… Adrien Reland’s 1714 Palaestina ex monumentis veteribus illustrata!
And so the winner is me, too, for I guessed it correctly.
A two weeks’ post
But one thing after the other. First, the date: this is my blog post for
Saturday, March 9th, 2019, for Friday no. 22;
I seem to acquire a bad habit of posting on Saturdays rather than Fridays. For today, my excuses are, in chronological order, a) I had to help out at my son’s school, fixing some shelves; b) I had to figure out how to clear some financial matters regarding how to pay my salary from this project in a way that some of it actually ends up with me in the end; c) my youngest daughter stubbornly refused to go to sleep this evening. Obviously I am not very good at scheduling my home office work hours, for although I started out at 8:00 in the morning, by 21:30 I had got down to a meagre seven hours of working time. And d) I made a tiny configuring mistake, messed up my calculations, and had to start all over again, ruining some two hours of work. I suspect I better had not started calculating only at 21:30, but a), b), and c) forced me to.
Going for some metrics, step 1: Gathering data
But the calculations are crucial, because that’s what I originally intended to show you. As I announced in my last post, I now have finished three-quarters of my projected sample of scholarly journals, which has taken me two weeks to complete, clean, and analyse now.
That is to say, I have gone through the digitized versions of the Journal des Savants, the Philosophical Transactions, and the Maandelyke uittreksels, of Boekzaal der geleerde waerelt (more info here), between 1700 and 1799. I have added all issues of these journals referencing one of my four protagonists in any way to my database. In numbers, this means 117 issues of the Journal des Savants, 9 of the Philosophical Transactions (yes, only nine, but I have already argued they are somewhat special here), and 89 of the Maandelyke uittreksels – or 205 journal issues in total. In going through these issues I have examined each page on which at least one of my protagonists was referenced, identified all other scholars and all publications on that page, and stored these data, too, as a basis for co-citation analysis to identify perceived epistemic communities and their changes over time. This netted me another 287 quoted publications, and another 739 scholars referred to and/or connected to quoted publications (as authors, editors, translators etc.). I must confess that I am a bit proud of having managed to completely identify close to 690 of these, or more than 90%. But today everything will be about publications, so the really interesting figure is that of 502 publications in this sample.
Going for some metrics, step 2: Setting a framework for analysis
The problem that I now got was how to deal with these data. Plain visualizing did not work out anymore to really map out the intriguing details. So it needed to be done the rough way, by calculating metrics for the sample, hoping for something interesting to turn up. The visualizations did help me, in the way of pointing out which ways to structure the relations to be investigated would likely not yield good results. I first thought I might try something like mapping ‘shared contributors’, that is, connecting publications by way of the same scholars contributing to them (as authors, editors, or translators). This turned out to be pretty useless because it only favoured large edited collections who assembled texts from many different authors. And that’s the reason why this post is not about persons but publications only; the real co-citation analysis still has to wait for a bit. So it seemed better to bypass persons for the time being and only to link publications to publications, and I did so by way of quotations, that is, two publications are seen as connected if at least one of them quotes the other. That brought some interesting results about.
Going for some metrics, step 3: Finally going for metrics!
With the framework set up to network this publication sample, it was high time (half past nine already!) to start calculating metrics. To facilitate calculation, I started with assuming the network edges to be undirected, that is, a link from publication A via a quote in A to publication B works both ways, from A to B and from B to A. I know that this might be a questionable simplification; but as this may be tested by comparison, I will set this matter aside for a rainy day when I don’t have any idea what to write in this blog for the week to have the opportunity to at least redo these calculations for directed edges. (And as I once started tracking time in this post, it is now 4:00 in the morning and high time that I get to bed to have at least some sleep. I’ll continue around noon.) Moreover, as the structure of connections within what one takes to be a network depends on what the question is, and I am interesting in tracing perceived epistemic communities here – that is, publications seen as belonging to shared domains of knowledge – edge directionality is less important than it might be for other questions to ask. (This is a piece of midnight reasoning, but it still looks sound now at 10:30 on the day after.) I could as well also have collapsed the journals into edges connecting the rest of the publications to more explicitly claim this, but I wanted to also get an impression of the position of the individual journal issues, and so I kept them as nodes. Admittedly, this model does have the drawback that relying on quotations only provides only a quite simplified picture of the interconnections structuring domains of knowledge, but it should serve to give a good first impression of the sample’s general structure. Having sample and model settled, I used the opportunity to test Nodegoat’s analysis functions and calculated some metrics.
A lot of numbers
To keep the scores comparable across different metrics, I chose to normalize them where possible. A short look at the visualization (see header for larger picture) made clear what was to be expected: the network is disconnected. Not all publications are referred to as situated in overlapping domains of knowledge; some are distinctly separate from the rest. This is important here because it directly impacts the calculations of the closeness metric. Closeness serves to indicate how close any given node is to all other nodes in the network. In mapping out shared domains of knowledge this might be quite interesting, as nodes with low closeness scores might be supposed to partake of many fields at once being referenced in differing contexts, and thus be important to look at. But closeness measures path lengths to calculate the average distance from node X to all other nodes, and this does not work in disconnected networks (because two nodes between which there is no path would be at undefined = infinite distance from each other). Nodegoat provides a workaround to that by substituting a maximum distance for path length between unconnected nodes, this maximum being equal to the total number of nodes in the network.
The first measure I calculated was betweenness (because of the problems with closeness). Betweenness works on disconnected networks and thus was the obvious first choice. Roughly put, betweenness serves to indicate whether a certain node may be considered a gatekeeper, that is, if it is situated at a vital connection point in the network. In assuming an undirected graph, for mapping shared domains of knowledge this resembles closeness: it should point to publications situated at the intersection of several domains, and thus of potential importance for each of these. I must qualify this as ‘potential importance’ because only being situated between different fields of knowledge does not equal making important contributions to any of these fields; this will have to be cross-checked with other metrics, then.
Top 10 Betweenness
These are the top ten results in terms of betweenness for the whole of the network:
And those are the respective results for the top-scoring publications of/connected to:
Adrien Reland, by Betweenness
Eusèbe Renaudot, by Betweenness
Johannes Braun, by Betweenness
Thomas Gale, by Betweenness
What becomes directly apparent is that there are a lot Reland’s publications in the network, not only on vital connection points but also in total. In fact, 37 out of 287 non-journal publications have Reland as their main author/editor, or 12,9 %; the number does matter because I only added publications to this sample when coming across a quotation within the sample. Compared to 2.8 % for Eusebè Renaudot (8 publications), 1.7 % for Johannes Braun (5 publications), and 1.4 % for Thomas Gale (4 publications) this looks even more impressive. But a large output as such does not tell anything about the quality or the reception of that output. There also is one publication by Eusebè Renaudot among the top ten in betweenness, too.
As already said, the closeness scores for this sample are to be taken with a grain of salt because of the disconnectedness workaround implemented in Nodegoat. But the prediction I theoretically made when thinking about betweenness in this network – that it would line up quite closely with closeness because pointing to structurally similar positions within the network – did come true in looking at the results for closeness, so I am tempted to regard these results as usefull still. Important: The first score in the “A” for Analysis column is always the one discussed!
Top 10 by Closeness
The top ten publications of the network in terms of closeness scores are:
This again underscores the relevance of Reland’s publications within the network as a whole, and especially of his Palaestina Illustrata.
And those are the respective results for the top-scoring publications of/connected to:
Adrien Reland, by Closeness
Eusèbe Renaudot, by Closeness
Johannes Braun, by Closeness
Thomas Gale, by Closeness
In undirected graphs such as this, Degree just counts the number of connections any given node in the network has. To be precise, Nodegoat counts the number of all edges starting from and ending at any given node, allowing for duplicates edges, thus producing high scores on average. For an analysis of shared domains of knowledge as proposed here Degree should be relevant as a corrective. Whereas Betweenness and Closeness both point to structural positions of publications in regard to their location between domains of knowledge, Degree points to the importance of a given publication at this structural position. Or, to put it more precisely, to the attention generated by the publication in question, as I am focusing on quotations made by scholarly journals to this publication; and many such quotations do not necessarily point to the scholarly but in any case to the public impact a work made.
Top 10 by Degree
Looking at the Degree scores from this perspective makes clear that while Reland’s publications might share in more domains of knowledge, within their respective domains Renaudot’s publications obviously attracted comparable attention. And looking at the respective results for the top-scoring publications of/connected to Johannes Braun and Thomas Gale in comparison makes clear that they were not only tied more closely to special domains of knowledge but also attracted less attention by the journals in question, perhaps because of this more stringent specialisation. So here are the Degree scores for publications divided by individuals:
Adrien Reland, by Degree
Eusèbe Renaudot, by Degree
Johannes Braun, by Degree
Thomas Gale, by Degree
A cautionary note: It does not pay to put too much trust in Degree scores, because they tend to push publications situated within certain reference patterns. Consider the example of Mathurin Veyssière de la Croze’s Lexicon aegyptiaco-latinum, the Coptic dictionary edited and published by Karl Gottfried Woide in 1775 which has already featured in one of my posts.
With a Degree of 33 it scores shortly below a top 10 place in Degree which, following the reasoning laid out above, should indicate its importance for its particular domain(s) of knowledge – it attracted a lot of attention, because it has a lot of quotes. But all of these quotes are in fact derived from one singe journal issue, the June 1774 issue, part one, of the Journal des Savants, as becomes visible from the cross-references section of its database entry.
And there it assembles all of these quotes because it features in many different respects in the announcement written by Woide himself to highlight his upcoming publication, which makes the reference section of this piece look a bit monothematic:
So while Degree may be taken as an indicator of importance within a given field by capturing public attention, this is easily manipulated, and has to be cross-checked against another metric for validation.
Nodegoat allows for calculating Pagerank scores, following the original Google algorithm. As Pagerank was originally invented to determine the relative importance of information sources (in this case, websites) in a network through which a user might randomly move, this model might also be applied to domains of knowledge in a web of publications, treating quotations as paper-borne hyperlinks. Random movement through the graph is facilitated by its undirectedness, so please keep in mind that modelling it as undirected may be a questionable decision, and don’t trust these metric too much. The good thing about Pagerank is that allows for determining both the relative importance of quoted publications and of quoting journals in this particular configuration, so I would like to use it to counterbalance the shortcomings of Degree pointed out above. In running Pagerank, Woide/la Croze’s dictionary disappears from the leading places all of a sudden, so this seems to work. The top publications according to Pagerank thus are:
Top 10 by Pagerank
Surprise, surprise: The main hubs for distributing quotes – and thus sorting domains of knowledge – are journals! Makes me almost wonder why I chose to go by them in the first place… But more interesting in here is that there one publication from the 287 quoted works in the sample which managed to get a place in the top 10, and that is – surprise again! – Reland’s Palaestina Illustrata. This in turn is due by it being quoted by a number of journal issues (from all three journal series) which are themselves important quotation hubs, as becomes evident when looking at the cross-references to Palaestina Illustrata, that is, the publications in the sample linking to it.
This looks as if Pagerank indeed might be a good tool to determine the importance of a publication at its respective structural position, at best in combination with Degree (and Palaestina Illustrata scores high on both). So what about the top scores for the rest of the field?
Adrien Reland, by Pagerank
Eusèbe Renaudot, by Pagerank
Johannes Braun, by Pagerank
Thomas Gale, by Pagerank
Well, that was a lot of tables, numbers, and scores. Well done! Only a few more to go. Now the last thing to do is to find a way to purposefully combine the different metrics results assembled so far to draw something relating to my larger research question from it. To do so, I ventured for a first try to identify the top 5 publications of each of my protagonists by comparison of the results I presented above. This yielded the following table:
|Top 5 by:||Betweenness||Closeness||Pagerank||Degree|
|Reland||Palaestina ex monumentis veteribus illustrata||Palaestina ex monumentis veteribus illustrata||Palaestina ex monumentis veteribus illustrata||Palaestina ex monumentis veteribus illustrata|
|Reland||De nummis veteris Hebraeorum||De nummis veteris Hebraeorum||Antiquitates sacrae vet. Hebr. (4th ed.)||De nummis veteris Hebraeorum|
|Reland||De religione mohammedica||De religione mohammedica||Antiquitates sacrae veterum Hebraeorum||De religione mohammedica|
|Reland||Antiquitates sacrae veterum Hebraeorum||Antiquitates sacrae veterum Hebraeorum||Verhandeling van de godsdienst||Antiquitates sacrae veterum Hebraeorum|
|Reland||Encheiridion studiosi||Dissertationum Miscellanearum||Oratio de galli cantu Hierosolymae||Decas exercitationum […] nomine Jehovae|
|Braun||Commentarius in epistolam ad Hebraeos||Commentarius in epistolam ad Hebraeos||Leere der verbonden (4th ed.)||Doctrina foederum|
|Braun||Leere der verbonden (4th ed.)||Vestitus sacerdotum Hebraeorum||Avertissement necessaire aux eglises||Leere der verbonden (4th ed.)|
|Braun||Avertissement necessaire aux eglises||Doctrina foederum||Commentarius in epistolam ad Hebraeos||Commentarius in epistolam ad Hebraeos|
|Braun||Doctrina foederum||Avertissement necessaire aux eglises||Vestitus sacerdotum Hebraeorum||Avertissement necessaire aux eglises|
|Braun||Vestitus sacerdotum Hebraeorum||Leere der verbonden (4th ed.)||Doctrina foederum||Vestitus sacerdotum Hebraeorum|
|Renaudot||Historia patriarcharum Alexandrinorum||Historia patriarcharum Alexandrinorum||Liturgiarum Orientalium Collectio||Liturgiarum Orientalium Collectio|
|Renaudot||La perpetuité de la foy, 4||Liturgiarum Orientalium Collectio||La perpetuité de la foy, 4||Defense de l'”histoire des patriaches”|
|Renaudot||Liturgiarum Orientalium Collectio||La perpetuité de la foy, 4||Anciennes relationes des Indes||Anciennes relationes des Indes|
|Renaudot||La perpetuité de la foy, 5||La perpetuité de la foy, 5||La perpetuité de la foy, 5||La perpetuité de la foy, 4|
|Renaudot||Anciennes relationes des Indes||Anciennes relationes des Indes||Historia patriarcharum Alexandrinorum||Genadii patriarchi homiliae|
|Gale||Antonini iter Britanniarum commentarius||Antonini iter Britanniarum commentarius||Antonini iter Britanniarum commentarius||Antonini iter Britanniarum commentarius|
|Gale||Jamblichii de mysteriis liber||Jamblichii de mysteriis liber||Historiae poeticae scriptores antiqui||Historiae Anglicanae scriptores V.2|
|Gale||Historiae Anglicanae scriptores V.2||Historiae poeticae scriptores antiqui||Historiae Anglicanae scriptores V.2||Historiae poeticae scriptores antiqui|
|Gale||Historiae poeticae scriptores antiqui||Historiae Anglicanae scriptores V.2||Jamblichii de mysteriis liber||Jamblichii de mysteriis liber|
Creating a Shortest Path Matrix
To fuse this into something more informative I thought I might utilize a special function of Nodegoat’s, and that is its ability to calculate shortest paths between given selections of nodes. In this case, this meant that I first settled on a matrix of four times four publications: The top 4 publications after comparing the scores of all metrics for each of my four protagonists. I chose to use the top four because only four of Gale’s publications made it into the sample, and this provides better comparability then. Now I used the Shortest Path function to calculate the length of the shortest path through this network from each of these publications to each other, and set the results down in form of a matrix. It looks like this.
What does this tell me now? Well, first of all it highlights the isolated position of some of these publications, which obviously do not share domains of knowledge with others; this is true for the five marked with grey lines which have no connections to the rest of the matrix. It moreover points to the broader diversity of Reland’s publications compared to the rest of the network: His four publications all have connections within the matrix, while for Renaudot one publication does not and for Braun and Gale two publications each. Reland’s and Renaudot’s oeuvres and positions are similar in that both are internally coherent – the smallest paths to those of their own publications connected to the rest of the matrix are two each – and well-connected: their publications are not only connected to more of the rest of the matrix, they are also connected by shorter paths, making their works appear to be more central. Braun and Gale on the other hand are similar in having less many publications connected to the rest of the matrix, and in those publications being situated in strongly differing fields, as indicated by their larger internal distance from each other compared to Reland and Renaudot. And both of them are on the outskirts of the network rather than in the centre as indicated by the long shortest paths to other publications in the matrix.
This buttresses the claims I have brought forward based on other impressions already: That Reland and Renaudot form a comparable pair of actors, as Gale and Braun do; and that Reland seems to be the most versatile of all four, which might be the reason why he was the last of the four to get forgotten. And, as I already suspected last week, that his Palaestina Illustrata might be more relevant for this process than his other works, even if they are better known today (as his 1705 De religione mohammedica for instance).
has been a fairly static picture of a phenomenon spanning one century, so the
next task will be to dynamize it. Work to do!
 So in looking at the closeness scores in the following, always keep in mind that the maximum path length taken into consideration is 502.
 With duplicated edges taken into account and weighted according to distance, that is, duplicates add edge length.
 And Nodegoat does not automatically normalize Degree centrality. But this is an easy operation: If you want to do so, just divide any absolute Degree score by the total number of edges in the network, in this case, 2577.
 Publications marked in red only appear once in the table and are therefore discounted from further comparison.
 Please keep in mind that shortest paths are elongated in my setting because two quoted publications A and B are (almost) always connected via a journal in between, so the usual shortest path possible between A and B is two links (A –link one– Journal –link two– B).