The first is the gospel of Mark, which unlike the other synoptic gospels starts with Jesus, probably around the age of 30, coming across John the Baptist and being baptized. Subsequently, Jesus went off into the desert where he prayed for 40 days.
Second is the alchemical process of creating the philosophers stone. Jung argued that this was a description of a process akin to individuation. He believed that what was on the surface metallurgical work (transmuting lead to gold) was actually an obscure formula for remaking the psyche, from whatever was pre-programmed by society into what the individual actually wanted. This process was said to take 40 days.
I think a big trap is mistaking who we are from who we appear to be. Some people try to "seem" a particular way, thinking that they can only change their appearance, like changing one's clothes. The alchemical view that Jung put forward was a bit more radical, suggesting that we can fundamentally change ourselves.
Many people in our modern society experiment on themselves to change their physical bodies and to change their minds. I believe it is interesting to consider similar experimentation on how we change our spirit/emotions.