We construct a machine that knows its own code, at the price of not knowing its own factivity.
In this study we investigated the effects of intracellular pH (pHi) and extracellular pH (pHe) on whole-cell currents in cultured glomus cells of the rat carotid body and small, intensely fluorescent (SIF) cells of sympathetic ganglia. The use of the perforated-patch recording technique along with established methods of cytoplasmic acidification allowed us… (More)
We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the infinite graphs it leads to. This assumption admits certain clusters of organisms which have some ideal theoretical… (More)
Reinhardt's conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated structural results about the ordinals and transfinite induction just beyond the first epsilon number. We prove a weaker version of the conjecture, by elementary methods and… (More)
A biologically unavoidable sequence is an infinite gender sequence which occurs in every gendered, infinite genealogical network satisfying certain tame conditions. We show that every eventually periodic sequence is biologically unavoidable (this generalizes König's Lemma), and we exhibit some biologically avoidable sequences. Finally we give an application… (More)