As a math teacher, I was thrilled to see the start of this episode. A young boy running through the corridors of the Enterprise collides with Riker and falls down. He was running from his math class and his father catches up. The father scolds the boy, telling him that everyone needs a basic understanding of calculus. This is stuff to prime the heart of mathematicians everywhere. Unfortunately, after that stellar beginning, the episode collapses.
The Enterprise is following a trail of faint energy readings, when suddenly a planet appears. It is the mythical planet of Aldea, where an ancient civilization chose to remain hidden from others so that the inhabitants could engage in intellectual pursuits. The cloaking device used to shield the planet for centuries is said to function by the selective bending of light rays. Of course the gravity well of a planet would still be discernable, even if it could not be seen.
The real absurdity of the plot is that the Aldeans can no longer have children, so they want to take some from the Enterprise. Being civilized beings, they are willing to pay for them by giving the Federation some of their advanced technology. That technology is very powerful, to demonstrate it to the crew of the Enterprise, they hit it with a force beam. The Enterprise is thrown so far that it takes them three days to get back at maximum warp. Since the children and their parents are not consulted, it is a case of kidnapping. The idea that an advanced civilization would engage in such an act is ridiculous. If they needed children they could contact the Federation and request that they be allowed to adopt some orphans. Even in such advanced times, there would still be children without parents. It is similar to "The Empath", an episode of the original series where a technically advanced civilization tries to save the population of a world by kidnapping and torture.
It then takes on a familiar technology run amok theme. The Aldean world is controlled by an extremely powerful central computer called the custodian. It has functioned flawlessly for hundreds of centuries, so the inhabitants have lost all knowledge of how it works. Dr. Crusher also discovers that the health problems of the Aldeans are due to radiation damage. The shield that hid the planet for all those centuries damaged the ozone layer, allowing solar radiation to leak in. Of course, Crusher discovers this in a matter of days, when the Aldeans with all their technology couldn't find it in a million years.
The Enterprise crew manages to overcome the Aldean technology and disable the sentinel. This allows Captain Picard to recover the children. As a final absurdity, Dr. Crusher is able to cure the Aldeans of their radiation-induced afflictions. The episode ends with the Enterprise crew and the Aldeans walking into the chamber containing the sentinel power source and engaging in some pathetically mushy promises to help each other.
All of the major premises that the plot is based on are ridiculous. Such an advanced civilization would not kidnap when they could adopt and there is no way that such an advanced technology could fail to determine the cause of their affliction. Didn't anyone on the planet ever think to ask the custodian why the inhabitants were experiencing their health problems?