There are no lines on the road — and very few paved roads to paint a line on. There are no chains and no commercialization. There is no A.T.M., no restaurant open year-round, and the first police station is currently under construction. Here, visitors are guests, not tourists. I stayed in Ms. Matas’s homestead property and was quickly incorporated into her daily life, including meals, chores and island events.

“How do you welcome in the modern world, but keep this ancient culture alive? They’re in this limbo state of trying to find the balance,” Silvia Soide, a folk dance teacher and photographer, said. Ms. Soide moved from Vancouver to Kihnu in December 2008 in honor of her Estonian grandmother who fled the island during World War II.

“The older generation wants to keep the traditions and culture alive so they’re teaching what they were taught. It should stay alive, it’s a beautiful culture but I know that younger people feel frustrated. They’re welcoming in the outside world because it offers them a way of survival. It’s a really great opportunity for Kihnu women to earn money during the tourism season,” said Ms. Soide, imagining jobs such as cooking, innkeeping, sales and waitressing.

Kihnu can feel much larger than its four-mile length and two-mile width, as I found out on a walk to the rocky coast and back one morning. The only signs of life I encountered were a hound dog, fast asleep on a sun-warmed road, and a curious seal bobbing in the waves off the jagged coast. I turned off the beach down one of the many unmarked sandy roads that cut through the towering forests. Behind me, waves from the Gulf of Riga crashed against rocks. An occasional tree branch creaked or snapped in the wind. The forest grew wild, allowed to do what nature intended it to.

I thought of the way Ms. Soide described the island. “Everybody from Kihnu really loves Kihnu. It grows roots around your feet.” The forest had a fairy-tale quality that made this seem plausible.

At home, Ms. Matas heated up her sauna cabin and raked the yard, while Timofei, the lamb, bounced around, trying to engage Pepe, her family’s increasingly annoyed dog. Ms. Matas was talking to the animals, encouraging Timofei to eat grass so she could finally stop bottle-feeding him.

“When he was born, his mother wanted nothing to do with him. He was going to die because she wouldn’t even feed him,” she recalled, looking distressed. “This was so upsetting to me. Imagine, no mothering instinct. So I had her killed.”