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The Gordian knot – A lesson in greatness
You all know the story. There is a famous knot which no one can open.
Alexander comes, looks at the knot, takes out his sword and cuts it. He later becomes Alexander the Great.

This is usually used as an example of thinking outside the box. Whatever. I saw it mentioned lately in a book I read, post and I was thinking the following: What kind of guts does it take to do that!
You come to an unsolvable problem, and you decide on a certain solution that would bar anyone else from ever trying to solve it after you. Maybe there were better ways to open the knot – no one will ever know. Who knows which amazing lessons we lost by that one action. No one can try again.
The solution was not ingenious, it was arrogant to the extreme. A willingness for destruction is needed. A feeling that the world was created for you.
There are many assholes who wouldn't mind destruction, but that kind of guts is rare; very rare.

We are not Alexander the Great, nor would we necessarily want to be (would you?), but we should still learn from this. We should learn the importance of demanding your place in the world. The importance of claiming your authority and place in the world. The world owes you nothing, but it might be willing to reward you if you convince it you deserve it. If you convince it you are willing to take the responsibility upon yourself - not the responsibility of failure, many are willing to do that, but the responsibility to make it work. The responsibility to fix things, and unite the world.

The story of the Gordian knot is not a story of the sphinx riddle, it's a story of the psychology of greatness. There are other ways to be great, or at least we hope so, but we should all take that story to heart.

(I obviously don't care if it actually happened or not. It's a story about how you become Alexander the Great.)
Maybe we should define "greatness." Alexander The Great is no doubt one of the biggest individual shapers in history. But who are some others? Caesar. Lincoln. Da Vinci. Newton. Martin Luther King Jr. But then there are the others. Napoleon. Genghis Khan. Who can deny Hitler and Stalin this title? They more than any single person shaped the events of the 20th century up to today. What does greatness mean really? It definitely doesn't mean good. And you bring up this story's relation to the Watchmen so how can we refuse to think of Ozymandias. Is he great? I should say so. Think of the amount of impact he delivered to the world. But is he good, is he right, is he just?

You are certainly right about the necessity for arrogance and a mind for destruction in this parable, but there is a shadow to the lesson you imparted. What's the spiderman cliche? "With great power comes great responsibility?" That someone like Alexander could demand the world listen to him, that he could assert his authority in this way means he has ventured beyond his birthplace into an almost demigod position. And that is a dangerous point to be in, for just as easily as he could become the most loved man in the world, good to all, he could also assert more and more power until he is nothing more than a tyrant.

So before we take a lesson from this story we need to thoughtfully regard power and greatness. Because the moment we as an individual among billions assert our authority and cut the knot, that is the moment we've come into power over others. And that sort of power is blinding. Ozymandias thought he was just in his actions, and so did Hitler...
The word that seems to be missing from this thread is narcissism. It takes a certain degree of internal processing and self-worth to have cut the knot. Narcissism isn't necessarily bad, it definitely comes with a bad connotation, but didn't Freud say it was an integral part of all humans? For the most part, a regular dose of narcissism evens out the playing field. I'm a narcissist to the degree that I am fully aware that I am as good as you are. If I had no semblance of a narcissistic tendency than I would cave next to everyone else in the world.

The "greats" as you say, are the ones who perhaps love themselves more than others. These are the ones who somehow received an imbalance of self-worth. I doubt we can name true innovators who regarded themselves lower than their contemporaries. The narcissist is the one is fully confident he is right so he becomes right.  Alexander could cut the knot because rules didn't apply to him because he exists on the narcissist's plane, a good place to be no doubt.

To lead others, to have people who are 99% biologically identical call you their leader means you have to have a level of confidence that only comes from a boosted or inflamed self-worth. Why are my words more important than the next guy's? My answer would be: they're not. Alexander's would be: Because they are. And that's why he was suited for greatness and leadership while I am not. The great narcissists live in a fantasy world, but the difference between their fantasies and ones we read in books is that they can turn theirs into reality because they will it so.

How to be confident is very much connected with this post on the Gordian knot as you say Arthur. But where are the lines that we should draw between confidence, arrogance, narcissism, and self-delusion?
The important word I wanted to re-mention from my original post was: responsibility. Taking responsibility upon yourself.
You mention Narcissism Clark, and Hanna you mention arrogance. Yes, those are perhaps included, but more importantly is not shying away from responsibility. Not simply not shying away but accepting a huge responsibility towards the world. (Ozymandias' responsibility made of him who he was). That responsibility, not giving excuses but seeing yourself holding the power to act as well as anyone, is crucial to become a serious person in the world. It's crucial for everyone, constantly.

You mention Spiderman's: "With great power comes great responsibility."  I would almost say the inverse: taking responsibility gives you power. (Not taking responsibility after the fact, that's a different issue).

To talk stereotypically, you can see that groups which take responsibility upon themselves are usually more successful than those who don't. Solveig Wright quotes Simone de Beauvoir from The Second Sex  (in the gender stereotypes discussion, post ):

"The men that we call great are those who -- in one way or another -- have taken the weight of the world upon their shoulders; they have done better or worse, they have succeeded in re-creating it or they have gone down; but first they have assumed that enormous burden. This is what no woman has ever done, what none has ever been able to do. To regard the universe as one's own, to consider oneself to blame for its faults and to glory in its progress, one must belong to the caste of the privileged; it is for those alone who are in command to justify the universe by changing it, by thinking about it, by revealing it; they alone can recognize themselves in it and endeavor to make their mark upon it. It is in man and not in woman that it has hitherto been possible for Man to be incarnated. For the individuals who seem to us most outstanding, who are honored with the name of genius, are those who have proposed to enact the fate of all humanity in their personal existences, and no woman has believed herself authorized to do this."

This is stereotypically true for different groups.

This is a (the) lesson to be learned, and it is an important one.
Books Discussed
The Second Sex
by Simone de Beauvoir
Watchmen (Absolute Edition)
by Alan Moore

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