Home / Essays / Who Feels More Alone?
Imagine you live in a world with only two types of people. Introverts (iâs ð´ââ ï¸) and extroverts (eâs ð¦ ). All introverts are the same. And so are all extroverts. It's a world with only two colors, and no shades in between.
Introverts (iâs ð´ââ ï¸) like to be alone, in our world they want to meet a friend every 14 days. Extroverts (eâs ð¦ ) 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 donât 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, iâs or eâs? Whose interpersonal needs are being met less, i´s or e´s?
Did you take a guess? Maybe you picked eâs ð¦ . Because they need more human interaction in general. Or you picked iâs ð´ââ ï¸. Because they shoot themselves in the foot by being such loners?
Letâs take a closer look at our protagonists:
Introvert | Nickname: i as in ay ay, captain ð´ââ ï¸ | |||||
Wants to meet a friend once every | 14 | days | ||||
Probability wants to meet a friend today | 7.14% |
Extrovert | Nickname: e as in eagle ð¦ | |||||
Wants to meet a friend once every | 2 | days | ||||
Probability wants to meet a friend today | 50.00% |
To answer this question I calculated the probability of âmeeting a friend todayâ for each friend group mix.
What is a âfriend group mixâ?
Each table cell (probability of meeting a friend today) is calculated like this: probability_self * sum_probability_friends.
i1 - Probability of meeting a friend today for an introvert ð´ââ ï¸ | |||||||||||
i / e | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
0 | 0.00% | 3.57% | 7.14% | 10.71% | 14.29% | 17.86% | 21.43% | 25.00% | 28.57% | 32.14% | 35.71% |
1 | 0.51% | 4.08% | 7.65% | 11.22% | 14.80% | 18.37% | 21.94% | 25.51% | 29.08% | 32.65% | 36.22% |
2 | 1.02% | 4.59% | 8.16% | 11.73% | 15.31% | 18.88% | 22.45% | 26.02% | 29.59% | 33.16% | 36.73% |
3 | 1.53% | 5.10% | 8.67% | 12.24% | 15.82% | 19.39% | 22.96% | 26.53% | 30.10% | 33.67% | 37.24% |
4 | 2.04% | 5.61% | 9.18% | 12.76% | 16.33% | 19.90% | 23.47% | 27.04% | 30.61% | 34.18% | 37.76% |
5 | 2.55% | 6.12% | 9.69% | 13.27% | 16.84% | 20.41% | 23.98% | 27.55% | 31.12% | 34.69% | 38.27% |
6 | 3.06% | 6.63% | 10.20% | 13.78% | 17.35% | 20.92% | 24.49% | 28.06% | 31.63% | 35.20% | 38.78% |
7 | 3.57% | 7.14% | 10.71% | 14.29% | 17.86% | 21.43% | 25.00% | 28.57% | 32.14% | 35.71% | 39.29% |
8 | 4.08% | 7.65% | 11.22% | 14.80% | 18.37% | 21.94% | 25.51% | 29.08% | 32.65% | 36.22% | 39.80% |
9 | 4.59% | 8.16% | 11.73% | 15.31% | 18.88% | 22.45% | 26.02% | 29.59% | 33.16% | 36.73% | 40.31% |
10 | 5.10% | 8.67% | 12.24% | 15.82% | 19.39% | 22.96% | 26.53% | 30.10% | 33.67% | 37.24% | 40.82% |
11 | 5.61% | 9.18% | 12.76% | 16.33% | 19.90% | 23.47% | 27.04% | 30.61% | 34.18% | 37.76% | 41.33% |
12 | 6.12% | 9.69% | 13.27% | 16.84% | 20.41% | 23.98% | 27.55% | 31.12% | 34.69% | 38.27% | 41.84% |
13 | 6.63% | 10.20% | 13.78% | 17.35% | 20.92% | 24.49% | 28.06% | 31.63% | 35.20% | 38.78% | 42.35% |
14 | 7.14% | 10.71% | 14.29% | 17.86% | 21.43% | 25.00% | 28.57% | 32.14% | 35.71% | 39.29% | 42.86% |
15 | 7.65% | 11.22% | 14.80% | 18.37% | 21.94% | 25.51% | 29.08% | 32.65% | 36.22% | 39.80% | 43.37% |
16 | 8.16% | 11.73% | 15.31% | 18.88% | 22.45% | 26.02% | 29.59% | 33.16% | 36.73% | 40.31% | 43.88% |
17 | 8.67% | 12.24% | 15.82% | 19.39% | 22.96% | 26.53% | 30.10% | 33.67% | 37.24% | 40.82% | 44.39% |
18 | 9.18% | 12.76% | 16.33% | 19.90% | 23.47% | 27.04% | 30.61% | 34.18% | 37.76% | 41.33% | 44.90% |
19 | 9.69% | 13.27% | 16.84% | 20.41% | 23.98% | 27.55% | 31.12% | 34.69% | 38.27% | 41.84% | 45.41% |
20 | 10.20% | 13.78% | 17.35% | 20.92% | 24.49% | 28.06% | 31.63% | 35.20% | 38.78% | 42.35% | 45.92% |
x-axis = number of extroverted friends, y-axis = number of introverted friends
e1 - Probability of meeting a friend today for an extrovert ð¦ | |||||||||||
i / e | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
0 | 0.00% | 25.00% | 50.00% | 75.00% | 100.00% | 125.00% | 150.00% | 175.00% | 200.00% | 225.00% | 250.00% |
1 | 3.57% | 28.57% | 53.57% | 78.57% | 103.57% | 128.57% | 153.57% | 178.57% | 203.57% | 228.57% | 253.57% |
2 | 7.14% | 32.14% | 57.14% | 82.14% | 107.14% | 132.14% | 157.14% | 182.14% | 207.14% | 232.14% | 257.14% |
3 | 10.71% | 35.71% | 60.71% | 85.71% | 110.71% | 135.71% | 160.71% | 185.71% | 210.71% | 235.71% | 260.71% |
4 | 14.29% | 39.29% | 64.29% | 89.29% | 114.29% | 139.29% | 164.29% | 189.29% | 214.29% | 239.29% | 264.29% |
5 | 17.86% | 42.86% | 67.86% | 92.86% | 117.86% | 142.86% | 167.86% | 192.86% | 217.86% | 242.86% | 267.86% |
6 | 21.43% | 46.43% | 71.43% | 96.43% | 121.43% | 146.43% | 171.43% | 196.43% | 221.43% | 246.43% | 271.43% |
7 | 25.00% | 50.00% | 75.00% | 100.00% | 125.00% | 150.00% | 175.00% | 200.00% | 225.00% | 250.00% | 275.00% |
8 | 28.57% | 53.57% | 78.57% | 103.57% | 128.57% | 153.57% | 178.57% | 203.57% | 228.57% | 253.57% | 278.57% |
9 | 32.14% | 57.14% | 82.14% | 107.14% | 132.14% | 157.14% | 182.14% | 207.14% | 232.14% | 257.14% | 282.14% |
10 | 35.71% | 60.71% | 85.71% | 110.71% | 135.71% | 160.71% | 185.71% | 210.71% | 235.71% | 260.71% | 285.71% |
11 | 39.29% | 64.29% | 89.29% | 114.29% | 139.29% | 164.29% | 189.29% | 214.29% | 239.29% | 264.29% | 289.29% |
12 | 42.86% | 67.86% | 92.86% | 117.86% | 142.86% | 167.86% | 192.86% | 217.86% | 242.86% | 267.86% | 292.86% |
13 | 46.43% | 71.43% | 96.43% | 121.43% | 146.43% | 171.43% | 196.43% | 221.43% | 246.43% | 271.43% | 296.43% |
14 | 50.00% | 75.00% | 100.00% | 125.00% | 150.00% | 175.00% | 200.00% | 225.00% | 250.00% | 275.00% | 300.00% |
15 | 53.57% | 78.57% | 103.57% | 128.57% | 153.57% | 178.57% | 203.57% | 228.57% | 253.57% | 278.57% | 303.57% |
16 | 57.14% | 82.14% | 107.14% | 132.14% | 157.14% | 182.14% | 207.14% | 232.14% | 257.14% | 282.14% | 307.14% |
17 | 60.71% | 85.71% | 110.71% | 135.71% | 160.71% | 185.71% | 210.71% | 235.71% | 260.71% | 285.71% | 310.71% |
18 | 64.29% | 89.29% | 114.29% | 139.29% | 164.29% | 189.29% | 214.29% | 239.29% | 264.29% | 289.29% | 314.29% |
19 | 67.86% | 92.86% | 117.86% | 142.86% | 167.86% | 192.86% | 217.86% | 242.86% | 267.86% | 292.86% | 317.86% |
20 | 71.43% | 96.43% | 121.43% | 146.43% | 171.43% | 196.43% | 221.43% | 246.43% | 271.43% | 296.43% | 321.43% |
x-axis = number of extroverted friends, y-axis = number of introverted friends
We can see that for extroverts the probability of âmeeting a friend todayâ rises much faster than for introverts. They need less friends to have a high probability of âmeeting a friend todayâ. But, if you are like me, your brain doesn't know how to work with percentages. So let's turn these % into days.
Now I calculated how many days iâs and eâs have to wait until they meet a friend - for each friend group mix.
i2 - Waiting days until meeting a friend for an introvert ð´ââ ï¸ | |||||||||||
i / e | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
0 | 1095 | 28 | 14 | 9.33 | 7 | 5.6 | 4.67 | 4 | 3.5 | 3.11 | 2.8 |
1 | 196 | 24.5 | 13.07 | 8.91 | 6.76 | 5.44 | 4.56 | 3.92 | 3.44 | 3.06 | 2.76 |
2 | 98 | 21.78 | 12.25 | 8.52 | 6.53 | 5.3 | 4.45 | 3.84 | 3.38 | 3.02 | 2.72 |
3 | 65.33 | 19.6 | 11.53 | 8.17 | 6.32 | 5.16 | 4.36 | 3.77 | 3.32 | 2.97 | 2.68 |
4 | 49 | 17.82 | 10.89 | 7.84 | 6.13 | 5.03 | 4.26 | 3.7 | 3.27 | 2.93 | 2.65 |
5 | 39.2 | 16.33 | 10.32 | 7.54 | 5.94 | 4.9 | 4.17 | 3.63 | 3.21 | 2.88 | 2.61 |
6 | 32.67 | 15.08 | 9.8 | 7.26 | 5.76 | 4.78 | 4.08 | 3.56 | 3.16 | 2.84 | 2.58 |
7 | 28 | 14 | 9.33 | 7 | 5.6 | 4.67 | 4 | 3.5 | 3.11 | 2.8 | 2.55 |
8 | 24.5 | 13.07 | 8.91 | 6.76 | 5.44 | 4.56 | 3.92 | 3.44 | 3.06 | 2.76 | 2.51 |
9 | 21.78 | 12.25 | 8.52 | 6.53 | 5.3 | 4.45 | 3.84 | 3.38 | 3.02 | 2.72 | 2.48 |
10 | 19.6 | 11.53 | 8.17 | 6.32 | 5.16 | 4.36 | 3.77 | 3.32 | 2.97 | 2.68 | 2.45 |
11 | 17.82 | 10.89 | 7.84 | 6.13 | 5.03 | 4.26 | 3.7 | 3.27 | 2.93 | 2.65 | 2.42 |
12 | 16.33 | 10.32 | 7.54 | 5.94 | 4.9 | 4.17 | 3.63 | 3.21 | 2.88 | 2.61 | 2.39 |
13 | 15.08 | 9.8 | 7.26 | 5.76 | 4.78 | 4.08 | 3.56 | 3.16 | 2.84 | 2.58 | 2.36 |
14 | 14 | 9.33 | 7 | 5.6 | 4.67 | 4 | 3.5 | 3.11 | 2.8 | 2.55 | 2.33 |
15 | 13.07 | 8.91 | 6.76 | 5.44 | 4.56 | 3.92 | 3.44 | 3.06 | 2.76 | 2.51 | 2.31 |
16 | 12.25 | 8.52 | 6.53 | 5.3 | 4.45 | 3.84 | 3.38 | 3.02 | 2.72 | 2.48 | 2.28 |
17 | 11.53 | 8.17 | 6.32 | 5.16 | 4.36 | 3.77 | 3.32 | 2.97 | 2.68 | 2.45 | 2.25 |
18 | 10.89 | 7.84 | 6.13 | 5.03 | 4.26 | 3.7 | 3.27 | 2.93 | 2.65 | 2.42 | 2.23 |
19 | 10.32 | 7.54 | 5.94 | 4.9 | 4.17 | 3.63 | 3.21 | 2.88 | 2.61 | 2.39 | 2.2 |
20 | 9.8 | 7.26 | 5.76 | 4.78 | 4.08 | 3.56 | 3.16 | 2.84 | 2.58 | 2.36 | 2.18 |
x-axis = number of extroverted friends, y-axis = number of introverted friends
e2 - Waiting days until meeting a friend for an extrovert ð¦ | |||||||||||
i / e | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
0 | 1095 | 4 | 2 | 1.33 | 1 | 0.8 | 0.67 | 0.57 | 0.5 | 0.44 | 0.4 |
1 | 28 | 3.5 | 1.87 | 1.27 | 0.97 | 0.78 | 0.65 | 0.56 | 0.49 | 0.44 | 0.39 |
2 | 14 | 3.11 | 1.75 | 1.22 | 0.93 | 0.76 | 0.64 | 0.55 | 0.48 | 0.43 | 0.39 |
3 | 9.33 | 2.8 | 1.65 | 1.17 | 0.9 | 0.74 | 0.62 | 0.54 | 0.47 | 0.42 | 0.38 |
4 | 7 | 2.55 | 1.56 | 1.12 | 0.88 | 0.72 | 0.61 | 0.53 | 0.47 | 0.42 | 0.38 |
5 | 5.6 | 2.33 | 1.47 | 1.08 | 0.85 | 0.7 | 0.6 | 0.52 | 0.46 | 0.41 | 0.37 |
6 | 4.67 | 2.15 | 1.4 | 1.04 | 0.82 | 0.68 | 0.58 | 0.51 | 0.45 | 0.41 | 0.37 |
7 | 4 | 2 | 1.33 | 1 | 0.8 | 0.67 | 0.57 | 0.5 | 0.44 | 0.4 | 0.36 |
8 | 3.5 | 1.87 | 1.27 | 0.97 | 0.78 | 0.65 | 0.56 | 0.49 | 0.44 | 0.39 | 0.36 |
9 | 3.11 | 1.75 | 1.22 | 0.93 | 0.76 | 0.64 | 0.55 | 0.48 | 0.43 | 0.39 | 0.35 |
10 | 2.8 | 1.65 | 1.17 | 0.9 | 0.74 | 0.62 | 0.54 | 0.47 | 0.42 | 0.38 | 0.35 |
11 | 2.55 | 1.56 | 1.12 | 0.88 | 0.72 | 0.61 | 0.53 | 0.47 | 0.42 | 0.38 | 0.35 |
12 | 2.33 | 1.47 | 1.08 | 0.85 | 0.7 | 0.6 | 0.52 | 0.46 | 0.41 | 0.37 | 0.34 |
13 | 2.15 | 1.4 | 1.04 | 0.82 | 0.68 | 0.58 | 0.51 | 0.45 | 0.41 | 0.37 | 0.34 |
14 | 2 | 1.33 | 1 | 0.8 | 0.67 | 0.57 | 0.5 | 0.44 | 0.4 | 0.36 | 0.33 |
15 | 1.87 | 1.27 | 0.97 | 0.78 | 0.65 | 0.56 | 0.49 | 0.44 | 0.39 | 0.36 | 0.33 |
16 | 1.75 | 1.22 | 0.93 | 0.76 | 0.64 | 0.55 | 0.48 | 0.43 | 0.39 | 0.35 | 0.33 |
17 | 1.65 | 1.17 | 0.9 | 0.74 | 0.62 | 0.54 | 0.47 | 0.42 | 0.38 | 0.35 | 0.32 |
18 | 1.56 | 1.12 | 0.88 | 0.72 | 0.61 | 0.53 | 0.47 | 0.42 | 0.38 | 0.35 | 0.32 |
19 | 1.47 | 1.08 | 0.85 | 0.7 | 0.6 | 0.52 | 0.46 | 0.41 | 0.37 | 0.34 | 0.31 |
20 | 1.4 | 1.04 | 0.82 | 0.68 | 0.58 | 0.51 | 0.45 | 0.41 | 0.37 | 0.34 | 0.31 |
x-axis = number of extroverted friends, y-axis = number of introverted friends
Think about what âkind of friendsâ you have. By that I mean: How many introverted and extroverted friends? Then check the table above: How many days do you (theoretically) have to wait to meet a friend?
Did you also get 1095 days ð ? 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 first 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 ð.
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. Â
i3: difference between likely waiting and optimal of 14 days for an introvert ð´ââ ï¸ | |||||||||||
i / e | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
0 | 1081 | 14 | 0 | -4.67 | -7 | -8.4 | -9.33 | -10 | -10.5 | -10.89 | -11.2 |
1 | 182 | 10.5 | -0.93 | -5.09 | -7.24 | -8.56 | -9.44 | -10.08 | -10.56 | -10.94 | -11.24 |
2 | 84 | 7.78 | -1.75 | -5.48 | -7.47 | -8.7 | -9.55 | -10.16 | -10.62 | -10.98 | -11.28 |
3 | 51.33 | 5.6 | -2.47 | -5.83 | -7.68 | -8.84 | -9.64 | -10.23 | -10.68 | -11.03 | -11.32 |
4 | 35 | 3.82 | -3.11 | -6.16 | -7.87 | -8.97 | -9.74 | -10.3 | -10.73 | -11.07 | -11.35 |
5 | 25.2 | 2.33 | -3.68 | -6.46 | -8.06 | -9.1 | -9.83 | -10.37 | -10.79 | -11.12 | -11.39 |
6 | 18.67 | 1.08 | -4.2 | -6.74 | -8.24 | -9.22 | -9.92 | -10.44 | -10.84 | -11.16 | -11.42 |
7 | 14 | 0 | -4.67 | -7 | -8.4 | -9.33 | -10 | -10.5 | -10.89 | -11.2 | -11.45 |
8 | 10.5 | -0.93 | -5.09 | -7.24 | -8.56 | -9.44 | -10.08 | -10.56 | -10.94 | -11.24 | -11.49 |
9 | 7.78 | -1.75 | -5.48 | -7.47 | -8.7 | -9.55 | -10.16 | -10.62 | -10.98 | -11.28 | -11.52 |
10 | 5.6 | -2.47 | -5.83 | -7.68 | -8.84 | -9.64 | -10.23 | -10.68 | -11.03 | -11.32 | -11.55 |
11 | 3.82 | -3.11 | -6.16 | -7.87 | -8.97 | -9.74 | -10.3 | -10.73 | -11.07 | -11.35 | -11.58 |
12 | 2.33 | -3.68 | -6.46 | -8.06 | -9.1 | -9.83 | -10.37 | -10.79 | -11.12 | -11.39 | -11.61 |
13 | 1.08 | -4.2 | -6.74 | -8.24 | -9.22 | -9.92 | -10.44 | -10.84 | -11.16 | -11.42 | -11.64 |
14 | 0 | -4.67 | -7 | -8.4 | -9.33 | -10 | -10.5 | -10.89 | -11.2 | -11.45 | -11.67 |
15 | -0.93 | -5.09 | -7.24 | -8.56 | -9.44 | -10.08 | -10.56 | -10.94 | -11.24 | -11.49 | -11.69 |
16 | -1.75 | -5.48 | -7.47 | -8.7 | -9.55 | -10.16 | -10.62 | -10.98 | -11.28 | -11.52 | -11.72 |
17 | -2.47 | -5.83 | -7.68 | -8.84 | -9.64 | -10.23 | -10.68 | -11.03 | -11.32 | -11.55 | -11.75 |
18 | -3.11 | -6.16 | -7.87 | -8.97 | -9.74 | -10.3 | -10.73 | -11.07 | -11.35 | -11.58 | -11.77 |
19 | -3.68 | -6.46 | -8.06 | -9.1 | -9.83 | -10.37 | -10.79 | -11.12 | -11.39 | -11.61 | -11.8 |
20 | -4.2 | -6.74 | -8.24 | -9.22 | -9.92 | -10.44 | -10.84 | -11.16 | -11.42 | -11.64 | -11.82 |
x-axis = number of extroverted friends, y-axis = number of introverted friends
e3: difference between likely waiting and optimal of 2 days for an extrovert ð¦ | |||||||||||
i / e | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
0 | 1093 | 2 | 0 | -0.67 | -1 | -1.2 | -1.33 | -1.43 | -1.5 | -1.56 | -1.6 |
1 | 26 | 1.5 | -0.13 | -0.73 | -1.03 | -1.22 | -1.35 | -1.44 | -1.51 | -1.56 | -1.61 |
2 | 12 | 1.11 | -0.25 | -0.78 | -1.07 | -1.24 | -1.36 | -1.45 | -1.52 | -1.57 | -1.61 |
3 | 7.33 | 0.8 | -0.35 | -0.83 | -1.1 | -1.26 | -1.38 | -1.46 | -1.53 | -1.58 | -1.62 |
4 | 5 | 0.55 | -0.44 | -0.88 | -1.12 | -1.28 | -1.39 | -1.47 | -1.53 | -1.58 | -1.62 |
5 | 3.6 | 0.33 | -0.53 | -0.92 | -1.15 | -1.3 | -1.4 | -1.48 | -1.54 | -1.59 | -1.63 |
6 | 2.67 | 0.15 | -0.6 | -0.96 | -1.18 | -1.32 | -1.42 | -1.49 | -1.55 | -1.59 | -1.63 |
7 | 2 | 0 | -0.67 | -1 | -1.2 | -1.33 | -1.43 | -1.5 | -1.56 | -1.6 | -1.64 |
8 | 1.5 | -0.13 | -0.73 | -1.03 | -1.22 | -1.35 | -1.44 | -1.51 | -1.56 | -1.61 | -1.64 |
9 | 1.11 | -0.25 | -0.78 | -1.07 | -1.24 | -1.36 | -1.45 | -1.52 | -1.57 | -1.61 | -1.65 |
10 | 0.8 | -0.35 | -0.83 | -1.1 | -1.26 | -1.38 | -1.46 | -1.53 | -1.58 | -1.62 | -1.65 |
11 | 0.55 | -0.44 | -0.88 | -1.12 | -1.28 | -1.39 | -1.47 | -1.53 | -1.58 | -1.62 | -1.65 |
12 | 0.33 | -0.53 | -0.92 | -1.15 | -1.3 | -1.4 | -1.48 | -1.54 | -1.59 | -1.63 | -1.66 |
13 | 0.15 | -0.6 | -0.96 | -1.18 | -1.32 | -1.42 | -1.49 | -1.55 | -1.59 | -1.63 | -1.66 |
14 | 0 | -0.67 | -1 | -1.2 | -1.33 | -1.43 | -1.5 | -1.56 | -1.6 | -1.64 | -1.67 |
15 | -0.13 | -0.73 | -1.03 | -1.22 | -1.35 | -1.44 | -1.51 | -1.56 | -1.61 | -1.64 | -1.67 |
16 | -0.25 | -0.78 | -1.07 | -1.24 | -1.36 | -1.45 | -1.52 | -1.57 | -1.61 | -1.65 | -1.67 |
17 | -0.35 | -0.83 | -1.1 | -1.26 | -1.38 | -1.46 | -1.53 | -1.58 | -1.62 | -1.65 | -1.68 |
18 | -0.44 | -0.88 | -1.12 | -1.28 | -1.39 | -1.47 | -1.53 | -1.58 | -1.62 | -1.65 | -1.68 |
19 | -0.53 | -0.92 | -1.15 | -1.3 | -1.4 | -1.48 | -1.54 | -1.59 | -1.63 | -1.66 | -1.69 |
20 | -0.6 | -0.96 | -1.18 | -1.32 | -1.42 | -1.49 | -1.55 | -1.59 | -1.63 | -1.66 | -1.69 |
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:
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 ð¨Â or Lisa ð©? 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 ârelative difference calculationâ for iâs and eâs and all friend group mixes.
i4: âHow Alone Does An Introvert Feelâ Factor ð´ââ ï¸ | |||||||||||
i / e | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
0 | 7721.43% | 100.00% | 0.00% | 33.36% | 50.00% | 60.00% | 66.64% | 71.43% | 75.00% | 77.79% | 80.00% |
1 | 1300.00% | 75.00% | 6.64% | 36.36% | 51.71% | 61.14% | 67.43% | 72.00% | 75.43% | 78.14% | 80.29% |
2 | 600.00% | 55.57% | 12.50% | 39.14% | 53.36% | 62.14% | 68.21% | 72.57% | 75.86% | 78.43% | 80.57% |
3 | 366.64% | 40.00% | 17.64% | 41.64% | 54.86% | 63.14% | 68.86% | 73.07% | 76.29% | 78.79% | 80.86% |
4 | 250.00% | 27.29% | 22.21% | 44.00% | 56.21% | 64.07% | 69.57% | 73.57% | 76.64% | 79.07% | 81.07% |
5 | 180.00% | 16.64% | 26.29% | 46.14% | 57.57% | 65.00% | 70.21% | 74.07% | 77.07% | 79.43% | 81.36% |
6 | 133.36% | 7.71% | 30.00% | 48.14% | 58.86% | 65.86% | 70.86% | 74.57% | 77.43% | 79.71% | 81.57% |
7 | 100.00% | 0.00% | 33.36% | 50.00% | 60.00% | 66.64% | 71.43% | 75.00% | 77.79% | 80.00% | 81.79% |
8 | 75.00% | 6.64% | 36.36% | 51.71% | 61.14% | 67.43% | 72.00% | 75.43% | 78.14% | 80.29% | 82.07% |
9 | 55.57% | 12.50% | 39.14% | 53.36% | 62.14% | 68.21% | 72.57% | 75.86% | 78.43% | 80.57% | 82.29% |
10 | 40.00% | 17.64% | 41.64% | 54.86% | 63.14% | 68.86% | 73.07% | 76.29% | 78.79% | 80.86% | 82.50% |
11 | 27.29% | 22.21% | 44.00% | 56.21% | 64.07% | 69.57% | 73.57% | 76.64% | 79.07% | 81.07% | 82.71% |
12 | 16.64% | 26.29% | 46.14% | 57.57% | 65.00% | 70.21% | 74.07% | 77.07% | 79.43% | 81.36% | 82.93% |
13 | 7.71% | 30.00% | 48.14% | 58.86% | 65.86% | 70.86% | 74.57% | 77.43% | 79.71% | 81.57% | 83.14% |
14 | 0.00% | 33.36% | 50.00% | 60.00% | 66.64% | 71.43% | 75.00% | 77.79% | 80.00% | 81.79% | 83.36% |
15 | 6.64% | 36.36% | 51.71% | 61.14% | 67.43% | 72.00% | 75.43% | 78.14% | 80.29% | 82.07% | 83.50% |
16 | 12.50% | 39.14% | 53.36% | 62.14% | 68.21% | 72.57% | 75.86% | 78.43% | 80.57% | 82.29% | 83.71% |
17 | 17.64% | 41.64% | 54.86% | 63.14% | 68.86% | 73.07% | 76.29% | 78.79% | 80.86% | 82.50% | 83.93% |
18 | 22.21% | 44.00% | 56.21% | 64.07% | 69.57% | 73.57% | 76.64% | 79.07% | 81.07% | 82.71% | 84.07% |
19 | 26.29% | 46.14% | 57.57% | 65.00% | 70.21% | 74.07% | 77.07% | 79.43% | 81.36% | 82.93% | 84.29% |
20 | 30.00% | 48.14% | 58.86% | 65.86% | 70.86% | 74.57% | 77.43% | 79.71% | 81.57% | 83.14% | 84.43% |
x-axis = number of extroverted friends, y-axis = number of introverted friends
e4: âHow Alone Does An Extrovert Feelâ Factor ð¦ | |||||||||||
i / e | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
0 | 54650.00% | 100.00% | 0.00% | 33.50% | 50.00% | 60.00% | 66.50% | 71.50% | 75.00% | 78.00% | 80.00% |
1 | 1300.00% | 75.00% | 6.50% | 36.50% | 51.50% | 61.00% | 67.50% | 72.00% | 75.50% | 78.00% | 80.50% |
2 | 600.00% | 55.50% | 12.50% | 39.00% | 53.50% | 62.00% | 68.00% | 72.50% | 76.00% | 78.50% | 80.50% |
3 | 366.50% | 40.00% | 17.50% | 41.50% | 55.00% | 63.00% | 69.00% | 73.00% | 76.50% | 79.00% | 81.00% |
4 | 250.00% | 27.50% | 22.00% | 44.00% | 56.00% | 64.00% | 69.50% | 73.50% | 76.50% | 79.00% | 81.00% |
5 | 180.00% | 16.50% | 26.50% | 46.00% | 57.50% | 65.00% | 70.00% | 74.00% | 77.00% | 79.50% | 81.50% |
6 | 133.50% | 7.50% | 30.00% | 48.00% | 59.00% | 66.00% | 71.00% | 74.50% | 77.50% | 79.50% | 81.50% |
7 | 100.00% | 0.00% | 33.50% | 50.00% | 60.00% | 66.50% | 71.50% | 75.00% | 78.00% | 80.00% | 82.00% |
8 | 75.00% | 6.50% | 36.50% | 51.50% | 61.00% | 67.50% | 72.00% | 75.50% | 78.00% | 80.50% | 82.00% |
9 | 55.50% | 12.50% | 39.00% | 53.50% | 62.00% | 68.00% | 72.50% | 76.00% | 78.50% | 80.50% | 82.50% |
10 | 40.00% | 17.50% | 41.50% | 55.00% | 63.00% | 69.00% | 73.00% | 76.50% | 79.00% | 81.00% | 82.50% |
11 | 27.50% | 22.00% | 44.00% | 56.00% | 64.00% | 69.50% | 73.50% | 76.50% | 79.00% | 81.00% | 82.50% |
12 | 16.50% | 26.50% | 46.00% | 57.50% | 65.00% | 70.00% | 74.00% | 77.00% | 79.50% | 81.50% | 83.00% |
13 | 7.50% | 30.00% | 48.00% | 59.00% | 66.00% | 71.00% | 74.50% | 77.50% | 79.50% | 81.50% | 83.00% |
14 | 0.00% | 33.50% | 50.00% | 60.00% | 66.50% | 71.50% | 75.00% | 78.00% | 80.00% | 82.00% | 83.50% |
15 | 6.50% | 36.50% | 51.50% | 61.00% | 67.50% | 72.00% | 75.50% | 78.00% | 80.50% | 82.00% | 83.50% |
16 | 12.50% | 39.00% | 53.50% | 62.00% | 68.00% | 72.50% | 76.00% | 78.50% | 80.50% | 82.50% | 83.50% |
17 | 17.50% | 41.50% | 55.00% | 63.00% | 69.00% | 73.00% | 76.50% | 79.00% | 81.00% | 82.50% | 84.00% |
18 | 22.00% | 44.00% | 56.00% | 64.00% | 69.50% | 73.50% | 76.50% | 79.00% | 81.00% | 82.50% | 84.00% |
19 | 26.50% | 46.00% | 57.50% | 65.00% | 70.00% | 74.00% | 77.00% | 79.50% | 81.50% | 83.00% | 84.50% |
20 | 30.00% | 48.00% | 59.00% | 66.00% | 71.00% | 74.50% | 77.50% | 79.50% | 81.50% | 83.00% | 84.50% |
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 ð .
Now because this âzero friends limitâ 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.
I know I`m not. And since I´m the mayor of âthought experiment worldâ 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 iâs and eâs feel depending on the number of friends they have. Hereâs this calculation for all possible friend group mixes:
Mixed friend groups | ||
Friends | ð´ââ ï¸ Introvert | ð¦ Extrovert |
1 | 700.00% | 700.00% |
2 | 225.00% | 225.00% |
3 | 115.55% | 115.50% |
4 | 77.77% | 77.80% |
5 | 62.63% | 62.58% |
6 | 56.43% | 56.36% |
7 | 54.23% | 54.25% |
8 | 53.97% | 53.89% |
9 | 56.00% | 56.00% |
10 | 58.12% | 58.14% |
x-axis = introvert or extrovert, y-axis = number of friends, colored cells = âfeeling alone factorâ
Now the numbers look different from what we saw before. Why is that?
If an introvert has 1 friend, this one friend can either also be an introvert or an extrovert. So the average âfeeling alone factorâ 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: Itâs because at some point iâs ð´ââ ï¸ and eâs ð¦ are stressed by having too many friends.
We made progress. Introverts feel more alone than extroverts ð¥². 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.
Because there is more: We make friends with people who are like us. Extroverts have more extroverted friends & introverts have more introverted friends.
If iâs and eâs only have friends of the same kind, the table looks like this:
Only friends of same kind | ||
Friends | ð´ââ ï¸ Introvert | ðExtrovert |
1 | 1300.00% | 100.00% |
2 | 600.00% | 0.00% |
3 | 366.64% | 33.50% |
4 | 250.00% | 50.00% |
5 | 180.00% | 60.00% |
6 | 133.36% | 66.50% |
7 | 100.00% | 71.50% |
8 | 75.00% | 75.00% |
9 | 55.57% | 78.00% |
10 | 40.00% | 80.00% |
x-axis = introvert or extrovert, y-axis = number of friends, colored cells = âfeeling alone factorâ
Now introverts feel shockingly more alone ð±. 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.
Now there's only one question left to ask: Are you an extrovert and want to hang out in 14 days?