“Human plus Time Lord” - Vastra
Two jump cuts after that scene, we hear Vastra (the lizard lady from 1888) say that Time Lords became the way they are due to exposure to the vortex, the untempered schism. The Doctor does add that it took billions of years. This would suggest that it’s impossible except for two things: the scientists at Demons Run finished the job and the TARDIS is a much more advanced piece of technology.
"I'm old, I'm fat, I'm blue"
We know, thanks to season 6 episode 4 - the doctors wife, that time travel technology advances even for the Time Lords. The TARDIS that we know and love is an old model. It was in a museum before the Doctor stole it (or it stole him). That suggests that the TARDIS, while old, is still newer technology then what changed the Time Lords. This newer technology is more stable then time travel technology like Jack Harkness uses (as the Doctor points out on several occasions). This stabilization, this focusing of the time stream could cause changes faster then the older technology that the Time Lords used.
I miss David Tennant, but Matt Smith is good
I don’t know if River Song has two harts, but we know (Season 6 Episode 8 - Let’s Kill Hitler) that she can regenerate. We know that it’s possible for humans to change into a Time Lord like being. The two harts can be explained by something else.
In Season 1 Episode 2 - The End of the World, Kassandra (the “bitchy trampoline”) tells a story saying that humans have touched every star in the sky. And what did they do when they got there? What humans do best, they mingled. Oh they called themselves new humans and proto-humans and digi humans, even humanish, but they still pulled DNA and traits from aliens. Even possibly a redundant circulatory system? Or it could have evolved naturally, it seems to be a useful trait for the Doctor.
However, Christopher Eccleston is my favorite.
What if some of these proto-humans went back in time to seclude themselves? Humans in reality do it all the time, hermits, gurus, and religious groups. Where would be a great place to seclude a religious sect? The beginning of time, when no one else was around. Hell, the Toclafane were willing to destroy their own ancestors just to survive. Another group could have done the same thing, but decided not to risk a paradox. Yes, the Toclafane were brought back in time thanks to the Master, but the Universe is a large place. It’s vary possible that a small group of time travelers still existed in seclusion.
This would also fit with Season 3 Episode 12 - The Sounds of Drums where the Doctor says the Time Lords are sworn to not interfere with the Universe. This may be something as simple as the Prime Directive in Star Trek, but it could be deeper. It could be based on legends lost to time, do not interfere with the galaxy or you may interfere with your own past.
Gallifrey was so amazing looking.
The Doctor my even know this. He’s always helping humans. He’s infinitely fascinated with humans. When he sees humans do something amazing he gets this look of amazement, but it’s more then that. Pride: he’s proud of what his humans can do. Like a parent being proud of their child. Maybe I have it backwards.
Humans can evolve, in Season 3 Episode 11 - Utopia, the Doctor states that humans spent millions of years evolving into clouds of gas, and then another million years as downloads, but they always returned to the same basic shape. This would not only explain why the Time Lords look like humans, but why so many other alien races look like humans (and humans can breed with them). They are all evolutions of humans that went back in time to escape the end of the universe. Humans went back in time and found an empty planet to live. Their simple existence on the planet would stop natural evolution on said planet. Other planets, that can’t support human life, would still have a chance to evolve life and that explains the non-humanoid races in the universe.
Wibbly wobbly timey wimey indeed.
Yeah, OK. That last part about all life being human is a little over the top.