Some scientists may not want to admit it, but analogy remains a means whereby we continue to anticipate in new fields. When the electromagnetic field was first tuned in, as a physical theory, with Maxwell's Equations and the like, people assumed several analogies (the rippling pond analogy being one of them), but when it came to wires and circuits, the analogy was a piped fluid. And it is a fluid of electron energy isn't it, pushed by repulsion from one cell in a battery, pulled by the other, until the two become equalized (battery dead, perhaps rechargeable from an external source, but with work done in the meantime).
When we see emergence, we recall other times we've seen it. Butterflies from caterpillars -- that's one of the big hand-drawn illustrations that stands out in Synergetics (from a Celtic source).
Synergetics works to set up a lot of stark prefrequency dynamic geometry (hypertoons) that don't really mean anything, except they're smoothly self-consistent and rich in relationships (instructive as pure patterns). But that's not the end of it. They're also suitable raw material for analogies. Doing DNA? Think about using a tetrahelix sometimes. Why? Because if a lot of sciences invest in a common set of dynamic geometry cartoons, we'll have a better superhighway system among disciplines, and that's what Synergetics aims to provide -- except Bucky was more into trains and Grand Centrals than highways per se (I love trains too).
Synergetics explores emergent behaviors in starkly geometric terms, as when those two triangles disclose their spiralness and conspire to breed a four-windowed beast -- an apparent capture of new order, a whole system, a synergetic event. Traditional geometry has had less tolerance for surprise. Euclideanism exults in a sense of having it all mapped out just with the axioms -- the theorems all follow already, even if little humans haven't explored all their ramifications.
It's a comforting image. But that's all it is: an image.
Mathematicians have worked for centuries to make us understand it ain't so simple. Bucky helps in that project. He reminds us our axioms might actually suck, compared to those used by ETs under the Denver airport. We're able to go wrong in our appeal to "self evidence". Infinitely thin planes of infinite extent: a given. Bucky retorts: "oh yeah? Show me one, just one!" We retreat into uncomfortable silence. A disruptor. Disrespectful. Euclid must not be called on the mat! At least not with such naïve challenges (jiggering with the 5th postulate was bad enough).
Euclid meets Sumo-Synergetics in manga I'd like to read.