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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

Cedar Rock Mountain January 8, 2010

Posted by Jenny in hiking, nature, Southern Appalachians.
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Northwest view from Cedar Rock Mountain

I’d heard about an unmaintained trail that goes over Cedar Rock Mountain in Pisgah National Forest.  It shows up on the USGS map, and my guide to Pisgah mentions “a red blaze on a white oak leading to an old trail.”  I did a little more digging and found out the important thing: the east part of the trail, from Sandy Gap off the Loeb trail, is not too bad, but the west part that goes from Butter Gap to the top leads up steep open ledges and is sometimes described as “dangerous.”  I’ll check that out sometime, but not in the winter when ice could be a problem.

Conditions at Cat Gap Loop trailhead weren't very appealing

It was an absolutely beautiful winter day, featuring the same kind of bright silent stillness that I experienced on my Hickory Knob hike.  It was in the upper teens when I started, mid to upper 20s when I finished this outing of 1800 vertical, 6.5 miles.  The Cat Gap Loop trail was very icy at the beginning, and there was enough ice or icy snow that I wore my microspikes the whole way.

I went up the east half of the Cat Gap trail, having decided during an earlier hike that it is more interesting than the west half.  At a crossing of Cedar Rock Creek, the rhododendron leaves looked very curly.  I wonder why the rhodo leaves curl in the cold and the ones of laurel and dog hobble do not—they are all part of the same family.

Curly rhodo, non-curly dog hobble

I came to a very appealing boggy area where the creek makes a sweeping serpentine shape through the flats.  The stones in the bottom of the stream looked very gold, framed by white frosty twigs.

Gold stones, silver frost

For no particular reason, as I started the moderate climb up to the gap, I was thinking about my mother and father, and how much I miss them.  Mom died in 2007 and Dad in 2001.  Sometimes when you are hiking by yourself, your thoughts take on certain themes and you just follow them where they go.

I saw an oddly contrasting pair of trees that seemed to illustrate some principle of chance: why should this one turn out weirdly distorted, and that one not?

The odd couple

I took a snack break at Cat Gap, then headed west on the Loeb trail, recalibrating my altimeter so that I’d be sure to identify the spot where the old trail turned off.  After climbing over a knob, I came down to Sandy Gap, and it was pretty obvious where the old trail had to continue along the ridge while the Loeb trail started slabbing down the southeastern slope.  It took me a minute to see the very faded red blaze.

Good thing I'm not colorblind

No one had made any tracks on the old trail, and it was somewhat hard to follow through the flat area of open woods at the beginning before it started to climb more steeply up the summit, which is a very distinctive sharp-topped cone.  I figured that if I lost the trail, it would be easy to bushwhack along the ridge to the top.  There were no more blazes, but as I’ve learned from past experience, sometimes you can identify the location of a snow-covered trail by looking for the duff that has rolled into the very slight trough formed by the trail (obviously, this only works starting a day or so after the snowfall, when the small twigs have had time to drop into the depression).

The dark-colored duff had rolled into the slight trough

In the background you also see another clue to the trail’s location—a sawed-off log end.

The trail was easier to follow where it wound up the steep cone.  It continued across the high point and over to some open ledges.  I could see where the west part of the trail came up, but ice had formed in irregular patterns on the top of the cliff, and there was no way I was going to risk stepping on some of the ice to take a closer look!

Ice ran down to where this pine was clinging to the ledge

The forest below is almost all hardwoods.  They made a pattern of waves, darker on the ridgecrests and lighter on the slopes.

The bumps on the rock and the bumpy ridges seemed similar in shape

I descended by the west half of the Cat Gap Loop, which was just as boring as I had remembered.  If I’d had time, I would have gone over John Rock, which I visited six weeks ago.

You have to see a photo of Cedar Rock Mountain from a distance to appreciate it.  It is such a perfect cone-shaped mountain, set off by its distinctive band of cliffs.  One of these days I may go up Looking Glass Rock and take a picture of its smaller pluton cousin, Cedar Rock.