In first Peter chapter 5 verse 13 we read “The church that is at aBabylon, elected together with you, saluteth you; and so doth Marcus my son.” Babylon could be a code word for Rome. It could be a euphemism for evil, corrupt, society. Also it could be referring to cities or states of being. Babylon was destroyed in the 1st century and became a heap of ruins.
In 2nd Tim Paul is in Rome and asks for Tim and Mark to come.
In 1st Peter Mark is in Rome (Babylon) where he arrives and remains. Peter is the secretary and arrives shortly. And Mark gives us Peter’s memoirs.
If this makes sense, the relationship between the 4 can be diagramed this way. (If the $ stands for reference points of where they are).
2nd Tim Rome 1st Peter
$ $ $
Paul Peter Mark
In short, Paul is in Rome and asks for Mark to arrive. And we assume that Paul is also in Rome, or if he is not, he was recently before.
