Scale refers to the size of a system or property that one is describing, or to the precision of observation or description.
Systems can be of various sizes, and thus different scales. For example, an elementary particle, an atom, a molecule, a cell, a person, a city, a planet, a galaxy, the universe, have progressively larger scales.
A single system can also be observed or described at different scales. Imagine using a zoom lens to look at a person. From far away you see the person's general shape. Closer up you see limbs and the color of the clothes. Closer still you see the facial expression, fingers, and patterns on the clothes. Closer still you see the creases in the skin, individual hairs, and the threads in the clothes. Closer still you see the cells of the skin, the fibers of each thread in the clothes. Closer still you see the molecules, and closer still you see the atoms.
The concept of scale is important for understanding many key concepts of complex systems, such as emergence and the complexity profile.
Emergence considers how properties and behavior at smaller scales give rise to properties and behavior at larger scales, such as how the properties of trees give rise to forest fires or how muscle cells work together to create muscle movements.
The complexity profile is concerned with the degree of independence of a system's parts at each scale. For example, a marching army displays very little independent movement at a scale where we see what each soldier is doing — all the soldiers are moving together in the same direction. The motion of interest is at the large scale. A corporation, on the other hand, may exhibit more independent behavior of each of the individuals who work there.
To consider the complexity profile we observe the entire system at different scales. Unlike a zoom lens, we think about the entire system at each scale. At a coarser scale one would see the limbs of the whole body, and at finer scale one would see all of the body's cells.
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