But the bright red that's already growing stronger than any of the other colours were - Jackie, Gwyneth, Pete, any of them - that's a different matter.
Rose is safe. Her pale pink is a comforting presence, one which makes him stronger by association, more able to fight back the darkness.
Jack... he's just not sure what he might do.
Red. In human terms, a sign of danger; more universally considered too camp for that. The colour of blood. The colour of passion. Somehow, all of those fit, and yet they don't even begin to communicate the whole of the problem that is Jack.
It's a dark red though; not bright and garish. That tempers the warning signs a bit, he'll admit. But the sheer strength of his presence, after such a short space of time, is a little overwhelming. Rose's presence started on the very edge of his mind, awakening it gently to experience the colours that surrounded him; Jack's seems to have stormed the walls and taken up court in the castle before he's even had time to take a breath.
What strikes him most forcefully isn't the fact that the red is so strong; it's the way it's already starting to join with the pink, their edges beginning to blur together, threads of pink and red winding around each other. That's not unusual - he sees it whenever there's a strong emotional connection between two people, and it's exactly what's happened with the silver and the pink - but for it to happen so quickly is a bit of a shock. If it wasn't for the obvious truth in the story of how they've just met, he'd be willing to bet they'd known each other for a lot longer than a couple of hours.
It's not until he's actually warning Jack away from Rose that he recognises what the problem really is.
He's jealous.
The thing about Rose is that she's become a fixed point in his life, something he can rely on. The TARDIS is the only other constant now. He'd thought it would be difficult to let someone else in, after all the losses he'd been through, but Rose somehow just slipped through his defences and that was that. Since then there've been times when the link's been slightly weaker, where there's been friction between them and the connection's kind of loosened a bit, but it's always been there. And he sees the links between Rose and her family and friends, but that's okay, because they've been a part of her life for a long time. Jack though... Jack's new - completely brand spanking shiny new - and yet he and Rose have already formed a bond that he's scared of. Because he doesn't know what he'll do if she leaves now, and he knows that kind of connection is difficult to break.
Taking into account all the facts - he's a con man, he nearly destroyed the human race, he seems to be reeling Rose in without even trying - it's maybe not so surprising that the red has such a strong presence.
What's more surprising is that despite all that, the silver is already beginning to reach out to join the red, already starting to become entangled with it.
He'd thought he had more control over himself than that.
He decides that Jack is just too charming for his own good, and that he should be dropped off as soon at their next stop. They've saved his life, and that means that he owes them, not the other way round.
He knows that's not going to happen though.
The colour red might mean many things, but he knows that the dark shade represents something much more important. Solidarity. Loyalty. To him and to Rose. He's already proved himself capable of sacrifice.
Quite suddenly, the Doctor becomes aware that they've become a team. And he can't blame Jack for pulling Rose in so quickly, because he's also done exactly the same to him. And they seem to have done it right back.
It's glaringly obvious that the knots being tied, joining pink to silver to red to pink, are going to be very hard to break. And somehow, in spite of the inherent dangers, that's comforting.