[geeks] History book suggestions?

[nate at portents.com]

Hey folks,

I was wondering if any of you had any suggestions on good history books. 
Ideally, I could find one volume (or set of volumes) that would cover the
last 5000 years of world history as a systemic whole (rather than break
things down into the artificially discreet regions we still divide the
world into), but that's not how people are writing books yet.  So I figure
the next best thing would be to get some books on Europe, Central Asia,
and China/Japan.  What I do know has come from my studies in Art History
and a few other basic history courses I've taken (most of which have been
American history), but since I've also lately taken an interest in the
philosophy of religion, I've found that my history background is lacking
in a larger, more comprehensive world perspective.

Ideally, the books would also have minimal western bias, and it would also
be great if I could roughly interleave reading them so as to create that
world cultural-historical perspective I desire.  Books I've initially
isolated in my search include:

"The World System: Five Hundred Years or Five Thousand?" by Gunder Frank
"Europe: A History" by Norman Davies
"A Brief History of Chinese and Japanese Civilizations" by Conrad
Schirokauer, Miranda Brown, David Lurie, Suzanne Gay
"The Empire of the Steppes: A History of Central Asia" by Rene Grousset
"A History of Inner Asia" by Svat Soucek
"A Peace to End All Peace: The Fall of the Ottoman Empire and the Creation
of the Modern Middle East" by David Fromkin

Anyone have any feedback on these books, or suggestions of their own?

Thanks,
Nate