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The GENIEs (Genetically Engineered Neural Imagination Engine) were a race of small, man-made creatures with the power to grant their owner's wishes. The name was possibly inspired by the genie in the lamp idea. It is also possible that they inspired this idea.
When introduced, the GENIEs took the Earth by storm. You could have anything you wished for, and get rid of anything you didn't want. H Soon it got out of control, however, and the entire earth was turning to ashes because of all the energy that was needed to make people's wishes come true. There were endless paradoxes because people would wish for something to have never happened; this meant meaning never needed to wish that it hadn't happened.
With the end of the world in sight, the original creators realised they had to do something and devised a plan that would end the chaos. They took the first GENIE ever made and wished that all the others had never existed. This took them back in time to when it was just being created. They destroyed the lab, along with all the research and blueprints, thus saving the human race from its own greed.
This required a huge amount of energy, however, and while the Genie would normally get energy from its surroundings, there wasn't enough. The creators knew this and therefore had to sacrifice the Sun to save the Earth and its people from themselves.They made the GENIE not only commit genocide on its own species but also commit suicide because there was no way it could survive taking in the energy of the Sun.
However the inventor had a daughter who had no thoughts for GENIEs and wishes in the time before the days where dreams and nightmares alike came true. Ignorant of the consequences of her actions, not knowing the original GENIE was in the basement, she wished to live in what she thought was a "better time." She was brought to ancient Rome, not knowing that the Doctor and Rose would arrive shortly after her.
When they eventually found the GENIE, the Doctor saw what evil would arise from it. He took the inventor's daughter home, keeping the GENIE with him til he could figure out what to do with it. It was Rose, however, that found the solution; he wished for the GENIE's freedom and the Doctor took him somewhere safe to live out his life in peace, only granting wishes when it chose and living happily ever after. (PROSE: The Stone Rose)