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You don't have to put yourself down to have an open mind or a beginner's mind. Realistically you are aware that you are not below average in all contexts, no? So what does it mean to tell yourself otherwise? False humility? Self deprecation? Doesn't seem very healthy.
I was going to say, if one is not below average, this seems like something someone would say if made aware of their narcissism all of sudden. There's some aspect of vulnerability here, which is why it's more vulnerable narcissism. Not assuming anything about the author, only speaking in generalities.
The thing is, many endeavors are not single dimensional nor are they designed to be competitive, so pairwise ranking doesn’t make any sense.

If you say, I’m better at bob than badminton. That makes sense since it’s designed as a competition and you can resolve the argument by playing Bob.

If you say “I’m better at Bob at software engineering” what does that even mean? Does Bob even know he is competing against you?

Imagine a divisive debate, carried on within the context of a humility contest. :)
This is useful advice, but please don't take it to the extreme of developing imposter syndrome [1]. Good engineers need to balance humility with confidence. Too humble, nobody listens (and you don't get funding). Too confident, people label you as a self-important "blow hard."

[1] http://phdcomics.com/comics.php?f=2042

There's also a time an place for admitting you are not normal.

I burned through a lot of social capital as a young adult because I assumed that if I thought of an idea, everyone else would think of it too if I just gave them a moment, or a few hints. I saw myself as thinking faster, not thinking deeper. When you think of people being slower than usual instead of the solution just being very non-obvious, you don't have the sort of patience the situation requires.

Why don't they let donkeys into universities? Because nobody likes a smart ass.

Personally, I find that trying to stay away from single-value representations of skills/health/etc is more helpful and facilitates more curiosity.

Instead of wondering, "Am I better at X than Bob?", I try to focus on "About which part of this problem might Bob have an insight I'm missing", for example.

It's probably true that I was better than 90% of students at some small sliver of something, but that's not super relevant in the larger scope of everything it means to be a student. Getting away from the "better"/"worse" dichotomy is the important thing, IMHO.

He could also assume that he is above average and aim to be in the top 0.1%. Would it change how (1) the results he is seeking will be achieved and (2) the effect his story has on others? My answers are: for (1), no, and for (2), yes.

As for (1), there is the added nuance of not wanting to hurt their ego: "if I'm not successful, it's because I started from a below-average level." But there are few things I dislike more than this very human and very popular form of cowardice. And it also works, which makes my dislike moral and not utilitarian.

Recently, I was listening to an interview with Jon Jones (the very famous and very talented MMA athlete), in which he related that he used to do something crazy a few days after his fights, maybe spend a night out partying and drinking, so that he would have the excuse card (for himself, not for others) ready if he happened to lose his next fight. It worked for him—-he is probably the greatest MMA fighter of all time--but I still found his approach a bit cowardly, weak, defensive.

I spent many years practicing jiu jitsu and got my black belt a few years ago. Now, it is common for fresh and not-so-fresh black belts to say that when you are a black belt is when you realize you know nothing about jiu jitsu. Like any social meme, it is hard to distinguish "true thinking" from "going with the flow"--everybody says that, why should I do otherwise--but I certainly know a lot more about jiu jitsu than I did when I was a white, blue, purple, and brown belt. This is not to say that there is much to learn and that I may be below average among practitioners 10 years younger than me and above average among those 20 years older. But why not be honest with ourselves and others, without thinking about ego bruises or the sympathy we may receive?

To your point about being a black belt, I find that more mastery of an ability makes you aware of how much you still have to learn. Like at first you assume you are 30% of the way there as a beginner but at the high levels you find that almost everyone at your level has something new to teach you and there is infinite potential for growth.
You are right, but the "I know nothing" after years of practicing whatever skill you are trying to develop sounds much more like feigned humility than a frank and frankly attractive assessment of someone's abilities.

I have a Ph.D. in physics, and I might consider myself below average among physics Ph.D.s coming out of Harvard or Berkeley, but am I "below average" in physics without further qualifications? It would be silly to say that, wouldn't it?

Like the mathematical genius saying, "I am not that talented, I can't even cook, my spouse has to tell me five times a day where I left the keys (haha), I simply loved math more than others, but anyone, with the right tenacity and guidance, could accomplish what I was fortunate enough to achieve". Come on, those are not serious people.

It is likely that my expertise gives me a more nuanced understanding of the complexities of the field, of how much there is to learn, than the understanding that a talented high school student should have of it -- I agree with you on that -- but a sober assessment of one's abilities and position within a population has never been a mortal sin, quite the contrary. It is the stuff that serious people are made of.

That is definitely true. "I know nothing" is an extremely poor way of putting it, more like false modesty than an accurate assessment of skill.
I assume I'm different, because it's hard to compare to the average when you have no car, no bed, no desk, no stainless/holeless clothes, no fridge, no TV, no dishes, no family, a remote job, foraging fruit as hobby, a weird life, we don't compare apples and oranges
The below avg. think they're above avg. The above avg. think they're below avg.

Dunning-Kruger strikes again.

Skill levels follow a power law distribution just like wealth so most people are below average if you think of the average as the mean value. But with skewed distributions the mean is almost meaningless. If you'll pardon the pun.
This is one of my favorite things to do, it reveals a lot about fundamental skills I never really actively think about...

If I'm below average at walking, what would it look like to be above the curve? ... at reading? ... at eating? ... at relaxing? ... at sitting or standing?

I've been spending a majority of my time lately re-examining the skills I will rely on for the rest of my life. Been surprisingly helpful so far.