Lime fruit

See: Citrus aurantifolia. Lime tree

Tilia europaea. The lime tree, or linden tree. Linden

See: Lime. Line

In genetics, a line of descent. The term is used most frequently in the concept of a pure lines. Linear system

The general systems theory originally concerned rather simple systems such as the solar system, and mechanical systems, such as clockwork. These are now called 'linear' systems, and they obey Newton's laws. Modern complexity theory concerns more complex systems, which are non-linear. Linear systems have parameters that are easy to measure, and outcomes that are easy to predict. Non-linear systems have parameters that are difficult to measure, and outcomes that are impossible to predict. The solar system is a linear system. It obeys Newton's laws of motion. Indeed, Newton formulated these laws to explain the behaviour of the solar system. We can predict the phases of the moon, and the tides, with great accuracy, for centuries ahead. Weather systems, on the other hand, are non-linear. They are also notoriously unpredictable. Weather forecasts of even a week ahead are famously unreliable.

In the context of complexity theory, 'linear' means that the parameters are fixed, while 'non-linear' means that the system parameters are likely to change. For example, a game of snooker is a linear system. But if the snooker table is on a ship in a rough sea, the game becomes a non-linear system. The mathematics of non-linear systems is a very new, incomplete, and complex sub-discipline, and it originated in fluid dynamics.

In the context of complexity theory, linear also means that the output is proportional to the input, and the whole is equal to the sum of the parts. Non-linear means that the output is greater than the input, and the whole is greater than the sum of the parts. This 'something extra' consists of emergent properties.

All living systems are non-linear. Life itself is an emergent. So too are all the attributes of life, that used to be called 'vital forces'.

See also: Self-organisation.

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