
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:
Bois Sec!
- When your current approach isn't working, you can scrap whatever you're doing and start again —
if you have enough time and money. There's a less radical solution, and if it works, it's usually both
cheaper and faster.
The Shower Effect: Sudden Insights
- Ever have a brilliant insight, a forehead-slapping moment? You think, "Now I get it!" or "Why
didn't I think of this before?" What causes these moments? How can we make them happen sooner?
Some Risks of Short-Term Fixes
- When we encounter a problem at work, we must choose between short-term fixes (also known as workarounds)
and long-term solutions. Often we choose workarounds without appreciating the risks we're accepting
— until too late.
The Rhyme-as-Reason Effect
- When we speak or write, the phrases we use have both form and meaning. Although we usually think of
form and meaning as distinct, humans tend to assess as more meaningful and valid those phrases that
are more beautifully formed. The rhyme-as-reason effect causes us to confuse the validity of a phrase
with its aesthetics.
Asymmetric Group Debate
- Group debates at work can be difficult when the domains of expertise of participants don't overlap by
much. Communicating is possible, though, if we believe in our shared goals and if we tackle the hard
parts without an audience.
See also Problem Solving and Creativity and Problem Solving and Creativity for more related articles.
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And on June 11: More Things I've Learned Along the Way: VI
- When I gain an important insight, or when I learn a lesson, I make a note. Example: If you're interested in changing how a social construct operates, knowing how it came to be the way it is can be much less useful than knowing what keeps it the way it is. Available here and by RSS on June 11.
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