> On Jun 16, 2015, at 8:35 PM, Logan Streondj <[email protected]> wrote: > > I've always had trouble understanding graphs, lines and boxes. > What are these topologies? can they be expressed in text?
Think of it as relationships between shapes embedded in space. Humans have an intuitive conceptual understanding of relationships in Euclidean 3-space because that is the environment we live in. An interesting and well-known problem in ordinary databases is that people generally have no idea how to represent spatial relationships such that a computer can understand it the way a human does. Consequently, spatial relationships in data can only be interpreted correctly by other humans. We assume that shared context in the encoding of the representation. But again, a lot of this is because the vast majority of software can’t represent topological relationships, only graph-like relationships. Humans have the ability to represent and reason about shapes in 3-space built-in. It is an impedance mismatch. There are some interesting theoretical requirements that make this much harder to solve than it sounds and which are missed by virtually every computer scientist that dabbles in it. You cannot tractably reason about N-dimensional topological relationships in N-dimensional spatial representations. In other words, if you want to reason about the physical world (a 3-space), you actually have to transform that 3-space into a significantly higher dimensionality complex topology, the manipulation of which efficiently produces the expected 3-space results. Your conventional human computer scientist is not accustomed to doing what feels like intuitive, ordinary reasoning about relationships in the physical world by mathematically folding, stretching, twisting, etc an exotic 7-dimensional surface or similar. Nonetheless, it is the only way to do it. That aside, it also has the advantage of naturally being an extremely parallelizable method of computation, even for traditional data models. In principle, you would expect a parallel computational system that is optimized for reasoning about an N-dimensional topological data models to also be effective for topological data models of lower dimensionality and graph-like data models. Not so much for anything else. It might be coincidence, but human reasoning capabilities look like what you would expect from a computer optimized for 3-space topological data models. ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
