### Movie Review: Darkest Hour

Before Churchill was ever appointed as Prime Minister, by 1938 Chamberlain had gone to Munich to negotiate the German annexation of the Sudetenland. He thought he had Hitler sign off on any further territorial claims over land in Europe, but Hitler reneges on his promise, invades Czechoslovakia and occupies Prague. Poland under increasing pressure to give up the free-city of Danzig, (carved out of east Prussia by the treaty of Versailles), Chamberlain reverses his policy of appeasement and rises to support Poland against any action that threatens its independence.

If ever there was a midnight hour for Europe, it was still to come with the Molotov-Ribbentrop pact, signed on August 24th 1939. The Nazis and the Soviet Union's non-aggression treaty, that delineated spheres of interest over Europe and the joint-invasion of Poland. That invasion fell on September 1st, three days later Chamberlain announces a state of war between Hitler and Great Britain. All of this occurs before the setting of the film, which starts with parliament's call for Chamberlain to resign.

The movie covers the events of May in 1940, Chamberlain's resignation, and the war cabinet crises, through to the siege of Calais and the plan for the evacuation of Dunkirk.

One thing historians remind us of, all the time is that we can't judge the actions of people in the past by what we know in the present. You can only imagine from their vantage point, the sense of utter despair and hopelessness across Britain, as its played out on screen, Churchill is the only one in the war cabinet with the sense of courage to go on fighting. Chamberlain (still in high office), then Foreign Secretary, Viscount Halifax and then monarch, King George VI all favored appeasement and plotted a leadership bid against Churchill.

His famous "Blood, toil, tears and sweat" speech was hardly received well among Conservatives either, even among those who did support Churchill's policy, many of them still saw him through a lens, tinted by the Gallipoli campaign and the return to gold at the pre-1914 rate. It was probably hard not to see Churchill's position as naive, on the same day he became Prime Minister, no less, Belgium and France were invaded, (Norway and Denmark had already been attacked), by the time Churchill would first address the nation, the Nazis would have broken through the Maginot line, within a week they were well into France and the Vichy would be installed later that same year. Albeit in July.

America signed a neutrality act (still in force in 1940) and every other country in Europe was either well on the way to defeat or neutral. Britain stood alone, facing increasing pressure to surrender, Mussolini even offered to act as a mediator between negotiations.

Yet, while often underplayed or unappreciated, the film captures incredibly the truly remarkable thing about Churchill–his stubbornness and refusal to surrender–as the man himself put it when he addresses the nation "never to surrender ourselves to servitude and shame, whatever the cost and the agony may be, conquer we must as conquer we shall". Even against unimaginable odds, Churchill's belief in individual liberty, the rule of law and limited government, values he had learned and cherished as a Conservative, were worth defending, with the force of arms if necessary.

Although the film is a fantastic rendition of events, and while some of the scenes are truly inspiring, the speech to the outer cabinet, the broadcast to the nation in an underground bunker, and Churchill's famous "we shall oppose them on the beaches" speech to parliament, there is one line that disfigures the movie. King George IV when talking to Chamberlain infers responsibility to Churchill for the Bengal famine (its not only misplaced, there's no way King George could have known about this in 1940, its outright false).

As far as I can trace back the original claim, it comes from a book dabbling in pseudo-history by Madhusree Mukerjee. In fact Churchill is known to have done everything he could to end the famine, trying to call in favours from America, Canada and Australiato transport wheat to India. Only Australia and Ceylon actually did. There's also recorded conversations he had with Lord Wevall where he stated unequivocally his desire to ensure in every way he could, to stop the famine. Yet the claim persists, t's almost like these accusers don't actually care about India, at least not nearly as much as Churchill did.

### Set Theory

This post is a very brief introduction to some of the basic concepts of set theory. Set theory is a branch of mathematical-logic, that has wide applications across disciplines. Its not just used in the obvious way of studying the foundations of mathematics by mathematicians but also in physics, social science, and even by philosophers as a theory of semantics for predicate logic (although you can do propositional logic without set theory).

A set is a collection of elements, or members; the notation for a set is specified by listing its components. So the set of even numbers can be represented a
$E: \left \{ 2,4,6,8 ... \right \}$$E: \left \{ x: x > 0 \wedge even\right \}$ Either of these notations is valid. Further, elements of a set can only be in that set, once. So   $E: \left \{ 2,2,2,4,4,6,8 ... \right \} = E: \left \{ 2,4,6,8 ... \right \}$ The notation used to indicate that something is an element of a set, is using the Greek symbol "epsilon". That is: $4 \epsilon S$…

### William Lane Craig and the Hartle-Hawking No Boundary Proposal

Classical standard hot Big Bang cosmology represents the universe as beginning from a singular dense point, with no prior description or explanation of classical spacetime. Quantum cosmology is different in that it replaces the initial singularity with a description in accord with some law the "quantum mechanical wave function of the universe", different approaches to quantum cosmology differ in their appeal either to describe the origin of the material content of the universe e.g., Tyron 1973, Linde 1983a, Krauss 2012 or the origin of spacetime itself e.g., Vilenkin 1982, Linde 1983b, Hartle-Hawking 1983, Vilenkin 1984.

These last few proposals by Vilenkin, Hartle-Hawking and others are solutions to the Wheeler-DeWitt equation and exist in a category of proposals called "quantum gravity cosmologies" which make cosmic applications of an approach to quantum gravity called "closed dynamic triangulation" or CDT (also known as Euclidean quantum gravity). I&#…

### Can inflation be eternal into the past?

Back in 2003 a paper appeared on the arXiv titled "Inflationary spacetimes are not past complete" that was published by Arvind Borde, Alan Guth and Alexander Vilenkin which has had considerable amounts of attention online. The theorem is rather uninteresting but simple and doesn't require a very complicated understanding of math. So I thought I'd explain the result here.

It's purpose is to demonstrate that inflationary models are geodesically incomplete into the past which they take as "synonymous to a beginning" but Vilenkin stresses that the theorem can be extended to non inflationary models so long as the condition of the theorem that the average rate of expansion is never below zero is met. These models too then are incomplete into the past. Consider the metric for an FRW universe with an exponential expansion

Where the scale factor is

Since the eternal inflation model is a "steady state cosmology" the mass density and the Hubble paramet…