The Paths of Understanding

In Kabbalah, the first three sephirot of the Tree of Life are associated with the ‘divine intellect’, in contrast to the lower seven, which are the ‘divine personality’. The relations between these three describe a theory of mind. The faculties of cognition unfold from the primordial will, starting with ‘wisdom’ (“Wisdom is first…” Proverbs 1:7), then proceeding from ‘understanding’ to ‘knowledge’.

These three principles are together known as chabad, an acronym of the first letters of their Hebrew names (chokhmah, binah, da’at). ‘Knowledge’ in this context refers to what we call empirical knowledge: observations and first-hand experiences– the intimate knowledge of having been there and done that. “Adam knew Eve.”

‘Understanding’ refers to what we call logic and math: the axioms and principles that allow us to conceptualize our experiences. The sephirah of understanding is also called “faith” (Heb. emunah). The parity of faith and reason gives an important insight into the way people frame their experiences.

The Hebrew word for ‘wisdom’ defines it as a kind of skill: the skill of life. This is the ability to balance rational and intuitive, empirical and logical, practical and theoretical considerations. You might think that wisdom flows from knowledge. But according to Kabbalah, understanding and experience proceed from wisdom. How does this work?


The biblical Book of Proverbs is an example of a  world religious literature called ‘wisdom traditions’. Wisdom traditions can be grouped with– and contrasted to– oracular, initiatory, and sacrificial cults, as major topics in Ancient and Classical religion. They represent the transformation of religion’s main regulatory mechanism from sacrificial and literal to ethical and symbolic.

Dying for your country is not actually a sacrifice; giving the local priest a goat, so God doesn’t blight your corn, is actually a sacrifice. In the world’s wisdom traditions, including post-exilic biblical texts such as Proverbs and Ecclesiastes, the emphasis changed for the first time, all over the world, starting around the time of Alexander the Great (give or take a few centuries). The change does not seem to be evolutionary, or revolutionary, but rather one of economies of scale. Sacrificial cults, where they thrive at all in the modern world, exist in highly tribalized areas– border lands and decaying urban fleshpots. The more civilized– and thus more economically interconnected– regions of the world place greater value on abstract principles and impersonal relationships. You pay your taxes in money, not goats. But when the levies break, people living in the aftermath go right back to goats, at least on a pro temps basis. And in a highly stratified society, the two cultural patterns can coexist, as in modern Miami, where Santeros and Presbyterians can pray just blocks from each other.

The Hebrew name for Proverbs is ‘Mishley‘, which is the plural of ‘moshel‘. An interesting word is ‘moshel‘. It can mean ‘an aphorism’ (like the quotables in Proverbs), ‘an example’, or ‘so to speak’. In yeshiva, I heard it constantly, in the expression, “le’moshel”— ‘for example, figuratively’. You know how some people use “literally” as a euphemism for “figuratively,” as when speaking in obvious cliche or exaggeration, but with un-ironic intent? Well, sometimes it seemed literally everything was “le’moshel” this, “le’moshel” that!

As religion has evolved from concrete sacrifices to abstract principles, the words used in religion have also taken on new significance. The original root of moshel is the meaning, “dominion, rule.” It is an attribute of God in Job. The meaning of moshel in the title ‘Mishley‘ (Proverbs) is an abstraction from rulers to rules, from the cult of personality to the rule of law, and by extension from there to logical structures and literary devices in general.

It can also mean ‘a paradigm’, in the original sense of the word: a typical case. For example, the Book of Proverbs is traditionally ascribed to Solomon, because Solomon was wise. Solomon is the paradigm– the instructional example— of wisdom, and therefore the archetypal author of the Book of Archetypes Paradigms Proverbs. Paradigms– collections of related examples– are also the basis of case law, which lays the brickwork of the Talmud (and of Sharia, btw).

Before there were ‘paradigm shifts’, paradigms were the knowledge frames students learned in Greek and Latin class. “Amo, amas, amat” belongs to the first conjugation, a category of verbs in Latin. It is the paradigm of grammatical paradigms, the first example taught in school. This is because teachers of dead languages are romantic fools, so the first word they teach students is “love.”

In a commentary on the biblical tradition that Solomon was wise, Nachmanides explains that the famed wisdom of the Egyptian magicians (with whom Moses competed before Pharaoh, and who wrote the Book of the Dead) was categorical in nature. They compiled endless tables, exhaustively cataloging astrological correspondences for everything under the sun . From this, they derived patterns, which were the source of all their power. They discovered the mysteries of writing in this way. They created the first formal grammar, the first taxonomy of language. With it, they built the first stable centralized authority, the first civilization. Magic indeed!

In a fine display of biblical literary style, Nachmanides was ascribing to the ancient foes of the legendary past (the Egyptians) characteristics really identified with his own contemporaries and competitors. Jewish scholars have been playing this card ever since the authors of Kings and Chronicles ascribed the practices of the hated Assyrians to the Canaanites their ancestors fought. Nevertheless, Nachmanides got it right. He knew history repeats itself. He successfully hacked the power of tropes. After all, he had read King Solomon’s books on the topic. “There is no new thing under the sun.”

A famous contemporary of Nachmanides was Abraham Abulafia, another major figure in the development of Kabbalah. He taught a meditative discipline that uses the phonetic analysis of words (especially divine names) as a trance-driver for achieving ecstatic states. Abulafia’s method involved decomposing words into their component sounds, then rearranging those sounds according to a pattern. When performed properly, it can induce glossolalia and automatic writing. Moses de Leon probably transcribed the Zohar using this or a similar technique.

The first European writer to explore the idea of a “generative grammar” was another contemporary of Nachmanides, Raymond Lull. Like Abulafia, Lull worked with a categorical system based on analysis of letters and numbers. Lull developed a sort of theological calculator, in which spiritual principles (virtues) were arranged into paradigms based on a system of categories.

The scholar Frances Yates wrote extensively about Lull’s powerful influence on European intellectual history. Just as the Egyptians went on to build the first civilization, the Lullians went on to lay the groundwork for the European rebirth of civilization in the Renaissance. The work of both Abraham Abulafia and Raymond Lull was known to Pico della Mirandola, the architect of the humanist revolution in ethics. Lull’s ideas were also taken up by the great mathematician and philosopher Gottfried Leibniz, who invented calculus at the same time as Newton, as well as developing the binary number system that is the foundation of all digital computers. Because of his systematic and categorical approach, he is sometimes known as “the father of Information Science.”


The grammar of a language can (largely) be described as (or inferred from) a collection of paradigms. In fact, that’s how grammars were written in the first place. A grammar is an abstraction– a mathematical model– of a language. A ‘scientific paradigm’ is also an abstraction and a mathematical model, a knowledge frame for organizing experimental data. So in both senses, a paradigm is the form you use to fill in the blanks on a predictable situation. That’s the significance of the expression, “paradigm shift.” It means updating the forms used to record scientific ideas.

If you bring up the word ‘paradigm’ in conversation, people will either stare blankly or assume you’re referring to the topic of The Structure of Scientific Revolutions, by Thomas Kuhn. According to Kuhn, every once in a while, a scientific field will throw a coup d’etat, tearing up all its old theories and declaring a new standard model. For example, the Copernican model overturned the Ptolemaic worldview, only to be overthrown in turns by Newton and eventually Einstein.

This is controversial, however. Kuhn was a literary type, not a scientist. And when scientists go looking for evidence Kuhn was right, they have trouble finding it. Some say he presents an explanation without a situation, a hypothetical cause with no measurable effect. If you chart the rate of data change (measured as scientific innovations) against the rate of paradigm change (measured as a function of scholarly references), they line up just like a technical trading model or a horoscope– which is to say, not at all. The rate of technological change bumps along in a logarithmically smooth progression, completely uncorrelated to the shifting phases of the “dominant paradigm.”

Actually, there is an exception to this claim. In mainly interpretive (as opposed to empirical) fields, such as literature and art history, there is evidence for the influence of paradigm shifts. Innovation in art and literature is driven by fashion, not physics. Untethered from the relentless pull of gravity closer to the earth’s surface, structures at the highest levels of the ivory tower grow to arabesque and gigantic proportions, periodically shatter in the face of new media and new aesthetic dispensations, and then grow again, like strange fungi.

So scientific paradigm shifts are not necessarily generative of scientific change. But scientific paradigms are nevertheless generative of scientific writing, as the understandings held in the minds of the (grant) writers and readers. And they change all the time. I think this is like the way Apple comes out with a new upgrade every year, so you have to buy the latest version. It may not be better, but it’s guaranteed to be newer.

You can look at Science synchronically as the state of the art in human knowledge, or you can look at it diachronically as a timeline of changing paradigms. Seen diachronically, data flows through a series of scientific paradigms like frames in a comic strip, appearing now as a falling apple, now as a bowling ball on a rubber sheet, now a snowflake in a collectible globe.

Scientific paradigms are like the tubes the Interwebs are made of, encapsulating observational data in messages that transmit knowledge between users of language. The Internet itself is a scientific paradigm, a take on Communication and Information theories. The TCP/IP protocols are each linguistic paradigms, defining knowledge frames for the interpretation of messages. Other paradigms also exist. Once they were more common, for example NetWare and NetBIOS networks in the 1990s. But language evolved, and the Internet is now the dominant species.

The rules of nature, like the rule of law, and like the rules of grammar, are represented as an arrangement of examples. A scientific paradigm, then, is a productive arrangement of examples. What it produces is called a technology. A productive arrangement of examples, or “generative grammar,” is also what Noam Chomsky calls the human faculty of language. Spoken language is an organic technology. It provides the ability to describe and interpret cognitive (goal-oriented) processes, as narratives. Written language and the Internet extend that ability to other media than sound. They are all technologies, evolved or invented by the human brain, to communicate examples, goals and expectations.


Kuhn has been influential in popular culture, but a more common term than ‘paradigm’ among most scientists is ‘model’. In computer science, a paradigm is called a ‘schema’, and the evidence is called ‘data’. Scientific models are made of math, but they work just like grammar does. They are knowledge frames, templates where you substitute for X. Scientific models are applied to data. This is known as “filling in the blanks.” The result is a scientific theory. The better the theory, the better the math fits the evidence.

Domain Abstract Concrete
science theory evidence
computers schema data
language grammar message

According to pragmatic philosophy, knowledge is demonstrated by the ability to predict and control phenomena, i.e. generate technology. “By their fruits you shall know them” (Matt. 7:16). The pragmatic definition of a ‘scientific theory’ seems to be that “theory = math + evidence,” where ‘math’ is predicting the weather and ‘evidence’ is winnings at the craps table.

Here’s what happens, right at the heart of science, in the belly of the beast: A game is played, and wagers are taken. It’s like Iron Chef, except they cook up gambling strategies instead of souffles, and there’s no big reveal of the secret ingredient at the start. Instead, players have to figure out how to win, without knowing what game they’re playing. Go!

Once people commoditized the trick of making up new mathematical structures, different maths began to compete and cooperate in a marketplace of ideas. The ones that are better at predicting and controlling phenomena (winning at the craps table, or predicting the weather) eventually wind up leading to the best new tools and technologies, and to the most successful grant proposals and article citations. This is called ‘fecundity’, because it leads to new generations of scientists having new hypotheses to test. Successful theories generate successful technologies. Consequently, whichever math is closest to the real rules of the game, wins the game.

Science = (math +  evidence) \div technology

It doesn’t always work perfectly. On the other hand, we did walk on the moon.


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