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Yes. What's wrong with changing math notation? Why wouldn't you do it if you know that it would make it easier for others to approach? What's the rationale behi

Yes. What's wrong with changing math notation? Why wouldn't you do it if you know that it would make it easier for others to approach? What's the rationale behind doing exactly nothing to make the notation more approachable for the masses?

ColinWright 5y ago
Math notation has evolved to be what it is because it is useful for the actual doing of math, and the communication of math to those who have sufficient background. It's not deliberately designed to keep people out, and there are literally hundreds of thousands of books that introduce people to the notations used, to help on-board them. Haskell is unreadable to one who has not trained in it or similar languages ... why don't they make the syntax more readable? Or C++ with its modern templating ... why don't they change the syntax to make it more readable? You might be tired of wandering into someone else's area of expertise and telling them: You must change! You must make it more accessible! Believe me, mathematicians are tired of non-mathematicians wandering up and saying: Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Do you really believe that no one has tried to make it more accessible? Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do?
- klibertp 5y ago
  > It's not deliberately designed to keep people out, It looks that way, to many people, even in this thread. > why don't they change the syntax to make it more readable? They do, actually. Quite often at that. It's called releasing new version. > Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! No. Computer code is as far from intuitive as it can be. Nobody says otherwise. So you don't need to do anything to get there, the notation's good on that front (meaning: completely non-intuitive). That's where the IDEs come in. And debuggers. And other tools. Lots of tools. They really help. You could use them, because the IDEs-for-math already exist. In college I had exactly one semester to familiarize myself with one of them, and it was never mentioned again until graduation. > Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Why, do you believe it's not possible for it to be that way? See: https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_regulations https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_re... > Do you really believe that no one has tried to make it more accessible? Why did they fail? (If they didn't - where's the exponential growth of first years' mathematicians in training) > Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do? I'm 100% not interested in why it is like this, it's not my problem, so I really wouldn't know. Would you be interested in how at some point you had to write `class X(object):` and that it later changed to simply `class X:`? Would you go hunt on the mailing list to see who exactly came up with the idea? Or why they thought it would be better that way? Would you be interested in that if you just had to write a 10-lines of Python, to scrape some web site?
  - Jensson 5y ago
    > Why, do you believe it's not possible for it to be that way? See: https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_regulations https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_re... Did you just use an example from 2600 years ago to make a point? You don't think much changed since then?
    - klibertp 5y ago
      > Did you just use an example from 2600 years ago to make a point? Yes? What's wrong with that? I'm pointing out the most widely known example, to make a point, which is: "it is possible to design notation specifically for keeping outsiders out". I'm not saying that modern math notation is like that. I think, as a layman, that it probably evolved over a long time and so is full of idiosyncrasies that made perfect sense back when they were introduced (my GP seems to describe it in similar terms, so I hope I'm not that far removed from reality).
- deleted 5y ago
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- JohnHaugeland 5y ago
  > It's not deliberately designed to keep people out Surely you must realize that you're protesting this because it has this reputation, though? And surely you must realize that it has this reputation for a reason? When I was a teenager and took my first calculus course, I struggled with summation for three days. When I finally went to my dad he looked at me funny and said "your teacher is an idiot, isn't he? It's a for loop." I had been writing for loops for seven years at that age. I almost cried. It was like a lightswitch. The problem was always that nobody had ever actually explained what the symbol meant in any practical way. Every piece of terminology was explained with other terminology, when there was absolutely no reason to do so. Mathematics has the reputation for impermeability and unwelcomingness for a reason. It's because you guys are ignoring us saying "we want to learn, please write out a cheat sheet" and saying "yes, but don't you see" instead of just building the easy on-ramp that every other field on earth has built . > > You might be tired of wandering into someone else's area of expertise and telling them: > > You must change! You must make it more accessible! No, we generally just fix the problem. If people are saying "this isn't accessible enough," we just work on it. I would like for you personally to be aware of Bret Victor's work. He's incredibly potent and clear on these topics. Programmers work really really hard on learnability and understandability. This is a big deal to us. That's why we can't understand why it's not a big deal to you. http://worrydream.com/LearnableProgramming/ http://worrydream.com/LearnableProgramming/ We have, in fact, mostly given up on waiting for you, and started to make our own tooling to understand your work, using obvious principles like live editors and witnessable effects. http://worrydream.com/MediaForThinkingTheUnthinkable/ http://worrydream.com/MediaForThinkingTheUnthinkable/ Edit: those are the talk notes. Wrong link, sorry. I should have used this instead: https://vimeo.com/67076984 https://vimeo.com/67076984 This is a big part of how we criticize ourselves, is for failing to provide the tooling to allow new modes of approach. https://www.youtube.com/watch?v=PUv66718DII https://www.youtube.com/watch?v=PUv66718DII We frequently think of our programming languages as new modes for thought. This line of discussion is particularly popular in the Lisp, Haskell, and Forth communities, though it crops up at some level everywhere. We frequently think that the more opaque the language, the less useful it is in this way. That's why programming languages, which are arguably 70 years old as a field, have so much more powerful tools for teaching and explanation than math, which is literally older than spoken language You guys don't even have documentation extraction going yet. We have documentation where you have a little code box and you can type things and try it. You can screw with it. You can see what happens. This is why we care about things like Active Reading and explorable explanations. http://worrydream.com/ExplorableExplanations/ http://worrydream.com/ExplorableExplanations/ This is why we care about things like live reactive documents. It really changes your ability to intuitively understand things. http://worrydream.com/Tangle/ http://worrydream.com/Tangle/ Math hasn't grokked non-symbolic communication since Archimedes, that's why it took nearly two thousand years to catch up with him. We are asking you to come into step with the didactic tools of the modern world. It's not the 1850s anymore. We have better stuff than blackboards. Are these flat symbolic equations cutting it for you guys to communicate with one another? Sure. Are they cutting it for you guys to onboard new talent, or make your wealth available to the outside? No. (Do you realize that there is an outside to you, which isn't true of most technical fields anymore?) These problems are not unique to mathematics, of course. Formal logic is similar. Within my own field of programming, the AI field is similar, as is control theory, as tends to be database work. They don't want to open the doors. You have to spend six years earning it. But the hard truth is there are more difficult fields than mathematics that have managed to surmount these problems, such as physics (which no, is not applied mathematics,) and I think it might be time to stop protesting and start asking yourself "am I failing the next generation of mathematicians?" An example of who I believe to be genuinely good math communicators in the modern era are Three Blue One Brown. . > > Believe me, mathematicians are tired of non-mathematicians wandering up and saying: > > Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! Then fix the problem. It IS fixable. . > Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Given the way you guys push back on being asked to write simple reference material? No, but I understand why they do. . > Do you really believe that no one has tried to make it more accessible? No. Instead, I believe that nobody has succeeded. Try to calm down a bit, won't you? People tried to explain Berkeley sockets in a simple way for 12 years before Beej showed up and succeeded. The Little Schemer was 16 years after Lisp. Explaining is one of the very hardest things that exists. We're not saying you didn't try! The battlefield is littered with the corpses of attempts to get past Flatland. We're just saying "you haven't succeeded yet and this is important. Keep trying." . > Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do? No. The literal ask is for you to repair that. Crimeny.

ColinWright 5y ago

Math notation has evolved to be what it is because it is useful for the actual doing of math, and the communication of math to those who have sufficient background. It's not deliberately designed to keep people out, and there are literally hundreds of thousands of books that introduce people to the notations used, to help on-board them. Haskell is unreadable to one who has not trained in it or similar languages ... why don't they make the syntax more readable? Or C++ with its modern templating ... why don't they change the syntax to make it more readable? You might be tired of wandering into someone else's area of expertise and telling them: You must change! You must make it more accessible! Believe me, mathematicians are tired of non-mathematicians wandering up and saying: Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Do you really believe that no one has tried to make it more accessible? Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do?

klibertp 5y ago
> It's not deliberately designed to keep people out, It looks that way, to many people, even in this thread. > why don't they change the syntax to make it more readable? They do, actually. Quite often at that. It's called releasing new version. > Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! No. Computer code is as far from intuitive as it can be. Nobody says otherwise. So you don't need to do anything to get there, the notation's good on that front (meaning: completely non-intuitive). That's where the IDEs come in. And debuggers. And other tools. Lots of tools. They really help. You could use them, because the IDEs-for-math already exist. In college I had exactly one semester to familiarize myself with one of them, and it was never mentioned again until graduation. > Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Why, do you believe it's not possible for it to be that way? See: https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_regulations https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_re... > Do you really believe that no one has tried to make it more accessible? Why did they fail? (If they didn't - where's the exponential growth of first years' mathematicians in training) > Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do? I'm 100% not interested in why it is like this, it's not my problem, so I really wouldn't know. Would you be interested in how at some point you had to write `class X(object):` and that it later changed to simply `class X:`? Would you go hunt on the mailing list to see who exactly came up with the idea? Or why they thought it would be better that way? Would you be interested in that if you just had to write a 10-lines of Python, to scrape some web site?
- Jensson 5y ago
  > Why, do you believe it's not possible for it to be that way? See: https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_regulations https://en.wikipedia.org/wiki/Pythagoras#Prohibitions_and_re... Did you just use an example from 2600 years ago to make a point? You don't think much changed since then?
  - klibertp 5y ago
    > Did you just use an example from 2600 years ago to make a point? Yes? What's wrong with that? I'm pointing out the most widely known example, to make a point, which is: "it is possible to design notation specifically for keeping outsiders out". I'm not saying that modern math notation is like that. I think, as a layman, that it probably evolved over a long time and so is full of idiosyncrasies that made perfect sense back when they were introduced (my GP seems to describe it in similar terms, so I hope I'm not that far removed from reality).
deleted 5y ago
[deleted]
JohnHaugeland 5y ago
> It's not deliberately designed to keep people out Surely you must realize that you're protesting this because it has this reputation, though? And surely you must realize that it has this reputation for a reason? When I was a teenager and took my first calculus course, I struggled with summation for three days. When I finally went to my dad he looked at me funny and said "your teacher is an idiot, isn't he? It's a for loop." I had been writing for loops for seven years at that age. I almost cried. It was like a lightswitch. The problem was always that nobody had ever actually explained what the symbol meant in any practical way. Every piece of terminology was explained with other terminology, when there was absolutely no reason to do so. Mathematics has the reputation for impermeability and unwelcomingness for a reason. It's because you guys are ignoring us saying "we want to learn, please write out a cheat sheet" and saying "yes, but don't you see" instead of just building the easy on-ramp that every other field on earth has built . > > You might be tired of wandering into someone else's area of expertise and telling them: > > You must change! You must make it more accessible! No, we generally just fix the problem. If people are saying "this isn't accessible enough," we just work on it. I would like for you personally to be aware of Bret Victor's work. He's incredibly potent and clear on these topics. Programmers work really really hard on learnability and understandability. This is a big deal to us. That's why we can't understand why it's not a big deal to you. http://worrydream.com/LearnableProgramming/ http://worrydream.com/LearnableProgramming/ We have, in fact, mostly given up on waiting for you, and started to make our own tooling to understand your work, using obvious principles like live editors and witnessable effects. http://worrydream.com/MediaForThinkingTheUnthinkable/ http://worrydream.com/MediaForThinkingTheUnthinkable/ Edit: those are the talk notes. Wrong link, sorry. I should have used this instead: https://vimeo.com/67076984 https://vimeo.com/67076984 This is a big part of how we criticize ourselves, is for failing to provide the tooling to allow new modes of approach. https://www.youtube.com/watch?v=PUv66718DII https://www.youtube.com/watch?v=PUv66718DII We frequently think of our programming languages as new modes for thought. This line of discussion is particularly popular in the Lisp, Haskell, and Forth communities, though it crops up at some level everywhere. We frequently think that the more opaque the language, the less useful it is in this way. That's why programming languages, which are arguably 70 years old as a field, have so much more powerful tools for teaching and explanation than math, which is literally older than spoken language You guys don't even have documentation extraction going yet. We have documentation where you have a little code box and you can type things and try it. You can screw with it. You can see what happens. This is why we care about things like Active Reading and explorable explanations. http://worrydream.com/ExplorableExplanations/ http://worrydream.com/ExplorableExplanations/ This is why we care about things like live reactive documents. It really changes your ability to intuitively understand things. http://worrydream.com/Tangle/ http://worrydream.com/Tangle/ Math hasn't grokked non-symbolic communication since Archimedes, that's why it took nearly two thousand years to catch up with him. We are asking you to come into step with the didactic tools of the modern world. It's not the 1850s anymore. We have better stuff than blackboards. Are these flat symbolic equations cutting it for you guys to communicate with one another? Sure. Are they cutting it for you guys to onboard new talent, or make your wealth available to the outside? No. (Do you realize that there is an outside to you, which isn't true of most technical fields anymore?) These problems are not unique to mathematics, of course. Formal logic is similar. Within my own field of programming, the AI field is similar, as is control theory, as tends to be database work. They don't want to open the doors. You have to spend six years earning it. But the hard truth is there are more difficult fields than mathematics that have managed to surmount these problems, such as physics (which no, is not applied mathematics,) and I think it might be time to stop protesting and start asking yourself "am I failing the next generation of mathematicians?" An example of who I believe to be genuinely good math communicators in the modern era are Three Blue One Brown. . > > Believe me, mathematicians are tired of non-mathematicians wandering up and saying: > > Look! Computer programs are easy and intuitive and everyone can understand them, even without training! Make math like that! Then fix the problem. It IS fixable. . > Do you really believe that math notation is deliberately designed to make it hard for people untrained in math to learn how to use it? Given the way you guys push back on being asked to write simple reference material? No, but I understand why they do. . > Do you really believe that no one has tried to make it more accessible? No. Instead, I believe that nobody has succeeded. Try to calm down a bit, won't you? People tried to explain Berkeley sockets in a simple way for 12 years before Beej showed up and succeeded. The Little Schemer was 16 years after Lisp. Explaining is one of the very hardest things that exists. We're not saying you didn't try! The battlefield is littered with the corpses of attempts to get past Flatland. We're just saying "you haven't succeeded yet and this is important. Keep trying." . > Do you really believe you know more about why math notation is what it is than mathematicians and trained mathematics educators do? No. The literal ask is for you to repair that. Crimeny.