Ringworld ultimately declares that the purpose of the expedition - indeed, the whole novel - was simply to get Teela Brown from here to there. This begs the question “Why was it so all-fired important for Teela to get there?” Niven acknowledges this, but the reasons we’re given in the book aren’t entirely satisfying. Probably they’re correct, but as with so many other aspects of this novel, there’s probably quite a bit more going on below the page, which only appears if we think about it. For instance, as to the question of who built the Ringworld, Niven himself has said “The story was already too complex. I couldn’t open that can of worms, too. I settled for letting Louis Wu deduce the wrong answer.”* If Louis was wrong about that, mightn’t he also be wrong about other things as well? What other reasons might there be for Teela to go there?
Speciation is the law of life. Over time, one species becomes two, becomes four, becomes more. This is an aspect of evolution, of course, but we tend to think of evolution as being red in tooth and claw. In fact, it generally is, but there are other ways to go about it. Take some ducks, put some on one island, some on another. Over time, the different environment changes them considerably. You end up with Island Gigantism (As in Hawaii) or if the food supply ain’t great, you end up with island dwarfism. Given enough time, these two families of ducks speciate into completely new species. “Duckoids,” call them. It goes without saying that any particularly unique traits in the genetic codes of these animals will be very prominently expressed. If something interrupts this process while our Duckoids are still just ducks, however--let’s say they’re rounded up and put back into the general population--then their unique qualities dissolve into the greater gene pool, and that’s pretty much that: a window of evolution is closed, and the boring old status quo wins out.
By the very definition of the Teela Brown gene, her new sub-species--let’s call them “Teeloids”--will flourish and ultimately supplant us. They have to. They’re invariably lucky, and we’re not. It’s a foregone conclusion that “Her kind” will ultimately win out over time.
Or is it?
The Teela Brown Gene compelled its owner to go to the Ringworld, a place vastly more friendly to humans than any natural world, with nigh unto limitless space, capable of holding untold trillions of Teloids in relative comfort and reasonable safety.
Let’s think about this a moment: There’s a new gene, probably only present in a few dozen people in the whole world-wide world. If it immerses itself in the vastly wider gene pool of humanity at the time of the novel, it will instantly be watered down, possibly to eventually become an infrequently-expressed recessive trait of the kind that’ll get your knees broken in ‘Vegas, or, more likely, to disappear forever. The gene wants to survive, and the chances of that happening on earth are very, very, very slim. Since the Teela Brown gene is all about luck and/or probabilities, then it needs to find some luckier place to hang out.
Enter: The Ringworld. The perfect island for gigantism, as it were. It’s remote, obscure, self-defending, difficult to get to, purpose-built to be conducive to human(oid) life, and full of things that are of absolutely no threat to someone of her skills. It is the ultimate cradle/nursery, a place where “Her kind” will propagate and prosper. They needn’t worry about competition or alien incursion there, the Ringworld will keep the gene safe.
“Ah, but how is she to reproduce? There wasn’t a clone-o-matic in her First Aid Kit.”
Teela wasn’t the only person with the gene, obviously. The book makes no qualms about the fact that there are more, and that there will be yet more still in the not-too-distant future. Teela is, if not the first, at least the first really powerful one. Her genes somehow - never explained how, really - led her to the Ringworld for reasons already detailed. These same advantages will invariably call others with the Teela Brown gene to the Ringworld eventually. The place is a magnet for Teeloids just like Star Trek is flypaper for people with Aspergers.
Once on the Ringworld itself, they will invariably find each other by the most ludicrously unlikely of coincidences, they will have families, expand rapidly.
“Ah,” you say, but the Ringworld isn’t all that safe or comfortable, and it’s got some inherent design flaws. Granted, the place itself is rather run down, but this too is fortunate. A fully-functioning Ringworld would be very dangerous to a new subspecies trying to take root, but a Ringworld that’s already killed off most of it’s population, gone to seed, and is sparsely populated by barbarians? That’s golden! And for people with her luck, it’s a foregone conclusion that they would eventually spruce the place up and return it to its glory days. We see some aspects of this happening in the very next book, actually. And by the end of the series, a golden future is assured.
So where does all this lead? The ultimate goal is, of course, the ultimate goal of any emergent new genetic expression: it wants to become an entirely new species. As history has proved again and again, the Ringworld is the perfect playground for that to happen. And after that? I don’t know: Build more Ringworlds? Replace humanity the way we replaced the Neanderthals? Outnumber us to such an extent that when we interbreed their genes quickly wash away our own, until we all become Teeloids? Swarm out across the galaxy, wiping out anything they perceive threatening? Somehow halt the core explosion? Any or all of these are possible, and all of 'em are disturbing. In the end, the Ringworld becomes their angelic (Or demonic) rookery, and “They” don’t need “Us” at all.
Given their luck--and Louis’ not-at-all-overstated fear that said luck could overturn the basic operating rules of the universe--people with the Teela Brown gene are somewhere between mortal and godlike, and the Ringworld is their halo and heaven in one.
*- Larry Niven’s “Afterword” to the anthology “Tales of Known Space,” 1975