Keystone Factors

A keystone factor is a small factor that has disproportionately large effects on the whole system. Analysis of keystone factors aims to identify such few critical factors, so that the whole system could be changed by merely altering the keystone factors.

Keystone Species

In architecture, a keystone is a final stone that is placed to lock and hold all other stones together. The keystone itself is under the least pressure, but it is structuring the whole arch—without it, the arch collapses.


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The 80/20 Principle

The 80/20 principle is essential for strategic problem-solving, because it allows you to achieve a lot with minimal efforts, provided you focus on the critical few factors. This popular principle is a good example of non-linearity. Its basic tenet is that a large number of effects are usually produced by a small number of causes—roughly 80% of effects by 20% of causes.Thus, it is often possible to achieve a lot with minimal efforts, and conversely, it is possible to address a large number of factors and achieve almost nothing if your efforts are directed at the trivial many. Continue reading “The 80/20 Principle”

The Fallacy of Identity

The fallacy of identity is one example of how our decision-making and problem-solving skills are often incapacitated because our thinking is predisposed to look for linear relationships and disregard non-linearity.

The fallacy of identity, according to a historian David Hackett Fischer, is the idea that effects must somehow resemble its cause.[1] One common form of this fallacy is the idea that big events must have big consequences, and small events small consequences. Another form is the idea that cause and effect must be similar in type or nature.

Causal Magnitude and Proportionality

A basic form of this fallacy is the assumption that big events must have big effects, and conversely, small events must have small effects. Yet, human history is full of examples of how big events failed to produce big consequences. Fischer points out one example from historical analysis: the English defeat of the Spanish Armada in 1588. Many historians mistakenly looked for some major effects of this event because of the fallacious assumption that such a big event must have produced big effects. But it didn’t. By 1603, Spain hadn’t lost a single overseas outpost and afterwards the British naval superiority not only didn’t increase but even slightly decreased.[2]Defeat of Spanish Armada - The Fallacy of Identity Continue reading “The Fallacy of Identity”


Our ability to solve more complex problems and think strategically is often impossible if we don’t grasp non-linearity in systemic relationships between causes and their effects. While we can usually see linear relationships without any problem, our minds persistently fail to grasp non-linearity.

In linear systems, actions have proportional effects, meaning we can easily see that if a little of some action does a little good, then slightly more of it will do slightly more good, and a lot of it will do a lot of good. In non-linear systems, on the other hand, an input produces disproportional output.  Continue reading “Non-Linearity”