> On Jun 22, 2015, at 6:57 PM, Samantha Atkins <[email protected]> wrote: > > I seldom ask this as I usually work at the level of abstractions. But could > you please give some examples of topological relationships that are difficult > to express computationally? I am not sure I follow exactly what you have in > mind.
There are two common cases handled poorly in computer science that are manifestations of topological relationships: - data types with no meaningful order (e.g. graph edges) - data types where intersection and equality are not equivalent (e.g. constraints or geospatial) In other words, “data that is not sortable” and “data that is not partitionable (also not sortable)”. Computing on representations of these data models are infamously difficult to parallelize and scale because there is no relationship-preserving mapping to integers, and traditionally we rely on the sortability and partitionability of integers to scale algorithms. You just cannot usefully represent what are essentially spatial relationships this way. However, both of these types of data models can be trivially embedded in a surface, and while a lot less obvious, you can parallelize computations on the data by manipulating the surface rather than the data directly. For example, the concept of a join in such a representation is closely related to topological homomorphism. Another way of thinking about it: What would data structures and algorithms literature look like if the most primitive data type was a hyper-rectangle instead of an integer? A hyper-rectangle is nothing more than a data type that cannot be represented by less than two integers of arbitrary dimensionality. Some important data types and relationships are of this nature. In this model, an integer is just a degenerate hyper-rectangle (i.e. volume is zero). Cheers, Andrew ------------------------------------------- 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
