C-K theory in a nutshell (or: a posthumous Da Vinci reference point)

“He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may cast.”

As an abstracted design reasoning process, C-K theory is a powerful approach for discussing design phenomena. Design is here intended as creative engineering, including new functional spaces, requirements, competencies, business models, etc. It’s an activity that spans industrial design, architecture, science, and usage at least [HAT 10] and enables to make a radical and definitive distinction between what’s uncertain (resorts to probabilities) and what’s unknown (resorts to logics).

C-K theory establishes a formal distinction between a space of “concepts” (C) and a space of “knowledge” (K) as a condition for design:

• – the K-space is populated with propositions that possess a logical status. Which means that “matching experts”, i.e. individuals having relevant expertise or knowledge, are able to evaluate them. It is gradually augmented and continuously (re-)organized, through mobilizing theories, practices, crafts, traditions, tests, verifications, validations, etc. – all of which can be dubbed knowledge. K looks like a collection of categorized islands of identifiable subspaces;
• – the C-space contains propositions always bearing undecidable status: otherwise a concept gets by definition thrown back to the K space.

To start a design process, an initial element is formulated through a blueprint proposition in a way that can be dubbed “undecidable”: hence it belongs to the concepts space. To trigger the design process, the blueprint gets progressively refined by successively adjoining attributes and this constitutes the basic C-K expansion process. Hence, the C space is unfolded through a tree structure(s) while the concepts are progressively adjoined attributes. Note that the attributes can only come from K, even the initial blueprint can only be forged by using known words!

An unbounded process expansion creates “design images”: progressive concepts growing a series of attributes. The obvious question is how to systematically dig an unknown space? Modeling the dynamics of design goes by expanding the space of concepts and the space of knowledge concurrently. Four operators, C➔K, K➔C, C➔C, and K➔K, compose what can be imaged as a “design square” (Figure A3.1) and their interplay captures the variety of design situations.

Relevance to Da Vinci practice methodology

C-K theory practice seems relevant in Da Vinci’s methodological context for at least three reasons:

1. 1) It organizes a rational and constructive way of designing unknown desired “objects”. For Leonardo, object categories have names paintings, sculptures, machines and mechanics, anatomy, geometry, maps, guidelines, etc., and his progressive way is no less rational.
2. 2) It returns the trace of the design steps – a genuine design intelligence as it sets a capacity notion rather that gets stuck into the effects – the target results. Here dwells a quintessence of innovation maturity. Leonardo remarkably understood this point as his work is an ongoing dance drawing on skill, creativity, and knowledge, by equally and constantly interplaying them.
3. 3) It rests upon the able practitioner – not the scientist - the practical task to conceive things. Likewise, Leonardo insisted on his engineering designs being busy with execution skills.

How to start from an empty space?

Express an undecidable proposition (can’t prove “true” or “false”) and separate the world into two spaces: K (existing and missing knowledge, where propositions have a logical status), C (concepts, where propositions have no logical status).

What the C-K approach means

Implementing C-K theory:

• – sets a clear departure from classical creativity methods and techniques, e.g. brainstorming or six hats techniques, or Delphi-based methods. Also a transcending departure from problem finding/solving approaches and other reasoning methods brought up by artificial intelligence (AI) over the past half-century [SIM 73]. As future products cannot be deduced solely from existing knowledge, designers are here tasked with coercing (i.e. forcing) a futures creation process that is by design rational, repeatable, traceable, documentable, and transferable;
• – supports the development of new breakthrough plans, solutions and alternatives with three novel and essential benefits: (i) help control the rationale of their developments; (ii) control and pace the degree of futures innovation (e.g. change, reform, progress, create, etc.) and the resulting time-scale futures lineages; (iii) support policy-makers in bringing the traced explanation of different design paths to decision.

Representing dualistically (polarizing two spaces) and operating Arte (playing the C-K design square)

“If the idea is not working with the hand, there is no artist.”

“With Leonardo, everything seems to have two sides” (Serge Bramly). An equal mixture of arts and sciences is a never failing postulate in Leonardo’s works. His drawings bear a dual role: art (creation) and tools for scientific analysis (knowledge) while it remains just impossible to separate the two.

We could first associate scientific knowledge with the K space but practicing art isn’t purely the C space as it needs a scientific understanding of the forms. Plus analyzing the forms of nature needs the artistic ability to draw them (akin to K). An intensive interlinking of features pertaining to art and science is rooting what we may confidently name innovating process.

Had a patent office operated during his days, he would have been eligible for thousands of patents, models, pictograms and copyrights, given his drawings and flanking notes joined in a pure play, a vivid and tutoring expression of ideas.

At first glance, his productions may seem to form a heterogeneous compilation: this isn’t so. Instead they reveal an intense, deep and intricate whole; in a way, intelligence shows up at every pixel. While the notebooks contain crossreferences between sparse drawings, deeper observation and analysis evidence the coherent and complex thinking process underpinning just all of his realizations. Actually, Leonardo’s way is consistently built from three self-named constitutive elements:

• – scienzia: meaning acquired, hopefully robust knowledge; which falls into the K-space;
• – fantasia: or creative imagination; the C-space with the ability to expand in any conceivable way;
• – arte: meaning skills, perhaps capacities; which we suggest to associate with the two reciprocal operators K➔C and C➔K of the design square. While a methodology for actuating the square is not clearly formalized in Da Vinci’s Notebooks, lots of hints are available, which we will discuss.

“He insisted again and again that the art (skill) of painting must be supported by the painter’s science (sound knowledge) of living forms” (Capra). This translates into: every single concept obtained from disjoining the K space is K-relative and the K space should never be left aside or lagging behind when progressing an overall design. The notebooks systematically juxtapose a drawing space and a textual notes space: he was capable of extracting knowledge given that he knew exactly where to make structure interact with content. A clear capacity to use knowledge models as a classification method.

As he was studying the science of art and reciprocally the art of science, he embarked in a creative, K-augmentation process. By leveraging this space, he professes a quest for knowledge robustness: “Ensure that you grasp the structure of all that you are endeavoring to paint. Each part is supposed to unite to the whole, which enables it to escape its own incompleteness.”

By saying that (i) a painting is a whole that connects the parts – but the parts aren’t left to themselves; therefore (ii) would they be so, they would tend to their “incompleteness” – i.e. the inherent blind spot or dead angle generated by the mere presence of the physical observation.

In other words, Da Vinci says that a mathematician’s Continuum Hypothesis should be preserved in painting, incompleteness can be reached by a thinker, and that a painting should escape it. It took Gödel’s famous 1931 intervention to prove the hypothesis false, then indirectly Cohen in 1963. Taine too praised his “infinity greed, incapacity to be content”.

With fantasia, he generated ideas with a process that could impact creativity methods structurally:

1. 1) Consult the information available anywhere (read: initiate a K0 mobilization) and induce a conceptual framework via a starting conceptual C0 point, e.g. a hypothesis or a blueprint.
2. 2) Test ideas against own scientific observations, i.e. augment K and play C➔K operator.
3. 3) Do not hesitate to modify older theories when experiments contradict them, i.e. reorder K.

A design process which evidences a tenacious use of C➔K and K➔C operators evokes Thomas Khun’s definition of a scientific paradigm: a constellation of concepts, value, perceptions, and practices. As a result, art does not reside in the C space but in finding a constructive path toward the K space (although impressionism additionally emphasized the C space).

Elaborating solid bodies of knowledge (or cognitive processes ever)

“Mystery to Leonardo was a shadow, a smile and a finger pointing into darkness.”

Kenneth Clark

In his direct observations of nature, Leonardo single-handedly developed a new approach to knowledge, known today as the scientific method. No doubt the starting point is systematic observation, yet through the human eye and the brain; a concept that today we would state as cognition – the process of knowing. Leonardo wrote “perspective is nothing else than a thorough knowledge of the function of the eye” and much emphasized experience (sperienza) through methodical observation and experimentation. “The painter is for Leonardo the cosmic eye which masters all visible things” [WÖL 99].

Goethe insisted on his dominant eye-based talent that favored painting, who said “he never accepted any arbitrary or fortuitous feature, everything had to be weighted up and thoughtful”, and added: “from pure proportion discovery to the most strange monsters made up with contradictory figures, all had to be natural and rational at the same time”. Such a mixture evokes a C-K interplay that C-K theory carries on methodically. “All our knowledge has its origin in the senses; experience, mother of all certainty” are reflections of epochal naked eye observation limits, not so in “for he who can go to the well does not go to the water jar”.

His anatomical drawings, which he calls demostrazioni (“demonstrations”, or, would we say today, proofs of concepts or mock-ups), are typically not straight pictures of what one would see in an actual dissection but often bear an enhanced rendering (sometimes 3D-like). They are “diagrammatic representations of the functional relationships between various parts of the body” (Capra) that denote a superior – i.e. deep and intertwined knowledge.

Moreover, his scientific sketches are never representations of a single observation. Rather, they are syntheses of repeated studies, crafted in the form of theoretical models. “Whenever Leonardo rendered objects in their sharp outlines, these pictures represented conceptual models rather than realistic images” (Arasse). They are foundational elements in building scientific theories where the understanding of patterns, relationships and transformations becomes crucial for understanding the living world.

By writing “everything comes from everything, and everything is made of everything, and everything turns into everything, because that which exists in the elements is made up of these elements”, Leonardo is creating K-complexity by way of a systemic – and not reductionist – way of thinking: not quantity first, but wholeness and quality. Which appears to be the way to understand knowledge in a multidisciplinary way – a “knowledge bandwidth”, in heavy demand today. Data doesn’t have a bandwidth, being K base-band only; information may be contextual (have in-band K structure). But with Leonardo, information becomes action, i.e. knowledge-in-motion: mobilized and structured, a kosmos – an ordered and harmonious structure, ready to be organically exported to third receiving domains.

His resolutely systemic thought has bidirectional causal effects: “Mountains are built from rivers flows; mountains are destroyed by rivers flows”, or “The earth is moved by the weight of a tiny bird who rests on it.” Facile cosa è farsi universale said Leonardo of himself who “asked many questions nobody asked before and transcended the disciplinary boundaries of his time. He did so by “recognizing patterns that interconnected forms and processes in different domains and by integrating his discoveries into a unified vision of the world” (Capra). Though “mutual generation of all parts of an organic whole” (Capra; see Kant’s selforganization), he creates, i.e. rhythms a wholeness.

Formulating root concepts (cognition – or plotting the undecidable)

“Material movement arises from the immaterial.”

“Leonardo only knows the sole infinite, eternal space, in which his drawings likely seem to mesh. One proposes a sum of isolated and known objects within his paintings, the other a piece of the infinitum” (Oswald Spengler). Leonardo would usually start from commonly accepted concepts and explanations, often summarizing before proceeding with his own observations, then formulating creative cognitive de-fixations. Example: a shadow “is” a cloth (or a variable denoting absence of a luminous ray), “it clothes the bodies to which it is applied”. He then jots down summaries in the form of many quick-sketched variations and even, after much investigation, as elaborate drawings.

His root concepts are often projected out of fantasia (K➔C) and retain distinct undecidable status at first. “The inventions of his fantasia, never out of harmony with universal dynamics as rationally comprehended, are fabulous yet not implausible, each element and their composition deriving from the causes and effects of the natural world” (Kemp). They amount to a “best start” which may perhaps reveal false later on, after complementary experiments (e.g. dissections, further observations…). A dual learning on how to form or vanish concepts: dying down concepts, subsuming them.

A story involving Steve Jobs and his original designer Jony Ive, comes to mind here.

The story behind the creation of Sunflower iMac: Jobs, Ive and the sunflower in the garden

One day, after his comeback to Apple, when a new Mac was about to be conceived, Steve and his first designer Jony Ive were walking in Jobs’ garden at his home.

The first wasn’t happy with what the second was proposing as a design for the new machine. Jobs walked with Ive in his garden:

“As they walked through the 1,000-square-meter vegetable garden and apricot grove of Jobs’ wife Laurene, Jobs sketched out the platonic ideal for the new machine. Each element has to be true to itself, Jobs told Ive. Why have a flat display if you’re going to glom all this stuff on its back? Why stand a computer on its side when it really wants to be horizontal and on the ground? Let each element be what it is, be true to itself. Instead of looking like the old iMac, the thing should look more like the flowers in the garden. Jobs said, It should look like a sunflower.”

Biodesign that is directly inspired from nature. That model sparked the iMac Sunflower, which succeeded the egg-shaped 1998 iMac G3.

The extract is from Time Magazine: http://www.time.com/time/magazine/article/0,9171,192601,00.html.

As he makes progress in his understanding of natural phenomena in one area, he becomes aware of the interconnecting patterns to phenomena in other areas and revises his putative ideas accordingly. Leonardo called all human creations “artifacts”, and works of art “inventions” (Capra referred to him as inventor and interpreter between nature and humans, i.e. who created an artifact or work of art by assembling various elements into a new configuration that didn’t appear in nature). This specification comes ever closer to our definition of a designer. Leonardo’s disegnatore term always means draftsman and he also uses compositore.

A striking formulation of root concepts comes through the interplay of opposites (or making conceptual expansion). Leonardo embodied a dynamic tension between contradictory paradoxes in his personality. He was also fascinated by opposites through his life. By consistently practicing conceptual separation, he extracted separate mechanisms (gears, levers, bearings, couplings, etc.) from the machines in which they were embedded. Examples of such root concepts with expansive property: a table lamp with “variable” intensity; doors that open and close “automatically” (by means of counterweights); {folding} furniture; how a human pilot might “generate enough force” to lift a flying machine off the ground (by flapping its mechanical wings); an octagonal mirror that “generates an infinite number of multiple images”, a spit in which the roast will turn “slow or fast” depending whether the fire is moderate or strong. These codes expansively splinter as many dominant designs.

On the process of emergence of design process (or embodying resulting concepts)

“Knowing is not enough; we must apply. Being willing is not enough; we must do.”

A process of embodiment is an invitation to experiment. In Leonardo’s works, it’s both a unifying cognitive representation of a seamless art/science unity and a tool that he uses for scientific analysis or forms understanding. His drawings aim to assert that they give “true knowledge of shapes, which is impossible without an immense, tedious and confused amount of writing and time”.

By contrast, Renaissance engineers’ drawings remain explanatory, while Leonardo’s are engaging, convincing, even compelling, persuading the viewer of the feasibility and design soundness by inviting a viewer’s questioning at knowledge level through aesthetic visual contextualization. They bear the concrete appearance of objects that exist. Examples: the angle(s) of view, the subtlety of shadows, their background treatment “all give them an extraordinary persuasive effectiveness” (Arasse). Furthermore, many drawings mix “the coldness of the scientific investigations with the emotional emphasis” (Nathan). Meaning, motion, engagement…speak for the emergence of a design science.

In preparatory drawings, he would go over a figure again and again, sketching several alternative lines and variations of position, until the ideal form be found. He tries out different possibilities: what are the different ways to represent the problem?

These sketches have high dynamic quality, a brainstorm of dynamic sketching. “Never before had any artist worked out his compositions in such a welter of alternative lines” (Kemp). “Such flexibility of preparatory sketching became the norm for later centuries; it was introduced almost single-handedly by Leonardo” (Capra). In movement, his eye perceives the hidden, latent, buried form striving to become a figure. First I shall do some experiments before I proceed further, because my intention is to cite experience first and then with reasoning show why such experience is bound to operate in such a way.

“And this is the true rule by which those who speculate about the effects of nature must proceed” (Leonardo in 1513). Concepts are thus drawn in C first, then grow as K representatives, ready for varied take ups.

Assessing designs and field explorations (or assessment criteria)

“Art is never finished, only abandoned.”

What would be the perfect value criteria for Leonardo? That “an ingenuous design be created, beautiful, easy and economical, in which nothing is wanting and nothing is superfluous” (he’s describing nature). He sees as useful to distinguish deep values (transposable, value for another domain: cross-innovation impact, verifiability: robustness) from shallow values (conceptual clarity, richness of alternatives, discovery of a transcending “invention”: originality, multidisciplinary spread: variety). Yet, how does Leonardo structure, compare, and assess design paths more specifically?

1. 1) Originality. “The solutions he imagines are invariably unconventional” (Arasse). Examples: simultaneously gothic and Mannerist, effortless integration of architecture and complex geometry, many designs of centralized, radially symmetric churches and “temples”. “Design for centralized temple is reminiscent of fractals: a mathematical integration of the parts, a sense of organic unity, the spatial vision which allows him to display his design as a fully 3D concept” (Capra). His cognitive depth and, as said above, expansive partitioning in C, serve an unconventional renewal of concepts.
2. 2) Variety. “The parameters of the experimental setting are varied in order to bring to light the essential unchanging features of the phenomena being investigated. He would often vary his parameters systematically to test the consistency of the results” (Capra). In conducting experiments, Da Vinci stresses the need for careful repetitions and variations. Painting Madonna and Child with Saint Anne took more than a decade (not an isolated example by far!), during which he made numerous drawings with variations on compositional and theological themes. He often uses catalogs of geometrical representations for de-fixing concepts (e.g. the concept of mapping as: transforming a circle into an ellipse; a gradual movement; a flow under continuous change), or uses motion with a sense of relationship to actual or potential forms where he will find transitional examples.
3. 3) Variable expansion. His notebooks contain examples of experiments he conducted again and again by just changing one variable. An arresting example is the bewildering 2-folios study of the activity of the lunulas of Hippocrates of Chios (only mathematically proven recently). Comparison (paragone) He used blue wash of varying hues to produce a striking resemblance between the flow of the river’s watercourses and the flow of blood in the bodies’ veins. Comparing the dome of a church to the human cranium, or vaulting arches and rib cage, or body metabolism process (ebb and flow of respiration, blood transport of nutrients) with a building “metabolism” (how stairs and doors facilitate movement through it), or a human blood vessels diagram next to sketches of stairs, or water as the veins of a living Earth. Genericizing by juxtaposition. The above contextual conversions amount to a code for obtaining a generic property by overlaying domains. Not seeking solutions, but domains!
4. 4) Robustness and integration. “For Leonardo, painting is an operation requiring all the available knowledge and almost all the known techniques – geometry, dynamics, geology, physiology. A battle to show up supposes whirls and lifted dust; and yet, he wants only to represent them after having observed them with eyes waiting to become learned and as if wholly penetrated by the knowledge of their laws” (Valéry). Complex secondary effects of light-reflected sheens, areas of diffused light, subtle glows. The garden is an integral part of the house. Milan after the plague: he sees the city as a kind of living organism. The Sala delle Asse: contents interlink with each other to form a harmonious whole. Descartes compared science to a tree (“the roots are metaphysics, the trunk is physics, the branches are all other sciences”); in anticipatory contrast, Leonardo’s science is already a complex interconnectedness of the branches of many trees! His unified vision of the world is highly relevant to our times (patterns of relationships, i.e. systemic knowledge) and places blazing calls for a universal science, while his exploration codes enhance reliability and functionality performance.

Let’s note that his architectural drawings are not imprecise: they’re free of details! It is the logical linking and the reciprocal organization of the part of, for example, the building, that interests him. In other words, the problems addressed are theoretical problems of architectural design and the questions he asks are the same which he explores throughout his science of organic forms: patterns, spatial organization, rhythm, flow.

EXAMPLES.– Living and non-living forms (studying the flight patterns of birds to create flying machines); anatomy: workings of the human heart, circulatory system; turbulence of water: vast knowledge of hydraulics, rebuilding Milan’s infrastructure, the plain of Lombardy (city planners still use these principles); growth patterns: of grasses; military: weights and levers, trajectories and forces, weapons and defenses (fortifications), optics, nature of light, etc.

In summary, Leonardo exceeds traditional criteria assessing an innovation and scores the maximum over the innovation capability maturity model scale [COR 15].

Unceasingly mapping cross disciplinary (or ever in search for conjunctions)

“A poet knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away.”

Leonardo never sees an own explanation as final (early view: the heart is a stove housing a central fire; later view: the heart is a muscle pumping blood through the arteries) but considers semantic networks.

EXAMPLES.– Water at the center: a medium of life; a source of power: trade systems; air and wind flows: investigated through birds flights, flying machines, aerodynamic principles; etc.

In a distinctive operating way, Leonardo works on many problems simultaneously. This enables him to pay special attention to similarities of forms and processes in different areas of investigation, including natural phenomena: living forms in different species exhibit patterns similarities. By understanding the processes and the forces underlying the formation, he compares organic forms and processes, studies homologies (structural correspondences between different species) due to their evolutionary descent from a common ancestor (inspired from Capra, as well as the below lists).

Comparisons of forms/patterns

The forces transmitted by pulleys and levers and transmitted by muscles, tendons and bones; mechanics: the tensions in cords, levers and pulleys as in tendons and muscles; patterns of turbulence in water and in air; the flow of water and of human hair; the leg of a man and of a horse; reflection of light on a surface and mechanical rebound of a ball thrown against a wall, and the echo of the sound and the jet of water from a wall (“The voice is similar to an object seen in a mirror”); spiraling whirlpools and coiling foliage of certain plants; the veins in the human body behave like oranges, in which, as the skin thickens, so the pulp diminishes the older they become; in The Battle of Anghiari painting, comparing expressions of fury in the faces of a man and a horse, and a lion; the flow of sap in a plant or tree and in the human body – the vital sap of plants as their essential life fluid, nourishes the plant’s tissues as blood nourishes the human body; the structural similarity between the stalk (funiculus) and the umbilical cord attaching the human fetus to the placenta (unity of life at all scales of nature); the circular light pattern with the circular spread of ripples of water, with the spread of sound in air; etc.

Interconnecting K domains

To Da Vinci, understanding human form means understanding the body in motion, which is often reflected by an emphasis on proportions: proportions of human body ⟺ of buildings; interlinking animal physiology and engineering to understand the animal body movements ⟺ exploring principles of mechanics; investigations of muscles/bones ⟺ studies and drawings of gears/levers; patterns of turbulence in water ⟺ in air flows; science of living forms ⟺ of movement and transformation; nature of sound ⟺ music theory, design of musical instruments; inspiration from science of transformations in mountains, rivers, plants ⟺ in human body; motion transformed into rhythm (the painting of the Last Supper conveys gestures emotions and sentiments); etc.

Counter analogies

“The spiral or rotary movement of a liquid is so much swifter as it is nearer to the center of its revolution but the circular movement of the wheel is so much slower as it is nearer to the center of the rotating object”, an observation that had to wait 350 years for Helmholtz. Opposing views, water as “diluting matter”: “without water nothing retains its natural form”(dynamic stability).

Metaphors

The flow of water represented through a channel of various cross-sections by using a model of rows of men marching through a street of varying width. When studying water: “take knowledge of the movement of a water surface, that behaves like hair, which has two directions, one that follows its own weight, and the other the loops injunctions; same wise, water describes swirling curves, of which one part follows the main current flow and the other the fortuitous and induced movement.” (Zöllner).

Theory infused in “sperienza” (or an enduring Leonardo/C-K thread)

“Simplicity is the ultimate sophistication.”

Practicing Da Vinci-based methodological lines exposed C-K theory in five extensive ways:

• – exercising the design square. C-K theory design power parallels Leonardo’s approaches to using the environment. All four operators are put into use through Scientia, Fantasia and Arte;
• – elaborating deep cognitive processes, with an intense propensity to force knowledge mobilization, by e.g. compositing sparse observations, plus constantly reordering knowledge;
• – playing with many variation techniques, e.g. opposites, with surprising defixing effect;
• – valuing everything in direct connection with augmenting knowledge base relentlessly;
• – the (almost massively) concurrent designing and engineering approach that he favored so ardently hided, and now reveal, a quest for genericity that is only matched by most recent industrial design research. Leonardo does much more with much less because he finds what’s underpinning. We would say he captures the DNA of things, by somewhat grasping the fabric of nature.

While “his focus was the nature of organic form” (Capra), Leonardo Da Vinci’s approach to art and science offers an experiential key to C-K theory and contributes to validating it experimentally. Even more, it seemingly pioneered several ideas encapsulated in it. Being Leonardo a genuine template of a transdisciplinary genius, whose worldview was not mechanistic but organic and ecological, his legacy may even instruct and guide the C-K practitioner in at least two ways:

• – disciplinary defragmentation. By not separating epistemology (the theory of knowledge) from ontology (the theory of what exists in the world), or philosophy from science and art, he freed cross-domains innovation processes. Examples: from perspective to effects of light and shade, to the nature of light, to the pathways of optic nerves, the “actions of the soul”;
• – bringing forward complexity views. Leonardo invariably emphasized the wholeness of things and fundamental interdependence of all natural phenomena, and the unity of things – a most humanistic view. C-K theory comes as a systemic conception of the process of knowing and its language blends several languages, in particular all those of a design activity. By widening C-K formulations at systemic level, defragmenting their disciplinary understandings, and disentangling reductionist frameworks, C-K theory tends to build a network of inseparable patterns of relationships which bear the power to redress, through design innovation, some of the complex economic, environmental and technological problems.

Such blended skill set is commanding. He seems too to expand C-K theory along two directions:

• 1) An engaging feature is his genuine ability to operate systemically, a trait humanity is still presently learning the hard way. With the rise of systemic thinking and its emphasis on networks, complexity, and patterns of organization, we can now more fully appreciate the power of Leonardo’s science and its relevance for our [post-]modern era. Rather than focusing on the countless overwhelming results, he admirably achieved in many different fields. By engaging in discorso mentale (mental discourse), the intellectual process of painting today becomes competitively more valuable than the actual completion of the work.
• 2) Through the “unifying picture of natural phenomena”, which Capra denoted, he’s able to open up a remarkable strategy for genericity in designing objects in that he: (i) indifferently works at several or many projects concurrently; (ii) directly addresses a bundle of different situations and problems, as if he had a capitalization platform at hand supposedly capable of providing him with answers, even if not solutions yet, which yields a genuine scaling up faculty. While routinely taking up multitudes of projects at once, he looks for common descriptors and properties and detaches them from their initial observed environment. Then, develops a “generic kernel” by superposition, away from specific constraints and which properties he applies widely (yet, he doesn’t explicit context-independent generic assertions). All is reminiscent of recent work by Kokshagina [KOK 13] in using design theory for designing generic technology and founding a theory of genericity in design.

A basket of paradoxes? (or you need ecosystems)

“I have offended God and mankind because my work didn’t reach the quality it should have.”

Many original facets of Leonardo’s work have been neglected so far, his work having had an utmost emphasis of interest on the outcomes and not on the method, if any. Filling this gap unearths singular implications for education and management as society still resorts to sequential planning in execution situations and linear thinking in teaching: we have yet to tackle complexity upfront. Leonardo did, and thus benefited from a scaling up ability. Should Leonardo be a post-modern design innovation consultant, he would presumably work not in, but across all domains and industrial sectors concurrently, interconnect them, being gifted in each single project with an extreme compartmentalization for achieving every single piece of art or engineering, etc., while still mastering perfection.

Recent literature [SCH 15] dissects another, more recent exemplar: “Steve [Jobs] was capable of extraordinary compartmentalization” while “helping him turn around Apple”. Leonardo capitalizes on mixed situations in depth, thus minimizing the space between design activity and his “real world”, instead of doing separate projects: how long would it take to perform his works one at a time? This suggests that design is an intrinsically global activity.

Huge masses of books depicting Da Vinci’s realizations have hypnotized us with his plentiful, often unbelievable achievements, yet, besides Fritjof Capra to some extent, their vast majority fell short of digging a Master’s way: his thinking and operating codes before the yields (a key to advancing design thinking may be understanding processes). This appendix evidenced the following relative key elements:

• – Leonardo’s operation codes are strategies for enhancing a man’s knowledge, yet, he fell short of widely sharing his intellectual capital (which was his regular income) except for his contracted work with clients and factions. He “did not share his scientific knowledge although he shared his knowledge of painting with fellow artists and disciples” (Capra). He had “no real understanding of the way in which the growth of knowledge was a collaborative process” (Hope). His still enduring legacy indicates that Leonardo (not a mere thinker but an utmost doer) exemplifies a unique operating model: working alone with rare helpers, yet talking “straight to mankind”.
• – In this avatar-like position, the Da Vinci-to-mankind model delivers a “genius ecosystem” capacity that can map out much of engineering design thinking. What if we applied his way collectively and collaboratively? What if clusters of organizations – becoming “Living Ecosystems” beyond Living Labs – would operate Leonardo ways? Partners attracting systems and vice versa in an accelerated whirl of coherent innovation capacity.

All this amounts to elevating design innovation to the rank of a fully-fledged liberal art. C-K Theory is a collective and cooperative dance in which creativity and constant re-commissioning of knowledge are driving forces. That such a theory comes of age about five centuries after an ancestral Da Vinci’s method may be seen as a confident sign, as depicted in this annex, of mankind ability to methodically progress from singular science, creativity, and arts achievements. C-K theory may appear apt to making up the “Leonardo way” of our post-modern times, prefiguring steady avalanches of interwoven innovations for mankind.

Still, with the recent emphasis on complexity, networks, and patterns of organization, could a new science of quality be emerging? Wouldn’t a more thorough investigation of a handful of most remarkable selected personalities, artists and engineers alike, be poised to offer a basis for undertaking a real paradigmatic change in our education and management methods for future generations – a new intelligence tooling for society?

And, after five hundred years of relative factual analysis concerning Da Vinci works, would it be a too distant goal to set for the advancement of mankind? Hippolyte Taine would likely not object, he who praised his extreme forward-thinking inclination “beyond his century and the following ones”. Same for Steve Jobs, who is likely to inspire both business leaders and business schools for the decades to come?

Acknowledgments

Thanks to Dr. Philippe Blanchard – an Apple Distinguished Educator – from École du Bois, Nantes, France, for bringing a number of textual formatting improvement to the contents of this appendix.