Imagine you live in a world with only two types of people. Introverts (i’s 🏴☠️) and extroverts (e’s 🦅). All introverts are the same. And so are all extroverts. It's a world with only two colors, and no shades in between.
Introverts (i’s 🏴☠️) like to be alone, in our world they want to meet a friend every 14 days. Extroverts (e’s 🦅) like to be around other people. In our world they want to hang out with a friend every 2 days.
I´s and e´s also have something in common. They have short term memory loss. Everyday at midnight their brain does a full reset. So they never remember what happened yesterday.
Now that you know the basics of our thought experiment, take a guess: Which personality type feels more alone? Introverts or extroverts?
What does this question even mean? Let's say I'm an introvert. I wake up one morning and want to meet a friend. But when I call my friends, they don’t want to hang out with me.
That day I will go to bed feeling alone. But as I said above, the next morning will be a fresh start.
Here's two more ways to ask the same question. Who, on average, feels alone on more days, i’s or e’s? Whose interpersonal needs are being met less, i´s or e´s?
Did you take a guess? Maybe you picked e’s 🦅. Because they need more human interaction in general. Or you picked i’s 🏴☠️. Because they shoot themselves in the foot by being such loners?
Let’s take a closer look at our protagonists:
Are You Going To Meet a Friend Today?
To answer this question I calculated the probability of “meeting a friend today” for each friend group mix.
What is a “friend group mix”?
If you have one introverted and one extroverted friend, your friend group mix is 1/1, one i 🏴☠️ & one e 🦅.
If you have 5 extroverted friends, your friend group mix is 0/5, zero i 🏴☠️ & five e 🦅.
Each table cell (probability of meeting a friend today) is calculated like this: probability_self * sum_probability_friends.
If an introvert has one introvert friend its: 7.14% * 7.14% = 0.51%.
If an introvert has one extrovert friend it’s: 7.14% * 50% = 3.57%.
If an introvert has two extrovert friends it`s: 7.14% * (50% + 50%) = 7.14%
x-axis = number of extroverted friends, y-axis = number of introverted friends
x-axis = number of extroverted friends, y-axis = number of introverted friends
We can see that for extroverts the probability of “meeting a friend today” rises much faster than for introverts. Extroverts need less friends to have a high probability of “meeting a friend today”. But, if you are like me, your brain doesn't know how to work with percentages. So let's turn these % into days.
In X Days You Will Meet a Friend
Now I calculated how many days i’s and e’s have to wait until they meet a friend - for each friend group mix.
x-axis = number of extroverted friends, y-axis = number of introverted friends
x-axis = number of extroverted friends, y-axis = number of introverted friends
Think about what “kind of friends” you have. By that I mean: How many introverted and extroverted friends? Then check the charts above: How many days do you (theoretically) have to wait until you meet a friend?
Did you also get 1095 days 😅? But hold on! Where do the 1095 days for 0 friends come from?
I chose to limit the number of waiting days to a maximum of three years. Otherwise the 0/0 cell would show the number infinity for i´s and e´s. This would have messed up the charts and following calculations.
Why did I choose three years (or 1095 days)? I guess in three years everybody should be able to make and meet at least one friend.
If you haven't met a friend in three years, let's hang out quickly so my charts are correct 😁.
This Might Be a Popular Person Problem
Below we can see the difference between likely waiting days and optimal waiting days for i`s and e`s. Negative numbers indicate that the likely waiting is shorter than optimal, leading to social stress.
x-axis = number of extroverted friends, y-axis = number of introverted friends
x-axis = number of extroverted friends, y-axis = number of introverted friends
These charts can show us what friend group mix would be optimal for introverts and extroverts. To find optimal friend groups we have to look for the cells that contain a 0.
I double checked my calculations many times because I couldn't believe it. Introverts and extroverts need the same combination and number of friends.
Unfortunately the previous calculations still don't tell us who feels more alone. For that we need the relative (percentage) difference between what a person wants and what a person receives.
An analogy:
Ben 👨 wants to earn 100€/h but gets only 50€/h. His salary is 50% below his expectations.
Lisa 👩 wants to earn 1000€/h but gets only 950€/h. Her salary is 5% below her expectations.
Who do you think is pissed off more? Ben 👨 or Lisa 👩? I think it's Ben. Because even though, just like Lisa, he earns 50€ less than what he wants. His relative difference (50%) is much higher than Lisas relative difference (5%).
Back to our own problem: Below you can see the same “relative difference calculation” for i’s and e’s and all friend group mixes.
The “How Alone Do You Feel” Factor
x-axis = number of extroverted friends, y-axis = number of introverted friends
x-axis = number of extroverted friends, y-axis = number of introverted friends, colored cells = “feeling alone factor”
Wow, both tables are exactly* the same. This means that introverts and extroverts are both feeling alone the same.
*The only difference is the first cell. Why is that? Earlier in the essay I told you I set a maximum waiting time of 1095 days if somebody has no friends at all 😅.
Now because this “zero friends limit” is exactly the same for i´s and e´s the relative difference for extroverts is much higher.
This means if you lock an extrovert in a single prison cell for 1095 days he will feel much more alone than an introvert. That's a no brainer. You probably already knew that.
Are You Satisfied?
I know I'm not. And since I'm the mayor of “thought experiment world” I'm making up one more rule: Extroverts have more friends than introverts. Which might also be true in real life?
To simplify this last chapter I calculated how alone i’s and e’s feel depending on the number of friends they have. Here’s this calculation for all possible friend group mixes:
x-axis = introvert or extrovert, y-axis = number of friends, colored cells = “feeling alone factor”
Now the numbers look different from what we saw before. Why is that? If an introvert has 1 friend, this one friend can either be an introvert or an extrovert. So the average “feeling alone factor” for one friend is: (1300% + 100%) / 2 = 700%
Let's say in our thought experiment extroverts have one more friend than introverts. This means that, until an introvert has 8 friends, extroverts will always feel less alone.
If you're wondering why the numbers rise above 8 friends: It’s because at some point i’s 🏴☠️ and e’s 🦅 are stressed by having too many friends.
Introverts Feel More Alone
We made progress. Introverts feel more alone than extroverts 🥲. Introverts feel about 85% more alone (For 1 - 9 friends).
If we consider only a lower number of friends, introverts feel even more alone. For 1 - 5 friends, introverts feel about 120% more alone.
Are You An Introvert?
Because there is more: We become friends with people who are like us. Extroverts have more extroverted friends & introverts have more introverted friends.
If i’s and e’s only have friends of the same kind, the table looks like this:
x-axis = introvert or extrovert, y-axis = number of friends, colored cells = “feeling alone factor”
Now introverts feel shockingly more alone 😱. Introverts feel about 500% more alone (For 1 - 9 friends).
Do we have to keep going? For 1 - 5 friends, introverts feel about 1180% more alone. That's almost 12 times more.
Conclusion
Introverts 🏴☠️ need some extroverts in their life to reduce feeling alone.
Extroverts 🦅 can benefit from an introvert friend if they have social stress.
Now there's only one question left to ask: Are you an extrovert and want to hang out in 14 days?
The clean lines make me think you didn't use hypergeometric calculations. If I have 2 extrovert friends, on any given day 0 (25%), 1(50%), or 2(25%) of them will want to hang out.
If I want to hang out on day N, there is a 25% chance I fail to.
Imagine you live in a world with only two types of people. Introverts (i’s 🏴☠️) and extroverts (e’s 🦅). All introverts are the same. And so are all extroverts. It's a world with only two colors, and no shades in between.
Introverts (i’s 🏴☠️) like to be alone, in our world they want to meet a friend every 14 days. Extroverts (e’s 🦅) like to be around other people. In our world they want to hang out with a friend every 2 days.
I´s and e´s also have something in common. They have short term memory loss. Everyday at midnight their brain does a full reset. So they never remember what happened yesterday.
Now that you know the basics of our thought experiment, take a guess: Which personality type feels more alone? Introverts or extroverts?
What does this question even mean? Let's say I'm an introvert. I wake up one morning and want to meet a friend. But when I call my friends, they don’t want to hang out with me.
That day I will go to bed feeling alone. But as I said above, the next morning will be a fresh start.
Here's two more ways to ask the same question. Who, on average, feels alone on more days, i’s or e’s? Whose interpersonal needs are being met less, i´s or e´s?
Did you take a guess? Maybe you picked e’s 🦅. Because they need more human interaction in general. Or you picked i’s 🏴☠️. Because they shoot themselves in the foot by being such loners?
Let’s take a closer look at our protagonists:
Are You Going To Meet a Friend Today?
To answer this question I calculated the probability of “meeting a friend today” for each friend group mix.
What is a “friend group mix”?
Each table cell (probability of meeting a friend today) is calculated like this: probability_self * sum_probability_friends.
x-axis = number of extroverted friends, y-axis = number of introverted friends
x-axis = number of extroverted friends, y-axis = number of introverted friends
We can see that for extroverts the probability of “meeting a friend today” rises much faster than for introverts. Extroverts need less friends to have a high probability of “meeting a friend today”. But, if you are like me, your brain doesn't know how to work with percentages. So let's turn these % into days.
In X Days You Will Meet a Friend
Now I calculated how many days i’s and e’s have to wait until they meet a friend - for each friend group mix.
x-axis = number of extroverted friends, y-axis = number of introverted friends
x-axis = number of extroverted friends, y-axis = number of introverted friends
Think about what “kind of friends” you have. By that I mean: How many introverted and extroverted friends? Then check the charts above: How many days do you (theoretically) have to wait until you meet a friend?
Did you also get 1095 days 😅? But hold on! Where do the 1095 days for 0 friends come from?
I chose to limit the number of waiting days to a maximum of three years. Otherwise the 0/0 cell would show the number infinity for i´s and e´s. This would have messed up the charts and following calculations.
Why did I choose three years (or 1095 days)? I guess in three years everybody should be able to make and meet at least one friend.
If you haven't met a friend in three years, let's hang out quickly so my charts are correct 😁.
This Might Be a Popular Person Problem
Below we can see the difference between likely waiting days and optimal waiting days for i`s and e`s. Negative numbers indicate that the likely waiting is shorter than optimal, leading to social stress.
x-axis = number of extroverted friends, y-axis = number of introverted friends
x-axis = number of extroverted friends, y-axis = number of introverted friends
These charts can show us what friend group mix would be optimal for introverts and extroverts. To find optimal friend groups we have to look for the cells that contain a 0.
I double checked my calculations many times because I couldn't believe it. Introverts and extroverts need the same combination and number of friends.
Both need:
How Pissed Off Is Ben?
Unfortunately the previous calculations still don't tell us who feels more alone. For that we need the relative (percentage) difference between what a person wants and what a person receives.
An analogy:
Who do you think is pissed off more? Ben 👨 or Lisa 👩? I think it's Ben. Because even though, just like Lisa, he earns 50€ less than what he wants. His relative difference (50%) is much higher than Lisas relative difference (5%).
Back to our own problem: Below you can see the same “relative difference calculation” for i’s and e’s and all friend group mixes.
The “How Alone Do You Feel” Factor
x-axis = number of extroverted friends, y-axis = number of introverted friends
x-axis = number of extroverted friends, y-axis = number of introverted friends, colored cells = “feeling alone factor”
Wow, both tables are exactly* the same. This means that introverts and extroverts are both feeling alone the same.
*The only difference is the first cell. Why is that? Earlier in the essay I told you I set a maximum waiting time of 1095 days if somebody has no friends at all 😅.
Now because this “zero friends limit” is exactly the same for i´s and e´s the relative difference for extroverts is much higher.
This means if you lock an extrovert in a single prison cell for 1095 days he will feel much more alone than an introvert. That's a no brainer. You probably already knew that.
Are You Satisfied?
I know I'm not. And since I'm the mayor of “thought experiment world” I'm making up one more rule: Extroverts have more friends than introverts. Which might also be true in real life?
To simplify this last chapter I calculated how alone i’s and e’s feel depending on the number of friends they have. Here’s this calculation for all possible friend group mixes:
x-axis = introvert or extrovert, y-axis = number of friends, colored cells = “feeling alone factor”
Now the numbers look different from what we saw before. Why is that? If an introvert has 1 friend, this one friend can either be an introvert or an extrovert. So the average “feeling alone factor” for one friend is: (1300% + 100%) / 2 = 700%
Let's say in our thought experiment extroverts have one more friend than introverts. This means that, until an introvert has 8 friends, extroverts will always feel less alone.
If you're wondering why the numbers rise above 8 friends: It’s because at some point i’s 🏴☠️ and e’s 🦅 are stressed by having too many friends.
Introverts Feel More Alone
We made progress. Introverts feel more alone than extroverts 🥲. Introverts feel about 85% more alone (For 1 - 9 friends).
If we consider only a lower number of friends, introverts feel even more alone. For 1 - 5 friends, introverts feel about 120% more alone.
Are You An Introvert?
Because there is more: We become friends with people who are like us. Extroverts have more extroverted friends & introverts have more introverted friends.
If i’s and e’s only have friends of the same kind, the table looks like this:
x-axis = introvert or extrovert, y-axis = number of friends, colored cells = “feeling alone factor”
Now introverts feel shockingly more alone 😱. Introverts feel about 500% more alone (For 1 - 9 friends).
Do we have to keep going? For 1 - 5 friends, introverts feel about 1180% more alone. That's almost 12 times more.
Conclusion
Now there's only one question left to ask: Are you an extrovert and want to hang out in 14 days?
Thanks to Maria for reading drafts of this.