How long can a man survive underground without going insane?
A traveler is buried under stones in a cave system. His only sources of food are mushrooms and creatures that live in the caves. Some of them will try to eat him. He has a source of light and heat that also scares the dangerous animals.
Given the fact he is highly intelligent while the animals are not, and the fact that he has Medieval Age technology, how long could he survive without going fully insane?
According to studies on everyone's favorite test subject—college students—the answer is: no more than 7 days.
Studies on human subjects are rare — in part because most modern universities would never consent to them — but in 1951 researchers at McGill University paid a group of male graduate students to stay in small chambers equipped with only a bed for an experiment on sensory deprivation. They could leave to use the bathroom, but that’s all. They wore goggles and earphones to limit their sense of sight and hearing, and gloves to limit their sense of touch. The plan was to observe students for six weeks, but not one lasted more than seven days. Nearly every student lost the ability “to think clearly about anything for any length of time,” while several others began to suffer hallucinations. “One man could see nothing but dogs,” wrote one of the study’s collaborators, “another nothing but eyeglasses of various types, and so on.”
While this study is problematic due to questions about the ethics of McGill researchers at the time, it is widely cited. Other studies about social isolation (solitary confinement) with or without sensory deprivation (in both humans and animals) come to similar conclusions about mental state (though not necessarily hallucinations).
This wasn't being trapped underground, but it seems like a reasonable approximation. The difference is that the graduate students knew they were safe and getting out. Your character doesn't know if he'll ever be rescued and is likely to just give up after a while.
Now, if your character were trapped with a group of people, the answer is months. A group of Chilean miners were trapped underground for 2 months, with the first part of that being without anyone knowing if they were alive and without any evidence they might be rescued. After that they had communication with the outside world and a conduit for food and supplies, though only a small hope of a successful rescue. After their amazing rescue (every one of them survived), they had psychological issues, but not insurmountable ones.
In another case, a man who was trapped underwater for 3 days but survived continues to have nightmares and has vowed never to return to the ocean. He was in a shipwreck and was rescued by divers working to recover bodies from the wreck. He had no contact with other people, no realistic hope of rescue, no light (after his flashlights died), almost no food or water (just a soda), and horrible conditions.
Being alone, being in the dark, not knowing if rescue is possible, those are all things that worsen the effect on the mind.
With heat, might, food, water, breathable air, and most important, shelter, this person can be in it for the long haul. Indefinitely, I would say, the limitation is his own - disease, being eaten, misfortune.
Humans have survived years in such conditions. Being in a cave or on an island makes little difference. The other animals are there to keep him company - and the added challenge, to keep him sane, is to outwit them to stay alive.
The only factor we do NOT know, is the state of his mind and the fragility of his own psyche. Does he have a reason, and the will, to survive?
As long as the traveler has light, there can be some hope of using the intelligence to survive. Once in the darkness he will be as dumb as a stone against the darkness dwelling predators.
With medieval technology a light source will last at most few hours (oil burner, wooden torch). That's also, give or take, the lifespan the traveler can count on.
