GIA: Research: Article Detail

There are many ways to present information visually. Popular media (e.g., newspapers, magazines, and television news shows) use a variety of formats to present information to their readership and viewers. For most of us, maps, graphs, and pie charts are familiar sights. We are used to seeing weather reporters use maps and tables to show us the weekly forecast, or watching business analysts use graphs to illustrate the movement of the stock market. Many of us are also familiar with topographic maps that use colors to show the elevations of mountains, or the depths of oceans. All of these formats are different methods of conveying information, and we have used many of them to present and analyze our research on diamond cut.

Although the visual presentation of information can be simple or complex—ranging from single-dimensional graphs to multi-dimensional contour maps—all informational graphics [Footnote 1] share one common goal: To convert "bare" numbers or facts into a readily understandable picture. As is the case with these other forms of informational graphics, we used such illustrations in our analysis of diamond cut to: (1) emphasize the essential relationships among the data, (2) highlight which data out of a larger group might be more important, (3) condense many separate data values into a single informational space [Footnote 2], and (4) provide another format (i.e., visual, rather than verbal or linguistic) to help readers understand a set of data.

Executive Summary:

This article explores the use of informational graphics in the presentation of data. It also explains how to understand the information that is presented in this format.
Informational graphics condense and clarify data so that they may be understood visually.
Different types of informational graphics are used to concisely present GIA's research on diamond cut.

Technical Summary:

Informational graphics can be used to present information in a clear and condensed format; we found this essential when presenting the complex data from our research on diamond cut, which included tens of thousands of proportion combinations.
Informational graphics are multi-dimensional, both in the types of information from which they are derived and the manner in which they are presented.
Informational graphics consist of independent and dependent variables; independent variables can be chosen freely (such as direction of travel), whereas dependent variables are determined from the independent variables and the environment (such as temperature at a given spot).
Information and the format of its presentation do not always have the same number of dimensions (for example, three-dimensional information—that is, information that consists of three variables—may be presented in a two-dimensional format).

DIMENSIONALITY

Before we look at specific examples of informational graphics from the world of diamonds, let us first use more commonplace examples to explain the differences in graphic formats.

It is helpful to consider informational graphics in terms of the number of dimensions they display. For example, a line drawn on a piece of paper is perceived as one-dimensional (it has only the dimension of length). If the endpoints of the line were joined so that it became a circle, it would be seen as two-dimensional (it now consists of height and width). An actual ball is three-dimensional (consisting of height, width, and depth).

An example of a situation that can be represented with a one-dimensional graphic is a train that travels from Los Angeles (California) to Denver (Colorado). The train is limited to a single line (i.e., the railroad track) and can only travel forward or backward on that track [Footnote 3]. Because the railroad track is one dimensional, the train must pass through all points on the track if it is to travel from Los Angeles to Denver (figure 1).

Figure 1. A singular, linear train route from Los Angeles (California) to Denver (Colorado) can be represented by a one-dimensional illustration, as in figure 2.

For these reasons, we can always locate the train (i.e., map its location) as a point on a single straight line (even if the actual railroad track is far from straight; see, e.g., figure 2).

Figure 2. If only presenting the order of cities that a train will travel through, the information in figure 1 can also be presented as a straight line.

A good example of a situation that can be represented with a two-dimensional graphic is an automobile that can drive in any direction on its way from Los Angeles to Denver. Unlike the train, the driver of the automobile is not limited to a single, specific path of travel. To get to its destination, the automobile can travel north, south, east or west. It can travel along the highway, take an alternative scenic route, or even drive straight across the desert landscape. Even though the automobile's travel can be represented by a line, the locations that it travels through are not limited or predetermined. Two different drivers in separate automobiles are free to vary the paths of their travels, and therefore vary the points at which they might be located on a graph or map at any point in time (figure 3).

Figure 3. The driver of one automobile (depicted in red) may choose to take a different path to Denver than the driver of the other automobile (depicted in blue) in this two-dimensional graphic.

A three-dimensional graphic can be used to illustrate a helicopter that flies from Los Angeles to Denver. This is because the pilot of the helicopter is not limited to traveling only north, south, east or west, but can also travel at various heights (up or down).

An important point to note is that the dimensionality of the information does not necessarily have to match the dimensionality of the presentation. Most graphics, whether they are one-, two-, or three-dimensional, are presented in two dimensions (e.g., as illustrations printed on paper in magazines, or as images that appear on the flat screen of television monitors). In these cases, information is expanded or condensed (and may even be coded using symbols) to make it easier to see and understand.

INDEPENDENT AND DEPENDENT VARIABLES

In addition to dimensionality, informational graphics can also be understood in terms of the number of variables—that is, different categories of information—they present in relation to each other. In the above examples, the variables might be distance, time, speed, and/or elevation. Variables can be independent or dependent, based on their relationship to each other. Independent variables are those that can be varied freely (e.g., the direction chosen by the driver of the automobile) and are not predetermined by the situation. Dependent variables are determined by the values of the independent variables, under the specific conditions of the analysis (e.g., the temperature at any particular spot driven to). Also, variables may alternate between being independent and dependent, according to the specific situation that is being analyzed and presented. In addition, the number of total variables determines the dimensionality of the information (but not necessarily the presentation of that information). It is helpful to reexamine the previous examples to see how this might work.

In the one-dimensional example of the train (again, see figure 1), the independent variable is the distance from Los Angeles that the train has traveled along the track (or the distance to Denver that the train has yet to travel). One choice of a dependent variable might be the distance to the next train station. For this example, however, assume that the dependent variable is the elevation above sea level. Elevation is a dependent variable in this case because it is determined by the location along the track where the train is located. Also, each location will have a specific elevation value associated with it, while each elevation value may have several different locations where it applies.

This information can be graphically presented in several ways. A truly one-dimensional presentation of this two-dimensional information would be a line (or length of string) that represented the total path from Los Angeles to Denver. Different measured segments of the string could be painted different colors to represent the different elevations at those points. This could also be represented graphically as a line with the different elevations marked along its length (figure 4, top).

Figure 4. Top: Information about the elevation at which a train travels can be presented along a one-dimensional line.

Bottom: The presentation of the information can be expanded to two dimensions by illustrating cities along one axis and the elevation of those cities along another axis.

In addition, this same information could be expanded and presented in a much more two-dimensional format (figure 4, bottom). In this case, individual cities are listed in one direction (i.e., along an axis), and their corresponding elevations are listed in another direction (along a perpendicular axis) [Footnote 4]. Notice that in all of these cases, the method of presentation may change, yet the number of independent and dependent variables remains the same.

The example of the automobile is similar to that of the train, but it needs two independent variables to accurately present its location at any point in time. This is because the automobile is not limited to a single specific path. Two independent variables that could be used are latitude and longitude. The dependent variable would remain elevation. One way to present and view this three-dimensional information would be a two-dimensional graphic in which one axis represents latitude, the other axis represents longitude, and the elevation is shown as numbers (values) located at specific points (figure 5).

locations and elevations of cities graph

Figure 5. This map shows the locations and elevations of cities passed through for each automobile. The three-dimensional information consists of the two independent variables of latitude and longitude, and the dependent variable of elevation (i.e., three-dimensional information presented in a two-dimensional graphic).

The example of the helicopter becomes a bit more complicated. Because the helicopter can travel in all directions (including up and down), elevation now becomes an independent variable. Having three independent variables allows us to pick another dependent variable to measure, such as air pressure. Since it would take a three-dimensional model (or sculpture) to present this four-dimensional information as it appears in real life, situations such as this are often condensed, and illustrated in two dimensions. In this case, the axes could remain the same and colors could be used to represent the different elevations of travel. The corresponding air pressure could then be listed near a colored spot that represented an elevation along the helicopter's path (figure 6).

Figure 6. This graphic illustrates three independent variables (latitude, longitude, and elevation), and one dependent variable (air pressure) in a clear and condensed manner (i.e., four-dimensional information presented in a two-dimensional graphic).

Also, in any situation where there is more than one independent variable, one or more of the variables can be held constant to reduce the number of independent variables in the situation. An example would be if the helicopter was limited to a single specific elevation on its flight. This might be done to get a better understanding of certain aspects of the dependent variable (in this case, the air pressure differences on a stormy day across a range of space at precisely 1,000 feet above ground elevation).

USING GRAPHICS TO UNDERSTAND THE DIAMOND CUT RESULTS

Now let's bring this back to our main concern: How can this information help us to understand different aspects of the diamond cut research project?

Once you are comfortable with the concepts of informational graphics, it is fairly easy to apply them to the world of diamond cut. Taking examples from GIA's 1998 article on diamond cut [Footnote 5], one situation that can be illustrated with a two-dimensional graphic (p. 171) is the change in WLR values (GIA's metric for calculated brilliance for a virtual diamond [Footnote 6]) over a range of crown angles (figure 7). This is basically similar to the above example of the

Figure 7. This graph has one independent variable (crown angle) and one dependent variable (WLR). It therefore presents two-dimensional information in a two-dimensional graphic.

train, in that for each different crown angle there is a determined value for WLR. In this case, the independent variable is crown angle and the dependent variable is the WLR value. (The other diamond proportions are held constant in this particular analysis.)

A three-dimensional situation from the same article (p. 174) would be the graphic that illustrates the change in WLR values (the dependent variable) caused by changes in crown angle and table size (the independent variables). In this graphic, the value of WLR for any one combination of table size and pavilion angle is represented by a color (figure 8). In some sense, this is very similar to

Figure 8. This contour map of continuous space for two independent variables (table size and crown angle) and one dependent variable (WLR) presents three-dimensional information in a two-dimensional graphic.

the elevation graphic that we used for the automobile example; latitude has become crown angle, longitude has become table size, and elevation has become WLR. The only difference is that we have moved from a representation of discrete space (in which only single points in space are being notated) to a representation of continuous space. Instead of only illustrating values at particular locations, the graphic is illustrating all of the values of the dependent variable across the whole range of informational space. In this way, we can more easily see the exact locations where the value of the dependent variable changes. These "lines of change" are called contours, and they provide another way to analyze the information contained within the graphic. For example, since the area between contour lines has the same range of value (WLR) we can visually identify all of the combinations of independent variables (in this case, crown angle and table size) that yield a certain range (WLR).

As stated above, a situation with three independent variables is more challenging to illustrate. Again, this is because the variables usually need to be condensed to fit on a two-dimensional page. In the 1998 article (p. 175), this is illustrated by the graphic that depicts the change in WLR across changes in crown angle, table size, and pavilion angle (figure 9). Although discrete

Figure 9. Visually displaying information with three independent variables creates interesting graphic challenges. This illustration presents four-dimensional information in a "quasi" three-dimensional format. [Note, however, that although this graphic attempts to recreate three dimensions, it is still only two-dimensional.]

locations can be mapped in the information space, as in figure 5 above, the need to illustrate continuous space creates a more complicated graphic. To refer back to our helicopter analogy, the colors representing WLR could also represent different air pressures as the helicopter flies through the ranges shown. Although this figure is visually accurate, it is difficult to use to analyze specific informational spaces (especially in the "back" portions of the graphic, those that are not shown). For this reason, a different presentation format is needed to usefully illustrate information with three or more independent variables. We will explore this format in our next article.

CONCLUSION

This ends the first part of this short series on presenting and reading informational graphics. The concepts of independent and dependent variables, as well as multi-dimensional graphics, will be further examined in part 2. We will also explore alternative formats that can be used to display information composed of three or more independent variables.

We received great inspiration for this article from Edward Tufte's three-volume set of books that explore visual information. We have provided the full references for these volumes in our bibliography.

We hope that you found this article useful, and invite any feedback or comments that you may have. You may contact us by email at DiamondCut@gia.edu.

If you would like to view a printable version of this article, click here.

Bibliography
Hemphill T. S., Reinitz I. R., Johnson M. L., Shigley J. E. (1998) Modeling the Appearance of the Round Brilliant Cut Diamond: An Analysis of Brilliance. Gems & Gemology, Vol. 34, No. 3, pp. 158-183; available through subscription services at 760-603-4595 ext. 7142, or at https://www.gia.edu/gandg/ggOrderform.cfm.

Tufte E. (1983) The Visual Display of Quantitative Information. Graphics Press, Cheshire, CT, 197 pp.

Tufte E. (1990) Envisioning Information. Graphics Press, Cheshire, CT, 126 pp.

Tufte E. (1997) Visual Explanations. Graphics Press, Cheshire, CT, 157 pp.

[Footnote 1] For the purpose of this article series, informational graphics are illustrations used to present data in a visual format. [back]

[Footnote 2] Information space (also known as data space) consists of the complete set of data points that are the relevant part of the analysis in question. For example, if we were analyzing the salaries of employees at a company, the data space might include the data of salaries, age of employees, time with company, position in company, and previous experience, as well as the relationships among these data. [back]

[Footnote 3] For this example, assume that there is only a single railroad track from Los Angeles to Denver without any alternative routes that may be taken. [back]

[Footnote 4] Here, as in the other graphics from this short series of articles, each axis has only one variable attributed to it. However, his does not always have to be the case. Some graphics may map several variables along the same axis. [back]

[Footnote 5] Hemphill T. S., Reinitz I. R., Johnson M. L., Shigley J. E. (1998) Modeling the appearance of the round brilliant cut diamond: An analysis of brilliance. Gems & Gemology, Vol. 34, No. 3, pp. 158-183. [back]

[Footnote 6] WLR was calculated using computer ray tracing to follow millions of light rays (each with a specified source, direction, and wavelength) as they interacted with a modeled ("virtual") round brilliant cut (RBC) diamond. The WLR value is a measure of brilliance which depends on the specific proportions of the modeled RBC diamond for which it is calculated. [back]