Imagine you live in a world with only two types of people. Introverts and extroverts. All introverts are the same. And so are all extroverts. It’s a world with only two colors, and no shades in between.
Introverts like to be alone, in our world they want to meet a friend every 14 days. Extroverts love to be around other people. In our experiment 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:
Introvert
Nickname: i as in ay ay, captain 🏴☠️
Wants to meet a friend once every
14
days
Probability wants to meet a friend today
7.14%
Extrovert
Nickname: e as in eagle 🦅
Wants to meet a friend once every
2
days
Probability wants to meet a friend today
50.00%
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% * (1-(1-7.14%)^1) = 0.51%.
If an introvert has two extrovert friends it’s: 7.14% * (1-(1-50%)^2) = 5.36%
If an introvert has two extrovert and one introvert friend it’s: 7.14% * (1-((1-50%)^2 * (1-7.14%)^1)) = 5.48%
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.
i2 - Waiting days until meeting a friend for an introvert 🏴☠️
(i) / (e)
0
1
2
3
4
5
6
7
8
9
10
0
1095
28
18.67
16
14.93
14.45
14.22
14.11
14.05
14.03
14.01
1
196
26.13
18.23
15.84
14.86
14.42
14.21
14.1
14.05
14.03
14.01
2
102
24.61
17.85
15.69
14.8
14.39
14.19
14.09
14.05
14.02
14.01
3
71
23.35
17.5
15.56
14.74
14.36
14.18
14.09
14.04
14.02
14.01
4
55
22.28
17.2
15.43
14.68
14.33
14.16
14.08
14.04
14.02
14.01
5
46
21.38
16.92
15.32
14.63
14.31
14.15
14.08
14.04
14.02
14.01
6
40
20.6
16.67
15.22
14.58
14.29
14.14
14.07
14.04
14.02
14.01
7
35
19.93
16.45
15.13
14.54
14.27
14.13
14.07
14.03
14.02
14.01
8
32
19.35
16.24
15.04
14.5
14.25
14.12
14.06
14.03
14.02
14.01
9
29
18.83
16.06
14.96
14.46
14.23
14.11
14.06
14.03
14.01
14.01
10
27
18.38
15.89
14.89
14.43
14.21
14.11
14.05
14.03
14.01
14.01
11
26
17.98
15.74
14.82
14.4
14.2
14.1
14.05
14.02
14.01
14.01
12
24
17.62
15.6
14.76
14.37
14.18
14.09
14.05
14.02
14.01
14.01
13
23
17.3
15.48
14.7
14.34
14.17
14.08
14.04
14.02
14.01
14.01
14
22
17.01
15.36
14.65
14.32
14.16
14.08
14.04
14.02
14.01
14
15
21
16.76
15.25
14.6
14.29
14.15
14.07
14.04
14.02
14.01
14
16
21
16.52
15.16
14.56
14.27
14.13
14.07
14.03
14.02
14.01
14
17
20
16.31
15.07
14.51
14.25
14.13
14.06
14.03
14.02
14.01
14
18
20
16.12
14.99
14.48
14.23
14.12
14.06
14.03
14.01
14.01
14
19
19
15.95
14.91
14.44
14.22
14.11
14.05
14.03
14.01
14.01
14
20
19
15.79
14.84
14.41
14.2
14.1
14.05
14.02
14.01
14.01
14
x-axis = number of extroverted friends, y-axis = number of introverted friends
e2- Waiting days until meeting a friend for an extrovert 🦅
(i) / (e)
0
1
2
3
4
5
6
7
8
9
10
0
1095
4
2.67
2.29
2.13
2.06
2.03
2.02
2.01
2
2
1
28
3.73
2.6
2.26
2.12
2.06
2.03
2.01
2.01
2
2
2
14.52
3.52
2.55
2.24
2.11
2.06
2.03
2.01
2.01
2
2
3
10.03
3.34
2.5
2.22
2.11
2.05
2.03
2.01
2.01
2
2
4
7.8
3.18
2.46
2.2
2.1
2.05
2.02
2.01
2.01
2
2
5
6.46
3.05
2.42
2.19
2.09
2.04
2.02
2.01
2.01
2
2
6
5.57
2.94
2.38
2.17
2.08
2.04
2.02
2.01
2.01
2
2
7
4.94
2.85
2.35
2.16
2.08
2.04
2.02
2.01
2
2
2
8
4.47
2.76
2.32
2.15
2.07
2.04
2.02
2.01
2
2
2
9
4.11
2.69
2.29
2.14
2.07
2.03
2.02
2.01
2
2
2
10
3.82
2.63
2.27
2.13
2.06
2.03
2.02
2.01
2
2
2
11
3.59
2.57
2.25
2.12
2.06
2.03
2.01
2.01
2
2
2
12
3.4
2.52
2.23
2.11
2.05
2.03
2.01
2.01
2
2
2
13
3.23
2.47
2.21
2.1
2.05
2.02
2.01
2.01
2
2
2
14
3.1
2.43
2.19
2.09
2.05
2.02
2.01
2.01
2
2
2
15
2.98
2.39
2.18
2.09
2.04
2.02
2.01
2.01
2
2
2
16
2.88
2.36
2.17
2.08
2.04
2.02
2.01
2
2
2
2
17
2.79
2.33
2.15
2.07
2.04
2.02
2.01
2
2
2
2
18
2.72
2.3
2.14
2.07
2.03
2.02
2.01
2
2
2
2
19
2.65
2.28
2.13
2.06
2.03
2.02
2.01
2
2
2
2
20
2.59
2.26
2.12
2.06
2.03
2.01
2.01
2
2
2
2
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 😁.
How Pissed Off Is Ben?
Unfortunately the previous calculations still don’t tell us who feels more alone. For that we need the relative 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
i4 - Relative difference between actual waiting and the optimum of 14 days 🏴☠️
(i) / (e)
0
1
2
3
4
5
6
7
8
9
10
0
7721.43%
100.00%
33.36%
14.29%
6.64%
3.21%
1.57%
0.79%
0.36%
0.21%
0.07%
1
1300.00%
86.67%
30.23%
13.13%
6.16%
2.99%
1.47%
0.73%
0.36%
0.18%
0.09%
2
625.93%
75.79%
27.48%
12.08%
5.70%
2.77%
1.37%
0.68%
0.34%
0.17%
0.08%
3
401.65%
66.76%
25.03%
11.12%
5.27%
2.57%
1.27%
0.63%
0.31%
0.16%
0.08%
4
289.81%
59.17%
22.83%
10.25%
4.87%
2.38%
1.18%
0.58%
0.29%
0.15%
0.07%
5
222.96%
52.71%
20.86%
9.44%
4.51%
2.21%
1.09%
0.54%
0.27%
0.14%
0.07%
6
178.59%
47.17%
19.09%
8.71%
4.17%
2.04%
1.01%
0.50%
0.25%
0.13%
0.06%
7
147.07%
42.38%
17.48%
8.04%
3.86%
1.90%
0.94%
0.47%
0.23%
0.12%
0.06%
8
123.58%
38.19%
16.03%
7.42%
3.58%
1.76%
0.87%
0.43%
0.22%
0.11%
0.05%
9
105.45%
34.52%
14.72%
6.86%
3.31%
1.63%
0.81%
0.40%
0.20%
0.10%
0.05%
10
91.06%
31.29%
13.53%
6.34%
3.07%
1.51%
0.75%
0.37%
0.19%
0.09%
0.05%
11
79.39%
28.42%
12.44%
5.86%
2.85%
1.40%
0.70%
0.35%
0.17%
0.09%
0.04%
12
69.76%
25.86%
11.45%
5.42%
2.64%
1.30%
0.65%
0.32%
0.16%
0.08%
0.04%
13
61.71%
23.58%
10.55%
5.01%
2.44%
1.21%
0.60%
0.30%
0.15%
0.07%
0.04%
14
54.88%
21.53%
9.72%
4.63%
2.27%
1.12%
0.56%
0.28%
0.14%
0.07%
0.03%
15
49.04%
19.69%
8.96%
4.29%
2.10%
1.04%
0.52%
0.26%
0.13%
0.06%
0.03%
16
43.99%
18.03%
8.27%
3.97%
1.95%
0.96%
0.48%
0.24%
0.12%
0.06%
0.03%
17
39.61%
16.53%
7.63%
3.68%
1.81%
0.89%
0.45%
0.22%
0.11%
0.06%
0.03%
18
35.77%
15.17%
7.05%
3.41%
1.67%
0.83%
0.41%
0.21%
0.10%
0.05%
0.03%
19
32.38%
13.94%
6.51%
3.15%
1.55%
0.77%
0.38%
0.19%
0.10%
0.05%
0.02%
20
29.39%
12.81%
6.02%
2.92%
1.44%
0.71%
0.36%
0.18%
0.09%
0.04%
0.02%
x-axis = number of extroverted friends, y-axis = number of introverted friends
i4 - Relative difference between actual waiting and the optimum of 2 days 🦅
(i) / (e)
0
1
2
3
4
5
6
7
8
9
10
0
54650.00%
100.00%
33.34%
14.29%
6.67%
3.22%
1.58%
0.78%
0.39%
0.19%
0.10%
1
1300.00%
86.67%
30.24%
13.13%
6.16%
2.99%
1.47%
0.73%
0.36%
0.18%
0.09%
2
625.93%
75.79%
27.48%
12.08%
5.70%
2.77%
1.36%
0.68%
0.34%
0.17%
0.09%
3
401.65%
66.76%
25.03%
11.12%
5.27%
2.57%
1.27%
0.63%
0.31%
0.15%
0.08%
4
289.81%
59.17%
22.83%
10.25%
4.88%
2.38%
1.17%
0.58%
0.29%
0.14%
0.08%
5
222.96%
52.72%
20.86%
9.44%
4.51%
2.20%
1.09%
0.54%
0.27%
0.13%
0.07%
6
178.59%
47.17%
19.09%
8.71%
4.18%
2.05%
1.01%
0.51%
0.25%
0.12%
0.07%
7
147.08%
42.38%
17.49%
8.04%
3.87%
1.90%
0.94%
0.47%
0.24%
0.11%
0.06%
8
123.59%
38.19%
16.04%
7.42%
3.58%
1.76%
0.87%
0.44%
0.22%
0.11%
0.06%
9
105.45%
34.53%
14.72%
6.86%
3.32%
1.63%
0.81%
0.41%
0.20%
0.10%
0.05%
10
91.06%
31.29%
13.53%
6.34%
3.07%
1.51%
0.75%
0.37%
0.18%
0.10%
0.05%
11
79.39%
28.42%
12.44%
5.86%
2.85%
1.40%
0.70%
0.34%
0.17%
0.09%
0.05%
12
69.77%
25.86%
11.45%
5.41%
2.64%
1.30%
0.65%
0.32%
0.16%
0.08%
0.04%
13
61.71%
23.58%
10.55%
5.01%
2.45%
1.20%
0.60%
0.30%
0.15%
0.08%
0.04%
14
54.88%
21.53%
9.72%
4.63%
2.27%
1.12%
0.55%
0.28%
0.14%
0.07%
0.04%
15
49.04%
19.69%
8.97%
4.29%
2.10%
1.04%
0.51%
0.26%
0.13%
0.07%
0.03%
16
44.00%
18.03%
8.27%
3.97%
1.95%
0.96%
0.48%
0.24%
0.12%
0.06%
0.03%
17
39.61%
16.53%
7.63%
3.68%
1.80%
0.90%
0.45%
0.22%
0.11%
0.06%
0.03%
18
35.77%
15.17%
7.05%
3.40%
1.68%
0.83%
0.42%
0.21%
0.11%
0.05%
0.03%
19
32.39%
13.94%
6.52%
3.16%
1.56%
0.77%
0.38%
0.19%
0.10%
0.05%
0.03%
20
29.39%
12.81%
6.02%
2.92%
1.44%
0.71%
0.35%
0.18%
0.09%
0.05%
0.02%
x-axis = number of extroverted friends, y-axis = number of introverted friends
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 this “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:
Mixed friend groups
Friends
🏴☠️ Introvert
🦅Extrovert
1
700.00%
700.00%
2
248.65%
248.64%
3
130.49%
130.49%
4
80.76%
80.77%
5
54.77%
54.77%
6
39.36%
39.36%
7
29.46%
29.46%
8
22.71%
22.71%
9
17.92%
17.92%
10
14.40%
14.41%
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%
Introverts Feel More Alone
As you can see, the feeling alone factor for an introvert with 1 friend is higher than for an extrovert with 2 friends. We made progress. Introverts feel more alone than extroverts 🥲.
But to be honest this feels too much like cheating. So I kept thinking: Isn’t there something I might have forgotten? Yes, there is: We become friends with people who are like us. Which means extroverts have more extroverted friends & introverts have more introverted friends.
If i’s and e’s only have friends of the same kind, the new table looks like this:
Only friends of same kind
Friends
🏴☠️ Introvert
🦅Extrovert
1
1300.00%
100.00%
2
625.93%
33.34%
3
401.65%
14.29%
4
289.81%
6.67%
5
222.96%
3.22%
6
178.59%
1.58%
7
147.07%
0.78%
8
123.58%
0.39%
9
105.45%
0.19%
10
91.06%
0.10%
x-axis = introvert or extrovert, y-axis = number of friends, colored cells = “feeling alone factor”
As you can see, introverts feel shockingly more alone 😱. If both, i’s and e’s have only one friend, introverts feel 12 times more alone. If they both have 10 friends, introverts feel over 900 times more alone.
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?
Thanks to Maria for reading drafts of this.
Thanks @Ericf for pointing out a mistake in my calculation
Who Feels More Alone?
Imagine you live in a world with only two types of people. Introverts and extroverts. All introverts are the same. And so are all extroverts. It’s a world with only two colors, and no shades in between.
Introverts like to be alone, in our world they want to meet a friend every 14 days. Extroverts love to be around other people. In our experiment 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:
14
7.14%
2
50.00%
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% * (1-(1-7.14%)^1) = 0.51%.
If an introvert has two extrovert friends it’s: 7.14% * (1-(1-50%)^2) = 5.36%
If an introvert has two extrovert and one introvert friend it’s: 7.14% * (1-((1-50%)^2 * (1-7.14%)^1)) = 5.48%
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.
(i) / (e)
0
1
2
3
4
5
6
7
8
9
10
0
1095
28
18.67
16
14.93
14.45
14.22
14.11
14.05
14.03
14.01
1
196
26.13
18.23
15.84
14.86
14.42
14.21
14.1
14.05
14.03
14.01
2
102
24.61
17.85
15.69
14.8
14.39
14.19
14.09
14.05
14.02
14.01
3
71
23.35
17.5
15.56
14.74
14.36
14.18
14.09
14.04
14.02
14.01
4
55
22.28
17.2
15.43
14.68
14.33
14.16
14.08
14.04
14.02
14.01
5
46
21.38
16.92
15.32
14.63
14.31
14.15
14.08
14.04
14.02
14.01
6
40
20.6
16.67
15.22
14.58
14.29
14.14
14.07
14.04
14.02
14.01
7
35
19.93
16.45
15.13
14.54
14.27
14.13
14.07
14.03
14.02
14.01
8
32
19.35
16.24
15.04
14.5
14.25
14.12
14.06
14.03
14.02
14.01
9
29
18.83
16.06
14.96
14.46
14.23
14.11
14.06
14.03
14.01
14.01
10
27
18.38
15.89
14.89
14.43
14.21
14.11
14.05
14.03
14.01
14.01
11
26
17.98
15.74
14.82
14.4
14.2
14.1
14.05
14.02
14.01
14.01
12
24
17.62
15.6
14.76
14.37
14.18
14.09
14.05
14.02
14.01
14.01
13
23
17.3
15.48
14.7
14.34
14.17
14.08
14.04
14.02
14.01
14.01
14
22
17.01
15.36
14.65
14.32
14.16
14.08
14.04
14.02
14.01
14
15
21
16.76
15.25
14.6
14.29
14.15
14.07
14.04
14.02
14.01
14
16
21
16.52
15.16
14.56
14.27
14.13
14.07
14.03
14.02
14.01
14
17
20
16.31
15.07
14.51
14.25
14.13
14.06
14.03
14.02
14.01
14
18
20
16.12
14.99
14.48
14.23
14.12
14.06
14.03
14.01
14.01
14
19
19
15.95
14.91
14.44
14.22
14.11
14.05
14.03
14.01
14.01
14
20
19
15.79
14.84
14.41
14.2
14.1
14.05
14.02
14.01
14.01
14
x-axis = number of extroverted friends, y-axis = number of introverted friends
(i) / (e)
0
1
2
3
4
5
6
7
8
9
10
0
1095
4
2.67
2.29
2.13
2.06
2.03
2.02
2.01
2
2
1
28
3.73
2.6
2.26
2.12
2.06
2.03
2.01
2.01
2
2
2
14.52
3.52
2.55
2.24
2.11
2.06
2.03
2.01
2.01
2
2
3
10.03
3.34
2.5
2.22
2.11
2.05
2.03
2.01
2.01
2
2
4
7.8
3.18
2.46
2.2
2.1
2.05
2.02
2.01
2.01
2
2
5
6.46
3.05
2.42
2.19
2.09
2.04
2.02
2.01
2.01
2
2
6
5.57
2.94
2.38
2.17
2.08
2.04
2.02
2.01
2.01
2
2
7
4.94
2.85
2.35
2.16
2.08
2.04
2.02
2.01
2
2
2
8
4.47
2.76
2.32
2.15
2.07
2.04
2.02
2.01
2
2
2
9
4.11
2.69
2.29
2.14
2.07
2.03
2.02
2.01
2
2
2
10
3.82
2.63
2.27
2.13
2.06
2.03
2.02
2.01
2
2
2
11
3.59
2.57
2.25
2.12
2.06
2.03
2.01
2.01
2
2
2
12
3.4
2.52
2.23
2.11
2.05
2.03
2.01
2.01
2
2
2
13
3.23
2.47
2.21
2.1
2.05
2.02
2.01
2.01
2
2
2
14
3.1
2.43
2.19
2.09
2.05
2.02
2.01
2.01
2
2
2
15
2.98
2.39
2.18
2.09
2.04
2.02
2.01
2.01
2
2
2
16
2.88
2.36
2.17
2.08
2.04
2.02
2.01
2
2
2
2
17
2.79
2.33
2.15
2.07
2.04
2.02
2.01
2
2
2
2
18
2.72
2.3
2.14
2.07
2.03
2.02
2.01
2
2
2
2
19
2.65
2.28
2.13
2.06
2.03
2.02
2.01
2
2
2
2
20
2.59
2.26
2.12
2.06
2.03
2.01
2.01
2
2
2
2
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 😁.
How Pissed Off Is Ben?
Unfortunately the previous calculations still don’t tell us who feels more alone. For that we need the relative 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
(i) / (e)
0
1
2
3
4
5
6
7
8
9
10
0
7721.43%
100.00%
33.36%
14.29%
6.64%
3.21%
1.57%
0.79%
0.36%
0.21%
0.07%
1
1300.00%
86.67%
30.23%
13.13%
6.16%
2.99%
1.47%
0.73%
0.36%
0.18%
0.09%
2
625.93%
75.79%
27.48%
12.08%
5.70%
2.77%
1.37%
0.68%
0.34%
0.17%
0.08%
3
401.65%
66.76%
25.03%
11.12%
5.27%
2.57%
1.27%
0.63%
0.31%
0.16%
0.08%
4
289.81%
59.17%
22.83%
10.25%
4.87%
2.38%
1.18%
0.58%
0.29%
0.15%
0.07%
5
222.96%
52.71%
20.86%
9.44%
4.51%
2.21%
1.09%
0.54%
0.27%
0.14%
0.07%
6
178.59%
47.17%
19.09%
8.71%
4.17%
2.04%
1.01%
0.50%
0.25%
0.13%
0.06%
7
147.07%
42.38%
17.48%
8.04%
3.86%
1.90%
0.94%
0.47%
0.23%
0.12%
0.06%
8
123.58%
38.19%
16.03%
7.42%
3.58%
1.76%
0.87%
0.43%
0.22%
0.11%
0.05%
9
105.45%
34.52%
14.72%
6.86%
3.31%
1.63%
0.81%
0.40%
0.20%
0.10%
0.05%
10
91.06%
31.29%
13.53%
6.34%
3.07%
1.51%
0.75%
0.37%
0.19%
0.09%
0.05%
11
79.39%
28.42%
12.44%
5.86%
2.85%
1.40%
0.70%
0.35%
0.17%
0.09%
0.04%
12
69.76%
25.86%
11.45%
5.42%
2.64%
1.30%
0.65%
0.32%
0.16%
0.08%
0.04%
13
61.71%
23.58%
10.55%
5.01%
2.44%
1.21%
0.60%
0.30%
0.15%
0.07%
0.04%
14
54.88%
21.53%
9.72%
4.63%
2.27%
1.12%
0.56%
0.28%
0.14%
0.07%
0.03%
15
49.04%
19.69%
8.96%
4.29%
2.10%
1.04%
0.52%
0.26%
0.13%
0.06%
0.03%
16
43.99%
18.03%
8.27%
3.97%
1.95%
0.96%
0.48%
0.24%
0.12%
0.06%
0.03%
17
39.61%
16.53%
7.63%
3.68%
1.81%
0.89%
0.45%
0.22%
0.11%
0.06%
0.03%
18
35.77%
15.17%
7.05%
3.41%
1.67%
0.83%
0.41%
0.21%
0.10%
0.05%
0.03%
19
32.38%
13.94%
6.51%
3.15%
1.55%
0.77%
0.38%
0.19%
0.10%
0.05%
0.02%
20
29.39%
12.81%
6.02%
2.92%
1.44%
0.71%
0.36%
0.18%
0.09%
0.04%
0.02%
x-axis = number of extroverted friends, y-axis = number of introverted friends
(i) / (e)
0
1
2
3
4
5
6
7
8
9
10
0
54650.00%
100.00%
33.34%
14.29%
6.67%
3.22%
1.58%
0.78%
0.39%
0.19%
0.10%
1
1300.00%
86.67%
30.24%
13.13%
6.16%
2.99%
1.47%
0.73%
0.36%
0.18%
0.09%
2
625.93%
75.79%
27.48%
12.08%
5.70%
2.77%
1.36%
0.68%
0.34%
0.17%
0.09%
3
401.65%
66.76%
25.03%
11.12%
5.27%
2.57%
1.27%
0.63%
0.31%
0.15%
0.08%
4
289.81%
59.17%
22.83%
10.25%
4.88%
2.38%
1.17%
0.58%
0.29%
0.14%
0.08%
5
222.96%
52.72%
20.86%
9.44%
4.51%
2.20%
1.09%
0.54%
0.27%
0.13%
0.07%
6
178.59%
47.17%
19.09%
8.71%
4.18%
2.05%
1.01%
0.51%
0.25%
0.12%
0.07%
7
147.08%
42.38%
17.49%
8.04%
3.87%
1.90%
0.94%
0.47%
0.24%
0.11%
0.06%
8
123.59%
38.19%
16.04%
7.42%
3.58%
1.76%
0.87%
0.44%
0.22%
0.11%
0.06%
9
105.45%
34.53%
14.72%
6.86%
3.32%
1.63%
0.81%
0.41%
0.20%
0.10%
0.05%
10
91.06%
31.29%
13.53%
6.34%
3.07%
1.51%
0.75%
0.37%
0.18%
0.10%
0.05%
11
79.39%
28.42%
12.44%
5.86%
2.85%
1.40%
0.70%
0.34%
0.17%
0.09%
0.05%
12
69.77%
25.86%
11.45%
5.41%
2.64%
1.30%
0.65%
0.32%
0.16%
0.08%
0.04%
13
61.71%
23.58%
10.55%
5.01%
2.45%
1.20%
0.60%
0.30%
0.15%
0.08%
0.04%
14
54.88%
21.53%
9.72%
4.63%
2.27%
1.12%
0.55%
0.28%
0.14%
0.07%
0.04%
15
49.04%
19.69%
8.97%
4.29%
2.10%
1.04%
0.51%
0.26%
0.13%
0.07%
0.03%
16
44.00%
18.03%
8.27%
3.97%
1.95%
0.96%
0.48%
0.24%
0.12%
0.06%
0.03%
17
39.61%
16.53%
7.63%
3.68%
1.80%
0.90%
0.45%
0.22%
0.11%
0.06%
0.03%
18
35.77%
15.17%
7.05%
3.40%
1.68%
0.83%
0.42%
0.21%
0.11%
0.05%
0.03%
19
32.39%
13.94%
6.52%
3.16%
1.56%
0.77%
0.38%
0.19%
0.10%
0.05%
0.03%
20
29.39%
12.81%
6.02%
2.92%
1.44%
0.71%
0.35%
0.18%
0.09%
0.05%
0.02%
x-axis = number of extroverted friends, y-axis = number of introverted friends
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 this “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:
Friends
🏴☠️ Introvert
🦅Extrovert
1
700.00%
700.00%
2
248.65%
248.64%
3
130.49%
130.49%
4
80.76%
80.77%
5
54.77%
54.77%
6
39.36%
39.36%
7
29.46%
29.46%
8
22.71%
22.71%
9
17.92%
17.92%
10
14.40%
14.41%
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%
Introverts Feel More Alone
As you can see, the feeling alone factor for an introvert with 1 friend is higher than for an extrovert with 2 friends. We made progress. Introverts feel more alone than extroverts 🥲.
But to be honest this feels too much like cheating. So I kept thinking: Isn’t there something I might have forgotten? Yes, there is: We become friends with people who are like us. Which means extroverts have more extroverted friends & introverts have more introverted friends.
If i’s and e’s only have friends of the same kind, the new table looks like this:
Friends
🏴☠️ Introvert
🦅Extrovert
1
1300.00%
100.00%
2
625.93%
33.34%
3
401.65%
14.29%
4
289.81%
6.67%
5
222.96%
3.22%
6
178.59%
1.58%
7
147.07%
0.78%
8
123.58%
0.39%
9
105.45%
0.19%
10
91.06%
0.10%
x-axis = introvert or extrovert, y-axis = number of friends, colored cells = “feeling alone factor”
As you can see, introverts feel shockingly more alone 😱. If both, i’s and e’s have only one friend, introverts feel 12 times more alone. If they both have 10 friends, introverts feel over 900 times more alone.
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?
Thanks to Maria for reading drafts of this.
Thanks @Ericf for pointing out a mistake in my calculation