There are various common cognitive maps, which visually represent ideas and their relationships in spatial terms, their brachial (branch-like), radial (spoke-like) or rhizomatous (like a network) arrangement—the first two, less; the last, more—disrupting the hierarchies of concepts typically associated with more linear (or rather, unilinear) taxonomies. (The term was devised by E. C. Tolman, “Cognitive Maps in Rats and Men,” Psychological Review 55.4 (July 1948): 189-208). They are akin to the classical art of memory, or more specifically, the method of loci, a inventive or mnemonic technique (mnemotechnic) that relies on memorized spatial relationships to find, order and recollect content. (All the quotes and images here are from wikipedia.)
An argument map is a visual representation of the structure of an argument in informal logic. It includes the components of an argument such as a main contention, premises, co-premises, objections, rebuttals and lemmas. Typically an argument map is a “box and arrow” diagram with boxes corresponding to propositions and arrows corresponding to relationships such as evidential support.
(See also Tim van Gelder’s weblog Earliest Argument Map, which refers to Richard Whately’s Elements of Logic textbook, first published in 1826.) The map branches in one direction (downward)—but not necessarily so (one can imagine a more complex networked structure)—as most concept maps seem to do . . .
A concept map is a diagram showing the relationships among concepts. Concepts, usually represented as boxes or circles, are connected with labeled arrows in a downward-branching hierarchical structure. The relationship between concepts can be articulated in linking phrases such as “gives rise to,” “results in,” “is required by,” or “contributes to.”
(See wikipedia on refined concept maps.)
Whereas concept-maps relate multiple words or ideas (they are based on relationships between concepts in diverse patterns), mindmaps usually focus on just one (they are usually represented as brachial or radial structures, denoting relationships with a central governing word or idea):
A mind map is a diagram used to represent words, ideas, tasks, or other items linked to and arranged around a central key word or idea. Mind maps are used to generate, visualise, structure, and classify ideas, and as an aid in study, organisation, problem solving, decision making, and writing. The elements of a given mind map are arranged intuitively according to the importance of the concepts, and are classified into groupings, branches, or areas, with the goal of representing semantic or other connections between portions of information. . . . Though the branches of a mind map represent hierarchical tree structures, their radial arrangement disrupts the prioritizing of concepts typically associated with hierarchies presented with more linear visual cues.
They were used by Porphyry of Tyros in the 3rd century (the Tree of Porphyry), and by Raymond Llull in the 13th century (“Arbre D’Amor” [“the “Tree of Love”]); in modern times they developed out of the research of Allan M. Collins and M. Ross Quillian into semantic networks in the late 1950s and early 1960s. Interestingly, the modern incarnation is predated by a Walt Disney Co business map (see Peter Duke’s site for the map.)
These different types of cognitive maps clearly shade into one another: for example, some mind-maps are multi-nodal, i.e., they have several “centres,” in which case they become more rhizomic than brachial or radial.
These cognitive maps (and others including dialogue mapping, information graphics, spider diagrams and network diagrams), are good for getting to the bottom of what Rittel and Webber call “wicked problems,” problems that are difficult or impossible to solve because of incomplete, contradictory, and changing requirements that are often difficult to recognise—especially because, due to complex interdependencies, the effort to solve one aspect of a wicked problem may reveal or create other problems (“Dilemmas in a General Theory of Planning,” Policy Sciences 4  155-69; Rittel first outlined the concept as early as 1967 [see C. West Churchman, “Wicked Problems,” Management Science 4.14 [Dec. 1967]).
Jeff Conklin identifies six defining characteristics of wicked problems (Rittel and Webber name ten):
- The problem is not understood until after the formulation of a solution.
- Wicked problems have no “stopping rule.”
- Solutions to wicked problems are not right or wrong.
- Every wicked problem is essentially novel and unique.
- Every solution to a wicked problem is a “one shot operation.”
- Wicked problems have no given alternative solutions.
(Dialogue Mapping: Building Shared Understanding of Wicked Problems [Wiley, 2005])
In Dialog Mapping: Reflections on an Industrial Strength Case Study (2000; Visualizing Argumentation: Tools for Collaborative and Educational Sense-Making, P. Kirschner, S. J. B Shum, C. S. Carr (Eds) [London: Springer-Verlag, 2003]), Conklin divides solutions to wicked problems into three types:
I might add a fourth: cognitive solutions. Here, we get our head around a problem by mobilising not a distributed but a spatial intelligence, as it were, distributing it in pseudo-three-dimensional rather than two-dimensional space. The “third dimension” added here allows semantic relationships to be represented multilinearly.
To extrapolate, all problems worth considering are wicked, “tame problems” not so. Problematisation—understanding the conditions of possibility of an issue existing (transcendental argumentation, as it were), i.e. mapping social and historical forces, and political and ideological motives—reveals wickedness.