Juergen Jost

We systematically analyze the conceptual structure of modern physics, i.e., the theory of relativity and quantum mechanics and quantum field theory, from the perspective of Leibniz’s three basic principles of identity, sufficient reason and continuity. We find that Leibniz’s way of thinking can still provide insight into fundamental problems of physics, such as the nature of physical constants, the relation between physical invariances and covariant coordinate representations, the role of the Planck scale and quantum mechanical indeterminism and the measurement problem. Leibniz himself could not possess all those insights, simply because physics was not yet sufficiently developed then, but he had already forged some conceptual tools with which some fundamental problems of modern physics can be addressed

In biological classification, a character is a property of a taxon that can distinguish it from other taxa. Characters are not independent, and the relations between characters can arise from structural constraints, develop- mental pathways or functional constraints. That has lead to famous controversies in the history of biology. In addition, a character as a tool of data analysis has some subjective aspects. In this contribution, I develop algebraic and geo- metric schemes to address these issues in a mathematical framework.