Looking for titles/authors of two books I read long ago

About ten years ago I read two books which I remmeber to be very good, but I have completly forgotten both the titles and the authors of them. If anyone regonices my memoires of the plots, please tell me where they are from.

set in an post-apocalyptical world, precumably earth after a mayor biotech meltdown
The heroine is of a genetically altered matriarcal amazon people, with livespans of about 200 years. They pay tribute to a people living in airships. Somehow she becomes the property of an ancient very powerful man living on one of the zeppelins, somehow escapes and finds some functional remains of very advanced AI/robotics, and starts a process of reindustrializing the world.

set in a not to distant future, earth
A strange meteorite starts cirkeling earth. When investigators are found the find a "singularity" incide the meteorite. This involves the use of a device which measures variations in mathematical and physical constants, among them pi. The investigators then somehow travels along it and find a society from the future living on a city somehow conected to this singularity. The inhabitants of this city are the decendants of man kind, but quite different. As they die they are loaded into cyberspace, and come back to the physical world a limited number of times, in whatever shape suits them. Some of them were the flags of ancient countries (the US, the Soviet Union etc) as badges to show their heritage.

Those descriptions are most probably wrong somehow, it was as I said about 10 years since I read them. If anyone does regonice them, pelase help me!

/Erik Ekengard
the second book sounds very much like Eon by Greg Bear
heres some of the major points i remember. see if they match with what you recall:
-Set during the cold war, or a future of it.
-there was a nuclear standoff on earth while researchers occupied The Stone
-Their were 7 chambers in the asteroid, the last one bigger than the exterior of the asteroid and acutally infinite. This function employed 'the singularity'
-The society in the asteroid, or at least on of their cities, was called 'Thistledown'. They were divided into two sects, the Geshels and The Naderites.
Im positive the second book you described is Eon. I read it just last year and its fresh in my mind. There is a sequel called Eternity. i began to read it, but it didn't have the flare that Eon had.
Yah, Eon was a great read, the concepts way ahead of their time. As to the first book you explained, I cannot help. But im positive on this one.