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In the Girl in the Fireplace episode, surely there were plenty of other 37-year-old females in France.

Why did the robots target Madame de Pompadour?

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The robots were tasked with harvesting her brain because their ship had suffered massive damage to its memory and had developed an obsession

with its namesake

This is described quite nicely in the show transcript;

ROSE: Why her? Why did they think they could repair the ship with the head of Madame de Pompadour?

DOCTOR: We'll probably never know. There was massive damage in the computer memory banks. It probably got confused. The Tardis can close down the time windows now the droids are gone. Should stop it causing any more trouble. 

The fireplace is on the scanner. The fire goes out. On the spaceship, the Tardis dematerialises to reveal a portrait on the wall labelled Madame de Pompadour 1721-1764, then we move outside to discover that the drifting vessel is the SS Madame de Pompadour.enter image description here

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  • Would the droids have been able to repair the ship with some other 37-y-o female? Surely, there were plenty of those in 18th-century France.
    – moonman239
    May 21, 2015 at 7:29
  • @moonman239 - That's worthy of its own two part question. My take was that A) Yes, any woman would have done. Their obsession was illogical (something the doctor comments on) and B) Wouldn't have worked. Their sister ship the Marie Antoinette tries to affect similar repairs and totally fails
    – Valorum
    May 21, 2015 at 7:42
  • So, their attempt to use the Madame's brain would have been unfruitful? Perhaps even just as unfruitful as if they had used someone else's brain?
    – moonman239
    May 21, 2015 at 7:51
  • @moonman239 - Yup. Almost certainly.
    – Valorum
    May 21, 2015 at 11:54
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    It makes sense from the point of view of a damaged computer. The Madame de Pompadour is broken and needs spare parts to be fixed. So where do you get them from? Another Madame de Pompadour. Logic!
    – Thomas Jacobs
    May 21, 2015 at 13:00
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It is implied that the robots chose Madame de Pompadour solely because that was the name of the ship they were attempting to repair (the SS Madame de Pompadour). This isn't stated directly, and the clue comes towards the end of the episode (if I recall correctly), when the camera pans over the name on the side of the ship, and is never otherwise addressed in the episode.

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Another thing to add to the already mentioned fact that the ship was called the "SS Madame De Pompadour": let's face it. They were 51st century robots that were running on gears. That seems unreliable and incredibly primitive for the 51st century. With incredibly limited AI, of course they were going to be severely confused! Remind me never to make a robot out of gears. To think The Doctor called them a beauty! Let's just stick with regular binary AI for now.

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    They were not running on clockwork items because it was the limit of their technology. They were running on it because it was the style. The technology was SO advanced that they could use clockwork mechanisms for significant parts and it would still function at a high degree of utility for a very long time. Also, Steampunk will always be cool, even in the 51st century.
    – Jeff
    Apr 12, 2018 at 23:06

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