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Tuesday, February 12, 2013

Are We Due For A Council?

Given that the next pope will almost certainly not be personally associated with the Vatican Council II, I raised the question of whether the next pope might lead us into a council.

The question is not purely speculative. Let's take a look at the numbers.

Council  EndYear
1st Council of Nicaea 325 4
1st Constantinople 381 8 56
Ephesus 431 50
Council of Chalcedon 451 20
2nd Constantinople 553 102
3rd Constantinople 681 44 128
2nd Nicaea 787 106
4th Constantinople 870 20 83
1st Lateran 1123 253
2nd Lateran 1139 16
3rd Lateran 1179 40
4th Lateran 1215 36
1st Lyons 1245 30
2nd Lyons 1274 10  29
Vienne 1312 30 38
Constance 1418 130 106
Basel-Ferrerra-Florence 1445 728 27
5th Lateran 1517 216 72
Trent 1563 93646
1st Vatican 1870 44 307
2nd Vatican 1965 164
Average 81

People frequently say that the "average time between councils" is about a century, but this is highly misleading. In order to get this number, they use what is called the "arithmetic mean" to calculate what most people think of as the "average" of the intervals between the councils.

But the arithmetic mean or average is only appropriate to use in a data set that has no outliers, no data that is significantly above or below the norm. As can be easily seen, this data set has two ENORMOUS outliers - the distance between the Councils of 4th Constantinople and 2nd Lateran (253 years), and the distance between Trent and the 1st Vatican Council (307 years). I've highlighted those two intervals in red in the data set. Every other interval is at least half the 253 years between , several are only a quarter of that interval, three are only around 10% of that interval. Those two big gaps, totaling 560 years out of 2000, are really skewing the data.

So what do we do to fix this?
We use the geometric mean. As ehow says:
Statisticians use arithmetic means to represent data with no significant outliers. This type of mean is good for representing average temperatures, because all the temperatures for January 22 in Chicago will be between -50 and 50 degrees F. A temperature of 10,000 degrees F is just not going to happen. Things like batting averages and average race car speeds are also represented well using arithmetic means.
Geometric means are used in cases where the differences among data points are logarithmic or vary by multiples of 10. Biologists use geometric means to describe the sizes of bacterial populations, which can be 20 organisms one day and 20,000 the next. Economists can use geometric means to describe income distributions. You and most of your neighbors might make around $65,000 per year, but what if the guy up on the hill makes $65 million per year? The arithmetic mean of the income in your neighborhood would be misleading here, so a geometric mean would be more suitable. (emphasis added)
That's exactly the situation we have here.  About one-quarter of the values in the data set vary by a factor of ten from the largest value in the data set. So, the arithmetic mean is really not the appropriate way to calculate this, the geometric mean is. When we apply the geometric mean, we find the interval between councils is actually about 60 years (59.806, if you want it to 3 decimal places).

Pope Benedict is leaving office on Feb 28, 2013, shortly after the 50th anniversary of the opening of Vatican II (11 Oct 1962). Of the 21 ecumenical councils of the Church, 12 of them occurred less than 60 years after the previous council, 11 of them (just over half) occurred within 50 years of the previous council. This matches pretty well with what the geometric mean tells us.

In other words, we have exhausted the time interval that the Church has typically had between councils. Statistically speaking, we are definitely due for another council.

This, of course, raises a second question: if another council is called, how long will it last?

I've normalized the length of the councils by expressing the length in weeks, instead of the more common months and years. This makes it easier to compare the various council lengths.

The printing press was invented in 1453. Ignoring Vatican I, which was invaded by the Italian army and forced to an early end, no council in the last 500 years has lasted less than 130 weeks - that's over two years in session. Apparently, when it is easier to record the council, the council length extends to accommodate that technological advance.

Alternatively, you might argue that after the Pope voluntarily left office in 1415, the length of councils suddenly jumped to a new and sustained high. Is this causation or merely correlation? I don't know.

But, putting that aside, why would a council be called? There are a lot of reasons. Demographic winter now affects about 40% of the countries in the world, and nearly all the richest, most technologically advanced countries. Islam is a continuing threat. Growing rates of apostasy in the richest countries are a plague on all Christianity. There are the internal problems posed by the SSPX, the appropriate way to handle the new Anglican Ordinariate, the problem of creating a better coordinated response to corruption within the hierarchy. There are doctrinal problems created by the post-VC II catechetical crisis, and the problem of Modernism, which Vatican I was intended to address, but which has never really received adequate treatment.

Do any of these problems rise to the level that requires an ecumenical council? That's hard to say. We seem to be living in a new era. Never before has a Pope left office for reasons of poor health. If the Pope could leave office for a reason never before given, a council might be called for a reason never before deemed important enough to do so. I don't know the answers. I'm just raising the questions.

So, there you have it.
We might not just get a new pope, but a shiny new council to go with him.


Ron Van Wegen said...

Anything fewer than four decimal places is unacceptable.

Steve Kellmeyer said...

Let me check my pockets.

I'm sure I have the fourth one in here somewhere...

Lynne said...

I don't want a new coucil yet! Not enough of the participants from the previous one have died off...

Ann said...

It's interesting that this discussion is going on right now. Pope Benedict just yesterday spoke about the Vatican II council and what is really meant and some of the misconceptions. This is the first part of a two part address. I don't have the second part yet. Here's the link:

Ann said...

The Vatican just published the full text of the Pope's address regarding Vatican II. Here is the link to the full text: