Bill Torbert

[Balder]

I came across a conversation with Bill Torbert this morning that I wanted to share here.  I referred to his work a couple years back in a blog I wrote on Integral Life (Three Nows, The Future Infinitive, and Triple Loop Awareness), and I enjoyed a workshop he gave at the Integral Theory Conference in 2008 (he seemed to find many of the "Integralites" at the conference to be a bit naive), but up to this point, his work has mostly been at the edges of the horizon of my attention.

 

~*~

  

Conversation with Bill Torbert

July 11, 2002

William R. Torbert, PhD, author and teacher, consultant and artist in his own right, works with Susann Cook-Greuter and others in the application of integral and transformational concepts in leadership and organizations. His most recent book, co-authored with Dalmar Fisher and David Rooke is entitled Personal and Organisational Transformations: Through Action Inquiry. After teaching at Yale, SMU, and Harvard, Bill has been at Boston College for the past 23 years,
serving as Graduate Dean of the School of Management for 9 years and Director of the PhD program in Organizational Transformation.

RV: I'm really interested in having conversations with people who are doing things that, for me, feed into the idea of an integral approach to leadership. And an integral approach to leadership, it seems to me, is one that is very much concerned with questions of development. And what I'm hoping to do in this interview involves three stages. The first stage is to have you talk a little bit about the role of action inquiry in your work. When I look at materials you have on your web site it is very clear that this has been the heart of your work ever since you were a graduate student. I would like to talk about your perspectives on leadership and leadership development. Third, I'd like you to talk about your current work because you mentioned it has something to do with time, and I'm fascinated to discover what that might be.

BT: Great.

RV: You were a student of Chris Argyris and the whole idea of action inquiry has been central to your work. What is unique about your work in action inquiry?

BT: Although it is definitely true that Chris is a central influence in my life, and that is because he clearly was concerned with putting action and inquiry together, it's also true that at the same time as I met him at Yale I also got to know Bill Coffin, the Yale minister. He's sometimes called the white Martin Luther King, was very involved in the Civil Rights movement, was one of the first Freedom Riders, and later stood in the opposition to the Vietnam War.

There should be a relationship not just between social science theory and professional action, but also between spiritual inquiry and political acts. Chris was relatively conservative, not spiritually oriented and not politically oriented. Bill Coffin was more radically oriented.

And at the same time I was getting to know, not what we think of as philosophy today, but real Socratic inquiry where you are taking action in the conversation and having an influence on one another, almost an alchemical influence. At the same time I found my way into the Gurdjieff Work. This direct spiritual work is a work on attention. Through Plato, Bill Coffin and the Gurdjieff Work, I had a sense that the kind of action inquiry I wanted to do was not only professional in nature, but personal, spiritual and political. It was meant to affect my every waking moment.

All of those were playing a role when I started to inquire further into Yale and the graduate program with Chris Argyris. I took an intervention theory course with him years before he wrote his intervention theory and method book [Intervention Theory and Method, 1970-ed.] and years before he had come up with the name action science. In fact, it was my 1976 book, Creating a Community of Inquiry, about the Yale Upward Bound Program that I had founded that first introduced the
term action science.

I went into the doctoral program in Individual and Organizational Behavior with the understanding that I could study myself trying to take some action in some way. This turned out to be leading the Yale Upward Bound program: creating it and getting the original grant for it. When it turned out that there was nobody of a proper age to lead it, the Yale people let me do it at the tender age of 22. I was not intervening in a large, Fortune 100 corporation, which was more typical of Chris's work. I was engaged in a very incendiary interracial situation that had a political element to it. It had a profound educational element in it in that the students in my program had never had a good experience in school before. I was working with people who really didn't necessarily share my sense of rationality at all.

RV: What I'm getting as I'm listening to you is already an integral flavor to the way you're engaging with the world or at least with a notion of action inquiry. Not only were you doing an inquiry into the context -- the systems, the environments around you -- but you were also engaged in conscious self-development, a process that could only happen in that context.

BT: Exactly. It seemed to me that the people who ought to be most affected by an action were the initiators of the action. Even though the intent was also to have an influence over somebody else, if you didn't see yourself as learning and transforming through the action, then it seemed to me you were almost certainly off base in a profound way. I'm not coming up with the way in which I knew that at the time except for the fact of all these different influences.

I read Plato's Symposium about Alcibiades who later became the leading general during the Peleponissian Wars. He was the great corporate raider of the third century BC, moving his allegiances back and forth between Athens, Sparta and Persia, trying to create a just environment in a situation in which none of the states seemed just to him. And there he was, as a student of Socrates, saying that only Socrates could make him feel his nothingness. This seems to me to be the place from which all possibility begins -- the meeting of the inner and the outer in the moment when, listening beyond one's ego, one feels one's nothingness. This is the actual experience of what we're now calling integral.

[The rest of the conversation is available here.]

[Edward theurj Berge]

There should be a relationship not just between social science theory and professional action, but also between spiritual inquiry and political acts.

Here, here! 

Direct spiritual work is a work on attention.

I discussed this in the "real and false reason"* thread:

Here is an excerpt from Torbert’s 2008 “Developmental Action Inquiry”:

“….in a figure/ground shift, the Alchemists and Ironists experienced ambiguity as the creative, ongoing element of all experience. This finding is consistent with the change from a primarily cognitive/structural approach to…a primarily attentional/spiritual approach in the shift from Strategist to Alchemist.”

*This thread is, to be intentionally self-attentional, one of my best works here and contains a virtual wealth of information with exacting and insightful analysis. I am rightfully proud of my production.

[Edward theurj Berge]

And this excerpt from that thread using Torbert's work to make a point about a "higher level" understanding of levels themselves and how they are formlated:

Note in the Commons article above he goes into the transitional steps between stages. It is more extended that Wilber’s fusion-differentiation-integration scheme but follows the same trajectory. It is classical Hegelian dialectics, from thesis to antithesis to a newer, higher, more coordinated and integrated thesis (313). But is this notion itself postformal or just an extension of formal operations?

Because the MHC assumes that it is only an objective and quantitative model that purports to eliminate qualitative content and distinction, you find very different descriptions of the postformal levels than one might in the more domain-specific models like cognitive or ego development. For example Torbert’s (cited below) action-logics defines formal operations as being logic oriented whereas the first postformal stage a Strategist seeks “to construct an explicit and distinctive integrative theory of self and world that recognized development (e.g., theories such as Hegel)” (185). So far this sound more like an extension of formal logic I’ve been criticizing. However he also notes that the Strategist is “aware of paradox” and “relativistic” (186) so this is not quite in line with Hegalian dialectics.

The next stage though, Magician/Clown, has some interesting characteristics. For example: “ego identity disintegrates, creates mythical events that reframe situations, blends opposites, treats time and events as kairatic, symbolic, alalogical, metaphorical” (186-7). Here we get into the kind of postformal dialectics discussed at length in an Integral Review forum on Gary Hampson’s article (cited below), excerpts of which reside at Open Integral (see links below). The whole notion of a Hegelian dialectic is replaced by understanding that core dualities cannot be “resolved” into a higher integration but rather a Magician “blends opposites” dynamically according to context through analogical, metaphorical narrative. This is further reinterated in his last stage, Ironist, who “cultivates a quality of awareness and action that highlights dynamic tensions of the whole enterprise” (189).

Nothing of this sort is seen in the MHC. As Hampson’s article suggests, “the way out [of postmodernism] is through it.” I suggest Hegelian models like MHC have yet to sufficiently go through this “stage” and hence, much like Wilber, continue to conflate, exaggerate and project formal operations into postformal stages.

Works Cited

Hampson, G. “Integral reviews postmodernism: The way out is through.” Integral Review, 4: June 2007.

Torbert, W. "Cultivating postformal adult development" at this link.

Open Integral links to Postformal Dialectics:
Part one
Part two
Part three

[Edward theurj Berge]

Also see the thread I started here with Bonnie Roy noting the following about nested levels and postformal levels according to Torbert:

One such overused exemplar of mainstream integral theory, is the notion of transcend-and-include and the holarchical organization that results from it. When “transcend-and-include” describes a dynamic, it is describing a simple, linear dynamic that creates nested sets of levels that are related in simple linear ways. If instead of associating the term “integral” with a set of exemplary beliefs and the community wit large that promote them, we identify the adjective “integral” in “Integral Theory” as pertaining to a level of cognitive abstraction, also known as meta-systematic [5], then no theory that entails simple, linear transcend-and-include dynamics can pass the test.

[5] This is consistent with the definition of “integral level” in cognitive-developmental theories such as Torbert, Cook-Greuter, and Fisher

[Balder]

*This thread is, to be intentionally self-attentional, one of my best works here and contains a virtual wealth of information with exacting and insightful analysis. I am rightfully proud of my production.

Rightfully so.  That is a great thread.

[Edward theurj Berge]

Here is a more recent interview with Torbert in the June 2010 issue of ILR. A teaser (with more later):

I think Ken is missing the second-person in his theory. He has the individual (first-person) and the collective (the third-person), in the kind of static, two-by-two table I’ve never liked... As if that isn’t non-processual, non-dynamic, and non-second-person enough, Ken also claims that developmental theory doesn’t operate at the social level, which is as completely wrong as I’ve ever found him to be.

[Edward theurj Berge]

Integrel Review, in its special issue on politics (6:1, 3/10), printed excerpts of Torbert's 1991 book The Power of Balance (Sage). Therein he correlated his action-logics to political power structures, from unilateral to diplomatic to rational/logistic to transforming. Here are some of the traits of the last: 

 

Hence, a person exercising transforming power invites mutuality—a mutual exercise of power guided by a living awareness of what is currently at stake for the particular systems participating in the transformation.

 

Transforming power cannot be insolently and unilaterally wielded. Instead, it requires a continual, humble effort—not just to be rational—but to be aware of the present moment in all its fullness. This awareness effort includes and transcends one's own material interests, emotional preferences, and intellectual theory about the situation, as well as those of the others and the institutions involved.

 

Transforming power is not merely open to, but actively seeks, challenge and contradiction.... The person seeking to exercise transforming power must seek challenges to his or her approach in every way possible.

 

Any theory of development and transformation, such as this one, clearly has general, universalistic elements to it, and may be applied “in general” without specific attention to the uniqueness of the given situation. This, again, is a danger of the Strategist who tends to identify with the theory. In fact (or, more precisely, in act) transforming power is never properly applied in general, but always in response to the unique circumstances of particular situations and systems—always in response to a living awareness that revivifies and revalidates (or else disconfirms) the general categories of the theory.

 

Put differently, transforming power is not enacted in a deductively logical fashion. It does not deduce a specific action from general principles. Instead, transforming power is enacted ana-logically. It seeks analogies between a general theory and an independent apprehension of the present situation, felt from the inside as a participant in it.

 

Transforming power empowers all who come within the radius of its influence, including those who oppose its influence.

 

But note the following, that the power of balance comes not from a strict identity with even the transforming power structure, but the ability to use each structure where appropriate:

 

There must be a “power of balance”....but the power of balance would, precisely, have each subordinate type of power (including transforming power) rather than being (fully identified with) any one type of power. It would exercise each type of power occasionally and intentionally, not always and assumptively.

 

 

 

[Balder]

At the 2008 Integral Theory conference, Torbert critiqued Wilber's quadrants as 'flat' and offered instead the 'deep four' territories of his action research.  Here are two summaries of his remarks, the first by Edward Kelly and the second by Marilyn Hamilton.

 

Kelly:

 

Torbert’s presentation on developmental action inquiry highlighted the four territories of experience (outside world, own sensed embodiment and performance, action logics and intentional attention), its interweaving of 1st, 2nd and 3rd person research in action, it’s recognition of three different types of research (single, double and triple loop feedback) and a discussion on the leadership development framework (LDF). Torbert noted how he liked to contrast his deep four (four territories) with Wilber’s flat four (quadrants) and how the deep four require both thinking and feeling whereas the flat four require only thinking – as a primarily a 3rd person 'thinking' map. Torbert’s presentation was extremely well received, due at least in part to his authenticity and the fact that he appears to have merged his theory and practice into his own life in a very strong 1st, 2nd and 3rd person sense.

 

Hamilton:

 

Torbert’s ‘Deep Four’ Action Inquiry

The research of Bill Torbert and his associates (Torbert, Livne-Tarandach, Herdman-Barker, Nicolaides, & McCallum, 2008) is well grounded in action as well as theory. Torbert critiques Wilber’s quadrant model as being the “Flat Four” cognitive map. He offers instead his Deep Four of First, Second, and Third Person along with Intention and Attention. Torbert incorporates an adult learning model into his action inquiry and maintains that he does not bifurcate individual and collective realities (another critique of Wilber) but interweaves them into a community of inquiry.  

Torbert proposes that a critical aspect of his leadership development framework is that the action aspect of his approach, provides an external validity through feedback (as does Action Research (Stringer, 1996)).  

Torbert’s associates supply three examples of Action Inquiry: One examines the effect that fear has on locking a leader into his solution-centred mode of operation. Another inquires about the effect of stressful life conditions that cause leaders to downshift from their normal centre of gravity. The third graduate student examines the relationship of leaders to ambiguity. 

Torbert et al, conclude that action logics are critical to success; ie. internal development impacts the performance of leaders in whatever context they operate in. The more developed leaders are the more resilient they will be to the impacts of fear or stress and the faster they will recover from downshifts and regain an advanced level of leadership capacity. 

Furthermore the study of ambiguity reveals that as leaders develop they change their relationship to ambiguity from viewing it as something to be endured or tolerated to an experience that can be surrendered to, or, at the most advanced stages, even generated for the creative opportunities ambiguity avails.

[Balder]

A little more from Torbert on the "deep four" (territories of experience) and his Developmental Action Inquiry in relation to AQAL.

 

 

Theoretically Distinctive Aspects of DAI: The Deep Four

In one of his early books, Learning from Experience: Toward Consciousness (1972), Bill Torbert critiqued the positivist, objectivist theory-data model of modernist science and instead named four distinctive territories of experience that humans seek to coordinate and align both in theory and in practice: first, the outer world (as seen and otherwise sensed by a person or measured by an instrument [including others’ actions seen from the outside – altogether, what modern science calls ‘the territory’]); second, the self-sensing of one’s own embodiment, breathing, moving, perceiving, etc.; third, one’s own ongoing structures of thinking and feeling (which in dialogue with others in a scientific community of practice generate what modern science calls ‘the map’); and fourth, the intentional attention (which can be distinguished from the other three territories, can experience all three simultaneously, and can be voluntarily cultivated in adulthood, but rarely has been in our culture, up until the recent growth of adult development theories and practices [Kegan, 1994; Ouspensky, 1949; Torbert, 1976, 1987; Trungpa, 1970; Wilber, 2000).

In the Power of Balance (1991), Torbert described how anyone can confirm for him or herself the reality of each of these four territories through thought and attention experiments, somewhat like Descartes’ doubting procedure to establish the indubitable fact that we think. To highlight this difference between his ‘theorizing about trans-theoretical experience’ and Ken Wilber’s (2000) effort to create a ‘comprehensive intellectual map of all experience,’ Bill sometimes calls these four, mutually-orthogonal “territories of experience” the Deep Four Ken’s four-quadrant AQAL model the Flat Four (since Ken’s four quadrants are all cognitive categories that tend to keep our attention fixated within the single ‘thinking’ territory [as most of you, our readers, are, likely, as you’ve been reading this; now?). The words for the Deep Four territories of experience are obviously also cognitive categories, but, as the “deep” four, these terms invite us, not just to ‘think’ the categories, but also to experience – now, in each present moment – the pre- and post-conceptual realities to which they refer (e.g. the color and texture of the ‘outside world,’ the ‘inner sensing’ of our own breathing, moving, and feeling, as well as the kind of ‘attending’ that can “taste” this external text, one’s own breathing, one’s thinking (about these words now), and one’s inquiring into the very source of attention all at once, simultaneously, e.g. now) (see Table 1).

Described in these ways, the Deep Four territories of experience constitute what we think of as the 1st-person field of action inquiry, bounded by the current limits and usually-unexamined assumptions of the self’s capacity for perception and sense-making (i.e. the specific developmental action-logic through which one currently encounters the world, as will be described below. Given these limits, a more full apprehension, understanding, and engagement of reality requires two additional aspects of all human lives -- the 2nd-and 3rd-person fields for 1st-person work and play.

1st-, 2nd-, and 3rd-Person Fields of Inquiry

The process of inquiry or research in action is a means of attending to experience of the world, including our dynamic sense-making of that experience, as well as adaptive engagement. By adaptive engagement, we mean those times when we (the person, team, or organization) are intentionally attempting to assess whether our intentions, plans, actions, and outcomes are aligned with one another and with changing conditions… and are responding accordingly. For some, this process is very rare, for others quite regular. An important question is whether and how one tests the validity of the information one is processing in real time, and DAI is one of a broader family of recent efforts to begin describing and defining this world of methods for valid inquiry in the midst of action (two others are action science [Argyris et al, 1985]) and Senge’s [1990] five disciplines).

The theory, practice, and research methods associated with developmental action inquiry (DAI) all point toward the capacity for individuals, teams or communities of practice, and larger organizations and institutions to conduct interweaving 1st-person, 2nd-person, and 3rd-person research (studying ‘myself,’ studying ‘ourselves,’ and studying ‘them’) in the midst of their daily practice (Chandler & Torbert 2003, Torbert, 2000). In contrast to modern science – which offers a model of 3rd-person research “on” “subjects” (who are, ironically treated as objects) – DAI is a model of research on oneself and with others that requires a high voluntary commitment by participants, as well as increasing mutuality and collaboration among them (McGuire, Palus, & Torbert, 2007).

A third distinctive feature of DAI is that progress occurs, not just by incremental single-loop hypothesis or market testing, but also by double- and triple-loop learning and change, whereby the very assumptions of one’s organization’s, team’s, or personal action-logic transforms (double-loop learning) or aligns across all four territories for a moment (triple-loop learning). When, during our personal, relational, and collective actions and inquiries, incongruities are found across the four territories of experience (e.g. an unintended result, an ineffective performance, a strategy that feels inconsistent with one’s integrity, a lie, etc.), action inquiry gradually generates, in the 1st-, 2nd-, or 3rd-person human system, the capacity for these three distinct orders of change.

The fourth distinctive feature of DAI (the D in DAI) is the developmental theory used to map the evolution of the action logics through progressive forms of increasing complexity, differentiation, and integrity at the personal, team, organizational, and institutional scales (Torbert, 2000a, 2000b). This theory hypothesizes a specific sequence of action-logics (Opportunist, Diplomat, Expert, Achiever, Individualist, Strategist, Alchemist, Ironist, Elder are the names of the personal action-logics) through which any human system can (but may not) transform, as it gradually gains the capacity to monitor all four territories of its activity and to develop greater congruity, integrity, and mutuality among them. Single-loop, incremental learning is practiced increasingly regularly as a person masters the Achiever action-logic. Double-loop, transformational learning is first explicitly recognized at the Individualist action-logic and becomes a touchstone of the Strategist action-logic. Triple-loop inquiry in-moments-of-action is increasingly practiced in everyday life at the Alchemist and Ironist action-logics (Torbert et al., 2004).

Overall, DAI theory and method strikes a different balance from Wilber’s AQAL model. DAI theory and method put primary emphasis on the four attentional and experiential territories of experience we can engage at each moment, rather than on four conceptual fields. DAI puts secondary emphasis on interweaving 1st-, 2nd-, and 3rd-person and practice, rather than bifurcating attention between the individual and the collective. And DAI puts tertiary emphasis on creating communities of living inquiry with single-, double, and triple-loop learning at their heart, rather than communities of shared belief.

In attempting to assess empirically who acts regularly at which action-logic and how persons at a given action-logic fare in the rough and tumble world of everyday life, let us look next at the historical evolution from the Loevinger SCT instrument to the Harthill LDP and then at some of the field research using the Harthill LDP.

 

The full article is available here.

 

[Edward theurj Berge]

The fourth distinctive feature of DAI (the D in DAI) is the developmental theory used to map the evolution of the action logics through progressive forms of increasing complexity, differentiation, and integrity at the personal, team, organizational, and institutional scales.

So one question for me is, as in the real and false reason thread, how does one formulate and measure "increasingly complex" stages? The terms he's using--increasingly complex, differentiated, integrity--seem akin to Wilber's (and the MHC"s) transcend-and-include holarchical subsumption of the prior and "smaller" holon/levels into the larger. But it appears that he doesn't "measure" levels in this way but rather does so, as he says, analogically to certain traits displayed at such levels, i.e., single, double and triple-loop learning.

Also from above one can see that while the higher action-logics in a sense transcend and include the lower ones the latter are not completely subsumed, because there is yet another aspect, this attentional focus,* that keeps up triple-looping around even the highest (as yet), transformational level so that one can consciously choose what level(s), and to what degree(s) and or mixtures, one might enact from among them depending on the unique particulars of a given circumstance.** This sounds much more akin to Gebser's integral-apersectival as I pointed out in the real/false reason thread.

* The intentional attention (which can be distinguished from the other three territories, can experience all three simultaneously...

** The singular event, in Caputo/Derrida terms. See this for example.

[Edward theurj Berge]

Now I do have a question about this "intentional attention," since it is apparently not synonymous with one's basic phenomenology, one's "self-sensing of one’s own embodiment, breathing, moving, perceiving, etc." What persactly then is this beast? Geber's awaring? Which only comes with the integral aperspective? See this, for example, and this, this, and this.

[Edward theurj Berge]

In the inaugural issue of Integral Review (June 2005) Torbert has an article called “Timely and Transforming Leadership Inquiry and Action: Toward Triple-loop Awareness.” Balder referenced this article in his IL piece. A few select excerpts:

He explains that triple-loop awareness re-presents a change in consciousness. It is the simultaneous awareness of all 4 territories of experience – of the outside world, one’s own behavior, one’s own feelings and thoughts, and at the same time, a kind of witnessing of all this. It can be called presencing (Senge et al, 2004). Triple loop awareness occurs in any moment when there’s an attention distinct from the mental thinking, from the physical sensing, and from the objects of perception, infusing them all with an immediacy that is at once passionate, dispassionate, and compassionate. You’re more likely to have these experiences when you put yourself in a position where you’re on the edge of your known reality – on the not-necessarily-comfortable threshold between the known and the unknown.

One-dimensional time awareness of sequential passing time permits us potentially to act, then identify a gap between act and intended outcome, then adjust one’s action, and achieve one’s goal (maybe), thus doing single-loop learning…. Double- and triple-loop awareness introduce us to the second and third dimensions of time, which are hidden within durational or passing time.

The second dimension of time can be imagined geometrically as orthogonal to linear durational time from the past to the future, passing through the present. From the point of view of our ordinary (zero or one-dimensional) temporal awareness, the present is a vanishingly small instant that can never be grasped because it is past by the time that its sensations, thoughts and feelings register within us. Is there a different quality of awareness that permits a timeless, conscious experiencing of the present – a quality of awareness that permits us to live nowhere but the present… inhabiting the eternal present in all of its unfolding fullness… experiencing a sense of our own presence and of other presences around us even while remembering something, or focusing on a particular task, or imagining a possible future?

A third dimension of time can again be imagined as orthogonal (the Z axis) to the plane defined by chronological time (X axis) and eternity (Y axis). The three-dimensional “volume” of time can be imagined as holding all possibilities, all the potentialities of the future and the still-hidden meanings of the past, some of which emerge into the present (become act-ualized) and then pass into linear, historical time, through a translation process that quantum physics now describes as a “quantum collapse”…. Is there really a different quality of awareness that goes beyond a deepened sense of presence in the present to sensing oneself as a creative subject actively participating in midwifing an emerging future?

[Edward theurj Berge]

Balder's IL blog post notes that the future infinitive of TSK is

not as something that will 'eventually arrive' or as a space into which we will eventually move, but rather as the unfoundedness and indeterminacy of being that is always with us.... This indeterminacy finds expression in our knowledge, as an active not-knowing that allows for the new.  To engage the future infinitive is to embrace openness and the unknown in the midst of the familiar.

I appreciate how Balder uses the infinity sign here to represent this future infinitive which is present along each point in time, from past to the future right now. I also use this symbol to represent the relationship of states to stages in the WC lattice in a similar vein.

As for Torbert's triple-loop-de-loop:

I believe [it] echoes the perspective explored in TSK as the future infinitive...and clearly defines a post-reflective, integral mode of time-consciousness that should not be confused with the present-centered and exquisitely sensitive, but nevertheless still narrow prereflective temporality of the Pirahã.

All of which reminds me of "someone" who said: 

But such progress does not move in a line from pure origin to guaranteed New Jerusalem. Its aim remains as Derrida insists, messianically yet to come, a to come that does not unfold as a predictable future outcome of present history. Progressive theopolitics might then entail an alternative temporality, the time of event–relations, in which our becoming together, now, makes possible but does not determine that which is to come tomorrow: a helical, fractal or rhizomatic kind of nonlinear progress.