Introducing Context Spaces
Roman numerals are a terrible way to represent numbers relative to the base 10 arabic numerals we use every day. Have you ever wondered if there could be an even more efficient number system, one which makes current systems seem as shoddy as the old Roman system? Problems like this motivated me to think about a general framework within which to mathematically approach such general information representation questions.
This post is about looking for a universal model of communication - one that’s independent of sequential systems and probabilistic models. I emphasize this independence since a lot of excellent work has already been done on strings, languages (of strings), and information theory. But all of these corpora of known works, while very useful in many cases, do make assumptions about the way information is conveyed which excludes some interesting cases.
Examples of non-sequential data
You can use cell phone towers with triangulation to determine where you are on a map - first generation iPhones used this technique before they got GPS capabilities. We can think of the raw data of a triangulation as a set of 3 known coordinates (the cell towers) along with distances to each. If that data is accurate, there is a unique point on the planet determined by it. Yet there is nothing special about the order of the 3 cell tower positions. This is a data format which can be considered a set of unordered clues, which, taken together, uniquely determine a piece of information...