In this part of the series I want to give an introduction on how to approach the evaluation of the Testimonium Flavianum controversy from a data scientist point of view.

There are mainly 2 steps involved:

1. Extracting the features that characterize Flavius writing style.
2. Analyzing these features in order to see (or not see) some anomalies.

I wont show specific code snippets in this tutorial as I want to be this as introduction friendly as possible. But if you are interested in the concrete implementations of my conducted experiments checkout this Git-repository.

As a frame of mind what we actually want to do is take the texts from the Jewish Antiquities but remove the Testimonium Flavianum. With these quantify the writing style of Flavius Josephus. Quantify the writing style of the Testimonium Flavianum. Compare if these writing styles differ significantly

1. Extracting the features

As I described earlier we want to extract the character n-grams of the Jewish Antiquities in order to quantify Flavius writing style. To keep this operation at computational bay I dont start with the analysis of the whole Jewish Antiquities but just the 18. book of it. This book contains 57 paragraphs in total, including one paragraph which is the Testimonium Flavianum As a first step I remove the Testimonim Flavianum from this set of paragraphs. Because these paragraphs are quite different in their length I rearrange the data split such that we have …100something… textsections that have almost the same length. This length is approximately the length of the Testimonium Flavianum. Now having these text sections at same length I extract the space free character n-grams of each text section and count the number of times they occur in the specific text section. These counts are then transformed into their respective tfidf-values, which is basically a value of the number of times a specific n-gram appeared in the text (term-frequency i.e. tf) normalised by the frequency with which this n-gram appears in other text sections (inverse document frequency i.e. idf). In conclusion we compute for each n-gram in each text section the tfidf-value of this n-gram which results in a huge datamatrix with …x… rows (the different text sections) and …x… columns (all n-grams) which looks something like this:

TODO: insert image for data matrix

In this setup the Testimonium Flavianum is also part of the data matrix, to be precise its row 27. Each text section therefore has a set of tf*idf-values of all the n-grams which represents for us the quantification of the writing style of Flavius Josephus. In the next step we want to compare all of these writing styles and look if and how they differ.

As also highlighted before choosing the correct value for n is essentiall. Thats why I repeat all the experiments with different n in the range between 3 and 9 to show robust results.

2. Comparing the writing styles

The easiest way to compare the different writing styles is to visualize them. This can be done if we employ a technique thats called a Principal Component analysis. This allows us to reduce the writing style of each text section (remember these are …x… tf*idf-values in total) to just two compressed values which we can then draw in a 2D plane. Doing this on our before created data matrix for n=4 looks something like this:

TODO: insert image

What we see are three distinct clusters. One in the upper left containing …x… element, one in the lower left containing …x… elements and one in the lower right containing just …x… elements. The Testimonium Flavianum is highlighted with a red cycle and as we see does not significantly differ from the majority of the text sections (at least in this visualization approach). The PCA does the reduction to just two values by finding out which features (in our case which n-grams) contribute the most variance to the dataset and then visualize the dataset along axis that maximize this variance (TODO: need refinement) So the natural question arises what are the factors that separate the clusters. It turns out these are primarily the single letters “O” as in text section 114 “Equal to this determination of yours, O Petronius” and “I” as in text section 4: “To be sure, I have spoken about them in the second book of the Jewish War”. This means in simple terms text sections that are on the right have a disproportionate high occurrence of the single letter “O” while text sections in the upper half of the diagram have a disproportionate high occurrence of the single letter “I”. The Testimonium Flavianum having neither of both stays in the lower left of the diagram as the majority of text sections.

This result does not majorly change when varying the n-parameter as the following gif indicates:

TODO: add GIF

3. Evaluation

These first findings are interesting as they make claims that nothing in the previous researches on the Testimonium Flavianum has found. It indicates that the TF is not really that different in writing style and the things that do separate different sections of the 18th book of the Jewish Antiquities are the single letters “O” and “I”. But they need to be taken with a pinch of salt as their is a lot of room for criticism

• this analysis is done on the english translation
• space_free character n-grams are just one feature set others might indicate different distinctions
• PCA only explains not even a half of the variance of the dataset To this criticism I will turn later. In the next Blog post I will explain another approach to the analysis of the Testimonium Flavianum controversy from a standpoint of Authorship Verification