IF anyone here doubts that when most theologians say that God is immutable that what they mean is that God cannot change IN ANY WAY WHATSOEVER, I offer the following quote from Augustine which illustrates the concept better than any other quote I've ever seen....
"But how did Thou speak? Was it in that manner in which the voice came from the cloud, saying, "This is my beloved Son"? Matthew 17:5 For that voice was uttered and passed away, began and ended. The syllables sounded and passed by, the second after the first, the third after the second, and thence in order, until the last after the rest, and silence after the last. Hence it is clear and plain that the motion of a creature expressed it, itself temporal, obeying Your Eternal will. And these your words formed at the time, the outer ear conveyed to the intelligent mind, whose inner ear lay attentive to Your eternal word. But it compared these words sounding in time with Your eternal word in silence,...." Augustine's Confession Book XI, chapter 6
The reading of that nonsense tends to glaze people's eyes over. The point he's making is that God did not say, "This is my beloved Son" but a creature said it in His stead because God exists in an at-temporal static state of silence. Augustine believed that little gem of heresy because He believed that God is UTTERLY immutable. He believed that for God to speak would imply a change and any change of any kind would break Him and disqualify Him as being God.
There are those here on this forum who have recently made a very similar accusation in regards to God's foreknowledge and, whether he knows it or not, he believes this for the same reason. Virtually the entirety of all aspects of Calvinism's (Augustinianism's) doctrinal distinctives are based on the single premise that God cannot change in any way whatsoever. Indeed, they are not merely based on that premise but they are logically dependent upon it. If God has ever changed in anyway at all then the whole of what makes Calvinism what it is falls into dust.
John 1:1 In the beginning was the Word, and the Word was with God, and the Word was God.
14 And the Word became flesh and dwelt among us, and we beheld His glory, the glory as of the only begotten of the Father, full of grace and truth.
"Do not be afraid; I am the First and the Last. I am He who lives, and was dead, and behold, I am alive forevermore." Revelation 1:17-18