Re:Examples of common false beliefs in mathematics
by kergonath on Monday January 31, 2022 @03:09PM
(#30153543)
> One could argue that to go full notation-less you should only write in proper sentences, and that would make it even more complex.
Reading Newton’s principia is humbling. He does that the whole book; it takes him pages to explain concepts we now learn before university and that can be condensed in a couple of equations. Finding words to describe the maths he uses is difficult, you can almost feel the insane amount of work just to translate the concepts into sentences. It’s a wonderful example, and of course a masterpiece. But reading it is also very difficult because of all the noise around the concepts. Words are fine to give an intuitive understanding, but at some point you need equations.
Same for Maxwell’s equations, for example. You’d spend less time learning basic calculus and algebra than trying to understand what the hell he was meaning.
Or 19th-century chemists, who used fancy and complicated names for compounds that are described much more clearly and succinctly with a chemical formula. Yes, you need to learn the formalism, but it pays off.
Some counter examples are Einstein and Feynman, who could communicate complex concepts with words in an understandable way. Though even them need some abstract notation at some point (lots of it, actually).
Reading Newton’s principia is humbling. He does that the whole book; it takes him pages to explain concepts we now learn before university and that can be condensed in a couple of equations. Finding words to describe the maths he uses is difficult, you can almost feel the insane amount of work just to translate the concepts into sentences. It’s a wonderful example, and of course a masterpiece. But reading it is also very difficult because of all the noise around the concepts. Words are fine to give an intuitive understanding, but at some point you need equations.
Same for Maxwell’s equations, for example. You’d spend less time learning basic calculus and algebra than trying to understand what the hell he was meaning.
Or 19th-century chemists, who used fancy and complicated names for compounds that are described much more clearly and succinctly with a chemical formula. Yes, you need to learn the formalism, but it pays off.
Some counter examples are Einstein and Feynman, who could communicate complex concepts with words in an understandable way. Though even them need some abstract notation at some point (lots of it, actually).