Peel the potatoes and grate them coarsely, by hand or in food processor. Let the potatoes rest for a couple of minutes and then squeeze excess water by hand. Reserve the water in a small bowl and leave it for about 15 minutes. After 15 minutes, pour off all the liquid from the bowl, but leave the white potato starch that settled on the bottom.
Grate the persimmons without peeling them.
In a large bowl, mix the potatoes, persimmons, starch, eggs, cumin, nutmeg, garlic, salt and pepper.
In a large skillet heat the oil over moderately high heat until hot but not smoking. Spoon about 1 1/2 teaspoons of mixture per latke into the skillet, spreading into somewhat flat rounds with a fork. Do not overcrowd the skillet. Reduce heat to medium and fry the latkes until undersides are dark golden, about four minutes. With spatula carefully turn the latkes over -- be gentle as there is no flour in the mixture and they will be prone to breaking easily -- and fry until undersides are dark golden, about four minutes more. Transfer the latkes to paper towels to drain. Serve immediately.