I want to compile a list of topics that could help inspire formal/mathematical abstractions for boundaries/membranes. (See my recent explainer.)
What technical topics are related to boundaries/membranes?
I've seeded the comments with some ideas. Please keep further comments organized in threads if possible. Also, please add high quality links to existing comments by others.
Related, consciousness frame: where is the boundary of it? Is our brain conscious, or the whole nervous system, or the whole human, or the whole human + the entire microbiome populating them, or human + robotic prosthetic limbs, or human + web search + chat AI + personal note taking app, or the whole human group (collective consciousness), etc.
Some computational theories of consciousness attempt to give a specific, mathematically formalised answer to this question.