From MathWeb

Notes & Queries

Dear Jon Awbrey,
welcome to the MathWeb community! For your first steps in this wiki, you may want to have a look at our help page or just start browsing from a central topic. You are invited to contribute content about your fields of interest or your projects, and don't hesitate to ask questions – for example, on my “discussion” page, or on the discussion page of any topic you are interested in.
Best regards, Christoph 15:33, 12 September 2007 (CEST)

JA: Thanks, it looks interesting. Jon Awbrey 04:44, 14 September 2007 (CEST)

Sample documents

Dear Jon, you may have noticed that I tagged your documents as "sample documents". With the admins of this wiki, we had a discussion about whether we should support mathematical research (as opposed to supporting research in mathematical knowledge management) in this wiki and decided to treat documents about mathematical theories as part of a test corpus that can be used to evaluate knowledge management tools. If you think of a collection of properly annotated mathematical documents in this wiki, together with the import/export features, this can (hopefully) develop into something really beneficial :-) Best, Christoph 12:20, 18 September 2007 (CEST)

JA: I think I grokked the orientation of the project well enough, at least, to a first approximation. Most of my research for the past 25 years has been directed toward what I eventually came to call "Inquiry Driven Systems" 1, 2 and "Differential Logic", more like two facets really of the same subject. The first is very much a process-oriented, systems-theoretic approach to knowledge development in general, including mathematical knowledge as a special case. But integrating the declarative or logic-based representation of knowledge with the dynamic or systems-theoretic study of knowledge evolution over time requires the development of specific mathematical tools tailored to that purpose. Of course, that specialized methodology always rests on more basic materials from logic and mathematics. That's about as tersely as I've ever said it, but I hope that all of this becomes clearer as the content accumulates. Thanks for the interest, Jon Awbrey 22:00, 18 September 2007 (CEST)

Sounds interesting; I should have a more detailed look at it. I like the idea of self-referentiality, that is, if your documents could give a theoretical background for knowledge management and at the same time serve as test cases for knowledge management, that would indeed be nice. Christoph 10:51, 19 September 2007 (CEST)

JA: This is what I rubricize under the theme of "Inquiry Into Inquiry". It is a ground-breaking observation of Charles Sanders Peirce that the process of inquiry has a (benign) cyclic or recursive character, bottoming out only with the very simplest forms of the three basic types of inference involved in it, namely, Abductive, Deductive, and Inductive reasoning. See Inquiry for the elements. Jon Awbrey 18:38, 19 September 2007 (CEST)