Dalek Caan was one of the four Daleks making up the Cult of Skaro. Like the other members, he thought like the Daleks' enemies in order to find new ways of defeating them. He had a mind of his own and could imagine and think for himself.
Battle of Canary Wharf
I will be the destroyer of our greatest enemy!
Dalek Caan was one of the three Standard Daleks who were created to follow the Cult's leader: the supreme Dalek Sec. During the Last Great Time War between the Daleks and the Time Lords, the Cult took the Genesis Ark and fled the war into the Void, resurfacing later in London in 2007.
Arriving in 2007, Caan, Jast, and Sec scanned the brain waves of Dr. Singh and discovered another species had invaded Earth. Upon discovering it was Cybermen, the Cyber-Leader declared war while the Cult claimed it to be pest control. Caan took part in the Battle of Canary Wharf while the Genesis Ark (accidentally activated by Mickey) released millions of Daleks onto Earth. Because they had been through the void, they were covered in void stuff. The Doctor was able to open the rift the Cybermen had come through and reverse it, sucking in all beings covered in void stuff. As the Daleks were sucked into the Void, Dalek Caan and the rest of the Cult activated an emergency temporal shift and escaped. (DW: Army of Ghosts/Doomsday)
The Final Experiment
You told us to 'imagine'... and we 'imagined' your irrelevance.
The Cult ended up in New York City in 1930 and recruited Mr. Diagoras, the head of construction for the Empire State Building. He kidnapped people for their research and for what they called the "Final Experiment". During their time in 1930, Dalek Caan served as the Cult's connection to Diagoras. Eventually, Caan took Diagoras to see their leader Sec who merged with Diagoras in his casing to become the first Human-Dalek. (DW: Daleks in Manhattan)
After Sec became a Dalek-Human, he showed feelings that their creator, Davros, was wrong about removing emotions and that the deaths at Hooverville were wrong. Caan and the other members felt that the plan Sec had for the new Daleks was unacceptable; it would change everything that makes a Dalek a Dalek and the Daleks would no longer be supreme. Feeling Sec was no longer a Dalek, Caan led a mutiny with Dalek Jast and Dalek Thay to imprison Sec, having poured a different gene solution into the Dalek-Humans than Sec had wanted, making the new bodies 100 percent Dalek.
Dalek Caan made himself Controller and became connected with the Dalek-Human army. When Thay and Jast ordered the new Daleks to destroy the Doctor, they questioned orders and the Doctor explained that he got in the way of the gamma strike which brought them to life, his DNA becoming mixed with theirs, giving them a little freedom. When a battle broke out between the Daleks and the Dalek-Humans, Jast and Thay were destroyed. Caan saw the new Daleks as failures and killed the entire species.
Caan was the last member of the Cult and, by extension, the only survivor of the entire Dalek race, therefore he was narrowed down to be the entire Dalek species. The Doctor confronted him and offered Caan help and compassion, being that he didn't want to cause a genocide. Caan activated an emergency temporal shift and escaped. (DW: Evolution of the Daleks)
Insanity
I flew into the wild and fire. I danced and died a thousand times.
It is revealed that Dalek Caan teleported to the Time War, despite it being time locked. Once there, he found and saved Davros, something which the Doctor himself had failed to do. After the Daleks moved Earth to the Medusa Cascade, Dalek Caan resided on the Dalek spaceship, giving cryptic information to Davros.
The Supreme Dalek on board the spacecraft claimed that Caan was insane, a notion which Davros dismissed, claiming that nothing would be possible without Caan. This shows that Caan had a certain amount of respect from Davros. However, Davros acknowledges that he had become mad due to the strain of time-traveling directly into the Time War, corroborated by Caan's insane laughter and talking in seemingly precognitive riddles in an almost sing-song voice. His battle armor is also badly damaged; the upper dome completely gone and the armor opened up to show the Dalek Caan mutant. (DW: The Stolen Earth)
While he was apparently aiding his creator and the New Dalek Empire, its discovered later that Caan had manipulated events in order for the Doctor to defeat the last remnants of the surviving Dalek race. This was because, while in the Time Vortex, Caan had forseen the actions of his race and deemed them evil. Thus, he sought to destroy his race and tricked Davros and the Supreme One. Therefore Caan truly thought as the enemy thought. The fires that engulfed the Crucible presumably put an end to him, either that or when it exploded as it is unlikely he attempted an escape as he wanted the Dalek race to end. (DW: Journey's End)
The Prophecy
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He is coming. The three-fold man. He dances in the lonely places. The Doctor is coming...and death is coming, everlasting death to the most faithful companion! So cold and dark and hot, fire is coming, the endless flames...the Doctor will be here as witness at the end of everything, the Doctor and his precious Children of Time...and one of them will die! At the time of ending, the Doctor's soul will be revealed. The Children of Time will gather, and one of them will die!
This prophecy was fulfilled in Journey's End: the three fold man is the Doctor who appeared as the original Doctor, the New Doctor who is the original's duplicate and as the Doctor-Donna, the half-human half-Time Lord Donna who had his mind. The Children of Time were Rose, Jackie, Mickey, Sarah Jane, Captain Jack, Martha and Donna who all acted as the Doctor's companions for the adventure. The Children of Time is what Davros, Dalek Caan and The Supreme Dalek called the Doctor's companions. The Doctor's soul was revealed as being a man who refused to use weapons but molded his companions into weapons as Davros revealed when Jack, Sarah Jane, Mickey and Jackie and separately Martha were threatening to kill a lot of lives in order to stop the Daleks and their plans. Apparently the companion who "died" was Donna whose memories had to be erased in order to protect her and the person she became died, as the Doctor told her family that the Donna she had become was dead and could never be revived. If Donna remembered The Doctor or the Daleks for one moment she would burn up. Dalek Caan pressured the New Doctor to destroy the Daleks which he did as they were too much of a threat to everything.