“THE TRICK WILLIAM POTTER IS NOT MINDING THAT IT HURTS” - What does it mean?

The first time I watched Prometheus I asked myself why David quotes the famous line from the movie Lawrence of Arabia: “the trick William Potter is not minding that it hurts”. At first I thought that was something related to David’s character alone, and maybe related to his silent struggle to tolerate his human masters. But at that time I had not watched the Ted Talk and the Prometheus deleted scenes yet. The first time I finally ended up watchig the Ted Talk I was surprised: Weyland was quoting the line too! And so I decided to try to figure it out why.
In Prometheus and Alien: Covenant the fire represents technology, knowledge, and probably also the dangerous things you have to do in order to “change the world”. In Lawrence of Arabia, T. E. Lawrence is pretty obsessed with this “trick”: he holds a match between his fingers and then blows off the fire not only among his comerades but also before starting his adventure in the desert. In that scene the spectator notices that even if his superiors think he’s mad and that the desert it’s not a place for “ordinary men”, Lawrence is extremely confident in his possibilities. He can do that: he touches fire, he extinguishes fire as an allegory of that confidence. It’s not a coincidence to me that Weyland starts his speech full of ambituious and megalomaniac declarations with a reference to the famous trick of Lawrence, and then he proceeds to speak about Prometheus, and then he concludes with the line:

“These rules exist because the people who created them were afraid of what could have happened if they didn’t. Well, I am not afraid! (…) If you’ll indulge me, I’d like to change the world”.

From Weyland’s point of view to touch the fire, to play with the fire, the gift of Prometheus, is not a problem: the trick will be not minding that it hurts, it will be not minding about the consequences, the same consequences that scare the people that made the laws Weyland talks about. But Weyland is “not afraid”. He will not mind that it hurts. And so, we see a Peter Weyland that in Prometheus, for example, is ready to get Elizabeth killed to accomplish his goal. All of this is inherited by David, that does even shapes himself as the Lawrence he sees in the famous movie, and it’s probably not a coincidence that the son’s favorite movie is one that is so ispirational for the father too.

I do believe that the line from Lawrence of Arabia, is repeated (in a subtly way) a third time in Prometheus, but unfortunately this happens in a deleted scene: the scene where Janek goes to visit Vickers to try to make her feeling better after Holloway’s death.
 We see a Meredith Vickers clearly shocked by what she has done to Holloway. She had to do kill him to prevent the ship from being infected by whatever was killing the man, yet she’s in pain for that: her hands are shaking and she’s absent, she hasn’t eaten her lunch. Janek explains to her what he thinks it happened on that planet 2000 years before, that an incident happened, and then says to her that she killed Holloway because it was “her turn to push the button”, that was her turn to took a cruel decision for a greater good. 
This reminds me of the scene where Lawrence has to kill a man to prevent the failure of his project to conquer Aqaba. After the execution Lawrence is shocked and Sherif Ali says to him that there’s no shame in what he has done because he was in a position that granted him the right to execute the man (he previously saved the life of the man, so he basically owned his life) and because it was necessary. When Janek finishes to tell her about an event that occurred when he was a militar, when a secret facility was destroyed and the people inside it were killed to prevent the spread of something surely terrible, she asks him why he had to tell her that story. And he answers:

“Because you killed a man today. Looks like you are in pain”.

Janek is right: Vickers is in pain, we see that. She looks terrible. But Vickers doesn’t want to appear “soft”, so, she raises her cold shield again and answers to him that she’s in pain only because:

“I burned my hand”

This sentence has an hidden meaning: Meredith cares about the consequences of her cruel decisions. Vickers pretending she’s suffering because she burned her hand is the opposite to Weyland and David’s “the trick is not minding that it hurts”. Unwillingly, Vickers is confirming to the spectator that knows the hidden allegory that she minds about the pain; she burned herself, she’s shocked by Holloway’s death; we see that. Meredith doesn’t manage to do not mind. 
Weyland and David “touch fire”, do unethical things without feeling regret, without minding that the “fire” burns. That burns their own fingers and that burns the people around them (again: let’s think to the threatening of Elizabeth in Prometheus and her destiny we discover in Alien: Covenant). 
In all of that David is more dangerous than Weyland because he’s even more good at being uncaring, unethical, amoral; he really lacks of real compassion, and he’s like that because he’s a synthetic. This is mirrored by another allegory hidden in the lines of Lawrence of Arabia: during the scene David is watching at the beginning of Prometheus, one character says, speaking about Lawrence and his obsession for the fire trick:

“He did it once too often. It’s only flesh and blood!”

The man cannot understand how is Lawrence able to extinguish the fire with his bare hands so many times if he’s made of “flesh and blood”, and this foreshadows Lawrence’s future downfall into an extremely tormented and suffering man. “He did it once too often”. But David is not “flesh and blood”. He’s not really hurt back by his cruel, amoral actions. He’s able to not care. He could really be able to do it “once too often” and not feeling the real pain of remorse.
 David is the real, ultimate personification of the “Lawrence archetype” Weyland adored so much.
Well, at least this is my opinion on the topic.