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> Verbosity is nice up to a point. Yes, agreed. But so is brevity. Up to a point, it's good. Beyond that point, it's a needless burden that could be eliminated

> Verbosity is nice up to a point. Yes, agreed. But so is brevity. Up to a point, it's good. Beyond that point, it's a needless burden that could be eliminated. > It's almost impossible to find someone who can do, say Griffiths level electromagnetics or quantum mechanics without that formalism. I'm not saying that the formalism is useless. I'm saying it's not zero-cost. I'm against handwaving away the difficulty of working with the specific syntax because "concepts!" Again, show me that learning to use the notation is not a problem, objectively, and then we can talk. Otherwise, you're just saying that "you just have to learn it, I did it and it wasn't that hard". OK, but that's not a proof that it isn't hard or it isn't a barrier to entry that could be lowered.

BeetleB 3y ago
> Again, show me that learning to use the notation is not a problem, objectively, and then we can talk. Otherwise, you're just saying that "you just have to learn it, I did it and it wasn't that hard". OK, but that's not a proof that it isn't hard or it isn't a barrier to entry that could be lowered. It's always believable that the barrier can be lowered. However, consider that on the one hand, you have millions of people who are quite comfortable with the current notation. On the other hand, there is ... nothing. As I said, show me the alternative notation where people are comfortable solving Griffith level EM/QM problems with it. I've heard this complaint for years - particularly on HN. An insistence that a superior notation must exist, that decades of SW experience shows this level of brevity makes working in the field harder, etc. Yet no one has come up with an alternative where one can solve higher level physics problems with it while maintaining sanity. The status quo is we have a widely used system working. The burden is on those who claim it can be better to come up with something better.
- klibertp 3y ago
  > The burden is on those who claim it can be better to come up with something better. We need to agree to disagree: in my mind, it's on those who say it's the best it can be to show that it indeed, cannot be better. Because otherwise their insistence on not even looking for ways to make it better looks drastically different. If you can show me that math notation is as closely aligned with how cognition works as possible without sacrificing its usability - that's great, you're right, I concede. OTOH, if the only thing you say is that it worked for a long time, worked for you, and therefore you're not interested in doing anything for it to work better - that strikes me as simply elitist. The other problem is that nobody who is not deeply involved with math cares enough to take a closer look. How many linguists, psychologists, cognitive scientists invested their time into researching ways of making math notation better? I bet even fewer than the ones who tried researching programming. On the other hand, mathematicians are simply not equipped with knowledge and skills required to objectively assess the notation they use (neither are programmers, BTW.)
  - BeetleB 3y ago
    > In my mind, it's on those who say it's the best it can be to show that it indeed, cannot be better. Indeed. The issue is that neither I nor most people are claiming it to be the best. I explicitly pointed this out in another comment. > OTOH, if the only thing you say is that it worked for a long time, worked for you, and therefore you're not interested in doing anything for it to work better - that strikes me as simply elitist. How is that elitist? If it works for me, why should I spend time making it better for? What do I gain from it? And this comment doesn't even make sense. Mathematicians invent notations for their own convenience all the time. There's no committee that says "Yes, this is the official accepted notation." A mathematician uses whatever notation works for him, and if others find it useful, they adopt it. > The other problem is that nobody who is not deeply involved with math cares enough to take a closer look. How many linguists, psychologists, cognitive scientists invested their time into researching ways of making math notation better? I bet even fewer than the ones who tried researching programming. On the other hand, mathematicians are simply not equipped with knowledge and skills required to objectively assess the notation they use (neither are programmers, BTW.) You're not wrong, but you're also not helping. This is basically saying "Look, someone should do this!" If you think it's worthwhile, go for it. The category of professionals you have mentioned (linguists, etc) - most of them do not see it to be worthwhile. Put yourself in their shoes. Are they really going to invest a lot of effort to unseat a notation that has evolved over so many centuries, and then fight a battle to convince people to use it? That may well be a career killer. And where the two of us will have to disagree on: Any improvement, although may be great for newcomers and amateurs, will barely have any impact on the productivity of a professional mathematician. As people have repeatedly pointed out: Notation is amongst the least challenging part of math. Sure, it is a barrier to entry, but at best you're simply lowering the barrier to entry - it won't benefit people who are already good at mathematics. A better notation will not enable them to suddenly grasp concepts they couldn't. That's why mathematicians don't bother. To be frank (and I say it in all seriousness), the English language has more problems than the mathematical one, and if we could fix those, it would have a much larger impact.

BeetleB 3y ago

> Again, show me that learning to use the notation is not a problem, objectively, and then we can talk. Otherwise, you're just saying that "you just have to learn it, I did it and it wasn't that hard". OK, but that's not a proof that it isn't hard or it isn't a barrier to entry that could be lowered. It's always believable that the barrier can be lowered. However, consider that on the one hand, you have millions of people who are quite comfortable with the current notation. On the other hand, there is ... nothing. As I said, show me the alternative notation where people are comfortable solving Griffith level EM/QM problems with it. I've heard this complaint for years - particularly on HN. An insistence that a superior notation must exist, that decades of SW experience shows this level of brevity makes working in the field harder, etc. Yet no one has come up with an alternative where one can solve higher level physics problems with it while maintaining sanity. The status quo is we have a widely used system working. The burden is on those who claim it can be better to come up with something better.

klibertp 3y ago
> The burden is on those who claim it can be better to come up with something better. We need to agree to disagree: in my mind, it's on those who say it's the best it can be to show that it indeed, cannot be better. Because otherwise their insistence on not even looking for ways to make it better looks drastically different. If you can show me that math notation is as closely aligned with how cognition works as possible without sacrificing its usability - that's great, you're right, I concede. OTOH, if the only thing you say is that it worked for a long time, worked for you, and therefore you're not interested in doing anything for it to work better - that strikes me as simply elitist. The other problem is that nobody who is not deeply involved with math cares enough to take a closer look. How many linguists, psychologists, cognitive scientists invested their time into researching ways of making math notation better? I bet even fewer than the ones who tried researching programming. On the other hand, mathematicians are simply not equipped with knowledge and skills required to objectively assess the notation they use (neither are programmers, BTW.)
- BeetleB 3y ago
  > In my mind, it's on those who say it's the best it can be to show that it indeed, cannot be better. Indeed. The issue is that neither I nor most people are claiming it to be the best. I explicitly pointed this out in another comment. > OTOH, if the only thing you say is that it worked for a long time, worked for you, and therefore you're not interested in doing anything for it to work better - that strikes me as simply elitist. How is that elitist? If it works for me, why should I spend time making it better for? What do I gain from it? And this comment doesn't even make sense. Mathematicians invent notations for their own convenience all the time. There's no committee that says "Yes, this is the official accepted notation." A mathematician uses whatever notation works for him, and if others find it useful, they adopt it. > The other problem is that nobody who is not deeply involved with math cares enough to take a closer look. How many linguists, psychologists, cognitive scientists invested their time into researching ways of making math notation better? I bet even fewer than the ones who tried researching programming. On the other hand, mathematicians are simply not equipped with knowledge and skills required to objectively assess the notation they use (neither are programmers, BTW.) You're not wrong, but you're also not helping. This is basically saying "Look, someone should do this!" If you think it's worthwhile, go for it. The category of professionals you have mentioned (linguists, etc) - most of them do not see it to be worthwhile. Put yourself in their shoes. Are they really going to invest a lot of effort to unseat a notation that has evolved over so many centuries, and then fight a battle to convince people to use it? That may well be a career killer. And where the two of us will have to disagree on: Any improvement, although may be great for newcomers and amateurs, will barely have any impact on the productivity of a professional mathematician. As people have repeatedly pointed out: Notation is amongst the least challenging part of math. Sure, it is a barrier to entry, but at best you're simply lowering the barrier to entry - it won't benefit people who are already good at mathematics. A better notation will not enable them to suddenly grasp concepts they couldn't. That's why mathematicians don't bother. To be frank (and I say it in all seriousness), the English language has more problems than the mathematical one, and if we could fix those, it would have a much larger impact.