I cannot think of a better description of glaciers than in Adalbert Stifter’s novella Bergkristall, where two young children, on their way home to their alpine village, get lost in a storm on a glacier.
The glacier becomes a symbol of frozen time, and hence death.
Here at Sólheimajökull, however, the abstract purity of Stifter’s glacier is contrasted by layers of ash, like many glaciers in Iceland.
Thus the glacier seems to transport time, much like it does in the glacier poems of Paul Celan.
On of my teenager dreams was to treck though Scotland. Like many things, it never happened, but I could not resist to accept the invitation of a friend to spend New Year 1994/5 near Fort Williams.
The landscape is harsh and appears alpine, even though one is just a few hundred meters above sea level.
In some sense, these are ideal conditions for some mild mountaineering. The little snow there is is very crisp and allows for easy climbing.
On the other hand, the days are very short. One has six hours at most to get up and down again. You don’t want to get lost there after dark.
Winter Break of 1994 I spent in England, and part of it in the Lake District. I had been to Britain only once before, spending time in Wales and London. This time, it was to be a few days in the Lake District and in Scotland.
I am reasonably familiar with the British literature, and I knew about the Lake District via the Lake Poets, but nothing could have prepared me for that landscape in winter.
Harsh landscapes are usually simplistic in the sense that there is a barren ground extending to the horizon, where it meets an equally barren sky. In the Lake District, there is often an ominous region in between, hard to define, that seems to open up or tear apart the well defined separation between heaven and earth.
And there is, of course, the lone tree that would suit many a poem.
The Galloway cow (I believe) has no comments. She is just happy here.
This image of an expecting woman should make it clear that trolls are not as close to extinction as some try to make us believe.
Of course they are hard to find. Not only are they well camouflaged by all the lava rocks, they are also in constant migration, like here a small family, with the child being carried piggyback.
But not only trolls roam Iceland. This large bird should rewrite a chapter of the theory of evolution.
Then there are the giants, always watching.
High school students taking geometry are until this day tasked to locate the incircle of a triangle: The circle that touches all sides. One learns that its center is where the three angle bisectors meet, and that’s that.
It’s less often taught that there are three more circles (the excircles), touching two sides of the triangle from the inside, but one form the outside. Their three centers are the corners of a triangle in which the former angle bisectors become the altitudes.
Of course things get really interesting when we move into space. Here the four planes of a tetrahedron can be touched by as many as eight spheres. In the simplest case, it looks like the picture above.
Curiously, this does not work with the regular tetrahedron, it needs to be either more or less elongated.
In 1997, my then-girlfriend and I spent two weeks in the village Rasen-Antholz in South Tyrol. Besides a famous and truly stunning landscape, this region has many surprises. As it is protected on all sides by tall mountain ranges, the climate is milder than one would expect for a mountain village, and allows for the existence of the biotope we are visiting below.
This ominous boardwalk lures the visitor into an unexpected terroir: Instead of harsh mountain meadows, we encounter humid swamps.
Here thrives the sundew, the only carnivorous plant found in South Tirol. Other predators have similar goals.
What better place to spend an early morning in the fog to listen to Giacinto Scelsi’s Preghiera per un’ombra for solo clarinet?
In Óskar Jónasson’s film Reykjavik-Rotterdam, a painting by Jackson Pollock plays a marginal but hilarious role.
The pictures in this post are inspired by drip-art and action painting.
They are not quite up to Pollock’s standard, but I must say I like them.
Of course they are not paintings, but landscape closeups taken off the coast of Westman Islands.
The artist? Hard to say, but at least partially responsible are the doves.
Visiting Turkey Run State Park in winter after snow fall is an expedition I often think of in the hot summer days of Indiana. The snow covered slopes of Sugar Creek look pleasant enough.
But the temperatures drop significantly after entering the Rocky Hollow canyon. This vertiginous view of Wedge Rock is due to the fisheye lens I used here.
Proceeding further, the walls become covered with icicles.
Ascending into the narrower parts of the canyon and navigating the ice covered walls is impossible without proper gear.
But the way back offers sun shine and hope for warmer days, which is what we came for, isn’t it?
We usually think of a crack as a blemish. A cracked window needs to be replaced. The cracked patina of old paintings is reluctantly accepted as a proof of age. In The Fall of the House of Usher, Edgar Allan Poe has turned the crack in a wall into a bad omen of the worst kind. Roman Polanski did likewise with cracks in concrete in his film Repulsion. Are cracks really that bad?
In geologically active regions like Iceland, cracks happen more often than elsewhere, and on a much larger scale.
The cracked wall above is from a house on the Westman islands that was half covered by the lave flow from 1973 and is kept as is as a monument.
Cracks appear everywhere. In individual rocks,
in the ground like here near a lava tube,
vertically, splitting entire mountains,
or here, where the crack is literally between the American and European continent.
A torus is obtained by rotating a circle around a axis in the same plane. As such, it has two families of circles on it: the ones coming from the generating circle, and the orbits of the rotation. This allows you to slice the torus open using vertical or horizontal cuts, with the cross sections being perfectly round circles,
Of course, when you do this to your bagel, you do not really expect circles. But neither would you expect the bagel to be hollow.
The surprise, however, is that there is yet another way to slice a torus, still with perfectly circular cross sections. These are the Villarceau circles.
Here is how to do it. Looking at a vertical cross section, cut along a plane that’s perpendicular to your cross section and touches the two circles just above and below. The deeper reason for their existence lies in the Hopf fibration of the 3-dimensional sphere; these curves are stereographic images of Hopf circles.
Even more surprising is that there are certain cyclides that have six circle families on them.
The Inner Frame 