Birthday Problem
What is it?
In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle (if n items are put into m containers with n>m, then at least one container much contain more than 1 item), the probability reaches 100% when the number of people reaches 367 (since there are 366 birthdays, including Feb 29). However, 99.9% probability is reaches with just 70 people and 50% probability with 23 people. These conclusions include the assumption that each day of the year (except Feb 29) is equally probable for a birthday. In the BuzzFeed video, the second hypothesis is tested, as shown:
The Mathematical Calculations
I will not bore anyone with this, since it did take me about 25 minutes to calculate it myself. Though I think if you used certain aids online, or just looked at the solution online, it doesn't take more than 2 minutes to understand it - I just wanted to put in some probability practice while I was at it. If you want to try, consider P(A) as the probability that at least 2 people in the room have the same birthday. However, common-sensically, it should occur to anyone who has studied probability before that P(A') is easier to calculate in this case. Then, you take 1 - P(A') to get your answer.
Assuming that people's birthdays are independent events (thus rendering the survey in the video rather inappropriate), each person's birthday in the room is an independent event. However, as I have mentioned, this is just an assumption. It is unusual, that within a tight group of friends, that two people share the same birthday. Thus, if a group shows up together in the room, the events are not exactly independent.
Given the situation with 23 people, P(A') = (365/365) x (364/365) x (363/365) x ... x (343/365). By collection and factorising out (1/365), you have (1/365)^23 x (365 x 364 x 363 x ... x 343) and P (A') = 0.492703. But why? You need to understand that the correlation between P(A') [and P(A)] and the number of people does not have a very strong product moment correlation coefficient. Moving into the topic of Correlation and Linear Regression, if a graph of Probability (y) is plotted against Number of people (x), there is a strong relationship, yes, but not a linear one. In fact, it will look something like this:
From the graph (it may be wrong because this is actually my own calculations), the correlation between y and x seems to follow y = -x^2, x E [0. 367]. That isn't important, actually. What is actually important is that, since the relationship between y and x is not linear, the probability of a match actually increases at an increasing rate, or in the case of the graph (dy/dx) becomes more negative.
Yes, I nerded out for a second there. In fact, I nerd out a lot, considering the number of times I went to calculate the chances of catching a Shiny and also, the chance of getting a Silcoon and Cascoon. Math, everybody. Now, for something else more "ranty" before MBTI.
This Intuition of Mine
I am definitely not psychic, I know that, and I cannot read minds either. Then what is it that makes INFJs such an intuitive type? The answer is, well, very simple, that very dominant Ni function that we have.
Of course, there are 8 types that are intuitive, 4 of which possess the Ni function (INTJ, INFJ, ENTJ, ENFJ). What differentiates INTJs and INFJs from their extroverted counterparts is the placement of the function in the dominant spot. A dominant function is a function that develops so early and so naturally in one's life that it feels almost "like I was born with it". So whereas ENTJs and ENFJs still need to continuously develop that function as they grow up, for the Introverts, there isn't much need for development. We pretty much have that patted down since we were 5 or 6.
Then what sets INTJs and INFJs apart? Really, not that much. We aren't more intuitive than them, they aren't more intuitive than us. It's just how we choose to "externalise" our intuition in our auxiliary function, which is extroverted (Fe and Te). INTJs channel their intuition into understand the world, primarily in scientific discovery, guiding them to understand how the world functions to an extent that other types can only be envious of. INFJs, in turn, channel their intuition into understanding human interaction. Make no mistake, INFJs do care about people, but we are still primarily obsessed with understanding people. Psychological tests? Mostly created by INFJs.
To other people, we seem like aliens. INTJs are like aliens too, because they are excessively smart, but we make it more obvious because we extrovert our intuition so much more (human interaction vs factual discoveries). I assure you, though, that we are definitely not aliens and the Ti-dominant types and extroverts seem amazingly alien to us too. The only thing that make us, perhaps, more alien, is just that Ni is extremely rare. No, it's not INFJs that are rare. It's Ni-dom that is rare, because developing something like that in childhood can be seen as psychic ability.
Well then, how does Ni work? Well, what is amazing about Ni is its ability to generate output that is drastically disproportionate to that of input. What I'm sayings is that - we aren't always right. Our "rightness" depends on how much we know, just like everyone else. The difference lies in that we can take a specific amount of information and generate an understanding out of it that exceeds what others can. For example, if you take an Ni-dom and an Ni-aux (yes, even dom and aux makes a huge difference) and put them in a situation with 2 strangers they have both never met before. After 5 minutes of watching them interact, the Ni-dom is much more likely to be able to decipher the relationship between these two people and their respective personalities.
In the real world, it doesn't work that obviously. Because INFJs are still introverted, we can be more wrong than extroverted Ni users because we cannot gather as much information as they do - we don't talk as much or spend as much time with people. Because of that, our input is limited. However, if you give an Ni-dom the same amount of input as the extroverted Ni, it is very likely that the Ni-dom can draw out much more information from the limited input.
....Hmmm so it's safe to say, my intuition serves me well, especially when my Ti (logic) tells me that I have enough evidence that my Ni is relatively accurate. I sense something unpleasant coming my way and I think I know what I have to do to avoid it. For once in these 3-5 years, I'm going to listen to my intuition and take action before I start regretting it again.
MBTI Yay
Most to Least Detached
1. INTJ
2. ENTJ
3. INTP (the most distant...but not necessarily the most detached)
4. ISTP
5. ENTP
6. ISTJ
7. ESTJ
8. ESTP
9. INFJ (they know when to leave a situation)
10. ENFP
11. INFP
12. ENFJ
13. ISFP
14. ISFJ
15. ESFP
16. ESFJ
MBTI Types as Stares
1. ENFP: A fun stare. Prepare to have the time of your life.
2. INFP: A dreamy stare. They love you, but they also love thinking about other things. Like how much fun it would be to live in a tree. It would be great.
3. ENFJ: A heroic stare. They're going to make the right choice no matter how long it takes them. They're your basic protagonists.
4. INFJ: A deep, knowledgeable stare. They know. They've always known. Your secrets are not safe around an INFJ. It's like their 6th sense.
5. ENTP: A smug stare. They've probably just proved their point so well you're probably speechless, so this moment is kind of an embarrassing one.
6. INTP: A distant stare. They're probably not even looking at you.
7. ENTJ: A intimidating stare. Basically if they're looking at you, run.
8. INTJ: A calculating stare. You've probably just said something really stupid...and they're probably gonna prove you wrong. It's okay. This happens.
9. ESFP: A playful stare. But they'll probably break contact because they've found something cooler and more interesting to look at, but it's whatever.
10. ISFP: A warm stare. They're some of the most emotional types. If they love you, you'll know. They're so nice, I can't handle it.
11. ESTP: A crazed stare. They're gonna fucking do the thing you specifically told them not to and it's gonna be fucking awesome. Yeah.
12. ISTP: A bored stare. God. Of all the things they could be doing right now, they have to be looking at you. Don't take it personally though. It's not you.
13. ESFJ: A polite stare. They just wanna be friends. Quit glaring at them.
14. ISFJ: A loving stare. They'll be there no matter what. Don't worry.
15. ESTJ: A determined stare. Basically if you're working for this person (and odds are, you probably are) you won't be long. I'm so sorry.
16. ISTJ: Probably an annoyed stare. Please don't annoy ISTJs they've probably already had a long day full of other annoying people. It's just a bad idea.
Things I Associate with the Types (Part I)
1. ESTP: The earth beneath your fingernails after a long day, waking up feeling full of light and ready to get up, summer evenings, the press of a friend's hand into yours, tan lines that pop on your skin, the chill of rainwater as it slides through your hair, feet sticking out of car windows, running around backyards as the sunlight fades
2. ESTJ: The jarring echo of a microphone when bumped, mowed grass, a newly immaculate room with everything accessible, the fresh smell of rental cars, neat calenders pinned above desks, new school supplies stacked up in your room, monopoly games, sliding into a perfectly made bed at the end of a long day, unpacking in a hotel room, taking yourself out for dinner
3. ESFP: Throwing your arm around a friend, gaudy beaded bracelets put together by your little cousin, the quick pant of an excited dog, the smell of campfires, paint stuck in the crevices of your hand, taking neat notes for the kid who's absent, an instagram full of pictures of you and your freinds, screaming the lyrics to songs as you ride down the highway
4. ESFJ: Staying after class to help a teacher clean up, biting your tongue to try to stop laughing during class, a sticky kiss from a child, kindergarten art rooms, listening patiently to stories you've heard before, walking around in your mom's high heels as a kid, walking around town with ice cream and friends, squeezing lemon juice into your hair
5. ENTP: Having to do a group project by yourself, walking back and forth to calm your excitement, desks cluttered with papers, the sound of quick typing, the rush of relief after walking out of uncomfortable situations, lying to get a reaction out of someone, the sting of tears brought on by anger, the perfect comeback, mascara smeared down your face
6. ENTJ: Protest signs, pinning magazine cut outs to your wall, walking to the front of a room to give a presentation, the click of high heels, tilting your chair back and crossing your arms to show your disapproval, the smell of paint, friendly debates with loud words and wide gestures, losing track of time and blinking tiredly at the clock, perfectly tailored suits left wrinkled on bedroom floors
7. ENFP: Bulletin boards with inspiring quotes, humming along off-key beneath your breath, bare feet on hot sand, p-interest projects, curling ribbon with scissors, sewing your own clothes, improvised road trips, bubblegum pink lipstick, convincing a friend to buy themselves that new outfit, silly nicknames, candy wrappers littered on the floor, compliments from strangers in public restrooms, good morning texts
8. ENFJ: Cute notes left in people's lockers, talking a friend through their self-confidence issues, cleaning your room at two in the morning, dark thoughts that only slip into your mind late at night, the press of a kiss to your forehead, picking out your clothes the night before, convincing a friend to come dance with you, the hand on your shoulder
9. ISTP: Taking apart pens and examining the individual parts, spilling out emotions that you've kept tightly wound inside, the smell of rubber tires on pavement, writing down your thoughts to better understand them, clenched fists, research papers laid out across a table, jumping off a rock wall and letting the cord catch you, polaroid cameras
10. ISTJ: Setting yourself deadlines, slipping candy to a worried friend, puns, stretching after a long day, downing too much coffee so you can stay up to work, drawing tablets, buying Christmas gifts a month in advance, the smell of grass after a rain, sitting in comfortable silence with a good friend, before and after pictures, old family trinkets
11. ISFP: Petitions passed around classrooms, a friend's artwork hanging on your wall, the weight of a child on your hip, getting up early to see the sunrise, interior design, vinyl albums, sitting on rooftops with friends, detailed journals from years back stacked in your closet, the warmth of a cat curled up on your lap, sleepy kisses goodnight, the walk up on stage to collect an award
12. ISFJ: Buying friends gifts for no occasion, old photo albums lining bookshelves, waking up knowing that today is not yesterday, holding a bun up with just a pencil, splattered paint on brick walls, doing homework on the way to school, bitten lips rather than angry words, tentative hugs, the smell of vanilla, hair falling in front of your face when you duck your head
13. INTP: Dead languages, long-winded speeches that change topics multiple times, sweater vests, chalk boards covered with writing, lost glasses that are on top of your head, botanical gardens, finals week, bouncing up and down on the balls on your feet as you rant, unbrushed hair, library fines, the flow of a laptop late at night
14. INTJ: Packing of college, perfectly winged eyeliner, beakers overflowing with bubbles, schedule overloads, chess games that last until late into the night, the feeling of silk on bare skin, locking your door while working, texting while walking, leaning forwards into discussions with your elbows on the table, rapid-fire conversations, makeup lined up along the sink
15. INFP: Community gardens, braiding flowers into a friend's hair, giggles, playing guitar to an empty room, yellow daisies, sudden anger, reading by candlelight, unexpected hugs, empty forest paths, make believe, whispers that you know no one can hear, understanding nods during rants, lifting someone up and spinning them around, the smell of new paper, forgotten tea that's turned cool
16. INFJ: Hanging lightbulbs, thick books where the spine curls inwards, shoulders shaking forwards when you won't let yourself cry, absent kisses laid on top of heads, lying beside a friend in bed and talking to the ceiling, dessert left at a friend's door, watching the people below from city windows, little notes from friends kept for years, the key to your childhood diary
Most to Least Likely to Worry Too Much
1. INFJ (Totally did not see that one coming *sarcasm overflow*)
2. INTJ
3. ISFJ
4. ISTJ
5. INFP
6. ESTJ
7. ENTJ
8. ENFP
9. ENTP
10. INTP
11. ENFJ
12. ESFJ
13. ISFP
14. ESFP
15. ISTP
16. ESTP (Master please teach me your ways!)
Types at the Beach
1. ISTP: Makes sure ENFP has enough sunscreen on
2. ISTJ: Goes to the end of the beach and reads their favourite book
3. INTJ: Is in their beach cabin
4. INFP: Laughing with ENTP in the water
5. ISFP: Walking around, collecting seashells
6. ISFJ: Making a sand castle, with a working moat
7. INTP: Laying down on heir towel, watching the waves
8. INFJ: Sitting right by the water so the waves splash them, staring out to sea with an unexpectedly intense and contemplative stare
9. ESTP: Snorkelling, looking at the fish below trying to poke them
10. ESTJ: Listening to music on the shore
11. ENTJ: Snacking and asking if somebody wants to play volleyball
12. ENFP: Is in the ocean playing around, with their shoulders burning because they don't have sunscreen on
13. ESFP: Dancing and jumping around in the sand
14. ESFJ: Chasing this one bird around everywhere
15. ENTP: In the water with INFP, convincing them to surf
16. ENFJ: Walking down the shoreline in the sunset
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