“Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that 'my ignorance is just as good as your knowledge.'” — Isaac Asimov
Science has finally confirmed what anybody who has ever met an i-banker, lawyer, or journalist already knew: People who work exhaustingly long hours like to drink themselves insensate at the end of the week.
To be specific, an analysis published in theBritish Medical Journalfound that working more than 48 hours a week was associated with a slightly higher probability of “risky” alcohol consumption. The authors reached their main conclusions by analyzing unpublished data from 27 studies conducted in the United States, Europe, and Australia. They also looked at the findings of 36 previously released papers, many of which were also from Japan—where after-work binge drinking is basically a cherished part of its office culture.
What, precisely, is “risky” drinking? The paper’s definition varied a bit depending on the exact data source. But in many cases, for a woman, it meant consuming more than 14 alcoholic beverages a week. For a man, it meant more than 21. In other words, it was defined as “the level of alcohol consumption at which there might be an increased risk of adverse health consequences, such as liver diseases, cancer, coronary heart disease, stroke, mental disorders, and injuries, as well as considerable social costs because of family disruption, violence, traffic incidents, healthcare costs, reduced work productivity, and permanent exclusion from the labour market.”
So, we’re not talking about, “Oooohhhhhhhh man, I got so wasted after work last Friday, ha ha” heavy drinking. It’s more like, “Ooohhhhhhhh, man, my doctor keeps warning me about cirrhosis” heavy drinking.
Overall, 6.3 percent of study subjects were risky drinkers. People who worked 49 to 54 hours per week were 1.13 times—or about 0.8 percentage points—more likely to be one. Those who worked 55 hours or more weekly were 1.12 times—or 0.7 percentage points—more likely to be one. But the data doesn’t give any clear answers on correlation vs. causation. Maybe those who tend to pull endless hours at the office are the same personality types who tend to imbibe heavily. Or maybe working long hours drives people to drink. Personally, I’d bet on the latter.
This holiday weekend, Americans will be cavorting on the beach, many of them in swimwear that covers as little as possible. In 2006, Julia Turner traced the history of the bikini to explain its exploding popularity. The article is reprinted below.
Sixty years ago, the world’s first bikini made its debut at a poolside fashion show in Paris. The swimsuit is now so ubiquitous—and comparatively so demure—that it’s hard to comprehend how shocking people once found it. When the bikini first arrived, its revealing cut scandalized even the French fashion models who were supposed to wear it; they refused, and the original designer had to enlist a stripper instead. The images below illustrate how the bikini slowly gained acceptance—first on the Riviera, then in the United States—and became a beachfront staple.
When the bikini was unveiled in 1946, it was by no means the first time that women had worn so revealing a garment in public. In the fourth century, for example, Roman gymnasts wore bandeau tops, bikini bottoms, and even anklets that would look perfectly at home on the beaches of Southern California today.
At the turn of the 20th century, though, such displays would have been unthinkable. Female swimmers went to extraordinary lengths to conceal themselves at the beach. They wore voluminous bathing costumes and even made use of a peculiar Victorian contraption called the bathing machine, essentially a small wooden or canvas hut on wheels. The bather entered the machine fully dressed and donned her swimming clothes inside. Then, horses (or occasionally humans) pulled the cart into the surf. The bather would disembark on the seaside, where she could take a dip without being observed from the shore.
OLENA SHMAHALO/QUANTA MAGAZINE. COLLAGE RESOURCES FROM THE GRAPHICS FAIRY AND AND OLD DESIGN SHOP.
In 1850, the Reverend Thomas Kirkman, rector of the parish of Croft-with-Southworth in Lancashire, England, posed an innocent-looking puzzle in the Lady’s and Gentleman’s Diary, a recreational mathematics journal:
“Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice abreast.” (By “abreast,” Kirkman meant “in a group,” so the girls are walking out in groups of three, and each pair of girls should be in the same group just once.)
Pull out a pencil and paper, and you’ll quickly find that the problem is harder than it looks: After arranging the schoolgirls for the first two or three days, you’ll almost inevitably have painted yourself into a corner, and have to undo your work.
The puzzle tantalized readers with its simplicity, and in the years following its publication it went viral, in a slow, modestly Victorian sort of way. It generated solutions from amateurs (here’s one of seven solutions) and papers by distinguished mathematicians, and was even turned into a verse by “a lady,” that begins:
Original story reprinted with permission from Quanta Magazine, an editorially independent division of SimonsFoundation.org whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.
A governess of great renown,
Young ladies had fifteen,
Who promenaded near the town,
Along the meadows green.
While Kirkman later bemoaned the fact that his weightier mathematical contributions had been eclipsed by the popularity of this humble brainteaser, he was quick to defend his territory when another prominent mathematician, James Joseph Sylvester, claimed to have created the problem “which has since become so well-known, and fluttered so many a gentle bosom.”
The puzzle may seem like an amusing game (try a simpler version here), but its publication helped launch a field of mathematics called combinatorial design theory that now fills gigantic handbooks. What started as an assortment of conundrums about how to arrange people into groups—or “designs,” as these arrangements came to be called—has since found applications in experiment design, error-correcting codes, cryptography, tournament brackets and even the lottery.
Yet for more than 150 years after Kirkman circulated his schoolgirl problem, the most fundamental question in the field remained unanswered: Do such puzzles usually have solutions? Kirkman’s puzzle is a prototype for a more general problem: If you have n schoolgirls, can you create groups of size k such that each smaller set of size t appears in just one of the larger groups? Such an arrangement is called an (n, k, t) design. (Kirkman’s setup has the additional wrinkle that the groups must be sortable into “days.”)
It’s easy to see that not all choices of n, k and t will work. If you have six schoolgirls, for instance, you can’t make a collection of schoolgirl triples in which every possible pair appears exactly once: Each triple that included “Annabel” would contain two pairs involving her, but Annabel belongs to five pairs, and five is not divisible by two. Many combinations of n, k and t are instantly ruled out by these sorts of divisibility obstacles.
For the parameters that aren’t ruled out, there’s no royal road to finding designs. In many cases, mathematicians have found designs, through a combination of brute force and algebraic methods. But design theorists have also found examples of parameters, such as (43, 7, 2), that have no designs even though all the divisibility requirements check out. Are such cases the exception, mathematicians wondered, or the rule? “It was one of the most famous problems in combinatorics,” said Gil Kalai, a mathematician at the Hebrew University of Jerusalem. He recalls debating the question with a colleague a year and a half ago, and concluding that “we’ll never know the answer, because it’s clearly too hard.”
Just two weeks later, however, a young mathematician named Peter Keevash, of the University of Oxford, proved Kalai wrong. In January 2014, Keevash established that, apart from a few exceptions, designs will always exist if the divisibility requirements are satisfied. In a second paper posted this April on the scientific preprint site arxiv.org, Keevash showed how to count the approximate number of designs for given parameters. This number grows exponentially—for example, there are more than 11 billion ways to arrange 19 schoolgirls into triples so that each pair appears once.
The result is “a bit of an earthquake as far as design theory is concerned,” said Timothy Gowers, a mathematician at the University of Cambridge. The method of the proof, which combines design theory with probability, is something no one expected to work, he said. “It’s a big surprise, what Keevash did.”
Mathematicians realized in the early days of design theory that the field was intimately connected with certain branches of algebra and geometry. For instance, geometric structures called “finite projective planes”—collections of points and lines analogous to those in paintings that use perspective—are really just designs in disguise. The smallest such geometry, a collection of seven points called the Fano plane , gives rise to a (7, 3, 2) design: Each line contains exactly three points, and each pair of points appears in exactly one line. Such connections gave mathematicians a geometric way to generate specific designs.
In the 1920s, the renowned statistician Ronald Fisher showed how to use designs to set up agricultural experiments in which several types of plants had to be compared across different experimental conditions. Today, said Charles Colbourn, a computer scientist at Arizona State University in Tempe, “one of the main things [experiment-planning software] does is construct designs.”
Starting in the 1930s, designs also became widely used to create error-correcting codes, systems that communicate accurately even when information must be sent through noisy channels. Designs translate neatly into error-correcting codes, since they create sets (groups of schoolgirls) that are very different from each other—for instance, in the original schoolgirl problem, no two of the schoolgirl triples contain more than a single girl in common. If you use the schoolgirl groups as your “code words,” then if there’s a transmission error as you are sending one of the code words, you can still figure out which one was sent, since only one code word will be close to the garbled transmission. The Hamming code, one of the most famous early error-correcting codes, is essentially equivalent to the (7, 3, 2) Fano plane design, and another code related to designs was used to encode pictures of Mars that the Mariner 9 probe sent back to Earth in the early 1970s. “Some of the most beautiful codes are ones that are constructed from designs,” Colbourn said.
Design theory may even have been used by betting cartels that made millions of dollars off of Massachusetts’ poorly designed Cash WinFall lottery between 2005 and 2011. That lottery involved choosing six numbers out of 46 choices; tickets won a jackpot if they matched all six numbers, and smaller prizes if they matched five out of six numbers.
There are more than 9 million possible ways to pick six numbers out of 46, so buying tickets with every possible combination would cost far more than the game’s typical jackpot. A number of groups realized, however, that buying hundreds of thousands of tickets would enable them to turn a profit by scooping up many of the smaller prizes. Arguably the best assortment of tickets for such a strategy is a (46, 6, 5) design, which creates tickets of six numbers such that every set of five numbers appears exactly once, guaranteeing either the jackpot or every possible five-number prize.
No one has found a (46, 6, 5) design so far, Colbourn said, but designs exist that are close enough to be useful. Did any of the betting cartels use such a design “to siphon money from the Lottery at no risk to themselves?” wrote Jordan Ellenberg, a mathematician at the University of Wisconsin, Madison, who discussed the Cash WinFall lottery in his book How Not to Be Wrong. If they didn’t, Ellenberg wrote, they probably should have.
It would be hard to make a complete list of the applications of designs, Colbourn said, because new ones are constantly being discovered. “I keep being surprised at how many quite different places designs arise, especially when you least expect them,” he said.
A Perfect Design
As the number of design applications exploded, mathematicians filled reference books with lists of designs that might someday prove useful. “We have tables that say ‘For this set of parameters, 300,000 designs are known,’” said Colbourn, a co-editor of the 1,016-page Handbook of Combinatorial Designs.
Despite the abundance of examples, however, mathematicians struggled to get a handle on just how often designs should exist. The only case they understood thoroughly was the one in which the smallest parameter, t, equals 2: Richard Wilson, of the California Institute of Technology in Pasadena, showed in themid-1970s that when t = 2, for any k there is at most a finite number of exceptions—values of n that satisfy the divisibility rules but don’t have designs.
But for t greater than 2, no one knew whether designs should usually exist—and for values of t greater than 5, they couldn’t even find a single example of a design. “There were people who felt strongly that [designs] would exist, and others who felt strongly that it’s too much to ask for,” Colbourn said.
In 1985, Vojtěch Rödl of Emory University in Atlanta offered mathematicians a consolation prize: He proved that it’s almost always possible to make a good approximatedesign—one that perhaps is missing a small fraction of the sets you want, but not many. Rödl’s approach uses a random process to gradually build up the collection of sets—a procedure that came to be known as the Rödl nibble, because, as Keevash put it, “instead of trying to swallow everything at once, you just take a nibble.”
Since then, the Rödl nibble has become a widely used tool in combinatorics, and has even been used in number theory. Last year, for example, mathematicians used it to help establish how far apart prime numbers can be.
But mathematicians agreed that the nibble wouldn’t be useful for attempts to make perfect designs. After all, at the end of Rödl’s procedure, you will typically have missed a small fraction of the smaller sets you need. To make a perfect design, you’d need to add in some additional larger groups that cover the missing sets. But unless you’re very lucky, those new larger groups are going to overlap with some of the groups that are already in your design, sending new errors cascading through your system.
Designs just didn’t seem to have the kind of flexibility that would allow a random approach to work. It seemed “obviously impossible,” Gowers said, that an approach like Rödl’s could be used to make perfect designs.
Last year, however—nearly three decades after Rödl’s work—Keevash showed that it is possible to control the cascade of errors by using an approach that marries flexibility and rigidity. Keevash modified Rödl’s construction by starting off the nibble with a specific collection of schoolgirl groups, called a “template,” that has particularly nice algebraic properties. At the end of the nibble, there will be errors to correct, but once the errors propagate into the template, Keevash showed, they can almost always be fixed there in a finite number of steps, producing a perfect design. “The full proof is extremely delicate and it is a phenomenal achievement,” wrote Ross Kang, of Radboud University in the Netherlands.
“I think a few years ago, nobody thought that a proof was on the horizon,” Colbourn said. “It’s an extraordinary breakthrough.”
For pure mathematicians, Keevash’s result is in a sense the end of the story: It establishes that for any parameters t and k, all values of n that fit the divisibility conditions will have a design, apart from at most a finite number of exceptions. “It sort of kills off a whole class of problems,” Gowers said.
But Keevash’s result leaves many mysteries unsolved for people who care about actual designs. In theory, his template-nibble approach could be used to create designs, but for now it’s unclear how large n has to be for his method to work, or how long an algorithm based on his method would take to run. And while Keevash has proved that designs almost always exist, his result doesn’t say whether a design will exist for any particular set of parameters you might care about. “People will presumably still work on this for generations,” Wilson said.
Still, Keevash’s result will shift the mindset of mathematicians who are trying to find designs, Colbourn said. “Before, it wasn’t clear whether the focus should be on constructing designs or proving they don’t exist,” he said. “Now at least we know the effort should focus on constructing them.”
And the shortage of information about specific designs leaves plenty of fun puzzles for recreational mathematicians to solve. So in the spirit of Kirkman, we will leave the gentle reader with another brainteaser, a slight variation on the schoolgirl puzzle devised in 1917 by the British puzzle aficionado Henry Ernest Dudeney and later popularized by Martin Gardner: Nine prisoners are taken outdoors for exercise in rows of three, with each adjacent pair of prisoners linked by handcuffs, on each of the six weekdays (back in Dudeney’s less enlightened times, Saturday was still a weekday). Can the prisoners be arranged over the course of the six days so that each pair of prisoners shares handcuffs exactly once?
Dudeney wrote that this puzzle is “quite a different problem from the old one of the Fifteen Schoolgirls, and it will be found to be a fascinating teaser and amply repay for the leisure time spent on its solution.” Happy solving!
Original story reprinted with permission from Quanta Magazine, an editorially independent publication of the Simons Foundation whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.
When Frederic Tudor, aka the “Ice King”, started his worldwide ice delivery service in the early 19th century—sailing massive blocks of as far as Europe and India—he probably didn’t realize he was launching an American obsession.
We shave it, crush it, cube it, and use finely-tuned machines to carve it into tiny pellets and cultivate 300-pound, crystal-clear blocks. We gnaw on snow cones and shaved ice, pack our soda cups to the rim, and slurp down Slushies 24-7 at the 7-11. We even take our tea and coffee on the rocks.
Now, bartenders across the land are staking their claim on ice, creating fancified cocktails where the frozen stuff takes a front seat.
“If you’re talking premium liquor, you expect premium glass and ice too,” says Andrew Bohrer, a longtime Seattle bartender and co-founder of the Washington State Bartender’s Guild.
This thirst for “premium ice” has resulted in a boom in boutique ice delivery services and specialized gear like the greaseless chainsaws and Japanese hand saws used to carve block ice. Of course, all of this specialized machinery and hands-on ice craft comes at a cost, and that’s where you, the customer, comes in. Bohrer estimates that an “ice program”—a phrase that he describes as a “terrible plague” in the bar business—adds about 60 to 80 cents to the cost of a drink. “That’s a pretty expensive ingredient,” he says.
Cloudy with a Chance of Whisky
As with diamonds, cocktail ice is judged by its clarity, density, size and cut, all of which add to the quality and aesthetics of the experience. As water freezes, air bubbles are trapped and eventually disperse inside the frozen mass to create a cloudy appearance. But if you slow the freezing process down, a lake effect sets in as air bubbles rise to the top or sides. The result is crystal-clear, dense ice, which is harder and colder than a typical ice cube. When you’re shaking and stirring drinks behind a bar, this is the ice you want.
Bohrer was one of the first bartenders to start slicing and dicing ice in the West Coast cocktail culture. In the early aughts he attended the Cocktail World Cup in New Zealand and watched a Japanese bartender carving a block of clear ice into a sphere in a matter of minutes—a party trick that’s commonplace in upscale Japanese bars. Before you could say blackberry bramble, he was back home carving up big blocks of ice with a chainsaw, and hand-carving spheres behind the bar for bemused bar patrons. When he brought his roadshow to San Francisco, it was game on at speakeasies and upscale eateries around the city. At about the same time, New York’s “artisanal ice” scene was kicking into gear at Richard Boccato’s Dutch Kills bar, and his affiliated Hundredweight Ice and Cocktail Services.
Nowadays, gonzo-sized cubes and spheres of ice can be found in barrooms across the country, along with the industrial-strength machines that crank them out.
Ice Cold Tech
The Clinebell Equipment Company builds a series of big-block ice machines, but the CB300X2E is its Bentley. The machine contains two 40-gallon chambers of water that are chilled from the bottom up, while pumps constantly circulate water on the top layer—a process that jettisons any bubbles and impurities from the block.
After three days of slow freezing, two giant 300-pound block of crystal-clear ice are born. At a price tag of six grand, though, very few bars have the means, much less the space to house this beast. Instead, they opt for ice delivery services, some of which will even carve up the product to order.
After the giant blocks are broken down into bar-ready chunks—be it spheres, extra-large cubes, or rectangular spears—they are used in spirit-heavy cocktails where the goal is to control and slow down dilution. An Old Fashioned, for instance, is often accompanied by an extra-large ice cube so you can taste every hint of oak and vanilla in that 10-year-old bourbon that’s costing you five bucks a sip. Martinis, too, demand minimal dilution, so bartenders will stir gin and vermouth with dense cubes for several minutes to get them to the right temperature.
It’s always dangerous to look to Florida — where headlines like “Senior Citizens Flock to Strip Club Offering Free Flu Shots” are the norm — for a glimpse of anything resembling forward-thinking progress, but here it is. At Walt Disney World, the Beauty and the Beast–themed Be Our Guest restaurant (“THE hot spot for dinner in Disney World,” per Yelp) offers one of the most high-tech sales systems of any restaurant in the world. Instead of waiting to be served by a waiter, customers can order their food online — up to 30 days before their actual reservation. When they do get to the restaurant, the park’s radio-enabled wristbands automatically alert staff members and indicate which table a group ends up choosing. French onion soup and vegetable quiche just arrive — and the customers don’t interact with any kind of traditional “waiter.”