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I am convinced whatever math people are doing is a completely different way of thinking, and math people seem to like their notation, so I defer to them. Perha

I am convinced whatever math people are doing is a completely different way of thinking, and math people seem to like their notation, so I defer to them. Perhaps there is some super notation that could somehow make math accessible to more people, but I doubt it would look like code, since they are two different tasks. Mathematicians often deal with systems of multiple equations and multiple variables. Every part connects to everything else. It's like those trippy analog and mechanical things where one part does 5 things at once. Programming is much more heirarchal. You can deal with one layer of abstraction at a time, thinking in terms of parts that become black boxes when you aren't actively dealing with them. Sometimes the only challenge in programming is just the size of a task, and it's more tedious than challenging. Math seems to demand a new way of thinking for basically every task. Math as code would be amazing for people like me, who basically never at any point have a need to actually do any math beyond copy and paste. But my opinion doesn't matter much, since I'm not actually doing anything interesting, and current notation isn't a significant part of my life. If I need to solve something, xcas or Maxima understand descriptive names just fine. If I needed to understand the things in a proper math paper... I would probably be doing the stuff the math people do, and I'd think the notation was great, just like they seem to. I don't know how they keep track of the meaning all those symbols. Maybe they don't, and the abstractness is useful?

suture 4y ago
I like what you wrote and here is my perspective as a mathematician. A lot of the notation is due to legacy and common practice. For instance, we write y=f(x) and think of x as the independent variable. If I switch it around and write x=f(y) that would confuse a lot of people (especially students and non experts). In one sense it doesn’t matter what letters I use but in terms of how things are normally communicated it does. If I break with tradition this causes a cognitive burden on the reader and that detracts from the purpose which is to communicate ideas. Also, the people who come up with a new idea tend to be the ones who decide on the notation. After using it for a while one acquires an intuition about the notation. When I see lim I think an infinite process is being described. That could be the limit from calculus or the direct limit in algebra. The result of how things have developed is that we end up with some things that are nonsensical if taken literally but do make sense as they are used. For instance it is nonsensical to say that x=1 is the solution to x+4=5. What is really meant is that both equations have the same solution set and it’s easy to see from the first equation that this solution set is {1}. Shakespearean language is weird to modern speakers of English even though it is correct English. In a similar way I think mathematical notation/usage is like a spoken language. One gets a feel for it after learning it and using it for a while. There are unwritten rules that people abide by to facilitate communicating ideas. I imagine a similar thing is true for programming languages.

suture 4y ago

I like what you wrote and here is my perspective as a mathematician. A lot of the notation is due to legacy and common practice. For instance, we write y=f(x) and think of x as the independent variable. If I switch it around and write x=f(y) that would confuse a lot of people (especially students and non experts). In one sense it doesn’t matter what letters I use but in terms of how things are normally communicated it does. If I break with tradition this causes a cognitive burden on the reader and that detracts from the purpose which is to communicate ideas. Also, the people who come up with a new idea tend to be the ones who decide on the notation. After using it for a while one acquires an intuition about the notation. When I see lim I think an infinite process is being described. That could be the limit from calculus or the direct limit in algebra. The result of how things have developed is that we end up with some things that are nonsensical if taken literally but do make sense as they are used. For instance it is nonsensical to say that x=1 is the solution to x+4=5. What is really meant is that both equations have the same solution set and it’s easy to see from the first equation that this solution set is {1}. Shakespearean language is weird to modern speakers of English even though it is correct English. In a similar way I think mathematical notation/usage is like a spoken language. One gets a feel for it after learning it and using it for a while. There are unwritten rules that people abide by to facilitate communicating ideas. I imagine a similar thing is true for programming languages.