view from Snowdon

Three ways to see Wrekin from Snowdon

Can Wrekin be seen from Snowdon? This question, originally rooted in the experience of standing on a mountaintop and gazing towards the horizon, was eventually settled in the domain of digital technologies and remote data sets, where sight becomes only an arbitrary limit. According to the topography data, there is no line of sight between these two mountains, contrary to the popular belief.

Where does this belief come from? It is not based in experience — nobody claims to have actually seen Wrekin from Snowdon. David Squires tracks the origin of this belief to a suggestion in an poem from 1833, but its subsequent persistence might stem from the fact that the abstract line between Wrekin and Snowdon is much more vivid in our imagination than the hazy view towards the horizon, exemplifying our preference for clarity, for ordering, for seeing patterns and well-defined relationships. We have learned that our sensory apparatus is fallible in ways in which our intellect is not. Seeing is no longer believing, but the opposite is true, knowing is seeing. We know Wrekin is there, so we believe it can be seen: imagination and knowledge extend human vision at its limit.

The more hazy the view towards Wrekin is, the more we rely on our mental model in inferring what we see. In this project I’m interested in how our models jut through the experienced world, and furthermore in how our models influence the object or process being modeled. Scientific models, in a mathematical form, are not merely representations: they generate predictions which then shape how we change reality. Climate models for example are used to determine environmental policy decisions. Moreover, climate models form epistemological basis for climate engineering, argues philosopher Clive Hamilton: a conception of the Earth as a digital system projected back on Earth makes geoengineering thinking conceivable. In the model domain the same tools are used to represent the world and to manipulate it, thereby positing nature as something technically manipulable. Technology “reveals the under­lying mechanism which generates [nature], “ writes Slavoy Zizek, “so that, in a sense, ‘natural reality’ itself becomes something ‘simulated’, and the only ‘Real’ is the underly­ing structure.”

In 2000 the Shuttle Radar Topography Mission (SRTM) onboard the Space Shuttle Endeavour obtained elevation data of earth to generate a nearly seamless digital elevation model (DEM). In this project I am using SRTM data to reconstruct the geography between Wrekin and Snowdon, and to place the imaginary line connecting the two mountains back in the experience of an eye looking over a landscape. Each of these three proposals accounts for a different notion of what the world is like to reconstruct geography in such a way that the line of sight between Snowdon and Wrekin is uninterrupted. The truisms accounted for are:

1. IMPOSING MOUNTAINS ARE IMPOSING
2. THINGS ON THE HORIZON ARE MYSTERIOUS
3. UNKNOWN IS INVISIBLE

The history of the Snowdon-Wrekin sightline is recounted in detail by David Squires in Can Snowdon be seen from Wrekin? A Topographic detective story. I was fascinated by this story, as well as by the work of Jonathan de Ferranti, whose website I found it on. Ferranti’s website is dedicated to accuracy in geographical representation.  His work includes filling in the voids in SMRT data and creating the digitally-derived panoramas for identifying geographic features seen from mountain summits.

Here’s a panorama from Snowdon created by Ferranti, which was the definitive word on the whether the line of sight was interrupted or not. Had Wrekin been visible, it would appear in the center, beyond Cadair Berwyn.

Part of panorama view from Snowdon, looking towards Wrekin.
Part of panorama view from Snowdon, looking towards Wrekin.

I used the SRTM data to recreate the region between Snowdon and Wrekin in Vue, a recent addition to terrain generation tools that followed Bryce: the software that arose from work with fractal geometry by Benoît Mandelbrot and his student Ken Musgrave, who first used the term fractals to describe mathematically modeling natural patterns.

Screenshot 2014-03-03 00.07.07

The virtual camera is placed on top of Snowdon: Wrekin is not visible.

Cadair Berwyn blocking the line of sight to Wrekin. Click on the image to enlarge.
Cadair Berwyn obscures the view to Wrekin. Click on the image to enlarge.

1. IMPOSING MOUNTAINS ARE IMPOSING

“In the field,” writes Jonathan de Ferranti,”the eye tends to magnify the vertical scale on the horizon.” In this proposal, a cartographic projection is created to simulate this effect of our perception on tall mountains. In keeping with the human perception of contrast, the effect is that of slight inflation of the isolated peaks.

wrekin_blank_inflate

wrekin_full_inflate

Contrast is one of the fundamental features of perception. The quality of an object is perceived as relative to its context. If one object is extreme on some dimension, then neighboring objects are perceived as further away from that extreme. This is illustrated in our very definition of a mountain: “a natural elevation of the earth surface rising more or less abruptly from the surrounding level and attaining an altitude which, relatively to the adjacent elevation, is impressive or notable.”

The magnifying aspect of the eye might be responsible for errors in measurements of mountain peak heights. According to Ferranti, the reported peak heights are frequently inflated as compared with topographic data measurements. The distortions in our representations of geographies are not only frequent, but also essential, writes Mark Monmoniker in How to lie with maps. “To portray meaningful relationships for a complex, three-dimensional world on a flat sheet of paper or a video screen, a map must distort reality.”

My new projection considers both the topographic prominence and topographic isolation: the mountains that are inflated are isolated steep peaks, rather than a part of a wider mountain range. ‘Topographic prominence’ is a technical term describing the also suggests the concept of importance associated with size.
An example of the cartographic distortion discussed as misleadingly portraying the prominence of Europe is the commonly used Mercator projection. The Mercator projector renders Greenland as large as South America, thanks to the North-South scale increasing sharply towards the poles, whereas a globe would show Greenland only about one-eighth as large.

2. THINGS ON THE HORIZON ARE MYSTERIOUS

At the limit of the human vision is imagination. It extends vision in a creative act of perception, shaping the understanding of what we see. Things close to a horizon don’t always appear as they are. David Squires considers atmospheric refraction in his detective story noting that “atmospheric refraction, i.e. the bending of light rays as they pass from lighter, high altitude air to denser low altitude air can account for features of the landscape becoming visible or invisible under special atmospheric conditions (e.g. temperature inversions).”

For this proposal conditions of extreme refraction are created in the simulated atmosphere (equivalent to the refraction coefficient of 0.75). Wrekin is now visible from Snowdon as one looks trough the highly refractive atmosphere.

wrekin_blank_refract

wrekin_full_refract

The following graphs generated at http://www.heywhatsthat.com/ demonstrate the line of sight.

profile-0904_03
Sightline from Snowdon to Wrekin, with a refraction coefficient of .03 (normal conditions)
profile-0904_05
Refraction coefficient of 0.5
profile-0904_75
Refraction coefficient of 0.75. In this case the sightline would clear the peak of Cadair Berwyn, which was obstructing the view in the two other cases.

After examining the possibility that special atmospheric conditions might sometimes make Wrekin visible, David Squires decides it would be very unlikely, as the refraction would have to be quite extreme, more extreme then is has ever been recorded in the UK. Squires writes:
“What would be needed for the summit of Snowdon to come into view is for the curvature of the light ray to be greater than the curvature of the earth. This unusual situation, in which flat terrain appears to rise around the viewer like a saucer, has been observed for rays near the ground in certain parts of the world. Such conditions were encountered on occasion, for example, by British surveyors working on the plains of India during the nineteenth century trigonometrical survey of that country. They have also been recorded by surveyors in the arctic taking readings over ice fields. But have they ever been encountered in Britain for long rays such as Wrekin-Snowdon?”
Squires references measurements of refraction taken in the UK by Ordnance Survey (which are well below 0.5) and concludes:
“It is reasonable to suppose that hills which would be brought into view by a refraction coefficient within the range measured by the Ordnance Survey will from time to time be visible. However, where viewing a hill would require a refraction coefficient outside that range, it is natural to be skeptical that the hill has ever been observed. Further, the greater the refraction coefficient required, the greater the degree of skepticism.”

3. UNKNOWN IS INVISIBLE

In this proposal, the terrain reflects that we only see what we pay attention to: all the mountains in between Snowdon and Wrekin are made invisible. This includes Cadair Berwyn, the peak which would block the direct sightline between the two mountains.

wrekin_blank_invisible

wrekin_full_invisible

“Inattentional blindness is the failure to notice an unexpected stimulus that is in one’s field of vision when other attention-demanding tasks are being performed. It is categorized as an attentional error and is not associated with any vision deficits. This typically happens because humans are overloaded with stimuli, and it is impossible to pay attention to all stimuli in one’s environment. This is due to the fact that they are unaware of the unattended stimuli. Inattentional blindness also has an effect on people’s perception.”

Inattention blindness has been demonstrated in different experiments, including a famous test in which a man dressed in a gorilla suit failed to be noticed when the viewers were given attention tasks.

Squires traces the beginnings of the Snowdon-Wrekin line of sight to a poem by Reverend Corfield, rector of Pitchford and vicar of Waters Upton in Shropshire, published in 1833.

From WREKIN’s summit cast the eye around,
To view the objects which th’ Horizon bound;
O’er Salop’s plains with beauteous verdure drest,
The Cambrian Mountains stretch along the West,
And though Snowdonia’s cloud-capt tops are hid,
Yet, through the vast expanse the eye is bid…

“Corfield’s comment on Snowdonia is dangerously ambiguous,” writes Squires. “Are Snowdonia’s tops hidden by intervening hills or are they hidden by clouds?”
This question makes it clear that mountains can be a little like clouds in that they might obscure the visibility of a peak which we know is there even though we can’t confirm it with our own eyes. Represented as the data the mountains are just as ephemeral as the clouds, and the imaginary Line of Sight can become more real than the surrounding landscape.

On most days the view from Snowdon wouldn’t be quite as far reaching. The atmosphere would obscure the topology, much like in the following images.

snowdon1

snowdon2

snowdon4