In a medium saucepan, cover the potatoes with water. Cook over medium heat until tender, about 20 minutes. Drain the potatoes, reserving water and using potatoes for another use. Cool the cooking liquid to lukewarm (110 degrees F).

In a large bowl, combine the potato water, dry yeast, and sugar. Let sit until the yeast blooms and becomes foamy, about 5 minutes. (If the yeast does not bloom, discard the mixture and begin again with a new yeast.) Add the flour and stir vigorously to work air into the mixture. Cover with a towel let sit in a warm, draft-free place for 8 to 12 hours. (The mixture should become very bubbly.) Use immediately or cover loosely with plastic wrap and store in the refrigerator.

Preserving the Starter: Each time you remove a portion of the starter for a recipe, reserve at least 1/4 cup and replace the amount you have taken out with equal amounts of flour and water.

For example, if you remove 1 cup of starter, you must replace it with 1 cup of flour and 1 cup of warm water. Whisk these ingredients into the starter until blended but not completely smooth, cover loosely, and return to the refrigerator.

Also, the starter must be maintained by feeding it every few days. Refresh by removing 1 cup of the starter (give to a friend or discard it) and adding 1 cup of flour and 1 cup of warm water. Whisk until blended but not smooth. Cover loosely and return to the refrigerator.

If you plan to be away longer than a week, freeze the starter in a sterilized, airtight freezer container. Thaw the starter 2 days before you plan to bake with it. Refresh as indicated above with 1 cup each of flour and warm water. Cover and leave at room temperature 12 hours or overnight before using.

CAUTION: Never keep your starter tightly closed! The gasses expelled by the yeast will build up pressure and may cause the container (such as a glass jar) to burst!