<p>The map I've been making by tracking myself over GPS does not display scale, or landmarks, or street names. It doesn't show which way is north, south, east or west.The map I've been making by tracking myself over GPS does not display scale, or landmarks, or street names. It doesn't show which way is north, south, east or west. I use geographic information system software that allows me to accurately position all the .gpx files I upload from my GPS tracker app on my phone.</p>
<p>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 knotted at places, representing social interactions, financial transactions, backtracking, and places where the GPS signal was obscured, or confused by bouncing off buildings.</p>
<p>The drawings I've been making by tracking myself over GPS 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>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>In a vector graphics editor I begin to simplify the line, sliding a scale that removes anchor points and unravels the knot into a completely straight line. As I do this, I notice smaller knots that were not so visible at the scale I saw them at originally.</p>
<p>I begin to simplify the line, sliding a scale that removes anchor points and unravels the knot into a completely straight line. As I do this, I notice smaller knots that were not so visible at the scale I saw them at originally.</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">klein worms</a>. When unravelled, the knot is <ahref="please_to_foshan.html#unknot"target="_self">a continuous loop</a>, and the links (edges) and the nodes (vertices) are the same.</p>
<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>
<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>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>
<divclass="indent">
<p><em>All viewpoints are allowed here, but please be respectful. This is a subreddit, not a court of law. Please don't badger users into providing concrete evidence. Short of flying us all up into the atmosphere with an evidence bag, you probably won't get it.</em></p></div>
<p>In early modern physics, the AEther (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 ether) was believed to be an invisible space-filling substance or field that was a transmission medium for electromagnetic or gravitational forces.</p>
<h2>Tait's Tabulature of Knots</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. while conducting experiments with a machine that blew smoke-rings. Tait observed that the rings had a regular donut-like form, which he hypothesised was the result of atoms within them bonding through the Ether.</p>
<p>1867<br>
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 experiment to test the German scientist 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 waft from a hole drilled in its front. Tait describes them "like solid rings of India rubber". His theory is that each smoke ring is structured around knots in the ether, a space-filling substance that was believed to transmit matter. Tait begins to tabulate possible forms of mathematical knots, contributing to the mathematical field of knot theory.</p>
<h2>Knots</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 experiements he conducted with William Thomspon (Lord Kelvin) in 1867 at the University of Edinburgh.</p>
<aid="knot"name="knot"><h2>Knots</h2>
<p>A knot is an entanglement, an intentional complication in cordage.</p>
<h2>Knot Theory</h2>
<p>Knot theory is a field of mathematics that studies the topology of knots.</p>
<h2>Unknot</h2>
<a id="unknot"name="unknot"><h2>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>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>
<h2>Knotworks</h2>
<p>Knotworks are visualisations of network topologies which use mathematical knots to represent a collapsing of the distinction between node and link. Just as a knot is a complication in which the tangle can conceal parts contained (as in <ahref="readings/cybernetic_guerilla_warfare.html"target="_blank">klein worm topologies</a>), unravelling the knot reveals that it is homeomorphic to a continuous link. The link and the node are the same, unravelled.</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>Somewhere above me, satellites trilaterate my position and decide where I am on the globe. They take snapshots and these are intermittently uploaded to a remote server - I don't know where exactly - which serves this data to the software on my phone.</p>
<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 a road? I'm still in the habit of walking on the left side of the road, following the direction that traffic moves in Australia. 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 dominant flow of traffic.</p>
<p>If you know Rotterdam, perhaps you can identify what the straightest part 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 also few other ways to cross the Maas River. It could be crossed by boat, and there is also the subterranean Maastunnel further up the river. Or perhaps swim. But any which way one crosses the river, the line represented by GPS tracking software would reveal itself as straight lines between the snapshots taken as the scale increased. On this 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>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 straightest part 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>
