Long ago my nonlinear systems prof observed that while linear systems are precisely defined (f(ax+by)=af(x)+bf(y)), “nonlinear” is a negative definition that can only be characterized piecemeal. It’s the math version of Tolstoy’s “happy families are all alike, every unhappy family is unhappy in its own way. And in a precise math sense almost all systems are nonlinear (linear systems are a “measure zero” subset of all systems).

Nonlinear systems are usually difficult but aren’t always “unhappy.” In math, I’d map that to “difficult in an inelegant way where dealing with the difficulty is not satisfying”. Nonlinearity is a grind in short. Lots of nonlinear systems are elegantly difficult, but the default is that almost all systems are inelegantly difficult. So it would be fair to say most of math is “unhappy.” Again in the formal sense — “elegantly difficult” nonlinear systems (ones with pretty strange attractors for example) are collectively a measure-zero set I suspect.

Linear systems are happy because they’re unreasonably easy. We use them so much not because they’re truly broadly applicable but because they’re easy to apply. Very much hammer in hand = everything looks like a nail. The streetlight under which the drunk mathematician looks for their keys. So a generalization of linear is “unreasonably easy to the point it’s tempting to apply inapproriately.”

Now that I’ve started nerding out a bit about nonprofits I’m thinking about the two ideas of “unhappy” vs “unreasonably easy.”

“For profit” is like “linear” — overapplied because it is unreasonably easy, not because it is appropriate

Almost all nonprofit ideas are probably “unhappy” as in “inelegantly difficult.” I suspect this is why the sector struggles so much and is generally so ineffective. The cause being worthy is not enough. It must also be elegant enough to sustain both human motivation and tractable agency. It must be elegantly difficult.

I’m frankly not interested in “unhappy” nonprofit ideas. But I do think the “for profit” form has been kinda exhausted. The “nonprofit” form needs better exploration, but along the elegance dimension rather than the worthiness dimension. Worthiness can be a minimum bar.

What are the elegant nonprofits you know of?