Alone on the water, I found comfort in something that had long been a source of anxiety: math. I constantly calculated when the tide would turn and what, all else considered, that would mean for my boat and me. Unlike the wind, the tide keeps its promises. It turns, rises and falls as predicted.

If I took my time with the figures, the Rule of Twelfths -- that a tide rises 1/12 of its range in the first hour, 2/12th in the second, 3/12ths in the third, 3/12ths in the fourth, 2/12ths in the fifth, and so on -- would tell me how high I needed to drag my boat to get it above the high-tide line at night. The 50-90-50 Rule told me what to expect of the speed of the current crossing wide passages: A current flows at 50 percent of its maximum speed in the first hour, 90 percent the second hour and 100 percent in the third, then backs off in the reverse order.

On Day 10, I pushed past a perfect campsite hoping to set myself up to cross the Strait of Georgia the next day. The island I camped on had horrible landing options, yet I could go no farther -- the next one ahead was in a Canadian military zone, and landing was prohibited. I figured the night's high tide would be somewhere in the middle of a wide zone of huge sharp and unforgiving rocks. Securing the boat was awkward, and my feet and the boat took a beating. The next morning, the kayak was well above the water -- but clearly it had shifted. I had not gone high enough, but I had tied it off with extra line, and that had held. Kayaks drift off in the night. It happens. The thought terrified me.

At Desolation Sound, long arms of water reach deep into snow-covered mountains, giving way to tightly packed islands where whirlpools form and cliffs stream waterfalls like tears. I entered the sound and faced the edge of the world. The disembodied mast of a sailboat slid through the water between two islands ahead. I saw no boat below the mast, and my mind convincingly constructed an abrupt edge to the sea -- an illusion created by the planet's curve, beautiful, humbling and a little frightening. The next morning, I interrupted a wolf eating a fawn that had washed up on a rock ledge. As soon as the wolf slipped into the forest, an eager mink moved in on the carcass.

Several days later, I walked a rough rock beach, looking for a campsite. I topped a small rise to see a cinnamon grizzly sow and her year-old cub flipping rocks for food. Did they spot me? Who knows? By the time I was 20 yards offshore, they were foraging where my boat had been.

On Day 20, I became windbound on uninhabited Yorke Island in Johnstone Strait. Stretching my legs, I stumbled across monolithic concrete bunkers covered with orange moss and unkempt vines, relics of Canada's World War II defenses. Suddenly, it seemed, I had ghostly company.

Queen Charlotte Strait, at the north end of Vancouver Island, is a seven-mile crossing that exposes a paddler to Pacific swells. The weather can be tempestuous. I decided not to take the risk and crossed it on a ferry instead.

Intermittently, I stopped at welcome -- and welcoming -- outcroppings of civilization, including First Nations villages, government moorings and small towns. I re-supplied as well as I could at these stops, with fare that ranged from cans of chili to organic almonds and Cadbury bars.

Steep shores and very high tides made campsites increasingly hard to find. I spent part of one night on top of a huge log, in a place where there was no tent site above the high-tide line. The next day, I pitched my tent next to another bear's snack spot; the alternative appeared to be its bedroom.

I ferried again across Dixon Entrance -- another exposed passage open to swells and storms. That allowed me to explore Prince Rupert, B.C., with its pleasant but pricey waterfront and a proprietary cellphone service that does not play well with others. The ferry left me in Ketchikan, Alaska, where a stranger I had hailed online from Prince Rupert met me late at night and stored my kayak while I was in town -- a gesture so helpful that I hope he is still coasting on the good karma.