Novel about two connected worlds: one ordered and Sci-Fi-based, one chaotic and Fantasy-based

I read this novel in 2007 or 2008. The story concerns two women, one from each world. The sci-fi world is divided up into castes, and the woman from here is from a high caste, but not the top. I think negotiator or diplomat?

The fantasy world is very fantastic, so much so that one end of it consists of mountains that extend forever, getting higher and higher as you go. For a long time this world did not even have consistent years, with months (as measured by full moon to full moon) taking longer or shorter periods randomly. Also, you only got a surname if you were immortal. Eventually, “contact” with the sci-fi world stabilized time and brought a consistent year. This is such a strong theme that the characters themselves remark that their world seems built to prevent humans from ever developing the idea that Nature has consistent laws that can be studied.

The descriptions of magic here are quite detailed, e.g. a wizard builds a reversed wizard’s tower (essentially a shaft into the ground) and learns a language that exists specifically to practice thinking backwards in time, in order to become deliberately smeared across time.

The last specific thing I remember is that the woman from the fantasy world is given a ring and told to never give it up. A spell is cast so that it cannot be taken from her unless she deliberately chooses to relinquish it, no matter what is done to her body.