De Bruijn's observation about typed sets being "close to their interpretations" versus ZF's coding tricks resonates deeply. I was part of that cohort - learned set theory by age 8 in 1971.
I'm working on spatial data organization where the same principle applies - forcing multi-dimensional relationships into rigid 2D grids creates the same kind of nonsense that x∈x creates in untyped set theory. The DOM becomes the type system: dragging tags to spatial zones determines valid operations polymorphically. The same tag exhibits different typed behaviors based on where you drop it.
De Bruijn wants types defined first, then populated. I do the opposite: dump data in, let semantic clustering reveal natural types, then let spatial manipulation expose different facets. The system is hereditarily finite - cards, tags, and workspaces are finite all the way down - which is sufficient for essentially all real-world productivity use cases.
Launching in the next few weeks. Might write a longer piece on practical typed set theory in productivity tools after that.
adamzwasserman•2mo ago
De Bruijn's observation about typed sets being "close to their interpretations" versus ZF's coding tricks resonates deeply. I was part of that cohort - learned set theory by age 8 in 1971.
I'm working on spatial data organization where the same principle applies - forcing multi-dimensional relationships into rigid 2D grids creates the same kind of nonsense that x∈x creates in untyped set theory. The DOM becomes the type system: dragging tags to spatial zones determines valid operations polymorphically. The same tag exhibits different typed behaviors based on where you drop it.
De Bruijn wants types defined first, then populated. I do the opposite: dump data in, let semantic clustering reveal natural types, then let spatial manipulation expose different facets. The system is hereditarily finite - cards, tags, and workspaces are finite all the way down - which is sufficient for essentially all real-world productivity use cases.
Launching in the next few weeks. Might write a longer piece on practical typed set theory in productivity tools after that.
multicardz: "Drag. Drop. Discover."
Thanks for the food for thought