PM-Xi

The name of this requested feature is a reference to the infamous APM-Xi and means "PlanetMath cross-index". Whatever its usefulness with qualifying examinations, it should help with finding further reading to complement the treatment of a subject in a textbook.

This feature is an extension of the centralized bibliographic database. Knowing that a certain piece of information is to be found in a book can be of limited use because that might only narrow down the location to one of 500 pages. What PM-Xi would do would be to pinpoint the exact location so that one does not have to fumble around looking for needles in literary haystacks.

The core of this new feature would be an extensive database composed of records. Each of these records would consist of four components:

1. There would be an identifier of a record in the centralized bibliographic database corresponding to the work within which a fact is to be found.
2. There would be a specification of exactly where in that work the fact in question is to be found. Examples might be "theorem 17" or "example 42" or "chapter 4, section 3".
3. There would be a links to PM entries which discuss this fact.
4. There would be a place for comments. In this field, one could note observations such as that the version in the PM entry is more or less general that that in a certain reference or that a book uses different notational conventions than the PM entry.

This feature could be used in several different ways.

• If one is reading a book and has a hard time understanding something, one could look for other discussions of the item.
• A cross index would expedite the work of identifying lacks in the coverage of PM by comparing it with various works.

Looking back a year later, I see that the form of this proposal is too focussed on books and PM encyclopaedia, hence should be redone in a manner which is not biased towards certain works. Here is an updated version of the proposal:

The basic notions underlying this database are factoids and loci. A factoid here is a piece of knowledge (specifically mathematical knowledge for the current project, but one could just as well do a similar cross-index for physics, bicycle repair, gardening, or any other subject) such as the definition of a term, the statement of a theorem, a proof of a result, etc. A locus is a portion of a work which mentions a single factoid.

The cross-index can be implemented as two tables: a factoid table and a locus table. The contents of the table would be organized in columns as follows.

Locus Table

• Genre — This column describes the type of work in which the item occurs, e.g. book, journal article, web page, thesis, lecture notes, conference proceeding, etc.
• Work — The particular work in which the item occurs.
• Location — Am indication of exactly where in the work to find the item. The exact form of data in this slot will depend upon the genre. As far as feasible, this should be in a form which enables a computer to select and highlight the locus in question from a digital version of the work.

Factoid Table

• Metadata — These fields will contain metadata describing the factoid in question. As a starting point, one can take the metadata fields attached to PM entries.
• Loci — A listing of the loci which mention this factoid.