Secondary notation

Visual cues improving the readability of a formal notation

Secondary notation is the set of visual cues used to improve the readability of a formal notation. Examples of secondary notation include the syntax highlighting of computer source code, sizes and color codes for easy recognition of consumer symbols such as bank notes or coins, or the regular typographic conventions often found in technical books to highlight sections with the same type of content. Secondary notation provides redundant (more than necessary) information; if the visual cues are the only way that some information is provided, such as in traffic lights, or a chart's key, it is not secondary. Secondary notation is often not a part of the formal notation itself. Rather, it is a method of organizing the formal notation to allow it to be more easily understood. Thus, secondary notation does not change the actual meaning of the formal notation, rather it allows for the meaning to be readily understood. In text such as programming languages, this can be done using cues such as indentation and coloring. In formal graphical notations, this can be done through the use of symmetry or proximity to indicate relatedness.

Secondary notation annotates formal notation in a number of contexts which can be broken down to two main domains: text and graphics.

There are a number of common instances of secondary notation that are seen in text. Secondary notation is common in typography and in code editors appearing as boldness, italics, and spacing/indentation.

Secondary notation is commonly used in graphical contexts to better convey information beyond what the formal notation of the graphic makes explicit.

While inadequate use of secondary notation can significantly increase the amount of effort necessary to understand a model, misuse of secondary notation can also be a detriment. Use of symmetry can make a graphic more visually appealing, but can also convey misconceptions if used incorrectly. For instance, placing unrelated items close together may cause a reader to perceive them as being related. Additionally, arbitrary use of coloring may distract a reader as they wonder about the meanings of the various colors.

The ability of individuals to understand and use secondary notation has been shown to vary based on experience within the relevant field. Experts in a field are generally more able to utilize the clues provided by secondary notation. Specifically, while reading diagrams, experts have been shown to have more skill at reading the larger structure of the diagram and using it to guide their examination of the details provided by the formal notation. This compares to novices who often focus on the details of the formal notation, ignoring the hints provided by the secondary notation. There are also differences based on level of experience/expertise when creating documents that utilize secondary notation. Experts tend to be more consistent in their use of conventions while novices tend to vary between conventions, sometimes adhering on a surface level, but failing to convey the desired information. In the case of circuit diagrams, this is illustrated by common novice mistakes such as creating visual symmetry where there is no logical symmetry and frequent transitions between differing secondary notation conventions.