Dork Scratchings

  The news here in the UK over the last couple of months has focussed on the unfolding catastrophe of Covid19 in India.  It has been implicit in pretty much all of the coverage that the situation there is much much worse than we have suffered in the UK, and this has been backed up by numbers showing just how many more people have died in India than here. True to form, our media have almost universally failed to take into account the fact that the population of India is nearly 25 times bigger.  I think dividing one number by another is not part of the training.... Here's a chart that puts things in context.  I've used 66.65 million for the UK population and 1.366 billion for India: INDIA OFFICIAL:   These are the Indian government official statistics republished by JHU CSSE COVID-19 Data showing 311,000 deaths INDIA ESTIMATE: These are from David Spiegalhalter and are based on excess mortality.  The best estimate is 1.6 million but could be as low as 600,0...

Simple example from The Theoretical Minimum I recently re-read The Theoretical Minimum - Classical mechanics , an excellent book. The authors give an example of the use of the Hamiltonian formulation of mechanics to illustrate how much easier it makes things (compared to the Newtonian formulation) and that inspired me to have a go myself. The example they give in the book is of a negligible mass charged sphere spinning in a magnetic field pointing in the z direction. In this case the Hamiltonian $H = T + V$ is proportional to $L_z$ where $\mathbf{L}$ is the angular momentum $L_x \hat{i} + L_y \hat{j} + L_z \hat{k}$. Let's say $H=\omega^2L_z$. The book explains that for any function $G(q,p)$ of the generalized coordinates $q_i$ and the conjugate momenta $p_i$ that $$ \dot{G} = \{G,H\} $$ i.e the time derivative of $G$ is the poisson bracket of $G$ and the Hamiltonian. And indeed this does make the solution simple because the components of angular momentum satisfy $$ \begin{align} ...