Previous posts in this series include:
1a. Born at a Time and Place 1
1b. Part 2
2a. A Change in Life Direction
2b Post 2
2c Part 3
Today the beginning of chapter 3 of Life Reflections on the Writings of Paul.
Paul's writings tell us little of the time between his coming to faith and when he started to write letters to churches he had founded. We do have several chapters in Acts about this period, chapters 13-18. But from a historical standpoint we should be careful. Anyone who carefully sets Luke's presentation of Jesus next to that of Matthew, Mark, and John will notice some differences in ordering and perspective. Even if these historical tensions can all be resolved, we can reasonably conclude that if these other gospels had second volumes like Acts, the same historical tensions would be there too. In short, our impressions of what happened might be different from what may seem obvious to us in Acts.
It seems reasonable to conclude that more than history telling was going on in the presentations of the gospels and Acts. These documents are arguing for something, and the manner of presentation arguably was meant more to serve those purposes than to serve some dispassionate, modern quest to present historical data as objectively as possible.  Nevertheless, after giving that warning, we have little choice but to rely on the Acts account if we have any desire at all to flesh out these years. We have little else to go on.
If we start with Paul's own comments, we can at least sketch a basic framework of his activities in the "lost years." He says in Galatians 1:16-17 that he did not go up to Jerusalem when God revealed Himself "in him." Instead he went to a place he calls, "Arabia." Then he returned to Damascus, and finally three years after the first revelation went up to Jerusalem for a brief period of about two weeks. He went up to see Peter (whom he calls by his Aramaic name Cephas). And he also met James, the brother of Jesus (Gal. 1:19). He says he did not see any of the other apostles.
Paul's comments here are a good illustration of what another version of Acts might look like, if we had one. We can fit most of what Paul says with the account in Acts 9. But Paul and Acts give us slightly different impressions of what happened. For example, Acts 9:19 does say that Paul spent "several days," even "many days" (9:23) with the disciples in Damascus. But if we did not have Galatians, we probably would not interpret those statements to mean three years.
The difference in impression is even greater when it comes to Paul's brief stay in Jerusalem. Galatians 1:18 says it was fifteen days and that Paul only met Peter and James. Acts says that Paul moved freely throughout Jerusalem and preached boldly (9:28). But more to the point, Acts presents Barnabas taking the initiative to introduce Paul to the apostles (9:27). In other words, the impression we get from Paul is that he had a rather brief, rather private meeting with Peter and James alone among the earliest believers. From Acts we get the impression of someone who met the entire leadership of the Jerusalem church and then only left Jerusalem because certain Greek-speaking Jews were after him (9:29-30).
Where the Arabia is that Paul mentions is open for debate. Many have thought Paul meant that he actually travelled to the Sinai peninsula where the Law was first revealed (cf. Gal. 4:25). However, the logistics of departure and return to Damascus north of Galilee really pushes us to see Arabia as the Nabatean kingdom just to the east of Damascus, whose leading city was Petra. This city is where the King Aretas IV ruled, the king whose Arab governor tried to arrest Paul outside Damascus (cf. 2 Cor. 11:32).
The difference between Paul's own account of his escape and that of Acts gives us more than a hint of Acts' approach to telling the early Christian story. Acts 9 tells us that "the Jews" of the city tried to kill him because they did not like his preaching. But Paul himself in 2 Corinthians says that it was the representative of the Arabian king Aretas that was trying to arrest Paul, presumably because of something he had done when he had visited Arabia.
We often picture Paul praying and studying during these first three years as a believer, going to seminary, as it were, to sort out the cognitive dissonance of his conversion. But it seems very likely that at some point he recognized God's call to the Gentiles and began to preach to them (cf. Gal. 1:16). Perhaps his earliest preaching was rather confrontational indeed.  Perhaps Paul's earliest preaching adopted whatever radical version of the gospel Stephen and the Greek speaking believers had preached, a radical message which got Stephen stoned... and perhaps left Paul treading some rough waters in his earliest days.
It is of course possible that both the Jews of Damascus and the ethnic leader of Arabs in the city were out to get him. But if we were to choose, we would clearly go with Paul's sense of who was after him, not least because Acts consistently seems to downplay opposition to Paul from secular authorities and to emphasize "the Jews" as his opponents. This is not an idle point or some fiendish desire to undermine a biblical account. What for Luke was perhaps a tacit explanation for God allowing the Romans to destroy Jerusalem--a focus in his presentation on mainstream Jewish rejection of Jesus as Christ--has sometimes in history become an excuse for anti-Semitism and the persecution of Jews. If we truly want to understand how the gospel first unfolded, we must take Acts' tendencies into account in our reconstruction.
The best guesses as to when Paul might have escaped Damascus put him in the city around AD36-37. This dating would put his coming to faith around AD33-34, about three years after Jesus had risen from the dead. Sometime around AD36, Herod Antipas--the one who beheaded John the Baptist--was driven out of power in Damascus for a short time by King Aretas. It was accordingly a point when Arab power in the city was probably greater than at other times.
Both Paul and Acts tell us that Paul returned to Asia Minor for some time. Acts tells us that Tarsus was his home town and, while Paul himself does not say so, we have no reason to doubt it. He does not emerge from that area in Acts until some ten years later, when Acts tells us Barnabas took the initiative to go bring him to Antioch (Acts 11:25-26). When we imagine what Paul was doing all those years, it is hard for us not to assume he was spreading the good news throughout his home territories. His tussle with Aretas in Damascus shows that his ministry did not just emerge after Barnabas went to get him. He was surely preaching all these years, a good explanation for why he never spends time in these areas during his missionary journeys.
Paul does allude to a major spiritual experience he had during those years. In 2 Corinthians 12:1-4, Paul speaks of "a man" who was taken up into the third heaven. He is unsure whether it was an out of the body experience or whether the man went even physically to the highest heaven. Since he goes on to tell of how God let him have a "thorn in the flesh" so that he would not boast about such revelations (12:7), it is clear he is talking about himself. Paul says this experience happened some fourteen years previous, which would put it in the early 40s, while he was in Tarsus... 
 Of course Paul's letters were also arguing for things, which is something to keep in mind as well--that they also present things from a perspective.
 Two books that explore these early years of Paul's Christian life are Rainer Riesner's Paul's Early Period, trans. by D. W. Scott (Grand Rapids: Eerdmans, 1997); and Martin Hengel and Anna Maria Schwemer's Between Damascus and Antioch (Louisville: Westminster John Knox, 1997).
 Some, particularly Seyoon Kim, The Origins of Paul's Gospel (Grand Rapids: Eerdmans, 1982)*, have argued that this story is Paul's version of his conversion experience. It is of course possible that the number 14 is a somewhat approximate term. But since 2 Corinthians probably dates from the second half of the 50s, "14 years" would be about ten years off. So while the possibility is enticing, we really do not have a good basis for equating the two.