In a small saucepan, combine the water, sugar and fresh ginger and bring to a boil. Cook over moderate heat, stirring just until the sugar is dissolved. Cover and let sit off the heat until cool. Strain pressing hard on the ginger. Fill a cocktail shaker with ice and add 2 tablespoons of the syrup and 1/4 cup of the vodka. Shake vigorously until quite cold and strain into a martini glass. Repeat with the remaining syrup and vodka to make 7 more drinks.