The purpose of this article is to explore the idea that, although Zeroness was coined by Deleuze and not by Peirce, there is no problem in considering it as the formal antecedent of Firstness. The argumentation will show that, without Zeroness, God could not have transformed nothingness into the empty set and, therefore, could not have created the elements of Firstness. This can be illustrated by a thought experiment in which it becomes evident that without the empty set, the continua of luminosity and color could not have arisen. In other words, without the Zeroness of the empty set, any attempt to create the colors would have been absorbed in the chaos of nothing.

https://dialnet.unirioja.es/descarga/articulo/8028977.pdf

¿Puede prescindir Dios de la Ceroidad? Deleuze, Peirce y un experimento mental con colores

Mutually unbiased bases (MUBs) are important in quantum information theory. While constructions of complete sets of d + 1 MUBs in Copfd are known when d is a prime power, it is unknown if such complete sets exist in non-prime power dimensions. It has been conjectured that sets of complete MUBs only exist in Copfd if a projective plane of size d also exists. We investigate the structure of MUBs using two algebraic tools: relation algebras and group rings. We construct two relation algebras from MUBs and compare these to relation algebras constructed from projective planes. We show several examples of complete sets of MUBs in Copfd, that when considered as elements of a group ring form a commutative monoid. We conjecture that complete sets of MUBs will always form a monoid if the appropriate group ring is chosen.

Anthony Murphy

Papers

Writings of Charles S. Peirce: A Chronological Edition, Volume 4