The widespread use of topological mapping for innovation sits in a general culture of analogy and metaphor as the standard tools for explanation.
How helpful is this in regards to creative processes?
A novel tool can be quickly explained via analogy — for example, we compare an emergent topology to a landscape (something we have often done), with some parts being “like islands of potential outcomes in a sea that is far more dynamic”. The problem is that in this case “topology” is something that is wholly immanent in what instantiates it — it is something that is not a thing but a statistical pattern of possibilities (a nothing that is a something). The analogy/metaphor helps with “understanding” something difficult but, the question for us is always — is this really helping?
We find that metaphors and analogies that are meant only as fast practical introductory aids to help ground a reader/learner can quickly take on a life of their own: the abstraction “landscape” becomes in the hands of the reader/learner a space of ongoing analogically creativity: “I see, mountains are like ________, ocean currents are like ____________…”
Now we have moved far from the practice in ways that are quite often destructive and not instructive.
It is interesting that two important philosophers of creativity and innovation, Alfred Whitehead and Gilles Deleuze both were strongly critical of such practices of analogy and metaphor.
For Whitehead the danger is one of “misplaced concreteness” — we confuse our abstractions with the underlying issue and perform an act of substitution: we now study our abstraction (which is what is happening in the above example).
For Deleuze, metaphor and analogy subordinate difference (genuine novelty) to sameness, resemblance and identity (this is a much more fundamental and widespread problem). He is famous for saying that his concepts such as “lines of flight”, “rhizomes” “deterritorialization” etc., are not metaphors, but must be taken literally. To which he adds, “There are no literal words, neither are there metaphors… There are only inexact words to designate something exactly”.
Deleuze proposes a language and a set of tools that should be considered purely qualitatively (as intensities).
In our cultural context of where metaphor and analogy are both widespread and everywhere subordinate difference to identity, their refusal can be challenging. That said, we feel a good argument can be made that it is pragmatically necessary for creativity and innovation to refuse them.
We are curious about other users of topological concepts in creative processes — how are you experimenting at the edge of, and outside analogy/metaphor?