It’s a habit of mine to think in very high levels of abstraction (I haven’t looked much into category theory though, admittedly), and while it’s fun, it’s rarely very useful. I think it’s because of a width-depth trade-off. Concrete real-world problems have a lot of information specific to that problem, you might even say that the unique information is the problem. An abstract idea which applies to all of mathematics is way too general to help much with a specific problem, it can just help a tiny bit with a million different problems.
I also doubt the need for things which are so complicated that you need a team of people to make sense of them. I think it’s likely a result of bad design. If a beginner programmer made a slot machine game, the code would likely be convoluted and unintuitive, but you could probably design the program in a way that all of it fits in your working memory at once. Something like “A slot machine is a function from the cartesian product of wheels to a set of rewards”. An understanding which would simply the problem so that you could write it much shorter and simpler than the beginner. What I mean is that there may exist simple designs for most problems in the world, with complicated designs being due to a lack of understanding.
The real world values the practical way more than the theoretical, and the practical is often quite sloppy and imperfect, and made to fit with other sloppy and imperfect things.
The best things in society are obscure by statistical necessity, and it’s painful to see people at the tail ends doubt themselves at the inevitable lack of recognition and reward.
Great post!
It’s a habit of mine to think in very high levels of abstraction (I haven’t looked much into category theory though, admittedly), and while it’s fun, it’s rarely very useful. I think it’s because of a width-depth trade-off. Concrete real-world problems have a lot of information specific to that problem, you might even say that the unique information is the problem. An abstract idea which applies to all of mathematics is way too general to help much with a specific problem, it can just help a tiny bit with a million different problems.
I also doubt the need for things which are so complicated that you need a team of people to make sense of them. I think it’s likely a result of bad design. If a beginner programmer made a slot machine game, the code would likely be convoluted and unintuitive, but you could probably design the program in a way that all of it fits in your working memory at once. Something like “A slot machine is a function from the cartesian product of wheels to a set of rewards”. An understanding which would simply the problem so that you could write it much shorter and simpler than the beginner. What I mean is that there may exist simple designs for most problems in the world, with complicated designs being due to a lack of understanding.
The real world values the practical way more than the theoretical, and the practical is often quite sloppy and imperfect, and made to fit with other sloppy and imperfect things.
The best things in society are obscure by statistical necessity, and it’s painful to see people at the tail ends doubt themselves at the inevitable lack of recognition and reward.