities, Galison (1999, p. 137) concludes, then, that “science is disunified, and—against our first intuitions—it is precisely the disunification of science that underpins its strength and stability.” Galison (1997, pp. 843-844) concludes with a section entitled “Cables, Bricks, and Metaphysics” in which the postpositivist disunity of science is seen to provide its unexpected coherence from the simultaneously convergent and divergent ways theories, experiments, and instruments interact.

But as Galison recognizes, a metaphor based on the intertwined strands in a cable is too mechanical to support the dynamic processes by which order arises from particular kinds of noise and chaos. Not cited by Galison is a burgeoning literature on the phenomenon of noise-induced order termed stochastic resonance (Andò  and Graziani 2000, Benzi, et al., 1981; Dykman and McClintock, 1998; Fisher, 1992, 2011; Hess and Albano, 1998; Repperger and Farris, 2010). Where the metaphor of a cable’s strands breaks down, stochastic resonance provides multiple ways of illustrating how the disorder of finite and partially independent processes can give rise to an otherwise inaccessible order and structure.

Stochastic resonance involves small noisy signals that can be amplified to have very large effects. The noise has to be of a particular kind, and too much of it will drown out rather than amplify the effect. Examples include the interaction of neuronal ensembles in the brain (Chialvo, Lontin, and Müller-Gerking, 1996), speech recognition (Moskowitz and Dickinson, 2002), and perceptual interpretation (Rianni and Simonotto, 1994). Given that Rasch’s models for measurement are stochastic versions of Guttman’s deterministic models (Andrich, 1985), the question has been raised as to how Rasch’s seemingly weaker assumptions could lead to a measurement model that is stronger than Guttman’s (Duncan, 1984, p. 220). Stochastic resonance may provide an essential clue to this puzzle (Fisher, 1992, 2011).

Another description of what might be a manifestation of stochastic resonance akin to that brought up by Galison arises in Berg and Timmermans’ (2000, p. 56) study of the constitution of universalities in a medical network. They note that, “Paradoxically, then, the increased stability and reach of this network was not due to more (precise) instructions: the protocol’s logistics could thrive only by parasitically drawing upon its own disorder.” Much the same has been said about the behaviors of markets (Mandelbrot, 2004), bringing us back to the topic of the day at Convergence XV earlier this week. I’ll have more to say on this issue of universalities constituted via noise-induced order in due course.

References

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Andrich, D. (1985). An elaboration of Guttman scaling with Rasch models for measurement. In N. B. Tuma (Ed.), Sociological methodology 1985 (pp. 33-80). San Francisco, California: Jossey-Bass.

Andrich, D. (1996). Measurement criteria for choosing among models with graded responses. In A. von Eye & C. Clogg (Eds.), Categorical variables in developmental research: Methods of analysis (pp. 3-35). New York: Academic Press, Inc.

Andrich, D. (2002). Understanding resistance to the data-model relationship in Rasch’s paradigm: A reflection for the next generation. Journal of Applied Measurement, 3(3), 325-359.

Andrich, D. (2004, January). Controversy and the Rasch model: A characteristic of incompatible paradigms? Medical Care, 42(1), I-7–I-16.

Andrich, D. (2011). Rating scales and Rasch measurement. Expert Reviews in Pharmacoeconomics Outcome Research, 11(5), 571-585.

Andrich, D., Lyne, A., Sheridan, B., & Luo, G. (2013). RUMM 2030: Rasch unidimensional models for measurement. Perth, Australia: RUMM Laboratory Pty Ltd [www.rummlab.com.au].

Benzi, R., Sutera, A., & Vulpiani, A. (1981). The mechanism of stochastic resonance. Journal of Physics. A. Mathematical and General, 14, L453-L457.

Berg, M., & Timmermans, S. (2000). Order and their others: On the constitution of universalities in medical work. Configurations, 8(1), 31-61.

Bond, T., & Fox, C. (2007). Applying the Rasch model: Fundamental measurement in the human sciences, 2d edition. Mahwah, New Jersey: Lawrence Erlbaum Associates.

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Dawson, T. L., Fischer, K. W., & Stein, Z. (2006). Reconsidering qualitative and quantitative research approaches: A cognitive developmental perspective. New Ideas in Psychology, 24, 229-239.

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Fisher, W. P., Jr. (2011). Stochastic and historical resonances of the unit in physics and psychometrics. Measurement: Interdisciplinary Research & Perspectives, 9, 46-50.

Fisher, W. P., Jr., Harvey, R. F., Taylor, P., Kilgore, K. M., & Kelly, C. K. (1995, February). Rehabits: A common language of functional assessment. Archives of Physical Medicine and Rehabilitation, 76(2), 113-122.

Galison, P. (1997). Image and logic: A material culture of microphysics. Chicago: University of Chicago Press.

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Hess, S. M., & Albano, A. M. (1998, February). Minimum requirements for stochastic resonance in threshold systems. International Journal of Bifurcation and Chaos, 8(2), 395-400.

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Moskowitz, M. T., & Dickinson, B. W. (2002). Stochastic resonance in speech recognition: Differentiating between /b/ and /v/. Proceedings of the IEEE International Symposium on Circuits and Systems, 3, 855-858.

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Smith, R. M., & Plackner, C. (2009). The family approach to assessing fit in Rasch measurement. Journal of Applied Measurement, 10(4), 424-437.

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Common Languages and Shared Vulnerability

A recent partner in conversation insisted that sometimes it just is not possible to arrive at a common language, and that it would never be possible for her to agree with those who hold out for that possibility. In the same conversation, we heard from another participant about the work of peace building in areas of the world that have suffered brutal crimes inflicted by neighbors on neighbors. The realization that there are people overcoming and learning to live with the most horrible pain considerably tempered our exchange.

I think we came to see that it is one thing to agree to disagree about something inconsequential, or even about something that leads to very different opportunities and challenges. But mutual understanding hinges on a shared language. To give up on it is to give up on the possibility of fully inclusive community. It is to give up hope for a future in which healing can happen, in which there are no permanent divisions.

Keeping the conversation going, keeping the dialogue open, changing the rules as we go along to keep the game in play: if there are any principles that should never be compromised, these are among my candidates. Our shared human vulnerability is incontrovertibly at issue most pointedly precisely at the moment when one says we will never agree on the possibility of a common language. This is exactly the time and the place when it starts to be OK to begin a process of delegitimizing and dehumanizing someone else. When there is no hope of a common language, the first step toward rationalizing ignorance, prejudice, misunderstanding, demonization, and scapegoating has been taken.

A shared language is not a prison or a smothering demand for conformity. For one thing, the refusal to hold out for the possibility of a common language is already stated in a common language. Saying “we will never agree” is an instance of what Ricoeur (1967/1974) calls the “violence of the premature conclusion.” The internal contradiction of using a common language to say that we cannot hope for one is the mirror image of the person who argues for violence. Arguing is already a step into a language others can understand, implying a choice in favor of meaning over violence. The fundamental ethical and philosophical human choice takes place right here, in the desire for meaning and, as Habermas (1995, p. 199) puts it, in considerateness for a shared vulnerability. Accordingly, Ricoeur (1967/1974, p. 88) asserts,

The importance of this subject derives from the fact that the confrontation of violence with language underlies all of the problems which we can pose concerning man. This is precisely what overwhelms us. Their encounter occupies such a vast field because violence and language each occupy the totality of the human field.

The process of working out shared meanings in a common language is not a prison sentence, however. Including opportunities and concepts for critical engagement and deconstructive rethinking provide a way to prevent common languages from being overly confining. The Socratic midwife comforting the afflicted is complemented by the Socratic gadfly afflicting the comfortable (Bernasconi, 1989; Risser, 1989).

Heidegger (1982, pp. 19-23, 320-330; Fisher, 2010; Fisher and Stenner, 2011) accordingly describes the ontological (or phenomenological) method in terms of three moments: reduction, application, and deconstruction. Putting things in words is inherently reductive. There are infinities of ways of representing any experience in words, but even the most poetic among us has to choose the words that work to serve the purpose. And we may come to see on repeated application that our purposes are compromised by ambiguities that threaten to enact the violence of premature conclusions. Attentive concern for implicit meanings may lead to ways of discerning new distinctions and new conceptualizations, leading to new reductions and new applications. Languages are living and changing all the time. New sensitivities emerge and come into words by general consensus.

Ironically, being caught up in the desire for meaning can lead to the closing off of opportunities for creating meaningful relationships. Parsing differences into ever more local distinctions and separate historical and cultural dependencies can lead to a feeling that the barriers between positions are insurmountable. This way of arriving at premature conclusions has been especially prevalent among critical theorists who focused so exclusively on the deconstructive moment in the ontological method that they forgot that their writing inherently put a new reduction into play.

For instance, Delandshire and Petrosky (1994, p. 16) proclaimed that one of the ways their “post-structuralist view of knowledge is incompatible with the necessities of measurement is that interpretations are not assumed to be consistent or similar across time, contexts, or individuals.” The extremes in this display of hubris were called out by a number of observers. Bloom (1987, p. 387), for instance, held that deconstruction “is the last, predictable, stage in the suppression of reason and the denial of the possibility of truth in the name of philosophy.”

In contrast with these opposite extremes, others have kept their critical perspective in close contact with philosophical principles. Gasche (1987, p. 5) offers a “determination of deconstruction” within which “the latter’s indebtedness to the basic operations and exigencies of philosophy comes clearly into view.” Similarly, throughout his career, Derrida (2003, pp. 62-63; also see Derrida, 1981, pp. 27-28, 34-36; 1982, p. 229; Caputo, 1997, p. 80; Kearney 1984, pp. 123-124) repeatedly took pains to explain that:

…people who read me and think I’m playing with or transgressing norms—which I do, of course—usually don’t know what I know: that all of this has not only been made possible by but is constantly in contact with very classical, rigorous, demanding discipline in writing, in ‘demonstrating,’ in rhetoric. …the fact that I’ve been trained in and that I am at some level true to this classical teaching is essential. … When I take liberties, it’s always by measuring the distance from the standards I know or that I’ve been rigorously trained in.

Derrida (1989b, p. 218) recognized that

As soon as you give up philosophy, or the word philosophy, what happens is not something new or beyond philosophy, what happens is that some old hidden philosophy under another name—for instance the name of literary theory or psychology or anthropology and so on—go on dominating the research in a dogmatic or implicit way. And when you want to make this implicit philosophy as clear and explicit as possible, you have to go on philosophizing…. That’s why I am true to philosophy.

To give up on philosophy is to give up on the desire for meaning, for the working out of a common language, to accept an inevitably premature conclusion as definitive and to choose violence as an acceptable means of working out differences. Spivak (1990, 1993) then speaks to the strategic pauses that must interrupt the critical process to allow new determinations to inform revitalized concepts and applications in dialogue.

Finally, moving forward from here to better understand what it means to measure distances relative to standards requires close consideration of mathematical issues of modeling and signification. These issues reside deeply in the motivating ideas of philosophy, as has been widely recognized over the course of the history of Continental philosophy, through the works of Husserl, Heidegger, Gadamer, Derrida, and others (Derrida, 1989a, pp. 27, 66; Fisher, 2003a, 2003b, 2004, 2010; Kisiel, 2002). Much more remains to be said and done in this area.

References

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