Imagine a world without patterns, a featureless, colorless canvas of nothingness.

Such a world cannot exist because we live in a world rich with sensory, physical and social patterns of many different kinds. Patterns represent organization and order.

There are only a few basic shapes that provide all of the visual richness of nature: line, circle, polygon, spiral, helix, meander, branch, radiant. No one knows how the human brain, the most complexly organized structure that we know of anywhere in the universe, puts these shapes together to recognize objects that are made from combinations of those shapes.

Equally puzzling is how the brain can use symbols based on the properties of counting numbers to describe the patterns that we find in nature, and which exist in our minds. But through the millennia we have found many ways to describe them that have become so complex as to be beyond the abilities of most of us.

We call it mathematics, the science of order that uses the logic and rules of operations that are ultimately derived from the simple act of counting to study quantity, shape and arrangement. We also use it as a tool of analysis to study relationships and to perform calculations.

There are few if any areas of human endeavor that mathematics cannot characterize or enhance, and not only in the sciences. In art, music, linguistics, literature and dance, mathematics augments and helps to add beauty to performance and analysis. In business, economics, politics and population dynamics, it is indispensable. It is used in information theory and signal processing, for security encryption and decryption, optimization, game theory and even for recreation. The list goes on and on.

There are visual patterns as well as time-ordered patterns. Patterns of repetition, cycles and discrete countable objects all exist and interact in the physical domain of the universe. Regardless of what is behind it, our brains are part of it. They are highly organized groups of 10 billion cells that exchange signals in an orderly fashion in order to function in a variety of ways, organizing, storing, retrieving and communicating information.

Certain specific brain cells are responsible for recognizing lines that lean certain ways and intersect at different angles. By putting together these shapes and lines, we each construct our own unique map of our world. It is a giant leap from those primeval shapes to equations that describe the behavior of an electron around a black hole.

Researchers have found that the shapes that newborns see in the earliest days of life affect the way the brain develops. This implies not only that mathematics is hard-wired into our brains, but also that these earliest perceptions play a role in our cultural development and help us to learn about our environment.

There are many numerical patterns, such as the nonrepeating, infinite digits of pi that seem to have no significance, while others, such as the wavelengths of light emitted from excited atoms, have led to deeper understanding of the laws of nature.

The kinds of patterns that mathematics describes are as diverse and variable as nature itself, but mathematics goes beyond the physical and connects with the deepest part of the abstract brain. Many mathematical structures were conceived in the mind and studied before any examples were found in nature. There are no doubt many more.

Richard Brill is a retired professor of science at Honolulu Community College. His column runs on the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.