Jackson Lake

Jackson Lake was a 19th century mathematics teacher who briefly believed himself to be an incarnation of the Doctor. As the real Doctor told him, the Infostamp that backfired, and made him believe he was the Doctor, only gave him information about the Doctor; all the bravery and his invention of a different kind of TARDIS, were things he was capable of doing on his own.

Biography
Lake was a mathematics teacher. In 1851, he moved to London with his wife, Caroline, and son, Frederick. They soon encountered the Cybermen, who killed Caroline and abducted Frederick. He somehow used an infostamp to defend himself, but the device backfired, filling his mind with information the Cybermen had gathered on the Doctor. In his anguish over the loss of his family, his mind cracked. He entered a fugue state in which he believed he was the latest incarnation of the Doctor, newly regenerated and amnesiac due to the Cyberman attack.

Some time after this, he rescued a woman named Rosita from a "man made of metal." Dubbing her his companion, he began to work on his own "Tethered Aerial Release Developed In Style," or TARDIS.

Lake continued to act as the Doctor would, investigating the "disappearance" of a man named Jackson Lake as well as the kidnapping of local children. His exploits soon bought him into contact with the actual Doctor. At first, the real Tenth Doctor believed Lake to be his own future incarnation, but began to suspect that the man was not who he claimed to be when Lake attempted to use an ordinary screwdriver to ward off an attacking Cybershade. After uncovering enough evidence, he deduced Lake's true identity, and revealed it to him. With the sudden knowledge that he was not who he thought he was, Lake had a breakdown and told Rosita to accompany the real Doctor as he confronted Mercy Hartigan.

The Doctor and Rosita discovered the location of the kidnapped children, as Lake struggled with the devastating truth. Having recovered most his memory, but unable to remember what the Cybermen "took" from him, he found the courage to join Rosita and the Doctor, arming himself with a bandolier full of infostamps. Using the devices to attack the Cybermen, Lake, Rosita, and the Doctor fought their way under the River Thames. There the kidnapped children were used as slave labor, forced to construct the CyberKing Dreadnought, a massive weapon and Cyber-conversion factory, created for the invasion of Earth. As the Doctor and Rosita evacuated the rescued children, Lake recovered his memory completely, remembering what the Cybermen had taken from him - his son.

Finding his son in the factory, but too paralyzed with fear to save him, Lake marvelled as the Doctor leaped into action and rescued the boy. He watched from the streets as the Doctor took the hot-air balloon to confront Hartigan and end the Cyber threat. Having shared memories of the Doctor from the infostamp, he knew that the Doctor was rarely ever thanked for his exploits, and so he rallied the assembled masses to cheer for and thank the Doctor.

The crisis averted, Lake and the Doctor met near the TARDIS. With Lake now a widower looking after a young son, there was no question of the Doctor inviting Lake to join him in his travels. He was unlikely to do so anyway, given his recent experience with Donna Noble. Still, Lake begged for a look inside the TARDIS, to which the Doctor agreed. Overcome by the unbelievable, Lake forced himself to exit, ecstatic to have finally seen the ship but quite through with adventure. Reunited with his son, and appointing Rosita as his nanny, he invited the Doctor to a Christmas dinner, an offer that the Doctor refused, even when Lake suggested it be "in honour of those we have lost. However, when Jackson insisted, the Doctor finally accepted, happily." (TV: The Next Doctor)

Personality
Lake was a somewhat shy, average man. Due to the effect of the infostamp, and under the belief that he was the Doctor, Lake became a brave, dashing hero. Once his memories as Jackson Lake returned, his confidence waned, but as the threat of the Cybermen loomed, he discovered true bravery deep within himself. The Doctor informed Lake that this was his own doing, not an effect of the infostamp. Even after his true identity reasserted itself, Lake retained much of the knowledge he had obtained through his brief experience as the Doctor, although he found it hard to accept the reality of the Doctor's TARDIS. (TV: The Next Doctor)

Other information
Jackson Lake carried his own version of a sonic screwdriver which was, in fact, an ordinary screwdriver. When asked how it was "sonic," he said it made a sound, demonstrated by tapping it against a doorframe. He also carried a fob watch. The Doctor initially suspected this to be a Chameleon Arch fob watch, but discovered otherwise when he opened it and found only a normal watch face. The watch did contain the secret of Lake's true identity; his initials were engraved on the back. (TV: The Next Doctor)

Behind the scenes

 * Lake is sometimes considered a companion of the Tenth Doctor by fans, but, as mentioned in the episode, the Doctor is a companion to Lake. However, unlike (for example) Christina de Souza, the BBC has not officially declared him to be one.
 * Lake's residence was at Number 15, Latimer St. Tim Latimer was another character who accidentally obtained some of the Doctor's memories.