Parallel-worlds tied to The Dark Tower -- Jack Sawyer’s adventure

Computational complexity of this novel and the background: Very high. I could not figure out what is actually going on and what is still hidden, by my computational complexity calculation program. (smile)

This book charts the adventure of a young teen boy named Jack Sawyer --- an analogy to the classic Tom Sawyer. The adolescent hero sets out from Arcadia Beach, New Hampshire in a bid to save his mother, who is dying from cancer, by finding an enchanted crystal called "the Talisman." Oh, what a nice wording!!! --- Talisman.

The premise of the novel involves the existence of a parallel world to Earth, called "the Territories"a strange fantasy world with ties (though these ties did not exist at the time of publication) to King’s The Dark Tower. Individuals in the Territories have "twinners," or parallel individuals, in our world. Twinners’ births, deaths, and (it is intimated) other major life events are usually paralleled. Twinners can also flip, but only share