May 23, 2019

Inconsistencies in Counting Overlapping Synoptic Stories

A side note to the previous posts on how best to graphically display overlap among the synoptic gospels. When we are using the pericope/section/story/number divisions as provided in the Aland Synopsis, I ran into places where I was having to make a judgment call in how I counted a section. What that means is, my resulting data was not above reproach. It would be simple if the gospel sections were all in the same order, and all discreet sections. Where an outline would be:

§ Matt Mark Luke
§1 Birth 1 - 1
§2 Baptism 2 1 2
§3 Healing A 3-4 2 3
§4 Healing B 5 3 -

But that's often not the situation. Because they occur in different order, sections in Aland are repeated, in particular, they are repeated each time that collection of verses occurs in the order for a given book. We even have a couple stories that occur in three different places in the triple tradition. Sometimes this is innocuous.
The Parable of the Great Supper that is in Matthew and Luke shows up twice in the synopsis and both times with the same verse reference:

§ Matt Mark Luke
§216 Great Supper 22.1-14 - 14.15-24
§279 Great Supper 22.1-14 - 14.15-24

The bold indicates that this is the place that it occurse in that books order. Luke's §216 occurs before the parables of salt and lost sheep. In Matthew, §279 is well after that, in a completely different act of the book. No problem. But one must use a consistent method so that the results are repeatable, because sometimes it's tricky.

My method for listing "which gospel sections overlap with sections of another gospel" has been:

  1. note the bolded sections in Mark, counting whether that section is also in Matt &/or Luke
  2. note the bolded sections in Luke that aren't also already bolded sections of Mark, counting whether that section is also in Matt or is stand alone, and
  3. note the bolded sections in Matthew not already accounted for that don't have corresponding material in Mark or Luke and count them.

A synoptics person might say, Mark sections, plus Luke's Matthew and Luke's sondergut, and Matthew's sondergut.
I also do it again switching Matthew's and Luke's place for comparison. And that's where I get most of my problematic results.
As one example, look at the The Women at the Tomb and Jesus Appearing to the Women.

§ Matt Mark Luke
§352 The Women At the Tomb 28.1-8 16.1-8 24.1-12
§353 Jesus Appears to the Women 28.9-10 - 24.10-11

When I'm trying to count how many pericopes/sections/stories/numbers overlap using the Aland divisions, I will get a different result depending on my method. In my first count, looking at bold Mark, then bold Luke, then bold Matthew, I will get one less Matthew and Luke count than when I prioritize Matthew's divisions before Luke's. This is because the same story is broken into two sections in Matthew, but remains as one primary section in Luke, according to Aland's method.
Of course I'm tempted to count them both no matter what, but methodologically, that's problematic since I'm not counting stories like the Great Supper twice.
This issue introduces subjectivity and bias into the procedure. I can't just make it up as I go along. This is one of the reasons that using Aland sections as a datapoint for this purpose falls short. Aland was set up to be descriptive of each book's order and divisions, and include it all. It was not set up to ensure 1 to 1 parity between content.

To further illustrate the flaws in what I'm doing, Goodacre (and Larsen) find 107 overlapping pericopae between Matt and Mark. My tables have 106 sections. They both have published books and I haven't, so I yield to their intelligence, but in looking over, I can't even see what I'm missing.
My sections are:
Matt and Mark only: 34, 130, 147, 148, 151, 152, 153, 162, 272, 275, 342
And Triple Tradition: 1, 13, 16, 18, 20, 30, 32, 37, 38, 40, 42, 43, 44, 45, 46, 47, 48, 49, 117, 118, 121, 122, 123, 124, 125, 128, 136, 137, 138, 139, 142, 143, 144, 146, 150, 154, 155, 158, 159, 160, 161, 163, 164, 166, 167, 168, 251, 252, 253, 254, 255, 262, 263, 264, 269, 271, 273, 276, 278, 280, 281, 282, 283, 284, 287, 288, 289, 290, 291, 292, 293, 294, 305, 306, 307, 308, 310, 311, 315, 330, 331, 332, 333, 334, 336, 339, 341, 343, 344, 345, 346, 347, 348, 350, 352

Unless they are counting the long ending? Still, the big issue is between Matthew and Luke, and my counts are different from theirs.

Having said that, when our purpose is inputing the data into broad-stroke Venn diagrams, a few differences in data points won't even perceivably alter the graphic.
Arbitrary decisions on how you decide to display the data make a much bigger impact. I hope to post on that in time.

May 22, 2019

Circles and Boxes and Comparing Gospels

Following on two previous posts looking at the efficacy of rectangular shapes in Venn diagrams for displaying synoptic overlap, I'd like to offer a bit more discussion of the options. For consistency, I'll continue to use the pericope divisions in the Aland Synopsis (as long as we all agree that we could and should do better).
I looked first at side by side two-corpus diagrams and then at a 3-way combination diagram. I'd like to reflect on the difference between the two, as well as one more look at circles and rectangles. The data I displayed in a rectangular diagram in that last post can also easily be displayed in a more typical circular Venn diagram:

Again, circle diagrams are fantastic for today's ASMR sensibilities.  But other than the aesthetic, I can't think of a single advantage of circular diagrams over rectangular Venn diagrams for two- and three-way comparisons. Look at the same data, displayed both ways, side by side. The Matthew blue circle and the Matthew blue square have the same area. Same goes for Luke and Mark, and each overlap section.
Both are able to display the data very well. To my eye, the circles are more pleasant to look at. However, the rectangles are more illustrative, in particular in ascertaining proportional relationships to the groups. In the circle diagram, I'm confused for instance in the area difference between the red uniquely Markan section and the orange Mark-Luke overlap. In the circle diagram, how do the slices for Mark-Matthew and Mark-Luke compare to each other. It's easy to see this in the rectangular diagram.
In the circle diagram, I have a hard time guessing the proportional relationships among the blue, green and yellow  (uniquely Matthew, Matthew-Luke, and uniquely Luke) sections. It is much more apparent in the rectangular diagram. For pedagogy and research, I would always choose the rectangular Venn diagram.

But is the three way comparison always the ideal? Is it everything you need? Maybe not.
Here is the data in three separate two-way Venn diagrams:
If you are not focusing on the triple tradition shared component, three discreet diagrams give information you can't see in the combined graphic. Of course, it gives you, for instance, the whole amount of Mark (red) not in Luke (yellow), without regard to whether it is in Matthew. In other words, these red sections are larger than in the combined three-way diagram.
Also nice is that this configuration allows you to line up each pair so that their relative lengths stand out better. The main point is that it is illustrative, even necessary to look at both styles. They each display information not available in the other.
It is easy to say, "Well, I just need the one, because the combined three-way diagram contains all the info that was contained in the three separate ones." But because you must make decisions on how to display the diagram (what edges align, which shape/proportion to make a given area), this is far from the case. I may, in one final blog post, explore the "prolegomena"—the assumptions/decisions—when making such a diagram.

May 20, 2019

Graphically Displaying Three Synoptic Gospel Data

Yesterday I offered why prefer to use rectangular shapes when displaying synoptic data in a Venn diagram. I have created several instances of these examples using verses, sentences and even words as data points. Using the Aland Synopsis Index as a quick and dirty (very dirty) easily accessible set of data, displaying each pair of synoptic gospels could look like this:

However, the superiority of rectangular shapes really shines when combining all three. I did not take the time to gather the specific numbers (yet maybe), but this is approximately what a resulting Venn diagram looks like compairing all three gospels.

Again, the proportions are very accessible upon examination. You can see that Unique Luke is what proportion larger than unique Matthew, and how it relates to what Luke shares with Mark, etc.
It is only when you add a fourth source that you need to create it as a polygon. And with that... the result is still a series of variously overlapping rectangles. Visually comparing rectangles is much more helpful for proportional comparison than common circles and ovals of Venn diagrams.

Note that there are still advantages for keeping the three separate pairs overlap comparison side by side, as three discreet diagrams.

Graphically Displaying Synoptic Data

A surprising thing popped up on my newsfeed today. (Yes, I still consume my RSS newsfeed daily. Call me a dinosar.) Mark Goodacre has reanimated his NTBlog for the purpose of reflecting on Matthew Larsen's book (which I have not seen). Mark @Goodacre has since microblogged (ie. Tweeted) on one particular feature in Larsen's book as a teaser for his next blog post, namely, the displaying of proportional synoptic data between two gospels. How much of Mark is in Matthew? How much of Matthew is in Luke? Etc. He has repurposed (colorized) Larsen's "proportional Venn diagram".

I do so enjoy such discussions, but seeing Larsen's graphic prompts me to revisit some work I have done for years but never completed on models for visualizing synoptic data.
I would like to publicly come out (momentarily reanimating my own blog in the process) in favor of rectangular Venn diagrams for comparing Gospel Synoptic Data. To explain:
Venn diagrams are most commonly thought of, and produced, as overlapping circles. This is because circles are gorgeous and tremendously satisfying.
However, a Venn diagram can be comprised of any shape (or variety of shapes). And given that the goal of comparing synoptic data is to, well, compare it, a rectangular application of Venn diagrams serves much better. Two primary reasons:

1. Visualizing proportionate size

Circles are fine for highlighting "relative" sizes, but not proportional ones. The areas of circles are very difficult to ascertain. To illustrate, look at these two diagrams:
In the first diagram, what proportion of the blue shape is overlapping with the red shape? What proportion is uniquely blue, or uniquely red?
One third. One third each. It's easy to tell. Immediately.
Now, what proportion of the blue circle is overlapping with the red circle?
Uh... er... Hmmm... "Honey, where are my calipers?"

2. Compare diagrams to each other

In the same way that rectangular shapes are easier to get a sense of their not just relative, but also proportionate size within a diagram, two or more diagrams beside each other can also be better evaluated in rectangular format.
To illustrate, let's look at the synoptic data that Mark Goodacre and Matthew Larsen are wrestling with. They are looking at how many "stories" or pericopes in one gospel are also in another. There will be stories unique to each, along with some overlap. This can be seen in the graphic tweeted above, where the unique blue Matthew passages and the unique red Mark stories overlap with purple. Likewise, yellow Luke pericopes and blue Matthew pericopes in another graphic would also share green overlap.
Ignoring for the moment how horrible it is to do this kind of comparison based on the pericope divisions in the Aland Synopsis (which doesn't inspire me to read Larsen), let's have a look at all three Venn diagrams (Mt-Mk, Mt-Lk, Mk-Lk) in the much more useful, boxier formats:

There are a lot of decisions that go into making such a diagram. I won't go into all those. But look how easy it is to compare the relative differences in each section. I don't think I need to say more about the graphics… they speak for themselves.

See here for a followup post on visualizing a comparison of all three gospels using a rectangular Venn diagram.

Couple notes:
I should say that my count of Aland pericopes shared among Mark and Luke was hasty and is bound to be off some, but I find that data point so useless, I didn't care to spend more time on it.

I've thought Mark Goodacre was brilliant for years, and consider myself his student though I've never been in his classroom, but I knew I was going to like Mark the first time I read his stuff many years ago and saw that he advocated the same primary-color-based system for marking a gospel synopsis that I had begun using in seminary (to Gene Boring's dismay). Though, I prefer to use 60% transparent white versions of the primary colors for true blending, because, you know, ugly.