How could it possibly be that God never changes, when there are actually areas in Scripture where it is said that He changed his mind about something when approached in prayer? (Genesis 18:20-26 and Exodus 32:7-14, for example) Sunday evening we were singing a song in church about how God never changes, and I was wondering how that could be and how Jesus could have been "slain from the foundation of the world (Revelation 13:8 in many translations; ESV renders it differently), and a theory came to me.
A CAT scan is made up of a series of 2-dimensional cross-sections (x-rays) of whatever is being scanned (usually a human). Imagine for a second that there was a being that existed in only two dimensions. His experience of what a human being is would likely be something like one cross-section from a CAT scan. Now remember that God exists in all of time at once, but we humans only perceive a single point in time at once. Maybe the reason we perceive what seems like "changes" in God is that we can only see one snapshot of the CAT scan at once. As we travel through time, we come to different parts of the landscape of what God is. It's like our 2-dimensional guy is traveling slowly across someone's body, just like the CT machine. The body may be lying perfectly still, not moving or changing in position at all, but in the perception of the 2D man, the body looks like a circle which slowly expands and then contracts in size (the head), then an oval (the shoulders), and so on, ending in two circles (the legs) and then two ovals (the feet). The body is not changing at all in ultimate reality, but the way the 2D man experiences it change dramatically.
The analogy breaks down at several points (for example, the body in the CAT scan analogy is inert, and God is characterized in the Bible as very active), but I think it's conceptually useful. We just have to remember that there is far more to God than our human brains are likely to be able to totally comprehend this side of Heaven (maybe even on that side!)