Re:Examples of common false beliefs in mathematics
by BeetleB on Monday January 31, 2022 @07:02PM
(#30156709)
Regarding using some notation for multiplication:
You'll be hard pressed to find any symbol/notation that isn't overloaded with other operators in math. Things like '*' and the 'x' symbols have different meanings in different contexts, and when you're doing those things, and need multiplication, you run into problems.
Personally, and I know I'm not alone, when I convert physics equations to code, the '*' symbol is one of the ones that make reading code challenging.
For function application, I can see the problem, and I'm sure most have gotten confused at one point or other where they're not sure if it's a function application vs multiplication. But as others have pointed out, the context makes it clearer.
I think one of the key differences between many here and those who favor the notation is that in SW, the wish is the formalized version (i.e. the code) is readable enough to understand, without much prose (i.e. comments). In mathematics, it usually is not the case - in fact, one of my math professors often had to point out to students that it's better if they wrote part of their answer in prose rather than purely logic symbols. In that sense, there often is little ambiguity. It really should be clear from the context whether you're dealing with the sine function or multiplying symbols. If it isn't, the problem isn't the notation, but the lack of understanding of the context. Having a guide to the notation will not elucidate much.
And for the one who uses a lot of math (some engineers, physicists, and of course mathematicians) - having to write (any) symbol for multiplication is crazy tedious - even if it is just a dot. There is a reason they opt not to put it.
You'll be hard pressed to find any symbol/notation that isn't overloaded with other operators in math. Things like '*' and the 'x' symbols have different meanings in different contexts, and when you're doing those things, and need multiplication, you run into problems.
Personally, and I know I'm not alone, when I convert physics equations to code, the '*' symbol is one of the ones that make reading code challenging.
For function application, I can see the problem, and I'm sure most have gotten confused at one point or other where they're not sure if it's a function application vs multiplication. But as others have pointed out, the context makes it clearer.
I think one of the key differences between many here and those who favor the notation is that in SW, the wish is the formalized version (i.e. the code) is readable enough to understand, without much prose (i.e. comments). In mathematics, it usually is not the case - in fact, one of my math professors often had to point out to students that it's better if they wrote part of their answer in prose rather than purely logic symbols. In that sense, there often is little ambiguity. It really should be clear from the context whether you're dealing with the sine function or multiplying symbols. If it isn't, the problem isn't the notation, but the lack of understanding of the context. Having a guide to the notation will not elucidate much.
And for the one who uses a lot of math (some engineers, physicists, and of course mathematicians) - having to write (any) symbol for multiplication is crazy tedious - even if it is just a dot. There is a reason they opt not to put it.