Hacker Newsnew | past | comments | ask | show | jobs | submitlogin

Nice, but why do mathematicians always overload their symbols? For example, on page 2, the right-arrow already has two meanings!

This isn't making things much clearer.



Two things.

Firstly, there simply aren't enough symbols. In programming, naming functions and variables is hard, really hard, and in math you don't have the luxury of giving long names to every separate concept. Part of the value of the notation is its compactness.

Secondly, symbols that are overloaded usually have related meanings, and much of the value in the notation is the abuse of notation that you get from it. You may think it just makes everything confusing and harder, but in truth, learning how to work with the notation is incredibly valuable, and leads to a deeper understanding of what things really are, and how they work.

The overloading is a feature, not a bug.


There are lots of things a mathematician can do to avoid overloading.

Use colors, use boldface, use special markers to make the symbols slightly different. Or, using computers, provide mouse-over information.

I agree that sometimes overloading can be useful, but imho when learning new stuff, it complicates matters more than necessary.


That depends. Disambiguating these things makes them easier to read, easier to think you understand what's going on. However, in my experience the mental effort involved in working out what the symbols mean in their different contexts is essential to actually internalize and understand.

Yes, if you just want to read it without actually gaining any deep understanding or skill, use boldface, colors, words, mouse-over pop-ups. But if you want to learn something and be able to do it, you need to struggle with it. Only by doing the work do you gain the skill.

As in programming, simply reading programs gains you little, if anything. If you want to grow in skill, you need to work through the detail of programs you read, and do some programming yourself.


> As in programming, simply reading programs gains you little, if anything.

But at least in programming, I can do a "grep" for the symbols I want to understand :)


Ever tried grepping for an overloaded "+" in C++?


This is exactly why I never overload such symbols, or at least I try to keep it at a minimum.




Guidelines | FAQ | Lists | API | Security | Legal | Apply to YC | Contact

Search: