Who Feels More Alone?

post by marvinscheffold · 2024-09-22T11:54:06.324Z · LW · GW · 2 comments

Contents

  Are You Going To Meet a Friend Today?
  In X Days You Will Meet a Friend
      (i) / (e)
      0
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
      0
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
      (i) / (e)
      0
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
      0
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
  How Pissed Off Is Ben?
    The “How Alone Do You Feel” Factor
      (i) / (e)
      0
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
      0
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
      (i) / (e)
      0
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
      0
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
      11
      12
      13
      14
      15
      16
      17
      18
      19
      20
  Are You Satisfied?
      Friends
      🏴‍☠️ Introvert
      🦅Extrovert
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
    Introverts Feel More Alone
      Friends
      🏴‍☠️ Introvert
      🦅Extrovert
      1
      2
      3
      4
      5
      6
      7
      8
      9
      10
  Conclusion
None
2 comments

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 [LW · GW] for pointing out a mistake in my calculation

 

 

 

 

2 comments

Comments sorted by top scores.