Time of Useful Consciousness (TUC) is the sort of number none of us ever want to have to deal with in everyday life. Simply put, for any given altitude above sea level, TUC is how long you have before you black out - and probably never come to. Wonderful, eh?For example, at 35,000 feet - a nice, normal cruising altitude for a jet airliner - the TUC is about 30 seconds. So when the nice cabin crew tell you "in the unlikely event of a sudden change in cabin pressure, a mask compartment above your seat will open automatically," they leave out the that by the way, you've got 30 seconds to get it on and get that oxygen flowing.
Anyway, as you go lower, the TUC gradually gets longer, and at 15,000 feet or less, it's presumed to be "indefinite." This doesn't necessarily mean that everyone can hang around at 15,000 feet for as long as they want without blacking out, but some people might manage it, so there's not a handy little number.
Of course, even below 15,000 feet, there are other issues to deal with, primarily hypoxia or "blood oxygen starvation." As altitude above sea level increases, availability of oxygen in the air decreases, as does the saturation of oxygen in your blood. Spending time at 10,000 feet, it's only about 90% of what it is at sea level. At 14,000 feet, it's about 84%. And so on. As your blood oxygen saturation drops, so does your ability to think clearly, react quickly, make good judgements, etc.
This, of course, is why airliner cabins are pressurized to the equivalent of 8,000 feet or less. And why Air Force crews are required to use supplemental oxygen at altitudes of 10,000 feet or more. And why there are FAA regulations about using oxygen at various altitudes. And why tourists who are going up for a 2-hour tour of the summit of Mauna Kea (nearly 14,000 feet) are required to acclimate at 9,000 feet for at least a half-hour, and preferably longer.
So now that you have a good understanding of the risks involved with spending lots of time above 10,000 feet... I'll confess to being an intermittent telescope operator on Mauna Kea. Every now and then, I find myself at almost 14,000 feet for a half-night (6-7 hours), or a full night (12-13 hours), or, in some cases, for four 12-13 hour nights in a row, sleeping days at 9,300 feet in between.
And no, they don't give us supplemental oxygen. :)