William Gibson revolutionized the world of science fiction with his dark and gritty but somehow impossibly cool cyberpunk novel Neuromancer. Dystopias have always been a staple of science fiction, but in this case the dystopia didn’t seem too horribly dystopic. Sure some computer might try to take over the world or some vat-grown ninja might shiv you in a space station, but it would sure be an interesting life even if it was short and weird. Gibson’s skill with language helped. The first line of the novel resonates in fiction circles to this day:
The sky above the port was the color of television, tuned to a dead channel.
Neuromancer was written in 1984. I think it’s a little funny that in the modern world of digital TV the color of a television tuned to a dead channel is in fact a solid bright blue. It’s probably not a coincidence. If your TV is showing a dead channel there’s probably something wrong with it. And if it’s broken, the manufacturer probably can guess that you don’t want to be looking at some frustrating color like red. If you’re going to be calling their support department you should probably have a nice blue sky in mind.
The sky itself blue due to the scattering action of the atmosphere. Carrying the explanation beyond that is something we’ll save for later, but for now it’s good enough to say that it is in fact the atmosphere that’s doing the scattering.

This is from the Wikipedia article on the sky, and you’ll notice that at this high altitude the blueness gets deeper and at high angles you have even less total atmosphere to do the scattering and so the blueness fades to black. So just how much atmosphere have you managed to get above at airline altitudes? Most of it. The cabin is pressurized for a reason.
The barometric formula gives a pretty good estimate of exactly how much. At typical airline altitudes you’re above more than 2/3 of the atmosphere. If you’re sufficiently clever you could estimate your altitude by judging how dark the blueness of the sky was. It wouldn’t be easy or very accurate, but you could do it.
I don’t fly often, but when I do I notice that most people keep their windows closed and do something boring like sleep the whole way. I think it’s a better idea not to do that. Open the window and take a look, and see what you can notice about this ocean of air we inhabit.