No, Sol Weintraub isn't a houseplant. Houseplants don't have "sad, luminous eyes" (1.28), which the Consul notes Sol has. He's Jewish (but not exceptionally religious) and he's wandering the galaxy in search of a cure for his infant daughter, Rachel.
But Rachel wasn't always an infant. She's cursed with Merlin's sickness, and is aging backwards until one day, we assume, she'll just disappear. (For more on Rachel's sad condition, check out her "Character Analysis.") He's a man who has devoted his life to science, but when science fails to save his daughter, where is he to turn? To the god he abandoned years before?
We get a good picture of Sol even without hearing his story. He's patient, and is often the calm voice of reason when things get heated between the pilgrims. (When Brawne Lamia pulls a laser on Martin Silenus, Sol simply says, "Madam […] need I remind you that there is a child present?" [4.129].)
But, as with the rest of the pilgrims, we learn the most about him when he tells his tale.
Sol's a scholar, teaching history, classical studies, and ethical evolution at Nightenhelser College. He and his wife, Sarai (incidentally, the name of the Biblical Abraham's wife. This will be important later!), are happy raising their well-mannered, intelligent daughter, Rachel. Rachel grows up to be a very intelligent young woman, and she and her father have talks about religion.
Sol considers himself Jewish, but he has no faith or belief in a higher power. The main reason is that Earth no longer exists. How can someone be Jewish without the Promised Land? God broke His promise: "So much of the dream is dead. Israel is gone" (4.169), Sol tells Rachel. But he doesn't seem all that sad about it. When asked if he believes in God, he tells Rachel, "I'm waiting to" (4.178).
Everything's all well and good until Rachel treks off to Hyperion and catches the Merlin sickness, which causes her to start aging backwards. Science can't cure her. It seems that Sol never had a high opinion of medicine: "Sol's opinion had been and continued to be that medicine hadn't really changed much since the days of leeches and poultices [...] The only thing that had changed was that the bills were bigger" (4.266).
So, we're getting the sense that Sol is here to remind us that, sometimes, science doesn't have all the answers. Even in a work of science fiction.
With science at a loss, where's a man to turn? Before he discovered what had happened to Rachel, he had been dreaming of walking toward two glowing ovals (where have we seen glowing red orbs before?) when he hears a voice: "Sol! Take your daughter, our only daughter Rachel, whom you love, and go to the world called Hyperion and offer her there as a burnt offering at one of the places of which I shall tell you" (4.200).
At the time, Sol found the dream pretty silly. But after Rachel contracts an incurable illness, the dreams take on a whole new meaning, casting Sol in the role of an unwilling Abraham, asked by God to sacrifice his child. And where's science now?
You might think all this would strengthen Sol's faith in God. If anything, it destroys it once and for all. He thinks he's crazy for talking to a God he doesn't even believe in, especially when no one is talking back. He spends a lot of time thinking about his own story and comparing it to that of Abraham. Finally, Sol concludes that "any allegiance to a deity or concept or universal principal which put obedience above decent behavior toward an innocent human being was evil" (4.540).
Got it? Sol thinks that religion is evil because sometimes it forces you to do things that seem really, really bad—like murder your own child—to please a "deity" or even "universal concept." Note that this isn't just about religion. You could say the same of any concept, like "democracy," or "environmentalism": if it makes you behave indecently to another, innocent human, then it's evil.
Now that the matter of faith is settled, Sol and Sarai can go on acting like everything's normal with Rachel. They do the best they can to adjust their appearance and routine to how they acted when Rachel was 15, 10, 5, and so on as she continues to age backward to non-existence.
Their weird little routine continues until Rachel is about to forget how to read. That's when Sarai confesses that she's been having the same spooky red-eye dreams Sol had. She wants to take Rachel to Hyperion, but instead of sacrificing her, she thinks she and Sol should sacrifice themselves.
Anyway, Sol decides that Sarai needs a vacation and sends her off to visit her sister. She does. While on vacation, Sarai dies in a car accident. Great: if there's one thing his life needed, it was more tragedy.
With no other choices, Sol takes Rachel on the Shrike pilgrimage. But we still don't know what he'll do when gets there. Sol's story is tragic on so many levels. Death has claimed his wife and disease is taking his daughter. Sol lived his whole life for education and science, but neither did a thing to save his family. And neither did God. Sol turns to the cult of the Shrike desperately seeking salvation.
And this kind of sheer desperation is what happens when you lose everything.