Through The Sandglass

Sand Puzzles #1: Cooking pasta

 

 Nina must cook some pasta for 15 minutes. The only way she has of measuring time is a 7-minute sand-timer and an 11-minute sand-timer.

How can she use these timers to measure exactly 15 minutes?

I just came across a website called NRICH, a superb UK-based resource for maths teachers at all levels, a joint project between the Mathematics and Education Departments at the University of Cambridge. I'll let them describe the aims of their project themselves:

NRICH aims to:

• Enrich the experience of the mathematics curriculum for all learners
• Offer challenging and engaging activities
• Develop mathematical thinking and problem-solving skills
• Show rich mathematics in meaningful contexts
• Work in partnership with teachers, schools and other educational settings

For teachers of mathematics, we:

• Offer you FREE enrichment material (Problems, Articles and Games) at all Key Stages that really can help to inspire and engage learners and embed RICH tasks into everyday practice.
• Help to promote RICH thinking in classrooms by offering on-line and face-to-face support at Primary and Secondary level.
• Deliver professional development courses and workshops in rich mathematics.
• Help teachers to think strategically about 'next steps' and progression in problem solving.

And for those learning mathematics, we:

• Provide FREE and interesting mathematical games, problems and articles.
• Encourage you to share your solutions to our mathematical problems.
• Have Mathematicians that can help you to solve problems - just 'Ask NRICH'!
• Offer a safe online space where you can meet others with similar interests.

A note for parents:

• NRICH is a joint project between the Faculties of Mathematics and Education at The University of Cambridge
• Our FREE and extensive Rich Resource Bank has been designed to meet the needs of learners from ages 5 to 19 (Key Stages 1 to 5).
• Our resources are tested and proven and do make a difference.
• Rich tasks are suitable for learners of all ages and abilities.

I found several items in which sand cropped up (well, of course I would - as any reader of this blog is well-aware, the stuff is everywhere), but the puzzle caught my eye. It's geared towards kids in the 5-10 age group, but I'll readily admit that it took me a couple of minutes. And the interesting thing is that, if you go on the solution page, there are three different (but clearly related) methods of achieving what's needed.

So, this post is titled "Sand Puzzles #1" - anyone want to contribute number 2?

[Sandglasses image borrowed, with appreciation, from La Crosse McCormick, "Manufacturers of Fine Timepieces"]

Arenaceous sporting trivia - the baseball World Series

 

My daughter and her grandfather, both in Philadelphia, will probably, to put it mildly, have less than kind words for me when they see this post. For the Phillies (last year's champions) were beaten in the baseball World Series last night by the New York Yankees - of all teams, it had to be the Yankees (for non-North American readers, I have appended some brief explanatory notes at the end of the post). Angst, tears, and rage in Philadelphia, exuberant celebration in New York. But, for Through the Sandglass, it's just another opportunity, to point out the ubiquity of my topic - in the continuing tradition of my daughter's Simpsons challenge.  

For a start, like many sporting surfaces, the construction of a world-class baseball field relies on first-class sand. The iconic diamond, its grass and its surrounding "dirt," are made from specialty materials. Go to the website of the Beam Clay company of Great Meadows, New Jersey ("Your 'one-stop source' for America's baseball and sports turf surfaces and supplies!") and you will be bewildered by the choice of over 200 products for the construction, care, and maintenance of your dream infield - for example, their "Premium infield mix":

Made from uniform orange sand and red Beam Clay® with our special binding process that reduces wind and water erosion. Doesn’t separate and blow away! Doesn’t become dusty in stadiums! With proper maintenance, provides firm traction without tracking, good drainage while retaining playing moisture, distinctive reddish/orange color, works up readily, no separation of ingredients, long lasting, safe to slide on - for safe, attractive, consistent professional quality baseball diamonds.

The nature and performance of the materials used for the batter's and catcher's boxes are particularly important, but as in the action of a game, the pitcher's mound has to be a focus of attention. A good history of the pitcher's mound and how to construct one can be found here; the ingredients and recipes vary little - although the climatic environment of the stadium is important. This particular summary is from http://www.baseball-almanac.com/:

The mix used to build the pitcher's landing area (and often the batter's box and catcher's box) should have a significant concentration of clay to provide the necessary stability to resist degradation from increased traffic. A good material will be about 40% sand, 20% silt, and 40% clay. If necessary, you can mix individual components together. Just be sure that individual components are evenly distributed throughout the material.

     A quality infield material will have a lower concentration of clay than the pitcher's mound. The infield skin should be moist and firm, not hard and baked dry. To achieve firmness, an infield mix should not be too sandy. An infield mix with greater than 75% sand causes unstable footing for ballplayers and increases infield skin maintenance problems. A sandy infield will create low spots more quickly and is more likely to create lips at the infield skin/turf interface. Ideally, the infield mix should be between 50% and 75% sand and 25% to 50% clay and silt. A combination that has been successfully used is a 60% sand, 20% silt, 20% clay base mix (sandy clay loam to sandy loam). The silt and clay give the mix firmness. If the mix contains too much silt and clay, compaction and hardness become a problem.

So, a skilful (and well-paid) pitcher can stride out to his patch with confidence that its consistency will provide a reliable foundation for his art. And, in the case of Mariano Rivera ("Mo"), who finished off the Phillies last night and has been called "the best closer in the history of the game," his appearance on the field - if the game is in New York - is accompanied by a loud rendition of Metallica's "Enter Sandman" - "we're off to never-never land." It is said that this is by no means Mo's favourite song, but that it is played on his entry because when he comes into a game, you can pretty much put it to bed. If you wish, you can see a video of this from last night's game at http://www.wikio.com/video/1925785.

And then, of course, there's sand lot baseball. And plastic baseball-shaped bottles that can be filled with coloured sand - but one example of a wide range of such things; I couldn't possibly comment on their artistic merit - but I suspect that Andrew Clemens will not be rolling in his grave..... 

 

Notes for non-American readers:

1. The "World Series" has been widely derided by non-North Americans as being no such thing, since no countries other than the USA and Canada can compete for it. In order to combat such accusations of sporting arrogance, it has often been declared that the name originates from the original sponsorship of the championship by the newspaper, The New York World, early in the last century. Indeed, my (American) wife firmly corrected me to this effect a long time ago. But it's a myth - the "World Series" is, and always has been, exactly that (see Snopes). Not that I would in any way revert to my earlier derisive remarks ..... Always remember that the other life of Steve Gould, the extraordinary and revered evolutionary biologist and writer, was as a devoted and passionate baseball fan - of the Yankees. 
2. I would no more attempt to explain baseball to non-Americans than I would cricket to baseball fans (both are challenges equivalent, in Shakespeare's words, to "numbering the sands and drinking the oceans dry.") Suffice it to say that both games are very much like the classic description of a soldier's life - long periods of boredom interrupted by brief moments of terror (well, generally not exactly terror, but action, something to actually engage the senses and the emotions).
3. In the later stages of a game, the starting pitcher is often replaced by a specialist finisher - a "closer" like Mariano Rivera.
4. A baseball signed by Mo and with the words "Enter Sandman" can be purchased from http://www.mlbfansite.com/ for a mere $399.99 (knocked down, so to speak, from the original price of $501.86).
5. Herewith, from http://www.baseball-almanac.com/stadium/baseball_field_construction.shtml, a simple illustration of the layout of the diamond and the infield. From now on, you're on your own.
   
   
   
   
   

Local ingredients - the sands of the Thames

 

Contrary to the benign atmosphere of the old print, above - kids having fun on a day out - the occupation of mudlarking on the Thames in London during the 18th and 19th centuries was anything but fun - it was appalling. The river and its banks were stinking, fetid, and festering, awash with raw sewage, industrial waste and dead bodies, and the poor souls, as often as not children and old women, whose last resort was to scavenge the sand and mud at low tide, wading in between barges and under wharves, faced disease and death for a penny a day. In 1851, Henry Mahew wrote in his book on "London Labour and the London Poor":

THEY generally consist of boys and girls, varying in age from eight to fourteen or fifteen; with some persons of more advanced years. For the most part they are ragged, and in a very filthy state, and are a peculiar class, confined to the river. The parents of many of them are coalwhippers--Irish cockneys--employed getting coals out of the ships, and their mothers frequently sell fruit in the street. Their practice is to get between the barges, and one of them lifting the other up will knock lumps of coal into the mud, which they pick up afterwards; or if a barge is ladened with iron, one will get into it and throw iron out to the other, and watch an opportunity to carry away the plunder in bags to the nearest marine-storeshop.

1858 was the year of "the great stink" in London. It was a particularly hot summer, and, exacerbated by the increasing use of flush toilets, the river and its tributaries overflowed with waste; cholera was rife. Something plainly had to be done, and Joseph William Bazalgette was the man to do it. As the Chief Engineer for the city's Metropolitan Board of Works, he designed and oversaw the construction of a modern sewage system, the benefits of which we Londoners (and visitors) still enjoy today. And one of those benefits is that mudlarking now carries a much-reduced health risk (rat urine is cited as something to be cautious about, but exactly how that caution should be applied escapes me, and, having just watched Ratatouille, I just can't take it seriously). For yes, mudlarking is a thriving activity along the Thames of central London today, and, as locals, something that we periodically much enjoy - it's fun and it's free. However, we try to indulge in sandlarking, exploring the stretches of beach that appear in places at low tide. The tide is a critical factor - the Thames is a dramatically tidal river, and the battle between incoming waves rushing upstream and the natural flow of the river is a sight to see; the tidal range in central London is between 5 and 7 meters (16 to 23 feet), so timing is critical. As shown in the photos below, there's a patch of largely sandy (but also somewhat muddy) "beach" exposed at low tide just downstream from the Millennium Bridge (the one that used to be wobbly), below St. Paul's Cathedral, and it's easily accessible.

 

And here, from Stephen Croad's wonderful book, Liquid History: The Thames Through Time, is this stretch of the riverside in 1865.

 

Mudlarking today is open to everyone, although there is the Society of Thames Mudlarks, formed in 1980, that issues official permits, with wording such as "on behalf of the Queen's Most Excellent Majesty," and allowing the holder to "search the bed and shore as a recreational pursuit." Digging without a permit is illegal, and any items of value must be submitted to the Museum of London, but digging is not really necessary - the power of the tides and the river itself are more than sufficient to excavate and refresh the banks.

Walk over the sand banks of the Thames and you are walking through history. The banks of this part of the river have been a focus of life and commerce for millennia and the sediment bears witness to this. The surface (see photo above) is covered in natural and manmade detritus, stuff that fell into the river, was thrown into the river, was transported by the river. Oyster shells, roof tiles (some dating back hundreds of years), roof slates, bones, coal, foundry slag, pottery, glass bottles and shards (also a health risk), and thousands of pieces of clay pipes, smoked over a drink on the bank or on a boat and tossed into the river. I am no archaeologist, nor an expert on artifacts, pottery, or bones, but the spectrum of life laid out beneath a mudlark's feet is staggering - and fascinating. The top of a broken frosted glass bottle, a corroded cork still stuck firmly in the neck - who was it that last corked that bottle? The treasures from an hour or so's scavenging are shown below - nothing of any value in a monetary or historical sense, but resonating with value to the mudlarker. Past commerce has included cheap riverside pottery factories, churning out cheap imitations of Delft and Willow patterns - the fragments of designs are a delight. The Whitefriars Glass Works, started in the seventeenth century, and the manufacturer, in 1913, of the stained glass for the east window of the Cathedral of St. John the Divine in New York, stood close to our beach: are the iridescent pieces of slag from there?  

 

And then there is the sand. I have samples of the glorious diversity of sands from around the world, but I realised that I had never collected any of the sand closest to home. Sand, like a cuisine, is a celebration of local ingredients, making use of whatever is available. And, not surprisingly, I found that the sand from the Thames beach is indeed a microcosm of the medley of materials one sees at the surface - plus more natural ingredients. The images below illustrate this. I am, ashamedly, no expert on local geology, but the sand must be a mixture of grains eroded from the upstream reaches of the River, the local geology, and, surely, given the power of the tides, components from downstream towards the estuary. Plus the witnesses of local history and commerce. The city is underlain by the London Clay, but there are many sand beds within that clay, and so perhaps some of the glittering quartz grains are derived from those, or other chapters of riverside geology. Or many of them could have simply fallen off the barges that have carried sand up and down the river for centuries. But the incredibly pure and transparent ones - could they be detritus from raw materials for the Whitefriars Glass Works? I discovered that the works used the world-famous high-purity glass sands from Fontainebleau in the forests outside Paris - could some of these be grains that succeeded where Napoleon failed? I picked out a few individual grains, shown on the right of the picture - clay fragments, bits of bone, bits of slag and coal, glass shards, slate - the microscopic record of the visible history.

 

The microscopic view of Thames sand grains illustrates, yet again, the beauty that lies behind the apparently mundane. And, in looking into bits and pieces of river history, I came across an artist who senses that too. Below is a work by Nicola Rae, titled Five Sands, Gravels, and Mud from the Thames; the sediment-filled cylinders are suspended side-by-side; she comments that

The beach sands and mud bordering the Thames between Deptford Creek and the Thames Barrier vary surprisingly. Different industries on the working wharves have affected the nature of the beach sands and mud.

 

And I'll finish with my own image of Thames beach sand and mud.

 

[for those interested in a mudlarking expedition, information about organised walks can be found at http://www.walks.com/Homepage/Beachcombing_Walks/default.aspx; Nicola Rae's website is at http://www.a2arts.co.uk/nrae/index.html; online resources on London history and the river in particular are extraordinary but I wouldn't know where to begin - the Museum of London is as good a starting point as any.]  

 

Summertime: the palette of beaches

Look closely, and even Hawaii's famed black sand beaches, while stark and dramatic, display their own spectrum of hues. But the diversity of origins and composition of beaches around the world leads to a more overtly dazzling palette. I recently came across, via Andrew Alden's  http://geology.about.com/, a post by travel writer Barbara Weibel that captures the spectrum of the world's beaches with some stunning photos. So, go to  http://beaches.uptake.com/blog/rainbow-beaches-colored-sand.html and enjoy.

I just couldn't resist: Michael Jackson and sand

My daughter has long been a devoted fan of The Simpsons, and sometimes puts her encyclopedic knowledge to the test by challenging us to find any random topic for which she can't cite an episode that includes or addresses it; so far she has succeeded in all challenges. In recent times it has occurred to me that the same game can be played with sand and I thought that the subject of the recent and ongoing world headlines would be an interesting test. Now I will readily admit that a comprehensive inventory of the works of Michael Jackson is not something that I devote a lot of my increasingly precious brain cells to, and so this required a little research (cheating, by my daughter's standards). The image below was easy, since it's all over the net, a tribute sand sculpture by the Indian sand artist, Sudarsan Patnaik, on Orissa’s Puri beach and created in four hours with the help of students of his Golden Sand Art Institute and a couple of tons of sand. But this is a tribute, a posthumous creation - what about the classic works, surely some sand references there?

It didn't take me long, and I draw your attention to the 1992 video of "Remember the Time," an extravagant production set in ancient Egypt in the times of the cruel but song-'n-dance-loving Pharaohs and their glamorous consorts. Jackson performs some impressive magic disappearing tricks, including his final exit, with granular materials, but most impressive is the introduction which, after a brief homage to the angle of repose, resolves itself (above) into a swirling storm of sand grains - and a sandglass. 

 

Oh, and yes, Michael Jackson did guest star in an episode of The Simpsons.

All that glitters ...

 

At the end of my last post on granular segregation and placer mineral deposits, I included a photo of a sand sample from Yosemite that is reputed to contain flakes of gold, with a slightly enigmatic candidate grain. Lockwood at Outside the Interzone and the Lost Geologist kindly commented with testing advice - press the grain with a needle and, because gold is relatively soft and malleable, it will deform, the needle leaving an imprint; mica, being flaky and brittle, will split apart. I couldn't find the same grain, but found a similar one, and gave it a poke with a needle. The point left a dent - aha, I thought, my hopes rising. But, on applying further pressure, the grain fragmented, flying apart into tinier flakes. It was muscovite, a mica, coloured in this case yellow, and slightly rotten from the processes of weathering - hence the dent, and its deceptively lustrous appearance. I should have known - these are really young sand grains, the recent sawdust of the crumbling Sierran granites, and the mica minerals (including an almost perfectly hexagonal biotite grain, left) form a significant membership of this granular tribe - they'll rot out of existence as time goes by.

So, all that glitters is not gold. Of course, pyrite, the shiny yellow iron sulphide mineral, is the traditional "fool's gold" (left in the photo above) but I'm not that foolish: if I found something that looked like the placer gold shown on the left, below, I like to think that I might have leapt to the correct conclusion. But the little muscovite grains (above, right) do sparkle in a most alluring way - I came across the second photo, below right, which purports to show placer gold nuggets and, while I'm no mineralogist, they look a bit suspicious. But then most prospectors know a lot more about what they're doing than I do.

 

My wife would agree. When we got married, she found the old picture below and felt that, with a geologist for a husband, this would be illustrative of the way her life would evolve (note the contents of the woman's bag). We still, ever-hopefully, have this picture on the wall, but alas, so far ......  

Father's Day, sand and culture

I was delighted to see this morning that Google UK had elected to celebrate the joys of paternity with the image above. I was surprised, however, on going to Google.com that no such celebration seemed to be in order. Having spent a chunk of my life living and working in the US, and being married to an American, cultural contrasts have always been of interest ("two nations separated by a common language", hoods, bonnets, trunks, and boots, sidewalks and pavements and the completely different meanings if anyone were to say "I'm mad about my flat") - but I always thought thought that the Brits were supposed to be the dour, reserved ones compared with the more exuberant Americans. So why the Googles are behaving counter-culturally is beyond me.

This is also a reminder that the holiday (vacation) season is upon us, and, along with that, the season of sand sculpture festivals around the world. The Queen (of England) has just visited our south coast to see, amongst other things, a gigantic sand sculpture of her even more gigantic home of Windsor Castle - she apparently remarked that it "looked just like the real thing" (which is, after all, largely built out of sandstone). And these days you don't even have to be at the beach for such festivals - Berlin is not renowned for its coastal location and glorious beaches, yet it is right now the home of this year's Sandsation and Philadelphia is celebrating its World Series champions, the Phillies, (currently heading up the National League East) with a sculpture in Franklin Park (scene of an Egyptian extravaganza a couple of years ago). If you were to visit one of India's beaches, your enjoyment might be dampened but your health awareness raised by a sand sculpture warning on the threat of swine flu. All in all, the silly season is upon us - but then why not?

And, in preparation for relaxation on the beach, sand castle building and a general intimacy with granular materials, there's a great book I would recommend that you take along .......

 

[Phillies sculpture photo via creative commons license, Samjcohn's flickr photostream]

The Story of Sand - in cigarette cards

Back in the old days when smoking was not only not politically incorrect but positively romantic and character-enhancing (think Bogart, think Bergman, think Bacall – and those are only the “Bs”), cigarette manufacturers came up with all kinds of interesting marketing ideas. In the second half of the nineteenth century, American purveyors of tobacco came up with the idea of using the card that provided stiffening to the paper pack to carry advertising. Then, in 1894, Ogden’s, a British company operating out of Liverpool, came up with the idea of putting interesting pictures on the cards; this evolved into producing themed sets of cards with an illustration on one side and information on the other – the first complete set came out in 1904. This generated, as baseball cards would also, a following of collectors (who presumably became increasingly heavy smokers as the compulsion to complete a set grew). Sporting heroes, historical themes, and the natural world were the main subjects of different series, but there were also some unique topics – in 1938 one company produced a set titled “Air Raid Precautions.” They were all entertaining and often educational.

All of these have today become collectors’ items (I’ve seen the habit described as “cartophily” – as in “I confess that I’m a cartophiliac”). But what does this have to do with my particular topic? Well, in 1934, Ogden’s produced a series of cards titled “The Story of Sand,” a set of fifty different topics. A complete set in decent condition goes for around $90 – and, of course, I have one. The theme and the diversity of topics covered essentially anticipated my book by seventy years – or perhaps my book is simply a reprise and an update. Essentially all of the topics covered in the set of cards have found their way into my book somewhere, but this is, as much as anything, simply a reflection of the diversity of roles that sand, the unsung hero, plays. Of course, one of my favourites is the hourglass card – a reminder of the short duration hourglass that Queen Victoria had installed next to the pulpit at Windsor Castle.

 

And also among my favourites is “The Sand Diviner”

 

and below a selection of some of the rest of the series. Out of the fifty, I have several more favourites – these may well form the subject of a later post.

 

Dr Who and the Sands of Time

For those non-UK readers who are saying to themselves, "Dr Who?" and suspecting that this might be a version of the "who's on first?" routine, I'm referring to a British science fiction TV series. A distinctly cult series, if ever there was one. The first episodes were back in the early 1960s and it was revived,very successfully, a few years ago after a hiatus. The programme has a huge following, of all ages, and, of course, like all cult things, an industry surrounding it. "The Doctor" is a strange alien time-traveller, immensely old, but always looking like whatever actor is starring in any given series; there have been eleven Doctors over the years, every one of them the ingenious solver of bizarre problems, always able to, in the end, avert imminent catastrophe. As one actor moves on, he mutates, regenerates, into the new one. The Doctor travels about - through space and time - in the Tardis, which looks for all the world like an old UK police callbox (right), but open the door and inside it's huge, filled with all kinds of weird and wonderful  time-travelling propulsion and calculating contraptions.

These days, the programmes go out not on a regular schedule but as periodic, and eagerly awaited, specials. Last month, for Easter, we were treated to Dr Who and the Sands of Time (I know I'm a bit late describing this but I have been otherwise occupied with kitchen physics and proof-reading). It was filmed in February in Dubai - as the producer commented, "We always looked at going abroad. A beach in Wales, especially in February, would have just looked like, well, a beach in Wales." The typically strange story required the presence of a red double-decker London bus in the middle of the desert, so the BBC shipped one out to Dubai. Unfortunately, on arrival, a cargo container was dropped on it so the script had to be rewritten to incorporate its revised appearance. Then shooting was disrupted for some time by a major sandstorm - and in the story, blowing sand penetrates the engine of the bus, causing agonising delay and tension as the voracious aliens (not the poor guy in the picture, who was also stranded but was, sadly, consumed) approach.

 

The show is highly creative and extremely well-written and the latest incarnation of The Doctor, David Tennant, has been superb (at the same time playing a highly-acclaimed Hamlet for the Royal Shakespeare Company). In every series, Dr Who has always been accompanied (platonically, of course, since he's an alien and this is prime-time TV) by a lissome female companion, sometimes just for one episode, sometimes for many. In the desert, this was Michelle Ryan, star of the remake of The Bionic Woman and English TV soap opera, fetchingly attired in a black cat-suit. But everyone knows that David Tennant's time is up, he is due to be regenerated by the end of the year. Everyone knows who his replacement is to be (this is news in the UK) and everyone, including, presumably, his replacement, is apprehensive - Tennant's time-travelling shoes (generally suede) are big ones to fill.

Dr Who and the Sands of Time, was good TV from every point of view, but, naturally, particularly mine given the place and the ubiquitous material. I have read that there is also a classic desert episode (I think I missed it, but then again, my memory...), in which the Tardis arrives in the Gobi Desert, just in time to meet Marco Polo on his way to visit the fabled palace of Kublai Khan. Forced to travel together, they witness "singing sands," the bizarre variety of sounds emitted periodically and spontaneously, by dunes. This is entirely accurate - in his description of his journey, Marco Polo tells of the spirits of the desert and the strange and terrifying musical and drumming sounds that they make. But undoubtedly more of that in a later thrilling Through the Sandglass episode.

[pictures from the Radio Times]   

Rugby: England 34, France 10

Right, a new category for this blog - sport. I tend, not surprisingly, to collect images that use sand in any way, and the picture above comes from an advertising campaign last summer by the major sponsor of the English Rugby team. The campaign was designed to promote interest in the game amongst the country's youth by setting up beach festivals where England players would show up, sometimes in exotic costumes. The campaign culminated on an urban beach in London. Now, given that English rugby had just suffered a series of humiliating defeats in the southern hemisphere over the summer, it struck me that an image of the sport based on sand, not the most tough or durable construction, might stand me in good stead for the winter internationals (although, of course, I hoped not). After further defeats and endless hand-wrung column inches in the press, and accusations flung around about the ability of the new coach and manager to coach and manage, we came down to yesterday's match, always one of the high profile and emotional conflicts, England versus France. Aha, I thought, time for the resonance of my sand image. And I'm in France right now, so, for a match billed in advance as "le crunch," I was prepared for putting up with the far-from-impartial enthusiasm of the French TV commentators, the triumphant headlines in today's newspapers.

BUT, in an extraordinary game, England not only won, but, to put it bluntly, thrashed the French (they were leading 29-0 at half time). The headline in the sporting press is shown below. In other reports "le crunch" became "le crash," and humiliation was a commonly used word. So, it was just a game, and does not necessarily signal the renaissance of English rugby - but what a game!

I should mention, for American readers, that yes, rugby is peculiar in some ways (being required to throw the ball backwards does not make immediate sense), but it is a great sport. I am, after all the years I spent in the States, a fan of American football (should I admit, the Philadelphia Eagles?), but I remain an ex-rugby player at heart; and you could watch two rugby matches in the time it takes to get through one NFL game.  

And one more connection between rugby and sand. Points can be scored by kicking the ball between the posts, the ball being placed these days in a kicking "tee." But it was not that long ago that the ball would be set up for the kick by an assistant running on to the pitch with a bucket of sand, out of which the kicker would build a small pile into which he would carefully embed the ball.