Post Modern Bell Wear

Watch a fun video The Evolution of Tap Dance by Post Modern Jukebox with tap dancer Sarah Reich. Note the bell-shaped distribution pattern of wear on her tap platform: most wear in the middle and less towards the edges.

Stepping Up

This is a ladder leading to an elevated playhouse for kids visiting Brookside Gardens in Maryland. The ladder reveals a frequency distribution of foot placement wear. On most steps we see more wear in the middle of the ladder rung and less wear towards the left and right edges. This leaves a bell-shaped pattern of use.

But a rung near the bottom has a bi-modal pattern, showing the wear resulting from both left and right feet. This doesn't persist on higher rungs. There the wear seems more central. So why not on the lower rung as well? Perhaps central steps on higher rungs feel safer. A care that is not that needed closer to the ground.

A Distribution on a Cylinder

Here's a utility pole at a traffic intersection in Aspen Hill, Maryland. The pole has served as display for the many yard sales, community meetings, and businesses that have had their advertising flyers posted on the pole. The flyers have long since been removed. Only their staples and nails remain. These accumulated staples show a distribution of the heights of flyer postings. 

The close-up view below shows the distribution of individual staples and nails on the cylinder of the pole. The staples are distributed both around the pole and vertically up and down the pole. Vertically, it's too difficult to put flyers high on the pole and few staples can be found there. Flyers very low on the pole wouldn't be easily seen by those passing by, so few staples are also found there. Most staples and nails are at a comfortable shoulder and viewing height. If we imagine the height of a staple above the ground is our random variable, we find few staples with small height, few with large height, and many more with a medium height. This is a bell-shaped pattern up and down the pole that we have seen often.

Horizontally, the staples are distributed circularly around the pole. They would also have greatest frequency towards the traffic and lesser frequency on the backside of the pole. This is likely also a bell-shaped distribution, wrapped around a circle. We have seen such a distribution before connected with the characteristic function of a random variable. We've also seen a distribution on a pole at the Rodin museum in Paris.

YADDA Boston

Yet Another Door Distribution Again, this time at the Summer Shack Restaurant in Boston. Not many patrons grab the door near the handle, not many reach it much higher. Most grab the door, and wear away its paint, at a comfortable, likely shoulder height. A bell-shaped frequency distribution results. Thanks Laura.

Scuff and Wear

This is an doorway threshold between two rooms of a thrift store in Easton, Maryland. People step on or over scraping their feet on both sides of the edges of the raised threshold. More frequent steps and wear in the middle and fewer steps and less wear on the left and right edges all scuff away the black painted wood revealing a bell-shaped frequency distribution of wear.

YADDA on TV

Seen on an episode of Major Crimes on TNT, a wear pattern of hand placement in holding a door open. Not many hands are placed low, many more higher, and not many are placed still higher. The frequency of hand wear shows us, yet again, the bell-shaped pattern of wear. Yet Another Door Distribution Again.

YADDA New York's Penn Station

Yet Another Door Distribution Again. Doorway to a train track at New York's Penn Station showing the two halves of nearly circular bell-shaped curves of wear. But from what? Most likely the edge of Amtrak luggage carts pushing the door open. The carts seem to push equally on each door, with perhaps a slight bias for the left side. Compare this to the bookstore doors or the Dulles airport doors from earlier posts.

YADDA BBQ 2

Here's another picture of the entry door to Sonny's BBQ in Sanford, Florida. You can see the vertical wear pattern of the many hands that have held open the door. The most frequent use is on the brown wood of the door. Those hands have left grease and grime that has mixed with the finish on the door producing a mottled white central portion of a bell-shaped curve. The lower tail of the bell-curve comes from the polishing that hands have done on the door's copper entry plate. The break between the mottled white pattern and the polished copper tail seems to fall at the inflection point of the bell-curve. Properties of the normal curve tell us that the wear beyond the inflection point in the copper tail accounts for about 16% of the total wear. The corresponding upper inflection point seems to fall just were the mottled white pattern ends. This also indicates about 16% of wear in the upper tail. These divisions likely correspond to the normal distribution of the height of hands as they open the door, perhaps just below shoulder level.

Stepping Up 2

This is an another image of the checkout counter at a deli in Rockville, Maryland. We saw before the pattern of customers standing and awaiting completion of their purchases, and wearing away the floor tiles with their shuffling feet, revealing contours of their use.

Her we see the wear patten made by their purchases that are placed and slid across the counter to be totaled up on the register. The white of the counter top has been worn away to the brown board underneath. There is greater wear near the customer who perhaps sets down several items, but the wear patten narrows as the checker selects one at a time to ring up their prices on the register. What remains is the pattern of support for the joint distribution of purchase placement.

But there's more (as they say on TV commercials). Look along the front edge of the counter nearest the customer. Along this edge we see the bell-shaped marginal distribution of left/right item wear as the items are either placed on or slide off the counter.

Ceaseless Tread of Pictures of Pictures

In his Sherlock Holmes story "The Man with the Twisted Lip" Arthur Conan Doyle had his character Dr. John Watson notice:

Ordering my cab to wait, I passed down the steps, worn hollow in the center by the ceaseless tread of drunken feet

Above is a detail from the drawing "Twin Staircases in Vitorchianoby" by Rhode Island School of Design  Professor Fred Lynch from his blog. It nicely illustrates Dr. Watson's observation. I found a comparable photograph of such stairs here.

The tread of those ceaseless drunken feet have worn away the stone most in the center and less along the edges. The worn steps give us a profile of a normal, bell-shaped pattern of wear. A pattern we've seen often.

But Design Professor Lynch tells how he included this image along with a drawing of a historic and often reproduced, tourist-popular image of an Italian piazza. When he asked his students to critique his drawings he found that such beautiful and historic images were of less interest to his students than this drawing of stairs. One student noted "one kind of drawing was of what I, the artist had found to be interesting. The other kind were drawings of subjects that others have found interesting". He had made a drawing of an image many people knew well, and were then more critical or bored with yet another rendition of something they had seen often. The stairs, on the other hand, were something not so ingrained in their visual memory. It was an image the artist cared about, not one that history and tourist traffic had made famous and ubiquitous.

It reminded Professor Lynch of a passage from the novel "White Noise" by Don Delilo:

“Several days later Murray asked me about a tourist attraction known as the most photographed barn in America.  We drove 22 miles into the country around Farmington.  There were meadows and apple orchards.  White fences trailed through the rolling fields.  Soon the sign started appearing.  THE MOST PHOTOGRAPHED BARN IN AMERICA.  We counted five signs before we reached the site.  There were 40 cars and a tour bus in the makeshift lot.  We walked along a cowpath to the slightly elevated spot set aside for viewing and photographing.  All the people had cameras; some had tripods, telephoto lenses, filter kits.  A man in a booth sold postcards and slides — pictures of the barn taken from the elevated spot.  We stood near a grove of trees and watched the photographers.  Murray maintained a prolonged silence, occasionally scrawling some notes in a little book. 

“No one sees the barn,” he said finally.
A long silence followed.
“Once you’ve seen the signs about the barn, it becomes impossible to see the barn.”
He fell silent once more.  People with cameras left the elevated site, replaced by others.

We’re not here to capture an image, we’re here to maintain one. Every photograph reinforces the aura.  Can you feel it, Jack? An accumulation of nameless energies.”
There was an extended silence.  The man in the booth sold postcards and slides.
“Being here is a kind of spiritual surrender.  We see only what the others see.  The thousands who were here in the past, those who will come in the future.  We’ve agreed to be part of a collective perception.  It literally colors our vision.  A religious experience in a way, like all tourism.”
Another silence ensued.
“They are taking pictures of taking pictures,” he said.
He did not speak for a while.  We listened to the incessant clicking of shutter release buttons, the rustling crank of levers that advanced the film.
“What was the barn like before it was photographed?” he said.  “What did it look like, how was it different from the other barns, how was it similar to other barns?”

Concrete Diffusion

Here is pattern I have seen often on concrete sidewalks. Wear that often begins in a crack in the sidewalk spreads out (horizontally in this picture) in a pronounced bell-shaped pattern. Here is another example.

I was  told by one colleague that this is simply the basic result of a diffusion process, as wear tears up the opening and propagates through with walk. I'm not fully clear on the physics involved, but it is quite reminiscent of my very first posting on this blog back in 2007.

YADDA BBQ

Yet Another Door Distribution Again this one from Sonny's BBQ in Sanford, Florida near my late parents home where I grew up. On this door, we see a thin stretch of wear just above the metal latch handle. This is the result of many hands opening a door, with few hands pressing on the left, few on the right with many more pressing in between and wearing away the brown paint on the door. This results in a bell-shaped wear pattern we've seen often on doors.

Gas Pump Dings

Here's another gas pump distribution. Inattentive users of the pump's nozzle have carelessly returned it to its home. In the process they have dinged the vertical panel on the left. The nozzle has its set home, but the users have sometimes started too high for its return resulting in a few dings on the upper regions of the panel. Similarly, there are a few dings on the low end of the panel. The majority of the dings are in-line with the nozzle's home. It's a distribution pattern we've seen often: few marks high, few marks low, and most marks in between.

Gas Pump Wear

The wear pattern in this image shows a frequency distribution of customers’ finger placement as they take their receipt from a gasoline pump. They likely target their grab at the center of the receipt. As they remove the receipt, the paper and their fingers rub paint off the dispenser. The wear pattern seems to be symmetric about the center, that is, the right side of the wear pattern is a near mirror image of the left side. This shows that users favored neither left nor right more often in removing their receipts. The image of wear shows more wear near the center of the dispenser and less on the edges but it seems balanced at the central target point. The bell-shaped curve of appears to be a very good match for a normal curve. 

Elementary Steps, Dr. Watson

“Ordering my cab to wait, I passed down the steps, worn hollow in the center by the ceaseless tread of drunken feet,” Dr. Watson in The Adventure of the Man with the Twisted Lip by Arthur Conan Doyle. (Bell-shaped carpet wear from the ceaseless feet at a restaurant in Snow Hill, Maryland.)

YADDA: There when you need them

This past week I gave a talk "Normal Distributions: Photographic Confusions" at the University of Maryland. On the way to the lecture room I pointed out this bell-shaped distribution of wear on a stairway door. Yet Another Door Distribution Again.

YADDA: No Time for Lefties

Here is a bell-shaped pattern of, what appears to be, only right-hand thumb placement on the handle of a door entering a gas station convenience store, (Yet Another Door Distribution Again, late summer vacation find).

YADDA Frank Lloyd Wright

Yet Another Door Distribution Again (YADDA)

We stayed for two nights, this past Fourth of July weekend, in the Haynes House, a Frank Lloyd Wright designed Usonian home in Fort Wayne, Indiana. Completed in 1952, it has seen much use. Here is a view of one of a pair of cabinet doors in the master bedroom. It shows the pattern of wear that we have seen often, more in a central area around the door knobs, with less wear extending toward the two extremes, a bell-shaped pattern of wear and use, (Thanks Nick).

Bell-Curve Table Wear

The restaurant table above has a polished tile center that is bordered with mitered wood trim. These wooden borders seem to have been installed a little proud of the tile center. Plates and silverware set in front of a seated diner have repeatedly sanded down the proud edge of the trim to more smoothly match the level of the tile center. This can be seen as the vertical, lighter region of the trim where it meets the tile center. Plates, silverware, cups, glasses, etc. are most often placed along the center of the edge, causing much more repeated sanding of the center of the trim. This can be seen in the broader, lighter colored wooden edge next to the tile. Less often, table settings are placed to the left or right of the diner (bottom and top in this picture). This is results in less wear on the trim and the progressively narrowing of the lighter sanded area next to the tile center. What results is a broad, bell-shaped patten of the frequency of wear: more wear in the center, less on the edges.

Kitchen Distribution

Here is a well-used cutting board. Every morning it protects the counter top from an errant knife cutting slices of bread for breakfast. The loaf is most often placed so that the cuts fall near the middle of the board, with the knife's blade repeatedly marring the front edge of the cutting board. Less often the cuts continue and extend off to the right or left of the middle. In this contest right seems to win out. This leaves us with a frequency distribution of the knife's marks skewed a bit to the left: the fewest marks along the left of the front edge, the most along the middle, and then a bit fewer marks on the right of the edge. This is a bell-shaped, although somewhat skewed to the left, pattern that we've seen often.