On Tue, Jun 23, 2015 at 11:44 AM, J. Andrew Rogers <[email protected]> wrote: > > 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) >... > 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. >... > 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). > Andrew
I think Data types with no meaningful order can be difficult but it is not impossible to create things like keyed (I can't remember what the data structure is called) indexes and even more elaborate indexes as needed. But this can become a more serious issue when you have to have a lot of specialized indexes. That is what I was getting at when I mentioned hyperspace in a previous message. We cannot assume that every relation between conceptual objects can be categorized by kind and then found to have similar effects between every other categorized conceptual objects. You have to expect that there would be many different kinds of relations that existed (or worked) between some conceptual objects but not others (even when they shared many of the same kinds of features.) As the number of these build up they become more difficult to use and their potential usefulness to other conceptual objects can be obscured. (For example, we would like our (future) programs to be able to examine metaphorical similarities without having to first do some extended and elaborate search.) In logic I noticed that intersection and union can become exponentially difficult to encode but I am working on that and think that I might be able to come up with the basis for a few new tricks. (For real). I can intuitively see that data types where intersection and equality are not equivalent could be a problem but I am not sure what you mean. Since you have derived more than one example of bad-computer science thinking from relational database concepts I am guessing that this has something to do with database processing. So searching on a constraint can become time consuming? But that can be parallelized by minor redesigns. Many computer scientists have thought about expressing topological relationships between data objects. So it is not in itself a new idea that I have never heard of or thought about before. So I am not getting what you are talking about. Jim Bromer On Tue, Jun 23, 2015 at 11:44 AM, J. Andrew Rogers <[email protected]> wrote: > >> 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/303/24379807-653794b5 > Modify Your Subscription: https://www.listbox.com/member/?&; > Powered by Listbox: http://www.listbox.com ------------------------------------------- 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
