We finally see how to get a k-dimensional geodesic manifold through a point in a q-manifold. We just had to rely more heavily on the geodesics. The key is not only to look at (k+1) geodesics of length 1 but of (k+1)! directions and go to length 2. This produces a spider and encodes the manifold locally. The spiders all fit together. The manifold is constructed in the discrete Grassmannian.
Some of the footage at the beginnin and end were photographed in Woburn and Medford and over the Fells.
