I had the idea of working with math objects but applying all possible facts about such objects and collect those together. A kind of web of math. One could interactively choose what is possible. Each property makes for an object. A mathematical object made of a couple of syntactical facts, where each fact is a property. Such objects together make for a kind of indirect practice. Like psychology plus philosophy and reading/researching there. Perhaps the ability to expand upon certain traits of objects.

I think this is a good idia. I can see use in the VR and AR world for this. Like that you could integrate new objects in to your space. Just that you eventually will need a software to render those objects.
I know it’s not only about VR you are talking about but this can be an usecase.

Perhaps I should add an example:
To add a two to a number and differentiate that.
In the above ascription: 2n^1 is made from n^2.
So, {2, n, ^, 1} is the first object collection (C1).

I want to add all combinations of C1 explained and put together.
Each step has a single object (2 or n for example), and a single algorithm.
I call such single instances spots because.

Each object has only one spot.
All spots added together make for a single ‘object’.

So if one combines 2 objects (alphabet??), or two spots.
One must recreate it as an object with a single spot.
And such a spot makes for a combination of multiple spots.

It is about single objects but all with a certain amount of spots.
I.e. this could mean that some truth values arent created but can be assumed.
Plus: could be fillled in. Adding spots.