How To Build Knowledge Skyscrapers

Knowledge skyscrapers are a metaphor to help explain how learning works. Floors contain ideas. Higher floors build on ideas from previous floors. When learning, floors (new knowledge) are constructed one at a time on top of previous floors. There is advanced, complex knowledge at the top of the skyscraper.

Here’s how it works:

1. The max height of your building is at most 10 floors more than the first floor with a major error. Errors can’t support the weight of too many more floors above them.
2. The effects of major errors increase with distance. A major error on floor 5 means floor 6 will be damaged at least a little, while floor 15 will definitely be super broken if it exists at all.
3. You can’t ignore old errors. They don’t become irrelevant when they are far away. It’s kind of like how taking lower Jenga pieces out is more dangerous. Or think of a support beam that isn’t strong enough: put 1 floor on top of it and maybe it still holds up, but 10 floors built on top would collapse.
4. To build a higher building, you must review previous floors for major errors.
5. When things are going smoothly, you can start looking for major errors at the current level and work downwards floor by floor.
6. When things are harder, you can go down 10 floors and start looking for errors there and work your way up if you don’t find any. You want to quickly find the earliest error. To do that, you should go down many floors at once so you have a good chance to go past it. Don’t go down floor by floor, because that’s too slow for descending to find underlying causes.
7. A “major” error is an error that blocks your ability to build more floors in your skyscraper. It’s not an exact categorization but, roughly, errors are either minor/small/local (annoying on this floor but irrelevant to other floors) or major (can’t hold the weight of many more floors above).
8. The vast majority of errors either limit additional floors to a number from 0-10 or allow thousands of additional floors. “Medium” errors (e.g. you can only build 100 more floors on top of it) are rare. This is related to the concept of a jump to universality.
9. There are several converging, abstract reasons why medium errors are rare. But let’s look at it in terms of actual skyscrapers. Many possible errors won’t limit the number of floors at all, e.g. if the curtains on floor 7 are ugly (in the field of writing, those ugly curtains could be a non-confusing typo). And for structural errors that are unsafe to build much on top of, usually the errors will show up pretty fast as you put weight on them. If you have faulty concrete, it’s probably going to cause a problem when adding the next few floors. It’s implausible that the concrete is flawed in a way that could support 92 more floors but not 93. It’s hard for a problem with the building to be effected by such a distant floor in a crucial way. But it’s plausible that flawed concrete could hold the next 2 floors but not 3.
10. Unlike real skyscrapers, ideas scale up exponentially instead of linearly. In short, think of every floor as being twice as heavy as the previous floor.

Critical Rationalist Objections

Critical Rationalist (CR) objection: There’s more than one way to reach a conclusion. Many different knowledge skyscrapers are valid.

Reply: Yeah sure, so what? Whatever one(s) you’re building need to be non-broken. CR never said “Numbers, counting, addition, multiplication, exponentiation, algebra, calculus – learn them in any order, it doesn’t matter.” CR denies that it’s literally impossible to learn stuff out of (the standard) order, and I agree with that. CR also says to be tolerant about intellectual differences instead of assuming that everything different is bad, which I also agree with.

CR objection: Foundations don’t matter.

Reply: No, CR says that there are no ultimate or essential foundations. That is, we can add an unbounded number of basement levels, and there are many different valid skyscraper designs. But what sub-parts you build an idea from does matter, particularly when learning, even if that idea ends up fairly autonomous and could have been built in other ways. There’s more than one good answer to how to build up to or organize ideas, but also most logically possible approaches are bad (there are many more ways to be wrong than right).

CR objection: Knowledge is a web not a skyscraper.

Reply: Yeah, but a skyscraper, tree or pyramid is an easier to understand mental model that makes a good, useful approximation for many purposes. CR’s arguments don’t contradict that.

Minor Errors

99% of errors are small or large. Medium errors are rare.

The more you want to build on an idea, the better it has to be. Build one idea on top of it and it might work with several large errors. Build 10 layers of ideas on top of it and it better be really high quality.

Really high quality means no large errors. Since, approximately, there are no medium errors, then we have a nice cutoff. If you have any large errors, you can’t build past 10 more layers at most. If you have only small errors, you’re OK, you can build thousands of layers.

Errors that limit you to 0-1 more layers are “obvious”. These are pretty common but we generally notice them fast and do something about them.

With an error 7 layers ago, it can be really hard to figure out what’s going wrong. We often fail to connect our current problems to that error. We’re building on tons of things within the last 7 layers, so we don’t know where to look for the problem.

The really dangerous errors are large errors with effects that don’t show up very soon in a very obvious way. They allow building a max of 3-10 more layers of knowledge on top of them. These are the errors that cause big problems but are hard to find.

Most errors are either pretty easy to find (you know what’s wrong) or pretty minor (who cares). But some errors are both major and subtle. These get people stuck.

We must focus only on major errors. But I often point out errors people think are small. I disagree with them about which errors are major. Commonly, they don’t ask why the errors I bring up are major. They instead assume I’m picky, pedantic, etc. without saying so. I can’t accurately predict what major errors they will think are minor or preemptively explain why every major error is major. Their approach to discussion is another major error.

In my preferred terminology for epistemology, minor errors are not even errors. I don’t think of them as errors because they can be ignored, which means they do not cause failure at your goal(s). So I often say “error” to mean “major error” or “decisive error”. Why? Some other terms for minor errors are: irrelevant error, imperfectly optimized non-bottleneck, non-constraining issue, local optima. It’s an error that won’t stop us reaching our goal – an error that is entirely compatible with success. Do those things sound like errors? They are “problems” we should not solve. Working on them would be losing focus. Trying to solve them would be an error.

A type of error people often think is pedantic are communication errors. E.g. they use a pronoun and I don’t know what it refers to. Is that a minor writing error or a major error? The way to judge is to consider whether it blocks success at the goal or not. In a conversation, understanding each other is a sub-goal of the main goal (which is e.g. sharing ideas about science). Errors that prevent understanding each other are major. They aren’t just ignorable. You can’t just go on like nothing happened.

It’s true that you can say some unclear things if you build enough redundancy into your communication for me to understand anyway. People need to be tolerant about communication and put some work into figuring it out. But clarifying questions are still commonly needed. Relying more on talking about what’s being said, instead of just listeners just making guesses, also helps clarify the listeners’ perspectives, which makes it easier to communicate to them effectively.

Conclusion

People’s learning progress usually gets stuck because of an error several layers (or skyscraper floors) earlier. To get unstuck, they need to revisit stuff that they think they already know.

When learning things, you should consider whether they are important ideas that you’ll reuse many times in the future or build other ideas on top of. Are these ideas core/foundational ideas, or are they decoration or side-interests? If you want to reuse and build on ideas, then you need to learn them to quality standards suitable for that goal. If the ideas seem right, and you can use that, that doesn’t mean they can hold a large weight above them. You need to practice them a bunch to make the ideas more reliable, robust, intuitive and quick to use.

When you get stuck and revisit older ideas, you need to apply high quality standards in order to find and fix the problems. The problem was moving on without having high enough quality standards in the first place. That’s not the only thing that can go wrong, but it’s the the top thing you should look for when you have to revisit earlier floors due to problems with hard-to-identify causes.

In short, the higher quality standards you’re able to use, the more advanced knowledge you can build. When one top scientist has a more productive career than another, your first thought should not be that he is more talented – you should guess that he has higher quality knowledge of the basic and medium-level parts of science.