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The mathematical waterfall March 31, 2010

Posted by Jenny in hiking, nature, Southern Appalachians.
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Falls on Grogan Creek, Pisgah National Forest

If you happen to visit a waterfall in the company of a pair of mathematicians, it may occur to you to see things in a different way.  I think it has something to do with the link between complexity and beauty.

Last Saturday I went on a hike with my friend Gary and his 16-year-old son Zach.  I’ve known Gary since college.  He is a professional mathematician who likes to tinker with algorithms, and Zach (and his sister Noura) grew up playing with math.  Zach could certainly follow in the footsteps of his dad, if he decides to do that.

We did a variation of a hike that I tried out back in January to Cedar Rock Mountain. We started at the Fish Hatchery trailhead in Pisgah National Forest, went up John Rock, and had lunch at Cat Gap on the Loeb trail.  Then we followed the Loeb trail to the unmaintained manway that goes up to the top of Cedar Rock, finding a lot of blowdown still lingering from the winter’s bad ice storms.  We met someone on top who told us the blowdowns had been at least partially cleared on the section of the Loeb trail west of there, so we retraced our steps to the trail and followed it to Butter Gap.  Then we went down the Butter Gap trail to the Fish Hatchery.

View from Cedar Rock Mtn. (taken in January)

We could have shortened our route considerably by descending via Cedar Rock’s other manway, the one on the northwest side that goes directly to Butter Gap.  But since that is said to involve tricky scrambling over steep ledges, I would first like to scout that from the bottom up.  For future reference, I noted where the path starts at the gap.

By the time we descended the Butter Gap trail, it was getting into the phase of the afternoon when the sunlight takes on a golden color.  Suddenly we heard the deep roar of water on rock.  There we were at the top of a waterfall.  It was hard to see very much, because the water simply disappeared over the edge.  But just down the trail we found a steep little side path that led to the bottom.

The water as it fell looked creamy white.  It cascaded over a series of ledges until it reached a final flat stairstep of rock, where the water somehow seemed to turn clear again (see top photo).  From this perspective, the water at the top glowed bright.  It came out of nowhere, as if out of a slot cut into the side of the mountain.  All around us, the pillars of hardwood trees gleamed in the afternoon light.

The falls does not have a name, and in the “Waterfalls of North Carolina” map used by western NC waterfall aficionados, it gets a “beauty rating” of only 4 out of 10.  I guess I can understand the relatively low rating.  After all, people who take waterfall aesthetics seriously have to maintain their standards! This one isn’t all that high (about 20′), and it doesn’t have any unusual bumps or bounces or dramatic, photogenic features.  But something about the simplicity of the waterfall’s overall shape made it easier to see how incredibly complicated it really was, in what was going on with the flow of the water.

It was Zach who pointed out that in a particular spot he was watching, a strand of water was dividing into two strands, then merging, then dividing.  I went over and looked at it.  The path of the water changed back and forth in a kind of pulsation.  It seemed that some sort of limit was reached in each half of the cycle, and then the pattern flipped over to the other half.  I probably wouldn’t have seen it this way, or seen it at all, except that I was in the company of mathematicians.

Zach and Jenny

The thing of it was, the tiny little portion of the water we were looking at represented—of course!—only an infinitesimal part of everything that was going on with the water flow.  Before our very eyes, an astronomical number of droplets were tumbling, gliding, bouncing, merging, separating, flowing in an unending sequence.  It was absolutely and ridiculously complicated!

We continued on our way, admiring a couple of well-crafted beaver dams in the lower section of the stream, looking for early spring wildflowers (we saw none) and for songbirds (none of those either), eventually wending our way back to the Fish Hatchery.

Gary found the best seat for viewing the waterfall

Deneys Reitz in WWI/ Arrival in the trenches. March 26, 2010

Posted by Jenny in military history, World War One.
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Reitz arrived near Bapaume after the road had reached this state

Reitz arrived near Bapaume after the local road reached this state

This is the eighth part of a series that starts here and alternates with other posts.

German East Africa had been a “sideshow” in which men struggled desperately for their lives while the rest of the world knew and cared little about it.  In an interesting symmetry, the men fighting there forgot about the outside world.  Reitz wrote, “We had been in the wilds for so long that we had almost forgotten that there was another war, so remote did things in Europe seem to us.”*  For a man who’d grown up on the dry Free State veld, the dense tangles, the rains, the dark jungles of German East were the opposite of everything familiar.  Years earlier, fighting had meant seeing miles through crystalline air, making out small figures of the enemy etched against the skyline.

But after he’d put in his year in German East (February 1916 to February 1917), he opted not to settle in for a well-deserved rest back home in the Free State.  He would embark for the Western Front.  He said, “With the greatest war in the history of the world going on in Europe, I did not feel that I could return to a quiet village life, so I decided to go overseas.”

His plan was to enlist in the British army as a private: “I had lately come to hold the view that it was one’s duty to share the dangers of the greatest crisis in human history with the common run of men.” So he sailed to England, figured he might as well do a bit of sightseeing in London, then after a week went to a recruiting office in Chelsea.  The doctors examined him, told him he had a malarial heart, but passed him for service anyway.

But, as it turned out, his effort to slip anonymously into the ranks was unsuccessful.  Too many people became aware that he’d arrived in the UK, and strings were immediately pulled.  It started with an uncle who thought he should have a place as a lieutenant in the Coldstream Guards; then Jan Smuts arranged that he should report for senior officer’s school at Aldershot with the rank of major.

Typically enough, Reitz made fun of himself.  “I was getting used to rapid promotion.  During the South African War I rose from batman to Chief of Staff in twenty minutes.  During the rebellion I jumped overnight from village lawyer to Commandant of a district, and in East Africa I unexpectedly found myself a colonel.  Now I had graduated from Private to Second Lieutenant, to Major, in the course of a week.”

Everything seemed unfamiliar.  Having grown up on horseback, his first thought was to join the cavalry—but the cavalry were about as useful for trench warfare as sabers against machine guns.  In fact, most British cavalry in those days were engaged in patrolling rebellious Ireland—the Easter Rising had occurred just a year earlier—and he had no interest in playing that role.  Boers and Irish had a long history of mutual sympathy.

So he spent months in infantry drills, taking courses in “Stokes’ mortars, Lewis guns, bombing, mapping, air photography, night scouting, trench-making, gas, smoke screens” and many other things particular to this war that was utterly unlike any ever fought before.

Major General John French at the time of the Boer War

Toward the end of his time at Aldershot, Reitz’s body of officers-in-training were reviewed by John French.  This was an episode that might have caused resentment in another sort of personality.  French had played a significant role in the Boer War, and it was his cavalry that had nearly captured Reitz and his exhausted comrades near the Stormbergen in the Cape Colony.  As an aide to Smuts, Reitz had actually met French in person aboard a train, May 1902, that was puffing its way toward Vereeniging for the peace talks.  French had tried questioning them, hoping for some careless admission that would help the British in their negotiations.  The silent, impassive Smuts was probably the last person in the world who would brim over with impulsive revelations.  French had been irritable back then: now, 15 years later, he had made questionable decisions as the commander of the British Expeditionary Force in France.  He’d been replaced by Douglas Haig, and returned to England to command the British Home Forces, in which capacity he oversaw the suppression of the Irish uprising.

In August 1917 Reitz completed his training and finally went to France.  A battle of nearly unimaginable scope had been grinding on, not far away, for two months then—3rd Ypres, or Passchendaele—it would continue until November.  But British command did not send a new officer such as Reitz directly into that bloodbath.  For him, it was a massive event just offstage that sent continuous ripples in his direction.

As he rode the train slowly toward the front, he passed through a landscape that had gone through a kind of entropy.  Distinct objects with distinct functions had dissolved into formlessness.

An example of entropy: Passchendaele before and after

Reitz was assigned to the 7th Royal Irish Rifles, then in rest billets at Ervillers, between Arras and Bapaume.  The second in command had been recalled for service in Ireland, and the colonel in charge had applied for a substitute.  He was quite surprised to be sent a South African, but Reitz had a gift for easy friendship, and one reads between the lines that he was soon accepted by the battalion. The very next day the 7th Royal Irish were ordered into the front line.  For the first time Reitz entered the trenches, for nearly a mile following the communications trench that ran perpendicular to the line of fighting.  They occupied a segment of the Hindenburg Line that had been captured in the spring offensive at Arras.

Reitz set about exploring the portion of the line for which his men were responsible.  His new home featured a grim sort of decor.  “On every side lay relics of the recent battle; broken rifles, machine-guns and mortars, bloodstained tatters of clothing, and out in no-man’s-land were withered corpses that could not be fetched in, and several derelict tanks.”

(To be continued)

*All quotes from Trekking On.  In The Trilogy of Deneys Reitz, Wolfe Publishing, Prescott AZ, 1994.

The "Carriere Wellington": now part of a museum

Peakbagger extraordinaire meets the A.T. March 21, 2010

Posted by Jenny in hiking, peakbagging.
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Peter shows he's ready for adverse conditions

I’ve only hiked with Peter J. Barr one time.  But that was quite a time.  He was one of the five participants on the famous Woolly Tops expedition.  On that outing, he maintained an admirable calm and good humor while clawing his way through rhododendron thickets, wading down flooded streams, and even while suffering a temporarily dislocated shoulder as he lunged his way up to a rock ledge.

Peter starts thru-hiking the Appalachian Trail tomorrow.  You can follow his adventures here.  I think of his thru-hike as a kind of “deluxe” thru-hike—that’s my word, not his.  He’s actually planning on doing some side trips to various peaks in the northeast, in particular the New England Hundred Highest, with possibly a couple of Adirondack 5000 footers thrown in.  In some cases he’ll be able to do short bushwhacks off the A.T. to get an extra peak (for instance, for Mt. Mendon in Vermont, which is near the A.T. as it approaches Killington).  In other cases he’ll have to either rent a car or get a ride to points a bit further away (for Boundary, White Cap, and Cupsuptic Snow in Maine: closest A.T. point is around the Crockers and the Bigelows).  If he goes for Marcy and Algonquin in the Adirondacks, that means a pretty long car ride (closest A.T. point looks to be, actually, also around Killington).

And he is going to attempt this without sacrificing the bottom-line thru-hiker standard: to do every foot of the A.T.!

If anyone can do it, Peter can do it.  He already has a ridiculously impressive list of peakbagger accomplishments.  He’s done the 6000 footers of the south, but not only that, he’s done the 5000 footers, which I’m not sure anyone else has accomplished.  That involves an awful lot of bushwhacking.  And he’s done the 900 miles of trail in the Great Smoky Mountains National Park.

Peter is also very active in preserving the North Carolina fire towers and in getting people to enjoy them—and he’s published a book on the subject.  In keeping with that interest, he is making the preservation of the tower on Mt. Shuckstack in the Smokies a goal that will be furthered by his thru-hike.  He’s asking that people consider donating $21.78 toward that cause, or one cent for every mile of the A.T.  You can do that through a click on his website.

Best of luck to you, Peter.  You’re embarking on a great adventure!

Peter strolls up a log on Woolly Tops