Eternity (1988) is a science fiction novel by Greg Bear. It is the second book in his The Way series, dealing largely with the aftermath of the decision to split Axis City and abandon the Way in the preceding book, Eon.
In Eon, Axis City split into two: one segment of Naderites and some Geshels took their portion of the city out of the Way and through Thistledown into orbit around the Earth; they spend the next thirty years aiding the surviving population of Earth heal and rebuild from the devastating effects of the Death. This effort strains their resources and the government of the Hexamon. As time passes, sentiment grows to have Korzenowski reopen the Way. Firstly, to learn what has happened to the Geshels' long-sundered brethren (who took their portion of Axis City down the Way at relativistic near-light speed). And, secondly, to benefit from the commercial advantages of the Way (despite a very real risk that the Jarts will be waiting on the other side).
In a parallel Earth, known as Gaia, the mathematician Patricia Vasquez (who was the primary protagonist of Eon), dies of old age; she never found her own Earth where the Death did not happen and her loved ones were still alive, but remained on the one she discovered (in which Alexander the Great did not die young and his empire did not fragment after his death). She passes her otherworldly artifacts of technology to her granddaughter, Rhita, who appears to have inherited her gifts. Rhita moves away from the academic institute the "Hypateion" (a reference to Hypatia) which Patricia founded and to that world's version of Alexandria. Patricia's clavicle claims that a test gate has been opened onto this world of Gaia, and that it could be expanded further.
Ser Olmy is distracted by three concerns; the growth of his son, the prospects of the Way being re-opened (which he believes inevitable) with the attendant consequences, and by the revelation to him by an old friend that one of the deepest secrets of the Hexamon was a captured Jart whose body died in the process but whose mind was uploaded. Its mentality was alien and powerful enough that it took over or killed many of the researchers who attempted to connect to and study it, so it was hidden away deep in the Stone. As he studies the Jart, Olmy comes to believe that the Jart had been captured on purpose, that it was in fact a Trojan Horse. The Jart reveals tidbits about the Jart civilization: in essence, they are a hierarchical meta-civilization that ruthlessly modifies itself, attempting to absorb all useful intelligences and ways of thinking that it encounters, in the service of the Jarts' ultimate goal - to transmit all the data they can possibly gather to "descendant command". Olmy investigates further and discovers that descendant command is the Jart name for what they know as the "Final Mind" - a Teilhardian (or Tiplerian) conception of an ultimate intelligence which will be created at the end of the universe when all intelligences merge themselves into a single transcendent intellect which will effectively be a god.
Olmy underestimates the Jart, and it begins to slowly take over his body and mind. Its original mission, assigned to it hundreds of years ago was to engage in sabotage and transmit its freshly acquired understanding of humanity back to present command, but the arrival of Pavel Mirsky changes everything.
Pavel Mirsky had elected to go with the Geshels down the Way more than thirty years ago, after which the Way had been sealed off. It should have been impossible for him to return, but yet one day he quietly re-appears on Earth to deliver an urgent message. He had indeed traveled down the Way when the Way was sealed off with that portion of Axis City, and he and its citizens had voyaged hundreds of years and billions of kilometers; they advanced and changed radically on the way. At the end of the Way was a finite but unbounded cauldron of space and energy - a small proto-universe. They transformed themselves into ineffable beings of energy in order to survive the transition. They became as gods to this place, and for a time their creating went well. But it began to corrode and collapse without conflict and contrast between the creators, threatening to take the would-be gods with it. But they were rescued by the Final Mind of this universe, which took pity on them and freed them from the Way. The Final Mind is not quite omniscient or omnipotent, however, and many grand efforts are being balked and frustrated by the precocious accomplishment that the Way is. Mirsky had been reconstituted from what he had become and sent back in time to try to persuade the Hexamon to order the re-opening of the Way - and its destruction.
On Gaia, Rhita persuades the aging queen to support her like the queen had supported Patricia. Their expedition leaves for the location of the test gate somewhere in the barbarous hinterlands of Central Asia in the nick of time, as the queen is deposed during their trip. Rhita's clavicle succeeds in expanding the test gate to a usable size, but it warns her that whoever opened the gate in the first place was not human.
That night, the Jarts arrive on Gaia en masse. They begin the mammoth task of storing and digitizing all the data and life forms on Gaia to transmit down to descendant command. Rhita's consciousness is of special interest to the Jarts, particularly what she knows of Patricia.
In the meantime on Earth proper, consensus has been reached to re-open the Way but not to destroy it. Mirsky disappears. Another entity who should not be there, Ry Oyu, the former gate opener for the Gate Guild, appears. He prods the president of the Hexamon into covertly ordering Korzenowski into destroying the Way regardless of the decision of the citizens. The backlash destroys the Stone. Ry Oyu, Korzenowski, Ser Olmy (who connived at the destruction), and the Jart controlling Olmy, outrun the Way's destruction and arrive at a Jart defense station located over Gaia. The Jarts respect the wishes of Ry Oyu as a representative of descendant command, and before the Way dies, transmit their accumulated data in a single immensely long fluctuation along the singularity/flaw of the Way to the Final Mind.
Korzenowski has himself digitized and sent with the transmission. Olmy is dropped off on the homeworld of the Frants, a communal mind civilization whom he likes. Ry Oyu has Rhita's mind freed; her consciousness gives Ry Oyu the last piece of data needed to reconstitute Patricia Vasquez. Ry Oyu intends to make up for his failure to instruct Patricia properly when she was trying to open a gate back home in Eon; he correctly opens the gate, and bare moments before the Way completely disintegrates around him, finally sends her back home to an Earth where the Death did not happen. Rhita is also returned to Gaia, a Gaia where she never opened a test gate and where the Jarts did not invade. And Pavel Mirsky, still unsatisfied, returns to the beginning of the universe to witness all interesting events between then and the Final Mind, when he will return and report back to it.
The "Taylor algorithms" are a set of fictional mathematical algorithms that allow intelligent programs or agents in a simulated reality to determine the true nature of their environment, and even to change it. They were introduced by science fiction author Greg Bear in his novel Eternity, set in the fictional universe of the Way. Within the historical background of the story, the algorithms were developed by a team of Hexamon investigators led by Doria Fer Taylor. The algorithms were determined to be a potential danger if they were to fall into the wrong hands, and so they were classified.
The algorithms were eventually discovered by police investigator Olmy ap Sennon, who later came to recognize signs of their use by a captured alien mentality known as a Jart.
It has been suggested that the physical form of the Jart specimen as described in the novel is a tribute to the real-life bizarre fossil species Hallucigenia.