Wikipedia. Some of the questions I've had about the book are right there. Here are some of the big ones:
(Note: This has spoilers for the book if you haven't read it)
Q: Why did the US military launch Operation Screaming Fist if they knew about the Russian EMP weapons?
A: The Russian military had learned of [Screaming Fist] and installed defenses to render the attack impossible, but the military went ahead with Screaming Fist, with a new secret purpose of testing these Russian defenses.
Q: How is Peter Riviera able to create the illusions they see around him?
A: Peter Riviera is able to project detailed holographic illusions with the aid of sophisticated cybernetic implants.
Q: If Wintermute and Neuromancer were both created by Tessier-Ashpool, why are they split into two halves?
A: Wintermute...is one-half of a super-AI entity planned by the family, although its exact purpose is unknown. The Turing Law Code governing AIs bans the construction of such entities; to get around this, it had to be built as two separate AIs.
Q: What exactly is the mission Case and his team are hired to do?
A: Wintermute (housed in a computer mainframe in Bern, Switzerland) was programmed by the Tessier-Ashpool dynasty with a need to merge with its other half - Neuromancer (whose physical mainframe is installed in Rio de Janeiro, Brazil). Unable to achieve this merger on its own, Wintermute recruited Armitage and his team to help complete the goal. Case is tasked with entering cyberspace to pierce the Turing-imposed software barriers using a powerful icebreaker program. At the same time, Riviera is to obtain the password to the Turing lock from Lady 3Jane Marie-France Tessier-Ashpool, an unfrozen daughter clone and the current leader of Tessier-Ashpool SA. The password must be spoken into an ornate computer terminal located in the Tessier-Ashpool home in Villa Straylight, and entered simultaneously as Case pierces the software barriers in cyberspace - otherwise the Turing lock will remain intact.
Q: How did Wintermute turn Corto into Armitage?
A: It is revealed that in the past, Wintermute had originally contacted Corto through a bedside computer during his convalescence, eventually convincing Corto that he was Armitage.
Q: How did Case escape from Neuromancer's virtual reality prison?
A: Case manages to escape flat-lining inside the construct by choosing of his own free will not to stay.
Q: What's the significance of Case hearing Dixie's laughter in the matrix?
A: In the matrix, Case hears inhuman laughter, a trait associated with Pauley during Case's work with his ROM construct, thus suggesting that Pauley was not erased after all, but instead worked out a side deal with Wintermute/Neuromancer to be freed from the construct so he could exist in the matrix.
Q: Why does Case see himself, Linda Lee, and Neuromancer together at the end?
A: The implication of the sighting is that Neuromancer created a copy of Case's consciousness when it previously tried to trap him. The copy of Case's consciousness now exists with that of Linda's, in the matrix, where they are together forever.
Man, how'd I miss all that.
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