I'm not sure I quite understand jet lag. Side note, I saw someone on Facebook a while back use the term, "Jet Leg" after describing their "strenuous United States flight." and I thought that was funny.
Anyway, in theory (or so I thought), someone could be SO tired at the end of a long day of traveling, and a few nights of little sleep, that they could sleep through the night. Wrong. I slept 9:30pm-1:00am and have been up ever since. It's currently 4:30am, and breakfast isn't served until 7:00.
I got up at 1:00, took a shower, and walked the canal near my hostel for an hour or so. There was no one on the street, and it glowed a beautiful dim yellow tint from the lights. It was much more enjoyable not seeing an abundance of tourism on the streets, and have Paris to myself for a bit. I had John Mayer's "Where the Light is." album playing in my shirt pocket, and I just walked. I could be more emotional due to lack of sleep, but I was tearing up a bit at how peaceful I felt, yet being utterly alone. I don't usually enjoy alone-travel as much as with friends, but this trip has been eye-opening for me. I can potentially see myself traveling all over Europe alone, and meeting strangers along the way.