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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

Toxaway waterfalls, with a rope climb! February 19, 2010

Posted by Jenny in hiking, nature.
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Waterfall #4. Click for zoom to get a feel for the millions of bouncing water droplets.

There are two ways that you can see these waterfalls on Toxaway Creek without breaking some rules.  One is to join the Pisgah Hikers, a wonderful group of people based in Brevard, NC, on their annual hike to this area, which is privately owned.  The other is to become a Christian camper.

The Pisgah Hikers have obtained permission to hike here once a year—in the off-season—from “The Wilds,” the very large Christian camp that owns this stream.  But I’m not going to delve into the ethics of private ownership of this wild and beautiful stream—I don’t want to jeopardize the Pisgah Hikers’ access to this place, and also, I see the camp’s ownership as a symptom of a larger problem.

It’s all too common.  Very close to where I live, Connestee Falls, a very appealing waterfall at the junction of two streams, is privately owned, and I guess I’d have to say that I’ve been party to this situation, as I have been living in a short-term furnished rental within the development of Connestee Falls—the gated community whose property includes the waterfall.  By the way, I’ll also mention that I’m moving to a more permanent living situation in Asheville in a couple of weeks.  So I’ll not only say goodbye to living in a gated community, but I’ll have to say goodbye to Brevard’s famous white squirrels!

I saw this squirrel in my own backyard

The situation of “private waterfalls” seems parallel to the situation of “private beaches” that sometimes causes big problems in New England.  I can only hope that one day all of these places will become accessible to the public.

At any rate, this morning the Pisgah Hikers started from the central lodge of the Christian camp and followed a wide trail that parallels Toxaway Creek.  Before very long we reached a suspension bridge over the creek.

Jay and Dave hang out at the bridge

Then we went west a very short distance and visited the bridge that crosses the much larger Toxaway River, which soon (due to the dam) becomes Lake Jocassee.

This is the northernmost arm of Lake Jocassee

People told me that when they were here two years ago in drought conditions, there was a huge “bathtub ring” of bare dirt around the perimeter of the lake.  Downstream, this water collects additional volumes from the Horsepasture River and Bearcamp Creek, and eventually becomes a gigantic artificial lake.  (Sorry, my Southern friends, I don’t consider a reservoir to be a real lake.  But it sure is pretty.)

So this was a down-then-up hike.  We climbed back up along the creek and took a side trail to Waterfall #4.  We negotiated a slightly difficult section with the help of a fixed rope—there would be more of this later on.

Our group negotiates the descent to the waterfall

At the bottom of our slippery descent, we confronted the amazing waterfall.  The best way I can describe it is to say that it is a complicated waterfall.  It drops down in two major tiers, with some of the water diverting to the side and then rejoining the main flow, and with many bumps and lumps that make for a giant intricate display of splashing, foaming, sliding, bouncing water.

Jim took a picture of me, Jay, and Dave in front of the falls

Since the whole falls wouldn’t fit in the lens, I took a separate picture that shows the upper falls as it erupts out of the woods:

The upper section of Waterfall #4

We had lunch there, then tackled the most difficult part of the hike.  And I have to admit that it was pretty challenging.  We climbed up very steeply, holding onto roots and rocks.

It flattens out in the picture, but it's probably a 30% grade

The “crux” of the climb gives you a choice of two ropes to hang onto.  I had thought beforehand that I wouldn’t use the ropes, but there was a section where it would have been hard to do without them.

Jim tackles the steepest section

I got up to the top and admired the technique of the other hikers:

Dave grunts his way up the rope

The next lengthy stop was at Waterfall #2.  Just another beautiful waterfall?  Ho, hum!

It ran down into a deep, crystalline pool

But, in a strange sort of way, the shoals above Waterfall #1 seemed even better: a tumbling, racing, sliding place where the water glided more than it fell.

It all had to do with the curvature, the speed, like a luge run

We got back up to the giant Christian camp complex, with its many dormitories and parking lots, around 2:30 in the afternoon.  The whole day, we were very happy to feel the clear sunny air after a lot of cold, gloomy weather.