A5.1. Introducing trialectics

This appendix introduces a ternary methodology of thought processes, named “trialectics", as a tool for deepening the multidimensional understanding of any concept. It was conceived by Gérard Gigand [GIG 15] over several years and is used in various environments ranging from executive coaching to professional consulting. Trialectics is useful to deepen the understanding of the innovation intensity at Apple.

We position trialectics as a genuine methodology (method of methods) with two essential properties:

1) It proposes a systematic ternary thinking approach to perform conceptual variations and expansions relatively to three fundamental and generic invariants: incompleteness, auto-reference and indeterminacy.

2) It helps formulating systemic concepts that clarify the expression of the initial concept.

Trialectics supports the development of C-K diagrams further, especially enhancing originality and variety when exploring the concepts in the C space. For doing so, we target the two terms, “competitiveness” and “innovativeness", whose diagrams are elaborated in Chapters 17 and 18, for approaching specific features pertaining to Apple’s capacity under these two keystone fields of operations. Ours is a unique approach to know what can be understood in a motto such as “think different” in deeper ways.

Trialectics has profound roots in the complexity of phenomena, a fundamental thinking that began in the 1960s and for which Edgar Morin [MOR 04] has been an outstanding forerunner. It posits the existence of the limit in the face of the knowable: how to know in the face of infinitum? How can thought thinks of itself?

Here, knowledge and actions are connected; this relational approach to knowledge leads to transdisciplinarity. A binary approach is based on antagonisms and “excluded thirds”. Trialectics, a genuine ternary approach, produces “smoother antagonisms” differentiated at various degrees. The resulting gradation in antagonistic relationship is capable to harness the systemic interactions present in contextualizing concepts.

The approach is instrumental in:

• – uniting and merging concepts without confounding them;
• – distinguishing among concepts without severing them.

A5.2. Using trialectics

The use of trialectics, a method based on complexity, requires thinking of the relations between concepts. Five operators are used in sequence: invariants, attractors, influence agents, non-symmetrical antagonisms and including thirds. What results captures the essence of the initial concept through a relational cartography of words. The resulting words are concepts that will be fed in C-K diagrams.

Let’s discuss the three invariants first:

• – Incompleteness. It is the blind spot, the dead angle generated by the presence of our physical observation: “where I see from, I can’t see”. It induces a partial knowledge (in deficit) of the object of perception. It also concerns a “critical mass” beyond which the object destroys itself. However, it does not mean “unfinished”.
• – Self-reference. It is self-persuasion, self-appropriation or involvement: “within the field allowing my perception, I can see what I want to see”. Our perception is the outcome of a personal interpretation implying a partial knowledge (biased) of the object of perception – a viewpoint. For instance, the conscious process of observing innovation integrates an auto-referring dimension which we perceive as “deviance from the mainstream”. However, self-reference does not mean self-centeredness.
• – Indeterminacy. It underpins a choice, or is background flexibility, or focusing: “within the field allowing my perception, the precision of my vision requires a selection”. Hence, another form of partial knowledge (selectivity, resolution and fragmentation). However, it does not mean vagueness.

The three forms “knowledge partiality” constitute the generic triple limit of the process of perception. It is essential to distinguish between the three statuses:

Unknown – Uncertain – Indeterminated

We can link each of them to three fundamental pillars in science and philosophy:

• – Incompleteness links to Gödel’s 1931 theorems. They say in essence that any logics formalism that includes arithmetics also contains undecidable assertions: that are not demonstrable by applying the formalism rules.
• – Self-reference links to Kant and Heisenberg. In essence, no observation is objective. Reality can be accessed, but not designed as an object per se, only through self-referencing, subject and object together.
• – Indeterminacy links to Heisenberg’s fundamental work. Our perception requests accuracy and therefore will strive to select and focus. Perception engages a degree of resolution which is constrained by how we observe. Any precision is selective. Understanding the observation entails a selection, a scoping and a focusing. Paradoxically, it is indeterminacy that permits rigor and Werner Heisenberg is of great help in this matter.

A5.3. Operating trialectics on the concept of “Brand”

Given an initial concept to work on, trialectics operates the five operators (invariants, attractors, influence agents, non-symmetrical antagonisms and including thirds) in four main phases:

1) Identifying the three-dimensional attractors. They are “the influence of the three invariants on the root theme”. They delimit the validity domain of the initial concept. The dimensions are respective to the three invariants (incompleteness, selfreference, indeterminacy).

2) Defining the influencing agents (6) and the antagonisms (6).

3) Defining the resulting three “including thirds”.

4) Synthesizing the findings. The resulting analysis uniquely deepens the understanding of the initial concept.

The trialectics process engages a relational analysis throughout because it invites the thinking on a relational and dynamic understanding of the concept at hand:

• – what are the various dimensions of the concept or the phenomena studied?
• – what are the interwoven aspects, given the radical unknowability underpinning any observation that is conscious of its own limits?

Let us operate the method on a relevant example, branding. In Chapter 4, we match the present findings with the Apple brand. The working out of a trialectics diagram is not easy at first glance and routinely requires a collective effort. But, the value that results is worth the effort as it lightens the initial concept by unparalleled understanding.

Figure A5.2 evidences the dimensional image/genericity/designation trilogy for any brand and ends up with the three “including thirds”: vocation, creativity and authority. This chart lays out where the power of correct branding resides.

Let us first define the three attractors based on the three generic invariants:

• – The incompleteness of a brand is ultimately the notion of genericity: where it looses its peculiar specificity. A generic product is the limit of a specific product.
• – The self-referentiality of a brand is simply the image it produces on our perception.
• – The indeterminacy of a brand is its relative capacity to designate a particular category of product.

Having obtained the three attractors, we now derive six agents (three pairs):

• – The influence of the incompleteness attractor on image is only bounded by imagination. Reciprocally, the influence of self-referentiality onto genericity is the unavoidable classification that results.
• – The influence of incompleteness on designation reduces to the function itself. Reciprocally, the influence of indeterminacy on genericity is the communalized degree, or commensality (an old word signifying the sharing capacity at a same mensa or host table).
• – The influence of self-referentiality on designation is the referencing that results, or referentiation. Reciprocally, the influence of indeterminacy on image is the relative model that may be used.

Having now the six agents, working the method ends ends by contrasting these two-by-two. We reduce the three antagonisms obtained as follows:

• – Imagination and classification come together (fuse and integrate) into utopia, and contrast into structuration. Then, we resolve these into the “including third”, named vocation.
• – Function and commensality unite into cohabitation, and maximize their disparity into distinction. We resolve the two views into authority.
• – Referentiation and model blend into norm, and diverge into exemplar. We resolve the two perspectives with the word creativity.

At this stage, what remains to perform is an interpretive explanation of the findings. In the present case of a brand, we begin to sense the peculiar pulsation that it is supposed to exert in its environment. There is a notion of persistence and beat, both density and exactness, or fidelity in a genuine brand, which explains why the word frequency can be suggested as a definite and definitive whole compositing the building aspects of the concept of brand.

In the case of Apple, the exposition of the intermediary words and the synthetic essence is provided in Chapter 4. The findings denote a particularly appreciative and robust brand.

A second chart (Figure A5.4) focuses on the routine use of a brand, its category, exposure and appropriate authentication aspects. A mundane object that pervades our lives, showing meaning (is it addiction or a generic affair?), recognition (identifying it in sociable settings) and a degree of confusion (what degree of (in-) significance, perhaps imitated?).

The reason we show these two diagrams is to unequivocally show how definite, strict and specific the Apple brand has become through the years: a scrupulously distinct symbol resonating with the first diagram. The Apple frequency is a clear-cut emblem.

A5.4. Articulating trialectics with C-K theory

C-K theory introduces the systemic interplay between concepts and knowledge. By concepts we mean propositions that are neither true nor false, that you cannot prove anything about, just conjecture. Our mind experiences difficulty in accepting that something seems a sort of negation of knowledge, a non-knowledge. Zen masters instruct that the key to radical evolution lies in the art of transcending contradictions. In Western culture, oxymorons are well known (e.g. a bitter sweet sauce, a virtual reality, a working holiday, a peace force, a dark light, etc.). Oxymoronic expressions actually open a fantasy space that contains nothing.

Such emptiness can spark a whole creation cycle. Accepting to start from an empty space is an act of transcending humility found in great innovators and artists of all vests: it calls for dipping in infinite realms. Formally, the implication:

{contradictions, oxymorons, etc.}➔ø(empty starting space for designing new concepts)

But, how would you sanely start from an empty space? Frank Zappa had his eclectic quote: “Art is making something out of nothing and selling it”. Hatchuel and Weil [HAT 07] found the way thanks to post-modern mathematics. Trialectics gives insights for working with any concept C at three specific stages:

1) when disjoining C from reference knowledge K;

2) when expanding C systematically through the addition (or suppression) of attributes that are dependent on knowledge;

3) when joining back a resulting concept X to the knowledge space.

When starting with trialectics, the three attractors open an initial expansion which already ontologically maximizes the power of the variety criterion. This is of interest for practitioners, as they genuinely strive to place the high-level conceptual expansions as close as possible to the root concept at hand. Increasing expansion power goes by using either the antagonisms created between the six agents or the including thirds which result from them.

A5.5. Conclusion

Using C-K theory specifies a design practice in particular. The trialectics approach evidences that the border between the “singularities” in knowledge and its practice is not clear because they are present in each other. Further, it makes the clarification of their coextensive relation and singular identity a subject of study “par excellence”. We found that such study deepens conceptual disjunctions, expansions and conjunctions when operating in the context of implementing C-K theory. The virtue of trialectics is to be found in refining two of the four value criteria of C-K theory, those more concerned with the conceptual C space, and in these terms:

• – Variety. Distinguishing without severing. Trialectics diagrams unfold progressively. The interrelatedness of the successive agents (renamed agents and including thirds) ensure they don’t separate.
• – Originality. Combining without merging. Single trialectics diagrams combine as one whole (any is co-extensive of the others). They don’t merge as the three invariant dimensions bear singular authority.

Together with C-K theory, the application of trialectics to mundane target problematics at first reinforces and redefines the rapport between knowledge and practice. Moreover, it also helps a decisive diving into the unknown due to its unique methodology rooted on the pioneering works of Gödel, Kant and Heisenberg.