This analysis is based on PK (from 2014 movie PK). And the character comes as a very strong ET(N) candidate. I will also debunk the bahavior-based stereotype which label him as IT(N) or equivalent INTP in MBTI. Extroverted Thinking (Principal Function + Attitude): Thinking is a rational function associated with logical reasoning and conceptual relations, opposed to judgment through values. While extraversion is the attitude where the objective factor has more influence than the subjective factor, meaning what is observed as it is, is given more importance than what criteria the individual prefers to perceive or judge something. When you combine thinking and extroversion, you get a type which judges object (situation or problem) through objective factors. That's why this type might appear more inductive in reasoning. And principal function is the habitual orientation of a person, seen dominantly in them. Same applies to PK as since he came to earth and lost his remote, he started figuring our how societies on earth work and how humans interact. And for the same, his guiding information becomes what he observes directly, based on which he creates his conceptual model of earthlings. Dancing cars become ATM because he always finds wallet full of cash there, use on currency notes were tested out to be specifically where Gandhi's photographs were there, God stickers become utility for "self-defense" as people consider it holy, and many more. These aren't shaped through his idea of logical systems, but through what data those logical points present themselves. That's what makes it extraverted thinking. Intuition (Auxiliary Function): Intuition is an irrational function that perceives possibilities associated with a given object. And auxiliary function supports the principal function. PK includes strong examples for intuition auxiliary. His minds hits strong unconscious contents that reveal connection among various facts he studied, or connecting irrelevant concepts through possible relations. For example perceiving that His Holiness might be getting call from a prankster instead of God, triggered after witnessing Jaggu pranking someone who was continuously dialing her as a wrong number. Another example would be him understanding how to use very disconnected objects like rock and leaf to set up a small religious business outside college where unprepared students pay fees. These aren't something already manifested in sensory reality, but coming from the unconscious part of the mind. Introverted Feeling (weak/inferior function): Feeling is a judging function that is concerned with values - good vs bad, acceptable vs unacceptable, honor vs dishonor, etc. PK's high attention to logical reasoning and concrete adherence to building his understanding directly resulted in somewhat repressed feeling, which is seen in how he coldly yet not maliciously points out logical fallacies to people, detached from their significance in terms of value or how acceptable they are. Like asking three Muslim ladies if their husband died as they wore burkas (black), relating to what Christian woman told her about dress code after demise of one's husband, despite being aware with the fact its socially inacceptable. This shows opposing values in favor of logic and the curiosity raised from it. Not literal opposition, but psychological repression where he unconsciously ends up neglecting values, public's and his own. While he has intense emotions regarding his nostalgia for home, death of the human who took care of him and he considered him equivalent to his brother, and even falling in love with Jaggu. But Jung's feeling function isn't about literal emotions, but about values as explained before. This establishes him as principal thinking type with lower preference to values, whether his subjective influence or objective influences like proper social conduct. Counterargument against the most popular type IT(N): Over many casual typology platforms without strict vetting process like here in Typology Atlas, PK is very overwhelmingly typed as IT(N) or equivalent MBTI as INTP. People attribute the reason to his social awkwardness, curiosity to understand the world, and detached demeanor. However, Jung never mentioned these as exclusive characteristics for any type of function. The argument for IT(N) assumes Ti, which is a judging function associated with logical and conceptual relations, but oriented more towards subjective factor than the objective factor. As we discussed, PK was collecting objective data and using them to make logical induction towards his conclusions (as mentioned in examples above). While introverted thinking assumes dominance of subjective factor, meaning the logical structures or models he is forming comes more from his personal understanding and influence. If he was to be IT type, we would have expected him to make some custom understanding of the world, where object or objective observation serves more as a test case than the decisive factor. PK had a very clean understanding of how socio-religious beliefs worked in the world, and that's why people were speechless when he introduces contradictions to them through arguments. For example, when he asked studio owner about why people avoid picking up fallen condom packets unlike wallets where they would fight each other. The owner says this is private matter, no one screams outside after having sex. PK asks, "Then why they play loud music and burn firecrackers during wedding?" He follows a very directional way in thinking. In summary, his influence on objective observations to point out contradictions and get answer to his questions. Not subjective understanding or guessing about "why something might be in a way".