Everytime I look at something written in mathematical notation I can prevent myself from thinking "this is exactly what we do NOT want to do in programming: one letter variable, super super dense code, no comments, symbols/infix operators instead of obvious functions names"
And the result speak for itself : you need to **study math** things to understand it.
We you need to do that for programming you are just reading shitty code not meant to be share with humans.
Math is just shitty code.
@mona trying to understand this but what does lucid mean?
@bram I must thank you, in fact, for assisting me toward this understanding of myself. the symbols and manipulations of algebra and trigonometry and calculus are almost recreational to me, and I have more than once wished that programming was more like math homework.
@Thib @bram i always feel a bit skeptical when reading mathematical notation in a programming paper, in that the idea needs to be validated in two different domains, only one of which i'm really very qualified to operate in. the vocabulary of math tracks across so many different fields, i tend to feel overwhelmed pretty quickly with all i need to unpack in a few symbols.
@bram mathematics is a social community and people in that community spend years working with others getting to learn the subtly nuances of all that dense stuff. It’s meant to be shared with others and the there’s a reason for the dense code but it takes a conceptual shift to be fluent in it.
@noflashphotography and I think that's the problem: it has never been built to be accessible nor easy to understand and that has never been (is very rarely?) questionned.
Appart from one exception, I've only see the question "how to teach math better" and never the "how to make math easier to teach".
That and the fact that sociologically math is used in the educational system to exclude the "not good enough" students (which is nearly always the poors).
@bram yes/no. I can speak from experience that learning advanced math is a slow going process not because of the notation but because there’s so much to learn and people are usually having to do double or triple learning: concepts, notation, and problem solving strategy. If you have one of two of those down notation usually isn’t an issue If you put in the time.
@bram notation is questioned all the time. There is always a decades even centuries long process of crafting and whittling down notation. The problem is that notation for competent practioners isn’t always what’s best for beginners.
@noflashphotography on that point I really have the feeling that you get the same problem than with old programming language where once people get used to something they don't realised that it's actually bad and in the programming field we had the chance of having a lot of different programming languages that helped refine better ideas/notations/abstractions and prove that older programming languages where actually less good at that, a thing that you don't have in math (from what I know)
@bram Notation has been changed a lot in many fields. Look into the precursors of tensors and matrices that popped up in the 1860s till the 1920s. Same goes for differential equations and their representations. Differential geometry (language of general relativity) has changed substantially
since Einstein's time.
@bram I dunno. They fit into several broad categories in terms of mindset.
The problem is, you can refactor the code to make things "readable," but the structure of the code may now be in a *worse* state of being able to communicate intent, actually making it harder to *comprehend*, despite being easier to read.
Raymond Hettinger has a video on when it's OK to ignore conventions.