And, whoosh, we're away from the Neanderthals, and into the future (that is, the future from the standpoint of when the book was written in 1968. The year here is actually in the 1990s, supposedly. Only in the 1990s there was no regular shuttles up to the moon. And there was the Internet. So Clarke didn't get it quite right. But just ignore those temporal anomalies, please, and get on with the story.)
And, whoosh, we're away with the Neanderthals, and into the future.
Dr. Heywood Floyd is the protagonist now. He is on a plane to Florida.
He is really, truly, a boring nothing. Why we have to spend time with him Shmoop does not know.
The future seems filled with boring people, actually. Sort of a dystopia in that regard.
Anyway, he's excited by Florida.
He's over the space station and talks about old rocket series. Main point here is that people have space flight.
He gets off the plane, and the press asks him why there's been a blackout of news from the moon.
So now you know that there are folks on the moon, and that something has happened there, and that boring Dr. Floyd knows, and that he's top secret and important. Also boring.
There's a quick sketch of the political situation. The population has increased by a lot; China is dangerous.
It's basically an extension of the Cold War between the U.S. and Russia which was going on at the time the novel was written, but with China replacing Russia as the U.S. antagonist.
Clarke actually calls the Chinese "inscrutable", which is a longstanding and racist stereotype. The future is different, but some things don't change.
Anyway, the Chinese are offering to sell other countries nuclear warheads, but the American coalition doesn't know why.
But that's not the problem of our boring hero at the moment.
Instead, he's aboard a plane/ship to take him to the Moon.
It's much like a commercial airline flight; there's a stewardess, cabin announcements, etc.
The only difference is that Heywood is the only one on the plane.
As he leaves Earth he thinks briefly that he has three children and his wife is dead. This is a feeble attempt to make him seem like a person rather than a narrative device. It is ineffective.
The stewardess tells him she has a fiancé on the Moon, and asks if he can tell her what's wrong, but he won't, because he is strong and silent and manly. Or maybe just a jerk. One or the other.