Why Anki Works: Part 4
Why facts work
Application (part 3) is all well and good. Back to theory (continuing from part 1 and part 2).
What’s a fact? It’s a true statement about reality. As opposed to a true statement about delusion, then. Fact: Harry Potter was sorted into Gryffindor. Read another book. “Harry Potter” was a character in a moral tale for children and Twitter pundits who was sorted into a house called “Gryffindor.” Fact: you should read another book. You’re breaking the is-ought distinction. They forced me to read Plotinus in college, not Hume.
XI. A Theory of Facts
Which of the following three statements are facts?
Helsinki is the largest city in Finland.
Neon-hydrogen excimer lamps emit a narrow band of radiation with a peak at approximately 121.26 nanometers and a width at half-max of 0.03 nanometers.
Abraham Lincoln was elected to three consecutive terms as president of the Moon.
Definitely Fact 1 and definitely not “Fact” 3. I can’t tell with Fact 2. You’ll have to trust me that Fact 2 is a fact. That’s an appeal to authority. So is half of what you learn in school. Are you going to make me remember it? I don’t know, can you remember it? I’ll definitely remember the third one.
Why is the third statement here easier to remember than the second statement is? It’s not because of its truth value. Rather, it’s because
facts are mappings between concepts, and
a fact is learned when the concepts are known well enough to make sense of the mapping.
“Abraham Lincoln,” “president,” and “moon” are all comprehensible concepts. Correct. That’s because truth value isn’t relevant for learning. You’ve redefined “fact” to mean “any statement,” regardless of truth value. I didn’t, your brain did. I thought we were going to learn what facts are. No, we’re going to learn how facts work.
Consider the following additional two statements, both of which—I promise you—are true. Which one did you learn something from?
Lord North was Prime Minister of the United Kingdom during the American Revolution.
The stemma of Tacitus has only one witness.
Did it commit a crime? No, statement 2 is a pretentious way of saying that we only have one surviving manuscript of the Roman historian Tacitus1. Why didn’t you just say that? I didn’t do a Classics degree for nothing.
Even if you’d never heard of this Lord North figure, you were likely able to comprehend Fact 1 and learn something new. That’s because Fact 1 is a mapping, or linkage, between a new concept (this Lord North guy) and two concepts you were already quite familiar with (Prime Minister of the UK and American Revolution).
You might have heard of the Roman historian Tacitus, but odds are good (unless you’re a classicist or historian) that you don’t know what a stemma is. Witness is not an unusual word, but it has a particular and specialized meaning in this context.
No learning occurs. We can memorize it on its own and repeat it on command (The mitochondria is the powerhouse of the cell!), but so can a parrot.
We can go further. The reason that the concepts PM of the UK and American Revolution are comprehensible in the first place is that those concepts are nodes for multiple other facts which, themselves, are linkages between further concepts.
Here is a mental map of the average American’s understanding of the concept PM of the UK when they first become aware of it at the age of 5 or 6:
This is comprehensible only because we’ve already got the concepts “president (of the US)” and “Britain”.
As we mature, PM of the UK becomes the central node for other facts:
Indeed, “prime minister of the UK” is defined as the node between those facts. The concept is the node where all those facts intersect, and the linguistic string “PM of the UK” is an index to that fact, like a variable name on an array or dictionary.
I can already hear the education gurus in the back of the room. We didn’t actually learn anything about Lord North, we just learned a factoid. Learning requires understanding, not just rote memorization.
Au contraire: we understand more of “Lord North was PM of the UK during the American Revolution” than we understood of “the stemma of Tacitus has only one witness”. Yes, but— “Lord North” is a semi-orphaned concept because he’s a trivial intersection with only one fact on it. We don’t know anything else about the man2, but we can probably work some other things out by looking at the facts the other concepts included intersect with: for example, his premiership was after Robert Walpole’s, but before Pitt the Younger’s. That’s just pattern-matching. Yes. All higher-level analysis ultimately is.
No learning can occur when a fact has no connections to the broader network, or has too few connections:
Pseudofacts, on the other hand, can fit into the schema just fine.
Learning and understanding something seems to require a decent connection density; the concepts inherent to some fact need to have lots of other connections to other concepts in the brain. “Understanding” and manipulating a fact involves travelling these connections and perhaps creating new ones.
An orphaned fact simply has fewer connections and nodes it can make.
This is, I suspect, a large part of why the mind does well with things it learns in lists and groups even if the lists are artificial in some sense: the act of making the list creates more connections.
We can also, now, return to the question of why cloze deletions work so well. Cloze deletions choose some “fact”—or connection between concepts—and ask the user to pick the correct pathway out from all the various connections that intersect at the given concepts to find the right node.
Free recall works even better, because it doesn’t get you going on the right pathway, but forces you to pick it out from scratch:
We can now start theorizing what a chunk is: it’s an index to a pathway. We don’t index concepts themselves, we’re indexing a pathway from a prompt to the concept. (This assumes there’s a hardwired distinction between concepts and pathways/facts. I don’t know enough neuroscience to say. I wouldn’t be surprised if there isn’t but, again, all models are wrong but some are useful).
Not shown in the diagrams above are problems of directionality. These make more sense if you assume that the mind indexes certain pathways, rather than the concepts themselves:
And this gives us a way to think about the various kinds of forgetting.
And that’s learning3; go do some. τέλος.
(Return to part 1, part 2, part 3. If you would like to get in touch with me or have me come talk to your school’s teachers, leave a comment and I’ll be happy to email you).
(I don’t think there’s going to be a Part 5, per se. There may be an appendix post digging into what this model might have to tell us about the structure of language.)
Technically, we’ve got multiple manuscripts, but none of them overlap.
From what I’ve read, there isn’t much else to know, at least not anything terribly interesting.
This model is obviously insufficient for a subject like woodworking and doesn’t get too deeply into how to reinforce those pathways (via deliberate practice, etc). You can’t solve everything.
Thanks for the clear explanations.