6 February 2022

The Psalms

Everything must be fulfilled that is written about me
in the Law of Moses, the Prophets and the Psalms.
— Jesus Christ, told by Luke the Evangelist (Luke 24:44)

The importance of the Psalms was quite hidden for me even several years after I became a Christian. I can recall some brothers who gathered together and studied systematically the Psalms, at the end of the 1990s. I admired these brothers, but I was somehow not enthusiastic enough to join, once in a month, or so.

In this blog entry some mechanical experiments will be shown via the bibref tool. We are interested if the getrefs command can find potential quotations in the New Testament, where the quoted texts appear from the Psalms. To achieve this, we mechanically run the command getrefs SBLGNT LXX n where the number n stands for the given Psalm.


We will collect the longest matches for each psalm. For Psalm 1, the required command will be getrefs SBLGNT LXX Psalms 1. The computation will take a couple of seconds, but for other psalms this may be either faster or slower. (For example, for Psalm 18 I needed about 5 minutes on my 4-years-old laptop.) To save time for you, I performed the commands on my computer for all psalms, it took about 40 minutes (in the native version of bibref, it is significantly faster than the version that runs in your browser), and I created the following table that shows the outputs:

  1 2 3 4 5 6 7 8 9 10
0 19 131 12 24 19 20 14 120 18 19
1 13 21 10 318 25 282 12 33 74 17
2 13 63 18 20 14 13 16 21 16 15
3 18 97 27 82 18 13 23 22 15 64
4 14 20 19 53 124 13 20 16 17 15
5 38 17 14 17 18 17 19 18 20 15
6 25 14 21 19 18 19 16 18 74 12
7 15 19 18 13 18 14 18 28 15 15
8 14 15 14 23 21 34 13 13 22 21
9 53 14 12 35 134 14 18 15 26 17
10 13 133 20 57 21 25 23 13 23 81
11 20 59 11 17 30 19 22 114 17 11
12 9 20 17 11 14 13 13 16 11 13
13 9 17 14 27 18 13 13 13 15 12
14 15 17 23 14 26 20 14 17 13 15

The table shows the outputs consecutively in all 150 psalms. For example, the entry on line 4, column 5 stands for the output for Psalm 45: the longest maximal extension of the minimal unique passages is 124 characters long. The same output for Psalm 40 (on row 3, column 10) is 64 characters.

Surprisingly, all outputs are at least 9. Their average is about 29.47. Many of them are below the average, but some of them are quite high – for Psalms 2, 8, 14, 16, 45, 95, 102 and 118 the longest literal matches are above 100 characters.

We give two visualizations on this dataset. The first one is a 3D surface plot, provided by the plotly library. The high peaks show those 8 remarkable psalms with the longest matches, but some lower peaks are also nicely visualized.
In the above 3D surface plot we can rotate the view by using the left mouse click and in the same time drag the object (without releasing the mouse button). For each peak an x and y value are shown, here their concatenation xy gives the number of the given psalm, and z stands for the longest match.

A second visualization is a density estimate via the statistics software R, the package sm.
Here we can see that the longest matches (shown in the horizontal axis) are dense about the value 20. The vertical axis illustrates the frequencies of the longest matches. Actually, the blue curve is an estimation of an assumed probability density function.

What can we predict about the potential quotations when studying these graphs, without knowing any preliminary information on the verified quotations? First of all, the outputs can be classified into two sets: there are no lengths between 40 and 50, so “below 40” and “over 50” could be the two classes. We can predict that over 50 characters there will be verified matches, and presumably most potential matches below 40 characters will be just allusions or random matches. Second, if there are verified matches below 40 characters, their identification cannot be done mechanically.

So let us check our predictions by having a look on the table of the verified quotations. Here the entries with pink background are verified. In fact, a couple of psalms have been used multiple times in the New Testament, either by quoting the same passage or different ones. Also, the entry 14 for Psalm 41 corresponds to a random match between Psalm 41:1-2 and James 5:15, but the verified match is between Psalm 41:9 and John 13:18 (that's why a somewhat different background color is used). Actually, this verified quotation cannot be found with the getrefs algorithm, but this is the only one for the Psalms – all other correspondences are present in the outputs!

  1 2 3 4 5 6 7 8 9 10
0 19 131 12 24 19 20 14 120 18 19
1 13 21 10 318 25 282 12 33 74 17
2 13 63 18 20 14 13 16 21 16 15
3 18 97 27 82 18 13 23 22 15 64
4 14 20 19 53 124 13 20 16 17 15
5 38 17 14 17 18 17 19 18 20 15
6 25 14 21 19 18 19 16 18 74 12
7 15 19 18 13 18 14 18 28 15 15
8 14 15 14 23 21 34 13 13 22 21
9 53 14 12 35 134 14 18 15 26 17
10 13 133 20 57 21 25 23 13 23 81
11 20 59 11 17 30 19 22 114 17 11
12 9 20 17 11 14 13 13 16 11 13
13 9 17 14 27 18 13 13 13 15 12
14 15 17 23 14 26 20 14 17 13 15

Here we provide another table that highlights the entries from the class “over 50” (by using blue numbers).

  1 2 3 4 5 6 7 8 9 10
0 19 131 12 24 19 20 14 120 18 19
1 13 21 10 318 25 282 12 33 74 17
2 13 63 18 20 14 13 16 21 16 15
3 18 97 27 82 18 13 23 22 15 64
4 14 20 19 53 124 13 20 16 17 15
5 38 17 14 17 18 17 19 18 20 15
6 25 14 21 19 18 19 16 18 74 12
7 15 19 18 13 18 14 18 28 15 15
8 14 15 14 23 21 34 13 13 22 21
9 53 14 12 35 134 14 18 15 26 17
10 13 133 20 57 21 25 23 13 23 81
11 20 59 11 17 30 19 22 114 17 11
12 9 20 17 11 14 13 13 16 11 13
13 9 17 14 27 18 13 13 13 15 12
14 15 17 23 14 26 20 14 17 13 15

Here 19 psalms are colored in blue (all belong to at least one verified quotation). By contrast, 12 psalms remained black (they also belong to some verified quotations), but they are too short to be predicted as real quotations in advance, by a mechanical method. All other entries are non-verified (they have a white background), and that is OK, they are in the “below 40” class.

It is, actually, useful to have a look on the longest entries in the “below 40” class. The longest one shows up in Psalm 86. By using getrefs SBLGNT LXX Psalms 86 – this took for me about one minute in the browser and 10 seconds in the native version – we can learn that Revelation_of_John 15:4 is a strong candidate to be a real quotation: When looking up the two passages, we find indeed several literally matching phrases and even the contexts seem to be quite identical:
  1. lookup LXX Psalms 86:9
  2. lookup KJV Psalms 86:9
  3. lookup SBLGNT Revelation_of_John 15:4
  4. lookup KJV Revelation_of_John 15:4
But there is no introduction in the book Revelation that a quotation follows. So we need to accept the fact that this is not a strict quotation according to our own definition, but something like a strong allusion – I guess John, author of Revelation, had of course in mind the text of Psalm 86:9, but still this is not a quotation unlike several other passages in the New Testament that explicitly claim: “hey, here comes a quotation!” I hope this makes sense! (Actually, a recent PhD thesis by Sung Kuk Kim: Psalms in the Book of Revelation, University of Edinburgh, 2013, confirms our statement that there are no quotations in the Revelations.)

So we conclude that some manual work is unavoidable. But it is worth taking the time, because we can discover the wonderful world of connections between the Psalms and the New Testament. This topic will be the focus of the next entry.

Entries on topic internal references in the Bible

  1. Web version of bibref (12 January 2022)
  2. Order in chaos (17 January 2022)
  3. Reproducibility and imperfection (20 January 2022)
  4. A student of Gamaliel's (23 January 2022)
  5. Non-literal matches in the Romans (26 January 2022)
  6. Literal matches: minimal uniquity and maximal extension (31 January 2022)
  7. Literal matches: the minunique and getrefs algorithms (1 February 2022)
  8. Non-literal matches: Jaccard distance (2 February 2022)
  9. Non-literal matches in the Romans: Part 2 (3 February 2022)
  10. A summary on the Romans (5 February 2022)
  11. The Psalms (6 February 2022)
  12. The Psalms: Part 2 (7 February 2022)
  13. A classification of structure diagrams (15 February 2022)
  14. Isaiah: Part 1 (19 February 2022)
  15. Isaiah: Part 2 (26 February 2022)
  16. Isaiah: Part 3 (2 March 2022)
  17. Isaiah: Part 4 (7 March 2022)
  18. Isaiah: Part 5 (15 March 2022)
  19. Isaiah: Part 6 (23 March 2022)
  20. Isaiah: Part 7 (30 March 2022)
  21. A summary (7 April 2022)
  22. On the Wuppertal Project, concerning Matthew (17 July 2022)
  23. Matthew, a summary (25 July 2022)
  24. Isaiah, a second summary (31 July 2022)
  25. Long false positives (23 August 2022)
  26. A general visualization (25 August 2022)
  27. Stephen's defense speech (19 September 2022)
  28. Statistical Restoration Greek New Testament (31 July 2023)
  29. Qt version of bibref (11 March 2024)
  30. Statements on Bible references (5 August 2024)
Zoltán Kovács
Linz School of Education
Johannes Kepler University
Altenberger Strasse 69
A-4040 Linz