I think seemed is the key word here. Many people that are good at what they do give the impression that it's a breeze for them. When examining it closer, it isn't: they spend plenty of time studying. I've never really gotten to the bottom of it, but the difference seems to be that they simply talk less about the studying and more about the material itself, which gives the impression they know their stuff very well, even though they studied hard as well.
Basically, we humans are really bad at judging things, particularly abstract things like "intelligence". Heck, we can't even really define it yet.
Just get your results, and be happy with those.
A comforting half-truth.
Subject to the (entirely reasonable, I believe) presumption that humanity is finite, a lack of maximal and minimal elements implies that "is smarter than" is not a strict partial ordering. (All finite partially-ordered sets have maximal and minimal elements.)
This seems profoundly counterintuitive to me; both the asymmetry and transitivity of the "is smarter than" relation seem almost axiomatic (and the irreflexivity is indisputable).
It seems to me that there must be thousands of individuals who are maximally smart -- each of them, naturally, incomparable to the others.
Hah, you can't be serious! Look around you - asymmetry is so painfully obvious that even pop theories propose to split intelligence into "book smarts", "street smarts", "social smarts", etc.
In reality, I don't think "smart" is a word that makes much sense, outside of the context of signaling social status (pIQ).
Which is really total agreement with your point. "Smart" is as much a partial ordering as "friendly" is, for a lot of the same reasons.
I don't see the connection. Asymmetry in the relation "is smarter than" simply means that it is impossible to have both "X is smarter than Y" and "Y is smarter than X" (for X != Y).
In the context of individuals of incomparable intellect, it is inappropriate to say that either is smarter than the other -- never mind that they are both smarter than each other.
I think that's the core truth of "genius". Melville put it, "Genius all over the world stands hand in hand, and one shock of recognition runs the whole circle round".
Joseph Campbell, Isamu Noguchi, Martha Graham, and Rudy Arnheim were all geniuses in very different fields, but they were also drawn to each other in friendship & collaboration. They can't compare to each other on any scale, but somehow shared something in common.
Secondly, even for someone X who is maximally smart, the statement "Y is smarter than X" can be true if its in a particular context. E.g. take two people who are maximally smart... there no one smarter than X in math (or whatever) and no one smarter than Y in history. Then X is smarter than Y and Y is smarter than X... depending on how you use the word.
Edit: So long as no one is maximumly smart.
Now define "smartness".
Then I went to a top university in Computer Science. I was suddenly surrounded by people that were orders of magnitude better at computer science than I was. I had to study for hours to understand something they seemed to understand implicitly. It took two years of struggling to finally reach a point where I considered myself "good" at computer science. After that, it came fairly easily but I still had to work much harder than my friends who did it effortlessly.
I learned over time that I am fairly smart. Not off the charts smart, but I've got my strengths. I still have to work harder than those in the top of my field, but I'm certainly on the down slope of the bell curve.
But the most important thing that I've learned is that it doesn't matter how smart you think you are. There will always be those more or less smart than you. What's important is what you do with it, and how hard you work to achieve what you want.