I wrote:
On 13/06/2020 22:56, James Propp wrote:
Here's a link to the current draft of my June essay. Comments of any sort are welcome [...]
I think "if you ignore nonlinearities in the equations" is one of those things that seems clear and simple to the expert while mystifying the uninitiated. I'm not sure whether this is fixable by adding a few more words of motivation. "In fact, if you assume all the changes are small so that deviations from linearity are small enough to ignore ..." or something. It may be that anyone for whom that would be enough would actually be OK with the current wording, though.
... Though I see that anyone who's been reading the notes will by that point have been exposed to the relevant idea, so perhaps I retract my comment. (I'm not sure, because the readers who need it more are less likely to have read the note.) Your neurotic-couple example is interesting but it seems a little too schematic somehow. (It seems like it might come straight from the pages of R D Laing -- though I just checked through "Knots" and didn't find anything that quite matches.) I'd expect that in most actual instances of the schema something more specific than "love" would be involved in some of the steps. E.g., A loves B _and smothers B with affection_; B finds that excessive and loves A less as a result; etc. My first introduction (so far as I recall) to the idea of negative feedback loops was at age eight or thereabouts when I saw a description of how an old-fashioned electric bell (of the sort that used to be used in telephones) works. I remember being transfixed by the elegance of it. Very similar to your example of a car whose driver's seat is free to slide. In note 4, I think you may want "the upshot" rather than "but upshot". -- g