Incanters are a subset of the avout linked to the Halikaarnian orders who, according to Saecular legend, are able to alter reality through the incantation of certain coded words or phrases. This physical change is somehow accomplished through Polycosmic Manipulation.
Most avout believe that Incanters are merely a Saecular iconography, and Incanters and their "enemies," the Rhetors, are popular in Saecular speelies. Because the officers of the Daban Urnud have encountered speelies, they are aware of the character tropes, and fear that they are real. To discover if Incanters and Rhetors actually exist, they intercept the Mataharite contingent on its way to Convox, because that order of avout wear face-coverings that would disguise that they have been replaced by non-Arbrans. The Geometers' fear, especially of the Incanters, arises from their supposed powers, specifically their ability to change the shape of history. The Incanters usually alter history only after someone else - in spelies, the Rhetors - has already acted to change history, and the Incanters "change it back." The Daban Urnud's intrusion into the Arbran polycosm constitutes a massive change. Moreover, the ship expend the last of its fuel - atomic bombs - changing orbits around Arbre; if the Incanters decided to change history by "removing" the ship, it could be stuck in another polycosm without any access to a fuel source.
Despite the fact that most avout scoff at the existence of Incanters (and Rhetors), there is in fact solid proof of their existence: the "parking ramp dinosaur." Near the concent of Saunt Muncoster, the local city had a large shopping mall, which they were expanding. A workman uncovered a massive skeleton inside the cement of a parking ramp - either a dinosaur or a dragon - despite the fact that the ramp was created only a few years before, using newstone. In short, there was no natural way that the skeleton could have appeared on its own. The discovery aggravated already-tense relations between Saeculars and the avout. Then one night, "chanting was hear from the Millenarian math," and in the morning, the skeleton was gone. What had not been erased, however, was the evidence that it had been there: peoples' memories, tire wear and fuel mileage on drummonds, receipts in lumber yards. The disappearance of the skeleton exacerbated relations between Saeculars and avout even further; a general Sack occurred several months later.
Fraa Jad is an incanter, and is described by Fraa Erasmas as a "mad sorcerer." Several times in the book, Jad explores millions of possible futures at random (by placing tiles, entering the correct code on a lock on the first try despite there being 10,000 possible combinations, etc) then forces his Narrative to the single one he prefers. This technique is akin to the functioning of a quantum computer, which (in theory) tests all possible solutions to an equation simultaneously, then collapses its wave function to the correct answer.
Jad's probable manipulations are so subtle that most go unnoticed, or unrealized, by the crew of Cell 317. The vast majority are directed at correcting the kind of problem that existed with the "parking ramp dinosaur," that is, leaving behind records that it existed. He does not swallow his Big Pill (which supposedly contained a transponder that would have sent back a data stream regarding his health). Another manipulation is Jad's near-death from accidental re-entry. Both Arsibalt and Erasmus volunteer to save him; in the Narratives in which Erasmus tried, he failed, and in some Narratives, was killed as well. Arsibalt successfully retrieves Jad, but in Ala (along with everyone else on Arbre) recalls that Erasmus tried but failed. After being saved, Jad refuses to speak, and rarely interacts with anyone, until after he has destroyed the transmitter. When he does destroy it, Sammann - who might otherwise be expect to try to stop Jad, or to repair the transmitter - admits that he has dreamed on multiple occasions of destroying it himself, and felt great relief on doing so, to the point that he was shocked when he woke up and discovered it was still intact. From the beginning, the Antiswarm support cells are unsure of who lived (Suur Esma reports that her team thought her dead for a while; not coincidentally, she is the one who looked after Jad, and would have reported on his survival). Along this line, when Suur Tulia emails Erasmus asking for their headcount, he emails back, "Are you asking how many of us are alive?" and does not realize until after they are out of transmission range that he has not, in fact, answered her question. More frighteningly, after boarding the Daban Urnud, Erasmus co-exists with Jad in a Narrative in which Jad activates Erasmus' Everything Killer, killing Erasmus, destroying a huge portion of the ship, and sending the images of horrific destruction to Prag Eshwar. In another Narrative, into which Erasmus is pulled by Jad, Jad confirms that Prag Eshwar has received the visions, then announces that his work is done. Erasmus' next experience is being brought of out cryosleep, when he learns from Ala that Jad did not survive the launch. The remaining members of Cell 317 - the Provener team, Sammann, and Jules Verne Durand - all recall the truth, but agree, in coded phrases and subtext, to accept the "truth" they've been told rather than reveal Jad's manipulations.
There is some similarity between Fraa Jad and Enoch Root from the novel Cryptonomicon and the The Baroque Cycle. Furthermore, the concept of changing reality through the incantation of certain words is a familiar Stephenson idea, dating back at least to the use of Nam-Shub in Snow Crash. The nature of Fraa Jad's chants are suspected to be Buddhist.
There is some similarity between Stephenson's Incanters and Stanislaw Lem's School of Higher Neantical Nillity.