In the early 1700s, Edmund Halley developed methods for computing the tracks of total eclipses of the sun. He determined that a total solar eclipse would sweep over southern England and Wales on Friday, April 22, 1715, the first time since 1140. He prepared a pamphlet titled The Black Day, or a prospect of Doomsday exemplified in the great and terrible eclipse which will happen on the 22nd of April 1715.

He prepared this map of the predicted path of the shadow of the moon over England. But, how to describe the process that created an eclipse? Halley used the diagram at the left to show how the moon passed between the earth and sun, creating the eclipse. The letters A, B, C, D, etc. to describe their relations. C, for example, refers to the part of England predicted to be most darkened (Northhampton, 54 miles from London).

Minard's main career was as an engineer for the Ecole Nationale des Ponts et Chaussees in Paris. In 1840 he was asked to investigate the cause of the collapse of the bridge at Bourg St. Andeol on the Rhone. His report consisted of this drawing, to which words provide little extra by way of explanation.

Why did the bridge collapse? As shown, the bed beneath the left side of the bridge had washed away.
Image source: Tufte (1983, p. 39)

Proofs are usually dry, dusty stuff sprinkled liberally with symbols. What about proving something with a picture? This proof of the Pythagorean Theorem is attributed to Bhaskara, a Hindu mathematician of the 12th century. We are given the bottom right triangle. Construct a square by making three copies of the triangle, as shown.

Got it? The side of the small square is b-a, and its area is (b-a)² or b²-2ab+a². The area of our triangle is ab/2. The area of all four triangles is 2ab. Then the area of all four triangles, plus the area of the small square is b²+a². So c²=a²+b².

Classical suppression refers to the paradoxical result that a predictor variable (X1) may have no correlation with an outcome variable (Y), yet it increases the variance accounted for (R²) in a multiple regression with another predictor (X2). A variety of other paradoxical effects (enhancement, redundancy) can also occur, depending on the correlations among these variables.

This diagram, by Friedman and Wall (2005), puts all these effects in context. It shows the regression coefficients and R² for particular values of the correlations of Y with X1 and X2, as the correlation r₁₂ between X1 and X2 varies over its range. The regions in which various effects occur are demarked by vertical lines.

Reference: Friedman, L. and Wall, M. (2005), Graphical views of suppression and multicolinearity in multiple linear regression, The American Statistician, 59(2), 127-136.

Mark Lombardi (1955-2000) was an abstract painter, best known for his network diagrams of crime and conspiracy. Lombardi's drawings attempt to document financial and political frauds by power brokers. Nodes in the diagrams represent individuals, corporations and government agencies, connected by lines showing associations, deals and so forth.

His 1999 drawing, entitled George W. Bush, Harken Energy and Jackson Stephens, ca 1979-90, shows the proven connections between James Bath, the Bush and bin Laden families, and business deals in Texas and around the world. Thirteen lines originate with or point to James R. Bath, more than any other name presented. Among those linked to this obscure yet central character are George W. Bush, Jr., George H.W. Bush, Sr., Senator Lloyd Bentsen of Texas, Governor John B. Connally of Texas, Sheik Salim bin Laden of Saudi Arabia, and Sheik Salim's younger brother, Osama bin Laden.

Lombardi's other network diagrams relate to the Iran-Contra Affair, World Finance Corporation, the Bay of Pigs invasion, and so forth. Each was based on thousands of notes gathered from news reports and written on index cards.

See also: Review of George W. Bush, Harken Energy and Jackson Stephens for the complete story behind this image. Notes on Mark Lombardi from ArtCritical.com.

Description: Telling stories of history in words provides for rich detail, analysis, and subtlety, but the linear form of text does not provide for overview, multiple layers or zoomable levels of detail -- abstraction that might be possible in a visual representation. See also our timelines page for other visualizations of events in time.

These images are from one of a series of beaautifully designed, poster-size charts prepared by Larry Gormley and Bill Younker of HistoryShots. This one shows the history of the US political parties from 1892--2005, on a horizontal time scale with details about political events, issues and administrations.

Description: These images, also from HistoryShots, provide a visual analysis of the Confederate Army in the US Civil War. The main organization is by date (horizontal) and by geography (vertical). Flow lines, chart the size of armies over time, and many details of important battles are shown as annotations.

Questions: How can such visual portrayals of events in time be made better or more useful? Are there better ways of representing time than a linear scale? How can other dimension(s) be used? What can be done with dynamic, interactive graphics that can't be shown in a static image? See our page on Timelines and Visual Histories for a gallery of timeline visualizations, and A Timeline of Timelines for a history of ideas about representations of time.

Description: There are a number of schemes or theoretical approaches to classifying methods of information visualization. Among the highlights are Jacques Bertin's Semiologie Graphique and Lee Wilkinson's Grammar of Graphics, the latter being also a computational scheme, inplemented in several statistical packages (SPSS, R).

This image, from the Visual-Literacy.org web site takes a purely visual approach, attempting to show various aspects of visualization methods collectively in a form modeled on the periodic table of the elements. Colors refer to a classification of what is visualized: Data, Information, Concepts, Strategy, etc. As in the periodic table of the elements, the methods are supposed to increase in complexity from the top row down.

The web page is implemented in Javascript; each "element" has a corresponding pop-up example image. The rational behind the design is explained in a paperToward a periodic table of Visualization methods ....