Imagine you were a wealthy writer — so wealthy that you could pay servants to look stuff up for you. Instead of drudging through tomes (or internet searches) to fact-check yourself, find original references, and so on. You just do the fun part: pontificate on paper.
Now let’s say after you have finished an essay, your servant / employee / virtual personal assistant comes back from his footnote research and tells you that statement #13 should be revised based on the best-known research on the topic. In fact, statement #13 is almost the reverse of the truth.
I can imagine things going one of two ways from here.
- In the less interesting case, statement #13 is an offhand remark upon which little else in the essay depends. You correct yourself, modify some text directly before and after statement #13, and move on. The only neighbours of the concepts in statement #13 are the transition sentences directly before & after it on a 1-dimensional topological line.
- In the more interesting case, what you said before statement #13 was meant to lead up to the exact statement you made. Perhaps #13 was a key point, or the thesis of the essay. And let’s further imagine that the text following statement #13 depended critically on the exact value of statement #13 being as you wrote it. When #13 is altered, the preceding text is no longer necessary and the succeeding text no longer works.
In an especially dire scenario, your PA’s research might overturn the worldview that led you to write the essay in the first place.
Like Holger Lippmann’s “Flower Circles 13”, changing one element renders the entire whole needful of alteration. Everything is so thoroughly enmeshed (see “complete graph” below for the neighbourhood relations) that no element of the text speaks in isolation.
That’s in distinction to the calculus, where smooth functions can be approximated by a differential.
In physicists’ language, due to tightly, globally connected topology, perturbations cannot be localised. Rather, the opposite: local perturbations cause global changes in the object.
OK, someone dared me. I’ll say it: Gestalt.