### Brexit Transition Worries

In recent headlines, a lot of the debate over Brexit has now shifted to a debate over the transition period Theresa May proposed in her Florence speech. Overall, the speech she made was well-judged and statesmen like, and for whatever it's worth I think Theresa May is a competent politician of sound mind. I hope she stays on as Prime Minister.

There's nothing wrong in principle with an implementation period after the time limit of Article 50 has expired. As one MEP put it "Brexit is a process not an event" it's going to involve the gradual repatriation of powers back to the United Kingdom, rather running off a cliff edge and imposing multiple changes on businesses all at once, but there is a serious worry about the terms of implementation.

If under the transition phase we remain a member of the single market, the custom's union, and under the jurisdiction of the European Court of Justice, come March 2019, we will in fact have not left the European union. We'll have become a vassal state, losing our seats in the EU's commission, council and parliament, hostage to EU undertakings. If that is the terms of our transition, it is worse than EU membership.

We will in effect be subject to foreign law with no say in making them (something that hasn't happened in the UK since the Norman conquest), that is "taxation without representation".

The transition is time-limited period, intended only to be 21 months, fair enough but what if the EU seeks to push through laws that actively punish the UK for voting to leave the block? Rules that make our economy noncompetitive or that indefinitely extend the period for which we are members. After all that's what happened to Norway, a member the EEA (but not of the European Union).

An exert from Daniel Hannan's signature book, Why Vote Leave:
I'm not the first and I'm sure I won't be the last to say that "damage-limitation" is not the right way to approach Brexit, it needs to be approached with ambition, as a seed for radical change.

Leaving Europe is not an end in itself, after all, its a means to joining the rest of the world. In my estimation then, we could either join the European Free Trade Association or we could walk away without an agreement, compensating for our losses with drastic cuts to regulation and corporation tax. Either of these option are much better than surrendering our veto, and remaining in, indefinitely.

### 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…