The Enterprise is sent to investigate the shutdown of the Argus Array, a deep-space telescope and subspace antenna. In a shuttlepod Geordi La Forge and Reginald Barclay investigate, and discover an alien probe in the vicinity. It fires a pulse which disables the shuttlecraft and knocks out Lt. Barclay. They return to the Enterprise, where Barclay regains consciousness. Meanwhile, the probe begins to chase the Enterprise. It is found that Barclay's intelligence has dramatically increased, when he uses his knowledge to reinforce the shields to resist the explosion of the probe (which they were forced to destroy at extremely close range). Barclay estimates his own IQ at 1200-1450. Doctor Crusher tells him that he may well be the most advanced human being ever, and Barclay casually agrees that he is.
The array continues to deteriorate. If it is allowed to explode, invaluable scientific data will be lost, and the ship itself would be at risk. The Enterprise crew attempt to shut down the array's reactors one by one in order to effect repairs, but they estimate it will take two to three weeks to fix all 19 of them. Barclay casually mentions that he can fix them all simultaneously by reprogramming the controller system, a feat he claims he can accomplish in two days with Geordi's help. Geordi is amazed and alarmed at this but promises to assist. However, the array quickly starts to go critical again; the computer on board the Enterprise is too slow to keep up so it cannot shut down the reactor. Barclay goes to the holodeck to attempt to control the reactors; he is forced to build a new, faster interface from scratch, which involves hooking his own brain into the ship's systems. Barclay safely arranges for the array's shutdown, but by this point he is completely integrated into the Enterprise computer.
Realising that Barclay cannot be 'downloaded' back into his body - since he and the computer are now virtually inseparable - the crew must consider the real possibility of killing him in order to regain control. Unfortunately, Barclay overhears this, and prevents all the crew's attempts to shut him down. He modifies the ship to create a 'subspace inversion', to 'jump' them a greater distance than warp could take them. Data, who is at ops when this happens remarks that it is a progressive phase distortion, doubling in intensity every six seconds. They arrive near to the center of the Milky Way galaxy, where contact is made by the Cytherians - an advanced alien race, whose representative appears on the bridge (manifesting as a giant, disembodied head) and remarks aloud on the Enterprise crew, expressing amazement (and an almost childlike sense of wonder) that they have 'bipedal locomotion' and a 'hierarchical collective command structure'. When Captain Picard demands to know why they are here, the Cytherian replies that his race's goals are the same as those of the Enterprise crew, except that instead of visiting other races, the indigenous peoples draw the other races to them, since studying something in rapidly changing environments is almost as "pure" as studying them in their natural environments.
Barclay, now fully restored to his normal self, arrives on the bridge to explain. The probe which disabled the Argus Array (and, later, Barclay and Geordi's shuttle) was attempting to re-write key systems to bring those 'entities' to Cytherian space. The probe was successful in reprogramming Barclay's mind, making him intelligent enough to take over the Enterprise with the stated goal of bringing the entire crew to Cytheria. The crew spends ten days with the Cytherians, exchanging information and providing the Federation with "decades" of advanced information to study. The Enterprise is "jumped" back to its last position, with Barclay restored to his own body, although deprived of his enhanced intelligence and confidence. He does, however, find that there is some residual intelligence left when he glances at a crewman's chess game and offhandedly predicts checkmate will be achieved in nine moves. Counselor Troi expresses ignorance of his chess abilities. Barclay confirms that he has never played chess before escorting Troi on a casual date to walk in the arboretum.