kakaze wrote: About the cigar butt and beer bottle, I think they don't matter. I think Lu Tze just acted annoyed so Vimes would stop persueing a pointless digression to their conversation.
So why didn't Lu Tzu just tell younger Vimes about Carcer and where to find him easily in the future, and avoid having older Vimes & Carcer being sent back in time and getting Keel killed ahead of schedule?
First, the beer bottle is mentioned only in Sam's first visit, but the beer bottle is just Terry having a small joke, while building up the garden as representative of the pattern of life and history--a point which will become important later. This time the spell in the garden restores Sam to the tranquility to accept the actions of the Monks of History and to accept what has happened and that what he does now matters.
"So what people do matters!" said Sweeper. "People invent other laws. What they do is important! The Abbott's very excited about this.... It means the multiverse isn't infinite, and people's choices are far more vital than they think. They can, by what they do change the universe."
Terry is doing two things with the passage here--one is setting up in a way the fact that the Garden is indeed a Mandala (like he does with the small one he shows Lobsang on the way to Ank-Morpork). Second, he is explaining why it is so important to history that Sam act as Vimes.
Sam is old enough and wise enough to understand and accept the existence of the Monks of History even if he doesn't grasp all the details of what they do. And he knows that what he does as "Keel" will affect how Vimes grows up.
There are two answers to your last question. First, Terry chooses to write the book in this fashion (with the time travel) partially to enjoy telling us about Vimes's younger self and the world 30 years ago. But he also uses this book to stress the importance of decisions and actions. Your question then becomes irrelevant, since there would be no book then.
The fact that the Garden/Mandala begins to move when Sam tosses his cigar butt down in the 2nd visit is a sign that things are changing in the world. The two monks, watching the garden shifting by Sam's action of tossing the cigar butt and ..."felt the fingers of History spreading out and into the world."