Here is what I wrote back:
No, this verse does not mean there are no memories at all in heaven and in the age to come.
1) Notice the parallel between "former things" in verse 17 and "former troubles" in verse 16. Verse 16 says, “He who blesses himself in the land shall bless himself by the God of truth, and he who takes an oath in the land shall swear by the God of truth; because the former troubles are forgotten and are hidden from my eyes.” The close parallel between “former troubles” in verse 16 and “former things” in verse 17 make me think that “former things” does not mean all things, but things that, if we remembered them would trouble us. And we will not be troubled in the age to come. “He will wipe away every tear from their eyes, and death shall be no more, neither shall there be mourning, nor crying, nor pain anymore, for the former things have passed away” (Revelation 21:4).
2) The book of Revelation says that in heaven we will sing the song of the Lamb and of Moses (Revelation 15:3), which is a song about past history. So if we are going to sing about the great works of God in history we can’t forget them.
But here’s a catch. The crucifixion of the Lamb was one of the troubles of the world. It was horrific. So it seems to be in the class of things that should be remembered no more—it was so full of pain.
So my conclusion is: What we will forget and what we will remember is not a simple class of bad and good. Rather we will forget and remember things in accord with what will maximize our enjoyment of God. If remembering something enhances our worship, we will remember it. If it would hinder our worship we will forget it.
As an analogy consider this. In Philippians 3:13-14 Paul says, “But one thing I d forgetting what lies behind and straining forward to what lies ahead, I press on toward the goal for the prize of the upward call of God in Christ Jesus.” So Paul seems to commend “forgetting” the past. But in Ephesians 2:11-12 he says, “Remember that at one time you Gentiles in the flesh...were at that time separated from Christ.”
So again, as I try to discern what should be remembered and what should be forgotten, I answer: Remember whatever deepens your love to Christ and zeal to obey, and forget whatever would paralyze your will to follow him with joy.