As for what experimental theology was, Lyra had no more idea than the urchins. She had formed the notion that it was concerned with magic, with the movements of stars and planets, but that was guesswork, really. Probably the stars had daemons just as humans did, and experimental theology involved talking to them. Lyra imagined the Chaplain speaking loftily, listening to the star-daemons' remarks, and then nodding judiciously or shaking his head in regret. But what might be passing between them, she couldn't conceive. - Page 35 (in the black-covered hardback 3-in-1 book), Chapter 3 Lyra's Jordan
It makes me wonder whether Lyra actually fully understood the nature daemons, and therefore other people in L-world might not understand it either. You'd expect Lyra to know if others did, as it's the kind of thing you'd expect to just be inherently known due to the fact that daemons are such an important factor in L-world.
Or maybe it's just that the nature of stars is not understood, which would also surprise me, as I kinda thought that the level of technology in L-world, while not high, would at least have progressed to telescopes or something of the sort if something as complex as the alethiometer was able to be made.
Meh, I don't know. I just found it interesting really, like I said. Discuss it at your leisure
I really wish I had my book with me right now... 
I was very much into astronomy then and still am now, though not as much. I also knew my 
