Same River Twice

Diagrammatic thought derives from Kant's notion of schema.  Hegel viewed Kant's triadic schema as an empty formalism and suggested instead "Notions" for science that are the "inner life and self-movement" of the existent thing.

"Science dare only organize itself by the life of the Notion itself. The determinateness, which is taken from the schema and externally attached to an existent thing, is, in Science, the self-moving soul of the realized content. The movement of a being that immediately is, consists partly in becoming an other than itself, and thus becoming its own immanent content; partly in taking back into itself this unfolding [of its content] or this existence of it, i.e. in making itself into a moment, and simplifying itself into something determinate."[§53, Phenomenology of Spirit, Translated by A. V. Miller]

This sounds a lot like Mark Twain's riverboat pilot.  The "becoming other than itself" and "taking back into itself this unfolding" certainly sounds like what the river itself does, and perhaps its not a bad description of what science, via its experimentation, does as well.  The scientist, like the riverboat pilot, seems to their theory as tightly to its object or subject matter and to then build that theory (or Notion) by experimentally reaching beyond itself and then "taking back into itself" the results.  Perhaps Kant and much of modern thought is too close to mathematics, that more abstract, non-experimental kind of diagrammatic thinking.  Peirce tried to tie the two together:

"The chemist mounts an apparatus of flasks and tubes, places certain substances in the flasks, lights a Bunsen burner underneath, and watches to see what the result will be.  The mathematician constructs a geometrical diagram according to a certain prescription which describes the relations of the parts sufficiently for the purpose, and then looks out for new relations, not thought of in the construction.'' [Writings of Charles S. Peirce, Vol. 5, p. 381]

but I'm not sure it really works.  The mathematician may draw a diagram and then construct and look for new relationships, but the validity of those relationships does not then depend upon an experimental application of the diagram.  They are, instead, constructed and validated within the formal confines of the diagram itself.