Questions I'd like to tackle, if only I had more time... Here's a grab-bag of questions that I've pondered over the years, but have never had sufficient time to tackle.  Help yourself to any you find interesting; I'd be interested to hear from anyone who makes progress with them. I'll add more from time to time. Biochemistry/genetics The Michaelis-Menten equations of enzyme kinetics are a set of non-linear differential equations first written down almost a century ago. Back then, the absence of computers meant there was no hope of getting insights from the equations without first casting them into a linearised form. Today there's no such excuse - yet biochemistry textbooks still give the impression that the linearised versions are the be-all and end-all. I'm sure there is a wealth of interesting insights to be gained from tackling the full equations computationally. In particular, I suspect that the non-linearities are  strong enough to undermine all hope of linking the genes that code for enzymes to all but the most simple diseases. The obvious parallel is with the futility of long-range weather forecasting, but so far I've been unable to obtain prototypical rate constants to allow me to check this out. Cosmology Symmetry principles have long played a key role in particle physics, but they are also important in cosmology. In particular, spacetime metrics are highly constrained by the demand that they possess Killing vector fields. Thus the demand that the metric describe a universe that is spatially homogeneous and isotropic leads directly to the well- known Robertson-Walker metric, with allowable values of the curvature index k of 0 or + 1 and scale-factor R(t) of unspecified time dependency.  It seems, however,  to be less well-appreciated that the space-time metric of the universe can be completely specified by symmetry principles, without any field equations!    Specifically, if we require that the space-time metric be maximally symmetric and possesses a time-like Killing vector, then the metric must be Robertson-Walker with either R(t) = constant, or   of the form R(t) = exp(Ht) where H is non-zero and k = 0. Physically, the addition of the time-like Killing vector has led to a universe that is unchanging though not necessarily static.   The resulting de Sitter metric is best-known through the Steady State model, so soundly refuted in the 1960s by the discovery of the 3K microwave background. However, within recent years there has been renewed interest in the notion that the Big Bang may have been just a interlude in the otherwise infinitely long history of the spatially infinite cosmos.  Seen in that light, the Steady State model may yet be worth considering as the asymptotic state towards which our universe will revert as t tends to infinity. The pay-off is impressive: the observational fact that the universe is expanding (H >0) allows the symmetries of the space-time metric to lead us to a unique model of a spatially flat universe undergoing exponential expansion with negative deceleration constant. This is, of course, the currently preferred kinematic description of our universe - yet spacetime symmetry principles have led us to it without recourse to any field equations !  The Steady State model may thus be the correct model after all, its original proponents having erred through "temporal parochialism". That is, while they (like cosmologists generally) happily accepted that homogeneity and isotropy are concepts that apply only on colossal spatial scales, they failed to recognise the similar enormity of the temporal scales required for the metric to become valid. Seen on these scales, the Big Bang of around 14 billion years ago and the resulting injection of matter (from conversion of scalar field energy) may in reality be just a brief interlude in the history of a universe usually dominated solely by vacuum energy (save for the occasional scalar field fluctuation that triggers another Big Bang).  In short, I suspect that symmetry principles breathe new life into this old but timelessly elegant cosmological model. Cryptology Can an efficient search algorithm such as a Genetic Algorithm cast light on the as-yet unbroken D'Agapeyeff Cipher ? Here are some notes on it. In 1993 I published one of the first papers to apply GAs to the problem of code- breaking, showing how they can "breed" the correct key for transposition ciphers. Since then, others have applied GAs to a range of other cipher systems, and to judge by a recent review  all the GAs published so far have the same surprising feature: to a greater or lesser degree, they suck. One obvious reason is that the fitness functions are less than optimal, and there is some interesting work to be done on testing out various possibilities.    Atmospheric physics/history Did the aerosol concentrations produced by smoke etc released during the First World War offensives lead to anomalously severe downpours ? Physics What are the scaling laws that determine the depth to which a human diver plunges during a vertical dive from height H (a problem in dimensional analysis, presumably). Psychology What is the typical psychological profile of journalists ? Given that the media serves up a view of the world refracted through the prism of the journalistic mindset, it might be an idea to know something about it. In a similar vein, what is the typical psychological profile of sceptics ? There is a considerable literature on the characteristics of people who are superstitious,  religious, or believe in the supernatural (and in some cases, pretty well anything). I'd be interested in those at the opposite end of the Normal distribution, who insist there is a rational explanation for everything. Climate change/geophysics Is global sea-level rise detectable through its effect on the rotation rate of the Earth ? The principal source of the increase in sea-level is thought to be thermal expansion. This should result in changes in the moment of inertia of the Earth, and thus (by conservation of angular momentum) in changes in the length of the day (LoD).  Do LoD measurements have sufficient sensitivity to detect this ? Cultural/historical The flags of several nations (Azerbajian, Pakistan, Tunisia, Turkey) feature a crescent moon with a star in its "arms". Are these depictions of a "diamond ring effect" of the type sometimes seen during total solar eclipses ? Is an "auspicious" eclipse linked to some key event in the cultural history of these nations ?