Beethoven's 7th

When my undergraduate orchestra was rehearsing the second movement of Beethoven's 7th symphony, our rather dramatic conductor described the underlying bass rhythm as "that is the heartbeat of humanity."

Tom Hooper, director of the recent hit film "The King's Speech," may have thought of that same rhythm as the march of soldiers in a nation preparing for war.

At the end of the film, King George VI overcomes his struggle with a speech impediment in a scene of triumph but also of ultimate irony, as his victory is achieved during the delivery of his broadcast on the outbreak of Britain's declaration of war with Germany.  His words become the libretto for Beethoven's 7th symphony which accompanies the speech in the film, bolstering the heaviness of his message to the British people and the rest of the world on 3rd September 1939.

Whether heartbeat of humanity or marching of soldiers or an undying steadfastness and resolve, the rhythmic cello and bass material continues throughout the whole movement, underlying the king's words:  "In this grave hour, perhaps the most fateful in our history, I send to every household of my peoples, both at home and overseas, this message, spoken with the same depth of feeling for each one of you as if I were able to cross your threshold and speak to you myself."

The upward rising melody briefly touches on a major cadence and alludes to an effort at peace:  "Over and over again we have tried to find a peaceful way out of differences between ourselves and those who are now our enemies."

The melody--barely more than an exercise in counterpoint from music theory class--is traded amongst the violins, violas, and lower strings; once for each time the camera cuts to a different group of people gathered round their radio.  "For we are called, with our allies, to meet the challenge of a principle which, if it were to prevail, would be fatal to any civilised order in the world."

Gradually more insistent brass join the strings, lending increasing resolve and calling the nation to arms  "for the sake of all that we ourselves hold dear, and of the world's order and peace, it is unthinkable that we should refuse to meet the challenge.  It is to this high purpose that I now call my people at home and my peoples across the seas, who will make our cause their own."

The rise and fall of the upper voices and the persistence of the bass make it difficult to decide whether melody or accompaniment is more important.  The meoldy's brief brushes with a major key further convolute the the ominous message of "dark days ahead" that "can no longer be confined to the battlefield" with a call for the hope, requisite optimism, and resolve of "do[ing] only the right as we see the right...we shall prevail."

The age of ice

The Perito Moreno Glacier, fed by the Southern Patagonian Ice Field in Argentina.  Photo credit:  Bill Onorato (Journal of the Cambridge University Mountaineering Club)

The Patagonian Ice Sheet covered all of southern Chile during the last glacial period.  Now the Southern Patagonian Ice Field, one of its remnant parts, is one of the largest non-polar ice fields in the world and provides fun and games for mountaineers and scientists alike.

Geologists have for the first time been able to directly determine the age of early Pleistocene glaciers in the Lake Pueyrredon valley in Patagonia. The extensive sequence of moraines—glacially formed accumulations of debris—in Argentine Patagonia provide a geologic record of the Patagonian Ice Sheet.   The age of sediment on outwash terraces, which are deposits that extend along a valley downstream from a moraine, shows the age of glacial advances, according to a study published in Geology this month.

Researchers at the University of Edinburgh and the Scottish Universities Environmental Research Centre measured surface exposure ages of elements (¹⁰Be and ²⁶Al) in the outwash sediments.  A cobble from the outermost glacial sequence, which marks the greatest extent of the ice sheet, dates to 1.2 million years old.  A cobble from a younger outwash terrace dates to 600 thousand years old.  This is consistent with age constraints obtained elsewhere in Patagonia via argon dating, and indicates that major glacial advances occurred at 1.2 Ma and 600 ka. Combined with existing data, there is evidence for five major advances of the Patagonian ice sheet since the early Pleistocene.

Boulders on a moraine related to the outwash terrace that yielded the 1.2 Ma cobble are significantly younger, suggesting that boulders underestimate deposition age.

How accurate is this sediment outwash dating?  Outwash terraces indicate long-term stability and original surface morphology because they become isolated after deposition when a reverse in drainage direction occurs.  Outwash sediment ages are tightly clustered, suggesting that age determination is fairly accurate.  Accuracy could be improved by increasing sampling density and pairing depth profiles within the terrace sediment.  

If the stability of outwash terraces is common throughout the Lake Pueyrredon valley, this new information would provide insight into how regional climate signal has developed alongside global trends and has implications for understanding terrestrial climate change.

Ref:  Andrew S. Hein, Tibor J. Dunai, Nicholas R.J. Hulton and Sheng Xu. Exposure dating outwash gravels to determine the age of the greatest Patagonian glaciations,  Geology, published online 5 January 2011.

9.8 metres per second per second

Climbers on Arboneum (5), Oeschinensee, Kandersteg, Switzerland.
Photo Rachel Berkowitz, Jan 2011

Gravity.  It works every time.

In day-to-day life, people don't really think about it all that much.  I doubt that many people have much concept of how fast 32 feet per second per second is.  But last week, I got a very good visualisation as a 3m x 2m x 5m-long icicle broke off from an overhanging rock several hundred metres up the side of a mountain and came tumbling down just the other side of the rock from the two climbers pictured in this photo.

The icicle shattered into watermelon-sized shards as it boomed its way down the chute.  Accelerating at 9.8 ms^-2, one of these blocks would be plenty to kill a person.  Fortunately the two gentlemen climbing that particular icefall at the time were well sheltered at a bolted belay stance around the corner of a rocky ledge.  The part of the icicle still attached to the cliff far above now exposed a gaping hole in its centre.

That day was warmer than it had been for awhile, so the booming of ice pillars as they tumbled off their perches was audible throughout the valley (and did not increase my confidence in ice climbing).  But the air temperature was increasing; a temperature inversion meant it was warmer higher up the valley walls where the hanging icicles were; the ice began to melt and solid slowly turned to liquid; the ice core was no longer solid and the structure of the icicle was compromised; then the perfect combination of thermal and fluid dynamic conditions were tugged on by gravity and the whole thing collapsed.

It makes me appreciate physics more.