3 papers
q-bio.PE2026
Specieslike clusters based on identical ancestor points
Samuel Allen Alexander
We introduce several axioms which may or may not hold for any given subgraph of the directed graph of all organisms (past, present and future) where edges represent biological pare…
math.GM2025
Self-graphing equations
Samuel Allen Alexander
Can you find an xy-equation that, when graphed, writes itself on the plane? This idea became internet-famous when a Wikipedia article on Tupper's self-referential formula went vira…
math.LO2024
Hyperreal differentiation with an idempotent ultrafilter
Samuel Allen Alexander, Bryan Dawson
In the hyperreals constructed using a free ultrafilter on R, where [f] is the hyperreal represented by f:R->R, it is tempting to define a derivative operator by [f]'=[f'], but unfo…