Near-miss math provides exact representations of almost-right answers

The appeal, I think, is in being able to succinctly represent a random or irrational mathematical object with some other object that's not exactly the same, but is simpler to describe and equivalent to some high degree of similarity. Normally these ideas are applied to things that are thought of as random in a physically stochastic sense, but you could apply them to things that are random in an information-theoretic irrationality sense also.

I'd say the polyhedra they discuss are kind of examples of this, maybe in reverse or something: they are simplified constructs that work as representations to some close extent.

There's some interesting ties here to pseudorandom numbers, in that usually we think of them as approximating true randomness, even though they're entirely reproducible and predictable. This seems similar to me at some level.

> There’s no precise definition of a near miss. There can’t be. A hard and fast rule doesn’t make sense in the wobbly real world. For now, Kaplan relies on a rule of thumb when looking for new near-miss Johnson solids: “the real, mathematical error inherent in the solid is comparable to the practical error that comes from working with real-world materials and your imperfect hands.” In other words, if you succeed in building an impossible polyhedron—if it’s so close to being possible that you can fudge it—then that polyhedron is a near miss. In other parts of mathematics, a near miss is something that is close enough to surprise or fool you, a mathematical joke or prank.