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MBTI is a system of personality types. 

There are 8 cognitive functions:

Thinking functions

Ti: People with Ti, or introverted thinking, analyze the irremoveble components of how an object functions.

Te: People with extroverted thinking (Te) are fact- oriented and efficient.

Feeling functions

Fi: People with introverted feeling (Fi) are individualistic and want to be themselves. They are also very moral.

Fe: People with extroverted feeling (Fe) are compassionate and focused on social norms a lot. They aren't as focused on being authentic.

Intuitive functions

Ni: People with introverted intuition (Ni) are strategic planners and have epiphanies and intuition about people, science, situations, etc...

Ne: People with extroverted intuition (Ne) are focused on possibilities and are very creative. 

Sensing functions

Si: People with introverted sensing (Si) have detailed memories and focus on the past.

Se: People with extroverted sensing (Se) are good at getting in synch with their environment and people around them. A lot of people with Se are athletic. 

Everyone has four functions: A thinking function, a feeling function, a sensing function, and an intuitive function. The order they're placed in depends on how well developed they are and how frequently they're used.

For example, an INTP is Ti dominant, Ne is their auxiliary function, Si is their tertiary, and Fe is their inferior function. So they are good at understanding how things work, they are creative, they have good memories and are somewhat past oriented, but not as focused on it as someone with auxiliary or dominant Si, and they're usually not as good with social norms. 

The letters are determined like this:

I is for introvert. Someone with a dominant introverted function is an introvert. That's because the function is internally focused. (Fi, Ti, Si, or Ni.)

E is for extrovert, someone with a dominant extroverted function. (Fe, Te, Se, or Ne.) 

N is for Intuition. Someone with Ni or Ne as their dominant or auxiliary function.

S is for sensor. Someone with an auxiliary or dominant sensing function. Si or Se.

T is for Thinker. Someone with a dominant or auxiliary thinking function. Ti or Te.

F is for Feeler. Someone with a dominant or auxiliary feeling function. Fi or Fe.

P is for Perceiver. Someone with a perceiving function as their auxiliary. Which is an intuitive or sensing function. (Si, Se, Ni, or Ne.)

J is for Judger. Someone with an auxiliary judging function. Which is a feeling or thinking function. (Fi, Fe, Ti, or Te.) 

There are sixteen types: INTP (Ti Ne Si Fe), INTJ (Ni Te Fi Se), INFP (Fi Ne Si Te), INFJ (Ni Fe Ti Se), ISTP (Ti Se Ni Fe), ISTJ (Si Te Fi Ne), ISFP (Fi Se Ni Te), ISFJ (Si Fe Ti Ne), ENTP (Ne Ti Fe Si), ENTJ (Te Ni Se Fi), ENFP (Ne Fi Te Si), ENFJ (Fe Ni Se Ti), ESTP (Se Ti Fe Ni), ESTJ (Te Si Ne Fi), ESFP (Se Fi Te Ni), and ESFJ (Fe Si Ne Ti).

SPs, Sensing perceivers (Sensors who are also perceivers) live in the moment and are impulsive. 

SJs, Sensors who are also judgers, are very stable and are focused on the past.

NTs, Intuitives who are also thinkers, are very intellectual and make decisions based on logic.

NFs, Intuitives who are also feelers, make decisions based on emotions, are compassionate, and are often intellectual. 

I want to type the characters in the Alcatraz books based on this system.

Here's my opinion:

Alcatraz: INFP (Fi Ne Si Te)

He is unique and different. He is also clever and good at solving problems, which is him using Ne to creatively problem solve.

Grandpa Smedry: ENFP (Ne Fi Te Si) 

He is nice to everyone and he is moral. So I think he's an ENFP. In the Knights of crystallia he gets upset because Alcatraz's friends don't really like him. That's introverted feeling.

Attica: INTP (Ti Ne Si Fe)

He is a scientist who is well liked and he enjoys attention from people. This is Fe. He wants people to like him. He also doesn't know what to do with Alcatraz, which means he doesn't really know how to be a parent. I think this is inferior Fe. And he just isn't used to him.

Kazan: ENFP (Ne Fi Te Si)

Kazan is creative and funny. He has a list of reasons why short people are better than tall people, which is Ne. He is also very genuine and in the Scrivener's Bones, he tells Alcatraz to look past people's differences and judge them for who they are, which means he has Fi.

Sing: ISFJ (Si Fe Ti Ne)

Sing cares a lot about the people of Mokia. He is traditional and he wants to save his people from the Librarians. I think that means Sing is an extroverted feeler (Fe) and an introveted sensor (Si). 

Folsom: ENFP (Ne Fi Te Si) 

Folsom is creative and he likes to be a critic. I think he is a feeler because he cares a lot about Himalaya. He is also Te because he is using it to criticize people. 

Himalaya: INFP (Fi Ne Si Te) 

Himalaya is moral and joined the Free Kingdoms after she found out Librarians were evil. She is also kind to Alcatraz. And she is intelligent, which INFPs tend to be. 

Quentin: INFP (Fi Ne Si Te)

Quentin is moral and he is intelligent. I think he is an introverted feeler. (Fi). 

Bastille: ISFP (Fi Se Ni Te)

She is moral (Fi) and she's a good fighter and one of the youngest knights (Se). 

Australia: INFP (Fi Ne Si Te) 

Australia is moral and she is kind (Fi). 

Aydee: ENFP (Ne Fi Te Si)

She is kind and talkative, which makes me think she's an ENFP. 

Pattywagon: ESFP (Se Fi Te Ni)

She is outgoing and cares about people. I think she's an introverted feeler. 

 

 

 

 

 

 

 

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