>> mathematical notation is often clean and expressive, while programming language and its string-of-chars constraint makes for much more difficult to understand notation.
Yes, it's clean, if you know all symbols. But it's an unnatural mental burden. We think in patterns and structures. Our language should be similar, because what we express with language is unavoidably self-similar.
I'm gratefull for all the replies, as it seems to underline that this thought resonates strongly. Notation hinders understanding and the farther away symbols deviate from structures we use everyday, the stronger. Even though I personally prefer Unicode/Pictograms, it can't be that we have to reinvent Notation evertime that subsums recurring structures in programming, mathematics, physics, chemistry and every other conciously disconnet field in the same way. Because of universal properties I don't know about.
Yes, field specific notation has it's local and inherent beauty, but the price is too high! We can't fix education globally, at least not at this stage of our development. Thus we should drop efforts put into keeping Notations diconnect. It will widen the knowledge gap between the systemically uneducated majority stronger and stronger.
A solution? Biomimicry has always been our strongest weapon! I think nature is also far ahead in adopting a universal and often times visual language, we only acknowledge when we become isolated experts in a narrow sub-field, such that the language reveals itself.
It's acceptable to have rich symbols, if we can't get an universal notation based on a better generalizing (structural?) representation instead. I guess some of you may think about a more readable form of set-theory, others of geometric computing or mathematical manifold theory. Whatever it is that makes nature so efficient in reusing sub- and system-languages via controlling structures is what we should also define, understand, formalize and adopt throughout all fields via government backed efforts. I believe this is more important than I can currently imagine for our long-term future. An universal language, able to describe not only other languages, but also defining properties of complex systems, that's so alien it might work.
I think I've unknowingly stated a probably open mathematical problem. But can't put my finger on it. Can someone help?
PS: Sorry for coming late, deadlines coupled with a awfully slow laptop...
I am very sorry, I wish english was my mother language or I had better writing skills. But you can catch me up off HN, I'd be glad to talk and listen to a fellow mind :)
Yes, it's clean, if you know all symbols. But it's an unnatural mental burden. We think in patterns and structures. Our language should be similar, because what we express with language is unavoidably self-similar.
I'm gratefull for all the replies, as it seems to underline that this thought resonates strongly. Notation hinders understanding and the farther away symbols deviate from structures we use everyday, the stronger. Even though I personally prefer Unicode/Pictograms, it can't be that we have to reinvent Notation evertime that subsums recurring structures in programming, mathematics, physics, chemistry and every other conciously disconnet field in the same way. Because of universal properties I don't know about.
Yes, field specific notation has it's local and inherent beauty, but the price is too high! We can't fix education globally, at least not at this stage of our development. Thus we should drop efforts put into keeping Notations diconnect. It will widen the knowledge gap between the systemically uneducated majority stronger and stronger.
A solution? Biomimicry has always been our strongest weapon! I think nature is also far ahead in adopting a universal and often times visual language, we only acknowledge when we become isolated experts in a narrow sub-field, such that the language reveals itself.
It's acceptable to have rich symbols, if we can't get an universal notation based on a better generalizing (structural?) representation instead. I guess some of you may think about a more readable form of set-theory, others of geometric computing or mathematical manifold theory. Whatever it is that makes nature so efficient in reusing sub- and system-languages via controlling structures is what we should also define, understand, formalize and adopt throughout all fields via government backed efforts. I believe this is more important than I can currently imagine for our long-term future. An universal language, able to describe not only other languages, but also defining properties of complex systems, that's so alien it might work.
I think I've unknowingly stated a probably open mathematical problem. But can't put my finger on it. Can someone help?
PS: Sorry for coming late, deadlines coupled with a awfully slow laptop...