A smiley-face is very expressive, statistically. By tweaking the eyes, mouth and other bits, you can literally put a meaningful face on any jumble of numbers. Herman Chernoff pointed this out in 1973 in the Journal of the American Statistical Association, in a monograph called “The Use of Faces to Represent Points in K-Dimensional Space Graphically.”

Subsequently, folks took to calling these things Chernoff faces. Chernoff faces can make statistical analysis into a recognizably human activity.

Most people, when shown some statistics, sigh and get boggled. But Herman Chernoff realized that almost everyone is good at reading faces. So he devised recipes to convert any set of statistics into an equivalent bunch of smiley-face drawings.

Each data point, he wrote, “is represented by a cartoon of a face whose features, such as length of nose and curvature of mouth, correspond to components of the point. Thus every multivariate observation is visualized as a computer-drawn face. This presentation makes it easy for the human mind to grasp many of the essential regularities and irregularities present in the data.”



“The Use of Faces to Represent Points in K-Dimensional Space Graphically” is one of the few statistics papers that is visually goofy, rather than arid.

One page is filled with 87 cartoon faces, each slightly different. Some faces have little beady eyes, others have big, startled-wideawake peepers. There are wide mouths, little dried-up “I’m not here, don’t notice me” mouths, and middling mouths. Another page shows off some of the cartoony variety that’s possible: roundish simpleton heads, jowly alien-visitor heads, and a smattering of noggins that look froggy. Elsewhere, the study perhaps inevitably includes conventional statistics machinery — charts of numbers, differential and intergral calculus equations, and plenty of technical lingo.

Chernoff discovered, by experiment, that people could comfortably interpret a face that expresses quite large amounts of data. “At this point,” he wrote, “one can treat up to 18 variables, but it would be relatively easy to increase that number by adding other features such as ears, hair, [and] facial lines.”


Chernoff faces made from data gathered by measuring rocks, and presented in Chernoff’s original paper in the Journal of the American Statistical Association. The paper explains that “Eight measurements were made on each of 88 nummulited specimens from the Eocene Yellow Limestone Formation of northwestern Jamaica.

The world has gone on to employ Chernoff faces a little, but not yet a lot. A 1981 report in the Journal of Marketing, for example, used them to display corporate financial data, with this explanation: “From Year 5 to Year 1, the nose narrows as well as increases in length, and the eccentricity of the eyes increases. Respectively, these facial features represent a decrease in total assets, an increase in the ratio of retained earnings to total assets, and an  increase in cash flow.”

A note at the very end of Chernoff’s 1973 paper hints at a practical reason why his idea would not catch on immediately: “At this time the cost of drawing these faces is about 20 to 25 cents per face on the IBM 360-67 at Stanford University using the Calcomp Plotter. Most of this cost is in the computing, and I believe that it should be possible to reduce it considerably.”

Chernoff faces representing data about a series of Swiss bank notes, some real, some forged, from Bernhard Flury and Hans Riedwyl,’s 1981 study in the Journal of the American Statistical Association. The main variables are:
Xl length of the bank note
X2 width of the bank note, measured on the left side
X3 width of the bank note, measured on the right side
X4 width of the lower margin
X5 width of the upper margin
X6 length of the print diagonal from the lower left to the upper right corner

References
“The Use of Faces to Represent Points in K-Dimensional Space Graphically,” Herman Chernoff, Journal of the American Statistical Association, vol. 68, no. 342, 1973, pp. 361–8.

“Facial Representation of Multivariate Data,” David L. Huff, Vijay Mahajan and William C. Black, Journal of Marketing, vol. 45, no. 4, Autumn 1981, pp. 53-9.

“Use of Chernoff Faces to Follow Trends in Laboratory Data,” John A. Lott and Timothy C. Durbridge, Journal of Clinical Laboratory Analysis, 1990, pp. 459-63. The authors are at Ohio State University in the USA and the Institute of Medical and Veterinary Sciences in Adelaide, Australia.

“Graphical Representation of Multivariate Data by Means of Asymmetrical Faces,” Bernhard Flury and Hans Riedwyl, Journal of the American Statistical Association, vol. 76, no. 376, December 1981, pp. 757-65. The authors are at the University of Berne, Switzerland.

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This article is republished with permission from the July-August 2010 issue of the Annals of Improbable Research. You can download or purchase back issues of the magazine, or subscribe to receive future issues. Or get a subscription for someone as a gift!

Visit their website for more research that makes people LAUGH and then THINK.

Inflatable Van Gogh | $11.95

For those times when you feel the need for emergency art, there's the Inflatable Van Gogh in a can, now available at the NeatoShop. It's Van Gogh's most famous work, Starry Night, that can be inflated to hanging size or stored in its full-color illustrated tin. Never be caught short on art again! Add some class to your condo or cubicle with this Inflatable Van Gogh painting! Each 19-1/4" x 15-3/4", vinyl masterpiece is a stunning example of high concept kitsch for the cultured cosmopolitan. Makes a great gift!

Check out other decorative items for your home at the NeatoShop!

The following is an article from Uncle John’s All-Purpose Extra Strength Bathroom Reader.

Anyone who says one person can't make a difference has never heard the story of the Statue of Liberty.

BIRTHDAY GIRL

In 1865 a young French sculptor named Frédéric-Auguste Bartholdi went to a banquet near the town of Versailles, where he struck up a conversation with Edward de Laboulaye, a prominent historian.

De Laboulaye, a great admirer of the United States, observed that the country's centennial was approaching in 1876. He thought it would be a good idea for France to present America with a gift to commemorate the occasion. But what? Bertholdi proposed a giant statue of some kind... and thought about it for the next six years.

COMING TO AMERICA

By 1871 Bartholdi had most of the details worked out in his mind: The American monument would be a colossal statue of a woman called "Liberty Enlightening the World." It would be paid for by the French people, and the pedestal it stood on would be financed and built by Americans.

The idea excited him so much that he booked passage on a ship and sailed to New York to drum up support for it. As he entered New York Harbor, Bartholdi noticed a small, 12-acre piece of land near Ellis Island, called Bedloe's Island. He decided it was the perfect spot for his statue.



Bartholdi spent the next five months traveling around the U.S. and getting support for the statue. Then he went back to France, where the government of Emperor Napoléon III (Napoléon Bonaparte's nephew) was openly hostile to the democratic and republican ideals celebrated by the Statue of Liberty. They would have jailed him if he had spoken of the project openly- so Bartholdi kept a low profile until 1874, when the Third Republic was proclaimed after Napoléon III's defeat in the Franco-Prussian War.

Bartholdi went back to work. He founded a group called the Franco-American Union, comprised of French and American supporters, to help raise money for the statue. He also recruited Alexander-Gustave Eiffel, soon to become famous for the Eiffel Tower, to design the steel and iron framework to hold the statue up.

A WOMAN IN A HURRY

By now the centennial was only two years away. It was obvious that the huge statue couldn't be designed, financed, built, shipped, and installed on Bedloe's Island in time for the big celebration. But Bartholdi kept going anyway.



Raising the $400,000 he estimated was needed to build the statue in France wasn't easy. Work stopped frequently when cash ran out, and Bartholdi and his craftspeople missed deadline after deadline. Then in 1880 the Franco-American Union came up with the idea of holding a "Liberty" lottery to raise funds. That did the trick.

In the United States, things were harder. There was some enthusiasm, but not as much as in France. It was, after all, a French statue ...and not everyone was sure the country needed a French statue, even for free. The U.S. Congress did vote unanimously to accept the gift from France... but it didn't provide any funding for the pedestal, and neither did the city of New York. Neither did the state.

Kids these days don't know what hazardous fireworks are... why, back in my day, when we walked six miles to school uphill both ways, fireworks were dangerous. I mean real dangerous, like the M80s we used to by all the time. How dangerous were they?

Federal law now caps the flash powder content of firecrackers at 50mg per firework. Typical M-80s contained somewhere in the neighborhood of 3,000mg of powder apiece, or roughly 60 times as much explosive. (This power makes sense given the M-80’s original purpose: simulating the sound of gunfire and artillery during military training missions.)

Read about how these changes came about at mental_floss. Link

Jeff Wysaski at Pleated Jeans put together 13 scenarios in which we are most likely to do or say something extremely dumb. Have you ever said, "You, too!" after someone wishes you a happy birthday? I have. Link

(YouTube link)

Nyan Cat gets a makeover for the Fourth of July! Music by John Philip Sousa. -via Buzzfeed

Previously: "Stars and Stripes Forever" on trombone, by the Muppets, and barbershop quartet style.

Crazy Calculator | $8.95

Have you heard about the Crazy Calculator, the calculator that hates math? It's both a prank calculator and a real calculator! When your friends are around, use it in prank mode. Whatever equation you enter, the answer will come up crazy: I H8 MATH, ASK NICELY, TRY LATER, WHO CARES, GO AWAY, and more! But when you really need an answer, switch it to normal mode and get the correct answer. Sweet! It's solar powered with battery backup and has an automatic shut off timer. Get your Crazy Calculator today at the NeatoShop!

And check out all the other prank toys and gifts at the NeatoShop!

(YouTube link)

Can't a cat take a decent nap around here without some annoying dinner entree bothering him? -via The Daily What

In the USA, we are taking a holiday weekend in honor of the 235th anniversary of the founding of our nation on Monday. Expect a lot of loud noises. In between picnics, parades, and fireworks, you'll want to spend some time catching up on the great things we've posted this week at Neatorama. Here are the exclusive articles you won't find anywhere else.

Jill Harness wrote 2 True and 2 False Origins of Tongue Twisters And Nursery Rhymes.

Guest blogger Eddie Deezen told us about Cheerleading and Some Famous Cheerleaders.

From Uncle John's Bathroom Reader, we got the second part of the history of professional wrestling in The Legend of Gorgeous George.

Mental_floss magazine gave us 9 Essential Facts for the Crustacean Enthusiast.

A Tribute to the Edible Dormouse was the contribution this week from the Annals of Improbable Research.

Congratulations to the winners of last week's Tokyo Flash Treasure Hunt!

In the What Is It? game, the object in question is a mailing machine for putting addresses on newspapers and magazines. Villaridge knew that, and won a t-shirt from the NeatoShop. Meanwhile, DocKami said, “it’s a …. IT’S A TRAP !” which made me laugh, so he wins a t-shirt for the funniest answer. It does kind of resemble a trap, doesn’t it?

I also want to remind you of the “one guess per comment” rule, because we had a lot of people with multiple guesses this week, and that’s not really fair to everyone else. Of course, you are welcome to leave as many comments as you want.

When you've seen all this, you can find some wonderful weekend reading material at The Best of Neatorama. Use the slider at the top of the page to pull up features from different years.I've gone ahead and selected a few that are particularly appropriate for the holiday:

Yankee Doodle Fun Facts

5 Neat Facts About The Declaration of Independence

5 Obscure Facts About the Declaration of Independence

Thomas Paine: Hero, Patriot ... and a Paine in the Butt!


Top Ten US Generals

Little Known Facts About American History

43 Facts about 44 Presidents

Also join us at Facebook for more links, discussions, and trivia. And have a great Independence Day!

The British creative team called Concept Shed produced this odd but beautiful vending machine to performed automated weddings for Marvin's Marvellous Mechanical Museum in Detroit. Enter your information on the keyboard, and it spits out a plastic ring, asks you to enter your vows, and prints out a certificate! The eight-foot-tall computerized machine has a beautiful retro look. They'll make you one to your specifications if you want. See a video of the machine in action at their website. Link -via the Presurfer

Bob Rosinsky was asked to restore a tintype photograph from the 19th century. On his blog, he walks us through the process of how he did it. No, we don't watch him change every pixel, but you'll be surprised at the difference between a scanner image of the tintype and a photograph using an ultra-high resolution camera with a macro lens. Here, you see the before-and-after pictures. Link -via Boing Boing

Maze Cafe Cup and Saucer | $14.95

What a neat saucer to put under a coffee cup! It looks like an everyday cup and saucer, but just a drop of coffee on the saucer becomes a game as the drip finds it ways through the maze of grooves. The Maze Cafe Cup and Saucer was designed by artist Erdem Selek and is available now in the NeatoShop. Get your morning coffee and your morning puzzle at the same time! And be sure to check out the many other clever cups and mugs from the NeatoShop!

Hot Dog N Bun Soap | $10.95

Don't eat that hot dog -no matter how tempted you are! Some dogs are made for grilling; others are made for washing up. This dog is really a bar of soap, complete with a soap bun and soap mustard, made with completely vegan ingredients. Get yours at the NeatoShop! The Hot Dog N Bun Soap is only one of a series of delightfully-shaped soaps that will bring a smile to the face of guests in your home. Check them all out at the NeatoShop. And order your hot dog today!

When we Americans are young children, we are taught the basics of our nation's founding. But often those stories get shortened into easy-to-recall sound bites that don't tell the whole story. Most of the historical "facts" you remember are oversimplifications of a more nuanced story. For example, I bet you thought the Declaration of Independence was adopted in the fourth day of July in 1776.

Independence Day is celebrated two days too late. The Second Continental Congress voted for a Declaration of Independence on July 2, prompting John Adams to write his wife, "I am apt to believe that [July 2, 1776], will be celebrated, by succeeding Generations, as the great anniversary Festival."

Adams correctly foresaw shows, games, sports, buns, bells, and bonfires—but he got the date wrong. The written document wasn't edited and approved until the Fourth of July, and that was the date printers affixed to "broadside" announcements sent out across the land. July 2 was soon forgotten.

Learn other historic tales that were different from what you recall in this article at National Geographic News. Link

(vimeo link)

This is what Pac-Man would be like as a first person RPG, if you were playing it in a car. Maybe. -via The Daily What