Place blackberries in a small saucepan over medium heat. Add the simple syrup (if using sugar and water, bring to a boil before adding the berries), reduce heat, and add balsamic vinegar. If it looks dry, add a tablespoon or two of water then cover, and simmer about 10 minutes until fruit is quite soft, then mash a bit with a spoon. Taste and adjust flavor with additional sugar or a few drops of lemon juice.