People don’t realize how much complexity is around them. Pick up a rock. Simple? Think again. The rock is made of trillions of atoms. The rock is mostly empty space. When you touch it, lots of what’s going on is electrons from atoms in your hand repelling electrons from rocks in the atom. It’s related to magnets. Lifting the rock is resisted by gravity, but the force of gravity is a actually myth – our best understanding, to replace a force of gravity, is about the theory of relativity and curved spacetime. The real nature of the rock involves quantum physics. When you lift it, you’re changing its position at a rate – so the topics of position, speed and acceleration are relevant. When you lift it, it holds together. You only directly lift a small fraction of the atoms in the rock. They are connected to other atoms which are connected to other atoms which are connected to other atoms, and so on, until the whole rock lifts. Almost – a few atoms probably fall off. The atoms are bonded together in molecules which are bonded together to make up the rock. The atoms are made of sub-atomic particles.
Reading is like picking up a rock. Every word has hidden complexity. What does this word mean? Why does it exist? Who made it and for what purpose? How did they think about the world and how does the word fit into their worldview? How has the word changed over time to fit a modern worldview? What differences are there between how it fits into a standard, mainstream view and how it fits into your own mind? Are there any current controversies involving the word? What are examples of the word? Would people disagree about any potential examples? Are there edge cases? And there’s much more complexity when you look at sentences or paragraphs, and try to understand their meaning, instead of just looking at individual words.
It’s important to be aware of this complexity – both in physical objects and words – so you can make good choices about how much attention to focus on which complexity. There’s too much complexity to explore all of it. You have to be selective. But you shouldn’t just blindly ignore it and hope it never matters. A short explanation of why most debates are unproductive is because something goes wrong in some of the complexity that people aren’t paying attention to. Doesn’t it seem kind of natural and inevitable that that’s a common failure case? We pick out under 1% of stuff to focus attention on, and sometimes things will go wrong in the other 99.99%.
It’s hard to stop overreaching if you’re blind to all the complexity you’re trying to use, understand, control and build on. If you don’t even know it’s there, and can’t even roughly estimate how much there is, then it’s hard tell when there’s a problem.
People make errors which are in the complexity they don’t know exists and then it’s hard to fix those errors. They don’t know where to look. They can’t break down what they’re doing into parts and zoom in on the area with the mistake because they are unaware of those parts. To them, “2+2” or the word “freedom” is like an indivisible whole, a smallest possible chunk of thought, an atom with “irreducible complexity” or no complexity. They don’t view it entirely this way, though. They aren’t consistent. But it’s kinda like this.
The “2+2” example is interesting because obviously you can break it up into “2”, “+” and “2”. But people say that “2+2=4” is unquestionable and deny there is hidden complexity there that could be analyzed. Those same people have no idea how addition is implemented in a computer (using smaller parts – multiple basic logic operators). But they figure that, for human beings, it’s just one step: you just somehow know the answer. That’s after you learn it, of course – babies don’t know arithmetic. And kids generally don’t learn it until after they learn the numbers and learn to count. But still, it seems like a foundational axiom to people. If anything’s infallible, their understanding of that is! If it’s one step in humans, what does one step mean? One neuron firing? Only one neuron involved? Realistically, there are at least thousands of neurons involved – millions wouldn’t be surprising. Addition is broken down into multiple smaller parts or steps in our brain, as it is in a silicon computer.
If people could break stuff into parts and zoom in on more detail in response to problems, they could then start guessing which parts they suspect might have an error and which they doubt have an error. They could prioritize what parts to investigate and then start investigating.
People might also need to break parts into sub-parts. And do that again. And again. But the more your investigation involves repeatedly breaking things into parts, the more you should be suspicious that you overreached. Most of your errors should be in a layer near what you’re currently working on. If you frequently have to search for errors ten layers below what you’re doing, it’s going to be a huge distraction. You’re not ready to do this yet, since you haven’t built up to it.
The more layers removed an error is, the more work it tends to be to find it. Think of it like a pyramid (or a tree). You’re working at the top level. If an error is within the top three layers, then you can imagine a pyramid of height three, and that’s the search space for where the error could be. Let’s say there is one block on the top level, two on the next level, three on the next, and so on. Then there are six blocks in a pyramid with height three. This is conservative. Doubling or tripling the blocks for the next level is reasonable too.
What if the error is in the top five layers? Then there are 15 blocks to search instead of six. What if it’s in the top 10 layers? Now there are 55 blocks (ideas) to search. 20 layers? 210 blocks.
It’d be even worse with a less conservative model. If each layer has double the number of blocks in the previous layer, then it’s over a million blocks for 20 layers, or over a thousand blocks for 10 layers.
It’s a lot more work to find an error if you have a larger pyramid to search. Yes, you can use search strategies that don’t look everywhere, which helps. But bigger search areas are still harder to deal with. And you often have to do multiple searches to find one error. You might look for one type of error, search the pyramid, not find an error, and then search for a different type of error. If you don’t clearly know what you’re looking for, you could have to look through the search space ten or more times before you figure it out.
The conclusion is that you need to get the lower layers of your knowledge (the bottom of the pyramid) really reliable. If you almost never have to review anything but the top five layers of the pyramid you’re working on – because the lower layers are reliable – then that’s much easier. People basically get stuck around five layers above their first low quality layer of knowledge. You can’t build up more knowledge very high above that shoddy foundation.
Note: All the numbers are just loose estimates. The number of layers depends on the size of the ideas that you count as “one” idea or layer. The important thing is the concept: You need your lower level ideas to rarely need to be searched for errors, that way you keep your search space small enough so that when you have an error (and you ought to commonly find errors in new knowledge) it isn’t a ton of work to find it.
Recognizing how complex the world is helps people realize that twenty or more layers of knowledge is necessary to understand the world. If you see that your learning is like building a skyscraper-height pyramid, it’ll help you respect the need for very solid foundations, and for having strategies to manage complexity.