Published 2021-08-21T00:58:00.003Z by Physics Derivation Graph

The following aspects are "nice-to-have" in the Physics Derivation Graph:

- validation of derivation steps using computer algebra systems
- validation of consistency expression dimensions
- validation of consistency of units when present in expressions
- visualization of the graph
- make the code pretty and easy to navigate for contributors
- document the source code and design decisions
- searching the graph (see this and this and this)
- ability to determine whether paper is written by a crackpot
- ability to detect unintentional errors in an article or book
- cross-document references
- semantic tagging of Latex documents
- converting Latex from arxiv into formats supporting the above objectives
- linking Physics Derivation Graph to existing ontology databases

The core objective of the Physics Derivation Graph is identifying the mathematical connectivity of the various domains of Physics. The same connectivity should be able to relate "basic" Physics (e.g., *F=ma*) to advanced Physics (e.g., the theory of the Standard model, string theory).

I know of two ways to document the connectivity:

- identify symbol re-use
- identify inter-related derivations at the level of expressions

The symbol re-use is less interesting than the re-use of expressions.

I've previously documented a plan,

but I didn't specify what would qualify as sufficient to show completeness.

What core expressions are representative of all of Physics? Are there a set of expressions that, if shown to be connected by derivations, would be sufficient to demonstrate the span of the concept?

I expect that, for any given subdomain of Physics, there are central expressions. The task list is then

- identify every named expression in Physics
- identify every variable in that list of named expressions
- enter all named expressions and variables into the PDG database
- determine which expressions are not connected to anything