Abstraction layers and learning

The other day I heard an interview (in French) with electronic music megastar Jean-Michel Jarre (who is, incidentally, the estranged son of film composer Maurice Jarre and the ex-husband of actress Charlotte Rampling).

Paraphrasing one segment of the interview from memory: “Some people tell me that electronic music is abstract. On the contrary! Especially with analog instruments, it’s visceral, hands-on. I twist this knob or push that pedal, and I immediately hear the sound change in response. It’s classical music that is more abstract! They play off a score, which is an abstract representation of the music.”

Bingo. To borrow a term from information technology, the score is one “abstraction layer” above the music. A jazz music “lead sheet” would be one more abstraction layer above: it specifies the lead melody, the chord progression, and the meter — and the details on how to translate the progression into notes are left to the performer!
The next higher abstraction level is sometimes seen when experienced musicians are jamming together, and all the lead player needs to say is “slow 12/8 blues in G minor”: everybody else knows what to do and fills in the details on the fly, according to their best musical judgment. (Fixed chord progressions like “the blues” as improvisational frameworks are not a recent invention: suffice to mention “La Folia” in Renaissance and Baroque contexts.) An Indian raga is, likewise, a meta-structure for improvisation.

A paradigmatic example of abstraction layers in information technology — one that many readers will be familiar with — are network addresses. Individual network cards have a permanent, unique “MAC address” or “hardware address”, six bytes in hexadecimal notation: something like 4c:33:73:9d:40:42 We do not use such addresses directly to send Email or access web servers though, since everytime a server or even network card would go on the fritz, you’d have to update directories.
So one abstraction layer above that, we have the numerical addresses of the form These can be defined manually on a device, or (this is what happens in most home WiFi networks) assigned using a DHCP (dynamic host configuration protocol) service. You replace a server or swap out a network card? Update the DHCP configuration table, and you’re good to go.
But if you moved to another provider, you’d still have to change addresses. Or you may have so much traffic that you need to deploy multiple servers, and load-balance traffic between them. Which is why we have yet another abstraction layer above that: the more conventional, human-readable addresses like www.pjmedia.com or www.berkeley.edu A domain name server (DNS) keeps track of which name corresponds to which number (or knows which other DNS to ask if it can’t resolve the query from cache), and hence you only need to deal with the “link”: you can leave the concrete details on how to translate this into an actual connection to the “abstraction layers” below.

The above puts me in mind of the laments of a friend of mine (a college lecturer in a humanities subject) about the atrocious writing of his students. Effectively, he says, the students have only learned the English language by imitation: they parrot words and phrases, rely on their spelling checker to fix spellings (sometimes coming up with unintentionally hilarious malapropisms as they do so), and often display a disregard for grammar and syntax that has non-native speakers like myself flabbergasted. The thing is, grammar and syntax are abstraction levels above the words: they can be learned by immersion — but that would have to be by “neural network training” from a very large corpus of high-quality written text. (I frankly didn’t know most of the grammatical rules in English consciously — but could apply them just fine on autopilot, as I’d been a voracious reader from a young age. Only when I found myself needing to explain edits to scientific papers — and of course learned that “it sounds wrong otherwise” is not an acceptable answer to thinking people — did I end up hitting the grammar and usage books.)
Prose style and essay structure are, of course, yet further abstraction levels above. But the problem is much broader than language: at one research institution where I was a guest faculty member, I saw distressing levels of learning by imitation in the lab — newer grad students basically being shown “this is how it goes” by the older ones. Now if this is just a matter of “kickstarting” then this is fine — the real problem was that only a few had any desire to actually understand what they were doing. (This became painfully clear when they attempted to write a paper — which in practice usually boiled down to compiling tables and graphs as required, and the professor or his amanuensis writing the actual paper—or rewriting the sorry excuse for a manuscript so thoroughly as to qualify as writing from scratch.)

Pretty much everybody who lives near a Jewish community has heard of Chabad (a.k.a. the Lubavitch movement): Chabad (חב׳׳ד) is, however, originally the Hebrew acronym for a much broader concept: the three levels of understanding. This is how I see them outside a religious context.
D (ד) stands for the lowest layer: da’at ([factual] “knowledge”)
B (ב) stands for the layer above: bina (“insight”) or, if you like, analytical understanding. That which is required for the higher “abstraction layers” of learning.
Ch (ח) stands for the highest layer: chochma (“wisdom”), or, if you like, synthetic understanding, creativity. The levels of “meta-insight” that allow you to apply the structural principles of that which exists, for creating something new.

Our current educational system effectively sacrifices insight on the altar of creativity (or, worse, the students’ self-esteem) — while at the same time, perversely, ensuring that students only have quite shallow knowlegde by declaring a kind-of war on memorization at exactly the ages children most easily learn by rote. The end products are students that have never progressed beyond some nuts-and-bolts knowledge picked up by imitation—and even that is not to be taken for granted.

The system stunts students while claiming to empower them, and it boosts a brittle, hollow self-esteem that shatters on the first contact with reality. It “creates a desert, and calls it peace.” Or self-esteem, “or something”

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