Did You Grok That?
Understanding understanding, or the difference between grokking and knowing
For the sake of being internally complete on this platform, here’s some more foundational background, brought to you by my desire to rant about how we live in a society and the knowledge that the basis for the nuance of that particular argument lives in a concept that probably deserves its own post.
Yes, the concept of grokking. This one is near and dear to my heart, and it’s become so ingrained in my particular vernacular that I pretty easily lose sight of its prevalence (or lack thereof) in other circles.
Thinking today about the informational content of well-known phrases, the things we relegate to platitude status. Shocking when, after many years of hearing and dismissing a phrase, we suddenly grok it. Like "knowing" what a bridge is without ever looking beyond the desert.
Sure, you say, cool, I can go across it and end up "on the other side." Big whoop.1
To fully grok grokking as it was originally “defined”, go read Heinlein’s Stranger in a Strange Land, or refresh your memory via the term’s Wikipedia page, because of course one exists.2 The term in its original (fictional) use was “untranslatable in Earthling language” but we have worked very hard to translate it for ourselves, because, again, of course. And then, of course, it was adopted by computer nerds, because who else reads Heinlein? (Note: Everyone should read Heinlein.)
Anyway. To grok in the modern sense is, effectively, to fully incorporate something into your own cognitive experience and “understand” it in a highly intuitive, highly personal sense. In simpler terms, perhaps, we can say that one who groks X is able to operate intuitively upon X.
To operate intuitively… Well, that’s what makes us human, isn’t it? That’s what distinguishes us from mere machines that hallucinate endlessly upon patterns without “understanding” the output on some “conscious” level. Right?
Well, maybe. That gets into a whole different can of worms. For now, let’s give ourselves the benefit of the doubt when it comes to the whole mess regarding the experience of subjectivity: we have a subjective experience of Understanding, and that’s what matters for the purposes of right here, right now.
I read a thread the other day that stuck with me:
I have been this student, and I have been this teacher. I distinctly remember coming up with a dumb little song as a last-ditch memory aid for a calculus exam in high school — clearly a poor one, as I can recall the tune but not the content — without having a shred of understanding of what the lyrics actually meant. What mattered was that I could recall the terms in order, because if I could recall the terms in order then I could auto-complete a statement that had the correct beginning. And wouldn’t you know it, Markov chain brain did me dirty.
I failed to grok a few things in that scenario. Most obviously, I failed to grok the statement that served as lyrics for the dumb little song, but I also failed to grok the purpose of studying for an exam (to assimilate loose nodes), and I further failed to grok the relationship between my strategies and my performance.3 Turns out that one of my lyrics involved a sign error; I memorized a relationship that, in practice, made absolutely no sense at all.
Bruno’s observation serves as a perfect example of the difference between grokking and knowing. To know is to possess relevant information. If you know something, you can provide a correct response when queried about that particular thing. The sky is blue because of light scattering. You can find the velocity equation by taking the derivative of the distance equation. Dinosaurs had feathers.
Knowing is an atomic measurement, a measurement of the presence or absence of a particular node in your node bag. Knowing says very little at all about how richly connected that node is in the context of your overall node collection.
You can know that the mitochondria is the powerhouse of the cell without having any sort of working understanding of cell biology. If I say, Hey there stranger, what’s the powerhouse of the cell? you’ll say, Why, the mitochondria of course! Maybe you’re a cell biologist yourself, or maybe you just saw it as a meme somewhere. Either way, your answer is correct.
Conversely, grokking is a structural measurement. How densely connected is the relevant area of a graph? Are there important edges missing? Starting from point A, can I reasonably make my way to point B? And, perhaps most importantly, how well connected is this area to other areas? Is it floating off on its own somewhere, or have I thoroughly incorporated it into my larger cognitive landscape?
Heinlein’s description seems quite literal.
It’s worth noting here that the aforementioned Markov chain brain represents a purely linguistic or syntactical representation of a world that inherently extends beyond the frameworks used to describe it. A tree and a description of a tree are quite clearly not the same thing; it makes little sense to act as if they are!4 Yet this is precisely what Markov chain brain does; this is precisely how we teach students to approach mathematics.
The distinction here is that the ability to manipulate symbols — to make use of these representations of things — is indeed necessary for communication in the relevant symbolic language. It is not, however, sufficient, given that soundness, which is inherently exogenous to the symbolic system, is a second critical component of truly meaningful communication.5 6 Intuitive operation requires one to make the link between framework and context.
As above, you may “know” the “definition” of a bridge, but without the context of something to be bridged you will not grok the bridge.
This is one of the traps that I myself have fallen into, and one that snares many others: it is very easy to mistake knowing for understanding. More often than not, we’re ignorant of what we don’t know. If we don’t know to look for context beyond the symbols, if we take every representation to be an object rather than a description, we feel not as if we have not grokked the thing, but that we have and it just wasn’t very meaningful to begin with.
Consequently, in this delusional state, we do not press further, for what’s the point of exploring when you’re convinced you’ve seen everything there is to see and it was really all just sorta meh? Don’t waste your time! Don’t peer into the shadows! Don’t question the shape of the space around you!
I cannot in good faith fault people for this particular behavioral pattern, as it can sometimes prove to be beneficial. It’s mostly just good brainstats. But. But.
Presuming we have the self-control and good taste to terminate a potential rabbithole when we do genuinely recognize that digging deeper will not contribute to a more optimal or more interesting version of the future, I’d argue that it is always worth digging at least a bit. Just a smidge. Just, like, with a trowel or something. Presume that you have not grokked when something seems just sorta meh, and make your decisions from there.
In conclusion, curiosity kills delusion, instills confusion, and leads to subgraph fusion ;)
TL;DR for real: Objects and representations are not the same thing; the difference between grokking and knowing is the difference between operating intuitively and operating syntactically; it can be easy to mistake knowing for grokking, so be vigilant and stay curious.
Since this is one of those “anchor posts” I talked about way back when, let me know if there’s anything I should expand upon, anything unclear. I’ll be linking back to this whenever I start rambling about nodes and such, so I’d like it to be as complete as possible.
Coming Soon: case studies in failure to grok; the cursed UnGrok; situational grokkage, etc. etc.
The term was, perhaps intentionally, not defined in the book until it had been used several times.
Gifted Kid Syndrome™ is some potent stuff. More to come on fixed vs growth mindsets and why “telling the kid they’re smart and talented” is not the (biggest) problem.
An interesting notion here is that the set of descriptors of an object is potentially infinite, constrained only by our imaginations. Even when considering a “simple” object, such as a (mathematical) sphere, we can extend its set of descriptors (S) beyond the obvious by examining its relations to other constructs. Of all members of the power set of S, only one element can be said to “fully” describe the sphere, namely S itself, assuming the absence of an element from a set implies that it does not apply to the object in question.
A sentence can be thoroughly grammatical regardless of whether or not it “means” anything. One could argue that any grammatical sentence is “meaningful” but this requires a constructive rather than descriptive view of the relationship between language and meaning.