A recent proposal by Norton (2003) to show that a simple Newtonian system can exhibit stochastic acausal behavior by giving rise to spontaneous movements of a mass on the dome of a certain shape is examined. We discuss the physical significance of an often overlooked and yet important Lipschitz condition the violation of which leads to the existence of anomalous nontrivial solutions in this and similar cases. We show that the Lipschitz condition is closely linked with the time reversibility of (...) certain solutions in Newtonian mechanics and the failure to incorporate this condition within Newtonian mechanics may unsurprisingly lead to physically impossible solutions that have no serious metaphysical implications. ‡I thank Steven Savitt of the Philosophy Department at the University of British Columbia for drawing my attention to the Lipschitz condition, and Alexei Cheviakov of the Mathematics Department at the University of British Columbia for useful discussions. †To contact the author, please write to: Department of Philosophy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada; e-mail: [email protected]. (shrink)

A recent attempt to compute a (recursion‐theoretic) noncomputable function using the quantum adiabatic algorithm is criticized and found wanting. Quantum algorithms may outperform classical algorithms in some cases, but so far they retain the classical (recursion‐theoretic) notion of computability. A speculation is then offered as to where the putative power of quantum computers may come from.

In the cytoplasm of practically all living cells, potassium is the major cation while sodium dominates in the media (seawater, extracellular fluids). Both prokaryotes and eukaryotes have elaborate mechanisms and spend significant energy to maintain this asymmetric K+/Na+ distribution. This essay proposes an original line of evidence to explain how bacteria selected potassium at the very beginning of the evolutionary process and why it remains essential for eukaryotes.

A recent proposal to solve the halting problem with the quantum adiabatic algorithm is criticized and found wanting. Contrary to other physical hypercomputers, where one believes that a physical process “computes” a (recursive-theoretic) non-computable function simply because one believes the physical theory that presumably governs or describes such process, believing the theory (i.e., quantum mechanics) in the case of the quantum adiabatic “hypercomputer” is tantamount to acknowledging that the hypercomputer cannot perform its task.

The singularity arising from the violation of the Lipschitz condition in the simple Newtonian system proposed recently by Norton (2003) is so fragile as to be completely and irreparably destroyed by slightly relaxing certain (infinite) idealizations pertaining to elastic phenomena in this model. I demonstrate that this is also true for several other Lipschitz-indeterministic systems, which, unlike Norton's example, have no surface curvature singularities. As a result, indeterminism in these systems should rather be viewed as an artefact of certain infinite (...) idealizations essential for these models, depriving them of much of their intended metaphysical import. (shrink)

ABSTRACTOne of the central claims of democratic theory is that the institutional features of democracy systematically cause government to respond to the people's needs. In fact, however, democracy might logically be expected to be especially responsive only to the people's desires, not their needs. Responses to people's objective needs can be substantially different from responses to their subjective desires. Democratic institutions therefore cannot guarantee responsiveness to basic human needs. Democracy, should, at least in principle, thus be confined to the sphere (...) of wants rather than needs. (shrink)