This distraction causes the experiment to go wild, and when the ship stops, they discover they've gone 2.7 million light-years in a few seconds. Wes, during the trip, sees the assistant "fade" in and out of normal reality. He tries to tell Riker about this, but Riker shushes him away. They decide to try to get back, and end up traveling to a place unlike any they have ever seen (as the assistant again "fades", being seen by Riker this time).
They are more than a billion light-years from home. Furthermore, in this place, the crew's thoughts seem to become reality. Worf sees a Klingon "targ", a pet from home; Tasha finds herself back on her home planet avoiding a rape- gang; Picard first almost falls out of the turbolift into warp-space, and then sees his long-dead mother, and so forth.
Eventually, they find out the truth. Kosinski had nothing to do with any of this: it was his assistant, the "Traveler", who accidentally brought them here. He claims to act like a lens, focusing the power of thought, which brought them to this place. Unfortunately, he is now dying. However, there is no choice; he must try to get them back.
Before the attempt, he talks to Picard alone, about Wesley. It seems that Wes has the potential to become a Mozart of engineering, if properly encouraged. The Traveler tells him to encourage Wes, but tell him none of this.
The attempt is made, and is successful, but the Traveler fades completely from normal space and does not return. Picard, acting on the Traveler's last wishes, appoints Wes an Acting Ensign, subject to Wes applying to the Academy as soon as he can. Until then, his assignment is to "learn this ship." Brought back to where they started, the Enterprise departs for their next assignment.