
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:
Ten Tactics for Tough Times: II
- When you find yourself in a tough spot politically, what can you do? Most of us obsess about the situation
for a while, and then if we still have time to act, we do what seems best. Here's Part II of a set of
approaches that can organize your thinking and shorten the obsessing.
Hill Climbing and Its Limitations
- Finding a better solution by making small adjustments to your current solution is usually a good idea.
The key word is "usually."
Playing at Work
- Eight hours a day — usually more — of meetings, phone calls, reading and writing email and
text messages, briefing others or being briefed, is enough to drive anyone around the bend. To re-energize,
to clarify one's perspective, and to restore creative capacity, play is essential. Play at work, I mean.
The Planning Dysfunction Cycle
- Some organizations consistently choose not to allocate enough resources or time to planning for their
most complex undertakings. Again and again, they decline to plan carefully enough despite the evidence
of multiple disappointments and chaotic performance. Resource contention and cognitive biases conspire
to sustain this cycle of dysfunction.
What Are the Chances?
- When estimating the probabilities of success of different strategies, we must often estimate the probability
of multiple events occurring. People make a common mistake when forming such estimates. They assume
that events are independent when they are not.
See also Problem Solving and Creativity for more related articles.
Forthcoming issues of Point Lookout
Coming September 3: Contributions in Team Meetings: Advocating
- An agenda in the form of an ordered list of topics might not provide an appropriate framework for a given meeting. For example, if A depends on B, and B depends on A, we must find a way to discuss A and B together in some orderly fashion. Here are some alternatives to linear, ordered agendas. Available here and by RSS on September 3.
And on September 10: Contributions in Team Meetings: Scoping
- Some meetings focus on solving specific problems. We call them "working sessions." More often, we delegate problem solving to task teams, while meetings wrestle with the difficult task of identifying or "scoping" problems rather than solving them. Scoping discussions can be perilous. Available here and by RSS on September 10.
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