Perth College is well known in academic circles as the home of the Centre for Mountain Studies, which celebrated its tenth anniversary in January 2011. This Centre focuses on mainstream mountain topics such as forestry, wildlife management, planning, biodiversity, sustainable development and so on. Nothing wrong with that, but researchers elsewhere have been looking into more esoteric topographical concepts. For example, Kuipers (1994), argued that:
'The result of a trajectory-following control law must be a state from which a hill-climbing control law will reach a distinctive state (though occasional failures can be tolerated).'
It is not clear how frequent the failures can be before they are regarded as intolerable. Smith and Mark (2003) tackled a more fundamental phenomenological question:
'The authors begin the paper with the question 'Do mountains exist?' They show that providing an answer to this question is surprisingly difficult ... individual mountains lack many of the properties that characterize bona fide objects'.
Fisher, Wood and Cheng (2004) tackled this issue from a more specific perspective (Helvellyn) but reached similar conclusions:
''Where is a mountain?' is a simple question to ask, but it is not easy to give a consistent, precise response ... The mountain is not a real (bona fide) feature'.
They also address the philosophy of bagging in a more rigorous way than most academic writers:
'If the summit is the mountain, then to have visited the mountain, you have to have walked to that specific point. If you walked near it, then you cannot say that you have been to the mountain. However, most people do not consider this a necessary or acceptable definition of the mountain, and 'summit' is not usually considered a synonym for 'mountain'. For most people therefore, the mountain is not a point, it is a region which to some degree they can visit. If they go to the summit (or near it), then they will feel that they have definitely visited the mountain (and generally others would agree). They may still feel that they have visited the mountain, however, if they only get close to the summit, although someone who has been to that, or another summit, may disagree.'
Fisher, Wood and Cheng also introduce an important new concept:
'The reverse fuzzy viewshed of Helvellyn delimits those areas from which it is possible to get a good view of the peak.'
Little has been heard of the reverse fuzzy viewshed in recent articles, possibly because the authors acknowledge that:
'The effect of aspects of relative elevation on patterns of fuzziness and the nature of error need to be explored.'
Its definition is certainly fuzzy compared to the clarity with which Burgess (1990) discussed the related concept of higher-order vagueness in relation to cairns:
'One thousand stones, suitably arranged, might form a heap. If we remove a single stone from a heap of stones we still have a heap; at no point will the removal of just one stone make sufficient difference to transform a heap into something which is not a heap. But, if this is so, we still have a heap, even when we have removed the last stone composing our original structure.'
Smith and Brogaard (2000) were also uncertain about the sustainability of cairns:
'A stone the size of your fist does, it is true, lose an atom from its surface about once every second - but this atom is almost always immediately recaptured by the stone.'
They were even more concerned about the ephemeral nature of some very large heaps in the Alps:
'The referring relation between a singular term and its object is itself more complex than might at first appear. For think of Mont Blanc, with its rabbits and foothills. Clearly, there is no single answer to the question as to what it is to which the term 'Mont Blanc' refers. Rather there are, at any given time, many answers, since there are many parcels of reality that are equally deserving of the name 'Mont Blanc'.'
Reverse fuzzy viewshed of Garbh Bheinn (18B)
The consensus of critical thinkers in this area is that mountains do not exist as entities but merely as vague social constructs. This is true even of very big mountains, as Smith and Mark show:
'Mount Everest exists only as a result of human beliefs and habits.'
The same argument applies to smaller hills, thereby removing the need for any distinction between a hill and a mountain, as neither exist. However, hill-like objects that are precisely defined, such as Marilyns, Humps, Nuttalls and Sims, do exist, by virtue of their clear definition. These objects do not exist until they are created by the act of defining them. This paradox is reminiscent of the well-known phenomenon in quantum mechanics whereby the behaviour of a small entity is dependent on the act of observing it. In set theory terms, the set of Marilyns exists as a subset of a larger set of undefined hills, which do not exist. So the subset exists but the set does not. It seems that list compilers such as Jackson and Trengove are not just creating lists that are handy for bagging purposes, they are creating the hills themselves. Had Rene Descartes been a mountain instead of a drunken fart, his famous insight would not have been 'I think therefore I am', but 'I am defined, therefore I am'.
The related concept of the spatial extent of hills has also puzzled Smith and Mark, and other philosophers of topology:
'What, precisely, do we mean by the territory that is delineated by our use of the name 'Mount Everest'? This is, unfortunately, a difficult problem, one which we will not attempt to resolve here.'
This problem can be solved by reviving the concept of the hillshed, which are lines that define the boundaries of a hill, in the same way that county boundaries define counties. Hillsheds usually follow rivers and streams until they reach a col and then flow down the other side. In this way the whole country can be partitioned into hill territories and every location in it belongs to a specific hill. However, the hill that a location belongs to depends on the listing used; there are far more hill territories for Humps than for Marilyns. Hillsheds are different from Maquacol lines (Everett, 2000):
'Maquaco-line: the Marilyn qualification contour line 150 metres below the summit.
Maquacol: the col between two Marilyns.
Maquacosh: the Marilyn qualification contour shape... all sorts from rabbits, cats, pigs, foxes, fish and a bucking bronco cowboy on a horse or bull (Hensbarrow Beacon) and a cartoon of Neil Kinnock with a duck on his head (Walton Hill).'
Some philosophers are not content with thinking about the existence and extent of mountains but actually go out walking to see if they can find any. According to Foley (2010):
'Nietzsche, the philosopher of exaltation, was a fanatical walker. So was his arch-enemy Christ... Nietzsche often walked for six to eight hours a day and had some of his best insights on these walks.'
Foley takes Nietzsche's enthusiasm even further and argues that walking is the secret of happiness:
'The more expensive, bulky and complex the hobby equipment, the less enjoyable the hobby. Perhaps there is a just God after all. Much more satisfying are walking and dancing, where the body is its own equipment and instrument. Walking and dancing, rhythm regular and ecstatic, the prose and poetry of the body.'
Although Foley is not referring explicitly to hillwalking, the notion of hillsheds shows that every location belongs to a hill. As all walking takes place in a specific location, it follows that all walking is in fact hillwalking. Even though, as many philosophers have shown, hills do not exist. Cogito, ergo, sum demens.
Burgess, John A: The sorites paradox and higher-order vagueness. Synthese 85, 1990.
Everett, Charles: Some definitions for you. Private email, 2000.
Fisher, Peter and Wood, Jo and Cheng, Tao: Where is Helvellyn? Fuzziness of multi-scale landscape morphometry. Transactions of the Institute of British Geographers 29, 2004.
Foley, Michael: The age of absurdity: why modern life makes it hard to be happy. Simon and Schuster, 2010.
Kuipers, Benjamin: An ontological hierarchy for spatial knowledge. AAAI Technical Report FS-94-03, 1994.
Jackson, Mark: More Relative Hills of Britain. Lulu, 2009.
Smith, Barry and Brogaard, Berit: A unified theory of truth and reference. Logique et Analyse, 43, 2003.
Smith, Barry and Mark, David M: Do mountains exist? Towards an ontology of landforms. Environment and Planning B, 2003.
Trengove, Mark: Europeaklist. Google, 2011. sites.google.com/site/europeaklist
