I'm just wondering. How legit is the claim?
Every detailed INTP description website tells that the charisma exists but couldn't get that much into the specifics of it. It doesn't help either that most MBTI forums have a saturation of INTPs, over-flattering themselves.
Being inherently INTP, this is something that I had interest with over the past recent years, and made some observations.
Among the rationals, my basic impression is...
ENTJ - thinks he's God
INTJ - can be as brutally sarcastic as the ENTJ, but based on my experience with one, I'd rather hang out in an INTJ than ENTJ because the former doesn't assert too much his biases, unless when provoked (in most cases, that is).
ENTP - the only archetype among rationals with a glaring charisma.
INTP is an interesting case. Right now, I can easily identify three INTPs that I know, two of them are incredibly hate-able social retards, it easily makes me question my archetype (mine usually varies. INTP, INFP, ENTP, depending on the test I take. Though as of the moment, I consider myself eNtP. Mildly dominant E, and T). The other INTP has INCREDIBLE charisma.
INTPs are hard to sub-categorize, in my opinion. It's like we have too much variants within an already apparently minority MBTI archetype. There seems to be a broad spectrum between the very likable variants of the INTP and the very hate-able.
To be fair (so that I won't get to flatter myself by involving myself), I looked at the charismatic INTP that I know, also observed all the charismatic ENTPs (and some close INTP archetypes) that I know, and I came up with some conclusions:
1. Putting INTROVERTED THINKING in the proper social context. The charismatic INTP I know does something like this. He lets the other person (or the group) initiate the talk. He later supplements the talk with his broad knowledge base, usually hardly contradicting the statement but further affirms it, focusing on the other person's statement's merits. The major point to consider is the supplement approach. The broad knowledge base is never initiated. The INTP guy never initiates the deep talk, thus reducing the chances of overwhelming others with his intellect.
If he couldn't supplement it, he asks questions. And this is where INTPs are good at. THEY ASK GOOD QUESTIONS. By doing this, it shows that the INTP is interested with the person's view, and asking good questions provide a good measure of the INTPs intellect. So at least this mode of conversation is good to both parties.
2. Introverted Thinking Simplifying Complicated Concepts - as they say in INTP websites, Introverted Thinking likes to simplify what is complex and making complex something that is apparently simple. I do tend to observe that the former is very well appreciated and the later is hated. The former displays an intention of the INTP person of keeping-things-light, which is a basic socializing protocol.
By simplifying something that is complex (basically putting it to its essentials), the INTP sends the impression that, "Hey, I may be smart, but I want you to have a full understanding of what I want to explain, and not overwhelm you with needless rhetoric.
Still, the other person learns from the INTP. (usually, number 2 is best combined with 1)
3. Self-deprecating humor - ENTPs have full mastery of this. INTPs may acknowledge their faults, but they hardly make jokes about it. The more socially inept ones are too defensive of their pride, they end up as opinionated as an irritatingly outspoken ENTJ sometimes. The more appealing INTPs I know are good at making fun of themselves.
4. Making something humorous/charismatic about what's perceived of you to be negative - I'll use an example. NTPs get accused all the time of being bums. One ENTP I know is PROUD of the image, he dresses up BUM style. But it's a stylistic BUM. It looks like an Otaku/Hiphop dress-up hybrid. Not so minimalist. Looks a bit hiphop ghetto, but stylistic.
Until he starts speaking. By dressing up BUM style, he makes a bit of an under-declaration of himself. But not under-declared enough to be considered ghetto. But when he speaks, it's articulate enough that it brings a surprising intellect factor that is not normally expected of him at initial glance.
5. Flirting -- INTPs underrated trait. the P function can help us create figurative open-ended statements, hence making us less accountable than J statements. Figurative statements give a sense of conversational control, unlike J statements that is easily more susceptible to accountability in cases where politically incorrect statements are made.
Based on experience, it helped me do wonders on ENFJ, INFJ, and ESFP. Though personally, I prefer ENFJs. They romanticize the context of the figurative statement. And they make sure that it has a better sense of clarity, so that the next statement from the INTP is progressively, but comfortably more defined.