4 ms·

Not just understanding, but how to parse it. For example, I can read a theorem that introduces a bunch of variables in the first sentence that don’t get used un

Not just understanding, but how to parse it. For example, I can read a theorem that introduces a bunch of variables in the first sentence that don’t get used until a few lines later and say “yeah those are probably just some constants they’ll use in an upcoming equation for an upper bound or something.” Before I was familiar with higher math, I’d say “what the hell are these where did they come from?” After reading enough books and papers, you can see a few steps ahead a lot of the time due to past experience (similar to what veteran chess players do). I can also jump to the middle of the document and see some notation that was defined earlier and guess what it is. Different authors might denote the space of continuous functions in a few different ways but they tend to be very similar for common objects. That said, there’s a lot of poorly written theory publications out there in my opinion. A big sin to me is that a lot of them will do stuff without explaining in simple English beforehand how they’re going to do it, why they’re doing it, and why it is important. The first item you can get if you’re going through the math line by line at least, but that can be arduous and often I want to understand the big picture before I dig into the details. It doesn’t take much — just a couple of sentences before or after the result can go a long way.

chongli 3y ago
A big sin to me is that a lot of them will do stuff without explaining in simple English beforehand how they’re going to do it, why they’re doing it, and why it is important. I don't fault theoreticians for not using simple English. In many cases you're dealing with objects that are built upon a tower of abstractions with which you and your colleagues are already intimately familiar. This is true in any technical field. Sit in a hospital cafeteria long enough and I'm sure you can overhear surgeons talking shop over lunch. I wouldn't expect them to use simple English either. They have a huge corpus of terminology for every muscle, tendon, ligament, and bone in the body. Skipping past the simple English allows them to be brief and fluid in their communication style, at the expense of leaving laypeople out of the loop.

chongli 3y ago

A big sin to me is that a lot of them will do stuff without explaining in simple English beforehand how they’re going to do it, why they’re doing it, and why it is important. I don't fault theoreticians for not using simple English. In many cases you're dealing with objects that are built upon a tower of abstractions with which you and your colleagues are already intimately familiar. This is true in any technical field. Sit in a hospital cafeteria long enough and I'm sure you can overhear surgeons talking shop over lunch. I wouldn't expect them to use simple English either. They have a huge corpus of terminology for every muscle, tendon, ligament, and bone in the body. Skipping past the simple English allows them to be brief and fluid in their communication style, at the expense of leaving laypeople out of the loop.