On the lighter side...
"I beseech Euodias, and beseech Syntyche, that they be of the same mind in the Lord." (Phil. 4:2)
Paul beseeches both individually to put away their squabbles. Apparantly unity and humility of mind seems to be the (or a) central theme of Philippians. God did not tell us the details of their rift, but through Paul, instructed them (and us) what to do about trifles. Their altercation caught God's attention to the point where He addressed them directly in this one verse. Could you imagine their reaction upon recieving this letter and then later having to realize that it was going to be copied and circulated to other churches? Could you imagine one of their grand kids: "Grandma, why are you mentioned in Paul's church-missions-thank-you letter?" Since the Bible is inspired and preserved, we have that to read and for generations to come. God is really interested in reconciliation. What is amazing is that God did not delve into the details of their disagreement. It seems to me that we have such an Adamic propensity to 'check out' things we have no business 'checking out' anyway.
Now "on the lighter side..."
I exercized my Adamic nature to check out what happened. No luck. The verse really did not tell us what, when, where, why and how (except for what needs to be done about it). BUT it did tell us WHO. So I checked out every 'language tool' in my e-sword (BTW, a big thanks to Mr. Meyers for making such a tool possible). I did get a kick when Strong's Concordence labeled the name meanings for these ladies:
Euodias - means 'fine travelling.'
Syntyche - means 'an accident.'
hmm...reconciling that could be difficult.