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Linear Causality

Newton's cradle, named after Sir Isaac Newton, is an icon of linear causation with on event leading to the the next in a linear deterministic fashion

Newton’s cradle, named after Sir Isaac Newton, is an icon of linear causation with one event leading directly to the next in a linear, deterministic fashion

Linear causality is a conception of causation as following a single, linear direction, i.e. event A causes effect B, while B has no demonstrable effect on A. This unidirectional causation may be in space as well as time, i.e. only incidents in the past can affect current events. Likewise, linear causality implies a unidirectional flow to causation between the micro and macro levels of a system where higher level effects are believed to be caused solely by lower level phenomena. Linear causality can be interpreted in terms of four basic rules, namely unidirectionality, uniqueness, necessity, and proportionality.1


Linear causality interprets events in terms of a unidirectional unfolding of cause and effect as they flow from the past to the future. The Axiom of Causality is the proposition that everything in the universe has a cause. This means that if a given event occurs, then it is the result of a previous, related event. If an object is in a particular state, then it is in that state as a consequence of another object interacting with it previously.2

Uniqueness and Necessity

Uniqueness means that the same cause will lead to the same effect. Uniqueness can be contrasted with two alternatives, one in which several different causes lead to the same effect and the other in which the same cause may result in a variety of different effects. Necessity means the same cause will produce the same effect always, without exception.3


Linear causality describes a relationship of proportionality between a given cause and a given effect that stays constant over time. Small causes always produce small effects; large causes always produce large effects. Because linear interactions exclude feedback, the intensity of the effect will tend to be proportional to that of the cause. The magnitude of an effect is proportional to the magnitude of its cause4. In mathematics when two quantities are linearly proportional their graph is a straight line with the slope representing the constant of proportionality.


These rules give linear causality the important property of additivity. The additivity principle means that if two components, A and B are the cause of event C, contributing independently to creating that event, then the total effect produced by this is the sum of their effects in isolation. However, additivity only applies if the causes are independent of each other.5


Linear causation is part of the analytical process of enquiry whereby systems are isolated from their environment and broken down to identify linear cause and effect relations

Linear causation is part of the analytical process of enquiry whereby systems are isolated from their environment and broken down to identify linear cause and effect relations

Linear causality is part of the analytical, reductionist paradigm that searches for a single, or a limited number, of lower level phenomena that can explain higher level events through the interaction between discrete component parts. Linear causal thinking starts with the assumption that events can be described by a limited number of causes. Analysis is conducted by breaking down the system into component parts.
Because effects are seen to derive from a single, or at least small, number of causes, the specific interaction that we wish to investigate must be isolated from external interventions from other variables in the environment. 
Smith(2011) identifies two requirements for the establishment of linear causality: a stable association between variables and the successful elimination of external factors. A stable association can be said to exist between two variables X and Y if an ordered relationship between the two is robust, persistent over time and not strongly influenced by other external variables.6

Bottom-Up Causality

Linear causal thinking is closely related to reductionism; that tries to explain the whole in terms of its parts through causal laws.7 In other words, linear causal thinking focuses on the parts. Searching for the cause means to search for that part of a system whose operation had finally produced the observed event. Within the reductionist paradigm, the cause is always seen to flow from the lower levels to the higher levels; this is a tacit assumption typically held within physics. That higher level biological and behavioral phenomena are derived ultimately from lower level physical causes. Change in the universe is seen to be a result of the regular application of low-level physical laws.8


When we combine these factors of a limited number of variables causing an effect, as derived from physical laws, where only the past can cause the present, the result is a deterministic vision of the world. If all events are cause and effect relationships that follow universal rules, then all events – past, present and future – are theoretically determinate. This deterministic vision of the universe that is a function of the linear analytical paradigm may also be called the clockwork universe. A metaphor for a vision of the world as a big clock, where the parts are analogous to the cogs, interacting in a linear fashion as determined by the laws of physics.


Chaotic systems, like the weather, are nondeterministic in nature and exibit dispropotinality between cause and effect, what is called the butterfly effct

Chaotic systems, like this weather pattern, are non-deterministic in nature and exhibit disproportionality between cause and effect, what is called the butterfly effect

The theory of linear causality which dominated modern science from the time of Newton to the early 20th-century has since been proven to be limited in its application. During the 20th-century quantum theory and chaos theory presented fundamental limitations to the idea of determinism, in that the state of subatomic particles within quantum physics is understood to be a product of a probability distribution. When this is extrapolated to the macro level of the cosmos, it is observed that quantum fluctuations in the origins of the universe – that have led to the specific formation of galaxies over the following billions of years – means that the universe is not deterministic but in fact its evolution has been derived from quantum probability distributions near its origins.9 Likewise by the latter half of the 20th-century chaos theory had revealed a deep uncertainty to the development of nonlinear dynamical systems. Added to this the butterfly effect came to describe a disproportionality between causes and effects within a broad class of systems. However, this being said linear systems theory remains relevant under certain conditions, but it is no longer generalizable to all phenomena as previously believed.

Cite this article as: Joss Colchester, "Linear Causality," in Complexity Academy, August 1, 2016,

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