Wednesday 18 January 2023

Shape of the labyrinth

Linear algebra is a most beautiful thing. Some mathematical number crunching turned my list of measured distances in a nice list of coordinates (in km): 

Now, it is important to keep in mind that the list of distances is invariant to any translation or rotation of these coordinates. In other words, you can shift the origin of the coordinates to any point you want, for example center it on the gate. You can also rotate everything however you want, for example to have the line between the gate and "site 0" correspond to north direction on the map. So, the numbers themselves matter less than the relation between them. This spatial relation is shown by visualizing the sites in a three-dimensional plot (again, coordinates in km):

Note that the labels have been given by capsuleers exploring the place, without knowledge of the spatial layout of the labyrinth. The rooms of the labyrinth are almost laid out on a plane. But a two-dimensional map can not get the distances right, the 3D map does (to within 20 km, i.e. an error not visible on the scale of the plot), proving that the sites are not exactly on a plane. The holy rock and the entrance gate are "highest". There's an upper level, with sites 3,4,8,9 and a lower level with the other sites.

What is already clear about the connections between the sites, is:  

  • the sites are not always connected to the closest nearby sites. Although site 0 is indeed connected via ancient warp portals to 6,4,1,2, for example site 5 is connected to 1,4,7,8.
  • the orientation of the warp gates on the octagon of gates is not related to the orientation of the connections in real space (this could also be seen from the direction your ship warps to).

These data hold more mysteries, I am certain of it. There is no obvious glaring hole in the labyrinth that would hint of a hidden room, but perhaps I need to play more with the visualisations, and turn this thing around in my head.