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*To*: <acad!alce!greg>*Subject*: disps, the rubik's cube, and group theory*From*: Eric Dean Tribble <tribble>*Date*: Mon, 18 Sep 89 19:51:31 PDT*Cc*: <us>, <tribble>*In-reply-to*: <Greg>,17 PDT <8909181710.AA00258@xxxxxxxxx>

A note to skeptics before diving in: General enfilade theory is the basis of Xanadu's technology. By implementing one data-structure that can efficiently index and edit coordinate spaces defined by dsps, we can rapidly accommodate new media and representations. As the underlying principles are worked out in further detail, the implementation is simplified and generalized. The particular coordinate space we should be able to address is that of Directed, Acyclic Graphs (DAGs). If we can handle DAGs, we will use them to address historical trace documents. If positions in the DAG are denoted with turning directions from some root (the home in enclosure terminology), then two distinct points might have two completely different paths connecting them. The turning directions describing each of these paths would be a dsp, and if they happened to be from the root, then they could be considered coordinates in the DAGspace. Note that the use of turning directions for dsps is derived f Wait a minute. A group is a set. The definition of equality between group elements is "they are the same set element". If you use a definition of equality which defines equivalence classes of some set S, then your focus is on the set E of equivalence classes of S, not directly on the set S. E might also be a group. Hmmm. Yes. See my motivation for all this below. In any case, how can the definition of equality be based on the definition of equality?: By induction. Since my definition wasn't an induction, I've come up with a better one. A = B iff A*inverse(B) = I and and we define the identity element I to be unique. I'll continue this later... dean

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