There’s a link to this article that makes a lot of sense. But I get the overall sense that there is a limit to consistency, expressibility, and ease of reading. If you try to go too far in one factor, you’re going to lose some of the other factors. It boils down to a presentation matter, and it depends on what purpose are you making the presentation.
Sure, but the current status quo is largely a result of chance and mathematical fads over the centuries than any concerted effort to find consistent and good symbols and notation (with Leibniz being an exception to this). There’s really no reason to think we can’t do better than the current state of mathematical notation.
Well, I was hinting at this, but I think you should also consider the idea that form follows function. I think the function of mathematical notation for the sake of mathematics proper is for greater and greater abstraction, which involves ignoring any element not considered necessary or relevant to what is being proposed.
Those of us who are, instead, more interested in practical reason and wish to gain some mileage from the achievements of mathematics, are more likely to adopt notation more similar to programming languages, where we want to express relationships that are more grounded and more concrete.
There isn’t any perfect mathematical notation, only notation that is most efficient for your particular usage. Like everything else, finding “good notation” is an economics problem.
There’s a link to this article that makes a lot of sense. But I get the overall sense that there is a limit to consistency, expressibility, and ease of reading. If you try to go too far in one factor, you’re going to lose some of the other factors. It boils down to a presentation matter, and it depends on what purpose are you making the presentation.
Sure, but the current status quo is largely a result of chance and mathematical fads over the centuries than any concerted effort to find consistent and good symbols and notation (with Leibniz being an exception to this). There’s really no reason to think we can’t do better than the current state of mathematical notation.
Well, I was hinting at this, but I think you should also consider the idea that form follows function. I think the function of mathematical notation for the sake of mathematics proper is for greater and greater abstraction, which involves ignoring any element not considered necessary or relevant to what is being proposed.
Those of us who are, instead, more interested in practical reason and wish to gain some mileage from the achievements of mathematics, are more likely to adopt notation more similar to programming languages, where we want to express relationships that are more grounded and more concrete.
There isn’t any perfect mathematical notation, only notation that is most efficient for your particular usage. Like everything else, finding “good notation” is an economics problem.