Inversions in the Bible

Inverse Functions and Derivatives

2 Kings 20:1-11 NIV

In those days Hezekiah became ill and was at the point of death. The prophet Isaiah son of Amoz went to him and said, "This is what the lord says: Put your house in order, because you are going to die; you will not recover."

Hezekiah turned his face to the wall and prayed to the lord, "Remember, lord, how I have walked before you faithfully and with wholehearted devotion and have done what is good in your eyes." And Hezekiah wept bitterly.

Before Isaiah had left the middle court, the word of the lord came to him: "Go back and tell Hezekiah, the ruler of my people, 'This is what the lord, the God of your father David, says: I have heard your prayer and seen your tears; I will heal you. On the third day from now you will go up to the temple of the lord. I will add fifteen years to your life. And I will deliver you and this city from the hand of the king of Assyria. I will defend this city for my sake and for the sake of my servant David.'"

Then Isaiah said, "Prepare a poultice of figs." They did so and applied it to the boil, and he recovered.

Hezekiah had asked Isaiah, "What will be the sign that the lord will heal me and that I will go up to the temple of the lord on the third day from now?" 

Isaiah answered, "This is the Lord's sign to you that the lord will do what he has promised: Shall the shadow go forward ten steps, or shall it go back ten steps?"

"It is a simple matter for the shadow to go forward ten steps," said Hezekiah. "Rather, have it go back ten steps."

Then the prophet Isaiah called on the lord, and the lord made the shadow go back the ten steps it had gone down on the stairway of Ahaz.

Investigation of real-valued functions on the real numbers includes some common questions. Some of these questions are about the behavior of the function: 

  1. Where does the function increase?  decrease?

  2. Where does the function have an increasing rate of change (i.e., where is the function concave up?) 

  3. Is this function monotone? 

  4. If so, what is the inverse of this function? 

  5. If not, can you find a smaller domain where the function is monotone with range on the modified domain the same as the original function?

  6. Under these conditions, what is the inverse?

Existence of an inverse function is a very useful property of a function--it is much easier to answer questions about where a function takes on a particular output value IF we can use an inverse function. 

Applying inverse functions in nature is something environmentalists know is very difficult to do.  Think about how difficult it is to restore a harvested rain forest or to undo the ill effects of an oil spill!  However, our God is able to restore nature and he will to do it completely at the second coming of Christ.  There are a few examples in the Bible of God's power over nature.  God can reverse or stop the spin of the earth (see 2 Kings 20 or Joshua 10).  God can make iron float on water (see 2 Kings 6) or stop the flow of a river (see Joshua 3).