Comment by chongli | Hacker News Reader

Comment by chongli | Hacker News Reader

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People tend to hate things they don't understand more than the things that are wrong. The comments under reflect to some degree about this observation.

I have noticed that most HN discussions on math topics seem to devolve into complaints about notation. There seems to be a fairly large contingent of people from the programming side of things who don't have a formal background in mathematics.

I get the feeling that it isn't just frustration from a lack of understanding. If the topic was from some other technical field like organic chemistry or medicine I don't think you'd see this kind of response. I believe where the frustration comes from is adjacency: people have an expectation that they ought to be able to understand it because programming (via computer science) is adjacent to math. This expectation combined with a lack of understanding is what leads to cognitive dissonance. And that cognitive dissonance is what leads to the complaints about notation.

The notation isn't the problem. Every field has its own notation, jargon, and conventions. Mathematics notation is very simple and terse but the underlying concepts can be very abstract. Understanding comes from a lot of mathematical practice, not a glossary of terms. To paraphrase Euclid: "there is no royal road to mathematics (geometry)."

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.

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.

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