Place unsweetened tamarind paste in a 2 quart pot with 4 cups of water and bring to a boil, cook covered for 10 minutes. Remove from the heat, add ginger and set aside covered overnight or to cool. This will help the separation of the seeds from the pulp.
Press pulp and water with your hands to remove all pulp from the seeds and discard the seeds. Pass mixture through a sieve and set aside.
Place whites and baking soda in a mixer over medium speed for one minute. Once the whites start to expand, start adding the sugar in a slow stream, it will take about 2 to 3 minutes more to add it all. Increase the velocity to high and keep mixing for 15 a 20 minutes or until the sugar is almost all disappeared and you can no longer feel it if you touch a bit with your thumbs.
Transfer the mixture to a pastry bag or a large Ziploc bag with a one-inch whole in the corner. Press to fill small 4 ounce glasses or cups.
Sprinkle with pecans and set aside until ready to serve.