Don,
About 40 years ago, right after college and grad school, a buddy of mine went to Jackson, WY to work for the summer. He met a young guy about our age who was a ranger in Yellowstone, stationed at Hart Lake. We got invited to hike in, spend the night (all a little disconcerting with heavy shutters on the cabin's windows to 'ward off grizzles, but if they want in they will get in). The ranger got a call to walk out 'the back way' to check on the river flowing through the area and invited us along rather than going the way we came in. 17 miles later and three fordings of the extremely cold river, we got out to the last crossing which was in some sort of bucket that we ratcheted across the now much bigger and faster river.
I still recall having a lunch break and having him tell us that fewer than 300 people per year saw what we were, in a National Park that is heavily visited. We didn't see a soul the whole day. In the time before cell phones and good radio coverage, I'm glad no one rolled an ankle, had a medical emergency or whatever, but it was exhilarating.
Enjoy the solitude, and hope that we slow down the rapid reproduction of the human species to a sustainable rate.