I've posted an expanded version of my CI Days talk on Google docs. I'd recommend looking at the speaker notes (click "actions" on the bottom left) since I won't be narrating it in person.
The presentation is an attempt to describe, somewhat formally, how PhiloLogic is capable of performing as well as it does. This comes from spending three years learning how Leonid's search core works, and attempting to extend and elucidate whatever I can. It's also the intellectual framework that I'm using to plan new features, like search on line and meter position, metadata, joins, etc. Hopefully, I can get someone who's better at math than I am to help me tighten up the formalities.
Basically, I refer to the infamous OHCO thesis as a useful axiom for translating the features of a text into a set of numerical objects, and then compare the characteristics of this representation to XML or Relational approaches. I'd love to know how interesting/useful/comprehensible others find the presentation, or the concept. What needs more explanation? What gets tedious?
If you look at the speaker notes, you can see me derive a claim that PhiloLogic runs 866 times faster than a relational database for word search. Math is fun!