Revisiones_bibliográficas TyO

sábado, 22 de enero de 2011

The Elements of Math

STEVEN STROGATZ

Steven Strogatz is a professor of applied mathematics at Cornell University. In 2007 he received the Communications Award, a lifetime achievement award for the communication of mathematics to the general public. He previously taught at the Massachusetts Institute of Technology, where he received the E.M. Baker Award, an institute-wide teaching prize selected solely by students. "Chaos," his series of 24 lectures on chaos theory, was filmed and produced in 2008 by The Teaching Company. He is the author, most recently, of “The Calculus of Friendship,” the story of his 30-year correspondence with his high school calculus teacher.

June 14, 2010, 4:33 PM

For Our Steven Strogatz Fans

By THE EDITORS

Professor Strogatz’s 15-part series on mathematics, which ran from late January through early May, is available on the “Steven Strogatz on the Elements of Math” page.

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May 9, 2010, 5:00 PM

The Hilbert Hotel

By STEVEN STROGATZ

TAGS:

DAVID HILBERT, GEORG CANTOR, INFINITY, SET THEORY

In late February I received an e-mail message from a reader named Kim Forbes. Her six-year-old son Ben had asked her a math question she couldn’t answer, and she was hoping I could help:

Today is the 100th day of school. He was very excited and told me everything he knows about the number 100, including that 100 was an even number. He then told me that 101 was an odd number and 1 million was an even number, etc. He then paused and asked: “Is infinity even or odd?”

I explained that infinity is neither even nor odd. It’s not a number in the usual sense, and it doesn’t obey the rules of arithmetic. All sorts of contradictions would follow if it did. For instance, “if infinity were odd, 2 times infinity would be even. But both are infinity! So the whole idea of odd and even does not make sense for infinity.”

Kim replied:

Thank you. Ben was satisfied with that answer and kind of likes the idea that infinity is big enough to be both odd and even.

Although something got garbled in translation (infinity is neitherodd nor even, not both), Ben’s rendering hints at a larger truth. Infinity can be mind-boggling.
Read more…

May 2, 2010, 5:00 PM

Group Think

By STEVEN STROGATZ

TAGS:

GROUP THEORY,MATTRESSES,SYMMETRY

My wife and I have different sleeping styles — and our mattress shows it. She hoards the pillows, thrashes around all night long, and barely dents the mattress, while I lie on my back, mummy-like, molding a cavernous depression into my side of the bed.

Bed manufacturers recommend flipping your mattress periodically, probably with people like me in mind. But what’s the best system? How exactly are you supposed to flip it to get the most even wear out of it?

Brian Hayes explores this problem in the title essay of his recent book, “Group Theory in the Bedroom.” Double entendres aside, the “group” in question here is a collection of mathematical actions — all the possible ways you could flip, rotate or overturn the mattress so that it still fits neatly on the bed frame.

By looking into mattress math in some detail, I hope to give you a feeling for group theory more generally. It’s one of the most versatile parts of mathematics. It underlies everything from the choreography of contra dancing and the fundamental laws of particle physics, to the mosaics of the Alhambra and their chaotic counterparts like this image.

Michael Field

As these examples suggest, group theory bridges the arts and sciences. It addresses something the two cultures share — an abiding fascination with symmetry. Yet because it encompasses such a wide range of phenomena, group theory is necessarily abstract. It distills symmetry to its essence.
Read more…

April 25, 2010, 5:00 PM

Chances Are

By STEVEN STROGATZ

TAGS:

BREAST CANCER SCREENING,CONDITIONAL PROBABILITY, GERD GIGERENZER,MAMMOGRAMS,NATURAL FREQUENCIES,O.J. SIMPSON

Have you ever had that anxiety dream where you suddenly realize you have to take the final exam in some course you’ve never attended? For professors, it works the other way around — you dream you’re giving a lecture for a class you know nothing about.

Cameron
Miles | Dreamstime.comRolling the dice: Teaching probability can be thrilling.

That’s what it’s like for me whenever I teach probability theory. It was never part of my own education, so having to lecture about it now is scary and fun, in an amusement park, thrill-house sort of way.

Perhaps the most pulse-quickening topic of all is “conditional probability” — the probability that some event A happens, given (or “conditional” upon) the occurrence of some other event B. It’s a slippery concept, easily conflated with the probability of B given A. They’re not the same, but you have to concentrate to see why. For example, consider the following word problem.

Before going on vacation for a week, you ask your spacey friend to water your ailing plant. Without water, the plant has a 90 percent chance of dying. Even with proper watering, it has a 20 percent chance of dying. And the probability that your friend will forget to water it is 30 percent. (a) What’s the chance that your plant will survive the week? (b) If it’s dead when you return, what’s the chance that your friend forgot to water it? (c) If your friend forgot to water it, what’s the chance it’ll be dead when you return?
Read more…

April 18, 2010, 5:00 PM

It Slices, It Dices

By STEVEN STROGATZ

TAGS:

ALGEBRA, CALCULUS,GEOMETRY, INTEGRALS,SIGNS, SYMBOLS

Mathematical signs and symbols are often cryptic, but the best of them offer visual clues to their own meaning. The symbols for zero, one and infinity aptly resemble an empty hole, a single mark and an endless loop: 0, 1, ∞. And the equals sign, =, is formed by two parallel lines because, in the words of its originator, Welsh mathematician Robert Recorde in 1557, “no two things can be more equal.”

In calculus the most recognizable icon is the integral sign:

Its graceful lines are evocative of a musical clef or a violin’s f-hole — a fitting coincidence, given that some of the most enchanting harmonies in mathematics are expressed by integrals. But the real reason that Leibniz chose this symbol is much less poetic. It’s simply a long-necked S, for “summation.”
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April 11, 2010, 5:00 PM

Change We Can Believe In

By STEVEN STROGATZ

TAGS:

CALCULUS,DERIVATIVES, MICHAEL JORDAN, SNELL’S LAW

Long before I knew what calculus was, I sensed there was something special about it. My dad had spoken about it in reverential tones. He hadn’t been able to go to college, being a child of the Depression, but somewhere along the line, maybe during his time in the South Pacific repairing B-24 bomber engines, he’d gotten a feel for what calculus could do. Imagine a mechanically controlled bank of anti-aircraft guns automatically firing at an incoming fighter plane. Calculus, he supposed, could be used to tell the guns where to aim.

Every year about a million American students take calculus. But far fewer really understand what the subject is about or could tell you why they were learning it. It’s not their fault. There are so many techniques to master and so many new ideas to absorb that the overall framework is easy to miss.

Calculus is the mathematics of change. It describes everything from the spread of epidemics to the zigs and zags of a well-thrown curveball. The subject is gargantuan — and so are its textbooks. Many exceed 1,000 pages and work nicely as doorstops.

But within that bulk you’ll find two ideas shining through. All the rest, as Rabbi Hillel said of the Golden Rule, is just commentary. Those two ideas are the “derivative” and the “integral.” Each dominates its own half of the subject, named in their honor as differential and integral calculus.
Read more…

April 4, 2010, 5:00 PM

Take It to the Limit

By STEVEN STROGATZ

TAGS:

APPROXIMATION,ARCHIMEDES, CALCULUS,INFINITY, ITERATION,PARADOXES, PI,POLYGONS

In middle school my friends and I enjoyed chewing on the classic conundrums. What happens when an irresistible force meets an immovable object? Easy — they both explode. Philosophy’s trivial when you’re 13.

But one puzzle bothered us: if you keep moving halfway to the wall, will you ever get there? Something about this one was deeply frustrating, the thought of getting closer and closer and yet never quite making it. (There’s probably a metaphor for teenage angst in there somewhere.) Another concern was the thinly veiled presence of infinity. To reach the wall you’d need to take an infinite number of steps, and by the end they’d become infinitesimally small. Whoa.

Questions like this have always caused headaches. Around 500 B.C., Zeno of Elea posed a set of paradoxes about infinity that puzzled generations of philosophers, and that may have been partly to blame for its banishment from mathematics for centuries to come. In Euclidean geometry, for example, the only constructions allowed were those that involved a finite number of steps. The infinite was considered too ineffable, too unfathomable, and too hard to make logically rigorous.

But Archimedes, the greatest mathematician of antiquity, realized the power of the infinite. He harnessed it to solve problems that were otherwise intractable, and in the process came close to inventing calculus — nearly 2,000 years before Newton and Leibniz.

In the coming weeks we’ll delve into the great ideas at the heart of calculus. But for now I’d like to begin with the first beautiful hints of them, visible in ancient calculations about circles and pi.
Read more…

March 28, 2010, 5:00 PM

Power Tools

By STEVEN STROGATZ

TAGS:

EXPONENTIAL GROWTH,FOLDING PAPER,FUNCTIONS,LOGARITHMS

If you were an avid television watcher in the 1980s, you may remember a clever show called “Moonlighting.” Known for its snappy dialogue and the romantic chemistry between its co-stars, it featured Cybill Shepherd and Bruce Willis as a couple of wisecracking private detectives named Maddie Hayes and David Addison. While investigating one particularly tough case, David asks a coroner’s assistant for his best guess about possible suspects. “Beats me,” says the assistant. “But you know what I don’t understand?” To which David replies, “Logarithms?” Then, reacting to Maddie’s look: “What? You understood those?”

(Click image to play clip.)

That pretty well sums up how many people feel about logarithms. Their peculiar name is just part of their image problem. Most folks never use them again after high school, at least not consciously, and are oblivious to the logarithms hiding behind the scenes of their daily lives.

The same is true of many of the other functions discussed in algebra II and pre-calculus. Power functions, exponential functions — what was the point of all that? My goal in this week’s column is to help you appreciate the function of all those functions, even if you never have occasion to press their buttons on your calculator.
Read more…

March 21, 2010, 5:00 PM

Think Globally

By STEVEN STROGATZ

TAGS:

DIFFERENTIAL GEOMETRY, GEOMETRY,STRAIGHT LINES, THE GLOBE

The most familiar ideas of geometry were inspired by an ancient vision — a vision of the world as flat. From parallel lines that never meet, to the Pythagorean theorem discussed in last week’s column, these are eternal truths about an imaginary place, the two-dimensional landscape of plane geometry.

Conceived in India, China, Egypt and Babylonia more than 2,500 years ago, and codified and refined by Euclid and the Greeks, this flat-earth geometry is the main one (and often the only one) being taught in high schools today. But things have changed in the past few millennia.

In an era of globalization, Google Earth and transcontinental air travel, all of us should try to learn a little about spherical geometry and its modern generalization, differential geometry. The basic ideas here are only about 200 years old. Pioneered by Carl Friedrich Gauss and Bernhard Riemann, differential geometry underpins such imposing intellectual edifices as Einstein’s general theory of relativity. At its heart, however, are beautiful concepts that can be grasped by anyone who’s ever ridden a bicycle, looked at a globe or stretched a rubber band. And understanding them will help you make sense of a few curiosities you may have noticed in your travels.
Read more…

March 14, 2010, 4:15 PM

Square Dancing

TAGS:

GEOMETRY,MATHEMATICS,PYTHAGOREAN THEOREM

I bet I can guess your favorite math subject in high school.

It was geometry.

So many people I’ve met over the years have expressed affection for that subject. Arithmetic and algebra — not many takers there. But geometry, well, there’s something about it that brings a twinkle to the eye.

Is it because geometry draws on the right side of the brain, and that appeals to visual thinkers who might otherwise cringe at its cold logic? Maybe. But other people tell me they loved geometry precisely because it was so logical. The step-by-step reasoning, with each new theorem resting firmly on those already established — that’s the source of satisfaction for many. Read more…

The Road to ‘Ten Unknowns’

By JAMES MCMULLAN

This is the final installment of this series.

In this last column of the series, I will show you the process of conceptual thinking, sketching, research photos, painting and lettering that led to a finished theater poster, in this case one for Jon Robin Baitz’s play “Ten Unknowns,” which was presented at Lincoln Center Theater in 2001.

Nearly all the steps in creating the poster involved drawing.

In “Ten Unknowns,” Malcolm Raphelson, the central character played by Donald Sutherland, is a figurative artist who had a period of New York success in the late 1940s, just before the rise of Abstract Expressionism as the dominant painting style.

As the play begins, it is now the 1990s, and Malcolm has retreated to a remote Mexican town, dispirited and contemptuous of the current art world. His art dealer, trying to encourage him to exhibit again, has sent him a young man to assist him in his work. Crassly oversimplifying a plot that has two other characters and many dramatic interweaving tensions, the central crux of the story is that Malcolm is in a state of deep creative anxiety, so incapacitating, questions arise regarding recent paintings in the studio. Did Malcolm actually paint the pictures? Or are they the work of the young assistant?

Although this mystery involving the paintings and the relationship between the assistant and Malcolm was intriguing, I felt it was too complicated to represent visually, so I chose to use the more fundamental dilemma of the artist facing painter’s block as the conceptual theme of my poster.

James McMullanCLICK TO ENLARGE

The idea of facing an imaginative void made me think about an actual void, the empty canvas, or an empty sheet of paper, and how that moment of beginning is loaded with possibility and fear. In these first sketches, I am playing with a straightforward depiction of the artist facing the blank canvas, an artist becoming a canvas, an artist painting in the wrong direction and an artist seen through a transparent canvas.

Any of these ideas might, with some inspired painting, have been turned into a poster, yet none felt right. There’s a theory about writing that applies — that, when you reach a serious sticking point, the key to moving on successfully is to throw out the element that you had been hanging on to because it is your favorite thing. My favorite thing here had been the canvas, and in a moment of clarity I realized that if I got rid of the canvas I’d be left with an empty easel, a much more powerful and poignant way of expressing the painter’s sense of creative emptiness.

Besides, an easel might become a kind of skeletal structure that the painter could hold onto in some emotionally charged way and through which we could see him — as though looking at a man through prison bars.

James McMullanCLICK TO ENLARGE

This small pencil sketch gave me the basic idea. Now, I had to create a real ambience for the elements in the image and had to make some decisions about the figure himself. Heat, light and a certain mood of exhaustion were in my head as I started my color sketch. I imagined the painter hanging onto the easel almost as though he needed it for support. He would be bare-chested to emphasize the tropical heat of the Mexican locale and also to suggest his state of vulnerability. I imagined the light flooding in from an open door behind this tableau of artist and easel.

James McMullanCLICK TO ENLARGE

As the little painting developed, I made the easel quite dark as a kind of anchor for the whole image and as a strong centered shape through which we see the artist posed slightly off-center and with his face partly obscured. I made the edges of the doorway soft and indeterminate to give more sense of the light pouring in and also to let the hard shape of the easel dominate. I added a canvas leaning on the floor and a table with art supplies. I decided on very straightforward lettering that slightly disappeared as the letters crossed into the darker areas, perhaps suggesting the idea of the “unknown.”

I was satisfied enough with this sketch to show it to Bernard Gersten, the executive producer of Lincoln Center Theater, and he and his creative team agreed that the concept worked and that I should proceed with the finished art.

Because I work on the poster many weeks before play rehearsals start, the actors are often not available for me to photograph as research. Pre-existing photographs of the actors or head shots are useless to me since my images depend entirely on the nuances of the gesture I am imagining, so I don’t do portraits of actors unless I can photograph them myself. Lincoln Center Theater is usually satisfied to have the character in the poster portrayed as a type rather than a specific actor, so I went ahead and persuaded a good friend, Mirko Ilic, to pose as the painter. He is considerably younger than both the character in the play and Donald Sutherland, but I was fairly sure that Mirko could give me the information I needed for my painting.

James McMullanCLICK TO ENLARGE

I did five fairly elaborate paintings, partly because the light effect in the background wash had to be done quickly and didn’t turn out quite right, or the figure became overworked. But I also kept painting because the image really intrigued me and I wanted to do it again and again to see what else would happen. Below are two of these preliminary paintings, one in which the figure looks too young and one in which I went overboard with the wrinkles.

James McMullanCLICK TO ENLARGE

Finally, I produced a version I liked. It had the sense of light I wanted and the figure looked haggard yet interesting in the right way. I did lettering that was not quite as simple as my original sketch but that suited the density of this particular painting. I sent it over to the theater.

James McMullanCLICK TO ENLARGE

By this time, however, I had used up four weeks and the play was in rehearsal, so the reaction to my art became colored by the fact that the star was on the premises. For the producers, it was now paramount that my poster show a likeness of Donald Sutherland. Whatever disappointment I felt about my art being rejected was balanced by the great opportunity of photographing Sutherland and then making a poster out of those shots.

I took the easel over to the theater and showed Sutherland my sketch. He said that he understood my idea and would give me a couple of variations. His variations were so full of a great actor’s physical imagination and sense of what his face and body could project that I knew, watching his changes through my camera’s viewfinder, that he was giving me the basis for a whole new kind of image. In place of the somewhat generalized melancholy of the figure in my sketch he was giving me a specific man, a heroic figure saddened by circumstance.

James McMullanCLICK TO ENLARGE

As I did the sketch on the left, I became convinced that it wasn’t the pose I should use — Sutherland seemed almost too concealed by the easel. In the right-hand sketch, parts of his figure emerge in an intriguing way from behind the easel and the angles of his arms contrast with the straightness of the easel frame. The composition needed an element in the foreground, so I added the corner of a table and a can of brushes. Also in this sketch, I conceived the beginnings of my idea for the type, which was to play the lettering against and around the easel.

James McMullanCLICK TO ENLARGE

In this study I am still hanging on to the background idea and the general color mood from my previous sketches, but allowing the easel to touch the top edge of the poster rectangle gave me the idea of a tighter, flatter composition that would be much more designed to its borders. Also, because the easel is lighter here, I saw how interesting the shape of the black pants became. Even though the effect of this watercolor is too gloomy and graphically too even-toned, it was a necessary step in moving me from the first idea of the poster into the possibilities that the Donald Sutherland photographs had opened up.

There was a big jump in my thinking at this point. I realized that the light atmosphere that I had hung onto through all the previous versions was wrong for the information in the new photos. This insight led me to make the basic drawing in a flatter way, forgoing a deeper sense of depth and playing all the shapes as a pattern within the border rectangle. I then painted a simple orange background fading at the bottom to a darker hue. Now there was no suggestion of a door or light coming from behind.

At this point I saw that leaving the shirt white was a dramatic graphic element. The white shirt and the orange background set up a brighter, higher color key and led me to make the easel much more subtle and to allow the contrasts of the shirt, the pants and the skin tones to dominate the image.

I wasn’t bound by the things I had learned from the earlier sketches — this felt like a piece of art that was making its own rules. It was one of those happy experiences where I made the painting in a state of complete focus and in the space of three or four hours. I designed the lettering to continue the game of playing elements against the border and against edges within the composition. When I was finished, I was fairly sure I had created the piece of art that would become the printed poster, and, fortunately, everyone at Lincoln Center Theater agreed.

James McMullanCLICK TO ENLARGE

The emotional center of the poster was now the face of the painter, because the photographs of Donald Sutherland had given me an intensity and a specificity to work with that was far beyond any way I could have imagined the figure or achieved from using a stand-in.

This column brings to a close this 12-part series. It has been absorbing for me and a great pleasure to write these columns, and to revisit aspects of drawing I haven’t thought about analytically for some time and to find new ways to articulate my deep interest in drawing the human figure. I am grateful to all of you who have followed the series. To those of you who have taken the time to have written comments in response to the columns, you have made it incredibly interesting and rewarding for me. Thank you, all.

Obama’s Gun Play

By CHARLES M. BLOW

Published: January 21, 2011

REPRINTS

President Obama is under renewed pressure from his base to demonstrate that he is, indeed, a principled man of unwavering conviction rather than a pliant political reed willingly bent and bowed by ever-shifting winds.

Enlarge This Image

Damon Winter/The New York Times

Charles M. Blow

Go to Columnist Page »

Multimedia

Graphic

Firearms and Fatalities

Times Topic: Barack Obama

This time the issue is gun control.

Pre-presidency, Obama had been a strong supporter of gun-control initiatives. Since then, however, he has remained curiously quiet on the issue in general and following the Tucson shooting in particular.

The question now is: which Obama will show up at the State of the Union?

Obama, the politician, must be hesitant. He’s enjoying a surge in the polls following a successful lame-duck session of Congress in which a few concessions bought substantial gains. And his handling of the shooting seemed to strike the right balance with the overwhelming majority of Americans. He’s on a roll!

Furthermore, according to a 2005 Gallup poll, gun owners are almost twice as likely to be white as nonwhite, are more than three times as likely to be male as female and are more likely to live in the South and Midwest than in the East or West. Yes, you guessed it: This fits the profile of the voters Obama has lost and needs to win back if he wants to be re-elected.

And no one wants to upset the powerful gun-rights lobby, whose campaign-finance clout dwarfs that of the gun-control lobby. According to data from the nonpartisan campaign finance watchdog group the Center for Responsive Politics, the gun-rights lobby has contributed more than $24 million in election cycles from 1990 to 2010. About 85 percent went to Republicans. By comparison, the gun-control lobby donated less than $2 million in the same period, mostly to Democrats.

That said, Obama the gun-control supporter surely knows how anomalous we are among comparable nations. We are a violent society whose intense fealty to firearms has deadly consequences. Sensible restrictions on the most dangerous weapons could go a long way toward making us safer.

According to 2005 data from the U.N. Office on Drugs and Crime, a comparison of member countries of the Organization for Economic Cooperation and Development for which data were available showed that the U.S. is in a league of its own, and not in a good way. We have nearly 9 guns for every 10 people, and about 9 out of every 10 of our homicides are committed with one of those guns. No other country even comes close.

At the moment, there is popular support for more restrictions. According to a NBC/Wall Street Journal survey, 52 percent of Americans asked believed that laws covering the sale of guns should be made more strict. Will Obama seize the sentiment? This is a test of character: Will the president choose what is right over what is convenient and speak out for what he believes in?

Next week we will see which Obama emerges: a stalwart of conviction, an exemplar of expediency or someone still stuck in the ambiguous middle of conciliation and pseudocourage.

•

A version of this op-ed appeared in print on January 22, 2011, on page A21 of the New York edition.

En este día...

	Saturday, January 22nd The 022nd day of 2011. There are 343 days left in the year. Go to a previous date.

Today's Highlights in History
See a larger version of this front page.		On Jan. 22, 1973, the Supreme Court handed down its Roe vs. Wade decision, which legalized abortion. (Go to article.)On Jan. 22 , 1890, Fred M. Vinson ,13th Chief Justice of the United States , was born. Following his death on Sept. 8 , 1953, his obituary appeared in The Times. (Go to obit. \|Other Birthdays)
		On January 22, 1887, Harper's Weekly featured a cartoon about New York City's government. (See the cartoon and read an explanation.)

On this date in:
1901	Queen Victoria died at age 81 after 63 years on the British throne.
1905	Russian troops opened fired on marching workers in St. Petersburg, killing more than 100 in what became known as "Bloody Sunday."
1922	Pope Benedict XV died.
1938	Thornton Wilder's play "Our Town" premiered in Princeton, N.J.
1944	Allied forces began landing at Anzio, Italy, during World War II.
1953	The Arthur Miller drama "The Crucible" opened on Broadway.
1968	"Rowan & Martin's Laugh-In" premiered on NBC.
1970	The Boeing 747 went on its first regularly scheduled commercial flight, from New York to London.
1973	Lyndon Baines Johnson, the 36th president of the United States, died at his ranch in Johnson City, Texas, at age 64.
1995	Rose Fitzgerald Kennedy, the mother of President John F. Kennedy, died in Hyannis Port, Mass., at age 104.
1997	The Senate confirmed Madeleine Albright as the nation's first female secretary of state.
1998	Theodore Kaczynski pleaded guilty in Sacramento, Calif., to being the Unabomber in return for a sentence of life in prison without parole.
2006	Evo Morales, Bolivia's first Indian president, took office.
2008	Actor Heath Ledger, 28, was found dead of an accidental prescription drug overdose.
2008	Jose Padilla, once accused of plotting with al-Qaida to blow up a radioactive "dirty bomb," was sentenced by a U.S. federal judge in Miami to more than 17 years in prison on terrorism conspiracy charges.
2009	President Barack Obama ordered the terrorist detention center at Guantanamo Bay closed within a year and banned harsh interrogation of terror suspects.
2010	Conan O'Brien ended his brief tenure on "The Tonight Show" after accepting a $45 million buyout from NBC to leave the show after only seven months.

Current Birthdays

Diane Lane turns 46 years old today.

AP Photo/Dan Steinberg Actress Diane Lane turns 46 years old today.

83	Birch Bayh Former U.S. senator, D-Ind.
79	Piper Laurie Actress
74	Joseph Wambaugh Author
71	John Hurt Actor
62	Steve Perry Rock singer (Journey)
58	Jim Jarmusch Director
54	Mike Bossy Hockey Hall of Famer
52	Linda Blair Actress ("The Excorcist")
46	Jazzy Jeff Actor, rapper ("The Fresh Prince of Bel-Air")
30	Beverley Mitchell Actress ("7th Heaven")

Historic Birthdays
Fred Vinson
1/22/1890 - 9/8/1953 Chief Justice of the United States (Go to obit.)

36	Lord George Gordon Byron 1/22/1788 - 4/19/1824 English Romantic poet
63	August Strindberg 1/22/1849 - 5/14/1912 Swedish playwright/novelist
82	Robert Brookings 1/22/1850 - 11/15/1932 American businessman/philanthropist
73	D. W. Griffith 1/22/1875 - 7/23/1948 American film director
94	Marcel Dassault 1/22/1892 - 4/18/1986 French aircraft designer
84	Rosa Ponselle 1/22/1897 - 5/25/1981 American coloratura soprano
79	George Balanchine 1/22/1904 - 4/30/1983 Russian-bn. American choreographer
65	U Thant 1/22/1909 - 11/25/1974 Myanmar 3rd U.N. Secy. General
65	Howard Moss 1/22/1922 - 9/16/1987 American poet/editor of The New Yorker