The Catholic Church (and also other Christian denominations, but RC is what I’m talking about here) applies a doctrine called apostolic succession, whereby each bishop or priest must derive his ordination from another bishop who was consecrated by yet another bishop, and so on, all the way back to the original apostles appointed by Jesus.
My question is not about the theology or history of this rule but its mathematics. It seems that the vast majority (95 % of all Catholic bishops, according to Scipione Rebiba - Wikipedia) trace their lineage back to the same 16th century bishop (whose own consecrator is unknown, hence the line cannot be traced further). Even beyond this one, there seem to be only three more known lineages of apostolic succession in the entire Catholic Church.
Is there a mathematical reason why these four lineages, and in particular one heavily dominant one, crowded out all the others? As opposed to, say, a situation where all bishops who were contemporary with Rebiba show up in the lineages of today’s bishops about equally? My guess is that once a particular lineage had, by sheer coincidence, a slight lead over the others, that lead had a tendency to intensify (because more members in that lineage means even more consecrations by those members to create the next generation). But that’s more of an intuition, and I wonder if there is a branch of mathemathat can shed light on the behaviour of such systems.
From your article, it looks like this is more historical than mathematical. It says that in the early 18th century, Pope Benedict the somethingth personally consecrated a bunch of bishops representing various countries, and thereafter those bishops (and their descendants) were responsible for consecrating almost all the bishops in their countries. So it seems like, for some reason, the process got changed fairly dramatically at that time.
Another possibility is that this isn’t what actually happened but is a retconned policy and wasn’t particularly happening before the 16th c. individual.
If you start making mathematical assumptions like that each bishop’s ordainer is random, then one would expect to go back thousands of generations to get to the most recent common ancestor, which seems not to be the case. Or is that overlooking something?
ETA obviously fewer generations are needed to get to 95%… need to think about it…
It’s the same mathematical principle that means that everyone in (say) 100 AD is either the ancestor of the vast majority of people living today - or the ancestor of no one living today. A chain of descent (genealogically or apostolic succession) once broken can’t be repaired, while a successful branch will spread out.
Looking into Scipione Rebiba, it appears that someone in his line of succession happened to be a Pope who consecrated a lot of bishops personally, including several bishops who were responsible for consecrating most bishops in their nations - that gave Scipione Rebiba a big advantage - and also eliminated opportunities for other lineages to go forward (an analogous case would be Genghis Khan’s grandfather - he’s apparently the ancestor of a large proportion of the Earth’s population, because his grandson happened to be a hugely successful conqueror).
The first mentions of apostolic succession as a guarantee of correct doctrine occur in the first century AD, and several church fathers in the second century talk about it as an established idea. Thereafter there are many mentions by different writers throughout the following centuries.
Just noodling around with a possible mathematical model. If we assume the total number of bishops is constant (not true, but good enough for now), and every 10 years, a new class of bishops is created and all the old ones die (again, ridiculous), with each new bishop consecrated by a randomly selected old bishop, it’s pretty clear that the odds are good that some particular bishop in the old generation will consecrate more than one bishop in the new generation - which means that at least one of the lines of succession dies out, and one line gets an even better chance of going forward. In just a few generations, the number of continuing lines is going to become pretty small - and that’s with random selection. With any sort of non-randomness (geographic effects), the reduction of lines of succession will likely be worse.
I think it’s more that prior to Benedict the Somethingth, the bishops in those countries were likely consecrating their own successors, but then Benedict basically effectively replaced (in ordination terms) a bunch of them with people he consecrated, meaning that any bishops consecrated in those countries after that was a “descendant” of his, and by extension Bishop Rebiba, whose chain of ordination can’t be tracked any further back.
Who decides what priests can be made a bishop? Can a RC bishop just consecrate whomever they want or does it need to come from someone higher up, a cardinal or the Pope himself?
That gets into the question of valid vs. licit acts. A bishop has full power to validly confer the sacrament of ordination: In fact, nobody has more sacramental power than a bishop (the Pope is, of course, himself a bishop). But just because you can, doesn’t mean you should, and I would expect that, in the ordinary course of affairs, a bishop would only do so in consultation with the rest of the hierarchy.
Currently, in the Roman Catholic Church, all bishops are appointed by the Pope (though with the input of the outgoing bishop, other bishops, the Roman Curia, priests and laypeople in the area where the new bishop will serve, and others).
I just want to say, for reasons I cannot explain, I find this thread fascinating. A similar laying on of hands, called a smiha, is done to ordain rabbis. Theoretically, an ordained rabbi can trace his (rarely her) smiha in an unbroken line to Aaron and Moses. The comedian Jackie Mason had a smiha.
There is a similar effect with surnames. Over time in any society with inherited surnames and no new ones, the number of surnames will reduce to stabilise at a very low number such as 3 or 4. This has happened in some Asian societies. In Japan, on the other hand, where inherited surnames are recent, there are 10s of thousands of surnames because the winnowing process has not had time to occur.
“Lineages” of apostolic succession are exactly analogous - each priest has a “father” who bestows the lineage. In each “generation” there is a possibility of that lineage becoming extinct, while there is no mechanism for new lineages to be created. Over the centuries the number of lineages will reduce. No special mechanisms are required other than random chance (although some mechanisms could speed the process).
Weren’t Aaron and Moses ordaining priests, not rabbis? As I understand it, there are no Jewish priests any more, because of the lack of the Temple. Were there separate priest and rabbi lineages dating back to Moses, or is a rabbi a sort of partial priest?
You are correct. With the destruction of the Temple, Judaism shifted from Temple and Kohen centered to Torah and rabbi centered. Various prayers include hope for the rebuilding of the Temple. But, most Jews don’t expect that to happen anytime soon.