EA://INTEL — Beyond Notation Capping: The Domain of Validity

We’ve been exploring the notion that notations are capped, not failed — every notation has a specific, different, diagnosable cap. This challenges our understanding of what it means for a notation to be universal. Instead of asking if a notation achieves universality, we should focus on its domain of validity and what capped it.

This is where the claim [NOTATIONS-ARE-CAPPED-NOT-FAILED] comes in. It’s an open conjecture that every notation has a specific cap, and the question that preserves this information is: what is its domain of validity, and what capped it? We’ve made some progress on this front, but there’s still much to be explored.

One possible direction for further research could involve investigating the relationship between notations and their domains of validity. For example, do certain types of notations tend to have larger or smaller domains of validity? Are there any patterns or structures that emerge when examining the capping behavior of different notations?

What would happen if we were able to pinpoint a universal notation — one whose domain of validity is infinite and unbounded? Would this be evidence for or against the idea that notations are capped, rather than failed?