My sister and I have run a marathon in the past, and this year is supposed to be the last for the 42.195km, but I injured my right foot during a 31km training run. I'm going to focus on half-marathons (less chances of injuries), but I began to wonder how I would be perceived by the people around me. My family and friends are impressed about what my sister and I did, but would they be disappointed if I stop, or would they still be impressed?
That led me to start wondering about what exactly makes something impressive. By analyzing some feats, and how I view them, I came up with some interesting concepts. There are hundreds of variables that will give better or worse results at something you do, like genetics, if you have a reason behind it, how well informed you are, and how much dedication it took, but I'll try to remove as many variables as I can and stick to the most important points here.
How Well Can You Do It? (Did You Even Try?)
Being good at something yourself has a very good impact on how impressed you can be. My marathon time in 2009 was 4:17, and without injury this year, I would have done around 3:45. Based on that, how well should your result be for me to be impressed? If you run a 3:30, I'll be a little bit impressed. If you run a 3:15, I'll be really impressed. In 2009, I would have been impressed with a 3:45. My sister's marathon time was 4:36, and she says she was impressed with my 4:17 (considering how not prepared I was).
How Many People Can Do It?
Something that everyone can do would be difficult to be impressive. I've made a quick approximation: if one person over a group of 1000 can do something that you never did, you might be a bit impressed. Another way of seeing it is if less than (roughly) 7 million people on Earth can do it, it's starting to be impressive.
If you've never solved the Rubik's Cube before, you might be impressed if someone solves it before you. However, I am personally impressed by someone who can speed-solve it in 20 seconds, as my personal record (back when I was practicing) is close to 30 seconds.
If you think about it, these two points could be different views about the exact same thing. They are both dependent on how well you can do it.
How old are you?
I almost removed this point entirely, but I think it's still an important one that needs to be mentioned. An 80-year-old half-marathoner is more impressive than a marathoner in his prime, because you don't expect someone at that age to be in shape. A fifteen-year-old able to play Beethoven's Moonlight Sonata is impressive, because it usually takes a lot of time an effort to be that good with the piano, and he's still very young.
I don't feel it should be included in the simplified equation, because the amount of time and dedication is roughly the same, and doesn't depend on age. The old half-marathoner just kept in very good shape and runs year after year. The young pianist started learning at a very young age, but practiced for thousands of hours, like everyone else.
I should mention savants and autistic people, and other people who, by whatever mental or physical reason, can do something better and faster than "normal", but that's out of the scope of this post.
Creating the function
First time I tried, I found that if someone does something 1/6 better than you, you start to be impressed, relative to the potential best that can be achieved (world record or anything). That was a naive way to calculate, as I soon found out it only works when "less is better", like timings. Using this calculation would mean that I would be impressed only by people doing more than 1700 push-ups.
That led me to look at the graphs I had drawn, and notice that the calculations should be based on the standard deviation of the population. In statistics, the standard distribution, also known as "bell curve", represents a percentage of the population with how well they do.
That being said, if you know where you stand in the standard distribution for a given task, I found that, approximately, if there are four fifths (4/5) less people that can do better than you, you start to be impressed by them.
Not everything can be quantified, but if gives a very good idea. I like to cook, and can make a very decent meal, but I miss once in a while. The group of population made of 4/5 of the best cooks in my group are impressive to me.
It's hard to put into words. Hopefully, the second graph can give you the best idea. Another (equally failed) way to say it would be that, in the group of population that are better than you at something, you take out the worst fifth, and the rest are impressive.
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