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Math's Syntax and 'universal' language is a great barrier that unlocks the world's knowledge. Applied scientific fields take almost 10-20 years until they sieve

Math's Syntax and 'universal' language is a great barrier that unlocks the world's knowledge. Applied scientific fields take almost 10-20 years until they sieve/diffuse the knowledge, due to this barrier. (In my perception at least) I wish math used a pythonesque and popular alternative language, so that very low- or high-level 'assumptions' weren't blocking a greater audience from participating in the field. Although I'm familiar with it, I find it sometimes a little too elitist, because almost every symbol requires an explanation, before it can be used. Javascript and Python have this great balance, I feel is urgently needed in Maths.

donmatito 9y ago
As the joke goes Programmer : chooses her variables always different, with a name as explicit as possible Mathematician : chooses her variables from a handful of greek letters
- banku_brougham 9y ago
  You would grant that this is not a funny-haha joke.
- ska 9y ago
  ... from a handful of greek letters that usually already have agreed upon meaning or connotation within her subspecialty. So everyone reading it understands what is going on. Unfortunately, it doesn't generalize across specialties. By comparison, the programmer chooses names explicitly based her own understanding and modeling of the problem, which may confuse others. both approaches have their strengths and weaknesses.
  - taneq 9y ago
    > ... from a handful of greek letters that usually already have agreed upon meaning or connotation within her subspecialty I think you mean sub-sub-sub-subspecialty. I don't often read mathematics papers but when I do, it's infuriating how people think that [squiggle] has a universally understood meaning when in actual fact there are only a handful of people in the world (most of whom probably work in the same building as the author) who use [squiggle] to mean that.
    - ska 9y ago
      No, I mean sub-speciality. At least, my experience is nothing like you describe. For the most part, the people who are likely to attend each others conference talks agree on notation. They may, however, disagree with the people down the hall. Bear in mind, though, the papers are written for that same group. For good or for ill.
  - pps43 9y ago
    > that usually already have agreed upon meaning or connotation within her subspecialty. You mean, like p in statistics?
    - ska 9y ago
      No, which is why my statement is not stronger than it was.
sbmassey 9y ago
Well I guess you could write sum() instead of Σ, and dot() instead of ·, but I’m not sure it would really help people understand it. Do people find Mathematica expressions easier to understand than traditionally formatted equations?
- squeaky-clean 9y ago
  The reason I personally prefer sum() to Σ is I can google "what is a sum". If I Google "what is Σ" I get answers about the greek letter Sigma. If I Google "what is Σ math" it incorrectly says "Standard Deviation". Also if I don't know what Sigma is, it's very hard to ask someone else what the weird uppercase E means.
  - Cozumel 9y ago
    Search engine that focuses on symbols: http://symbolhound.com/ http://symbolhound.com/
  - njarboe 9y ago
    Putting in "what does the symbol sigma mean" into google (incognito mode) gives the google blurb of: "In addition to being the 18th letter of the Greek alphabet, sigma also means 'sum' and 'deviation' in the mathematics world. Learn what each symbol looks like and how each formula works." It first hit is titled,"Sigma Notation - Math is Fun", with the text 'Sigma Notation. Σ This symbol (called Sigma) means "sum up"' I think learning the names of the Greek letters is not too high a bar to get started on learning physics and math. Fun too. You really need to know the names of things to start to understand them and ask people about them. I think the reason people like compact formulas is that it is much easier to understand and check a formula if one can have the whole thing in eyes view.
    - squeaky-clean 9y ago
      That's part of my point though. You had to know Σ means sigma to search that in the first place. If you search "what does Σ mean" or "what does symbol Σ mean" you get answers for lowercase sigma saying standard deviation. At the very least it means it takes 2 searches, one to find the name of a symbol, and a second to search using that, sometimes I can't do that if the notation is an image of TeX output. Then it becomes "what does box symbol with line through it mean" or something. Thankfully StackExchange now renders math notation in a way that can be copy pasted, but still, here's an example I was reading recently that started as an ascii email chain and moved to stackexchange, I feel like it was more easily readable before. It's still tough to Google that Π(u) is the same as the rect() function https://dsp.stackexchange.com/questions/42495/implication-of-sampling-and-reconstruction-theorem https://dsp.stackexchange.com/questions/42495/implication-of... > I think learning the names of the Greek letters is not too high a bar to get started on learning physics and math. But the original point was that for someone who doesn't know math, writing it in a more english-like notation wouldn't be helpful. But because of search engines it is.
andrepd 9y ago
I dont get it. Are you saying new scientific fields take decades to become "known", and that this supposed delay is due to... notation? None of these theses make any sense to me. Also, a notation that is suited to one field (programming), may not be necessarily best suited to another (mathematics). Personally I feel much the opposite of you: mathematical notation is often clean and expressive, while programming language and its string-of-chars constraint makes for much more difficult to understand notation.
- FractalNerve 9y ago
  >> 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...

donmatito 9y ago

As the joke goes Programmer : chooses her variables always different, with a name as explicit as possible Mathematician : chooses her variables from a handful of greek letters

banku_brougham 9y ago
You would grant that this is not a funny-haha joke.
ska 9y ago
... from a handful of greek letters that usually already have agreed upon meaning or connotation within her subspecialty. So everyone reading it understands what is going on. Unfortunately, it doesn't generalize across specialties. By comparison, the programmer chooses names explicitly based her own understanding and modeling of the problem, which may confuse others. both approaches have their strengths and weaknesses.
- taneq 9y ago
  > ... from a handful of greek letters that usually already have agreed upon meaning or connotation within her subspecialty I think you mean sub-sub-sub-subspecialty. I don't often read mathematics papers but when I do, it's infuriating how people think that [squiggle] has a universally understood meaning when in actual fact there are only a handful of people in the world (most of whom probably work in the same building as the author) who use [squiggle] to mean that.
  - ska 9y ago
    No, I mean sub-speciality. At least, my experience is nothing like you describe. For the most part, the people who are likely to attend each others conference talks agree on notation. They may, however, disagree with the people down the hall. Bear in mind, though, the papers are written for that same group. For good or for ill.
- pps43 9y ago
  > that usually already have agreed upon meaning or connotation within her subspecialty. You mean, like p in statistics?
  - ska 9y ago
    No, which is why my statement is not stronger than it was.

sbmassey 9y ago

Well I guess you could write sum() instead of Σ, and dot() instead of ·, but I’m not sure it would really help people understand it. Do people find Mathematica expressions easier to understand than traditionally formatted equations?

squeaky-clean 9y ago
The reason I personally prefer sum() to Σ is I can google "what is a sum". If I Google "what is Σ" I get answers about the greek letter Sigma. If I Google "what is Σ math" it incorrectly says "Standard Deviation". Also if I don't know what Sigma is, it's very hard to ask someone else what the weird uppercase E means.
- Cozumel 9y ago
  Search engine that focuses on symbols: http://symbolhound.com/ http://symbolhound.com/
- njarboe 9y ago
  Putting in "what does the symbol sigma mean" into google (incognito mode) gives the google blurb of: "In addition to being the 18th letter of the Greek alphabet, sigma also means 'sum' and 'deviation' in the mathematics world. Learn what each symbol looks like and how each formula works." It first hit is titled,"Sigma Notation - Math is Fun", with the text 'Sigma Notation. Σ This symbol (called Sigma) means "sum up"' I think learning the names of the Greek letters is not too high a bar to get started on learning physics and math. Fun too. You really need to know the names of things to start to understand them and ask people about them. I think the reason people like compact formulas is that it is much easier to understand and check a formula if one can have the whole thing in eyes view.
  - squeaky-clean 9y ago
    That's part of my point though. You had to know Σ means sigma to search that in the first place. If you search "what does Σ mean" or "what does symbol Σ mean" you get answers for lowercase sigma saying standard deviation. At the very least it means it takes 2 searches, one to find the name of a symbol, and a second to search using that, sometimes I can't do that if the notation is an image of TeX output. Then it becomes "what does box symbol with line through it mean" or something. Thankfully StackExchange now renders math notation in a way that can be copy pasted, but still, here's an example I was reading recently that started as an ascii email chain and moved to stackexchange, I feel like it was more easily readable before. It's still tough to Google that Π(u) is the same as the rect() function https://dsp.stackexchange.com/questions/42495/implication-of-sampling-and-reconstruction-theorem https://dsp.stackexchange.com/questions/42495/implication-of... > I think learning the names of the Greek letters is not too high a bar to get started on learning physics and math. But the original point was that for someone who doesn't know math, writing it in a more english-like notation wouldn't be helpful. But because of search engines it is.

andrepd 9y ago

I dont get it. Are you saying new scientific fields take decades to become "known", and that this supposed delay is due to... notation? None of these theses make any sense to me. Also, a notation that is suited to one field (programming), may not be necessarily best suited to another (mathematics). Personally I feel much the opposite of you: mathematical notation is often clean and expressive, while programming language and its string-of-chars constraint makes for much more difficult to understand notation.

FractalNerve 9y ago
>> 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...