The notorious man-in-the-street: Hermann Weyl and the problem of knowledge.

Hermann Weyl's philosophical reflections remain a topic of considerable interest in the history and philosophy of science. In particular, Weyl's commitment to a form of idealism, as it pertains to his reading of Husserl and Fichte, has garnered much discussion. However, much less attention has been given to Weyl's later, and at that only partial, turn towards a form of empiricism (i.

Structuralism and the conformity of mathematics and nature.

Structuralists typically appeal to some variant of the widely popular 'mapping' account of mathematical representation to suggest that mathematics is applied in modern science to represent the world's physical structure. However, in this paper, I argue that this realist interpretation of the 'mapping' account presupposes that physical systems possess an 'assumed structure' that is at odds with modern physical theory. Through two detailed case studies concerning the use of the differential and variational calculus in modern dynamics, I show that the formal structure that we need to assume in order to apply the mapping account is inconsistent with the way in which mathematics is applied in modern physics.

Quantum readout and fast initialization of nuclear spin qubits with electric currents.

Nuclear spin qubits have the longest coherence times in the solid state, but their quantum readout and initialization is a great challenge. We present a theory for the interaction of an electric current with the nuclear spins of donor impurities in semiconductors. The theory yields a sensitivity criterion for quantum detection of nuclear spin states using electrically detected magnetic resonance, as well as an all-electrical method for fast nuclear spin qubit initialization.