<h2id="sevenBridges"name="sevenBridges">The Seven Bridges of Königsberg</h2>
<p>The Seven Bridges of Königsberg is a historical mathematical problem which laid the ground for graph theory, and prefigured topology. Königsberg, in former Prussia (now Kaliningrad, Russia), set on both sides of the Pregel River, included two large islands - Kneiphof and Lomse - which were connected to the mainland by a series of seven bridges. The problem was to devise a walk through the city crossing each of those bridges once and only once.</p>
<p>The negative solution came from Swiss mathematician and physicist Leonhard Euler, who pointed out that the choice of route inside each land mass was irrelevant; only the sequence of crossings mattered. Euler created a diagram in which each land mass was represented by a <ahref="beetroot_to_p_lions_es.html#networkTopology">"vertex" or node, and each bridge became an "edge", or link</a> between them. This allowed him to consider the problem in <ahref="ciao_to_wijnhaven.html#abstraction">abstract terms</a>, in the mathematical structure of a <ahref="please_to_wijnhaven.html#graph">graph</a>.</p>
<p>As only the connection information is relevant, the shape of the pictorial representations can be distorted in any way without changing the graph. For example, <ahref="#unravelingKnots">it does not matter if the links drawn are straight or curved, or whether a node is to the left or right of another</a>.</p>
<p>Euler observed that, except at the beginning and end of the walk, if one enters a land mass by a <ahref="wijnhaven_to_foshan.html#erasmusbrug_smoking">bridge</a>, one must leave a land mass by a bridge. In other words, at any time during the walk, the number of times one enters a non-terminal vertex equals the number of times one leaves it, meaning that the total number of bridges touching that land mass must be even, as half the crossings will be towards a land mass, and the other half away from it. However, all four of the land masses in the problem are touched by an odd number of bridges (one is touched by 5, the other three by 3). Since only two land masses can act as the beginning or end, it is impossible to cross each bridge only once during a walk.</p>
<h2id="quipu"name="quipu">Quipu</h2>
<p><em>Quipu</em> (also spelled <em>khipu</em>) or "talking knots", historically were cords with <ahref="please_to_foshan.html#knot">knots</a> made in them as a way to record numbers, used by various ancient cultures of Andean South America.</p>
<p><ahref="cybernetic_guerilla_warfare.html#topology"class="outOfNetworkLink"target="_blank"> Topology is a non-metric elastic geometry. It is concerned with transformations of shapes and properties such as nearness, inside and outside.</a></p>
<p>In mathematics, topology is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not <ahref="#torn_mandarin">tearing</a> or gluing.</p>
<p>The drawings I've been making by tracking myself over <ahref="please_to_wijnhaven.html#gps">GPS</a> makes a kind of map; however it does not display scale, or landmarks, or street names. It doesn't show which way is north, south, east or west. What it does show is some kind of graphic representation of the path I took by following my nose.</p>
<p>The drawings I've been making by tracking myself over <ahref="please_to_wijnhaven.html#gps">GPS</a> makes a kind of <ahref="wijnhaven_to_foshan.html#maps">map</a>; however it does not display scale, or landmarks, or street names. It doesn't show which way is north, south, east or west. What it does show is some kind of graphic representation of the path I took by following my nose.</p>
<p>After I return back to the studio at Wijnhaven 61, I save and export .gpx (GPS exchange) format, and then drop the files into geographic information system software which allows me to accurately position the paths, representing them as lines.</p>
<p>Later, I export a line to .svg (scalable vector graphics) format and start to zoom in on it using a vector graphics editor. When zoomed out, the line appears to be curved, jagged, definitely not straight. However, when zooming in there are many straight lines, and they only bend at anchor points where each snapshot is taken. The line becomes <ahref="please_to_foshan.html#knot">knotted</a> at places, representing social interactions, financial transactions, places where I backtracked, and where the GPS signal was obscured within or deflected by buildings in the urban landscape.</p>
<p>I begin to simplify the line, sliding a scale that removes anchor points and unravels the knot into a <ahref="wijnhaven_to_foshan.html#straightestPart">completely straight line</a>. As I do this, I notice smaller knots that were not so visible at the scale I saw them at originally.</p>
<p><ahref="cybernetic_guerilla_warfare.html#topology"target="_blank"> Topology is a non-metric elastic geometry. It is concerned with transformations of shapes and properties such as nearness, inside and outside.</p>
<p>A note from Peter Guthrie Tait scribbled on an envelope asks an unknown recipient "Can't you come on Monday the present at the performance? An elliptical hole gives the rings in a state of vibration!!!"</p>
<p>In a room, thick with smoke, Tait and William Thomson (Lord Kelvin) are conducting an <aclass="outOfNetworkLink"href="https://www.youtube.com/watch?v=SwG_uRuYkhg"target="_blank">experiment</a> to test the German physicist Hermann von Helmholtz's theory, that closed vortex lines in a fluid remain stable forever. Tait is using a box that emits smoke made from a pungent mixture of ammonia solution, salt and sulfuric acid. He taps the back of his makeshift vortex cannon, and thick rings he later describes as looking "like solid rings of India rubber" waft from a hole drilled in its front. Thomson develops a theory that each smoke ring is structured around knots in <ahref="please_to_foshan.html#theAether">the ether</a>, a space-filling substance believed to transmit matter. Consequently, Tait begins to tabulate possible forms of <ahref="please_to_foshan.html#mathematicalKnots">mathematical knots</a>.</p>
<pictureclass="drawing">
<p>In a room, thick with smoke, Tait and William Thomson (Lord Kelvin) are conducting an <aclass="outOfNetworkLink"href="https://www.youtube.com/watch?v=SwG_uRuYkhg"target="_blank">experiment</a> to test the German physicist Hermann von Helmholtz's theory, that closed vortex lines in a fluid remain stable forever. Tait is using a box that emits smoke made from a pungent mixture of ammonia solution, salt and sulfuric acid. He taps the back of his makeshift vortex cannon, and thick rings he later describes as looking "like solid rings of India rubber" waft from a hole drilled in its front. Thomson develops a theory that each smoke ring is structured around knots in <ahref="please_to_foshan.html#theAether">the ether</a>, a space-filling substance believed to transmit matter. Consequently, Tait begins to tabulate possible forms of <ahref="#mathematicalKnots">mathematical knots</a>.</p>
<p>Klein worms are forms based on the <ahref="please_to_foshan.html#kleinBottle">klein bottle</a>, drawn by the artist Claude Ponsot. These drawings made their first appearance as illustrations for the article <ahref="cybernetic_guerilla_warfare.html"class="outOfNetworkLink"target="_blank">Cybernetic Guerilla Warfare</a>, by Paul Ryan (not the politician) in Radical Software, Vol.1, Issue 3.</p>
<imgclass="drawing"src="img/Knotwork_06.jpg">
<h2id="knotworks"name="knotworks">Knotworks</h2>
<p><em>Knotworks</em> are visualisations of the topology of our small, humble digital network of eight home servers. Each <em>Knotwork</em> drawing is of a mathematical knot with eight crossings, each crossing representing a <ahref="p_lions_es_to_wijnhaven.html#node">node</a> of the network. The points where the parts of the loop overlap can conceal parts contained, like the internal sections of <ahref="cybernetic_guerilla_warfare.html#kleinWorms"class="outOfNetworkLink"target="_blank">klein worms</a>. When unravelled, the knot is <ahref="please_to_foshan.html#unknot">a continuous loop</a>, and the links (edges) and the nodes (vertices) are the same.</p>
<p><em>Knotworks</em> are visualisations of the topology of our small, humble digital network of eight home servers. Each <em>Knotwork</em> drawing is of a mathematical knot with eight crossings, each crossing representing a node of the network. The points where the parts of the loop overlap can conceal parts contained, like the internal sections of <ahref="cybernetic_guerilla_warfare.html#kleinWorms"target="_blank">klein worms</a>. When unravelled, the knot is <ahref="please_to_foshan.html#unknot">a continuous loop</a>, and the links (edges) and the nodes (vertices) are the same.</p>
<p>Mathematical knots, or knots which are studied in the field of knot theory, are based on the embedding of a circle within three-dimensional space. They are different from <ahref="beetroot_to_ciao.html#4_inca_quipu_knots">the usual idea of a knot</a>, that is a string with free ends. Therefore, mathematical knots are (almost) always considered to be closed loops.</p>
<h2id="networkOfPossibilities"name="networkOfPossibilities">Network of possibilities</h2>
<p>I'm making visualisations of things that are not visible in order to better understand them myself. The methodology I'm adopting is one based on a mind-map network, where possible ways to reflect are connected to subsequent actions and outcomes that infinitely loop into each other. In this way, an idea becomes an action (drawing, walking, sculpting, writing), which becomes an outcome (hand-drawing, GPS drawing, clay model, narrative text, explicatory text, and so on), then can become a new idea from which to act again, etcetera etcetera...</p>
<p>Network topology is the arrangement of the elements (links, nodes, etc.) of a communication network. Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and control radio networks, industrial fieldbusses, and computer networks.</p>
<p>There are two types of network topologies: physical and logical. Physical topology emphasizes the physical layout of the connected devices and nodes, while logical topology focuses on the pattern of data transfer between network nodes.</p>
<p>The chemtrail conspiracy theory is an erroneous belief that the contrails of aircraft are being used for nefarious purposes, ranging from altering the weather to mind control. Chemtrail (a portmanteau of "chemical" and "contrail") sightings are often reported on the <aclass="outOfNetworkLink"href="https://reddit.com/r/chemtrails"target="_blank">r/chemtrails </a>sub-messageboard of reddit.com, a discussion website which claimes to be "the front page of the internet".</p>
<p>The chemtrail conspiracy theory is an erroneous belief that the contrails of aircraft are being used for nefarious purposes, ranging from altering the weather to mind control. Chemtrail (a portmanteau of "chemical" and "contrail") sightings are often reported on the <aclass="outOfNetworkLink"href="https://reddit.com/r/chemtrails"target="_blank">r/chemtrails </a>sub-messageboard of reddit.com, a discussion website which claims to be "the front page of the internet".</p>
<p>On this sub-messageboard, under a section titled "Definitions & such" is the short description of a <em>chemtrail</em> as
<divclass="indent"><em>...a visible trail left in the sky by an aircraft and believed by some to consist of chemical or biological agents released as part of a covert operation.</em></p></div>
<p>Following this is a short text that encourages both believers and skeptics to adopt a tolerant attitude towards each other with a disclaimer:<p>
<p>A contingency plan; a fall-back, a plan B, what to do if all else fails.</p>
<p>Contingencies are incidental to something else, dependent on chance, possible, conditional, but usually unnecessary.</p>
<p>Contingencies are incidental to something else, <ahref="please_to_wijnhaven.html#dependencies">dependent</a> on chance, possible, conditional, but usually unnecessary.</p>
<p>A contingency is what something allows or doesn’t allow one to do, constrained by its form and use. For example, a pen is often used to write with, but also has the contingency of being used for other purposes, such as scratching one’s back.</p>
<h2id="contrails"name="contrails">Contrails</h2>
<p>Contrails (a portmanteau of "condensation" and "trail") are the line-shaped clouds left behind by the engines of aircraft flying at low altitude. They are commonly composed of water in the form of ice crystals.</p>
<h2id="taz"name="taz">Temporary Autonomous Zone (TAZ)</h2>
<p><em>THE CONCEPT OF THE TAZ arises first out of a critique of Revolution, and an appreciation of the Insurrection. The former labels the latter a failure; but for us uprising represents a far more interesting possibility, from the standard of a psychology of liberation, than all the "successful" revolutions of bourgeoisie, communists, fascists, etc.</em></p>
<p><em>The second generating force behind the TAZ springs from the historical development I call "the closure of the map." The last bit of Earth unclaimed by any nation-state was eaten up in 1899. Ours is the first century without terra incognita, without a frontier. Nationality is the highest principle of world governance--not one speck of rock in the South Seas can be left open, not one remote valley, not even the Moon and planets. This is the apotheosis of "territorial gangsterism." Not one square inch of Earth goes unpoliced or untaxed...in theory.</em></p>
<p><em>The "map" is a political abstract grid, a gigantic con enforced by the carrot/stick conditioning of the "Expert" State, until for most of us the map becomes the territory--no longer "Turtle Island," but "the USA." And yet because the map is an <ahref="ciao_to_wijnhaven.html#abstraction">abstraction</a> it cannot cover Earth with 1:1 accuracy. Within the fractal complexities of actual geography the map can see only dimensional grids. Hidden enfolded immensities escape the measuring rod. The map is not accurate; the map cannot be accurate.</em></p>
<p><em>So--Revolution is closed, but insurgency is open. For the time being we concentrate our force on temporary "power surges," avoiding all entanglements with "permanent solutions."</em></p>
<p><em>And--the map is closed, but the autonomous zone is open. Metaphorically it unfolds within the fractal dimensions invisible to the cartography of Control. And here we should introduce the concept of psychotopology (and -topography) as an alternative "science" to that of the State's surveying and mapmaking and "psychic imperialism." Only psychotopography can draw 1:1 maps of reality because only the human mind provides sufficient complexity to model the real. But a <ahref="wijnhaven_to_foshan.html#mapTerritory">1:1 map</a> cannot "control" its territory because it is virtually identical with its territory. It can only be used to suggest, in a sense gesture towards, certain features. We are looking for "spaces" (geographic, social, cultural, imaginal) with potential to flower as <ahref="ciao_to_wijnhaven.html#autonomy">autonomous zones</a>--and we are looking for times in which these spaces are relatively open, either through neglect on the part of the State or because they have somehow escaped notice by the mapmakers, or for whatever reason. Psychotopology is the art of dowsing for potential TAZs.</em></p>
<p>—Hakim Bey, excerpt from <ahref="the_psychotopology_of_everyday_life.html"class="outOfNetworkLink"target="_blank">'The Psychotopology of Everyday Life'</a>, T.A.Z, The Temporary Autonomous Zone, 1991.</p>
<p>To abstract is to pull or draw away rules and concepts in general from specific examples, first principles, literal signifiers, and other methods. So, abstraction becomes a conceptual process of creating super-categorical representatives for subordinate concepts, connecting related concepts as a group, field or category.</p>
@ -22,7 +28,8 @@
<h2id="autonomy">Autonomy</h2>
<p><ahref="the_psychotopology_of_everyday_life.html#taz">Autonomy</a> is the freedom to make an informed, uncoerced decision. Autonomous organisations, institutions and individuals have independence and the ability to self-govern.</p>
<p><ahref="beetroot_to_wijnhaven.html#taz">Autonomy</a> is the freedom to make an informed, uncoerced decision. Autonomous organisations, institutions and individuals have independence and the ability to self-govern.</p>
<p>The knotboard is a piece of wood, pre-drilled with a grid of holes. Accompanying this is an assortment of pre-made polymer clay knotted links. These links can be put into the holes in multiple configurations. By doing this, one can play with the structures of various network topologies. This is a hands-on technique for meditation on networks and a departure point for other forms of representation, including writing, drawing, and walking.</p>
<p>The knotboard is a piece of wood, pre-drilled with a grid of holes. Accompanying this is an assortment of pre-made polymer clay knotted links. These links can be put into the holes in multiple configurations. By doing this, one can play with the structures of various <ahref="beetroot_to_p_lions_es.html#networkTopology">network topologies</a>. This is a hands-on technique for meditation on networks and a departure point for other forms of representation, including writing, drawing, and walking.</p>
<p>In telecommunications networks, a node (Latin <em>nodus</em> "<ahref="please_to_foshan.html#knot">knot</a>") is either a point at which data is redistributed, or a communication endpoint.</p>
<p>Nodocentrism is an epistemological bias in which the nodes of a network take primary focus over the connections. In his book <ahref="https://www.upress.umn.edu/book-division/books/off-the-network"class="outOfNetworkLink"target="_blank">Off the Network: Disrupting the Digital World</a>, media scholar Ulises Alí Mejías outlines his theories of nodocentrism as the exclusionary network logic that cannot render anything except nodes, and in opposition, paranodality, the peripheral space, both inside and outside the network, which makes disidentification possible. Together, these concepts prepare the ground for decolonizing the internet by reframing ways of belonging to, and differentiating the self and the collective from, the network.</p>
<h2id="paranodal"name="paranodal">Paranodal</h2>
<p>According to Ulises Alí Mejías, the paranodal is "the space between the nodes", and further; "This space surrounding the nodes is not blank". In his essay <ahref="mejias_liberation_technology.html"target="_blank">Liberation Technology and the Arab Spring: From Utopia to Atopia and Beyond</a>, Mejías describes the paranodal as such; "it is inhabited by multitudes of paranodes that simply do not conform to the organising logic of the network, and cannot be seen through the algorithms of the network. The paranodal is not a utopia—it is not nowhere, but somewhere (beyond the nodes). It is not a heterotopia, since it is not outside the network but within it as well. The paranodal is an atopia, because it constitutes a difference that is everywhere."</p>
<p>In early modern physics, the <ahref="please_to_wijnhaven.html#ethernet">luminiferous aether</a> (or ether) was believed to be an invisible space-filling substance or field that was a transmission medium for electromagnetic or gravitational forces.</p>
<p>In early modern physics, the luminiferous aether (or <ahref="please_to_wijnhaven.html#ethernet">ether</a>) was believed to be an invisible space-filling substance or field that was a transmission medium for electromagnetic or gravitational forces.</p>
<h2id="tait"name="tait">Tait conjectures</h2>
<p>Peter Guthrie Tait (1837-1901) was a Scottish mathematical physicist, whose investigations in knot theory contributed to the field of topology as a mathematical discipline. His tabulations of knots with ten crossings, which became known as the <em>Tait conjectures</em>, arose out of experiments he conducted with William Thomspon (Lord Kelvin) in <ahref="beetroot_to_p_lions_es.html#1867">1867</a> at the University of Edinburgh.</p>
<p>Peter Guthrie Tait (1837-1901) was a Scottish mathematical physicist, whose investigations in <ahref="#knotTheory">knot theory</a> contributed to the field of topology as a mathematical discipline. His tabulations of knots with ten <ahref="beetroot_to_ciao.html#sevenBridges">crossings</a>, which became known as the <em>Tait conjectures</em>, arose out of experiments he conducted with William Thomspon (Lord Kelvin) in <ahref="beetroot_to_p_lions_es.html#1867">1867</a> at the University of Edinburgh.</p>
<p>If you like a drink, then a Klein bottle is not a recommended receptacle. It may look vaguely like a bottle, but it doesn't enclose any volume, which means that it can't actually hold any liquid. Whatever you pour "in" will just come back out again as the Klein bottle is an example of a non-orientable surface. It has no "inside" and no "outside", instead, just <em>a</em> side.</p>
<p>Knot theory is a field of mathematics that studies the <ahref="beetroot_to_ciao.html#topology">topology</a> of knots.</p>
<h2id="unknot"name="unknot">Unknot</h2></a>
<p>The unknot, or <i>torus</i>, is the first type of mathematical knot listed in knot theory. Intuitively, the unknot is a closed loop of rope without a knot in it.</p>
<p>The unknot, or <i>torus</i>, is the <ahref="please_to_foshan.html#tait">first type</a> of <ahref="beetroot_to_p_lions_es.html#mathematicalKnots">mathematical knot</a> listed in knot theory. Intuitively, the unknot is a closed loop of rope without a knot in it.</p>
<p>Mathematical knots, or knots which are studied in the field of knot theory, are based on the embedding of a circle within three-dimensional space. They are different from the usual idea of a knot, that is, a string with free ends. Therefore, mathematical knots are (almost) always considered to be closed loops.</p>
<p>Ethernet was developed at Xerox PARC (Palo Alto Research Center) between 1973-1974. The idea was first documented in a memo written by Robert Metcalfe, who <aclass="outOfNetworkLink"name="outOfNetworkLink"href="https://www.youtube.com/watch?v=g5MezxMcRmk"target="_blank">named it</a> after the <ahref="please_to_foshan.html#theAether">luminiferous aether</a>, a substance that was once thought to exist as an "omnipresent, completely-passive medium for the propagation of electromagnetic waves."</p>
<p>While topology is the study of forms that are preserved under deformations, such as stretching, crumpling or bending (but not tearing or gluing), graphology is the study of diagrams that represent these forms in a 2-dimensional space. Often 3-dimensional topologies can be collapsed into <ahref="...html#theSevenBridgesOfKonigsberg">2-dimension graphology studies</a>.</p>
<p>While topology is the study of forms that are preserved under deformations, such as stretching, crumpling or bending (but not tearing or gluing), graphology is the study of diagrams that represent these forms in a 2-dimensional space. Often 3-dimensional topologies can be collapsed into <ahref="beetroot_to_ciao.html#sevenBridges">2-dimension graphology studies</a>.</p>
<p>GPS (Global Positioning Service) is a satellite radionavigation system owned by the United States government, and operated by their air force. The system uses a process of <ahref="wijnhaven_to_foshan.html#trilateration">trilateration</a>, whereby at least three satellites are needed to determine position.</p>
<p>As I walked from server to server, I began to notice lines. <ahref="beetroot_to_wijnhaven.html#contrails">Contrails</a> in the sky, <ahref="ciao_to_wijnhaven.html#tyre_tracks">tyre marks</a> on bicycle lanes, overhead <ahref="p_lions_es_to_wijnhaven.html#tram_lines">tram lines and their corresponding tracks</a>...<p>
<p>"The map is a help provided to the imagination through the eyes"<br>
—Henri Abraham Chatelain</p>
<p>A map is not the territory it represents, but, if correct, it has a <ahref="ciao_to_wijnhaven.html#abstractionLayers"><em>similar structure</em><a/> to the territory, which accounts for its usefulness.<br>
<p>A map at a 1:1 scale would be of no use to a traveller wishing to simply get from A to B in the easiest possible way. A 1:1 map <em>is</em> the territory, and is therefore redundant.</p>
<p>Therefore, without some degree of <ahref="ciao_to_wijnhaven.html#abstraction">abstraction</a> (beginning with scale), maps would be useless. A map shows not only locations, but also concepts; marking what is public or private property is a way of mapping the world, and determining the difference between travel and <ahref="beetroot_to_wijnhaven.html#taz">trespass</a>.</p>
<h2>Taking a line for a walk</h2>
<p>I'm making drawings by walking and tracking myself over <ahref="please_to_wijnhaven.html#gps">GPS</a> using an app on my phone. I walk door-to-door between the geographical locations of our network. The app I'm using displays my path as a jagged line, alongside information about the distance, altitude, speed, pace and time elapsed. When I reach my destination I save the walk, export it as a .gpx file to my computer, and then load it into software for plotting geospatial information. In the graphic interface of this software the track points are connected with a series of lines that link them together into a route.</p>
<p>This is a visualisation of my movements, abstracted into a line for quick and easy representation. Ask someone to draw a route from A to B and they'll probably draw a similar series of lines, bending where you should make a left or right turn. The most direct route is a completely straight line (as the crow flies) but this is hardly useful to the average pedestrian. Utility here is predicated by a delicate balance between a certain level of detail, and a certain level of abstraction.</p>
@ -24,8 +37,8 @@
<p>As I walk from homeserver to homeserver, I'm relying on a mental mind-map of Rotterdam, one formed over the past 7 months that I've been here. If I follow my nose, I can usually end up in the general vicinity of where I'm supposed to be. Eventually I need to use an actual map to pinpoint my targeted destination, but for the most part I enjoy the increasingly rare occurence of being lost for a moment.</p>
<p>If I walk enough routes, this will eventually form a map of Rotterdam, though one reduced down to just simple lines against a blank background. These represent areas that are accessible on foot, most likely the streets and footpaths.</p>
<p>The line here meanders slightly, perhaps this is where I crossed the street? I'm still in the habit of walking on the left side of the road, following the direction that traffic moves in Australia. Sometimes I notice that oncoming pedestrians can't always tell which way I'm going to pass them on the pavement; even on foot we still follow the flow of traffic.</p>
<p>If you know Rotterdam, perhaps you can identify what the <aid="straightestPart"name="straightestPart">straightest part</a> of this path represents: the Erasmusbrug. It's easy to guess why; the bridge is a high traffic area, and it's not so easy to wander off the path here, or to cross the lanes of traffic going over it. There are few other ways to cross the Maas River apart from going over a bridge. I suppose it could be crossed by boat, and there is also the subterranean Maastunnel further up the river. Or perhaps you might be brave enough to swim. But any which way one crosses the river (and assuming your GPS tracking device doesn't end up in the drink), the path represented by tracking software would reveal itself as straight lines between the snapshots of your location. On this particular day the bridge was raised; trams stopped mid-way, and their drivers stood outside, smoking in a cluster. Impatient joggers ran on the spot, the rest of us huddled while we waited for the bridge to lower again.</p>
<p>If you know Rotterdam, perhaps you can identify what the <aid="straightestPart"name="straightestPart">straightest part</a> of this path represents: the Erasmusbrug. It's easy to guess why; the <ahref="beetroot_to_ciao.html#sevenBridges">bridge</a> is a high traffic area, and it's not so easy to wander off the path here, or to cross the lanes of traffic going over it. There are few other ways to cross the Maas River apart from going over a bridge. I suppose it could be crossed by boat, and there is also the subterranean Maastunnel further up the river. Or perhaps you might be brave enough to swim. But any which way one crosses the river (and assuming your GPS tracking device doesn't end up in the drink), the path represented by tracking software would reveal itself as straight lines between the snapshots of your location. On this particular day the bridge was raised; trams stopped mid-way, and their drivers stood outside, smoking in a cluster. Impatient joggers ran on the spot, the rest of us huddled while we waited for the bridge to lower again.</p>
Simon Browne
6 years ago
