The Power to Teach Concepts Better

by Liron 2mo23rd Sep 20198 min read14 comments

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This is Part VIII of the Specificity Sequence

When you teach someone a concept, you’re building a structure in their mind by connecting up some of their mental concepts in a certain way. But you have to go in through their ears. It’s kind of like building this ship-in-a-bottle LEGO set.

In this post, we’ll visualize what’s happening in a learner’s brain and see how a teacher can wield their specificity powers to teach concepts better.

Mind-Hanging A Concept

Reading a startup’s pitch begins as a learning exercise: learning what the startup does. In How to Apply to Y Combinator, Paul Graham writes:

We have to read about 100 [applications] a day. That means a YC partner who reads your application will on average have already read 50 that day and have 50 more to go. Yours has to stand out. So you have to be exceptionally clear and concise. Whatever you have to say, give it to us right in the first sentence, in the simplest possible terms. […]
The first question I look at is, “What is your company going to make?” This isn’t the question I care most about, but I look at it first because I need something to hang the application on in my mind.

It’s worth unpacking and visualizing this part of PG’s advice, because we’ll see that the power to mind-hang the concept you’re trying to communicate is closely related to the power of specificity. Stay tuned for that.

First, one more snippet from PG:

The best answers are the most matter of fact. It’s a mistake to use marketing-speak to make your idea sound more exciting. We’re immune to marketing-speak; to us it’s just noise. So don’t begin your answer with something like “We are going to transform the relationship between individuals and information.” That sounds impressive, but it conveys nothing. It could be a description of any technology company. Are you going to build a search engine? Database software? A router? I have no idea. […]
One good trick for describing a project concisely is to explain it as a variant of something the audience already knows. It’s like Wikipedia, but within an organization. It’s like an answering service, but for email.

I recently helped the founder of PierShare craft his YC application. For the “What is your company going to make?” question, he had originally written the first sentence:

PierShare is a new way for boat owners to easily rent a dock.

This is actually a pretty good answer because it’s matter-of-fact, not marketing-speak, and I can already guess at a plausible Value Prop Story. Still, I recommended taking PG’s advice to describe his company more concisely as a variant of something the audience already knows:

Liron: Why not just write that you’re “Airbnb for boat docks”?
Founder: Hm, how is that better though?
Liron: It builds the reader’s mental model better and faster. Notice how in the next part of your application, you currently spend a lot of words describing these predictable qualities of your business:
* You have a user-friendly online system for both parties
* You handle the payment processing
* You handle the insurance stuff
If you just say “Airbnb for boat docks”, they instantly load a mental model of all that stuff, so you don’t have to spell it out for them.
Founder: But it has important differences! Like, Airbnb’s typical user just makes a one-time payment to rent someone’s home for a night or two, while our typical user pays an ongoing monthly subscription to stay at someone’s dock.
Liron: I agree that this difference is important enough to mention in your application, but still, the fastest way to build their mental model of your business is to start with their pre-built mental model of Airbnb and then apply a patch. This is true to such a degree that if you don’t invoke Airbnb as a shorthand to explain your business, they’ll be wondering why not.

Here’s what we came up with in the end:

PierShare is an Airbnb-like subscription service for boat docks.

This diagram of the reader’s mind illustrates how we’re mind-hanging the concept of PierShare:

Since we know the reader is a savvy investor, it’s safe to assume that the concept of “Airbnb” has an associated web of preexisting knowledge and intuitions. The reader knows that Airbnb is a marketplace broker, that marketplace brokers cater to two types of users: renters and rentees, that Airbnb has a streamlined customer experience, etc.

Compare this to “a new way for boat owners to easily rent a dock”:

Sure, we can expect some preexisting knowledge and intuitions about renting stuff in general, and boating/docks in general, but it doesn’t mind-hang the way “An Airbnb-like subscription service for boat docks” does. For example, the investor won’t be able to confidently predict that PierShare handles payment processing, without reading farther into the application.

Specifics Are Mind-Hangers

Here’s the complete answer we crafted for “What is your company going to make?” Can you tell what trick we’re using in the second and third sentences?

PierShare is an Airbnb-like service to match owners of water-docked boats (4M individuals in the US) to private dock owners (500,000 individuals in the US).
For boat owners who typically pay $1,000–1,800/month to dock their boat (that’s $12–22k/yr, and they need this for their boat’s 10- to 15-year lifetime), we let them find a privately-owned dock and save 30% ($4k/yr).
For dock owners (people who live adjacent to a waterway) who typically leave their docks empty because it’s too much friction and hassle to rent it, we give them an easy $1k+/month revenue stream.

That’s right, we’re hitting them with two Value Prop Stories! (Notice that a two-sided marketplace business always needs two Value Prop Stories: in this case, one for boat owners and one for dock owners.)

One reason for using Value Prop Stories here is that we want to show off the strength of the value-delta for both sides of the marketplace: putting an extra $4k/year into the pocket of each boat renter and $1k/month into the pocket of each dock owner.

But the other reason we’re using Value Prop Stories is simply because they add specificity to the description of what the startup does:

  • Dock owners are people who live adjacent to a waterway
  • Boat owners pay a lot for docking
  • Every year, there’s a lot of money at stake for both

We’re using Value Prop Stories to slide “Airbnb for for boat docks” down the ladder of abstraction.

And in general, any time you’re trying to explain a concept to someone — in this case, the concept of PierShare — it’s helpful to slide it down the ladder of abstraction because specific details function as mind-hangers.

Teach With Examples First

When you want to teach someone an abstract concept, keep in mind that people love climbing the ladder of abstraction from bottom to top. Brains are good at generalizing from specific experiences, but bad at grasping general concepts directly from generally-worded statements.

Here, let’s ask your brain to grasp the following generally-worded statement of an abstract concept:

Don’t Fall for the Sunk Cost Fallacy: General Statement
When deciding whether to stick to a plan or change course, your current plan’s sunk costs shouldn’t affect your decision, as long as you compare the total expected value of each option.

Did you manage to load the general principle into your head? Unless you immediately recognized this as a familiar principle, you probably had to read the description multiple times, slowly.

As your author, I should try not to make your brain do this! It’s bad explanatory writing to hit you with a general principle without first giving you a mind-hanger for it. Look at this mess of dangling concepts I tried to fling at you:

While the concepts I tried to fling at you have some internal structure to hold them together, they’re currently just dangling over your brain’s huge web of preexisting knowledge and intuitions. Frustrating, right?

But you probably won’t even think to blame me for putting you in this situation. You’ll probably blame yourself for being too “dumb” to deal with the dangling concepts that the “smart” author is trying to teach you.

Why did I put you in this compromised position? I guess I expected that you’d just keep my general statement dangling in your precious working memory, and keep reading onward to the next thing I’m going to say.

But now that we have the language of mind-hanging and dangling, we can see that this is an authorially-rude thing for me to do:

Hey chump, just keep reading my explanation while your brain thrashes on my dangling concepts. I have no problem hanging this in my mind, so what do I care? I’ll give you some mind-hangers whenever I feel like it.

Alright, let’s see the kind of mind-hanger I should have given you.

Don’t Fall for the Sunk Cost Fallacy: Specific Example
Imagine you’ve paid $50 for tickets to see your favorite band perform a concert, but on the day of the concert, an unexpected blizzard hits your town. Now you have to decide whether to make the stressful one-hour drive through the blizzard to see the concert.
First, let’s assign dollar values to all your options (approximating your utility function):
We’ll define $0 to be the baseline value of your average evening when you haven’t bought concert tickets.
Seeing the concert is worth +$80 to you.
(In other words, you were happy to buy the ticket for $50, but you wouldn’t have bought it for more than $80.)
Driving through the blizzard is worth -$100 to you.
Now all you have to do is compare the expected value of your two options: You can drive to the concert for an expected value of (-$50 ticket) + (-$100 blizzard) + ($80 concert) = -$70, or do something else for an expected value of (-$50 ticket) + ($0 average evening) = -$50.
Since -$70 < -$50, you should forget about the concert. It’s not worth going because of the blizzard. But if you’re not trained in decision theory, your intuitive thought process might go like this:
“The concert is worth +$80, and I’ve paid $50 for the tickets, so if I don’t drive to the concert, I’m missing out on the value of the concert and the value of the tickets, which is $130 of value!”
Here we say that your intuition is committing the sunk cost fallacy, because the non-refundable ticket price ($50) is a sunk cost which has no bearing on how much value you’ll gain or lose via your current decision whether to drive to the concert.

Hopefully that example was pretty easy to follow. And now that you’ve loaded it into your mind, you can use it as a mind-hanger to understand the general statement I’m trying to teach you:

Don’t Fall for the Sunk Cost Fallacy: General Statement
When deciding whether to stick to a plan or change course, your current plan’s sunk costs shouldn’t affect your decision, as long as you compare the total expected value of each option.

The general statement probably feels more understandable now that you’ve installed mind-hangers for it.

My goal here obviously wasn’t to teach you about the sunk cost fallacy, it was to show you what it feels like when an author forces you to read a general description of a concept instead of spoon-feeding you specific details that build on your preexisting knowledge and intuitions. It’s easier to load a generic concept into your head if you first install mind-hangers for it.

By the way, my specific story even helped me understand the general concept better, because I realized that the -$50 of buying the ticket appears in both Expected Value terms, so it cancels out of the expected-value comparison. So I was able to connect my abstract concept of “sunk costs” more directly to my abstract concept of expected value:

The mind-hanging power of specific examples helps you teach others better and teach yourself better. Good to know, right?

In 2007, I stumbled on a life-changing blog post: My favorite pedagogical principle: examples first! by the mathematician Tim Gowers. It has transformed how I’ve been communicating concepts ever since. It was also the first inkling I ever got about the power of specificity. (It was a few more years before the dam broke and the other powers came rushing into my purview.)

Here’s what Tim says is “a very simple idea that can dramatically improve the readability of just about anything”:

Present examples before you discuss general concepts.

So I’m not making an original point here; I’m repeating Gowers’s point, albeit with a bit less math. I’m also classifying “teach with examples first” as a kind of specificity-based mind-hanging power that deserves to be collected and showcased together with other specificity powers in a stupendous listicle.

The Tragedy of Human Working Memory

Why does our reading or listening comprehension break down when we’re presented with a general concept before a specific example?

When you were first reading my 32-word general statement about avoiding the sunk cost fallacy, it taxed your working memory more than usual, and probably overloaded it. On the other hand, when you were reading my example of driving through a blizzard to see the concert that you bought tickets for, it didn’t demand as much of your working memory, even though the total number of words was almost 10x higher. Why is that?

One of the saddest things about the human condition is how underpowered your working memory is. Your brain has 100B neurons and is the smartest thing in the known universe, but remembering a seven-digit phone number is a struggle — are you kidding me?

You can be a highly intelligent person, but if I fling a handful of dangling concepts at you and you’re not ready with a sturdy mind-hanger, you’ll just try to fasten them down with whatever you can: a few measly strips of working-memory duct tape.

It’s sad because the amount of working memory we have might be an easily-tweakable genetic parameter. Natural Selection might have been stingy with this parameter’s value because we had enough for our ancestors’ needs. But now we’re trying to build a technological society and it’s clearly not enough working memory for our needs.

A superintelligent mind with a reasonable amount of working memory could process generic statements all day long and never whine about dangling concepts. (I feel like the really smart people on LessWrong and Math Overflow also exhibit this behavior to some degree.) But as humans with tragically limited short-term memories, we need all the help we can get. We need our authors and teachers to give us mind-hangers.

Mind-Hanging vs. Grounding

We’ve defined grounding a term as describing a specific stimulus that you’d mentally classify within that term. That kind of description falls within the shared space of both conversation participants’ preexisting knowledge and intuitions. So any grounding is also a valid mind-hanging.

On the other hand, you’re allowed to mind-hang a concept on any other concept that your conversation partner is familiar with, so it’s sometimes possible to offer people mind-hangings that aren’t also groundings. For example, if our conversation partner was extremely familiar with decision theory, our general statement about the sunk cost fallacy wouldn’t be dangling concept in their mind; the whole structure could hang entirely within their preexisting knowledge and intuitions.

Next post: Is Specificity a Mental Model?

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