Posts tagged with shape
We relate a category of models A to a category of more realistic objects B which the models approximate. For example polyhedra can approximate smooth shapes in the infinite limit…. In Borsuk’s geometric shape theory, A is the homotopy category of finite polyhedra, and B is the homotopy category of compact metric spaces.
—-Jean-Marc Cordier and Timothy Porter, Shape Theory
(I rearranged their words liberally but the substance is theirs.)
prod( factorial( 1/ 1:10e4) ) to see the volume of Hilbert’s cube → 0.
- • the structure group for lengths is
- • the structure group for angles is
- • the structure group for lines is the affine group
- • the structure group for
n-dimensional Euclidean geometry is the Euclidean group
- • the structure group for oriented 2-spheres is the (special) orthogonal group
(I rearranged his text freely.)
This is trippy, and profound.
(Alternating meaning it goes + − + − + − + − ……. Multilinear meaning linear in every term, ceteris paribus:
In conclusion, mathematics proves that Size is the same kind of thing as Angle
Say whaaaaaat? I’m going to go get high now and watch Koyaanaasqatsi.
Logic, like mathematics, is regarded by many designers with suspicion. Much of it is based on various superstitions about the kind of force logic has in telling us what to do.
First of all, the word “logic” has some currency among designers as a reference to a particularly unpleasing and functionally unprofitable kind of formalism. The so-called logic of Jacques François Blondel or Vignola, for instance, referred to rules according to which the elements of architectural style could be combined. As rules they may be logical. But this gives them no special force unless there is also a legitimate relation between the system of logic and the needs and forces we accept in the real world.
Again, the cold visual “logic” of the steel-skeleton office building seems horribly constrained, and if we take it seriously as an intimation of what logic is likely to do, it is certain to frighten us away from analytical methods. But no one shape can any more be a consequence of the use of logic than any other, and it is nonsense to blame rigid physical form on the rigidity of logic.