New graphic notation to express math relationships

Ideas
, , , , ,
1

Hi, my name is Joseph. I’m new here, but I’ve known wolfram’s technologies since some years ago. Please forgive me if I make some spelling mistakes, my english is not perfect.

I’ve worked some years ago to develop a new way to express math relationships. I believe there must be another simpler and smarter way to express math, without disregarding the natural beauty of it. Eventually, I developed a simple math notation that, I think, fits my expectations and goals.

front_example.png
front_example.png247×384 2.33 KB

I also believe it has some unexpected adventages over traditional math notation:

  • Order of operations is explicit; it’s a non linear notation (it is diagram-based).
  • Variable isolation to transform equations to other equivalent forms, is not requiered.
  • Many orthodox equations can be represented at the same time using just a simple expression in this new notation.
  • This new notation has less operators.

You can actually see the specification here (GItHub). More general information here.

I have not found another similar way to express math, so I dream it will be useful for educators and scientsts, someday.

I open this thread because I need your opinion, criticism and scrutiny. This is a big and organized forum, so I believe there are many brilliant people with a honest opinion to give. Suggestions are all welcome, and this notation open to changes and improvements based on your reviews.

Thanks.

More examples

  • Slope-Intercept Form

slope_intercept_example.png
slope_intercept_example.png200×160 772 Bytes

  • Point-Slope Form

point_slope_example.png
point_slope_example.png306×230 1.17 KB

8 Likes
2

This probably could be implemented in Wolfram Language. Do you have any code for this - I have not seen any Mathematica files in your linked GitHub repository.

Another question. How do you suggest dealing with self-overlapping branches for large enough expressions? First thing that comes to mind is scaling down the branch size on deeper tree levels.

2 Likes
3

Hi Vitaliy;

I have not yet implemented this on any programming language, since my main purpose was to design a notation. However, that would be a good project to implement it in code, and I hope to start a project like that in the future. I know some python and ruby, but I have never used Wolfram Programming Language for projects. I appreciate that suggestion, since I know it is a good language for this purpose.

Also, I would like to find flaws and ambiguity first, before implementing it, because I fear I could loose valuable time implementing something that may not work.

Another question. How do you suggest dealing with self-overlapping
branches for large enough expressions? First thing that comes to mind
is scaling down the branch size on deeper tree levels.

Good question. I suggest pipes (long lines and L’s) to avoid overlapping (you can actually play with the length of the branches), but also variables to replace whole sections of the expression and express them somewhere else (or omit them, if they are not being discussed).

My biggest concerns are redundant variables in the same tree. I know traditional notation would allow them, but I’m not sure they work very well with this notation.

Thanks.

4

Hi Joseph,

I guess I’m a bit confused. In your first diagram, how can you infer that the upper 2 and 3 means 2^3 and not 2*3, 2+3, etc?

Also how does your idea scale with arbitrary functions? For example can you make a diagram for y = sin(2x)?

p.s. Have you seen the function TreeForm?

TreeForm[y == m x + b]

Screenshot2015-06-1910.53.41.png
Screenshot2015-06-1910.53.41.png359×401 9.23 KB

1 Like
5

Have you seen this example

comm515257.PNG
comm515257.PNG711×818 31.8 KB

and did you know that physicist Richard P. Feynman (a big diagramatic person, by the way) in his youth used to use his own symbolics because he felt the official (common-sense) notation awkward and confusing … later on the wish to be understood and to be able to communicate with others let him switch back to the usual notation (invented on its own by some mindful people, too) …

6

Joseph have you had any progress on this? Seems like very interesting idea and you should probably look into Graph functionality.

7

Hi @Joseph Anglada, did you have any further progress with this?

1 Like