First, pickle jalapenos. Formula for pickling liquid: 1 part vinegar, 1 part water, salt/sugar to taste, garlic, ginger, peppercorn, bay leaf.
When you've eaten all the pickled jalapenos, instead of discarding the liquid, strain out the garlic/ginger/peppercorn/bay leaf. Thinly slice radishes and turnips, and pop in the jar with the jalapeno pickle juice. Refrigerate. Should be ready in all its pickled goodness in a few days, and gets better with time.