Summary of Classes 5 to 8
Class 5. – Where is St. Petersburg?
The limitation of 'relative location' is that the location of one point is 'dependent' upon knowing the location of another point. What is needed is a system of 'absolute location' by which all point locations are referenced to a single location or 'origin'. A 'rectangular coordinate' system is the answer, the simplest example of which is the well known sytem of 'graphical axes'. With the Y axis oriented south-north and the X axis oriented west-east, the location of any point to the north and east of the zero origin can be determined as the distance east of the origin and the distance north of the origin, a pair of values that are the 'coordinates' of the location. All locations can be 'independently' defined by two coordinates referenced to the origin. Applying this concept to a spherical earth is a little more difficult, but the equator is the obvious X axis. After much debate, the 'meridian' running through Greenwich was agreed upon as the Y axis. With this system of 'earth coordinates', location is measured from 0-180 degrees east and west of Greenwich, and 0-90 degrees north and south of the equator. The location of St. Petersburg (a central point) is 59° 57′ 0″ N, 30° 18′ 0″ E or 59.933151° N, 30.306089° E. While adequate for some uses, the system suffers from the need to use the suffixes N, S, E and W, and with 1” of arc being 30.92 metres on the earth's surface, it lacks the accuracy required by modern 'sub-metre' location.
The 'UTM Coordinate System' is based on the Universal Transverse Mercator projection of the earth, a 'cylindrical' and 'orthomorphic' projection that reasonably preserves shape between 84°N and 80°S, but not area. This area is divided into 60 north-south, 6° longitude wide numbered zones, and 20 east-west, 8° latitude wide lettered bands. Every rectangular zone has a 'unique' 'alphanumeric' code, e.g. 21T. In each zone, the zero origin is imagined as west of the zone, and location within the zone is defined as the number of metres east of the 'false origin' and the number of metres north of the equator. The location of the same central point of St. Petersburg is UTM 36V 349201 6648919. This conveniently dispenses with N, S, E and W and is a measurement in metres rather than in 60th's of arc.
Location becomes still more tricky when one admits that we do not live on a spherical earth but actually on an 'oblate' spheroid that is 'egg-like' in equatorial shape. On such a lumpy object, any parallel of latitude would be a different distance from the equator at different locations – an impossibly difficult situation. So, the actual shape of the earth has to be substituted by a 'model'. Being 'ellipsoidal' rather than spherical, there is now international agreement on an ellipsoidal model that is the 'best-fit' to actual earth shape, and the UTM system is superimposed upon it.
Related and equally problematic is the measurement of elevation. Historically, 'mean sea level' seemed a logical 'datum' to use as zero, but on a world scale, mean sea level is far from horizontal, the earth's rotation piling oceans up to higher levels on west coasts than east coasts. A model surface, the 'geiodal surface' represents mean sea level as if the oceans could run through and under the continents. Elevation is measured as above or below a selected point or datum on this theoretical surface.
So, defining the location and elevation of St. Petersburg is by no means easy. In reality, when we define where we are, it is only in relation to an agreed upon model of the earth, not actually where we are on a 'lumpy-bumpy' earth.
A close look at the natural world, at all scales, reveals the most common type of network to be a 'branching' network. The 'vascular' systems of many plants and animals is a branching network, as is the form of many living forms (such as trees, corals). Stream networks drain 'run-off' from every square cm of the continental surfaces. Are stream and other natural branching networks 'chaotic', 'random' or 'ordered'?
A stream or river network has the specific task of draining a particular area of the earth's surface termed a 'drainage basin'. The boundary between drainage basins is a line along the locally highest ground and is termed a 'divide' or 'watershed'. A look at maps will show that where there is much water to be drained, there is a more dense network of drainage 'channels' than in a basin where there is less water to be drained. Such systems or networks tend to operate on the principal of 'least-work', that is, they are designed to do the task in the most efficient manner possible. Though there are natural influences that can disturb a network and render it less efficient (at least temporarily), one can argue that every metre of stream channel is there for a purpose.
If one takes any natural, undisturbed drainage basin, one can demonstrate that these branching networks reveal a high degree of order in their arrangement. Horton (xx) proposed a scheme of steam numbering by which the smallest 'tributaries' draining the divide are termed '1st order'. Where two 1st order streams join they become 2nd order streams, etc. If a stream of one order joins a stream of a higher order, no change occurs. Thus every stream 'segment' is 'labelled'. There will obviously be many 1st order streams and only one of the highest order where it reaches a lake or the sea. Counting the number of streams of each order provides a string of numbers such as 60, 13, 9, 4, 1. Plotting these numbers against order will reveal that the numbers are a 'logarithmic progression'. If plotted on 'semi-logarithmic' graph paper, a straight line can likely be fitted through the plotted points. This shows that the two variables, one arithmetic, one logarithmic are 'correlated' to a high degree. If one took on the task of measuring the length of every stream segment and calculated the 'average' length of a segment of each order, one might develop a string of numbers such as 2, 5, 13, 20, 55 (km). Again, plotting these numbers on semi-log paper would show them to fall close to a straight line, demonstrating that there is a correlation, stream segment length increasing logarithmically downstream. Each stream segment drains a specific area or basin and if one took on the immense task of measuring the area of each basin and calculating the average area of each order of basin, one might develop a string of numbers such as 5, 12, 40, 110, 330 (sq km). Again, a close to straight line will likely be plotted.
Though sometimes referred to as 'laws' of stream drainage basin analysis, the word is more loosely applied than in the physical sciences. It would be fairer to say that if one took a representative sample of world drainage basin networks, it would be found that the degree of correlation between these variables would vary but would generally be high. Such analysis tells us that the branching stream network is not chaotic or random but in fact well ordered in its arrangement. Stream networks design themselves to do the work that has to be done. Should that work change, such as with climate change, stream networks will abandon channels or build new ones, will lengthen or shorten, widen or deepen their channels such that they efficiently meet the new challenge.
Other natural branching networks will be found to similarly arrange themselves in an ordered manner, designing themselves to perform 'least work' in completing their tasks.
Not a word that one is likely to use often, a 'palimpsest' is a parchment which has been reused such that several layers of writing may be discerned beneath the most recent. The concept of a palimpsest can be applied to both 'physical and cultural landscapes', each in different ways being composed of layers of history applied to the same area. Layers of 'strata', laid at different times in geological history, are subsequently sculpted by the forces of erosion to form the present topography of the earth's surface. Strata of many ages are left 'outcropping' on the surface, each perhaps holding evidence of the life forms of the time of formation as 'fossils' within them. Particularly in 'dome-like' ('anticline') or 'basin-like' ('syncline') formations, older strata may outcrop with younger strata exposed around it – an 'inlier', or younger strata be exposed with older strata around it – 'an outlier'. In the former case, the old strata forms a window through younger strata into the past, and in the latter case, the younger strata is the latest surviving addition to a much older history.
The same principal can be applied to cultural landscapes, as is well demonstrated by looking closely at a 'large scale' 'topographic map' of an area that has seen much history. Maps are published at a point in time, such that landscapes can contain new 'elements' that are not shown on the dated map, but will be shown when the map sheet is 'revised' at a later date. These new features of the cultural landscape can be thought of as 'outliers'. The map may show layer after layer of cultural features, many of more recent time and perhaps progressively fewer as older features are less likely preserved. The oldest feature in the present cultural landscape may be a single feature, poking through the more recent cultural 'fabric' as an 'inlier', a window into a distant past. Thus on a map of the 'chalk' 'downs' of southern England, one can find new roads, older, narrow 'lanes' and 'bridle paths', canals, 'hydro' lines, the site of the Battle of Roundway Down, 1643, the site of a 200AD Roman 'Villa', an 800BC 'Iron Age' 'Fort', 'Bronze Age' 'Barrows' or 'Tumuli' dating from 1200BC and a 'White Horse' cut into the chalk downs before 2000BC by people unknown and for purpose unknown.
The concept of a palimpsest is applied in the fields of architecture and in the fine arts, the theme always being the 'superimposition' of layer upon layer.
An 'opinion' is a belief or judgement that is personal and held on grounds insufficient to prove certainty. As such, an opinion cannot be said to be 'right' or 'wrong'. One can agree or disagree, perhaps strongly. 'Debate' is a discussion involving opposing viewpoints. Sometimes, for the purpose of debate, a speaker will deliberately take an opposing viewpoint, this being to take the part of 'devil's advocate'. A 'moderator' presides over a discussion or debate, and does not express his or her own opinion.
In this class, opinion was sought on a number of contentious issues, Brian attempting to act both as moderator and occasionally as 'devil's advocate', which are conflicting roles. Shoplifting is wrong but is it less so if done by someone in need or someone suffering from kleptomania? Is taking a paperclip from the workplace stealing? Is wasting food in a 'foodfight' excuseable? What is your opinion of same sex marriage? Is there a case for voluntary active euthanasia? All cultures are faced with difficult ethical dilemmas in which decisions must ultimately be made and, when revisited, perhaps later modified.
In every case, opinions are central to the difficult task of deciding where to draw lines between that which is acceptable and not acceptable. Ideally, the opinion of the majority should define the line, there always being extreme views to right and left. Different cultures, with different histories, experiences, religions, morals and customs, may make the ethical decision to draw the line in different places. We may agree or disagree with those decisions, depending on our opinion, but cannot declare them to be right or wrong. Essential, however, is the freedom to express one's opinion in a well moderated forum, and to participate in discussion and debate.