
Srinivasa Ramanujan (1887-1920) was an Indian mathematical genius, self-taught, who exploded onto the mathematical scene in 1913. He became a research scholar at Cambridge in 1914, where he was mentored by and collaborated with G.H. Hardy. He received a Bachelor of Science degree, later renamed PhD, in 1916. His genius was so extraordinary that he repeatedly encountered linear thinking bias.
Of the many ways of thinking about problem-solving methods, the linear/nonlinear 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.
Nonlinear 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. Nonlinear thinkers are more likely to accept — and seek — explanations for how the system itself drives the system.
But widely accepted explanations of nonlinear thinking take different views of nonlinear thinking. In these explanations, nonlinear 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 nonlinear
thinking describe it as
essentially piecewise linearof nonlinear thinking is that it is essentially piecewise linear. It models nonlinear 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 nonlinear 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 nonlinear thinker's results. This is what I call linear thinking bias. After a number of such experiences with linear thinking bias, some nonlinear 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, nonlinear thinkers. Don't ask me how I figured that out. Top
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Related articles
More articles on Problem Solving and Creativity:
Organizing a Barn Raising
- Once you find a task that you can tackle as a "barn raising," your work is just beginning.
Planning and organizing the work is in many ways the hard part.
Project Improvisation Fundamentals
- Project plans are useful — to a point. Every plan I've ever seen eventually has problems when
it contacts reality. At that point, we replan or improvise. But improvisation is an art form. Here's
Part I of a set of tips for mastering project improvisation.
Design Errors and Groupthink
- Design errors cause losses, lost opportunities, accidents, and injuries. Not all design errors are one-offs,
because their causes can be fundamental. Here's a first installment of an exploration of some fundamental
causes of design errors.
Office Automation
- Desktop computers, laptop computers, and tablets have automation capabilities that can transform our
lives, but few of us use them. Why not? What can we do about that?
Cost Concerns: Scale
- When we consider the costs of problem solutions too early in the problem-solving process, the results
of comparing alternatives might be unreliable. Deferring cost concerns until we fully understand the
problem can yield more options and better decisions.
See also Problem Solving and Creativity and Conflict Management for more related articles.
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