1st order stuck vs 2nd order stuck and structural epistemologyDate: 2020-11-20
Note: I think this is an advanced topic on learning. I mention this for two reasons: 1. it’s not something ppl should be worried about early on, and learning the basics is more important; and 2. I’m less sure about this than my other posts on learning so far. I would still be surprised if there were significant errors, though. I’m like 8/10 confident on 1st and 2nd order stuck. I’m 9+/10 confident on the structural epistemology parts.
What happens when two people learn the same thing? It’s common sense that there will be some differences in what they learn, how well they can apply it, etc. Some of that is due to pre-existing knowledge, but is there more to it?
Consider: Alice and Bob want to learn about something particular, and have similar background knowledge. The first two concepts they need to learn are X and Y. After that, there’s a third concept, Z, that builds on both of those. There’s also concept W that’s sort of similar to (X,Y,Z) but a bit different too.
Let’s consider a concrete example: building a computer. Alice and Bob have finished high school and want to build a computer over the christmas break. They will need to learn about the components of a computer so they know what to buy (cpu, motherboard, ram, ssds and/or hdds, the case, etc). They also need to know some super-basics about electronics: how to plug all their components together, what cables they’ll need to use or buy, calculating power consumption, etc. Those are concepts X and Y. Concept Z is how all the components work together in a complete computer and which configurations work for particular purposes (e.g. gaming, office work, video editing, streaming, music creation, digital art, etc). They need to know some other things too (like how to install an operating system, and background knowledge) – we don’t need to consider those things for this example.
Once they know Z they can choose and buy their components and then put it all together. They’re both successful.
As it happens, both of them applied for electrical engineering courses at university, and both are accepted. At the end of their break, they take their computers and their knowledge about computers – (X,Y,Z) – with them to to university.
Before we continue let’s think about what Alice and Bob learned while studying (X,Y,Z). Can we find out if they learnt the same thing or not? What does the same thing mean in the context of learning?
I think there are two important ways to look at whether they learnt equivalent things or not. One of them is about the tasks they can perform; and the other is about the ideas themselves.
If we’re only concerned with the results that certain knowledge gives, we are talking about the knowledge’s denotation. If Alice and Bob can perform the same tasks (they get equivalent results with only negligible differences) then we say they have the same denotational knowledge.
We can say that Alice and Bob learned the same thing because they both built a computer, and they can both answer the same questions about the configurations that make sense for certain use cases. This is like a standardized test that are common in schools. It’s a definition of a checklist of inputs (questions) and outputs (answers) that students should repeat. For some types of tests, like text analysis in English, the answers aren’t explicitly listed; rather, qualities of good answers are listed (like ‘identifies techniques’ or ‘discusses the interaction of themes’, etc). For other tests the answers are explicit (e.g. multiple choice tests); and finally some tests have a mix of both (like maths tests, where the final answer is explicit but the algebra to get there is not).
What if we’re concerned with the other option: the ideas themselves? How can we compare those?
We can’t directly observe ideas. Even if we could see inside Alice and Bob’s brains (something they might not like), how would we know what to look for? We can’t just ask them either: they can’t tell us exactly what their ideas are, and we can’t ask them questions on the topic either – that would basically be like a standardised test. So how do we know if they learnt equivalent things?
Even though we can’t directly observe ideas, there is a way ideas are used other than to produce results – ideas are building blocks for other ideas. This means that if Bob and Alice learnt the same thing, then they should be able to build similar new ideas with their (X,Y,Z) building blocks.
Alice and Bob will learn a new idea similarly if they have similar building blocks – if their knowledge has the same structure. It’s like they have same same lego set of ideas. If their knowledge has different structures, then they can’t build the same things, like if they had lego sets with different pieces. Sometimes they can build the same things, but not always. We can say Alice and Bob have the same structural knowledge if they can build the same ideas.
Let’s consider Alice and Bob learning a basic concept, W, about electronics in first yr uni and how it might interact with (X,Y,Z). W is similar to (X,Y,Z) but also different. Alice and Bob are told that to make electronics you need components and one of a circuit board, or a bread board, or maybe just a mess of wires. They’re told about attaching components to each other, and power, data, and ground and things like that. This is concept W. Alice and Bob each have a different question for the tutor:
How do you connect components if they’re the wrong shape, or have different wires?
His full idea was something like: computer components connect together using cables or directly using sockets. The wire components of particular cables go with particular connectors only – they don’t go with other connectors. The connectors you need on a cable are the male/female versions that correspond to the connectors on the devices. If a device connects directly, then you can use a cable with one male and and one female end to connect the device somewhere else. If you plug everything together with matching sockets, then it’ll all work out.
Bob asked his question b/c his understanding was at the level of emergence of cables and connectors and things you could plug together.
How can we replace components if some components are out of stock or too expensive?
Alice had a different idea, something like: sockets and connectors are chosen to make sure ppl plug the right things together. Manufacturers choose particular wires and shrouding based on: availability and price, the requirements of the components being connected (i.e. standards like HDMI), what the customer expects, and how the cable will be used (are there lots in a bunch, does it need to go round corners, etc). You can cut up multiple cables and join them together (splicing) to make cables with different combinations of male/female connectors, to change between compatible connectors (an adaptor), or to replace faulty wires – provided you are combining wiring of high enough quality (excess capacity). Cables are only there to deliver power to components or transmit signals between them.
Alice asked her question b/c her understanding was at the level of emergence of wires and semi-conductors with some economics thrown in.
I hope you can see how their knowledge differs in structure even thought they’re both able to use it to put together the same computers, diagnose the same problems, know which replacement parts or upgrades to buy, etc.
Structural knowledge matters when we want to build on, or change knowledge. When we want to use it for different things, or apply it to new situations. If the structure of (X,Y,Z) is different in different people, then they can still have the same denotational knowledge, but they will diverge when they learn new things.
Just because some knowledge has the same denotation does not mean that it has the same structure.
But ideas in the mind are different from ideas that are written down. We don’t know how to compare ideas directly. However, we do know some things about people and how ideas are created. Ideas aren’t written in to your brain like things are written on paper. Ideas are created through an evolutionary process – exactly how we don’t know. You learn something when your brain creates an idea that explains the things you’re trying to understand – or, for simple things, when you can repeat an action or achieve a result. That means your brain needs to combine pre-existing ideas repeatedly (thinking) until it finds an idea that satisfies some success criteria. Your brain can do a lot of auto-criticising; that’s when you’re thinking but it’s like work, like you’re waiting for your unconscious mind to tell you the answer. Sometimes you have an idea that’s nearly right, only to learn of a criticism later (maybe you came up with it or someone else did). Our brain makes guesses and nothing will guarantee any of those guesses are correct, but we can know when something is not correct if we know a criticism of it.
When two people learn the same thing, they might have the same denotational knowledge (within some scope), but they’ll ~never have exactly the same structural knowledge. There will always be some differences.
When you get stuck, there are two ways that can happen.
First, you can stop learning all together (this can be specific to a single topic or it can be bigger, too). This is 1st order stuck. It’s the normal kind. It’s fixed in the normal ways and normal techniques work. In the example above, Bob was first order stuck, he just needed to learn some new things about circuitry to move on.
You can be 1st order stuck because of problems with your learning method. You could be doing the wrong type of practice, or not learning from certain media types (e.g. if you hated videos), or overreaching in general.
Second, you can be making a mistake in the act of knowledge creation; you can have a structural problem with the results of your method. This is like whether you’re creating highly general knowledge or not. This is different to 1st order stuck b/c you can still make progress, and technically that progress can still be unbounded. But you will need to do more maintenance of your existing knowledge and it will be more fragile.
This is being 2nd order stuck and means the rate of your learning will suffer. You won’t be able to come up with ideas as well as exceptional people, you won’t be able to use ideas as well as exceptional people, and most importantly you won’t be able to learn as fast as exceptional people. It’s overhead on your velocity and acceleration, not on the distance you can travel.
2nd order stuck isn’t as clear cut or pervasive as 1st order stuck typically is. It can vary by topic.
Authors note: I think this is currently the limit of my understanding.
How do you tell if you’re 2nd order stuck and on what? How do you learn/practice/fix such a mistake? What are the techniques to get 2nd order unstuck?
Can you turn 2nd order stuck into 1st order stuck? … maybe? The only way I can think of is to learn about learning, but I’m not sure that’s enough.
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