Thinking this morning about strange borders, led there by a typically weird geepaw route.
If u didn’t know, coaches sit around all the time and bitch about their clients. This is perfectly ordinary and maps onto all jobs I think. Such behavior is "good thing, but". It’s important to do and it’s risky as hell. Bitching about clients brings a mixed lot of positive benefit and negative ill.
Co-bitching is bonding, for instance. A way for us share, a kind of breaking bread together. Co-bitching is relieving, too. It’s of great benefit to just get it out. Especially cuz, in-group, it doesn’t need to be sugared.
And yet it’s very risky. Co-bitching slides effortlessly into a kind of hardening-of-view. Co-bitching can lock in some of our most negative viewpoints of other people. In so doing, it tends to un-people-ize its victims.
No student of history can sit comfortably with dehumanization.
And in particular, co-bitching can lead us to a place of no longer wondering why the people we’re bitching at do the things they do.
My coaching practice is primarily at the bottom 3 layers of an organization’s hierarchy. I work for the most part with geeks & their direct collaborators, and I work with their bosses & grandbosses. And in VBCA’s, that’s quite low indeed. There are stacks of managers atop those first couple of levels.
Many of my coaching friends are in the same broad group. This means we bitch together quite a lot. 🙂 when we do that, when one does any "good thing but" behavior, the results can go in either direction, positive or negative.
Here’s a picture. it’s an argand map of a standard newtonian root calculation of a non-linear equation. W/o doing too much math, the picture can be interpreted as showing us where a "good thing but" behavior can wind up. Wherever we start on that map, the color is showing us where we’ll wind up when the process is over.
In the picture, there are 4 possible endpoints, the four "pools" of solid color. In this bitching case i’m just thinking of two: the good and the bad. Go with me a little further, tho.
Do u see that crazy intricate border in between the pools?
That border is a scale-similar fractal border. It is what I started by calling a "strange border". Every point on that border has a color, the pool it will fall into. Green points go to the green pool, red to the red pool, and so on. Remarkable property: every point on that border is itself bordered by a point (at the same precision) that goes to all of the other pools.
Every red point has a neighbor that’s red, one that’s green, and one that’s blue.and one that’s yellow. And so on, ad infinitum. And when we increase or decrease the precision of our numbers, it holds true. (self-similarity at scale).
By analogy then, co-bitching is like the newton-raphson method. It can go to "good" or "bad" result. And the border between these results is a strange border, too. Every point where it results good is surrounded by points where it goes bad. And every point where it goes bad is surrounded by points where it goes good.
That’s all, really.
If I have a conclusion at all, it’s just that there’s no easy analysis. I can say that some bitching is clearly good, some clearly bad. But when we get near the border, it’s virtually impossible to tell which is which. And the slightest jiggle of the point flips the result.
And my last thot for now on it? That such borders are rare in classical math, but commonplace in the domain of human discourse.