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The Doctor has always been a kind person, generating this characteristic through the years. Though thirteen has really nailed it. While her previous regeneration had to fight and struggle not to be insulting, she's careful and generous in most of her interactions with people. For example: while her previous regeneration would often give people insulting nicknames, 13 doesn't. Even when she nicknames people she asks first for ex. asking Yazmin if she can call her Yaz.

Another aspect of her kind and caring nature is that she goes about helping people. Usually it's to stop someone from hurting others, but she does save who she can (and this is important) and tries on the whole to make the universe a better place. She tries to help people on an individual level to when it's within her capacity to do so. For example being encouraging to Ryan and hurried but patient with him when he has to do things like climb a ladder in a tense situation. (which is difficult for him do to his coordination disability)

Being charismatic is how the Doctor gets into and out of most everything. Essentially she has a boatload of charm and is not afraid to use it. She does so on a daily basis, mostly in asking people questions and finding out about them and genuinely liking them-- but also by pretending she belongs in any given situation. For example, pretending she was invited to a party (she was not at all invited to) and playing and looking the part of a gambler. Also talking her way into a resort and security center to take a look at the inner workings because of some suspicious activity.

That being said, she's not as charistmatic as she once was. What I mean is that the Doctor often uses the charisma as a shield. Nothing wrong with me. Just fine. Just pleasant. But recently her companions can tell something is wrong with her and she does look a bit rougher about the edges. (But what is she refuses to say)

The Doctor has always been inquisitive. It's part of her getting into and out of everything. She routinely sticks her nose into situations and places to find out what's going on. She gets involved. She interferes. She is always exploring new worlds, times, people. And she likes to get to know them too. It's not uncommon for her to pepper people with questions. Though even as friendly and curious as she is, she keeps her own self private. As Graham states in Spyfall P. II: You know everything about us, but we don't know anything about you. And though she does divulge some details, most of her story she keeps to herself.

If the Doctor is manic or not depends on the regeneration, and this particular one, while not as manic as she has been in the past, is pretty on the go. She's energetic. Slightly loopy when she gets going. And always moves five times faster than anyone else. (in terms of processing, if not speed). If a situation comes up, she throws herself into it with enthusiasm. And anyone with her. Especially if it looks fun. For example, in the episode Kerblam! getting a fez that she hadn't ordered and realizing that it's kind of a call for help. Is it? She doesn't know. But she's going to go find out anyway because why not.

While the Doctor may not be as arrogant as she once was, there's the capacity for it, and it definitely shows in her high-handedness. Part of it is because she is a type A personality and a bit of a leader. She is the one who solves the crises so she is (by and large) the one who decides how the crises should be solved. Most of it has been fine and not particularly morally grey. Though this does on occasion lead her to doing foolish things like offering herself for a sacrifice in the Dream Universe. But lately things have gotten a bit darker. For example in Spyfall she erased the memories (of the adventure) of two women so that it wouldn't disrupt the future. One of these begged her not to do it but she did anyway, because it was the way she thought was right.

As for darkness, she has the capacity for so much more given the Doctor's history. Though we haven't seen much of it yet, there are hints of it here. She will do the hard thing in order to make things turn out for the best. For example, in the Rosa Parks episode, Graham (the white man) wanted to give his seat to Rosa but the Doctor told him to sit down. Because if he did, he would alter history. A darker example is in Spyfall P. II where she erases the memory of Noor, the first female radio operator and undercover agent in WWII-- but also leaves her to her (historical) fate, which is to be captured, tortured and put to death by the Nazi's. This is subtextual more than anything since her fate wasn't addressed on the show, but the Doctor had to know about it and it's in character that she would.

One final aspect to her personality which makes it unique is that after being a man for 2,000 years, she's getting used to being a woman. She's got the hang of it pretty much but there are still exciting new things open to her -- and she still addresses herself in masculine ways from time to time (eg. Come to Daddy... Mum. or: The Amazing Reappearing Man... Lady!)