Breadth-Depth Metaphors and Beyond

We commonly use a set of dynamic spatio-temporal orientation and observation conceptual metaphors to talk about knowledge, its communal organization, and individual styles of knowing. We use depth-versus-breadth to talk about track records and abilities, “long-term” versus “short-term” (and “upstream/downstream”) to talk about intentions and decision-making, and “big-picture” versus “details” to talk about the scopes of discourses. All these will come up for critique and more analysis as I continue developing the themes of this blog. But I want to start off this fresh new week with a question for you to ponder: how do you organize your view of knowledge, and how much faith do you have in your organization?

I’ll do a tutorial on conceptual metaphor and George Lakoff in a bit, but for now, all you need to do is understand a conceptual metaphor to be an organizing frame of reference rather than a figure of speech. We tend to use conceptual metaphors for talking about at least four (per my count) distinct aspects of the phenomenology of knowledge. These are, the organization of knowledge itself, the organization of communities of knowers (including notions of in-scholars and out-amateurs), perspectives and action-orientations of individual knowers, and the evolution over time of these three types of elements (knowledge, communities, perspectives). That’s a lot to talk about, yet we do it comfortably (though, as I will argue, not very soundly).

Organizing Knowledge

Consider just the first one: ways of organizing knowledge itself; the stuff in books, papers and people’s heads. Here is a sampling of metaphors: excavation, set theoretic, architectural and Newton’s beach (“I do not know what I may appear to the world, but to myself I seem to have been only a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”)

Metaphors of interdisciplinarity

There are several related metaphors here, all spatial. All the compliments and criticism I’ve received have been framed in terms of the breadth-depth metaphor for instance (which is shown here in its excavation form, but is equally used in its watery form: “deep dive” versus “drill down”). Newton liked the less structured land/ocean view of the known and unknown. Engineers and mathematicians, particularly those engaged in synthesis (be it of software or complex structures of theorems), seem to like architectural metaphors like the one shown on the bottom left.

When it comes time to talk about “interdisciplinary” and “multidisciplinary” matters, seem to have in mind some sort of Venn diagram (or possibly, archipelagos of known Newtonian islands in an ocean of Newtonian unknowns) in mind. We speak of bridges between fields, intersections among them, or gaps between them. The idea of intersection of paths of discovery seems much rarer (I’ve seen it once — the person involved was a research manager type who seemed to view discovery as regimented marching along various paths). I take it some people have metaphoric political or physical maps in mind as well, when they talk about turf boundaries, silos, frontiers and trails blazed (a peculiarly American idea) and unexplored versus explored regions. All these metaphors are organized around a metaphoric spatial orientation.

More recently, the explicit manifestation of associative webs in our technology (the Internet that is), suggests an organization that has no natural up/down/sideways orientation. We are left only with “near” and “far” measured via conceptual degrees of separation, as our spatial commitments within the metaphor.

I’ll talk about the other three gradually, but here is a sneak preview. How you view this spatially organized knowledge (big picture/details, up in the clouds/down in the weeds) brings up the next class of metaphors. Newton came up with a very human one for this category as well, the “shoulders of giants” idea. Outside of the humanities and social sciences, the geography of knowledge induces the geography of communities, but within, the reverse is often assumed, which gives us the third class, communitarian metaphors with sociological boundaries and notions such as center and periphery (though, you could argue, center-periphery organizations apply to more objective-seeming organization metaphors as well). Finally, the fourth class, involving time, is possibly the most interesting, involving historicist “accumulation”, order-chaos and creative-destruction models, upstream-downstream models, and the underlying metaphors of such things as Kuhn’s idea of paradigm shifts (“earthquakes”) and Feyerabend’s idea of methodological anarchy.

The Problem with Epistemic Metaphors

We need these metaphors. Without them, discovery and inquiry would be solitary enterprises and conferences would be dull. Yet, we need to probe, critique and evolve the metaphors themselves, because they can lead to many pathologies. In the mildest case, they can lead to pointless battles between self-styled (or other-labeled) breadth and depth people. In the worst case, they can steer inquiry away from rich discoveries. A more obvious problem is that a good proportion of people are extraordinarily tasteless and clumsy when they try to apply these metaphors. Few things are as frustrating as an idiot who has decided to adopt “Let’s look at the big picture” as a pet phrase.

It doesn’t take much work to break these metaphors. The breadth-depth one, for instance, can easily be broken by appealing to ideas of different perspectives: quarks are smaller than humans, so quantum physics is narrower/deeper than sociology by one account. But then, quarks make up much more of the universe than humans, making quantum physics broader by another account. Further problems can be created by turning to notions of recursive complexity (of the ‘universe in a grain of sand’ variety) and path dependence (it may take you a sequence of 5 courses according to the prerequisite structure of Podunk University to learn concept/technique X, while some prodigy finds a way to get there from high school algebra).

The Question

Which brings me back to the question behind this post: how do you organize your view of knowledge, and how much faith do you have in your organization?

Do these issues matter at all? Would shifting to a better set of metaphors for working with knowledge help us discover things we wouldn’t otherwise have discovered? What might replace this language?

My own answer is a tentative yes. These issues matter in profound ways. For instance, the depth-breadth distinction I believe, is a pernicious and damaging one. I have an alternative, but haven’t worked it out completely yet. But the key point is this: our ways of talking about knowledge have to evolve alongside knowledge itself. We have been stuck with one set of epistemic metaphors for too long.

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About Venkatesh Rao

Venkat is the founder and editor-in-chief of ribbonfarm. Follow him on Twitter