The first thing people often learn about how to play Sudoku is that there's no arithmetic involved. It's all one giant, convoluted logic puzzle. That part alone - the logic part - is enough to turn many away, but the convoluted part is what beats all of us, eventually. At least, most of the time. At any rate, the convoluted part is actually where the beauty of Sudoku truly hides.
At it's heart, Sudoku is Eastern Logic. There's not one certain starting point with a linear path towards any obvious finish line. Like a Japanese garden, there are many paths one might meander through without seeing the whole thing. Therefore, to actually solve the puzzle, you must master each and every piece - forwards, backwards, sideways and round-in-circles. Eastern Logic all by itself is a topic for another essay - by not by me.
What I can say is that I know my own scratch work. Chronology is four-dimensional arithmetic, and filling in the blanks is simple (ok, complex) logic. In every sudoku puzzle, especially at the expert level, there comes a critical point when you seem to run out of solid clues. You have to guess, and then proceed on that assumption until (a) it produces a contradiction or (b) leads to a complete, all-encompassing solution. If a contradiction appears, you go back to the point of the guess and begin again, but you also have to erase each and every move made on the basis of that guess. It's a lot to keep track of.
Obviously, one problem with this metaphor is that we don't have nice, tidy parameters for every facet of the NT event-sequence puzzle. The rules of Sudoku ensure a limited number of options when solid clues dry up. So in a way, this entire post is like comparing chess or football to actual war. Just like armies don't always line up and take turns, true history doesn't always give us a finite number of clues. The key point, however, is that sometimes it does!
This is all to say the following. One of my life goals is to work from identified critical points of NT chronology and try to show whether the "guessing" can be moderated by (1) conclusively reducing the number of plausible options at those critical points, (2) demonstrating a finite number of possible consequence-chains resulting from those critical points and (3) ultimately reducing the entire 'web' by seeing how each set of parameters affects all other sets.
Regarding a few particular critical points - Herod's Death, Paul's Conversion and counting the Passovers of Jesus' ministry are just some of the big ones. I've written about smaller ones during the past year, on this blog. One big critical point is the death of Paul, which depends on the number of days in Passover (in the diaspora), the timing (and singularity) of Fair Havens, and the distance to Dyrrachium from Ephesus. That's enough to get the "pastorals" before 64 AD with no invented itineraries... if you know what I'm talking about. If you don't, please stay tuned. By the way, what happened to Cestius could get John down to Patmos inside a six-month window if not less. Look that up, and you might even scoop me! But this is just for the early-record. I'm telling you now...
At the very least, we should be able to construct a framework for what data we have and for which data well-known guesses are based on. The goal here is finite reducibility, and with "luck", certain critical points will bear heavily enough on one another to force one most plausible solution to the entire puzzle. As I say, I know my scratch work. We'll just have to see how well it all holds up.
At the moment, when I read NT scholars doing any degree of event reconstruction, I most often get frustrated by missed ramifications. Journal articles understandably proceed through a series of potential considerations and qualified sub-conclusions, but I always feel like they're missing too many trees in the interest of painting the forest. I know a lot of folks don't expect things to get more concrete than a rough sketch, but I do. I believe the event history of Jesus and Paul can be - and for crying out loud, ought to be - every bit as clear as that of Augustus and Herod the Great. So far, based on published works to date, it ain't.
Even C.S. Lewis (famously) knew that arithmetic should all be scrapped and restarted if a problem appears at any point along the way. With chronal-spatial-math as my only defense for such arrogance - or maybe it's really just a unique collection of starting points - I'll admit I can't respect the 'scratch work' of most *complete* NT reconstructions that I've perused. But there are others I've not yet read that may prove me happily wrong. We shall see.
Like Sudoku, New Testament Chronology is a puzzle that can only get solved if we master each piece and part along the way towards mastery of the whole. It isn't a question of substandard logic or incomplete scholarship - though we have too much of that as well - no, it's mostly a matter of being comprehensive and exhaustive. Piecemeal considerations on isolated topics, that happen to include assumptions based on the same done by others, does not effectively deal with the problem - which may partly explain why it has not yet been solved. IMHO. ;)