The ending of Timescape really centers on a question: Given these exciting new developments in science, can mankind change for the better? And the answer is mostly yes. Emphasis on the mostly.
The Not-So Awesome Late 1990s
In 1998, we find John Renfrew sitting in his lab, still transmitting his message. He's tired, feverish, and, although he is unaware, his wife has cheated on him with Peterson of all people. Seriously, things are not breaking his way.
Then he receives an odd signal, which he decodes as reading, "ATTEMPT CONTACT FROM 2349 IN TAC" (45.12). Renfrew can't be certain of the message's origins –it might be from the future year 2349, or perhaps 234.9 kilowatt range tachyons—but before he can do anything else, the power goes out.
Without Markham and Wickham to provide assistance, Renfrew knows that "there was no longer even any hope of understanding what had happened" and likens the mysteries of time to "a Sphinx yielding none of her secrets" (45.22). With that, Renfrew leaves his lab with more questions than answers. He decides to live out his life with Marjorie and his children, but the world is in worse shape than before—the only silver lining to this future being that it will never know the horrors of Star Wars: The Phantom Menace in 1999.
Renfrew was unable to change anything. Or was he?
The Much Groovier 1960s
In the year 1963, President Kennedy is shot by Lee Harvey Oswald, but instead of killing the president, Oswald's famed third shot is disrupted by a teenager named Bob Hayes, who happens to be in the book depository looking for a magazine that details Gordon's research on the tachyon messages. Because of Gordon's research, then, President Kennedy lives.
Change has officially happened. President Kennedy survives, and thanks to the publicity of Gordon and Ramsey's experiments, the world will avoid the ecological disasters of Renfrew's time. (Okay, so we can't say this for certain, but it seems very likely.)
But why do the changes in Gordon's time not ripple through the timeline and alter Renfrew's? We can't say for certain, but Gordon's theory is this:
When a loop was set up, the universe split into two new universes. If the loop was of the simple killing-your-grandfather type, then there would result one universe where the grandfather lived and the grandson disappeared. The grandson reappeared in a second universe, having traveled back in time, where he shot his grandfather and lived out his life, passing through the years which were forever altered by his act. (46.51)
In order to prevent a paradox, the universe split into two separate universes. Gordon knows that some event in the fall of 1963 (likely Kennedy's assassination becoming an attempted assassination) "made Renfrew's experiment impossible or unnecessary" (46.52). So Renfrew's timeline keeps on keeping on, while Gordon's timeline forges a new path, one that will lead who-knows-where.
Put Some Science on It
Okay, so we've covered how change unfolds in Timescape, but what does this ending mean thematically? To answer that, we're going to have to travel all the way back to the beginning of the novel to this little exchange:
"Well, actually…" The boy hesitated. "He said the scientists got us into this beastly mess in the first place and they're the only ones who can get us out of it now, if anyone can."
"He's not the first to say that, Johnny. That's a truism." (1.16-17)
And it is a self-evident truth, but as this ending suggests, just because science can solve a problem doesn't mean it will solve it in the way one might expect. Science resolved the situation, yes, but there were unexpected consequences within the solution, namely the splitting of the timelines into two separate universes.
In the same way, you'll recall that the ecological problems of 1998 were the result of actions like herbicide pollution and deforestation in the Amazon Basin. In other words, both were scientific solutions to help agriculture grow more food to feed more people—and both majorly backfired.
Ultimately, while the novel puts forth the idea that science can solve our problems, it also suggests that science takes us into the realm of the unknown, a place where consequences are obscure. To mitigate this, there need to be people who can understand the theory behind the science and not simply apply the work of science to meet a certain end (22.25). Someone like Markham.
Note that the timeline heading into the certain disaster is the one where Markham dies tragically in a plane crash, unable to share his revelations with the world. On the other hand, the timeline heading into a new era of hope is the one where Markham survives.
The one quality both timelines have in common regarding the theme of science and truth is this: Any answers science can conceive of will never be absolute and will always lead to new questions. Both Renfrew and Gordon find themselves with new understandings of the universes they live in, but neither possesses a complete picture. And that ultimately leads both men to wonder and hope.