Even before the Overlords came to Earth, the sovereign state was dying. They have merely hastened its end: no one can save it now--and no one should try.
This quote is said by Stormgren, in Chapter 3. It makes plain an important idea in Childhood's End: that the Overlords, while certainly speeding up the process, have not done anything that humanity would not have eventually done itself. The existence of sovereign states, Stormgren knows, are the main source of conflict in the world.
"All political problems," Karellen had once told Stormgren, "can be solved by the correct application of power."
"That's a cynical remark," Stormgren had replied. " ...it's a little too much like 'might makes right.'" In our own past, the use of power has been notably unsuccessful in solving anything."
"The operative word is correct. You have never possessed real power, or the knowledge to apply it."
This discussion, from Chapter 6, highlights a somewhat flawed argument by Karellen and the Overlords. Stormgren's object is sound; Karellen's statement that all political problems can be solved through the "correct" application of power does sound like "might makes right." When Stormgren points this out, Karellen responds by defining it as a difference of efficiency—by "correct," Karellen means "efficient" and with the least amount of damage to the most people. But the flaw that Stormgren has recognized is that Karellen is still making a value judgment: he will put the Overlords' considerable power behind whatever he thinks is the "correct," or rather, the "right" action. This means that the Earth is subjected to whatever the Overlords think is "right." Essentially, Karellen sidesteps a good objection by Stormgren, ignoring the question of the Overlords' ultimate plans for Earth.
The stars are not for man.
This quote is from Karellen, in Chapter 14. Karellen gives it in a press conference, after showing the reporters a holographic projection of the galaxy, with its "thousands of millions of stars," and asking them, rhetorically, whether they thought mankind could handle so many worlds. This statement is later agreed with by Jan Rodricks, the human who so wanted to get into space. The reason the statement is important is because it is so out of line with all of Clarke's other writings. When the paperback edition of Childhood's End came out, Clarke added a warning in the front: "The opinions expressed in this book are not those of the author." One of the "opinions" he is referring to is undoubtedly this one. Almost all of the rest of Clarke's fiction supports the idea that Earth is just a frog pond where humanity is currently growing and developing but will eventually leave by reaching out to the stars.
So why, in this book, does Karellen say, "the stars are not for man?" This may be the result of the mythological and folkloric framework that Clarke used as the basis for Childhood's End. More than most of Clarke's novel, Childhood's End draws on allegory: the Overlords are Satan and his rebel angels, the Overmind is a God-like figure, and the assimilation of the children into the Overmind is the Rapture and Armageddon rolled into one. Saddled with his conception of a science fiction version of Armageddon, Clarke is almost forced to have the Overlords shut heaven off to mankind.
The world's now cold, featureless, and culturally dead; nothing really new has been created since the Overlords came ... there's nothing left to struggle for, and there are too many distractions and entertainments.
This quote is from Chapter 15, where a pitchman tries to convince George Greggson and his wife Jean to join the New Athens colony. It is the strictest and most concise warning of what may await humanity if a utopia were ever to be created (unlikely to happen in the real world any time soon, without the deus ex machina of a benevolent alien invasion). Since Thomas More introduced the idea in the Enlightenment, many philosophers have rejected the notion of a utopian society as completely imaginary: an idealistic, abstract idea. Childhood's End gives the reader a glimpse into what such a society might look like, were it ever to exist—and the results are not encouraging. Clarke's conception of utopia might differ from a more modern one now. A modern conception of utopia would probably involve people working on renewable resources, such as farming, and everyone would probably live on, at least, a slightly lower level of modernity. But in the 1950s, Clarke's conception of utopia meant that everything was industrialized: food, clothing, shelter, etc. are produced in factories and available to anyone who wanted it. It is questionable whether the Overlords' utopia would have been sustainable without the Overlords' frequent supply ships bringing new resources to Earth.
In any event, the notion that artistic achievement would begin to decline in a utopia, while entertainment becomes increasingly important, is probably a very accurate prediction. Something similar has happened in history before when a large number of people are relatively happy. Rome lost its sense of society in increasingly violent gladiatorial games. Even Americans, in the second half of the twentieth century—and particularly after the end of the Cold War—turned increasingly to entertainment as a way to get along with everyday life, which lacked the hardships and struggle of their ancestors. In its predictions, the utopia of Childhood's End has much to say to modern America.
For all their achievements ... for all their mastery of the physical universe, his people were no better than a tribe that had passed its whole existence upon some flat and dusty plain ... yet, Karellen knew, they would hold fast until the end: they would await without despair whatever destiny was theirs. They would serve the Overmind because they had no choice, but even in that service would not lose their souls.
This quote is from the end of Chapter 24, as Karellen watches the end of Earth. It gives an almost noble and spiritual coda to the plight of the Overlords, and also to that of humanity. There is an implication that in the process of joining the Overmind, the children of the last generation of humanity "lost their souls," whereas the individualistic Overlords still retain theirs. While Karellen may feel a sadness that his race is incapable of making the same leap that he has seen so many other races make, it is debatable whether Karellen wishes that the Overlords could join the Overmind in particular. The Overlords may hope to discover the Overmind's secrets and perhaps pose a challenge to it, or find a way to make the leap themselves into some higher form, without the Overmind's help.
Regardless of Karellen's intentions, there is a certain tragic, admirable nobility in the plight of the Overlords, and it is questionable who is to be admired: the humans who lose their individuality in the Overmind, or the Overlords, who live on to struggle against their own doubts, passions, and each other.