During Bible study last week, it was mentioned that people have used statistics to “determine” authorship of books of the Bible. Having a couple free hours last night, I tried my own experiment on the New Testament.

The procedure was easy: I downloaded the Nestle-Aland 26th edition of the New Testament; each book in the New Testament became a vector $v$, with $v_w$ counting the number of times word $w$ appears in the book. The cosine of the angle between two such vectors measured how similar the corresponding books are. I packaged these cosines into a matrix, the $(i,j)$ entry of which measured how similar books $i$ and $j$ are.

Of course, this is a $27 \times 27$ matrix. To turn these numbers into a nice picture, I projected the books onto a lower dimensional space spanned by the eigenvectors having the five largest eigenvalues (this is known as Principal Component Analysis); I chose five dimensions, displayed using location (two dimensions) and color (three dimensions, namely hue, saturation, and luminosity). The result is the following graph:

The dots represent each book, and nearby dots of similar colors represent similar books. Some things jump out right away:

• The Gospels are all in the lower right hand corner.
• Paul’s epistles (and Peter’s?) are mostly in the upper right hand corner.
• Revelation is close to John.
• Hebrews and James are close to each other? Why?

All told, I think this is a pretty good graphical display of the structure of the New Testament, especially considering we used nothing but the Greek text and linear algebra!

On a recent plane trip, I was reading a very abridged version of (the ten thousand page long!) Church Dogmatics by Karl Barth, and I found something totally beautiful.

Believing God to be entirely “transcendent in contrast to all immanence” and “divine in contrast to everything human,” and reading (e.g., in Philippians 2:7) that Jesus is God having emptied himself, having made himself nothing, I concluded that God somehow hid his divinity in order that he might become human and, in that form, redeem humanity.

This is wrong. Karl Barth writes:

As God was in Christ, far from being against Him, or at disunity with Himself, He has put into effect the freedom of His divine love… He has therefore done and revealed that which corresponds to His divine nature…

His particular, and highly particularised, presence in grace, in which the eternal Word descended to the lowest parts of the earth and tabernacled in the man Jesus, dwelling in this one man in the fulness of His Godhead, is itself the demonstration and exercise of His omnipresence… His omnipotence is that of a divine plenitude of power in the fact that (as opposed to any abstract omnipotence) it can assume the form of weakness and impotence and do so as omnipotence, triumphing in this form…

From this we learn that the forma Dei [Philippians 2:6] consists in the grace in which God Himself assumes and makes His own the forma servi [Philippians 2:7].

–Church Dogmatics, Volume IV, Part 1, page 185 and following.

My cutting hardly does justice to the original text, so I’ll paraphrase.

Jesus shows that God is everywhere, because God is fully in him; this doesn’t undermine omnipresence, instead, it strengthens it: the abstract “God is everywhere” is emphasized by a particular “And look, God is there–it’s Jesus.” Similarly, Jesus shows that God is all-powerful, because God triumphed in him in spite of weakness.

I had been thinking that Jesus was God with a veil over his divinity, when in fact, Jesus is God proving just how totally divine he is. For a God who is Love, the incarnation isn’t a denial of himself, but an affirmation of who he had been all along. It is often said that Jesus proved his divinity by rising from the dead; it ought to be remembered that he proved his divinity by being able to be obedient to death in the first place.

This is a beautiful perspective from which to understand the hypostatic union; the monophysites believed that Jesus’ humanity undermined his divinity, while as Barth explains, Jesus’ two natures are not only compatible, but necessary. This is another example of the sort of paradoxical argument I usually find unreasonably compelling (e.g., Chesterton’s Orthodoxy or Kierkegaard (fear and trembling appears in Philippians 2:12–a coincidence?) or Hume’s compatibilist explanation of free will).

Like most things viewed with hindsight, this perspective isn’t radical, but I (and probably a lot of people) view the divine and human natures of Christ as, essentially, in conflict when, ironically, Jesus came to reconcile those two natures, and did so first in himself.

Given a text in two languages, is it possible to uncover the meaning of individual words?

The Bible is a particularly easy text to work with, since corresponding sentences are marked (i.e., with the same chapter and verse numbers). I downloaded a copy of the Hebrew Bible and the King James’ Version, and looked at Deuteronomy 6:4.

For each word in Hebrew, I found all the other verses with that word, and gathered together all the corresponding English verses; by picking the most popular word from those English verses (ignoring “the” and “and” and such), I found a pretty good translation of the original Hebrew word. In short, I picked the most popular English word in all those verses containing the non-English word.

So here’s Deuteronomy 6:4, with the top six English words underneath each Hebrew word:

Remember to read this from left-to-right. Pretty impressive–it didn’t quite get the verb שְׁמַ֖ע but it did well enough anyway.

It also works in Greek. Here’s Galatians 3:26 with the most popular English words underneath each Greek word.

It didn’t quite figure out διὰ is by or through.

In the end, this isn’t shocking, but it’s surprising how easy it is: the Ruby program to do this is only 150 lines long (which includes the code to print out those nice HTML tables with Unicode).

Someone contacted me with some questions about Bayesian document clustering; with that inspiration and a free afternoon a few weeks ago, I took a Hebrew bible and built a matrix $(A_{ij})$ where $A_{ij}$ equals the frequency of the $i$-th (Hebrew!) word in the $j$-th chapter of Genesis. I calculated its singular value decomposition (supposedly this is “latent semantic analysis”), and then took some dot products (calculating the “correlation” of chapters)…

Anyhow, the result was astounding! The following table gives, for each chapter, a list of those chapters for which the given chapter is the chapter most highly correlated with it. Ah, that’s confusing; as an example to clarify this, the chapter most similar to chapters six, seven, eight, and nine is chapter one. With that, here’s the data:

The shocking thing is that for 21 chapters of Genesis–for nearly half the book–the most highly correlated chapter is chapter 22–the binding of Isaac. In my mind, that story is the most powerful in Genesis, central to the message, and so it is especially remarkable that this crazy game with matrices also “detected” that most of Genesis clusters around that story.