Benford’s law, also called the first-digit law, refers to the frequency distribution of digits in many (but not all) real-life sources of data. In this distribution, the number 1 occurs as the first digit about 30% of the time, while larger numbers occur in that position less frequently: 9 as the first digit less than 5% of the time. This distribution of first digits is the same as the widths of gridlines on a logarithmic scale. Benford’s law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution.
Tweets are 140 characters long. There are 26 letters in English—27 if you include spaces. Using that alphabet, there are 27140≈10200 possible strings.
But Twitter doesn’t limit you to those characters. You have all of Unicode to play with, which has room for over a million different characters. The way Twitter counts Unicode characters is complicated, but the number of possible strings could be as high as 10800.
Of course, almost all of them would be meaningless jumbles of characters from a dozen different languages. Even if you’re limited to the 26 English letters, the strings would be full of meaningless jumbles like “ptikobj”. Eric’s question was about tweets that actually say something in English. How many of those are possible?
This is a tough question. Your first impulse might be to allow only English words. Then you could further restrict it to grammatically valid sentences.
But it gets tricky. For example, “Hi, I’m Mxyztplk” is a grammatically valid sentence if your name happens to be Mxyztplk. (Come to think of it, it’s just as grammatically valid if you’re lying.) Clearly, it doesn’t make sense to count every string that starts with “Hi, I’m …” as a separate sentence. To a normal English speaker, “Hi, I’m Mxyztplk” is basically indistinguishable from “Hi, I’m Mxzkqklt”, and shouldn’t both count. But “Hi, I’m xPoKeFaNx” is definitely recognizably different from the first two, even though “xPoKeFaNx” isn’t an English word by any stretch of the imagination.
Fortunately, there’s a better approach.
Let’s imagine a language which has only two valid sentences, and every tweet must be one of the two sentences. They are:
“There’s a horse in aisle five.”
“My house is full of traps.” …
I take serious issue with how this so-called research was conducted and reported. Notice that in the notes, they admit to excluding samples that did not have quantifiable levels of inorganic arsenic, which smells an awful lot like inappropriate data manipulation.
For 2/5 of the tested products, the average is actually lower that the reported value. In the case of rice beverages, you’ll notice that 25 out of 28 data points (89% of the available data) were thrown away. I find this to be completely misrepresentative, then, of the actual risk–the value in the chart should be a miniscule ~0.4mcg/serving.
But even so, the amount of arsenic in rice is small enough that it’s not really a concern, according to their page here: Questions & Answers: FDA’s Analysis of Arsenic in Rice and Rice Products
What is the FDA recommending to consumers about eating rice and rice products?
Based on the available data and scientific literature the FDA is not recommending changes by consumers regarding their consumption of rice and rice products. Our advice for consumers is to eat a balanced diet including a wide variety of grains, not only for good nutrition but also to minimize any potential consequences from consuming any one particular food.
Is rice safe to eat? Is it safe for children to eat?
Rice is an important and nutritious staple for many people. We believe it would be premature for the FDA to recommend modifying your or your child’s diet because of concerns about arsenic levels.
In looking at the research, there is an absence of the necessary scientific data that shows a causal relationship between those who consume higher levels of rice and rice products and the type of illnesses usually associated with arsenic. However, we are continuing to study this and note that other potential factors, such as other food in peoples’ diets.
What about rice cereals eaten by infants and young children?
Infant rice cereal has been used for many years because it is gluten-free, less allergenic, more easily digested, and is a good source of iron and other vitamins. With the limited data available, we are not aware of any acute health risks linked with the consumption of infant rice in the U.S.
Should I be concerned about feeding rice beverages to my children?
As with other types of rice products, we believe it would be premature for the FDA to recommend modifying your or your child’s diet because of concerns about arsenic levels. However, we note that rice-based beverages are an inadequate substitute for cow’s milk or infant formula. For example, although close in caloric content with 2% cow’s milk, they contain fewer important macronutrients such as protein, carbohydrates, and fat.
To give you some idea of how little this amount of arsenic is: if you compare this to the federal standard of 10 ppb limit of arsenic in drinking water, eating a serving of rice will actually give you less arsenic exposure than what you’d get from drinking a liter of water (FDA Weighs Federal Standard To Limit Exposure To Arsenic In Rice : NPR).
Interestingly enough, this actually complicates things because the rice samples that were tested were cooked…with potable water. Um…oops? Scientific confounder present. This means that for the samples tested, it could well be partially a measure of the quality of water used. :-/
“I will give you my body to experiment; you can make as many mistakes on me, but never make a mistake on the patient.”
In Taiwan, there is a group of medical universities under the Tzu Chi Foundation who have a very successful body donation program (over 20,000 pledges). Cadavers are known as Silent Mentors; the donors’ final messages and a short biography are passed on to the students. This is quite different from the Western model where cadavers are anonymous – in this system students are more encouraged to see the personhood of the cadaver.
The students spend a year dissecting the body, and at the end replace the organs and sew back the skin. They then conduct a mass remembrance ceremony and funeral for the Silent Mentors.
Unlike a common misconception, humans beings did not evolve from the apes that live on Earth today. Apes and humans shared a common ancestor before diverging into individual branches. In a similar fashion, Sanskrit and Latin both share a common ancestor. Historical linguists posit a reconstructed language called Proto-Indo-European (PIE) that was a common ancestor to the entire Indo-European-Family of languages, including Latin (which comes in the Italic branch) and Sanskrit (which comes in the Indo-Iranian branch).
FEDERER LOSES used to be a headline you’d read about as often as LION STARVES or CLOONEY WEDS.
But the world’s greatest tennis player lost in the fourth round of the Sony Ericsson Open last week in Miami, the second tournament in a row he didn’t win. Just like that, he’s gone from being the tornado to being the trailer. The Federer Express seems to have forgotten how to deliver.
And, the thing is, I know why.
Roger Federer is decent, humble and kinder than Aunt Bee. He is constantly saying, “I’m just a normal guy.” All his winning shots were just “lucky.” Well, finally, opponents are starting to take his word for it.
Do you realize this man, whom most experts say is the greatest tennis player to ever live, actually goes to restaurants and sometimes waits in line?
He doesn’t have a full-time coach. Has no tattoos. His entourage is a joke. His publicity agent, his scheduler, his hitting partner and his girlfriend are all the same person. And she’s not even a lingerie model! Just an ordinary, very nice Swiss miss named Mirka. Derek Jeter has more babes than belts!
Federer flies commercial. Doesn’t own a jet. Here’s a guy who has dominated his sport far more than Tiger Woods has over the last three years, yet Tiger has a 155-foot yacht and Federer doesn’t even own a dinghy.
Federer made an estimated $28 million last year, yet he doesn’t own a house, just two “flats,” he says. He won four ATP honors in one day last week—Player of the Year, Humanitarian of the Year, Fans’ Favorite and the Sportsmanship Award for 2006—yet he has no trophy room. The hardware just piles up on his dining room table.
At 25 Federer has won 10 Grand Slam events yet still stays in the same hotel as the tour schmoes. Roger, you’re an immortal! Rent a mansion! Do you realize that when Tiger played at a tournament in Tucson in February he not only rented a house, but he also had all the furniture removed and his own brought in, so he could be more comfortable? Wake up and smell the indulgence!
“I don’t want to overlive,” Federer says. “I don’t need to be too big. It’s got to feel right when you go to bed at night.”
Get this: You can send an autograph request to his parents’ house—their address is on his website—and within a month you’ll get a photo hand-signed by Roger. “Well, if I were a child,” he says, “I wouldn’t want to wait two years for a picture of my hero, would you?” Damn, son, at least get one of those signing machines like everybody else!
Tell you what a sucker Federer is, when he’s done practicing, he picks up his own bench area. “Not many guys on tour do that,” says Federer’s best friend, Yves Allegro. “In fact, most don’t do that.”
That’s the other thing—this guy Allegro. Federer plays doubles with him a few times a year just to put some folding money in his friend’s pocket. Nowadays your average tennis superstar would rather join the Elks club than play doubles. But not Federer. Even if the doubles comes right after his singles match, he plays. It would be like Tiger playing the Sheboygan Ladies Par 3 Annual after winning the Masters. “How can I pay him back?” Allegro says. “He won’t even let me buy him dinner!”
You have to be who you are, Rog, and you are a heavenly body. Start acting like it! “I tell him all the time,” says his agent, IMG’s Tony Godsick, “you’re too nice.”
Too Nice Example No. 1: Federer sometimes throws pizza parties for the ball boys at tournaments because he was one himself. And he attends!
Too Nice No. 2: The other day he was in L.A. and called Pete Sampras out of the blue to see if he wanted to hit. No, no, no, Roger! He calls you! And you put him off for a week before you call him back!
Too Nice No. 3: I sent an e-mail to Godsick on Monday morning at eight, asking for a one-on-one interview. By four, I was sitting across from Federer. Eight hours? Barry Bonds will put a reporter off for eight years!
There were two chairs in the interview room. A large, cushy one with armrests and a plain straight-backed one. He looked at me sheepishly and said, “Would you mind very much if I took the larger chair? I am very tired from my match.”
Hello? Roger? Monster sports Goliaths don’t ask. Monster sports Goliaths plop down in the big one, then put their feet up on the smaller one.
Then they examine their fingernails, sniff once and go, “Make it quick. My exfoliator is waiting.”
You’re a tennis star, Roger. Go out there and get some faults!
Universality is thought to arise when a system is very complex, consisting of many parts that strongly interact with each other to generate a spectrum. The pattern emerges in the spectrum of a random matrix, for example, because the matrix elements all enter into the calculation of that spectrum. But random matrices are merely “toy systems” that are of interest because they can be rigorously studied, while also being rich enough to model real-world systems, Vu said. Universality is much more widespread. Wigner’s hypothesis (named after Eugene Wigner, the physicist who discovered universality in atomic spectra) asserts that all complex, correlated systems exhibit universality, from a crystal lattice to the Internet.
The more complex a system is, the more robust its universality should be, said László Erdös of the University of Munich, one of Yau’s collaborators. “This is because we believe that universality is the typical behavior.”
In many simple systems, individual components can assert too great an influence on the outcome of the system, changing the spectral pattern. With larger systems, no single component dominates. “It’s like if you have a room with a lot of people and they decide to do something, the personality of one person isn’t that important,” Vu said.
Mathematicians are using random matrix models to study and predict some of the Internet’s properties, such as the size of typical computer clusters. (Illustration: Matt Britt)
Whenever a system exhibits universality, the behavior acts as a signature certifying that the system is complex and correlated enough to be treated like a random matrix. “This means you can use a random matrix to model it,” Vu said. “You can compute other parameters of the matrix model and use them to predict that the system may behave like the parameters you computed.”
This technique is enabling scientists to understand the structure and evolution of the Internet. Certain properties of this vast computer network, such as the typical size of a cluster of computers, can be closely estimated by measurable properties of the corresponding random matrix. “People are very interested in clusters and their locations, partially motivated by practical purposes such as advertising,” Vu said.