sorry what's the deal with the other? is he the doctor???
You've just unlocked my unskippable cutscene.
So sometime in the 80s, one of the dw writers, Andrew Cartmel, thought that there wasn't enough mystery left in the Doctor's life. The trouble, according to him, began when we were introduced to the Time Lords and suddenly there was a straightforward explanation for the Doctor - thus, the Doctor needed to have less explanation and more enigma in his backstory. The Cartmel Masterplan, interrupted by the cancelation of the show and continued in the EU, would have given the Doctor a background shrouded in mystery and unearthly powers beyond human or Time Lord comprehension.
Now, according to the TV show, the main founder of Gallifrey was Rassilon, the architect and later despotic god-emperor of Gallifrey. Alongside him was Omega, who created time travel, and a mysterious third one called the Other, first appearing in the novelization of Remembrance of the Daleks: a being of unknown origin and vast powers, who Rassilon "acquired" through an unspecified deal in "Some sort of pact with God knows what". Almost like Rassilon has the Other as some kind of tool, powers he borrows for his own gain.
Marc Platt gives us our biggest picture of the Other in Lungbarrow, where some light is shed on the place where the Doctor was born and raised, and also a clandestine past reaching back to the dawn of Gallifrey. In Lungbarrow we see the Other, jaded and displeased with what Rassilon has created, trying to kill himself but the Hand of Omega won't let him. So the Other throws himself into the Loom, scattering his genetic material and is never seen again. Years later, the Gallifreyan who would become the Doctor is loomed into the House of Lungbarrow. When the first Doctor runs away, he encounters Susan Foreman, who was actually THE OTHERS granddaughter - and yet she seems to recognize the Doctor right away and accepts him as her grandfather. At the end of Lungbarrow we learn that Leela of the Sevateem is pregnant with the child of Andred, the first pregnancy seen on Gallifrey in countless years. Marc Platt confirms that he meant for the child of Leela and Andred to be the Other, who was sent back in time to the dawn of Gallifrey. I cannot stress enough that if you haven't read Lungbarrow, you really really should.
Now, if you're like me and you want to fit this into the TV Canon, the connection between the Other and the Doctor actually fits neatly into the Timeless Child origin story if you see it as: Leela has Andreds baby, which is somehow sent back in time. This child is found abandoned by Tecteun and taken in. Tecteun subjects the Child to experiments, and with it she develops the powers of regeneration. The Timeless Child grows up to be the Other, helping Rassilon with its otherworldly powers, which would explain Rassilon "acquiring" the Other through questionable means. The Other throws itself into the Loom to get away from Gallifrey, later being reborn as the Doctor, who then runs away from Gallifrey again.
If you want to know why this is my absolute favorite interpretation of the Doctor's backstory: there is NOTHING more delicious to me than the idea of the Doctor being the unwilling architect of their worst nightmare. The Doctor lives in active scorn of the society that created them, which is why it's so brilliant for them to have unwillingly created Gallifrey, thus having their hatred of the Time Lords have roots all the way back in the genesis of the Time Lords. There is some beautiful irony in Gallifrey abusing a Gallifreyan child from their own future, a stagnant society cannibalizing itself until the end of time. It also nicely laces into contradicting accounts. The Doctor is an ordinary Time Lord? Yep! The Doctor is an ancient founder of Gallifrey? Yep! The Doctor is half human? Yep! Come with me and be insane about the Other.