A Good Map is Hard to Find

The idea of mapping information is heavily used and widely favored today.  There are mind maps, geographical terrain maps, all manner of mathematical graphs to map relationships, and maps for “landscape analysis” used to summarize the state of the art in many fields.  But it turns out that when I look around the discovery literature a good map is hard to find.

Clearly I am biased (as evidenced by “Spark Point” and “The Idea Mill”) toward thinking about things in a map-like framework of (1) focusing on key points and connections, and then (2) refining and re-articulating those elements into a nice, neat shareable package.  At that stage, to me, the map becomes an externalized physical model that can be manipulated and played with, letting you toy with the underlying knowledge cluster sketched out by the map.  And going back to “The Physicist’s Repertoire”, if scientific discovery involves both content and skills then one might want at least one map outlining each arena.  So what kind of map might I use?

Mind maps are the easiest choice—free software or pen and paper, associative thinking, unconstrained.  But mind maps are so free form that the permutations are endless, making it hard to assess if adaptations of the map are fruitful; there can be too many options to try.  Luckily, I came across two other maps that seem to me to have more promising bones.

One is called a “territory map” from Susan Hubbuch’s book Writing Research Papers Across the Curriculum.  It lays out central points in a topic, the hierarchy of points, the direction of ideas between points, and the relationship between points.  This may just have been devised as a drafting device, but it strikes me as a potential foundation for a research tool.  If one laid out a set of knowledge, like scientific discovery skills, as Hubbuch suggests then you would have a territory map representing what is known, perceived, or believed.

Then you could play “what if?”  What if a given sub-hierarchy changes, or a directional was reversed, or relationships were added or subtracted?  Now since Hubbuch’s territory map also has built into it a “beginning” and an “end” (again, it’s designed for drafting a paper with an introduction and a conclusion) then that means there is an overall flow from foundation points to supported conclusion.  So, in a skills map, could this flow run from actions taken to supported outcomes?  In other words, could it be fashioned into a draft of a decision-making tool (more usually called a decision tree)?  If so, it could be a powerful way to articulate and refine scientific discovery paths.

Another possible type of map comes from Sanjoy Mahajan’s The Art of Insight in Science and Engineering, in a chapter outlining the technique of using “easy cases” to reduce complexity in order to foster insight.  The author calls it an “easy-cases map” and it’s essentially a flow chart showing the change of a wave equation between ocean regimes and the physical meaning of each regime.  It caught my eye because I once studied the reflection of sound waves, for submarine sonar under various ocean conditions, as part of a high school internship.  And I never felt I actually grasped the relationship between domains of different ocean conditions.  Where was this map 20 years ago?!  Better late than never I guess.

Mahajan’s map-like synthesis, especially between regimes bounded by some key variable or other (which is all-pervasive in physics), strikes me as so potentially useful.  Mahajan’s mathematical map is very much the counterpart to Hubbuch’s conceptual map.  The more variations of either map you have, for the same question or discovery goal, the more you can explore.  Because once something is mapped then you can compare maps for similarities and differences—it’s a powerful multipurpose abstraction.  The key would always be to capture the most “useful” features in a map, so that the meaningful similarities and differences that can act as a spark point for discovery jump out at your perception (which is much faster than cognition).

For now, I have started drafting my first map of discovery strategies and also one of open questions in neutrino physics.  The process will surely be iterative.  But who knows: I may find that the act of mapping and iterating itself will have a part to play in my pursuit of discovery, and in any case, when you’re out pioneering you can never have too many maps.