14 ms·

I understand the wish, and Mathematica does a pretty great job of making the mathematical notation less ambiguous, but I‘m surprised that this would be your hig

by davnn 4y ago

I understand the wish, and Mathematica does a pretty great job of making the mathematical notation less ambiguous, but I‘m surprised that this would be your highest priority. Do you actually enjoy writing in math notation?

laingc 4y ago
If you’re a working mathematician, it’s the only way you think.
- esperent 4y ago
  If you are the X then you must do/be Y is called gatekeeping. And of course this is not true. I know mathematicians who work almost exclusively on a computer, and others who have an old dusty computer from 20 years ago in the corner of their office that they barely touch. Most are somewhere in between.
  - qubex 4y ago
    Mathematics is one of the oldest disciplines in the world. Grumbling about the legacy of its ancient history as ‘gatekeeping’ is puerile.
    - Beldin 4y ago
      This started worth talking about notation. Notation of mathematics has changed significantly over time - Newton's Principae is not readable without accounting for changes. In the history of maths, that is a fairly recent work.
      - qubex 4y ago
        I actually agree with your premise: mathematics and it’s notations (plural) are ancient. The current notations are those that were found to be most convenient by centuries of practice by expert practitioners.
        tikej 4y ago
        This is of course very true but doesn’t take into account invention of computer that is relatively recent. Since it in principle never makes mistakes (in practice there are of course bugs, but they are usually different in nature than human errors) it changes what is possible and most convenient. You no longer have to optimise for simplicity as heavily for example. On the other hand computers basically can’t deal with ambiguity, so the rules and statements have to be stated very simply and clearly. EDIT: One example that comes to mind are indexes in functions. Usually they are just additional arguments that are different somehow from the “main” arguments, for example often being non-negative integers. For humans it makes it easier to think and operate about indices separately from the rest of arguments. But for the computer it’s all the same, as all arguments are treated just as argument, (of course it depends on the implementation etc) and there is no need to treat them separately, since every argument is “special”. I believe computers can change the landscape of what’s best notation. This is an interesting, interdisciplinary topic to explore.
        Qem 4y ago
        I think APL was originally created as a fix to this problem. A completely revamped math notation to make it more fit to computers as a medium, instead of pen and paper.
        hilbert42 4y ago
        If it was created thus then it could hardly be considered successful. To all but the dedicated and obsessive cognoscenti APL is nothing but gobbledygook.
  - hdjjhhvvhga 4y ago
    > If you are the X then you must do/be Y is called gatekeeping. Let's be precise here: the parent hasn't used "must" here, just stated their observation. It's possible that many if not most mathematicians work this way, but it's not definitely the only one, and it doesn't mean it can't be changed. Actually, there is a lot of work being done on theorem provers, for example.
  - traverseda 4y ago
    If you are a python programmer you must program in python.
adastra22 4y ago
Yes. I'm sorry but how is this not obvious? Do you enjoy hand-writing code on paper? The natural medium for math is on whiteboards and paper. A computer algebra system like Mathematica is useful, but it augments what is traditionally a paper-and-pencil activity. It makes sense that the standard notation for math is something that is amenable to physical tools. And it makes sense that the computer tools to assist mathematicians should more closely match this standard notation.
dagw 4y ago
In many cases yes. Especially non-programmers really like that the equation they type into their software looks exactly the the equation in the paper they are copying it from.
TheRealPomax 4y ago
Who said it was my highest priority? Obviously having a solver is the highest priority, but it turns out that if you purport to have made a mathematica competitor, that was the baseline. If you don't have that, you have nothing. So the question is never "can it do what it needs to", it's always "can it do the things which keep me using Mathematica, instead of Sage, like letting me compose notebooks that contain, and show, actual maths?" And yes, I enjoy writing in math notation because it's an immediately understandable notation compared to 500 character programming statement.

by davnn 4y ago

laingc 4y ago

If you’re a working mathematician, it’s the only way you think.

esperent 4y ago
If you are the X then you must do/be Y is called gatekeeping. And of course this is not true. I know mathematicians who work almost exclusively on a computer, and others who have an old dusty computer from 20 years ago in the corner of their office that they barely touch. Most are somewhere in between.
- qubex 4y ago
  Mathematics is one of the oldest disciplines in the world. Grumbling about the legacy of its ancient history as ‘gatekeeping’ is puerile.
  - Beldin 4y ago
    This started worth talking about notation. Notation of mathematics has changed significantly over time - Newton's Principae is not readable without accounting for changes. In the history of maths, that is a fairly recent work.
    - qubex 4y ago
      I actually agree with your premise: mathematics and it’s notations (plural) are ancient. The current notations are those that were found to be most convenient by centuries of practice by expert practitioners.
      - tikej 4y ago
        This is of course very true but doesn’t take into account invention of computer that is relatively recent. Since it in principle never makes mistakes (in practice there are of course bugs, but they are usually different in nature than human errors) it changes what is possible and most convenient. You no longer have to optimise for simplicity as heavily for example. On the other hand computers basically can’t deal with ambiguity, so the rules and statements have to be stated very simply and clearly. EDIT: One example that comes to mind are indexes in functions. Usually they are just additional arguments that are different somehow from the “main” arguments, for example often being non-negative integers. For humans it makes it easier to think and operate about indices separately from the rest of arguments. But for the computer it’s all the same, as all arguments are treated just as argument, (of course it depends on the implementation etc) and there is no need to treat them separately, since every argument is “special”. I believe computers can change the landscape of what’s best notation. This is an interesting, interdisciplinary topic to explore.
        Qem 4y ago
        I think APL was originally created as a fix to this problem. A completely revamped math notation to make it more fit to computers as a medium, instead of pen and paper.
        hilbert42 4y ago
        If it was created thus then it could hardly be considered successful. To all but the dedicated and obsessive cognoscenti APL is nothing but gobbledygook.
- hdjjhhvvhga 4y ago
  > If you are the X then you must do/be Y is called gatekeeping. Let's be precise here: the parent hasn't used "must" here, just stated their observation. It's possible that many if not most mathematicians work this way, but it's not definitely the only one, and it doesn't mean it can't be changed. Actually, there is a lot of work being done on theorem provers, for example.
- traverseda 4y ago
  If you are a python programmer you must program in python.

adastra22 4y ago

Yes. I'm sorry but how is this not obvious? Do you enjoy hand-writing code on paper? The natural medium for math is on whiteboards and paper. A computer algebra system like Mathematica is useful, but it augments what is traditionally a paper-and-pencil activity. It makes sense that the standard notation for math is something that is amenable to physical tools. And it makes sense that the computer tools to assist mathematicians should more closely match this standard notation.

dagw 4y ago

In many cases yes. Especially non-programmers really like that the equation they type into their software looks exactly the the equation in the paper they are copying it from.

TheRealPomax 4y ago

Who said it was my highest priority? Obviously having a solver is the highest priority, but it turns out that if you purport to have made a mathematica competitor, that was the baseline. If you don't have that, you have nothing. So the question is never "can it do what it needs to", it's always "can it do the things which keep me using Mathematica, instead of Sage, like letting me compose notebooks that contain, and show, actual maths?" And yes, I enjoy writing in math notation because it's an immediately understandable notation compared to 500 character programming statement.