Peel the potatoes (If you use waxy potatoes with delicate skin, you can get away with not peeling them). Cut into a 3/4-inch dice and put into a bowl of cold water.
Mince the garlic. Measure the coconut and whole cumin seeds. In a small bowl, combine the turmeric, ground cumin, and salt.
Heat the oil in a heavy 3-quart saucepan over medium-high heat. When hot, put in the minced garlic. Stir for about 5 seconds.
Now put in the red pepper and the cumin seeds. Stir for another 3 seconds. The garlic should brown lightly, the red pepper should darken, and the cumin seeds should sizzle.
Lower the heat to medium, put in the coconut and stir around for about 1 minute.
Drain the potatoes in a colander. Add them to the saucepan, as well as the turmeric, ground cumin, salt, tomatoes (including the juices in the can), plus 1.5 cups water.
Bring to a boil. Cover, turn heat to low, and simmer for about 45 minutes or until the potatoes are tender. Stir gently every 7-8 minutes or so to prevent sticking.
Add the sugar and vinegar. Stir again and cook, uncovered, for 1 minute.