Of the many ways of thinking about problem-solving methods, the linear/non-linear model, as widely understood, is perhaps the most linear. Linear thinkers are said to use thought processes dominated by logic and evidence. They follow a step-by-step progression in which the problem solver uses evidence and reason to move logically from starting point to solution. For example, linear approaches to complex problems often use analysis and synthesis. They decompose the larger problem into pieces, find solutions to the pieces, and then recombine the solutions, claiming (or, at least, hoping) that the combination of solutions to the pieces is a solution to the combination of the pieces. Linear thinkers seek basic facts, assumptions, or drivers, and a small set of laws that then predict whole-system behavior.
Non-linear thinkers are more likely to accept that complex problems aren't susceptible to analysis and synthesis. They're more likely to try to understand the whole, working from multiple starting points. They collect and sort through known patterns, connections, and insights. Then they apply them to find new patterns, connections, and insights. They recognize that the system might not be reducible to a few core elements governed by a few simple rules. Non-linear thinkers are more likely to accept — and seek — explanations for how the system itself drives the system.
But widely accepted explanations of non-linear thinking take different views of non-linear thinking. In these explanations, non-linear thinkers are said to search for solutions by striking out in various directions, sometimes selected at random or by whim, from multiple starting points. Then, so it is said, they apply logic and evidence to expand from wherever they are to wherever they can go.
A difficulty inherent in this model Some models of non-linear
thinking describe it as
essentially piecewise linearof non-linear thinking is that it is essentially piecewise linear. It models non-linear thinking as a sequence of linear forays into the unknown, from randomly chosen starting points, without necessarily applying to the next part of the exploration any of the knowledge gained from parts previously explored.
When we ask non-linear thinkers how they found the problem solution they just presented, they might not have a "logical" explanation, especially if they found their solution by other than logical means. Often, the absence of a logical, evidence-based discovery story causes some to doubt or even reject the non-linear thinker's results. This is what I call linear thinking bias. After a number of such experiences with linear thinking bias, some non-linear thinkers learn to retroactively invent linear discovery stories, sprinkled with appropriate amounts of evidence and logic, to explain to others how they discovered their results.
When this happens, the truth of their discovery method remains hidden. So, too, does a larger truth: we are all, to varying degrees, non-linear thinkers. Don't ask me how I figured that out. Top Next Issue
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Here's Part I of an approach to working on hard problems by breaking them down into smaller steps.
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