Regarding the problem of **design**ing 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*

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Tags: architecture, connection, design patterns, graph theory, industrial design, manufacturing, math, mathematics, maths, node, thinking, weighted bidirectional graph

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