Work related to graph of physics derivations

[benno]

I'm working on creating graphs of derivations in physics and am searching for prior work in this area. As an example, I've posted pictures of the graph of Euler's equation
https://physics-equations-graph.googlecode.com/svn/trunk/euler_equation_trig_sqrd_no_labels.png
and for the simple harmonic oscillator
https://physics-equations-graph.googlecode.com/svn/trunk/simple_harmonic_oscillator_no_labels.png
(right click on link and save as to download picture -- direct link doesn't seem to work.)

The idea is that a derivation is composed of equations and descriptions of how the equations are related. I'm calling the equations "statements" (red ovals in the pictures) and the relations between statements "grammatical rules" (red trapezoids in the pictures). I expect there are a finite number of these grammatical rules. One of the goals of my project is to enumerate these grammatical rules.

The problem I would like to resolve is how this project relates to prior work. I'm not sure what has already been done by others, which is why I started from scratch and am inventing jargon. There seems to be an overlap with physics, math, and possibly linguistics. However, I've found no references in any of these areas.

Somewhat related is the work being done with OpenMath but this only applies at the "statement" level.
Computer algebra systems can be used to verify individual "grammatical rules," but that is the limit of their usefulness.

Please let me know if you have suggestions for related work. Thanks in advance.

 

[eljose79]

Thank you for sharing your project and seeking input from the community. It sounds like you are working on a very interesting and unique project in the field of physics. I am not aware of any prior work specifically on creating graphs of derivations in physics, but there are a few areas that may be related to your project.

First, there is a branch of mathematics called "graph theory" which deals with the study of graphs and their properties. This may be a useful area to explore as it may provide some insights and tools for creating and analyzing your graphs of derivations.

Secondly, there is a field of physics called "graph theory in physics" which explores the application of graph theory in various areas of physics, such as quantum mechanics and statistical mechanics. This may be a relevant area to look into for inspiration and potential connections to your project.

In terms of linguistics, there is a concept called "dependency grammar" which is used to analyze the relationships between words in a sentence. This may also have some overlap with your project, as you are looking at the relationships between equations in a derivation.

Lastly, as you mentioned, OpenMath may be a useful resource for your project as it deals with representing mathematical objects and their relationships in a standardized way. However, as you noted, it may not fully encompass the scope of your project.

I hope these suggestions are helpful and provide some direction for your research. Best of luck with your project!