12 citations · 66 across the 25 of their papers we have counts for
27 papers
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…
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…
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…
Strengthening Consistency Results in Modal Logic
Samuel Allen Alexander, Arthur Paul Pedersen
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of backgro…
Universal Agent Mixtures and the Geometry of Intelligence
Samuel Allen Alexander, David Quarel, Len Du +1
Inspired by recent progress in multi-agent Reinforcement Learning (RL), in this work we examine the collective intelligent behaviour of theoretical universal agents by introducing…
Formal differential variables and an abstract chain rule
Samuel Allen Alexander
One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated di…