### No Deal is Better than a Bad Deal

With the consent of both houses of parliament, Theresa May moved to trigger Article 50 back in March, making it the expressed will of not just one Prime Minister, but of the people and of their elected representatives. If the reality hasn't set in by now, it should have: we are leaving the European Union.

The only question that remains is whether we leave on favorable terms with an agreement in place that covers, not least of all trade or in keeping with the Prime Minister's oft-repeated phrase "no deal is better than a bad deal", we leave without a trade deal, and make the necessary arrangements to keep our economy competitive.

This latter option which involves tariffs, is how most countries conduct their trade with the European Union, we would in affect, be left with a "US-style" or "Chinese-style" relationship to the EU. One conducted on WTO terms, instead of a more favorable bilateral basis.

The possibility of leaving without a deal is hardly something to aspire to but it's an option that must remain open, any serious negotiation has to carry the implied undertone that there is a line we will not cross. A price we will not pay, taking any softer tone, is to send our Brexit Secretary to sit at the negotiation table, unclothed and unprepared.

In fact not only does most of the world not have a trade deal with the EU, the UK already trades with several countries under WTO terms, including big economies the EU has not yet negotiated a trade settlement with, (US, China, Russia, Brazil, Australia etc.).

Once we leave the EU, on whatever terms, provided we're outside the custom's union, we gain the ability to sign our own trade deals. So we can make a choice, to bring down tariffs on foreign imports, increasing competition in our economy and ultimately decreasing the price of goods, particularly footwear, clothing and food with the scrapping of the Common Agricultural Policy.

Nobody wants talks with the EU to break down, one has to aim for the best but prepare for the worst outcome. If we don't, we're in danger of encouraging Eurocrats who believe that by making the process as difficult and painful for Britain, as humanely possible, that somehow we're going to change our minds and drop the whole idea. Anyone in the UK reading this, knows that is not going to happen. In that respect, our politics is hardly comparable to European nations like Russia or Belarus, votes in this country matter.

Nor is a break down in talks in anyone's interest. The moment we leave the EU, we become its largest export destination. With a deficit in trade. Meaning that the EU would gain more from a trade deal with us, than they would from any other country. Which ought to make us a priority. Countries after all don't trade with each other out of favour or kindness, but because an entrepreneurial spirit that seeks for profit and gain.

The same is true visa versa, it's in our interest as well. A recent study by the World Bank looked at the 'no-deal' option and found that "in the short run, leaving the European Union may cause the United Kingdom’s exports to the European Union to decrease by two per cent and the prospect of a major trade collapse post-Brexit is unlikely". In such a situation as this, a loss of two percent in exports (that's about one quarter of one per cent of GDP) is something we'd have to make up with further cuts to regulation and tax.

Wholly apart from considerations of commerce, both sides cooperation goes further than just the economy and leaving without a deal means we need to prepare for securing patenting rights, air line slots, widening the M20, producing drivers licenses that are valid internationally, investing in road networks and so on.

Either we should pursue an amicable divorce, something like an EFTA arrangement (or a 'Canada +++') or we should cut our loses, leave without a deal and compensate businesses restructuring our economic model, something along the lines of north sea Singapore.

What would be unforgivable, would be to prod along, trying to keep as many people happy, for as long as possible, without a contingency in place.

After all Prime Minister, to lead is to choose.

### 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…