Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.     

Continuation of travelling‐wave solutions of the Navier–Stokes equations

An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first‐order pseudospectral semi‐implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton–Raphson solver and is shown to be highly efficient in performing this task, even when high‐resolution grids are used. This method is well suited to three‐dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

Pit your wits against young minds!

This column is a place for those bits of contagious mathematics that travel from person to person in the community, because they are so elegant, suprising, or appealing that one has an urge to pass them on. Contributions are most welcome.     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.