After putting my earlier post to bed I continued thinking on the topics I raised in that discussion about Presbyterian reorganization and started to do additional analysis on some of those thoughts. This is a follow-up based on what I have contemplated and researched in the last couple of days.
To remind you of my thoughts from Saturday, in a nutshell I said that in historical Presbyterian divisions I regularly see certain proportions in the divisions. Those are generally about 1:1, 2:1, and 19:1. Put another way, when a division happens it regularly involves either 50%, 33%, or 5% of the Presbyterian branch.
What happened next was that I decided to be a bit ecumenical about this and look at some other Protestant branches:
Observation #1: The split of the Anglican Church of North America from the Episcopal Church is a 5% split. (Actually it is 4.5% if you use the ACNA membership of 100,000 but only 3.1% if you use the 69,000 number that is also floating around. This from a total of 2.2 million for the Episcopal Church.)
Observation #2: As I went looking for historical divisions in other traditions I started looking for the “family tree” type charts for other churches. Short answer, they are few and far between. There are charts for all of Christendom (example 1, example 2 – note the Pentecostals with no connection to the trunk of the church). There are a few that show division or union on a particular branch. But with the exception of a great chart for the United Church of Christ, I could find nothing comparable to the Presbyterian charts. Why?
The answer could be operational – I might not have found the right search terms for the search engines or things like this for other denominations might not be on line.
But I think the answer is also likely denominational. Are Presbyterians peculiar in some way that we need these charts?
One explanation could be retention of our shared tradition: Often, when divisions occur in denominations a new denomination is formed. (And it would therefore leave the chart.) A prime example of this is the creation of the Methodists from the Anglican church. Even within the Presbyterian tradition we have the Disciples of Christ originating from Presbyterianism, but never recorded on our family trees. But for Presbyterians that seems to be the exception rather than the rule and usually when Presbyterians split there is simply another flavor of Presbyterians formed. Our complexities of tradition could be attributed to dividing branches staying “in the neighborhood,” so to speak.
Another possible explanation is that there is something about Presbyterian governments that make our divisions, multiple branches, and reunions more likely than in other forms of church government. (It actually would be an interesting discussion of whether it is the polity itself or if it reflects the type of people who are attracted to that polity.) But given the recognition that, within the bounds of the collective judgment, a governing body can not bind an individual conscience the stage seems set for disagreements leading to a parting of ways. More on that another time.
So are Presbyterians just more inclined to these divisions and mergers that, if we are to keep track of our tradition, give us a need for these complicated charts? And can we take this a step further and ask if because we have these charts and are aware of our heritage of reorganizations, has that lowered our resistance to future divisions?
Put it another way, how much is it a part of, or maybe even inherent in, our system and how much is it because “that’s the way we have always done it?”
The bottom line is that as far as I can find on the web Presbyterians seem to corner the market, or at least dominate it, in diagrams showing our reorganizations over the last five centuries.
This led to the third point for today, (WARNING: this is about to get very geeky) I started thinking about the use of fractal behavior in numerical models of church division and recombination.
The numerical modeling of church division is not new to the last post — As you may have noticed from other posts I have some numerical models of mainline decline which I am working on to make them independent of denomination. One of the features of these models is that the decline of a mainline church is not linear to zero but will reach an equilibrium point. What I have been struggling with is what conditions to place on the calculation of that “plateau.” My recent thoughts on the possible fractal nature of denominational size may help provide those conditions.
It was at this point in my previous post that I made a logical jump that may have left a lot of my readers behind. I began by talking about proportions in church divisions and then turned to seeing if various Presbyterian traditions might be fractal. The thing I should have added there is that if divisions regularly occur with about the same proportions then the various branches that develop will have similar ratios of their sizes. That is to say that two small branches would have the same relative proportions compared to each other as two large branches. This “self-similarity” is what is known in the jargon as “fractal” behavior. A concrete example in a moment.
So what would the development of a fractal church look like?
A quick answer is taking the beginning population (Scottish churches in 1560?) and progressively divide them according to some ratio over a certain number of cycles. If you take five cycles you end up with 32 different churches that each has one of six possible sizes. Using a 70:30 split the continuing “main” church has 17% of the members and the “always minority” church has 0.2% of the population. For a 95-5% split (19:1) the numbers change to 77% “always majority” and an effectively zero “always minority.”
But the interesting thing is that if you compare the largest branch to the second largest branch it will have the same ratio as comparing the second smallest branch to the smallest branch. For the 70:30 split that ratio is 2.33 and for the 19:1 split the ratio is 19. Going back to the previous post I observed that a number around 6.5 was seen as a ratio for American Presbyterianism in several cases and that would result from an 87-13% division.
Two refinements are immediately obvious: 1) Provide for merger of branches based on theology and 2) Provide for merger of branches based on practicality when one or both are too small to survive.
How you introduce mergers will clearly influence the outcome. One simple model is that in each cycle the minority of one branch finds more theological kinship with the majority of the neighboring branch and merges with them. (Think PC(USA) churches moving over to the EPC.) This gives six separate branches after five cycles. The unmerged ends (only splits) have the same proportions mentioned above, but the four middle and successively reorganized branches have varying sizes. For the 70:30 split the largest branches end up being part of the reorganization with one having 36% and ano
ther 30% of the total population. For the 19:1 split no other branch has enough membership to grow to rival the unmerged majority with the second-largest branch having 20% of the population.
But with the mergers the ratio of sizes is now varied but lower than it was in the no-merger case. In the 70:30 split a number around 1.5 is commonly seen and in the 19:1 case there are a few lower numbers (3.8, 9.5, 1.5) but the very smallest branches have very high ratios (such as 473).
From here countless refinements are possible including pruning or merging of branches that fall below a particular threshold of sustainability, the introduction of a virtual coin-toss to decide if two branches would merge and add a component of variability, and some sort of rule or probability that would result in mergers with the edge branches. Maybe over the Thanksgiving holiday I’ll program up a Monte Carlo simulation.
So there are my extended thoughts on all of this. I’ll provide future updates on where my reading or modeling takes me with this.
From one geek to another… wow!
I am fascinated by this… and surprised. Several questions/surprises:
1. I am surprised that human behavior might be so predictable, particularly when organized as a group that purports to be led by the Spirit. I would be very interested to know if this is a Presbyterian phenomenon or more widespread.
2. I am surprised that the pattern is fractal in nature. I would have thought that church splits would produce groups either more or less proportionally inclined to split further. It is interesting that the “small-split” must usually either combine with another or disappear and that the phenomenon can’t be explored past a couple of splits. (though I am grateful spiritually that there are not an infinite number of splits within the church).
3. I’d be very interested in knowing whether similar patterns show up in a non-ecclesiastical but similar grouping of human beings. Would have to think what might have close enough similarity and history to consider. Hmmm… divorce and remarriage?? (recalling a 50% figure popped into my head)
Robert Austell
Charlotte, NC
More charts here: http://www.thearda.com/Denoms/Families/trees.asp.
Though, these aren’t done by the churches in question.
Thank you Eric,
I knew they had to be somewhere.
It is interesting looking at them since they are done in the same style so in theory they represent similar data. I’ll see what I observe in a side-by-side comparison.
A couple of quick notes:
The Baptists and Lutherans actually have more complicated charts than the Presbyterians.
The Presbyterian chart does not show the Stone and Campbell branches leaving but they are shown coming into both the Congregationalists and the Restoration Movement.
The Lutheran chart begins at 1800 and while there are some divisions it is dominated by the merging of all the various geographical synods. Is there anything interesting there before 1800?
Thanks again for that link.
Hi Robert,
Thanks for the observations and great questions:
1) Great question and I don’t know the answer. I’ll do a little research on this but for the moment concentrate on Presbyterians. I am hoping I can get “good” numbers on a lot of the divisions and see if there is a statistically verifiable pattern or if I’m just seeing things. There is also the complication of the first break and what sort of equilibrium it comes to within a few months or years. The Scottish Seceders of 1733 seem to start small and grow quickly after the break. Where do we measure?
2) I’m not quite ready to declare the pattern fractal, but some of the ratios look very intriguing. I would not be surprised if it is not purely fractal with one “fractal dimension” but human nature would favor bimodal results at the 2:1 and the small split. But given the starting population there must be a minimum size to be attained to sustain a branch. (Although you could argue a smaller group could continue as an individual congregation.) But based on my best estimates of branches like the Bible Presbyterian Church, Reformed Presbyterian Church General Assembly, and the Reformed Presbyterian Church – Hanover Presbytery, minimum numbers are in the neighborhood of 3000 members.
3) Interesting question, and an interesting example. Again, I’ll do some looking but I will concentrate on Presby’s for a while.
Thanks for the observations
Have you given any more thought to this? I became aware of some splits in some of the smaller Presbyterian denominations recently and started thinking about how to represent that in your charts.
Hi Jeffrey – Yes I have thought about it a bit more — but no big new ideas to share yet. I’m focusing on the three unions/resistance episodes around 1900 – UPC in Scotland, PCUSA/Cumberland in America, United Church in Canada. Was just reading an interesting article a couple of days ago where the pointed out that one of the Canadian resistance leaders was resisting because he had seen the outcome of the other two and the problems it caused made him think that church union of branches with too much individual identity led to too many problems in the merger.
I’ll be working some of this into a couple of upcoming posts if I actually get time to write.
Thanks for the update! Please keep us posted.
In the corporate world, “mergers of equals” rarely work – one reason is “too much individual identity”. Sometimes it’s thought of in terms of culture: Whose culture wins?
Responded too quickly on the last one. I didn’t think of the post from earlier this summer about the different models for mainline membership change – the last model with the partitioning of the denomination is essentially a gradual bifurcation that came out of the thinking about branches splitting and merging.