Structure: What Is It?

Structure here refers to the degree of order, organization, and regularity in something.

That something may be a physical structure or system, such as a house or a flower, or non-physical entities like signals or messages. Related opposing concepts are randomness, disorder, and chaos.

For example, the following is a string of 10 numbers from 0 to 9:

4, 7, 8, 1, 9, 0, 4, 4, 5, 4, 0, 9, 3, 7, 8, 6, 5, 9, 4, 2

The above list is random, allowing for an equal probability of each number appearing in each place. Thus any regularity is difficult to discern. Compare with a structured string:

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7

Here the structure is clear, and predictions about subsequent numbers in the pattern are easy to make. It is likely that to a large degree our thought processes are reliant on detecting structure in the world, making inferences based on that structure, and using those inferences to make predictions. If there were no structure in the world, we would not be able to make sense of it.

A useful distinction is between two types of structure: intentional and non-intentional.

Intentional Structure is an ordering or regularity brought about as a result of one or more agents acting on a medium. Examples include all the artifacts humans have become intimately integrated with. Our homes, beds, communication devices, transportation, and every other tool or device we use on a daily basis is an example of intentional structure.

Non-intentional Structure is any order or regularity that comes about as a result of unguided laws of the universe. For example, planets and stars are roughly spherical because gravitational forces are very large and pull roughly equally on all mass in the body toward the center (though they spin, so they bulge a little around the middle). The natural motion of waves and tides sorts rocks and sand along beaches. Crystals form from the physical forces acting on the constituent matter, from cold acting on water to form snowflakes light enough to be carried on the breeze to immense heat and pressure compressing carbon atoms into diamonds heavy and tough enough to drill through steel. In each case the structure of the resulting entity was brought about by unguided, unplanned processes.

The most complex forms of non-intentional structure that we know of are biological organisms. All life on earth is descended from a single common ancestor, a form of replicating molecule that duplicated sufficiently for the non-intentional process of natural selection to act upon the population, leading to single-celled organisms, then to multi-cellular organisms. Mutations provide sources of variation allowing natural selection to work, but while mutations are random, the process of natural selection is the very opposite of randomness. Natural selection is an optimization algorithm defined by principles as incontrovertible as the laws of gravity and motion.

There are also entities that are brought about by a mixture of intention and non-intention. The products of domestication, such as livestock, pets, and crops, are the result of a mixture of intention on the part of humans to select for certain traits, coupled with the non-intentional forces of evolution. And nearly any work of engineering or art includes attributes that initially were unintended mistakes that ended up being incorporated into the final product and actually enhancing it.

Function is also closely wedded to structure, and refers to the role a structure plays. Some entities have no inherent function, though they may be co-opted by an agent to fulfill a particular role (e.g. diamonds). Both non-intentional and intentional structures can be functional. Biological eyes were the product of evolution and serve the function of visual sensory input for a wide range of organisms. Photographic lenses were designed by humans to fulfill a similar function in artifacts.

Simplicity and complexity are also concepts closely related to structure. The degree of complexity refers to the amount of variability in structure. A diamond is a simple, but highly-structured lattice of carbon atoms. A multi-cellular organism is highly-structured and highly-complex, because even the simplest of such organisms is composed of cells which differentiate to varying degrees. Even if the number and types of cells is relatively small, each cell is composed of differential parts, specialized for various types of cell function.

The next section will discuss what it means to value structure.