Character Analysis
Markham is an American plasma physicist who comes to Cambridge to help Renfrew sell Peterson on the idea of backing the tachyon experiment. It works and Markham's job after that is basically to hang around and help Renfrew understand the theoretical implications of communicating with the past. And… that's what he does. Actually, Markham doesn't do much for this story in terms of plot, but he does play a very important role nonetheless.
Oh, and before we get too far, we should bring this up: Some readers see Markham as a stand-in character for Gregory Benford himself. Evidence for this includes their similar looks and academic histories, as well as the fact that they share a first name and a structurally paralleled last name. There's also the fact that Markham gets all the best lines in the story.
While there might be some merit to this type of comparing and contrasting, we're not going to take that route here. We're going to treat Markham as his own man since, if there is a Greg Markham floating around out there in the multiverse, we imagine he'd prefer it this way.
Mentor With a Thousand Faces
Beard? Academic degrees? A love of feasts and a penchant to die right when needed most? Dude, Markham is Dumbledore.
Or, to put it another way, Markham and Dumbledore both play similar roles in their respective stories: that of the mentor. Although Markham may not be super important to the plot of Timescape, he does help guide the other characters through the ins and outs of the theoretical physics at play within it.
In one of several such scenes, he helps Peterson understand the concepts of temporal paradoxes after seeing "in Peterson's face the hesitant puzzlement that swam over people when they struggled to visualize ideas beyond the comforting three dimensions and Euclidean certainties which framed their world" (15.44). His goal, then, becomes to turn lunch into a pub-based seminar and guide Peterson through the world beyond our everyday dimensional space.
It's the same way Dumbledore helps Harry Potter navigate the wizard world. The only major difference is that Markham won't stop lecturing, while Dumbledore prefers the silent approach. Well, that and the whole magic/science thing.
Markham plays the same mentor role for the reader, as well. No doubt there are several times when the physics of Timescape leave us with that same puzzled face, and Markham is the character who swoops in and explains to the reader what they need to understand to get the most out of the novel's plot. Thanks, man.
Rocket Man
This isn't to say that Markham has all the answers, however—he may be the mentor character, but he still has a lot to learn. This takes us to the second important fact about Markham's character: He represents the curiosity of scientific exploration.
Granted, Gordon and Renfrew have this, too, but with Markham, the exploration is entirely mathematical, taking place within his mind. As such, we get to go with him on his explorations of theoretical physics during his point-of-view chapters.
For Markham, such mental exploration is a joy to perform. Consider this telling scene when he is on his ill-fated airplane ride:
Markham relaxed for a moment, reflecting on how much he loved this state. Concentration on an intricate problem could loft you into an insulated, fine-grained perspective. There were many things you could see only from a distance. Since childhood he had sought that feeling of slipping free, of being smoothly remote from the compromised churn of the world. (31.14)
There's a lucid, ecstatic quality to this description of exploring the world through mathematics; it's like he's getting high on science. And that's kind of the point. Much ink has been spilt about the mind-expanding qualities of drugs, and it is almost like Benford is riffing on the concept and setting the record straight at the same time. Markham's mind is expanded by the use of exploring formulae, which is a pretty productive high. Plus, the comedown is probably way easier to handle the next day.
Although he is our mentor character, Markham never reaches any absolute truths. There's always something more to learn, just out of reach but never quite out of sight. On his airplane ride, Markham is trying to determine the tachyon impact on the universe and the potential outcome of a paradox when the airplane crashes into a Maryland forest. In his final moments, Markham sees "suddenly what should have been" (31.23) and dies. Bummer for us, we never get to know what exactly he saw.
Gregory Markham, the Undead
But while Markham dies, he doesn't exactly die. Confused? Stick with us. Again, this harkens back to the mentor characters of old. Obi-Wan Kenobi lives on through the force, Dumbledore hangs out at that ethereal train station to provide one last tidbit of sagely advice—you know the drill.
Markham also pulls this life-after-death bit, though it isn't the same Markham from 1998. This Markham's career path will be altered because Renfrew's experiment opens new doors in theoretical physics, so this other Markham likely won't perish by plane crash. This Markham is also the apprentice and not the master, but Gordon can tell he has "the right feel for the work" (46.56). Maybe because somewhere, in a different lifetime, he's figured it all out.