I would think being cool would automatically carry some level of being detached. I mean, you don't want to be a zombie, but if you're cool, you're detached from outcome. Nothing is more uncool than losing your sh!t over some woman.
I'd rather be a zombie

, and
still be detached from the outcome.
As for being mysterious, I'm not even totally sure what that means. I know some posters here swear by it, and it's fairly standard PUA advice, so I'm sure there's something to it.
Definitely something to it.
Please consider this thread (holy sh!t, it's been four years)...where I spoke at length on the philosophy behind simply ignoring women and becoming that
mystery.
. Yeah man, this is just some advice and insight. I already know that some of you guys on here are kiss ass beta males and worship the ground that women walk on, and this information will be hard for you to grasp. However, for those that are willing to pay attention, learn something, and...
www.sosuave.net
This strategy
continues to pay dividends, and allows me to feel empowered and masculine through the entire process, regardless of the outcome.
I don't believe any other strategy will achieve this.
To me it sounds like you're putting on some sort of act, which I don't like.
It is a strategy, in a game of chess.
You're intentionally not answering questions or being vague about them. I'm not sure how else you act mysterious, unless you carry some props with you and appear in a puff of smoke when you enter.

Do you have some examples?
My most profound RECENT example was with her...
Long story short; I worked at the airport making deliveries to
select restaurants in the terminals.
She is a waitress at one of the restaurants, and despite never noticing her, she
apparently noticed me and had been checking me out from afar.
One day, me and my coworker was getting our
free meal at the restaurant, and the lady who took our orders told me that her friend/coworker had a crush on me.
I didn't know who she was referring to, and the lady showed me a picture and I still didn't recognize her (nor was I attracted to her)...but I still gave her my number to give to her friend.
Now, there are two points to be made here...
1. As I tell you guys, IOI's are cool, but it doesn't tell the
full story.
Not only did this lady
ever give me IOI's, but I never even noticed her..despite my many deliveries to the restaurant.
Yet, she admired me from afar.
The point is; women will admire you from afar and will never say
one word to you.
So just because you ain't getting a signal, doesn't mean a DAMN THING.
Now, the
second and most
important point (as related to the subject matter).
2. I asked her why was she attracted to me (I wanted to know, for the record), and she gave two reasons...
A. She stated that when I made my deliveries, I never said anything to
anyone, I just made the delivery and LEFT.
She actually found that attractive!!! There is a certain mystique to being a confident man of little words.
B. My height.
I had a screenshot of her answers but I can't find it.
I shared other similar experiences of varying degrees of this "ignoring" strategy being in effect and working.
You can attract women by doing virtually nothing.
Bruce Lee: Fighting,
without fighting.