<p>Knot theory is a field of mathematics that studies the <ahref="beetroot_to_ciao.html#topology">topology</a> of knots.</p>
<p>Knot theory is a field of mathematics that studies the <ahref="beetroot_to_ciao.html#topology">topology</a> of knots. In mathematical language, a knot is the embedding of a circle in 3-dimensional Euclidean space, R3.</p>
<h2id="unknot"name="unknot">Unknot</h2></a>
<h2id="unknot"name="unknot">Unknot</h2>
<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>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>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>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>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>
<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>
<h2id="takingALineForAWalk"name="takingALineForAWalk">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>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>
<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>
Simon Browne
6 years ago