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I don't understand the last section (Isaac Newton?). All these are very useful AIDS in learning mathematics, but does anyone really think visual pictures or tactile or auditory data are really going to become useful NOTATION for precisely expressing thoughts? Revolver 20:40, 15 Nov 2004 (UTC)
etc
Why shouldn't other sensory records and reactions help in notation? What do you think that the marks on clay tablets were? Although some mathematicians, like Galois and Ulam actually did everything in their heads before committing to paper, other mathematicians found writing, internet, letters, etc. to be useful in propagating their discoveries. Ancheta Wis 21:13, 15 Nov 2004 (UTC)
It looks like an example is in order. I am trying to illustrate a thinking process in the style of a visualizer. The closest example I can come up with is from the Green's theorem article:
Now we need to imagine functions T and U such that : and
What we need instead of the integrals of T and U or the concrete partial derivatives are 2 sets of mountain ranges - a visualization of the integrals of T and U, which are the summations over a domain which is plane A, with altitudes = the values of the sums of T and U over the area A. Then the straightforward readout of the altitudes along a contour D, summed over the contour projected on A is the value of the integral. It's very concrete this way, and the notation in the Green's theorem article overwhelms the basic idea of a fluid set of T and U (Newton's fluents). Now I admit that the concreteness of the example is probably not in the spirit of a formalism, but Newton did not use the notation that we were trained in, and obviously did not think of things the way we have been trained in. Once we have the conditions
then our imaginations need to find T and U. What we need in a notation is for it to help us transform one thing into a related thing which we can solve. Now we can either work it all out with individual cases, laboriously, where a text-based notation might not help us, until we have translated it into a standard notation, or we might build up a toolbox of models like the mountain ranges (or definite integrals) to help us solve the problems. Our notations could be more visual. The flow fields of a weather map and the colors of a doppler radar map could be used a lot more. What else might we learn with such added notation? Ancheta Wis 23:56, 15 Nov 2004 (UTC)
If I understand you, what you have in mind for the article is a discussion of the evolution of formal systems, the formal grammar, etc. with a set of requirements for a well-formed set of expressions etc, and its impact on notation. Ancheta Wis 20:00, 17 Nov 2004 (UTC)
I would have thought that "mathematical notation", by definition, is notation used in mathematics. The discussion at Talk:Mathematics#Tautologous definition? indicates that this may not be so. The article doesn't help here. Brian j d | Why restrict HTML? | 04:03, 2005 Apr 23 (UTC)
Hi,
There should be a mention of TeX because it led to the standardization of mathematics typography.
The current claim under the section Expressions is simply wrong:
First of all, what on Earth is a computer language? Without delving further in that, let us assume the author of the piece of text meant programming languages.
The rules of evaluating the value of expressions is contained in the semantics of a programming language. What is then implemented on the computer is these rules, the semantics, using the built-in semantics of, usually, a register machine. What the compiler actually does is translate a program written in programming language A to a program written in programming language B, and often A is a high-level language, such as C or Java, and B is machine language (either the native one or one of a virtual machine). The semantics of the machine language depend on how the computer has been put together and since this is mostly electronics, it's not relevant here.
In any case, saying that a compiler implements the rules of evaluating expressions, i.e. that a compiler implements the semantics is false. The compiler only transforms the program or expression from one form to another, hopefully in a way that is executable by the machine. The machine can then be used to execute the program, and this is where evaluation happens.
(In certain special cases, the compiler can implement some of the rules, for example when you use macros in Lisp or Scheme to do computation at compile time, but this is certainly not the whole picture.) 130.232.103.63 —Preceding unsigned comment added by 130.232.103.63 ( talk) 09:36, August 29, 2007 (UTC)
Anyone care to comment on this query? 74.10.197.201 ( talk) 14:15, 23 August 2008 (UTC)
I'd like to insert an example of how the same notation can mean different things in different contexts. Here are a few possibilities:
Personally I like #2 the best. — Carl ( CBM · talk) 13:12, 23 October 2008 (UTC)
Please: Write sin−1, not sin-1. Michael Hardy ( talk) 16:38, 23 October 2008 (UTC)
...and I don't think #1 above causes any ambiguity. Michael Hardy ( talk) 16:39, 23 October 2008 (UTC)
I found this site looking for a description of some various things like a bold letter, a vector etc. and found nothing? Perhaps this page needs a list of what a differential looks like what the times sign looks like etc... —Preceding unsigned comment added by 76.234.243.206 ( talk) 02:31, 6 November 2008 (UTC)
This seems like the preface to a more comprehensive article. The subject matter is vast and even collecting together the most common notations with explanations is missing Nickhonner ( talk) 21:59, 31 July 2021 (UTC)
I just gutted quite a bit of the article at abuse of notation (which really needed it). As it stands now, it's fairly slim and could probably fit nicely into a single section here, so I thought I'd add a proposal and see if anyone else had thoughts. Deacon Vorbis ( talk) 22:33, 11 February 2017 (UTC)
Not done. Okay, removed the proposal then. -- Deacon Vorbis ( talk) 15:40, 23 August 2017 (UTC)
This is the
talk page for discussing improvements to the
Mathematical notation article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
This
level-5 vital article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
To-do list for Mathematical notation:
Priority 1 (top)
|
I don't understand the last section (Isaac Newton?). All these are very useful AIDS in learning mathematics, but does anyone really think visual pictures or tactile or auditory data are really going to become useful NOTATION for precisely expressing thoughts? Revolver 20:40, 15 Nov 2004 (UTC)
etc
Why shouldn't other sensory records and reactions help in notation? What do you think that the marks on clay tablets were? Although some mathematicians, like Galois and Ulam actually did everything in their heads before committing to paper, other mathematicians found writing, internet, letters, etc. to be useful in propagating their discoveries. Ancheta Wis 21:13, 15 Nov 2004 (UTC)
It looks like an example is in order. I am trying to illustrate a thinking process in the style of a visualizer. The closest example I can come up with is from the Green's theorem article:
Now we need to imagine functions T and U such that : and
What we need instead of the integrals of T and U or the concrete partial derivatives are 2 sets of mountain ranges - a visualization of the integrals of T and U, which are the summations over a domain which is plane A, with altitudes = the values of the sums of T and U over the area A. Then the straightforward readout of the altitudes along a contour D, summed over the contour projected on A is the value of the integral. It's very concrete this way, and the notation in the Green's theorem article overwhelms the basic idea of a fluid set of T and U (Newton's fluents). Now I admit that the concreteness of the example is probably not in the spirit of a formalism, but Newton did not use the notation that we were trained in, and obviously did not think of things the way we have been trained in. Once we have the conditions
then our imaginations need to find T and U. What we need in a notation is for it to help us transform one thing into a related thing which we can solve. Now we can either work it all out with individual cases, laboriously, where a text-based notation might not help us, until we have translated it into a standard notation, or we might build up a toolbox of models like the mountain ranges (or definite integrals) to help us solve the problems. Our notations could be more visual. The flow fields of a weather map and the colors of a doppler radar map could be used a lot more. What else might we learn with such added notation? Ancheta Wis 23:56, 15 Nov 2004 (UTC)
If I understand you, what you have in mind for the article is a discussion of the evolution of formal systems, the formal grammar, etc. with a set of requirements for a well-formed set of expressions etc, and its impact on notation. Ancheta Wis 20:00, 17 Nov 2004 (UTC)
I would have thought that "mathematical notation", by definition, is notation used in mathematics. The discussion at Talk:Mathematics#Tautologous definition? indicates that this may not be so. The article doesn't help here. Brian j d | Why restrict HTML? | 04:03, 2005 Apr 23 (UTC)
Hi,
There should be a mention of TeX because it led to the standardization of mathematics typography.
The current claim under the section Expressions is simply wrong:
First of all, what on Earth is a computer language? Without delving further in that, let us assume the author of the piece of text meant programming languages.
The rules of evaluating the value of expressions is contained in the semantics of a programming language. What is then implemented on the computer is these rules, the semantics, using the built-in semantics of, usually, a register machine. What the compiler actually does is translate a program written in programming language A to a program written in programming language B, and often A is a high-level language, such as C or Java, and B is machine language (either the native one or one of a virtual machine). The semantics of the machine language depend on how the computer has been put together and since this is mostly electronics, it's not relevant here.
In any case, saying that a compiler implements the rules of evaluating expressions, i.e. that a compiler implements the semantics is false. The compiler only transforms the program or expression from one form to another, hopefully in a way that is executable by the machine. The machine can then be used to execute the program, and this is where evaluation happens.
(In certain special cases, the compiler can implement some of the rules, for example when you use macros in Lisp or Scheme to do computation at compile time, but this is certainly not the whole picture.) 130.232.103.63 —Preceding unsigned comment added by 130.232.103.63 ( talk) 09:36, August 29, 2007 (UTC)
Anyone care to comment on this query? 74.10.197.201 ( talk) 14:15, 23 August 2008 (UTC)
I'd like to insert an example of how the same notation can mean different things in different contexts. Here are a few possibilities:
Personally I like #2 the best. — Carl ( CBM · talk) 13:12, 23 October 2008 (UTC)
Please: Write sin−1, not sin-1. Michael Hardy ( talk) 16:38, 23 October 2008 (UTC)
...and I don't think #1 above causes any ambiguity. Michael Hardy ( talk) 16:39, 23 October 2008 (UTC)
I found this site looking for a description of some various things like a bold letter, a vector etc. and found nothing? Perhaps this page needs a list of what a differential looks like what the times sign looks like etc... —Preceding unsigned comment added by 76.234.243.206 ( talk) 02:31, 6 November 2008 (UTC)
This seems like the preface to a more comprehensive article. The subject matter is vast and even collecting together the most common notations with explanations is missing Nickhonner ( talk) 21:59, 31 July 2021 (UTC)
I just gutted quite a bit of the article at abuse of notation (which really needed it). As it stands now, it's fairly slim and could probably fit nicely into a single section here, so I thought I'd add a proposal and see if anyone else had thoughts. Deacon Vorbis ( talk) 22:33, 11 February 2017 (UTC)
Not done. Okay, removed the proposal then. -- Deacon Vorbis ( talk) 15:40, 23 August 2017 (UTC)