Lucas DiCioccio's Blog - On Dualities

Functional programming has taught me to simplify superfluous concepts: identify what are primitive concepts and what are constructions on top these primitives. The constructions themselves need not be multiplied out of proportion: it is better to stick to few ways of combining entities and concepts. Overall, I think I found some internal peace with programming languages when I could recognize enough of such primitives and how to make use of them in various programming styles. Among the techniques that I use to recognize when two concepts complement each other is to emphasize when two things are in a duality.

A situation of #duality is when two concepts cohabit well while appearing in opposition. In a sense, two dual concepts connect and perform some symmetrical dance. I would say that finding that two things are dual is like realizing that it’s not the Earth that rotates around the Moon, nor the Moon rotates around Earth, but in fact both celestial bodies dance and rotate around a same point (the barycenter). Discovering such rules brings clarity and simplicity to our understanding of a problem. Since a key part of our job in software engineering is to tame complexity, recognizing such simplifications are useful.

The existence of the barycenter of the Earth-Moon system is a consequence of the mathematical formulas we use to model the physical world. It is worth training our sense starting from simple (even simplistic) equations. For instance, let’s take the simplest form of duality: the equality of two values. The two sides of an equality a = b are in a dual relationship: what happens to a requires a commensurate compensation on b. In the real world you rarely encounter some simple rule saying a = b, more often terms like a and b actually are contraptions. For instance b is the result of something involving c and d and other values. Whatever the particular instance you find, what happens to a likely has implications on these c and d and other values. As systems grow in complexity, such equalities may blossom unexpectedly, and if the formula for the equality is too obscured to be spelled-out, unfathomable dynamics will happen.

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