Monday, May 29, 2017

Patterns in the Torah

About twenty years ago, I was extremely mystically rather than rationalistically inclined. Related to this was my desire to see patterns in everything - especially fractal patterns. These are patterns that repeat at different scales, which appear in various forms in nature (such as fern leaves), and in a mathematical construct known as the Mandelbrot Set, pictured on the right - which I eventually used for the cover of my book The Science of Torah (subsequently banned and then rendered obsolete by The Challenge Of Creation).

I was therefore thrilled when, at that time, I came across an obscure and difficult book by Rabbi Yehoshua Honigwachs called The Unity of Torah. This work set out to answer a question that, to my astonishment, nobody had ever asked before: What is the overall structure of the Torah? Rabbi Honigwach's answer was that the structure of Torah reflects a five-stage approach to its central goal: Taking man from the extremes of egotism, in which society is an anarchy of selfish elements, towards a state of unity between all men and God. This pattern, argued Rabbi Honigwachs, is found in each of the five commandments on the Tablets of Law; it is also found amongst the five books of the Torah; within these books; within each fifth of these books; and so on - although, he noted, there are some places where a different version of this pattern is found, and there are others where it is not found at all. (There is a new book, Patterns on Parchment - The Structural Unity of The Five Books of Moses by Dr. Robert Appleson, which is an expansion of Rabbi Honigwachs' book, but I haven't read it.)

Needless to say, I was very much taken with this fractal pattern. I figured out a way to diagrammatically illustrate it in ways that made it easier to comprehend; I sent my illustrations to Rabbi Honigwachs, who was pleased at the result. In my book The Science of Torah, I made much use of fractal patterns, and I decided to include an overview of Rabbi Honigwach's approach in an appendix. You can freely download the appendix at this link, and it is also aided with the following schematic:

But my mentor Rabbi Aryeh Carmell was very unhappy with my interest in such patterns, being skeptical of this sort of pattern-seeking in general. I, on the other hand, was obsessed with it! We worked out a compromise, whereby I clearly restricted such discussions to distinct parts of the book, and he made it clear in his approbation that he was not supportive of those parts.

Today, I realize that pattern-seeking is both one of man's greatest strengths and one of his greatest weaknesses. In evolutionary terms, it was a helpful skill to learn; it enabled man to spot a camouflaged predator, and to discover causal relationships in the natural world. But, as a result, people also have a powerful propensity to see patterns even when none exist, and to ascribe causality even where there is none (as in much religion, and alternative medicine). And the thrill of discovering patterns can easily hamper one's objectivity. Of course, there are also those who deny patterns and causality even where they really exist (such as liberals with regard to Islamism, and smokers with regard to the dangers of smoking); but the former problem seems more innate and pervasive.

So what about this fractal pattern in the Torah? I don't have the time, or the objectivity, to study it all again and re-evaluate it. For a variety of reasons, I am certainly inclined to be skeptical. Nevertheless, I remain impressed at how Rabbi Honigwachs freely admitted that his pattern does not work in all places, which indicates a high degree of objectivity, and presented it as a model to be further refined. I was also interested to discover an article in Jewish Bible Quarterly that also discusses it.

Furthermore, with regard to the more limited suggestion of the pattern appearing in the two tablets of the Ten Commandments, it appears much more straightforward. As I noted in The Challenge Of Creation, a similar structure has been observed in the Six Days of Creation by scholars from across the theological spectrum. There is even more reason to expect it in the Ten Commandments, which from the outset are presented in two parts. I present an illustration of this pattern here (I hope it displays properly in different web browsers). Chag sameach!

Beginning with: Selfishness; Isolation; Focus on the Individual
Manifestation between Man and God
Manifestation between Man and Man
Accepting God
Acceptance of God’s existence
Acceptance of others’ existence
Do Not Murder
Other people’s right to exist; Value of life
Do Not Worship Idols
Accepting God’s ownership of the entire universe
Acceptance of their domain
Do Not Commit Adultery
Accepting the other person’s domain
Do Not Take God’s Name in Vain
No unlawful use of God’s Name
No unlawful use of property
(lawful coexistence)
Do Not Steal (Kidnap)
No unlawful use of another’s being, person or property
Observing Shabbos
Testifying to God’s authority
Readiness to cooperate
(particularly through speech)
Do Not Testify Falsely
No destructive talk; hence, cooperate
Honoring Parents
Unity with one’s source
Total unity
Do Not Covet
No resentment of others

Climaxing with: Selflessness; Unity with God and man; Integration into the Community


  1. cf. Robert Appleson, 2002. Finding harmony in anomaly: a window on the Torah's use of exceptional language (Margolin Hebrew Academy/Feinstone Yeshiva of the South), 1-140
    Robert Appleson, 2008. Is there a pattern to the Five Books of Moses? Jewish Bible Quarterly 36(1):39-48 [this is accessible on line]~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
    STEPHAN PICKERING / חפץ ח"ם בן אברהם
    Torah אלילה Yehu'di Apikores / Philologia Kabbalistica Speculativa Researcher
    לחיות זמן רב ולשגשג


  2. Is this post a repeat? I feel like I've read it before. (It was good both times.)
    "I was extremely mystically rather than rationalistically inclined. Related to this was my desire to see patterns in everything..." - Are these related to *you* or do you think they'd be related for everyone? I can see a rationalist who believes God gave a structurally united Torah, and delves as deep as he can to bring that unity to light.

    1. Ahh, yes. I read this before on Tuesday, June 7, 2011.

  3. Personal conversation between a RIETS R"Y and an actuary after the latter suggested a possible Brisker chiluk(underlying distribution function) based on several sugyot (data points) and concluded with "actuaries are trained to look for patterns in the data but also be suspect that they are seeing their own reflection. R"Y response - that's what we do!

  4. The parallels in the aseres hadibros is cute, and clever, but some of them are a stretch.

    "Ani Hashem elokecha" is not a declaration of God's existence. The existence of deities is something the Bnei Yisroel took for granted. It's a declaration that this particular deity is the god of the Jews, as opposed to Ra or Baal or Marduk.

    Stage 2:
    Don't worship idols is an extension of the first commandment, telling the Bnei Yisroel that not only is Hashem your god, but he is your primary god. It's not even a prohibition of henothesism, let alone a declaration of Hashem's ownership of the world.
    Who's domain is one accepting when he or she refrains from committing adultery? The husband's? That does fit with the time period, but the negation of the woman's agency in this interpretation is hardly morally edifying.

    Stage 4:
    Shabbos is not about "readiness to cooperate," at least, not any more than any other mitzvah. It's not a testament to God's authority, except indirectly in the sense that it's a testament to His role as Creator. And it has nothing to do with speech.

    Stage 5:
    Honoring your parents doesn't demonstrate unity.

  5. Rabbi Honigwachs was a classmate of mine at NYU School of Law. Among his many other talents and interests, he is still a practicing lawyer and has served as an associate professor of business law at Yeshiva University.

  6. Natan, I agree with Rabbi Aryeh Carmel, that pattern seeking in the torah can become addictive and counter-productive,as well as being subjective and time consuming - particularly if one has a talent for finding connections. For example, I disagree with the rationales and comparisons of the two groups in the aseret hadibrot that are featured in this post. As I see it, such comparisons are artificial and detract from an appreciation of the torah's message. For example, lo tinaf is not about respecting someone's 'domain'(that's more appropriate to the last dibra), but about loyalty.

    I, too, had once experienced a phase when I sought 'meaningful' gematriot in the torah. After a while I concluded that this was a very poor way to understand the torah. It added nothing new and only, at best, reinforced prior understandings. Years later, I was confronted with the then new popularity of using computer codes to 'find' hidden hints in the torah (Genesis)to future events and personalities. I analyzed the basic mathematical paper on the subject and concluded that it was arbitrary and meaningless. In the end, this arbitrary mathematical scheme it introduced produced the serious limitation that names formed from equidistant letter sequences could only be between 5 and 8 letters. I consider that entire enterprise to be a great waste of time and proper torah study, given the number of man-hours devoted to such matters.

    Y. Aharon

  7. Dear Rabbi Slifkin,

    Have you every pondered / considered that the names of G-d could be the seed of a fractal equation?
    Thanks for the website and the books!

  8. What about the hologram as a pattern paradigm.

  9. Love your chart on the 10 Commandments - brilliant


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