Regarding the problem of designing a vacuum cleaner, architect Christopher Alexander spells out the tradeoffs using a completely connected 2-coloured graph:
Four desirable properties = nodes, and 2-way connections between them = edges. The edges are “coloured” with {+, −}. Most of the desired properties come at the expense of one another and so are coloured −.
In the language of Jacobians, a minus on the edge between performance and simplicity means both that and that
. Increasing performance decreases simplicity, and increasing simplicity decreases performance.
You can let your imagination run with this thought-form. Besides mathematical generalisations (3-way connections, more edge types, partly connected graphs), lots of other kinds of things can be fit onto the nodes of a completely connected weighted coloured graph. If concepts as broad and multifarious as “economy”, “simplicity”, and “performance” fit into the form of a graph, ……
- politics: {parties with opposed interests, parties with mutual interests} (redundant edges if parties are both opposed and aligned)
- economics: {competitors, partners}
- artistic composition: as I said before, all elements of a composition are connected in a complete graph … lots of edge types
- philosophy: {opposed concepts, symbiotic concepts} (add edges for more options)
- sex: {correlated properties of a desirable mate, uncorrelated properties of a desirable mate}
By the way, C Alexander is the inspiration for the Gang of Four’s book on Design Patterns. Just ask a software engineer: you can program a model of anything.
Arming your imagination with bolas and trebuchets,
Isomorphismes
