Lets just  
You suddenly feel empowered by the power of Fez. You feel like you could steal an ancient yet technologically unmatched time machine with a really long name with clever initial letters that can be abbreviated to something catchy.  
Puting a random example, Time and Relative Dimension in Space, first thing that came to your head, randomly.  
And with said time machine, go on adventures through time and space, always acompanied by someone. Your companions use to have accidents or leave abruptly, but youd still carry on.  
You also think bowties are cool, that it would be totally amazing if you could ever say Allons-y Alonso! and that bananas are good, and you should always carry a banana with you, never to drop it.  
In short, this isnt the kind of hat youre looking for for a in-the-middle-of-a-mysterious-jungle adventure.  
But youll keep it around in case of space troubles. Or timey-wimey-wibbly-wobbly-stuff ones.