I thought the point of the booby trap assimilator things was that you couldn't destroy them because they just absorbed the energy and radiated it back at you. So how come they can just shoot torpedoes and blow them up at the end? Why couldn't they do that earlier?
Beverly states that 26 minutes of radiation exposure is a lethal dose. Radiation really doesn't work this way. Trek frequently behaves as if there is some particular dose of radiation that is fatal, but anything below that is perfectly fine. Rather, it's a progression; low doses will give you an increased chance of cancer, higher doses cause radiation burns, lost hair and teeth, etc, up to a fatal dose. Worse, the levels at which all that happen vary considerably from person to person.
The original idea was to have Picard be the one who falls for Leah, but the writers decided that in a crisis he would be on the bridge, whilst Geordi would be the one trying to solve the problem. It also seemed to make sense for Geordi to fall for one of the ship's designers.
Originally Leah Brahms was to have been Navid Daystrom, a descendant of the Dr. Richard Daystrom from the TOS episode "The Ultimate Computer". However the casting department didn't realize that this would require a black actress and hired the white Susan Gibney instead. They changed the name and put in a line stating that Leah graduated from the Daystrom Institute.
Guinan tells Geordi that her attraction to Picard began when a bald man was once kind to her. This may refer to the episode "Time's Arrow, Part II", in which Picard cares for the 19th century Guinan when she is injured.
In this episode O'Brien tells Picard that he used to build model ships in bottles. Picard references this to the alternate O'Brien in "All Good Things..."
They beam back to the Enterprise and Picard orders the ship out of the asteroid field, but when the engines are engaged then energy begins to drain from the ship, and the ship is flooded with deadly radiation. There seems to be no fault in the ship, yet nothing they try has any effect. Geordi estimates that within three hours they will exhaust their energy reserve. He seeks a way to boost their power system to last longer. He goes to the holodeck to generate a recreation of the ship's original design configuration for research purposes, and with a slip of the tongue he ends up recreating one of the original designers, Leah Brahms, in holographic form. Figuring that this might be useful he has the computer look up her personality profile and animate her as a character. The two work together on ways to generate more energy for the ship.
During this time Data and Riker find more memory coils on the old battlecruiser and discover that the asteroids have been booby-trapped with aceton assimilators; these absorb the energy of a ship in the field and convert it into harmful radiation, so that the harder the ship struggles, the more lethal the environment becomes. Geordi and Leah struggle to find some solution. He goes to the bridge to talk with Picard; Riker wants to try destroying the asteroids with phasers, but Geordi says that the shields might be swamped by enough radiation to bring them down. Picard decides to try anyway, and the ship blasts some of the nearby asteroids only to find that radiation does indeed surge. The ship goes into a restricted power mode, shutting down the holodeck simulation Geordi was using. Crusher estimates that they have 26 minutes until everyone has absorbed a lethal dose. Geordi has Picard reinstate his holodeck program, explaining that the simulation is proving to be valuable in solving the problem.
Geordi keeps working, and with Leah he develops a way to overcome the effect by changing the power systems at extremely short intervals, giving the assimilators no time to adjust to the changes. Picard comes to talk about the issue with Geordi, and the engineer explains that complete control of the ship would have to be turned over to the computer as only it is fast enough to make the necessary changes.
Picard talks to Riker about the solution; Riker is unimpressed by the idea of giving the computer control, as he is confident that they can take orders but not so confident that they can give them. On the holodeck Geordi and Leah run two simulations of the method, finding that one succeeds and the other fails. As they talk the shields fail, giving the crew 26 minutes to live. Although Picard wants to implement the plan, Geordi frantically works on another option. He rushes to Picard and suggests that since their power systems are the problem, the answer is to shut them down. Use one thruster to give the ship a burst of speed, and then coast out on manual control with minimal systems active. As he tells Picard, "sometimes you just have to shut it all off."
Picard takes the helm and fires the thruster, and the ship begins to drift. He makes some minor course corrections but the ship appears to have insufficient speed to clear the field. Picard pilots it directly at a large asteroid, apparently on a collision course, but at the last instant he skims past, using the asteroid's gravity to achieve a speed boost and just clearing the field. Picard orders torpedoes used to destroy the battlecruiser and the asteroids around it, ensuring that the trap will never catch another vessel.
Geordi has a last talk with Leah, wishing that he could know her for real. She comments that in a way, the ship and the engines are a product of her, so when he touches them he is touching her. They share a kiss, and Geordi ends the program.
Where it falls down are on the smaller points; the radiation thing I mention above is one, along with the Promellian ship still having gravity, the sudden effectiveness of the weapons, etc. The gravity slingshot idea is based on a real principle, but in reality it wouldn't really work much like it is shown (though showing it realistically would be quite a slow business), and wouldn't result in much of a nudge anyway. Still and all, a reasonable episode.
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