Orthogonal is a design concept: Incommensurable is not

Orthogonal is a design concept: Incommensurable is not By Michael Lissack

Abstract: Incommensurability is a rather poor design choice. It blocks rather than encourages dialogue and learning. This article elucidates the benefits of replacing that thinking framework with a different design choice: orthogonality. The varying perspectives which philosophers take with regard to the type of experiences labeled as “recognizant transformative experiences” are used as the main illustration. If, as this author has argued elsewhere, one views realism and constructivism as orthogonal rather than oppositional perspectives, it turns out that recognizant transformative experiences map to the intersection of that very orthogonality. Knowing the intersection point allows the orthogonality to be mapped or graphed rather than merely spoken of in abstract terms. The visual representation thus created provides common ground against which the notion of perspectival incommensurability yields to a potentially meaningful discussion of commonalities, differences, and inter-relationships. When confronted with assertions of incommensurability in the space of a request for dialogue or inquiry, the design challenge is that of overcoming the very notion of incommensurability itself. Mapping incommensurability into orthogonality is a design concept which can meet this challenge. Introduction To misquote Braithwaite (1968) “The business of a philosopher is primarily to make clear what is happening in thinking.” One goal of this article is to begin to make clear an oft-times muddle in philosophical thinking, namely, the idea of perspectival incommensurability. Thinking frames are designs. We create them for a purpose and they can be evaluated accordingly. Incommensurability is a rather poor design choice. It blocks rather than encourages dialogue and learning. The second goal of this article is to argue that by treating incommensurability as a design choice we can see how to replace that thinking framework with a different design choice: orthogonality. Our vehicle for doing so will be to treat recognizant transformative experiences as if they were natural kinds. Such treatment allows for the discovery of common ground amongst previously considered incommensurables and allows the common ground to be clearly seen from a perspectival framework of orthogonality. The well-worn expression that "the unexamined life is not worth living" is often countered with "but the unlived life is not worth examining." Experience involves both living and examining. “Much of our human mental life looks to involve a seamless unfolding of perception, action and |1 Orthogonal is a design concept: Incommensurable is not, September 2015

experience: a golden braid in which each element twines intimately with the rest.” (Clark, 2008) I come to this exploration from the perspectives of Cybernetics and Social Complexity Theory disciplines which together will help us to cogently and viably describe the process of transformative experience. The multiple-order feedback loops, which are endemic to transformative experience and affordances for next actions, are the building blocks of cybernetics, the raw material for Social Complexity Theory, and provide the contextual background for my claims. Social Complexity Theory leads one to question and examine the stories and narratives we tell ourselves and others, as we go through the processes of life experiences. The theory looks at the complex influences of models, and representations on how context and events are attended to and cognized (Letiche and Lissack, 2011). Cybernetics leads one to examine the feedback loops, observations, and affordances which allow for experiences to unfold in the way they do (Umpleby, 2014). One cybernetic observation regarding experience is that, quite often, "change" happens not directly through some linear cause, but indirectly in that the cognized view of a situation shifts and that shift changes the 'affordance set' which then leads to new actions. One consequence of actions is that their cognition can change the cognition of both prior actions and current understandings. Rosenblueth and Wiener (1945) argued that the key to understanding lay in abstraction. Deutsch (1951) opens with “Men think in terms of models.” Hutten (1954) continues: “The model prescribes a context … used to provide an interpretation of new phenomenon.” Bailer-Jones (2009) argues that this context acts as a visual representation. (“If access is not perceptual, it is often facilitated by visualization.”) The use of such a visual representation is as a metaphor. The interaction view of metaphor (Hesse 1966) suggests that the invocation of a metaphor shifts the understood meaning of both the target and source domain. Here what is being invoked is the idea of visual representation itself. If we make the notion of the resulting shift in meaning the explicit topic of discussion, the resulting hermeneutics provide a common ground upon which the entire notion of incommensurability shifts to a discussion of commonalities and differences in evoked assumptions and the mechanisms by which those assumptions get evoked. “Hermeneutics holds the promise of fundamentally altering the way one thinks about interpretation, understanding, and the communication of culture interpretation must be a matter of constant revision: revising one's sense of the whole as one grasps the individual parts, and revising one's sense of the parts as the meaning of the whole emerges.” (Gadamer 1988) Via the hermeneutics evoked by the visual representations obtained as per above, Husserl’s fundierungs (Rota, 1989) get made explicit as do their implications for Gibson’s affordances (Turvey, 1992).

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Incommensurability and Orthogonality The traditional sciences have always had trouble with ambiguity - defined as the simultaneous existence of multiple meanings and/or multiple potential expressions. In the hard sciences, ambiguity is often replaced with a probability distribution - a contingent form of uncertainty which works well when the underlying ontology consists of indexical properties. In the social and special sciences, the underlying ontology is different - individual properties play a role in identity as do combinations of expressed and not yet expressed properties. Here the use of probability distributions to stand for ambiguity requires either omniscience or assertions of assumptions and claims of ceteris paribus. Emergence, volition, and reflexive anticipation - the very qualities which distinguish the subjects studied in the special sciences - are both context dependent in instantiation and in observer attention. These observations make clear that the special sciences and the hard sciences each have vastly different approaches to pursuing the scientific method -- an underlying conflict which is difficult to reconcile and which many practitioners in both sciences hesitate to acknowledge. Ambiguity is often bracketed through the assertion of assumptions. These "bracketing" assumptions thus function as "enabling constraints" (to use the cybernetics term previously mentioned)- narrowing the degrees of freedom of the subject items to match or be below that of the suggested controller - the proclaimed "rule" or "law" or "heuristic" which supposedly allows the underlying ambiguity to be dealt with. Ashby's (1958) law of requisite variety suggests that the enabling constraints function to allow "science" to make predictions and to offer "explanations." But, predictions and explanations predicated on ceteris paribus demand explication, if they are to continue to have meaning once the ceteris paribus constraint is relaxed. Habermas (1996) notes, "There is no one Science which itself is neutral; scientific activity is anything but monolithic - it fragments into a number of competing viewpoints that are shot through with values." The use of these enabling constraints amounts to what Lakatos (1970) called a "protective belt," blocking inquiry into fundamental questions of how the constraints are chosen, what values are implicit in the choices and what happens when they are altered. "All cultures have ways of dealing with these anomalies and ambiguities. One way to deal with ambiguity is to classify a phenomenon into one category only and maintain it within the category, thus reducing the potential for uncertainty. Another method of dealing with anomaly is to physically control it, removing it. A third way is to avoid anomalous things by strengthening and affirming the classification system that renders them anomalous. Alternatively, anomalous events or things may be labelled dangerous." (Lupton, 2013)

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Scientists cannot always apply ready-made terms, concepts or procedures to interpret new or surprising features of the world. Traditional views of science have emphasized the established, accepted, finished product, [an] approach [which] hides the extent to which scientists invent and negotiate ways of representing aspects of the world they are investigating the meaning of a term is not given by a finite, fixed set of necessary and sufficient conditions for its application (as analytical philosophy assumes), nor by stipulating an exact set of referents. Rather, meaning is given by sets of objects and associations that are invoked when a term is used. Membership of these sets can change. In science-as in everyday life-words and phrases often emerge from concrete situations in which participants jointly work out ways of describing what is going on. New terms, symbols or images are situatedthey acquire meaning through collective use in real situations. (Gooding and Addis, 2008) Modern science has dedicated itself to finding certainty and in so doing has opted to bracket away [in Husserl's, 1913, terms] the ambiguous reality which fails to confirm to that immutable blind vision. When confronted with alternative definitions of the terms used (which per Gooding and Addis, Lupton, and Habermas is inevitable), modern scientists assert that those making use of the alternate terms are speaking of an incommensurable domain – that there is no common ground through which dialogue is possible. Incommensurability was a favorite concept of Kuhn (1962) and Feyerabend (1962). Incommensurability, or some form of it, is generally accepted as part of our multi-valued, many disciplined, cross cultural world. That incommensurability is often processed by layman and philosopher alike as if it were an irreconcilable opposition. As an opposition, the claim of incommensurability is then used to block or bracket discussion. Claims of incommensurability allow for the bracketing off of anomalies and ambiguities. Its use as a protective belt is well established. If a given scientist wishes to curtail a challenging discussion often all that needs to be asserted is a claim of incommensurability and the discussion stops. Approaching the notion of scientific dialogue and learning as a design problem suggests that claims of incommensurability are unnecessarily obstructionist and overlook the very items which are commensurable and thus able to be discussed. As this article will illustrate by means of example, the key to undermining the incommensurability claim is to assert the existence of one or more orthogonal variables which underlay the supposedly incommensurable domains (c.f. Lissack 2015b). These orthogonal variable are typically found not in the variables which are the subject of the scientific examination but in the underlying presuppositions which function as each domain’s enabling constraints. Lissack (2015a) discusses the use of nine such orthogonal variables which he |4 Orthogonal is a design concept: Incommensurable is not, September 2015

calls “uceps” (uncritically examined presuppositions): Context Dependence, Fundierung Dependence, Quantitative Indexicality, Holonification, Graining, Clustering, Communication/Attention, Anticipation, Memory. The usual treatment of the incommensurable has been to label it as dangerous. What the elucidation of the nine hidden uceps does is allow for the formerly incommensurable to be mapped to regions in a space defined by those same hidden variables. What may have been seen as incommensurable (or threatening) by each of two perspectives when viewed from within their own cognitive space, become comparable mapped regions in a commensurable third space. By making the hidden uceps explicit we can examine the impact of changes in those variables, and, by definition, turn the incommensurable (when measured against each other's' native words/language) into the directly comparable. The formerly incommensurable are no longer so when they are compared through the lens of the hidden uceps. Once the orthogonal variables are identified, it is then possible to see how each of the claimed domains maps onto the orthogonal variable space. With this mapping what have we accomplished? Simply put we have found a means to place the usual incommensurability discussion into the context of a visual representation which by definition is then capable of being discussed. While the abstract discussion of concepts and perspective may remain incommensurable when conducted solely in the realm of language, the creation of a visual representation now provides grounding for a meaningful discussion about how the concepts and perspectives shown relate to one another within the context of the representation itself. Let’s look at this by means of an example: how philosophers of the “realist” and “constructivist” stripes view the notion of experience – in particular the notion of a “transformative experience.”

Defining "Recognizant" Transformative Experience What makes an experience so significant that we refer to it again and again? What is it that allows us to point to that very experience and say it changed us, or our path? What is it about the experiences we call "transforming" that gives them their very power to create change in an individual's life? Perhaps the key to recognizant transformative experience derives from its power to affect shifts in our perception of the very background assumptions which we rely upon as we take subsequent action. While we "experience" life as a flow, it is only by virtue of how we cognize, refer to and incorporate the retrospective lessons or viewing of that experience which gives rise to the possibility of transformation. This article explores consequences stemming from the idea that what makes an experience transformative, is not a causal relationship (a causes b -where the transformation is due to some |5 Orthogonal is a design concept: Incommensurable is not, September 2015

causal force), but rather is the act of stopping to re- evaluate perspectives and assumptions. If the act of stopping and re-evaluating is memorable, the associated "experiences" will be transformative. Their transformative nature arises from their ability to get one to stop and reevaluate. I call these stop and rethink experiences “recognizant transformative experiences" (to be distinguished from both nominal memorable experiences and pathway transformative experiences defined below). The key to such recognizant transformative experiences is literally to be found in the act of re-specting (viewing again, re and spect) the assumptions and cognitions which are the precursors to our actions. Learning to re-spect is critical to the power to transform and forms the foundation for next actions. Such re-spect occurs recursively whenever a memory of the recognizant transformative experience is recalled. This recursive pattern of re-cognizing (experience, re-cognize, act, encounter trigger, re-cognize, act, etc.) can be reduced to an abstract form. As such, it can be viewed as if it were a “natural kind” (Ali Khalidi, 2013) or perhaps as an “investigative kind.” (Brigandt, 2003; Griffiths 2004) The consequences of such a view are rather unexpected. The insights gleaned therefrom seem to shed more light on philosophical perspectives – potentially re-cognizant-ly transforming the current dialogue about perspectival incommensurability into one about orthogonality. The literature on transformative experiences is long on description and woefully short on explanation. As far back as the ancient Greeks, transformative experiences have been presented as the test of an actor who overcomes some obstacle and emerges transformed. It is easy to find descriptions of how an observer/actor feels post the transformative experience; lengthy novels which describe the before and after of transformative experiences; and a variety of religious/spiritual texts which detail the "newness" resulting from having had a transformative experience (e.g. Metzner, 2010). Such presentations, however, do little to define the process by which an experience becomes (or is labeled) transformative, what prerequisites are determinant, or how 'next actions' are affected by the experience. What is clear is that there are several pillars of transformative experience which merit greater examination: • • •

A participant’s philosophical stance A participant’s understanding of the mechanisms which lead to a transformative experience The narratives one tells as a result

I make seven assumptions and assert three conditions on the use of these pillars, in the context of this discussion. These assumptions and conditions will be critical to the analysis of the orthogonality and incommensurability claims at the heart of this article.

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Assumptions Assumption 1: The philosophical stance with which an ‘experiencer’ approaches transformative experiences, for our purposes: realist versus pragmatic constructivist, influences the affordances for next actions which that experience then offers. Assumption 2: The self-reflection and re-cognition the experiencer applies to understanding the mechanism(s) which give rise to the transformative experience are significant. The understanding of the mechanisms will play a major role in the process by which that participant renders his/her context and actions -- both pre and post the experience – coherent. Assumption 3: The narratives told about the transformative experience by the experiencer, and their effect on that same person, is impacted by the degree of coherence experienced with regard to a set of background assumptions or fundierung. Fundierung is a combination of “aliefs” (Gendler, 2008, “an innate or habitual propensity to respond to an apparent stimulus in a particular way"), “habitus” (Bourdieu, 1990, “habitus allows for the smooth functioning of the agents' engagement with the social world by predisposing the agent to perceive and act within that world in a routine way.” and beliefs about both the meaning of concepts and the world at large. In this discussion, the relevant fundierungs are influenced by a) philosophical stance taken; b) the understanding of mechanisms, as cognized, and c) the subsequent affordances and actions which result. As Faye (2002) phrased it: "Pre-judgments comprise all the beliefs and attitudes constituent in the horizons of understanding we bring to the process of understanding. We acquire a fresh understanding whenever our pre-judgments fail to fit with what we are trying to understand." Assumption 4: Recognizant Transformative Experience is distinct among ‘types’ of experiences. Using Gadamer's (1960) explication of transformative experiences as a model, I distinguish between two categories of such experiences. The broader category -- "pathway" transformative experiences - can be seen as some segment of the experiencer's life journey which gave rise to a turn in direction and a path chosen or abandoned. Pathway transformative experiences tend to be spoken of as the "cause" of the change in direction in a life journey. However, pathway transformative experiences tend not to be recalled and recounted as distinct moments of introspection, re-cognization, and re-affirmation such that they are "relived" upon the moment of recall. Pathway transformative experiences seldom evoke strong emotional reactions upon recall, whereas recognizant transformative experiences seldom fail to evoke such reactions. Assumption 5) The transformative aspect of experience (recognizant form) occurs when we are captured by the need to re-cognize our fundierungs.

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Assumption 6) The encounter with a potentially transformative experience is emergent (in the strong emergentist sense). And, whether that potential experience proves to be either pathways transformative, recognizant transformative, or neither, is intimately related to the mechanisms used and processes undertaken by the experiencer. This occurs both while the experiencer is attempting to make that encounter coherent with both his or her perceived context, fundierungs, and self-identity and his/her actions post the experience itself. Assumption 7) For an experience to be considered "transformative" (recognizant form) one of either two scenarios are required: (a) That the observer have a "mismatch" between current explanatory narrative and current context - creating the "gap" which a new explanatory narrative can fill, or (b) the observer have an encounter with a new context which evokes the recognition of such a mismatch. (An example of such a mismatch might be a first encounter with a legally married Catholic priest by someone unfamiliar with the existence of the Eastern Rite.) In either case the observer, through the recognizant transformative experience, finds him/herself able to construct a new explanatory narrative which solves the mismatch. Conditions Yet, it must be stressed, that the process outlined by assumptions 1-7 is not, by itself, sufficient for the experience so encountered to be labeled as "recognizantly transformative." This label seems to have three additional requirements: 

That the explanatory narrative summoned up not be highly context dependent or constrained - instead, it must be transformative from the perspective of the participant (in the alternative, the experience might be considered transformative with regard to the context but not with regard to the participant observer), and



That the experience give rise to a new explanatory narrative by allowing the participant observer to revisit the experience when a non-articulable trigger is reencountered, (examples would be the "madeleines" of Proust and the "awe" experience which architects attempt to create in religious and state buildings), and



That the experience itself is a trigger, evoking thoughts that occurred before and after the experience, and an awareness that a transformation has taken place.

The three conditions listed above seem to be required for an observer/ participant to have and recognize a recognizant transformative experience. However, the absence of these conditions does not definitively rule out the possibility that a transformative experience may have occurred.

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Rather, a pathway transformative experience may in fact have occurred, but its recollection by the participant/ observer would evoke mystery and only be remembered as a "past event" -- not one which is relived when the trigger is encountered. Applying the Natural Kind Analogy Natural kinds are abstract categories – abstract categories which sort the world into “meaningful kinds.” ”Insofar as they succeed in this regard, they do so precisely because they are attuned to regularities and patterns in the natural world. …Our classification schemes and taxonomic practices enable us to focus on some features of reality while neglecting others in order to make sense of these patterns of constancy and change. Natural kinds correspond to those categories that enable us to gain knowledge about reality.” (Ali Khalidi, 2013) It is this goal of gaining knowledge about reality which is the focus of the arguments in this article. By treating recognizant transformative experiences as if they are natural kinds I argue we can learn much about how to better deal with the problems of “incommensurability” with regard to philosophical perspectives. To this end, please note I am NOT claiming that recognizant transformative experiences are a natural kind and I am also not claiming that by treating such experiences as if they are a natural kind we can learn more about the intrinsic nature of the experiences themselves. Instead I am arguing that by engaging in the thought experiment of treating recognizant transformative experiences as if they are natural kinds we can gain insight into the nature of reality itself. The use of the “as if” natural kind analogy demands that we abstract the essential features of such experiences away from the content and context which may describe their particulars. From this process of abstraction, we can gain insight into how the abstract category so obtained “fits” in with the rest of reality as we best understand it. Brigandt (2003) refers to such abstract categories as “investigative kinds…. An investigative kind is a group of things that are presumed to belong together due to some underlying mechanism or a structural property...is specified by some nontrivial underlying feature or process that is presumed to account for the observed similarities.” As if natural kinds need not be restricted to “things.” Heisenberg (1963) told us: "the world is not divided into different groups of objects but rather into different groups of relationships .... The world thus appears as a complicated tissue of events, in which connections of different kinds alternate or overlap or combine and thereby determine the texture of the whole."

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The observed similarities with recognizant transformative experiences are to be found in the recursive pattern of re-cognizing (experience, re-cognize, act, encounter trigger, re-cognize, act, etc.). By abstracting the experiences to this pattern (and thus eliminating reference to the particulars of any given such experience), we are not required to describe the mechanisms which give rise to the eliminated particulars and instead can see what inferences can be drawn by employing the abstractions themselves. Craver’s (2009) observation: “natural kinds are the kinds appearing in generalizations that correctly describe the causal structure of the world regardless of whether a mechanism explains the clustering of properties definitive of the kind” suggests that through such an abstraction we shed light on some aspect of the causal structure of the world. Realism, Constructivism and Recognizant Transformative Experience My first observation stemming from an examination of the abstract as-if natural kind described above (via the 7 assumptions and the 3 conditions) is that the very nature of that abstraction seems to evoke both realism and constructivism simultaneously. Karl Marx (1845) noted: "All mysteries which lead theory to mysticism find their rational solution in human practice and in the comprehension of this practice." Transformative experience is often regarded as such a mystery but it is well rooted in human practice. Although the philosophical perspectives which go by the names "realism" and "constructivism" have vastly differing outlooks on what it is about those human practices which allows for the elimination of mysticism, they seem to be caught in an interactive dance when it comes to the abstract natural kind – recognizant transformative experience. “human practices which evoke the interest of constructivists are to be found in reflective anticipation, volition, and emergence. These three properties are how constructivism gets enacted and provide the foundation upon which related science and philosophical inquiries rest. Because of these traits, the phenomena studied by constructivists are often less epistemically tractable than are the phenomena studied by realists. That relative intractability gives rise to epistemic uncertainty uncertainty which those who practice realism tend to reject. Indeed, the history of realism shows it to be quite successful at asserting ceteris paribus in its efforts to fend off such uncertainties.” (Lissack and Graber, 2014) With regard to the recognizant transformative experience, these differences are highlighted when the “kind” in question is merely the initial experience. While the realist attitude affords ontological status to the experience itself (it was a "real thing" and life "revealed" it to the experiencer), constructivism places the onus of the experience and its cognition on the experiencer (who constructed it in order to make sense of context).

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If the transformative experience is "real" (and not "constructed") then both it and its implications were in some sense pre-given and the experience was itself a revelatory one. Many accounts of Western spiritual and religious transformative experiences are described in this manner. The revelation of the pre-given which then changes cognition is then narrated as the taking of a "new path" and next actions are judged based upon coherence with that new path. “Coherence is about acting in a manner consistent with who you are. Identity and action need to be consistent and not in conflict.” (Letiche and Lissack, 2011) By contrast, if the transformative experience was “constructed” (and has no separate ontological status), then the experience of re-cognizing is an experience of self-actualization and next actions are judged upon growth and learning potential rather than by coherence with a pre-given pathway. Many descriptions of Eastern spiritual and religious transformative experiences are narrated in this manner. The development of this learning potential is seen as a path to coherence with nature, mindfulness, and enlightenment. These two perspectives thus have vastly different affordance sets regarding self-identity and next actions. This interplay of self-identity and next actions is part of the recognizing pattern (experience, re- cognize, act, encounter trigger, re-cognize, act, etc.) which forms our “as-if” natural kind. Our task is to draw inferences not only from the initial experience but also from the recursive pattern. And, it is the pattern which is the observed regularity. As an analogy, Network/Graph Theory (Watts and Strogatz, 1998) perhaps best describes and defines recognizant transformative experience. When a well-connected hub is removed from a given network, the nodes must reconfigure into a new network - analogous to a changing affordance set after a recognizant transformative experience. Comparatively, when an individual experiences something transformative, they must also reconfigure their context to put their definition of the world as they know it in perspective, according to this new "affordance" created by the transformative experience. In the efforts to re-assert coherence an individual (just as the transformed network) reexamines the previously held web of connections (beliefs and assumptions) and finds a new narrative. “In realist based science, explanations are about regularities and the task is to bracket (to commandeer from Husserl) the contingencies that otherwise can obscure the explained regularity. In constructivist based science, explanations are about the contingencies that have arisen and thus afforded deviance from expectation - where the expectation is a series of regularities. Contingencies often play the role of 'noise' in realist explanations and, along with volitions, often play the role of protagonist in constructivist explanations.” (Lissack and Graber, 2014)

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Both realists and constructivists recognize that the phenomenon labeled as "transformative experience" occurs, and that once having occurred, the phenomenon can have a major impact on the affordances and next actions of its experiencer. Both the realist and the constructivist recognize that a “new narrative” must be generated to render the perceived world/context/selfidentity coherent post the transformative experience. Just as a network needs to restabilize following the loss or introduction of a well-connected hub so as to regain its coherence and functionality, so too must the experience of a recognizant transformative experience generate a new coherent narrative which incorporates both that experience and the remainder of the experiencer’s world. For a philosopher observing, the transformative nature of this narrative generation process lies in its potential to illustrate a convergence between the realist and constructivist perspectives. As Noe (2012) might phrase it, the narrative generation process makes both perspectives available to one another and thus grants their respective adherents access to the other perspective. When a recognizant transformative experience has occurred, the realist is then forced to engage in a set of constructivist acts in order to establish the stabilizing coherence. Similarly, the constructivist is forced to acknowledge the "ontic realism" of the experience itself as it gets relived and reexperienced in the unfolding of the narratives which allow subsequent actions to be coherent. When the “natural kind” analogy is applied, the recursive pattern becomes the fundamental descriptor of the recognizant transformative experience. Through the abstraction of this pattern, it seems that the realist and pragmatic constructivist perspectives on recognizant transformative experience can be reconciled. To the extent that a recognizant transformative experience creates a new narrative, that narrative both becomes emblematic for one's self-identity and serves as boundary/constraint conditions for the evaluation of actions, values and beliefs undertaken thereafter. Challenges to coherence are viewed against the new narrative and not the prior narrative. Thus, the new narrative takes on "real" properties (albeit contextually determined and of an 'as-if' character) despite being the product of construction by the experiencer. The realist is forced to deal with the recursive construction and reconstruction of the new narrative as the experience itself (afforded the status of real) gets recursively retriggered. The constructivist is forced to acknowledge that the same (or seemingly very similar) constructions happen recursively when encountering any trigger for the recognizant transformative experience. This pattern of same construction when faced with triggers for a recursive memory suggest that the memory itself is of an encounter with something real. The recursive character of the natural kind abstraction evokes mirror observations between the two perspectives. We have thus found a meeting point.

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Orthogonality Having found a meeting point, the next step in this investigative process is to examine how the two perspectives arrange themselves as they “move away” from that meeting point. In this instance the moving away involves a minimization of both recursion and “re-cognization” and a normalization back to the nominal experience and to the flow which is our life experience itself. Given a prior belief that the two perspectives of realism and constructivism were “congruent but orthogonal” it would flow naturally to attempt to describe two perpendicular lines. Such an attempt was very successful with regard to the two “kinds” of Science (Science 1 and Science 2, c.f. Lissack and Graber, 2014) which plotted very nicely to perpendiculars described by “reliable prediction” and “attunement to context”. (Figure 1) (From Lissack and Graber, 2014: “Objectivity and a goal of reliable predictivity are the hallmarks of what we shall label Science 1. Science 1 excludes context dependence, thus when it is forced to deal with the possibility instead asserts ceteris paribus. Science 2 explicitly makes room for the context dependencies that Science 1 has excluded. These can be characterized as emergence, volition, reflexive anticipation, heterogeneity, and design, among others. In the Science 2 world, the focus is on individual actions and occurrences, whereas the regularities of Science 1 are part of the context in which these individual events occur.”)

However, when a similar effort was applied to the notions of realism and constructivism the perpendiculars did not reveal themselves. It seems the suggested belief (that realism and constructivism exhibit orthogonality) was wrong. Orthogonal was too wide a descriptor to apply to the differences between realism and constructivism. The two perspectives which do seem to map to a perpendicular are e ssen t ialism an d nominal e mp iric ism a s sho wn in Figure 2 . Here t h e d ef in in g scalar s a r e “quantitative indexicality” (the extent to which the abstract

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qualities can be expressed in scalar quantitative form) and “fundierung dependence” (the extent to which the background assumptions brought by the observer are involved in the co-production of the phenomenon being observed).

Within this perpendicular, it seems that realism and constructivism fall within a narrower band of perhaps 45 to 60 degrees separated by their relation to context dependence. (Figure 3) As Habermas (1996) notes, "There is no one Science which itself is neutral; scientific activity is anything but monolithic - it fragments into a number of competing viewpoints that are shot through with values." In the case of realism and constructivism, realism requires elements of constructivism to explain the actions that come after a transformative experience; constructivism requires that certain ‘real’ properties of a transformative experience be acknowledged in order to explain them using the constructivist framework.

My claim is that the existence of a visual representation providing common ground to the previously regarded as incommensurable can itself be recognizantly transformative. The key to | 14 Orthogonal is a design concept: Incommensurable is not, September 2015

both the re- cognition and the transformation lie in the power of defined orthogonal scalars to map to visual representations. Similar to the mathematical approach of the late Alexander Grothendieck, the goal of applying visual representations to the concept of perspectival incommensurability is to use the representations as a means of placing the problem within a broader context such that the answers “just appear.” When two planes intersect, they define a three dimensional space. For our purposes these two planes are those created in the effort to map the orthogonality of both realism/constructivism and Science 1/Science 2. The two planes intersect around the concept of context dependence (or as stated on the Science 1/Science 2 plane: attunement to context). The variables defining the two planes are: context dependence, quantitative indexicality, fundierung dependence, and reliable prediction. Recognizant transformative experiences would, when expressed as a natural kind, be located at or near the core of this three dimensional space. (Figure 4) With the “space” so defined, it now becomes possible to “map” perspectives and concepts as viewed through the frame of a given perspective into the space. Perspectives map as generalized areas and concepts as more point-like “places”.

The choice of visualization of the 3d space will affect its utility as a tool to allow for discussion of perspectives and concepts. For example, if we were to opt for a sphere, as in Figure 4, we run into the problem of the artificial zeros. Unlike the earth, located in a greater universe with an observable spin around an axis (which defines north, south, and the equator) our conceptual sphere comes with only one pre-defined point – the core. The depth of the sphere from the core is arbitrary as are the definitions for longitude and latitude. Conceptually this might be a nice analogy for relativism but it does not help us in attempting to create a useful visualization. For the sake of initial clarity (and subject to revision based upon feedback and criticism), I have opted to use a circle as the space, with the third dimension represented by the intensity of the | 15 Orthogonal is a design concept: Incommensurable is not, September 2015

color used. Two more dimensions can also be shown: dimension 4) the size of the shape displayed and dimension 5) the transparency of the color displayed. I would note that intensity of color and transparency of color can easily be confused and thus the use of this “fifth” dimension may present challenges. Figure 5

Implications Mapping the orthogonalities into a visual representation provides a means for discussion amongst a common element – the representation – even whilst the items being mapped (perspectives or concepts viewed from a particular perspective) are otherwise claimed to be “incommensurable.” A review of the literature concerning perspectival incommensurability has not revealed any similar mappings or even attempts to produce such mappings. While there are tables of “differences” in many articles and books on incommensurability, the data is not presented in a manner which allows conversion in any but an arbitrary manner to a visual representation. This arbitrariness defies Bohr’s (1954) edict regarding ambiguity: “Every scientist . . . is constantly confronted with the problem of objective description of experience, by which we mean unambiguous communication.” It seems that the key difference between the approach outlined above and most prior approaches lies in the very notion of orthogonal versus oppositional. If perspectives or concepts are initially viewed as both incommensurable and oppositional (i.e. that the ascription of “meaningfulness” or “correctness” or “truth” to one is the denial of that ascription to the other), then the notion that a shift to a more abstract plane on which to find commonalities seems foreclosed from the start. By contrast, if one starts with the view that these items are orthogonal, then by definition, at least in the abstract, there exists a meeting place to be both discovered and explored. Star and Griesemer (1989) defined such meeting points as “boundary objects … both adaptable to different viewpoints and robust enough to maintain identity across them.” “Boundary objects are | 16 Orthogonal is a design concept: Incommensurable is not, September 2015

a sort of arrangement that allow different groups to work together without consensus… the map did not need to be accurate to be useful. It could serve as the basis for conversation, for sharing data, for pointing to things --without actually demarcating any real territory.” (Star, 2010) Similar meeting points and strategies for accommodating the discussion to so-called incommensurability can be found in the notion of Buberian dialogue (Letiche, 2008) (where the audience plays a critical role in the discovery and articulation of the “held in common” items) and in the main technique for overcoming the clash in values which designers label as the “uncanny valley” (Mori, 1970) (where the movement towards abstraction and away from particulars allows for the assertion of an indexicality/ambiguity which then provides the common field of reference). What these examples have in common with the recognizant transformative experience examples is that all three require abstraction to “essence” in order to better understand the “meeting place” amongst the orthogonals and that re-cognization is a common element in all three abstractions. Further, all three involve the interaction of one or more observer/actors with a potentially transformative experience. Through the mapping exercise above, incommensurability amongst realism, constructivism, pragmatism and other philosophical perspectives has been given a visual context in which meaningful hermeneutic discussion can take place. Recursively, the exploration of recognizant transformative experiences as “as- if natural kinds” allows for the re-cognization of the incommensurability question – which itself is a rather transf ormat ive e xpe rien ce . The con seq uen ce s of that transformation must be explored elsewhere but the existence of the potential transformation suggests that there is much philosophical fruit to be gathered from the now low lying branches of the tree of recognizant experiences. Once claims of incommensurability have been stripped away – the value in exploring orthogonal dimensions asserts itself. Religious and spiritual experiences, artistic and creative epiphanies, intellectual “ahah” moments, the Mori uncanny valley and Buberian dialogue are all examples of recognizant experiences which seem to lie at the intersection of the realist and constructivist perspectives and which can benefit from explorations conducted in both the realms of Science 1 and Science 2. Most examples of such experiences have been explicated in the form of description. What this article suggests is that there is philosophical gain to be had by approaching these experiences more generally and treating them as “as-if natural kinds.” By extension the Grothendieck method of exploration can thus be applied to both the questions raised by recognizant experience and to the claimed issues of perspectival incommensurability. The resulting hermeneutics will not provide answers to problems so much as it indicates patterns of inquiry that one can undertake in the process of thinking them through and collaborating with others to solve them. Using orthogonality as a design concept can thus promote such inquiry – the very inquiry that assertions of incommensurability block. | 17 Orthogonal is a design concept: Incommensurable is not, September 2015

"In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility of the meaning of such a comparison." (Einstein and lnfeld, 1938) Vaihinger (1924) put it: "the object of the world of ideas as a whole is not the portrayal of reality this would be an utterly impossible task - but rather to provide us with an instrument for finding our way about more easily in this world." When confronted with assertions of incommensurability in the space of a request for dialogue or inquiry, the design challenge is that of overcoming the very notion of incommensurability itself. The resulting designs are those which accept Vaihinger’s task description “an instrument for finding our way in the world” while recognizing Einstein’s warning that one “will never be able to compare his picture with the real.” Mapping incommensurability into orthogonality (through uceps or other variable) is a design concept which can meet this challenge. References Ali Khalidi, M (2013) Natural Categories and Human Kinds: Classification in the Natural and Social Sciences, Cambridge University Press Ashby, W. R. (1958). "Requisite variety and its implications for the control of complex systems." Cybernetica, 1(2): 83-99. Bailer-Jones, D. (2009) Scientific Models in Philosophy of Science, University of Pittsburgh Press Bohr, N. (1954) “Unity of Knowledge” in Atomic Physics and Human Knowledge. John Wiley & Sons, Inc.. 67--82 (1958) Bourdieu, P. (1990) The Logic of Practice Stanford University Press Braithwaite (1968) Scientific Explanation, A Study of the Function of Theory, Probability and Law in Science, Cambridge University Press Brigandt, I. (2003) “Species pluralism does not imply species eliminativism.” Philosophy of Science 70: 1305–1316. Clark, A. (2008) Supersizing the Mind: Embodiment, Action, and Cognitive Extension, Oxford University Press | 18 Orthogonal is a design concept: Incommensurable is not, September 2015

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