May 26, 2010

An Irresistible Edge

Based on a trapezoid split into two triangles, the National Gallery of Art's East Building features walls that meet at odd angles, eschewing the right angles of more conventional structures.

One particularly sharp corner, visible to the right of the East Building's H-shaped, west-facing façade, has attracted a lot of attention. There, two walls meet at 19 degrees to form the apex of a narrow triangle. This 19-degree "fin" rises 107 feet from ground to roofline. If you look closely at the corner, you'll see a smudge darkening the lavender-pink marble.

Over the years, so many people have felt the urge to touch the unusually sharp corner that countless hands have deposited their oils on the marble to create a dark stain. It stretches over a span of about two feet, tapering off at its upper and lower ends.

In effect, the stain is a population distribution, representing all the people who have visited and touched the corner, given that most people naturally reach out to touch the wall just below shoulder height.

Normal distribution (bell curve).

The fin's stain is just one of many instances in which human use can leave its mark on objects in the environment. Such usage or wear patterns can often tell you something about the population or behavior responsible for the marks. See, for example, "Statistical Wear."

Statistician Robert W. Jernigan of American University has long studied such patterns and collected images that illustrate statistical ideas. His blog, "Statpics," includes a wide variety of such examples.

One of my favorite examples from my own travels is a stone staircase in Wells Cathedral, England, where centuries of foot traffic have worn characteristic concavities into the steps.

Photos by I. Peterson


Adriana said...


CholPhoto said...

and of course there is John Harvard's famous left toe:'s%20Toe.jpg

Dr. Urth said...

I recently heard that Benford's Law of the distribution of numbers was discovered by Benford noticing that the library's copy of the CRC table of logarithms was more worn in the 1xx pages than in the 8xx-9xx pages. See The Law of Anomalous Numbers, Proc Amer Phil Soc, Vol. 78, No. 4 1938.03.31), pp. 551-572