I would like to know how fasting came to be an acceptable demonstration of piety and why? I am also thinking of Isaiah 58.5 when the Lord speaks of the kind of fasting He requires.

In Judaism, the purpose of a fast is to lower the volume on our physical pursuits in order to focus more acutely on our spiritual selves. This facilitates the process of "teshuva" - literally "return." We return to G-d, and to our essential state of purity.

In the Book of Esther (4:16), Esther agreed to see the King uninvited, and asked the Jewish people to fast for three days beforehand. Esther called for a fast, knowing that through soul- searching the Jews would forge a spiritual connection necessary to make her mission successful. And it paid off, for indeed the Almighty sees and hears everyone at their time of need.

Similarly, there was another fast during the Purim story: The Jews fasted and prayed on the 13th of Adar in preparation for their defense against Haman's decree. The Torah prescribes that whenever a Jewish army goes to war, the soldiers should spend the previous day fasting. This ensures that when they go out to battle, the soldiers will be well-focused on the fact that success or failure is in the hands of God. And the fact that the soldiers are physically weakened when the battle begins assures that any victory cannot be attributed to physical prowess!