Sociology Mind
2013. Vol.3, No.2, 193-203
Published Online April 2013 in SciRes (http://www.scirp.org/journal/sm) http://dx.doi.org/10.4236/sm.2013.32026
Study of Pauline Epistles in the New Testament Using
Machine Learning
Wei Hu
Department of Computer Science, Houghton College, New York, USA
Received December 26th, 2012; revised February 7th, 2013; accepted February 26th, 2013
Copyright © 2013 Wei Hu. This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original
work is properly cited.
The New Testament of the Bible is a collection of 27 books, 13 of which are attributed to St. Paul, making
him a significant author of the New Testament. The Pauline letters were written to churches and individu-
als addressing various issues in the early church and offering instructions and encouragement to the be-
lievers of his day. To understand Paul’s message as a whole, we clustered his letters, their chapters, and
their verses respectively to identify the topics that are addressed repeatedly or once, offering different
views at three granularities with each complementing the other. Our calculation implied all Pauline letters
could be divided into six groups, well in line with the church tradition. They were First and Second Thes-
salonians, First and Second Corinthians, Colossians and Ephesians, Galatians and Romans, Philemon and
Philippians, and First and Second Timothy and Titus. Among all letters First Corinthians had the most
unique chapters, while First Corinthians and Romans had the most unique verses. Furthermore, similar
verses and chapters from his letters were also discovered. We also studied the authorship of the letter to
Hebrews, an anonymous letter in the New Testament. Using known Pauline and non-Pauline letters as
training data, we built nine highly reliable predictors, which collectively predicted that the book of He-
brews was not authored by Paul.
Keywords: Bible; New Testament; Paul; Topic Model; Clustering; Affinity Propagation
Introduction
The Bible is a collection of books written by human authors
inspired by God, in which God progressively reveals Himself to
man in creation, in history, especially in the history of Israel,
and ultimately in His son Jesus Christ. It is made of the Old
Testament comprising 39 books and the New Testament con-
taining 27 books. The books in the Old Testament could be
categorized into books of the law, history books, wisdom books,
and books of the prophets, while those in the New Testament
can be divided into the Gospels, Acts of the Apostles, epistles,
and revelation. The four Gospels describe the life and ministry
of Jesus, the Acts record the early days of the church, the epis-
tles are 21 books written in the form of letters to churches or
individuals, and the book of Revelation presents the revelation
of Jesus Christ. Of the 21 letters in the New Testament, St. Paul
wrote 13 of them. Some scholars regard the anonymous epistle
to Hebrews a 14th Pauline letter. The letters of Paul, addressed
to a given individual or community of his day, are the earliest
existing Christian writings, predating the four gospel books in
the New Testament. They represent a particular form of early
Christianity, which clearly is different from that developed in
Jerusalem. The former is Gentile and the latter is Jewish.
The Apostle Paul was born, as a Roman citizen, in the city of
Tarsus in the province of Cilicia (southern Turkey today) with a
Hebrew name Saul given at birth and a Latin name Paul. At
young age, he went to Jerusalem to study under Gamaliel, one
of the greatest rabbinical teachers of the first century (Acts
5:24). He was circumcised on the eighth day, of the people of
Israel, of the tribe of Benjamin, a Hebrew of Hebrews; in re-
gard to the law, a Pharisee; as for zeal, persecuting the church;
as for legalistic righteousness, faultless (Philippians 3:5-6).
One day on his way from Jerusalem to Syrian Damascus on a
mission to persecute followers of Jesus, Paul encountered and
conversed with the resurrected Jesus. As a result he was con-
verted from a zealous Pharisee who aggressively persecuted the
Christians to a fervent preacher of the gospel to the Gentiles, a
radical change in his life made by the saving grace of God. This
conversion influenced Paul’s viewpoint from “righteousness
based on the law” to “righteousness based on the death of
Christ alone”, which later became the centerpiece of his theol-
ogy. There was also a shift of referring to him as Saul to Paul as
recorded in Acts 13:9. It is speculated that the change to use his
Gentile name might be an indicator of his mission as an Apostle
to Gentiles. In the book of Acts, Luke devotes the majority of
the book to the life and journeys of Paul, including Paul’s three
missionary journeys to spread the news of salvation through the
death of Jesus. As a result he established several churches in
different regions including Ephesus, Corinth, Galatia, Thessa-
lonica, and Philippi. However, the churches in Roman and Co-
lossae were not established by Paul. Well-versed in Jewish
theology and language, and the Greek language and culture,
Saul was God’s chosen instrument to deliver the gospel to the
Gentiles, as the message from Christ to Paul through Ananias in
Acts says: “Go! This man is my chosen instrument to carry my

W. HU
name before the Gentiles and their kings and before the people
of Israel” (Acts 9:15).
In his work to create and strengthen the early churches, Paul
devoted much of his attention to writing letters to the churches
and individuals to address some relevant issues or topics. These
letters were an effective means of instructing a community
from a distance, since during his time travel and communica-
tion were slow and difficult. His letters aimed to help the cor-
responding congregations to be firmly rooted in the gospel of
Christ, which then naturally lead to his call for gospel-centered
living. The perfect balance between doctrine and the practice of
the doctrine is characteristic of his letters (Kostenberger &
Wilder, 2010).
Of all Paul’s writings, 13 of them are collected in the New
Testament and constitute a critical library of books that
churches and Christians use today. Unfolding the teachings of
Christ, the Pauline letters develop the doctrine of Christian faith
and the church including salvation, justification, reconciliation,
sanctification, and glorification. Paul’s writings are both letter
and epistle, since they often retain personal greetings, recom-
mendations of people and at the same time contain teachings.
Jesus used a simple language to describe the kingdom of God,
which was full of comparisons and parables taken from daily
life. In contrast, Paul typically used a more complex language
than that of Jesus to those people who had heard the gospel.
The letters of Paul have touched almost every important doc-
trine held by the Christian church today, emphasizing the strong
connection between faith and faith-based living as the fruits of
the spirit. Therefore they are really worthy of attentive and
earnest study. As Psalm 119:105 says, God’s word is a lamp to
our feet and a light for our path.
The aim of our work was to study all Paul’s writings through
clustering his letters, their chapters, and their verses to catego-
rize all topics covered by Paul. With this information, we were
able to develop a global view at different resolutions of the
important writings of Paul in the New Testament of the Bible.
Materials and Methods
The Text of the Bible
The text of the Bible used in this study is from the King
James version (1611 authorized version), downloaded from
http://printkjv.ifbweb.com. Because the letters of Paul were
used as data in our study, this section provided some back-
ground information about them.
The Pauline Letters
The letters of Paul could be classified into three groups in
their chronological order (Table 1): travel letters (First & Sec-
ond Thessalonians, Galatians, First & Second Corinthians, and
Romans), prison letters (Colossians, Ephesians, Philemon, and
Philippians), pastoral letters (First & Second Timothy, and
Titus). His letters tend to be written in response to specific is-
sues, and nine of them are addressed to churches while four to
individuals. These letters are known by the names of their re-
cipients. Their main purpose is to teach, encourage, and
strengthen the small house churches he was writing to, helping
them collectively to lay their foundation on the gospel of Christ.
Also the individual members in these churches were in urgent
need of further enlightenment on daily Christian life, which
reflects the very practical aspect of Paul’s writings. To this end,
the letters of Paul demonstrate a close connection between faith
and living that is a clear trait of Paul’s writings. Below we will
briefly summarize the contents of these letters.
Travel Letters
Paul’s missionary work in Thessalonica is described in Acts
17. The key topic in the First & Second Thessalonians is the
return of the Lord, especially its timing. Paul explains the un-
expectedness of Christ’s return and warns the believers for a
lifelong preparedness. The second letter to Thessalonians at-
tempts to correct the misunderstanding of the second coming of
the Lord, a topic Paul brings up in his first letter to Thessaloni-
ans.
The churches in Galatia were created by Paul on his first
missionary journal. The Gentile believers in Galatia were told
by Jewish believers that they should follow the Jewish law
along with faith in Christ, implying keeping the Law of Moses
is essential to their salvation. In this letter to Galatians, he de-
fends his position as an apostle, reaffirms the doctrine of justi-
fication by faith alone, and explains the freedom that the be-
lievers enjoy from the total sufficiency of faith in Christ, high-
lighting the redemptive death of Jesus on the cross. The word
“justify” means to “declare righteous.” The issue of righteous-
ness has been a historical one. The book of Job in Old Testa-
ment asks, “How can a mortal be righteous before God?” (Job
9:2), and the book of Habakkuk declares, “The righteous will
live by his faith” (Habakkuk 2:4). In this letter, Paul describes
faith as the sole means by which people can attain salvation and
as the only source of eternal life. This grace of God gives the
believers the freedom and power not to sin and to love one
another, as the famous verse in this letter says: “The fruit of the
Spirit is love, joy, peace, patience, kindness, goodness, faith-
fulness, gentleness, and self-control” (Galatians 5:22). It teaches
us how to relate to ourselves, others, and God. In this verse,
Paul makes a strong connection between faith and holiness
expressed as the fruits of the faith.
Table 1.
Timeline by year of Paul’s letters (http://www.blueletterbible.org/study/pnt/pnt02.cfm).
A Basic Time Line of Paul’s Letters
Conversion
of Paul
First
Missionary
Journey
Begun
Secondary
Missionary
Journey
Begun
Third
Missionary
Journey
Begun
First
Imprisonment
at Rome Second
Imprisonment
at Rome
36 48 51 52 - 53 54 57 58 62 63 65 66
Thessalonians
Galatians
1Corinthians 2Corinthians Romans The Prison Epistles 1Timothy, Titus 2Timothy
194

W. HU
The letter to Romans is the longest and regarded as most
important letter of Paul. It addresses many issues that are fun-
damental to Christian faith and its practice, an apparent con-
tinuation and elaboration of Paul’s theology stated in Galatians.
The theological principles covered in this letter include con-
demnation, justification, sanctification, glorification, and con-
secration, with a distinct exposition on salvation by the grace of
God through faith in Jesus Christ alone. In this letter, Paul in-
troduces himself to the believers of the Roman church and
strengthens their faith, and informs them his plan to visit their
city and hope they will assist him financially go from there to
Spain (Romans 15:24,28). He plans to use Rome as a base for
his missionary work similar to that in Antioch, since Spain is
far from Antioch. He also deals with some of the problems that
the church in Rome is dealing with such as the unity between
Jewish and Gentiles belie v e r s.
He begins in this letter with an explanation of the sinful state
of humanity that makes it impossible to keep the law in the
sight of God. He writes “For all have sinned, and come short of
the glory of God.” (Romans 3:23). He then teaches that salva-
tion from sin is only possible by the grace of God through faith
in Jesus and not through observance of Jewish law using Abra-
ham as an example. He writes: “For the wages of sin is death;
but the gift of God is eternal life through Jesus Christ our Lord”
(Romans 6:23). He further points out that “A man is a Jew if he
is one inwardly; and circumcision is circumcision of the heart,
by the Spirit, not by the written code” (Romans 2:29). Paul also
advises the Romans to live as a follower of Jesus with harmony,
humility, love, charity, forgiveness, and submission, since he is
aware of some conflict between Gentile and Jewish believers in
the Roman church. Paul presents his doctrine of justification
through faith in Galatians and Romans based on the examina-
tion of the Mosaic Law and quoting the story of Abraham’s
faith. In these two letters, the gospel of grace, in contrast to the
false gospel of works, is revealed more clearly than in his other
letters.
The major theme (or a concise summary of the content) of
this letter is “It is the power of God for the salvation of every-
one who believes; first for the Jew, then for the Gentile. For in
the Gospel, a righteousness from God is revealed, a righteous-
ness that is by faith from first to last, just as it is written: “he
righteous will live by faith” (Romans 1:16-17). Here Paul
quotes a verse in Habakkuk 2:4: “The righteous will live by
faith”, a truth illustrated throughout the history of Israel and
first modeled in Abraham’s life. He also quotes this verse in
Galatians 3:11. Further, Hebrews 10:38 uses this verse as well.
The death of Jesus on the cross reconciled the sinner, Jews and
Gentiles, with God, which signals the end of Law as a means of
justification. Paul emphasizes justification is by the grace of
God through faith in Christ and the children of God are not
based on genealogy or circumcision, but on faith in Jesus (Stott,
2001).
First Corinthians is written to correct many problems devel-
oped in the Corinthian community (divisions in the church,
trust in man’s wisdom, immorality) and to answer the questions
from the church regarding marriage and divorce, food, worship,
spiritual gifts, and resurrection. His own conversion provides
powerful testimony to the resurrection of Christ. This letter also
contains the greatest description and explanation of love ever
written (1 Corinthians 13). In regard to the wisdom of God,
Paul writes “The foolishness of God is wiser than man’s wis-
dom, and the weakness of God is stronger than man’s strength”
(1 Corinthians 1:25).
After the first letter to Corinthians, news of continuing prob-
lems in Corinth reached Paul. The second letter to Corinthians
is the least doctrinal of Pauline letters, but an intensely personal
and emotional letter revealing the personal character of the
apostle more than any other letters. At the same time, the con-
tent structure of this letter is evidently uneven and digressive,
as seen from the sudden shift of subject between chapters 10 -
13 and chapters 1 - 9. As a result, some scholars suggest that
this letter is a composition of a few letters of Paul. In this letter,
Paul affirms his affection for the Corinthians and expresses his
joy at the favorable response of the church to his ministry. But
most importantly, he defends the authenticity of both his apos-
tleship and his message. His final greetings in chapter 13:14
(“May the grace of the Lord Jesus Christ, and the love of God,
and the fellowship of the Holy Spirit be with you all.”) are fre-
quently used in the church today.
Prison Letters
After hearing from a church leader Epaphras (Colossians
1:7-8) about the gospel had born fruit and some dangers (pa-
ganism and heresy) facing the Colossian church, Paul wrote
Colossians to encourage the church in their faith in Christ and
elaborates the true gospel based on the supremacy and suffi-
ciency of Christ, and to guard them against the dangers facing
the church. Paul claims as in Ephesians that Christ is the head
of the church (Colossians 1:18). Colossians focuses on Christ
as the header of the church, while Ephesians teaches the con-
cept that church is the body of Christ.
Ephesians was written after Colossians, dealing with the
similar subjects in a more elaborate way and having a style
closer to a doctrinal letter (O’Brien, 1999; Goodspeed, 1933).
Colossians has 4 chapters, but Ephesians has 6. It does not deal
with problems of particular churches; instead it points the views
of its readers from an earthly/temporary reference to a heav-
enly/eternal reference. In this letter, Paul reveals the mystery
that Christ is the head of the church and the church is the body
of Christ. To keep the church pure and holy as Christ is pure
and holy, he encourages the believers to live in a manner that is
fitting with their position as believers. It contains no allusion to
the personal circumstances of people in the city of Ephesus.
The letter to Ephesians can be divided into two parts. The first
part, chapters 1 - 3, explains the doctrine, while the second part,
chapters 4 - 6, deals with the practice of Christian faith. He
writes: “For it is by grace you have been saved, through
faith—and this not from yourselves, it is the gift of God—not
by works, so that no one can boast” (Ephesians 2:8-9). The
Ephesians describes the church as the body of Christ and God’s
glory in the church, while in Corinthians Paul discusses the
details of establishing the church as a witness to Christ on
earth.
Paul established at Philippi the first Christian community in
Europe on his second missionary journey (Acts 16:9-40).
Comparing to his other letters, Philippians could be read as a
letter of joy, unity, and friendship in Christ. He states explicitly
his love for them such as “I have you in my heart” and “I long
for you with the affection of Christ Jesus” (Philippians 1:7-8)
and his thanksgiving and acknowledgement of their gifts such
as “I always pray with joy because of your partnership in the
gospel from the first day until now” (Philippians 1:4) and “you
sent me aid again and again when I was in need (Philippians

W. HU
4:16). These verses clearly suggest a strong mutual affection
between Paul and his converts in Philippi, not found in any
other churches. He does not open this letter with his credential
as an apostle, since he does not need to do so. He also informs
the church of his imprisonment situation and warns them
against the false teachers.
Philemon was a leader in the church at Colossae. One of his
slaves Onesimus had run away and found Paul imprisoned in
Rome, and became a convert and very useful to Paul. In his
letter to Philemon, Paul appeals to Philemon to forgive One-
simus and receive him as a brother in Christ.
Pastoral Letters
The greatest need in the church is effective leadership as
shown in the church history. Three pastoral letters were written
to Timothy and Titus, two young church leaders and close
co-workers of Paul. These letters resemble one another in their
content, and are exhortations and practical instructions on the
life, doctrine, and ministry of the church including qualifica-
tions for church leaders, church organization, worship, and
ethics in an effort to create a highly institutionalized church.
First Timothy and Titus share many topics. Like the second
letter to Corinthians, Second Timothy is a very personal letter,
containing the farewell remarks from Paul to a young coworker.
Affinity Propagation
The affinity propagation (AP) clustering algorithm (Frey &
Dueck, 2007) aims to search exemplars from data to represent
clusters through message passing. The data points within a
cluster connect to the exemplar that best represents them.
Topic Model
Topic models explore the correlation between the observed
words in documents and the latent topics in the documents,
where each topic is defined by a group of related keywords
(Steyvers & Griffiths, 2007; Griffiths, Steyvers, & Tenenbaum,
2007; Griffiths & Steyvers, 2004). The Latent Dirichlet Alloca-
tion (LDA) (Blei, Ng, & Jordan, 2003) is a simple topic model
that assumes each document is a mixture of various topics. It
uses generative probabilistic model to represent the topics in
documents as probabilistic distributions, which could then be
used to estimate the sim ilarity between docum ents.
In this study, the topic distribution identified by LDA from
each document is used to define a correlation to measure the
similarity between two documents. The standard Pearson cor-
relation formula for two vectors in n-dimensional Euclidean
space is defined as follows:


1
11
n
ii
i
XY
X
XYY
rnSS



where


123
,,, n
X
XXX X,


123
,,, n YYYYY.
X
and
Y represent the average of the two vectors, and
stand for the standard deviation of the two vectors. X
SY S
In the calculation of the correlation between two topic dis-
tributions from two documents, the Xi represents the probability
of topic i, and the sum of all these Xi is one. Since the contribu-
tions from different Xi to the correlation are not equal, we as-
sign a weight to each expression (i
X
X) and (i YY

) as
shown below:



1
21
n
iii
i
XY
i
X
XXYYY
rnSS



which suggests that the higher the probability of a topic is, the
greater its contribution to the correlation. Throughout the cur-
rent study, we used this weighted Pearson correlation r2 for
comparing two topic distributions.
In the present study, the AP clustering algorithm was used to
group the Pauline letters, their chapters, and their verses, where
each letter/chapter/verse segment was represented by its topic
distribution as a vector in Euclidean space.
Results
In this section, we report the outcome of out computational
analysis of Paul’s letters, conducted at three different resolu-
tions: letters, chapters, and verses. Our aim was to apply the
topic modeling and AP clustering algorithm to catalog the top-
ics discussed either once or repeatedly in all his writings, thus
rendering the whole picture of his messages.
Clusters of 13 Pauline Letters
We first clustered the 13 letters of Paul, which produced five
groups (Table 2). Because of the different contents of First and
Second Corinthians, they were not placed inside the same clus-
ter. But these two letters had many similar chapters as seen in
“Clusters of All Chapters of Pauline Letters ” S ection. All the other
Pauline letters were correctly grouped according to the church
tradition. Although there are 13 letters, but our clustering algo-
rithm was able to find five exemplars from them: Colossians,
Philippians, Romans, First Thessalonians, and First Timothy.
The word clouds in Figure 1 gives the visual display of the
most frequently occurring words in Paul’s letters. In Romans
and Galatians, the words “law”, “faith”, “righteousness”,
“spirit”, “sin”, “flesh” are emphasized. In pastoral letters, the
word “good” stands out; it is used to describe “good work(s)”,
“good conscience”. This word is mainly used in First Timothy
and Titus, but not in Second Timothy. In First and Second
Thessalonians, the word “brethren” (meaning brothers) appears
frequently, showing Paul’s personal affection towards the be-
lievers in that church. The word “Christ” is mentioned more
often than the word “God” in the groups of Colossians and
Ephesians, and Philippians and Philemon than in other groups.
Pairwise Correlations of Pauline Letters
Here we looked at the correlations between a pair of the
Pauline letters (Table 3), which was not readily available
through the clustering of these letters in “Clusters of 13 Pauline
Letters” Section. It turned out the most similar letters within the
Pauline letters were Colossians and Ephesians, Philemon and
Philippians, First and Second Thessalonians, First Timothy and
Titus, and Galatians and Romans (Table 3). This pairwise
comparison refined the clusters in Table 2. Say, the three pas-
toral letters were in the same group in Table 2, but actually the
First Timothy and Titus were the most similar of the three,
which is true when we compare the contents of these three let-
ters. Moreover, First Corinthians deals with many specific is-
sues at the church, so it is not strongly related to other letters of
Paul and is what makes it stand out. We should point out that
the thorough pairwise comparison of these letters was only
196

W. HU
Table 2.
Clusters of the Pauline letters.
Cluster Number Exemplar Let ter Name Letters in One Cluster
1 Colossians Colossians, Corinthians1, Ephesians
2 Philippians Corinthians2, Philem on, Philippians
3 Romans Galatians, Romans
4 Thessalonians1 Thessalonians1, Thessalonians2
5 Timothy1 Timothy1, Timothy2, Titus
Table 3.
Top 48 highly corre lat ed p ai r of Pauline letters.
Book1 Book2 Correlation Book1 Book2 Correlation
Colossians Ephesians .983 Corinthians2 Philemon .829
Philemon Philippians .983 Ephesians Timothy2 .822
Thessalonians1 Thessalonians2 .982 Philippians Timothy2 .821
Ephesians Philippians .976 Ephesians Galatians .811
Philippians Thessalonians2 .96 Philemon Timothy2 .809
Ephesians Philemon .957 Colossians Timothy2 .808
Timothy1 Titus .954 Galatians Philippians .793
Philippians Thessalonians1 .952 Colossians Galatians .789
Ephesians Thessalonians2 .95 Timothy1 Timothy2 .789
Colossians Philippians .948 Galatians Thessalonians2 .785
Philemon Thessalonians2 .944 Galatians Thessalonians1 .776
Ephesians Thessalonians1 .937 Galatians Philemon .763
Philemon Thessalonians1 .933 Ephesians Romans .749
Colossians Philemon .932 Romans Thessalonians2 .749
Colossians Thessalonians2 .928 Romans Thessalonians1 .741
Colossians Thessalonians1 .918 Colossians Romans .737
Galatians Romans .888 Corinthians2 Galatians .724
Corinthians2 Philippians .862 Philippians Romans .721
Corinthians2 Ephesians .851 Corinthians2 Timothy2 .718
Thessalonians2 Timothy2 .842 Galatians Timothy2 .695
Thessalonians1 Timothy2 .839 Corinthians2 Romans .687
Corinthians2 Thessalonians1 .835 Philemon Romans .682
Corinthians2 Thessalonians2 .834 Romans Timothy2 .678
Colossians Corinthians2 .829 Timothy2 Titus .673

possible with the help of computational methods.
Clusters of All Chapters of Pauline Letters
There are 87 chapters in the 13 letters of Paul, from which
our clustering algorithm generated 21 clusters (Table 4). These
clusters of various sizes revealed the structural grouping of the
different topics covered in the letters. In Colossians, there are 8
verses on rules for Christian households (verses 3:18-25), but in
Ephesians, Paul used 21 verses on the same topic (verses
5:22-6:9). As a result, chapter 3 of Colossians and chapter 5 of
Ephesians were grouped together in cluster 8.
Paul’s letters typically include doctrine and its practice. For
instance, Ephesians has doctrine in chapters 1 - 3 grouped in
cluster 12, and its practice in chapters 4 - 6, with chapter 4 in
cluster 21, chapter 5 in cluster 8, and chapter 6 in cluster 19.
Interestingly, these clusters (8, 12, 19, and 21) had the most
chapters, and the chapters from different letters in these 4 larg-
est clusters tended to be similar. Further, each of them selected
the chapters from specific letters. For example, cluster 8 se-
lected its most chapters from First and Second Corinthians,
cluster 19 liked the chapters from Second Corinthians and First
and Second Thessalonians, and cluster 21 favored the chapters
from Romans, First and Second Timothy. It was noteworthy
that First and Second Corinthians were in two different clusters
in “Pairwise Correlations of Pauline Letters” Section when

W. HU
Romans and Galatians Pastoral letters First and Second Thessalonians
Colossians and Ephesians First and Second Corinthians Philippians and Philemon
Figure 1.
Word clouds of top 50 fr eque nt words in six groups of Paul ’s letters.
Table 4.
Clusters of chapters of Pauline letters (To save space, we used abbreviation. Say, Corinthians2_4-6 stands for Second Corinthians chapters 4 - 6.).
Cluster
Number Chapters in one cluster: Subjects of the chapters Summary of large clusters
1 Corinthians1_11: Propriety in worship, The Lord’s supper
2 Corinthians1_12: Spiritual gifts, One body, ma n y parts
3 Corinthians1_13: Love
4 Corinthians1_14: Gifts of proph ecy and tongues, Orderly worship
5 Corinthians1_15: The resurrection of Christ, The resurrection of the dead,
The resurre ction of the body Doctrine of the resurrection
6
Colossians_ 4: Further ins tructions, fi n al greetin gs
Corinthian s 1_16: The collection for God’s people, Personal Request,
Final Greetings
Philem on _1 : Thanksgiving and prayer, Paul’s plea for Onesimus
Philippians_4: Exhortations, Thanks for the i r gifts, final greetings
Romans_16: Personal greetings
Final greetings
7 Corinthians1_3: On divisions in the church
8
Colossians_2-3: Free dom from human regulations t hrough life w ith Christ,
Rules for holy living, Rule s for Christian households
Corinthians1 _ 2: Wisdom from the spirit
Corinthians1 _ 4-6: Apostles of Christ, Expel the immoral brothers, Lawsuits
among believers, Sexual immorality
Corinthians1_9: The right of Apostles
Corinthians2_4-6: Treasures in jars of clay, Our heavenly dowelling, The
ministry of reconciliation, Paul’s hardship, Do not be yoked with unbelieve rs
Corinthian s 2_10-12: Paul’s defense of his ministry, Paul and the false apostles,
Paul’s boasts about his sufferings, Paul’s vision and his thorn, Paul’s concern
for the Corinthia ns
Ephesians_5: Living as children of light, Wives and Husbands
Daily Christian living including husband and wife relationship
and Paul’s exposition on his ministry (mainly from chapters in
First and Second Corinthia ns)
9 Corinthians1_7: Marriage
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Continued
10
Corinthians1_8: Food sac rificed to idols
Corinthians1_10: Warnings from Isra el’s history, Idol feast a nd Lord’s supper,
the believer’s freedom
Romans_14: The wea k and the strong
Food related to the church life
11 Corinthians2_3: The glory of the n ew covenant
12
Colossians_1: Thanksgiving and prayer, The supremacy in Christ, Paul’s
labor for the church
Corinthian s 1_1: Thank sgiving, D i visions in the church, Christ t he wisdom and
power of God
Ephesians _1-3: Spiritual blessings in Christ, Thanksgiving and prayer, Made
alive in Christ, One in Christ, Paul the preacher to the Gentiles, A prayer for
the Ephesians
Galatians_1: No other Gospel, Paul calle d by God
Romans_15: Pa ul the minist er to the Gentiles, Paul’s plan to visit Rome
Daily Christian living and Pa ul’s exposition on his minis tr y (First
chapters from different letters)
13 Galatians_3: Faith or observation of the law, The law and the promise, Sons of God
Romans_4: Abraha m justified by fa ith
Doctrine of Jus ti fi cation:
Justification by faith
14 Galatians _ 4: P aul’s concern for t he Galatians, Hagar and Sarah
15 Galatians_5-6: Freedom in Christ, Life by the spi rit, Doing good to all, Not
circumcis io n but a ne w creation
Romans_8: Life th rough spirit, F uture glory, More than conq u erors
Doctrine of sanc tification:
Christian’s freedom in Christ
16 Romans_11: The r emnant of Israel, Ingrafted branches, All Israel will be s aved Doctrine of Elec tion:
Election by grace, not by deeds
17
Galatians_2: Paul accepted by the apostles, Paul opposes Peter
Romans_2-3: God’s ri g hteous jud g ment, T he Jews and the law, God’s
faithfulness, No one is righteous, Righteousness through faith
Romans_9-10: God’s sovereign choice, Israel’s unbelief
Doctrine of Jus ti fi cation:
Righteousness through faith in Christ, not by the deeds of the
Law
Doctrine of Election:
Election by grace, not by deeds
18 Romans_6-7: Dead to sin, alive in Christ; Slaves to r i ghteousness, An
illustration from marriage, Struggling with sin
Doctrine of sanc tification:
Dead to sin, freed from sin, dead to the requirements of the law,
struggle with sin
19
Corinthians2 _ 1-2: God of all c omfort, Paul’s change of plans, Forgiveness for
the sinner, Ministers of the new covenant
Corinthians2 _7-9:Paul’s joy, Generosity encoura ged, Titus sent to Corinth,
Sowing generously
Corinthian s 2_13, Fin al warnings, Final greetings
Ephesians _6 , Children and parents, Slaves and masters, The armor of God,
Final greetings
Philippians_1-3: Thanksgiving and prayer, Paul’s chains ad v ance the Gospel,
Imitating Christ’s humil it y, Shining as stars, Timothy and Epapharodius, No
confidenc e in the flesh, Pressing on tow ard the goal
Thessalonians1_1-5: Thanksgiving fo r the Thessalonians’ fai th, Paul’s m inis try
in Thessalonica, Paul’s longing to see the Thessalon ians, Timothy’s encoura ging
report, Livin g to please G od, The coming of the Lord, Final instructions
Thessalonians2_1-3: Thanksgiving and prayer, T he man of lawlessness, Stand
firm, Request for praye r, Warning against idleness, Final greetings
Timothy2_1: Encouragement to be fait hful
Daily Christian living and Pa ul’s exposition on his minis tr y (First
chapters and l ast chapters from di fferent le tters, mainly f r om
chapters in Second Corinthians, Philippians, First and Second
Thessalonians)
20 Timothy1_3: Overseers and deacons Timothy1_5: Advice about widows, elders, and slaves
Titus_1-2: Titus’s task on Crete, What must be taught to various groups Dealing with various busines ses in the church
21
Ephesians_4: U nity in the body of Christ, L i ving as children of light
Romans_1: Paul’s longing to visit Roman, God’s wrath aga i nst mankind
Romans_5: Peace and joy; Death th rough Adam, life through Christ
Romans_12-13: Living sacrifice, Love, Submission to the auth or ities; Lo v e, for
the day is near
Timothy1_1-2: Warning against false teachers of the law, The Lord’s grace to
Paul, Instructions on worship
Timothy1_4: I nstructions to T i mothy
Timothy1_6 : Love of money, Paul’s charge to Timothy
Timothy2_2-4: A workman approved by God, Godlessness in the last days,
Paul’s charge to Timothy, Personal remarks, F in al greetin g s
Titus_3: Doin g what is good, Final remarks
Christian daily l iving as a tra nsformed life reflected in love ,
including instructions to Timothy and Titus as i nd ividuals
(mainly from chapters in Romans, pastoral letters)

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compared with their whole letter contents. But many of their
chapters were still similar as seen in cluster 8, implying that
chapter-wise clustering could reveal new information about
these letters. Cluster 12 featured many opening chapters of the
letters, including Colossians, First Corinthians, Ephesians, and
Galatians. Chapter 15 of Romans was included in this cluster
since Paul explains his role as a minister in this chapter, which
typically occurs in the opening statements of his other letters.
In general, the cluster of a single chapter indicate the topics
within the chapter are only discussed once in Paul’s letters,
while the existence of several chapters in one cluster suggests
same or similar topics are discussed in multiple chapters. For
example, chapter 3 of Colossians and chapter 5 of Ephesians
were in cluster 8, because these two chapters deal with the rela-
tionship between husband and wife. The clusters that each con-
tained only a single chapter were mainly made of the chapters
from the First Corinthians (chapters 3, 7, 11 - 15) and chapter 3
from the Second Corinthians in cluster 11, chapter 4 from Gala-
tians in cluster 14, and chapter 11 from Romans in cluster 16.
Therefore the topics in these chapters of First Corinthians, Ga-
latians, and Romans were unique.
In total there were 3 clusters, clusters 6, 12, and 19, contain-
ing the beginnings and/or ends of the letters. Cluster 6 had the
final greetings of 5 letters: Colossians, First Corinthians, Phi-
lemon, Philippians, and Romans. Cluster 19 contained both the
beginnings and ends of several letters. It had the opening chap-
ters of 5 letters: Second Corinthians, First and Second Thessa-
lonians, Second Timothy, and Philippians. The final chapters in
this cluster were from 4 letters: Second Corinthians, Ephesians,
First Thessalonians, and Second Thessalonians. As a matter of
fact, all chapters of First and Second Thessalonians, and the
first 3 out of all 4 chapters of Philippians were in this cluster.
These 3 clusters suggested that our clustering algorithm was
able to identify the structural features of the Pauline letters,
since they do resemble one another in the beginning or ending.
To further visually enlighten the correlations of chapters in
the Pauline letters, we chose the top 50 highly correlated pairs
of chapters as seen in Figure 2, where each pair of chapters
were connected with a straight line. The largest connected
group in Figure 2 was made of first chapters of Colossians,
Ephesians, First and Second Thessalonians, Philippians, Phile-
mon, and Second Corinthians, and First and Second Timothy.
This closely connected network of first chapters enlarged the
grouping illustrated in the clusters 12 and 21 in Table 4. The 4
letters whose first chapter was not included in this group were
First Corinthians, Galatians, Romans, and Titus. There were 5
letters whose final chapters were all in cluster 6 in Table 4.
Here the final chapters of Romans and First Corinthians were
connected as a refinement of the information revealed in cluster
6.
Several similar chapters of Galatians and Romans were
grouped together. Clusters 13 had chapter 3 of Galatians and
chapter 4 of Romans, both of which mention Abraham as an
example of righteousness through faith. Cluster 15 contained
chapters 5 and 6 of Galatians and chapter 8 of Romans, dealing
with the doctrine of sanctification.
Figure 2.
Top 50 highly corre lated pairs of chapters in Paul’s letters where each pair was connected with a line.

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Clusters of All Verse Segments in the Pauline Letters
Here we divided each chapter into numerous segments of 10
verses with the last segment having 10 verses or less than. As a
result, there were 231 segments created from all the 13 letters
of Paul. Our clustering algorithm produced 33 clusters with the
largest cluster, cluster 23, holding 158 segments, which showed
the similarity of the most segments in Paul’s letters (Table 5).
As in the discussion of different chapters in “Clusters of All
Chapters of Pauline Letters” Section, it was of interest to look
at the topics appeared in the small clusters, some of which over-
lapped with those in “Clusters of All Chapters of Pauline Let-
ters” Section but some didn’t.
In Romans, Paul greets many people by name in the Rome
church (Romans 16:1-21). In general, Paul does not offer such
extensive greetings in his letters. Our algorithm picked on
Paul’s personal request and greetings which contain several
names in First Corinthians along with Romans 16:1-21 in clus-
ter 24. The two letters, Romans and First Corinthians, had the
most unique verses or topics as detected by our algorithm.
Cluster 31 contained a verse segment that deals with the second
coming of the Lord, a topic not found in the chapter clusters in
“Clusters of All Chapters of Pauline Letters” Section, thus of-
fering new insight into the Pauline letters.
Authorshi p o f the Book of Hebrew s
Addressed to Jewish believers, the book of Hebrews lays out
Table 5.
Clusters of verse segments of pauline letters (To save space, we used abbreviation. Say, Corinthians1_10_2-3 stands for First Corinthians verse seg-
ments 2 - 3 in chapter 10.).
Cluster Number Segments in One Cluster Subjects
1 Corinthians1_8_1
Corinthians1_10_2-3 Food from i d ol f easts a n d t he Lord’s s upper
2 Corinthians1_11_1 Propriety in worship
3 Corinthians1_11_2 Propriety in worship, Lord’s supper
4 Corinthians1_11_3 Lord’s supper
5 Corinthians1_12_2 One body, many parts
6 Corinthians1_12_3 One body, many parts
7 Corinthians1_13_1 Love
8 Corinthians1_14_1-3 Gifts of prophecy and tongues
9 Corinthians1_15_2 The resurrec tion of the dead
10 Corinthian s 1_15_4 The resurrection b ody
11 Corinthian s 1_15_5 The resurrection b ody
12 Corinthians1_1_2-3
Corinthians1_2_1 Wisdom of G o d and wisdom of the spirit
13 Corinthians 1_3_2 On divisions in the chur ch
14 Corinthians1_7_1-4 Marriage
15 Corinthian s 1_9_2 The right of an Apostle
16 Corinthians2_11_3 Paul boasts a bout his sufferings
17 Corinthians2_3_1-2 The glory of the new covenant
18 Galatians_4_3 Hagar and Sarah
19
Colossians_1_1
Corinthians1_1_1
Corinthians2_1_1
Ephesians_1_1
Galatians_1_1
Philemon_1_1
Philippians_1_1
Romans_1_1
Timothy2_1_1
Opening statement of each letter
20 Romans_11_2 Ingrafted branches
21 Romans_11_3 All Israel wi ll be saved
22 Romans_14_1 The weak and the strong
23 All remaining segments of Paul’s letters (158 segments) Largest group containing va rious subjects
24 Corinthians1_16_2
Romans_16_1-2 Greetings to individuals
25 Romans_2_3 Th e Jews and the law
26 Galatians_3_1-2
Romans_4_1-2 Law, faith, promise of God, A braham justified by faith
27 Romans_5_2 Death through Adam, lif e through Ch rist
28 Romans_6_1 Dead to sin, alive in Christ
29 Romans_6_2 Slaves to righteousn ess
30
Galatians_2_2
Romans_2_2
Romans_3_2
Romans_7_1-3
Romans_8_1
Law, Jews, right eousness, justification, condemnation
31 Thessalonians1_5_1 Coming of the Lord
32 Timothy1_ 3_1 Oversee rs and deacons
33 Titus_2_2 What must be taught to various grou p s

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the superiority, perfection, and completion of Jesus Christ as
mediator of God’s grace for salvation. Jesus is the perfect high
priest who offers Himself as a sinless sacrifice, and through
Him we can receive eternal life. He is better than the angels and
the forefathers of Israel. The letter enumerates the faith heroes
in the history of Hebrews to demonstrate the overwhelming
evidence of God’s faithfulness, and therefore calls us to live by
faith as the saints in the Old Testament did.
In all Pauline letters, there were a collection of his favorable
words, “God”, “Christ”, “Lord”, and “Jesus”, as seen from the
word clouds in Figure 1. But here in Figure 3, only the word
“God” plus the words “faith” and “priest” are very visible. This
discrepancy was certainly not a proof of authorship, but dis-
playing some writing style difference between the 13 Pauline
letters and the book of Hebrews.
To compare the book of Hebrews with the 13 Pauline letters,
we clustered these 14 letters. The outcome showed that the
letter to Hebrews formed a single letter cluster and the 13
Paul’s letters appeared in 3 clusters (Table 6). The dendrogram
in Figure 4 also confirmed that Hebrews was quite different
from the 13 letters of Paul in terms of their contents.
To study the authorship of the letter to Hebrews, we em-
ployed the 13 Pauline letters and 13 of non-Pauline books in the
New Testament as training data to build our predictors. Using
10 fold cross validation, we selected 9 classifiers in Weka
(http://www.cs.waikato.ac.nz/ml/weka/) that had less than 4
errors, indicating that they were highly accurate for this kind of
prediction. The confusion matrices of these classifiers are pre-
sented in Table 7 along with their predictions of the authorship
of the book of Hebrews. Out of the 9 classifiers, only one pre-
dicted Paul as the author of the letter to Hebrews. By consensus
we therefore could conclude that these 9 classifiers collectively
predicted Hebrews as non-Pauline. It was worth noting that four
of the classifiers, SMO, SL, IBk, and Bagging, tended to pre-
dict non-Pauline as Pauline as shown from their predictions of
the training data in Table 7. But they all predicted Hebrews as
Figure 3.
Word clouds of top 50 frequent words in the
letter to Hebrews.
Figure 4.
Dendrogram of the clusters shown in Table 5.
Table 6.
Clusters of Pauline letters and the book of Hebrews.
Cluster Number Exemplar Letter N ame Letters in One Cluster
1 Colossians Colossians, Corinthians1, Corinthians 2, Ephesians, Galatians, Philemon, Philippians, Rom ans
2 Hebrews Hebrews
3 Thessalonians2 Thessalonians1, Thessalonians2
4 Timothy1 Timothy1, Timothy2, Titus
Table 7.
Confusion matri ces o f 9 cl assif iers and their predictions of authorship of the letter to Hebrews.
Classified as a b a b a b a b a ba b a b a b a b
Paul = a 13 0 11 2 13 0 13 0 13012 1 13 0 12 1 13 0
Non-Paul = b 1 12 2 11 2 11 2 11 1122 11 2 11 3 10 1 12
Classifier SMO SL Bayes Net NB IBk Bagging RBF Network RF BLR
Prediction of
Hebrews
Authorship Non-Pauline Non-Pauline Non-PaulineNon-PaulinePaulineNon-PaulineNon-Pauline Non-Pauline Non-Pauline
BLR = Bayesian Logistic Regression, SL = Simple Logistic, NB = Naïve Bayes, RC = Random Committee, RF = Random Forest, RT = Random Tree.
202

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non-Pauline. The one classifier that predicted Hebrews as
Pauline was a predictor that favored Paul as the author of other
known non-Pauline letters (Table 7).
Conclusion
Paul is the most prolific New Testament writer that contrib-
uted 13 books to the collection of 27 books in the New Testa-
ment. He played a key role in the formation of early Christian
faith and the church. In this work, we presented a computa-
tional approach to study of Paul’s letters. Our goal was to em-
ploy the topic modeling and AP clustering algorithm to catalog
the topics discussed either once or repeatedly in all his writings.
The distributions of the topics of each document were calcu-
lated and used as features, to which the AP clustering algorithm
was applied. This method provided a means to study Paul’s
messages as a whole at three granularities: letters, chapters, and
verses, offering different views of the Pauline letters.
Our computational analysis implied all Pauline letters could
be divided into six groups, well in line with the church tradition.
They were First and Second Thessalonians, First and Second
Corinthians, Colossians and Ephesians, Galatians and Romans,
Philemon and Philippians, and First and Second Timothy and
Titus. We were able to identify the topics covered either once
or a few times in his letters. Among all letters, First Corinthians
had the most unique chapters, whereas First Corinthians and
Romans had the most unique verses or topics. Moreover, simi-
lar verses and chapters from different letters were also discov-
ered. The grouping of the Pauline letters, their chapters, and
their verses provided a global view of all his writings at differ-
ent resolutions, with each complementing the other.
We also studied the authorship of the letter to Hebrews, an
anonymous letter in the New Testament. Using known Pauline
and non-Pauline letters as training data, we built nine highly
reliable predictors, which collectively predicted that the book of
Hebrews was not authored by Paul.
Acknowledgements
We thank Houghton College for its financial support.
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