When I read Alexander's The Nature of Order, it immediately struck me that the fifteen properties he lays out may not be entirely elementary, just as the 253 patterns in A Pattern Language turned out to be composites or special cases thereof.
If we imagine an object or built space as an information system, then we can analyze the fifteen properties in those terms:
Below is the list of properties laid out in Volume 1 of The Nature of Order, grouped first by aspect of information processing, then by the order they appear in the book. I should preface that is a sketch, literally banged off in a few minutes. I may return to fill out the descriptions eventually.
Furthermore: if you aren't familiar with the architect Christopher Alexander, and more specifically his twelve-pound magnum opus, this document may not mean as much to you as it otherwise would.
Information is, by definition, the difference that makes a difference. In order to encode information, you need contrast—you need differentiation. You also need meta-information about the information-bearing medium itself, as well as its relationship to the surrounding environment.
Information can be compressed by applying rules to the irreducible sample data. Compression affords a greater capacity for inference.
This section was inspired by Schmidhuber's paper, Driven by Compression Progress.
Any information-carrying medium is going to have a channel capacity. Often, controls on the channel capacity need to be imposed from the outside to prevent congestion or failure of the medium.
That's it for now. I'll probably come back to this though.